Finite Group Databasebeta

← C73×#34504 #32943908

Subgroups — C73×#34504 #32943908

Order 18688.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551×C73C211yesmaximal, characteristic
2C73×#2383C211yesmaximal, characteristic, complemented
3C73×#2378C211yesmaximal, characteristic, complemented
4C73×#2376C211yesmaximal, characteristic, complemented
5C73×#2375C211yesmaximal, characteristic
6C73×#2374C211yesmaximal, characteristic, complemented
7C73×#2373C211yesmaximal, characteristic, complemented
8C73×#2367C211yesmaximal, characteristic, complemented
9C73×#2362C211yesmaximal, characteristic, complemented
10C73×#2359C211yesmaximal, characteristic, complemented
11C73×#2354C211yesmaximal, characteristic, complemented
12C73×#2353C211yesmaximal, characteristic, complemented
13C73×#2347C211yesmaximal, characteristic, complemented
14C73×#2347C211yesmaximal, characteristic, complemented
15C73×#2342C211yesmaximal, characteristic, complemented
16C73×#2342C211yesmaximal, characteristic, complemented
17C73×#2337C211yesmaximal, characteristic, complemented
18C73×#2335C211yesmaximal, characteristic, complemented
19C73×#2335C211yesmaximal, characteristic, complemented
20C73×#2335C211yesmaximal, characteristic, complemented
21C73×#2334C211yesmaximal, characteristic, complemented
22C73×#2332C211yesmaximal, characteristic, complemented
23C73×#2323C211yesmaximal, characteristic, complemented
24C73×#2321C211yesmaximal, characteristic
25C73×#2318C211yesmaximal, characteristic, complemented
26C73×#2314C211yesmaximal, characteristic, complemented
27C73×#2312C211yesmaximal, characteristic, complemented
28C73×#2312C211yesmaximal, characteristic, complemented
29C4×#126×C73C211yesmaximal, characteristic, complemented
30C73×#2298C211yesmaximal, characteristic, complemented
31C73×#2293C211yesmaximal, characteristic, complemented
32#551×C73C4116yescomplemented
33C2×#126×C73C2211yescharacteristic
34C2×#126×C73C2211yescharacteristic
35C2×#124×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic
37C2×#123×C73C2211yescharacteristic
38C2×#123×C73C2211yescharacteristic
39C2×C22⋊Q8×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×#120×C73C2211yescharacteristic
42C2×C4×Q8×C73C2211yescharacteristic, complemented
43C2×C4×D4×C73C2211yescharacteristic
44C2×C4×D4×C73C2211yescharacteristic
45C2×C4×D4×C73C2211yescharacteristic
46C2×#117×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48C2×#117×C73C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50C2×#117×C73C2211yescharacteristic, complemented
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53C22×C22⋊C4×C73C2211yescharacteristic
54#391×C73C2211yescharacteristic, complemented
55#391×C73C2211yescharacteristic, complemented
56#391×C73C2211yescharacteristic, complemented
57#390×C73C2211yescharacteristic
58#390×C73C2211yescharacteristic
59#390×C73C2211yescharacteristic
60#390×C73C2211yescharacteristic
61#390×C73C2211yescharacteristic
62#389×C73C2211yescharacteristic, complemented
63#389×C73C2211yescharacteristic, complemented
64#389×C73C2211yescharacteristic, complemented
65#389×C73C2211yescharacteristic, complemented
66#389×C73C2211yescharacteristic, complemented
67#389×C73C2211yescharacteristic, complemented
68#389×C73C2211yescharacteristic, complemented
69#389×C73C2211yescharacteristic, complemented
70#388×C73C2211yescharacteristic
71#388×C73C2211yescharacteristic
72#388×C73C2211yescharacteristic
73#388×C73C2211yescharacteristic
74#388×C73C2211yescharacteristic
75#388×C73C2211yescharacteristic
76#388×C73C2211yescharacteristic
77#388×C73C2211yescharacteristic
78#388×C73C2211yescharacteristic
79#388×C73C2211yescharacteristic
80#388×C73C2211yescharacteristic
81#388×C73C2211yescharacteristic
82#388×C73C2211yescharacteristic
83#388×C73C2211yescharacteristic
84#388×C73C2211yescharacteristic
85#388×C73C2211yescharacteristic
86#388×C73C2211yescharacteristic
87#388×C73C2211yescharacteristic
88#388×C73C2211yescharacteristic
89#388×C73C2211yescharacteristic
90#388×C73C2211yescharacteristic
91#388×C73C2211yescharacteristic
92#388×C73C2211yescharacteristic
93#388×C73C2211yescharacteristic
94#388×C73C2211yescharacteristic
95#388×C73C2211yescharacteristic
96#388×C73C2211yescharacteristic
97#388×C73C2211yescharacteristic
98#388×C73C2211yescharacteristic
99#388×C73C2211yescharacteristic
100#388×C73C2211yescharacteristic
101#388×C73C2211yescharacteristic
102#388×C73C2211yescharacteristic
103#388×C73C2211yescharacteristic
104#388×C73C2211yescharacteristic, complemented
105#388×C73C2211yescharacteristic, complemented
106#388×C73C2211yescharacteristic, complemented
107#388×C73C2211yescharacteristic, complemented
108#388×C73C2211yescharacteristic, complemented
109#388×C73C2211yescharacteristic, complemented
110#387×C73C2211yescharacteristic, complemented
111#387×C73C2211yescharacteristic, complemented
112#387×C73C2211yescharacteristic, complemented
113#387×C73C2211yescharacteristic, complemented
114#387×C73C2211yescharacteristic, complemented
115#387×C73C2211yescharacteristic, complemented
116#387×C73C2211yescharacteristic, complemented
117#387×C73C2211yescharacteristic, complemented
118#387×C73C2211yescharacteristic, complemented
119#387×C73C2211yescharacteristic, complemented
120#387×C73C2211yescharacteristic, complemented
121#387×C73C2211yescharacteristic, complemented
122#387×C73C2211yescharacteristic, complemented
123#387×C73C2211yescharacteristic, complemented
124#387×C73C2211yescharacteristic, complemented
125#387×C73C2211yescharacteristic, complemented
126#386×C73C2211yescharacteristic
127#386×C73C2211yescharacteristic
128#386×C73C2211yescharacteristic
129#386×C73C2211yescharacteristic
130#386×C73C2211yescharacteristic
131#386×C73C2211yescharacteristic
132#385×C73C2211yescharacteristic
133#385×C73C2211yescharacteristic
134#385×C73C2211yescharacteristic
135#385×C73C2211yescharacteristic
136#385×C73C2211yescharacteristic
137#385×C73C2211yescharacteristic, complemented
138#385×C73C2211yescharacteristic, complemented
139#385×C73C2211yescharacteristic, complemented
140#384×C73C2211yescharacteristic, complemented
141#383×C73C2211yescharacteristic, complemented
142#383×C73C2211yescharacteristic, complemented
143#383×C73C2211yescharacteristic, complemented
144#382×C73C2211yescharacteristic, complemented
145#381×C73C2211yescharacteristic
146#381×C73C2211yescharacteristic
147#380×C73C2211yescharacteristic
148#380×C73C2211yescharacteristic
149#380×C73C2211yescharacteristic
150#380×C73C2211yescharacteristic
151#380×C73C2211yescharacteristic
152#380×C73C2211yescharacteristic
153#380×C73C2211yescharacteristic, complemented
154#379×C73C2211yescharacteristic
155#379×C73C2211yescharacteristic
156#379×C73C2211yescharacteristic
157C4×C4⋊C4×C73C2211yescharacteristic, complemented
158C4×C4⋊C4×C73C2211yescharacteristic, complemented
159C4×C4⋊C4×C73C2211yescharacteristic, complemented
160C4×C4⋊C4×C73C2211yescharacteristic, complemented
161C4×C4⋊C4×C73C2211yescharacteristic, complemented
162C4×C4⋊C4×C73C2211yescharacteristic, complemented
163C4×C4⋊C4×C73C2211yescharacteristic, complemented
164C4×C4⋊C4×C73C2211yescharacteristic, complemented
165C4×C4⋊C4×C73C2211yescharacteristic, complemented
166C4×C4⋊C4×C73C2211yescharacteristic, complemented
167C4×C4⋊C4×C73C2211yescharacteristic, complemented
168C4×C4⋊C4×C73C2211yescharacteristic, complemented
169C4×C4⋊C4×C73C2211yescharacteristic, complemented
170C4×C22⋊C4×C73C2211yescharacteristic
171C4×C22⋊C4×C73C2211yescharacteristic
172C4×C22⋊C4×C73C2211yescharacteristic
173C4×C22⋊C4×C73C2211yescharacteristic
174C4×C22⋊C4×C73C2211yescharacteristic
175C4×C22⋊C4×C73C2211yescharacteristic
176C4×C22⋊C4×C73C2211yescharacteristic
177C4×C22⋊C4×C73C2211yescharacteristic
178C4×C22⋊C4×C73C2211yescharacteristic
179C4×C22⋊C4×C73C2211yescharacteristic
180C4×C22⋊C4×C73C2211yescharacteristic
181C4×C22⋊C4×C73C2211yescharacteristic, complemented
182C4×C22⋊C4×C73C2211yescharacteristic, complemented
183C4×C22⋊C4×C73C2211yescharacteristic, complemented
184C4×C22⋊C4×C73C2211yescharacteristic, complemented
185#376×C73C2211yescharacteristic, complemented
186C2×#95×C73C2211yescharacteristic, complemented
187C43×C73C2211yescharacteristic, complemented
188C25×C73C2311yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×D4×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C23×C4×C73C2311yescharacteristic
194C23×C4×C73C2311yescharacteristic
195C23×C4×C73C2311yescharacteristic
196C23×C4×C73C2311yescharacteristic
197C23×C4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202#126×C73C2×C418yescomplemented
203#126×C73C2×C418yescomplemented
204#124×C73C2×C418yes—
205#123×C73C2×C418yes—
206#123×C73C2×C418yescomplemented
207#123×C73C2×C418yescomplemented
208C22⋊Q8×C73C2×C418yescomplemented
209C22⋊Q8×C73C2×C418yescomplemented
210#120×C73C2×C418yes—
211C4×Q8×C73—42no—
212C4×D4×C73—42no—
213C4×D4×C73C2×C418yescomplemented
214C4×D4×C73C2×C418yescomplemented
215#117×C73—42no—
216#117×C73—42no—
217#117×C73—42no—
218#117×C73C2×C418yescomplemented
219#117×C73C2×C418yescomplemented
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2311yescharacteristic
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2311yescharacteristic
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2311yescharacteristic
231C2×C4⋊C4×C73C2311yescharacteristic
232C2×C4⋊C4×C73C2311yescharacteristic
233C2×C4⋊C4×C73C2311yescharacteristic
234C2×C4⋊C4×C73C2311yescharacteristic
235C2×C4⋊C4×C73C2311yescharacteristic
236C2×C4⋊C4×C73C2311yescharacteristic
237C2×C4⋊C4×C73C2311yescharacteristic
238C2×C4⋊C4×C73C2311yescharacteristic
239C2×C4⋊C4×C73C2311yescharacteristic
240C2×C4⋊C4×C73C2311yescharacteristic
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C22⋊C4×C73—42no—
251C2×C22⋊C4×C73C2×C418yescomplemented
252C2×C22⋊C4×C73C2×C418yescomplemented
253C2×C22⋊C4×C73C2311yescharacteristic
254C2×C22⋊C4×C73C2311yescharacteristic
255C2×C22⋊C4×C73C2311yescharacteristic
256C2×C22⋊C4×C73C2311yescharacteristic
257C2×C22⋊C4×C73C2311yescharacteristic
258C2×C22⋊C4×C73C2311yescharacteristic
259C2×C22⋊C4×C73C2311yescharacteristic
260C2×C22⋊C4×C73C2311yescharacteristic
261C2×C22⋊C4×C73C2311yescharacteristic
262C2×C22⋊C4×C73C2311yescharacteristic
263C2×C22⋊C4×C73C2311yescharacteristic
264C2×C22⋊C4×C73C2311yescharacteristic
265C2×C22⋊C4×C73C2311yescharacteristic
266C2×C22⋊C4×C73C2311yescharacteristic
267C2×C22⋊C4×C73C2311yescharacteristic
268C2×C22⋊C4×C73C2311yescharacteristic
269C2×C22⋊C4×C73C2311yescharacteristic
270C2×C22⋊C4×C73C2311yescharacteristic
271C2×C22⋊C4×C73C2311yescharacteristic
272C2×C22⋊C4×C73C2311yescharacteristic
273C2×C22⋊C4×C73C2311yescharacteristic
274C2×C22⋊C4×C73C2311yescharacteristic
275C2×C22⋊C4×C73C2311yescharacteristic
276C2×C22⋊C4×C73C2311yescharacteristic
277C2×C22⋊C4×C73C2311yescharacteristic
278C2×C22⋊C4×C73C2311yescharacteristic
279C2×C22⋊C4×C73C2311yescharacteristic
280C2×C22⋊C4×C73C2311yescharacteristic
281C2×C22⋊C4×C73C2311yescharacteristic
282C2×C22⋊C4×C73C2311yescharacteristic
283C2×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C22⋊C4×C73C2311yescharacteristic
293C2×C22⋊C4×C73C2311yescharacteristic
294C2×C22⋊C4×C73C2311yescharacteristic
295C2×C42×C73C2311yescharacteristic
296C2×C42×C73C2311yescharacteristic
297C2×C42×C73C2311yescharacteristic
298C2×C42×C73C2311yescharacteristic
299C2×C42×C73C2311yescharacteristic
300C2×C42×C73C2311yescharacteristic
301C2×C42×C73C2311yescharacteristic
302C2×C42×C73C2311yescharacteristic
303C2×C42×C73C2311yescharacteristic
304C2×C42×C73C2311yescharacteristic
305C2×C42×C73C2311yescharacteristic
306C2×C42×C73C2311yescharacteristic
307C2×C42×C73C2311yescharacteristic
308C2×C42×C73C2311yescharacteristic
309C2×C42×C73C2311yescharacteristic
310C2×C42×C73C2311yescharacteristic
311C2×C42×C73C2311yescharacteristic
312C2×C42×C73C2311yescharacteristic
313C2×C42×C73C2311yescharacteristic
314C2×C42×C73C2311yescharacteristic
315C2×C42×C73C2311yescharacteristic
316C2×C42×C73C2311yescharacteristic
317C2×C42×C73C2311yescharacteristic
318C2×C42×C73C2311yescharacteristic
319C2×C42×C73C2311yescharacteristic
320#95×C73C2311yescharacteristic
321#95×C73C2311yescharacteristic
322#95×C73C2311yescharacteristic
323#95×C73C2311yescharacteristic
324#95×C73C2311yescharacteristic
325#95×C73C2311yescharacteristic
326#95×C73C2311yescharacteristic
327#95×C73C2311yescharacteristic
328#95×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364C24×C73—41no—
365C24×C73—41no—
366C24×C73—41no—
367C24×C73—41no—
368C24×C73—41no—
369C24×C73—41no—
370C24×C73C22×C414yes—
371C24×C73C2411yescharacteristic
372C24×C73C2411yescharacteristic
373C24×C73C2411yescharacteristic
374C24×C73C2411yescharacteristic
375C2×Q8×C73—41no—
376C2×Q8×C73—41no—
377C2×Q8×C73C22×C414yes—
378C2×D4×C73—41no—
379C2×D4×C73—41no—
380C2×D4×C73—41no—
381C2×D4×C73—41no—
382C2×D4×C73—41no—
383C2×D4×C73—41no—
384C2×D4×C73C22×C414yes—
385C2×D4×C73C22×C414yes—
386C2×D4×C73C22×C414yes—
387C22×C4×C73—22no—
388C22×C4×C73—41no—
389C22×C4×C73—41no—
390C22×C4×C73—41no—
391C22×C4×C73—41no—
392C22×C4×C73—41no—
393C22×C4×C73—41no—
394C22×C4×C73—41no—
395C22×C4×C73—41no—
396C22×C4×C73—41no—
397C22×C4×C73—41no—
398C22×C4×C73—41no—
399C22×C4×C73—41no—
400C22×C4×C73—41no—
401C22×C4×C73—41no—
402C22×C4×C73—41no—
403C22×C4×C73—41no—
404C22×C4×C73—41no—
405C22×C4×C73—41no—
406C22×C4×C73—41no—
407C22×C4×C73—41no—
408C22×C4×C73—41no—
409C22×C4×C73C22×C414yes—
410C22×C4×C73C22×C414yes—
411C22×C4×C73C22×C414yes—
412C22×C4×C73C22×C414yes—
413C22×C4×C73C22×C414yes—
414C22×C4×C73C2411yescharacteristic
415C22×C4×C73C2411yescharacteristic
416C22×C4×C73C2411yescharacteristic
417C22×C4×C73C2411yescharacteristic
418C22×C4×C73C2411yescharacteristic
419C22×C4×C73C2411yescharacteristic
420C22×C4×C73C2411yescharacteristic
421C22×C4×C73C2411yescharacteristic
422C22×C4×C73C2411yescharacteristic
423C22×C4×C73C2411yescharacteristic
424C22×C4×C73C2411yescharacteristic
425C22×C4×C73C2411yescharacteristic
426C22×C4×C73C2411yescharacteristic
427C22×C4×C73C2411yescharacteristic
428C22×C4×C73C2411yescharacteristic
429C22×C4×C73C2411yescharacteristic
430C22×C4×C73C2411yescharacteristic
431C22×C4×C73C2411yescharacteristic
432C22×C4×C73C2411yescharacteristic
433C22×C4×C73C2411yescharacteristic
434C22×C4×C73C2411yescharacteristic
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C22×C4×C73C2411yescharacteristic
441C4⋊C4×C73—22no—
442C4⋊C4×C73—22no—
443C4⋊C4×C73—22no—
444C4⋊C4×C73—41no—
445C4⋊C4×C73—41no—
446C4⋊C4×C73—41no—
447C4⋊C4×C73—41no—
448C4⋊C4×C73—41no—
449C4⋊C4×C73—41no—
450C4⋊C4×C73—41no—
451C4⋊C4×C73—41no—
452C4⋊C4×C73—41no—
453C4⋊C4×C73—41no—
454C4⋊C4×C73—41no—
455C4⋊C4×C73—41no—
456C4⋊C4×C73—41no—
457C4⋊C4×C73—41no—
458C4⋊C4×C73—41no—
459C4⋊C4×C73—41no—
460C4⋊C4×C73—41no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73C22×C414yes—
464C4⋊C4×C73C22×C414yes—
465C4⋊C4×C73C22×C414yes—
466C4⋊C4×C73C22×C414yes—
467C4⋊C4×C73C22×C414yes—
468C4⋊C4×C73C22×C414yes—
469C4⋊C4×C73C22×C414yes—
470C4⋊C4×C73C22×C414yes—
471C22⋊C4×C73—22no—
472C22⋊C4×C73—22no—
473C22⋊C4×C73—22no—
474C22⋊C4×C73—41no—
475C22⋊C4×C73—41no—
476C22⋊C4×C73—41no—
477C22⋊C4×C73—41no—
478C22⋊C4×C73—41no—
479C22⋊C4×C73—41no—
480C22⋊C4×C73—41no—
481C22⋊C4×C73—41no—
482C22⋊C4×C73—41no—
483C22⋊C4×C73—41no—
484C22⋊C4×C73—41no—
485C22⋊C4×C73—41no—
486C22⋊C4×C73—41no—
487C22⋊C4×C73—41no—
488C22⋊C4×C73—41no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C22⋊C4×C73—41no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73C22×C414yes—
500C22⋊C4×C73C22×C414yes—
501C22⋊C4×C73C22×C414yes—
502C22⋊C4×C73C22×C414yes—
503C22⋊C4×C73C22×C414yes—
504C22⋊C4×C73C22×C414yes—
505C22⋊C4×C73C22×C414yes—
506C22⋊C4×C73C22×C414yes—
507C22⋊C4×C73C22×C414yes—
508C22⋊C4×C73C22×C414yes—
509C22⋊C4×C73C22×C414yes—
510C22⋊C4×C73C22×C414yes—
511C22⋊C4×C73C22×C414yes—
512C22⋊C4×C73C22×C414yes—
513C42×C73—22no—
514C42×C73—22no—
515C42×C73—41no—
516C42×C73—41no—
517C42×C73—41no—
518C42×C73—41no—
519C42×C73—41no—
520C42×C73—41no—
521C42×C73—41no—
522C42×C73—41no—
523C42×C73—41no—
524C42×C73—41no—
525C42×C73—41no—
526C42×C73—41no—
527C42×C73—41no—
528C42×C73—41no—
529C42×C73—41no—
530C42×C73—41no—
531C42×C73—41no—
532C42×C73—41no—
533C42×C73—41no—
534C42×C73—41no—
535C42×C73C22×C414yes—
536C42×C73C22×C414yes—
537C42×C73C22×C414yes—
538C23×C73—21no—
539C23×C73—21no—
540C23×C73—21no—
541C23×C73—21no—
542C23×C73—21no—
543C23×C73—21no—
544C23×C73—21no—
545C23×C73—21no—
546C23×C73—21no—
547C23×C73—21no—
548C23×C73—21no—
549C23×C73—21no—
550C23×C73—21no—
551C23×C73—21no—
552C23×C73—21no—
553C23×C73—21no—
554C23×C73—21no—
555C23×C73—21no—
556C23×C73—21no—
557C23×C73—21no—
558C23×C73—21no—
559C23×C73—21no—
560C23×C73—21no—
561C23×C73—21no—
562C23×C73—44no—
563C23×C73—44no—
564C23×C73—44no—
565C23×C73—82no—
566C23×C73—82no—
567C23×C73—82no—
568C23×C73—82no—
569C23×C73C23×C412yes—
570C23×C73C23×C412yes—
571C23×C73C23×C412yes—
572C23×C73C23×C412yes—
573C23×C73C2511yescharacteristic
574Q8×C73—44no—
575D4×C73—44no—
576D4×C73—44no—
577D4×C73—44no—
578C2×C4×C73—21no—
579C2×C4×C73—21no—
580C2×C4×C73—21no—
581C2×C4×C73—21no—
582C2×C4×C73—21no—
583C2×C4×C73—21no—
584C2×C4×C73—21no—
585C2×C4×C73—21no—
586C2×C4×C73—21no—
587C2×C4×C73—21no—
588C2×C4×C73—21no—
589C2×C4×C73—21no—
590C2×C4×C73—21no—
591C2×C4×C73—21no—
592C2×C4×C73—21no—
593C2×C4×C73—21no—
594C2×C4×C73—21no—
595C2×C4×C73—21no—
596C2×C4×C73—21no—
597C2×C4×C73—21no—
598C2×C4×C73—21no—
599C2×C4×C73—21no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—44no—
648C2×C4×C73—44no—
649C2×C4×C73—44no—
650C2×C4×C73—44no—
651C2×C4×C73—44no—
652C2×C4×C73—82no—
653C2×C4×C73—82no—
654C2×C4×C73—82no—
655C2×C4×C73—82no—
656C2×C4×C73C23×C412yes—
657C2×C4×C73C23×C412yes—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C2×C4×C73C23×C412yes—
663C2×C4×C73C23×C412yes—
664C2×C4×C73C23×C412yes—
665C2×C4×C73C23×C412yes—
666C2×C4×C73C23×C412yes—
667C2×C4×C73H(5,𝔽2)12yes—
668C22×C73—22no—
669C22×C73—22no—
670C22×C73—22no—
671C22×C73—22no—
672C22×C73—22no—
673C22×C73—22no—
674C22×C73—22no—
675C22×C73—22no—
676C22×C73—22no—
677C22×C73—22no—
678C22×C73—22no—
679C22×C73—22no—
680C22×C73—41no—
681C22×C73—41no—
682C22×C73—41no—
683C22×C73—41no—
684C22×C73—41no—
685C22×C73—41no—
686C22×C73—41no—
687C22×C73—41no—
688C22×C73—41no—
689C22×C73—41no—
690C22×C73—41no—
691C22×C73—41no—
692C22×C73—41no—
693C22×C73—41no—
694C22×C73—41no—
695C22×C73—41no—
696C22×C73—88no—
697C22×C73C24×C411yescharacteristic
698C22×C73C2×H(5,𝔽2)11yescharacteristic
699C22×C73#58511yescharacteristic
700C22×C73#58511yescharacteristic
701C22×C73#58511yescharacteristic
702C22×C73#58511yescharacteristic
703C22×C73#58511yescharacteristic
704C4×C73—22no—
705C4×C73—22no—
706C4×C73—22no—
707C4×C73—22no—
708C4×C73—22no—
709C4×C73—22no—
710C4×C73—22no—
711C4×C73—22no—
712C4×C73—22no—
713C4×C73—22no—
714C4×C73—22no—
715C4×C73—22no—
716C4×C73—41no—
717C4×C73—41no—
718C4×C73—41no—
719C4×C73—41no—
720C4×C73—41no—
721C4×C73—41no—
722C4×C73—41no—
723C4×C73—41no—
724C4×C73—41no—
725C4×C73—41no—
726C4×C73—41no—
727C4×C73—41no—
728C4×C73—41no—
729C4×C73—41no—
730C4×C73—41no—
731#34504C7311yesmaximal, characteristic, direct product factor, Sylow
732C2×C73—42no—
733C2×C73—42no—
734C2×C73—42no—
735C2×C73—42no—
736C2×C73#342811yescharacteristic
737C2×C73#342811yescharacteristic
738C2×C73C4×H(5,𝔽2)11yescharacteristic
739C2×C73#356011yescharacteristic
740C2×C73#356211yescharacteristic
741C2×C73#356611yescharacteristic
742C2×C73#356811yescharacteristic
743C2×#551C2×C7311yescharacteristic
744#2383C2×C7311yescharacteristic, complemented
745#2378C2×C7311yescharacteristic, complemented
746#2376C2×C7311yescharacteristic, complemented
747#2375C2×C7311yescharacteristic
748#2374C2×C7311yescharacteristic, complemented
749#2373C2×C7311yescharacteristic, complemented
750#2367C2×C7311yescharacteristic, complemented
751#2362C2×C7311yescharacteristic, complemented
752#2359C2×C7311yescharacteristic, complemented
753#2354C2×C7311yescharacteristic, complemented
754#2353C2×C7311yescharacteristic, complemented
755#2347C2×C7311yescharacteristic, complemented
756#2347C2×C7311yescharacteristic, complemented
757#2342C2×C7311yescharacteristic, complemented
758#2342C2×C7311yescharacteristic, complemented
759#2337C2×C7311yescharacteristic, complemented
760#2335C2×C7311yescharacteristic, complemented
761#2335C2×C7311yescharacteristic, complemented
762#2335C2×C7311yescharacteristic, complemented
763#2334C2×C7311yescharacteristic, complemented
764#2332C2×C7311yescharacteristic, complemented
765#2323C2×C7311yescharacteristic, complemented
766#2321C2×C7311yescharacteristic
767#2318C2×C7311yescharacteristic, complemented
768#2314C2×C7311yescharacteristic, complemented
769#2312C2×C7311yescharacteristic, complemented
770#2312C2×C7311yescharacteristic, complemented
771C4×#126C2×C7311yescharacteristic, complemented
772#2298C2×C7311yescharacteristic, complemented
773#2293C2×C7311yescharacteristic, complemented
774C73#3450411yescharacteristic, direct product factor, Sylow
775#551C4×C73116yescomplemented
776C2×#126C22×C7311yescharacteristic
777C2×#126C22×C7311yescharacteristic
778C2×#124C22×C7311yescharacteristic
779C2×#123C22×C7311yescharacteristic
780C2×#123C22×C7311yescharacteristic
781C2×#123C22×C7311yescharacteristic
782C2×C22⋊Q8C22×C7311yescharacteristic
783C2×C22⋊Q8C22×C7311yescharacteristic
784C2×#120C22×C7311yescharacteristic
785C2×C4×Q8C22×C7311yescharacteristic, complemented
786C2×C4×D4C22×C7311yescharacteristic
787C2×C4×D4C22×C7311yescharacteristic
788C2×C4×D4C22×C7311yescharacteristic
789C2×#117C22×C7311yescharacteristic
790C2×#117C22×C7311yescharacteristic
791C2×#117C22×C7311yescharacteristic
792C2×#117C22×C7311yescharacteristic
793C2×#117C22×C7311yescharacteristic, complemented
794C22×C22⋊C4C22×C7311yescharacteristic
795C22×C22⋊C4C22×C7311yescharacteristic
796C22×C22⋊C4C22×C7311yescharacteristic
797#391C22×C7311yescharacteristic, complemented
798#391C22×C7311yescharacteristic, complemented
799#391C22×C7311yescharacteristic, complemented
800#390C22×C7311yescharacteristic
801#390C22×C7311yescharacteristic
802#390C22×C7311yescharacteristic
803#390C22×C7311yescharacteristic
804#390C22×C7311yescharacteristic
805#389C22×C7311yescharacteristic, complemented
806#389C22×C7311yescharacteristic, complemented
807#389C22×C7311yescharacteristic, complemented
808#389C22×C7311yescharacteristic, complemented
809#389C22×C7311yescharacteristic, complemented
810#389C22×C7311yescharacteristic, complemented
811#389C22×C7311yescharacteristic, complemented
812#389C22×C7311yescharacteristic, complemented
813#388C22×C7311yescharacteristic
814#388C22×C7311yescharacteristic
815#388C22×C7311yescharacteristic
816#388C22×C7311yescharacteristic
817#388C22×C7311yescharacteristic
818#388C22×C7311yescharacteristic
819#388C22×C7311yescharacteristic
820#388C22×C7311yescharacteristic
821#388C22×C7311yescharacteristic
822#388C22×C7311yescharacteristic
823#388C22×C7311yescharacteristic
824#388C22×C7311yescharacteristic
825#388C22×C7311yescharacteristic
826#388C22×C7311yescharacteristic
827#388C22×C7311yescharacteristic
828#388C22×C7311yescharacteristic
829#388C22×C7311yescharacteristic
830#388C22×C7311yescharacteristic
831#388C22×C7311yescharacteristic
832#388C22×C7311yescharacteristic
833#388C22×C7311yescharacteristic
834#388C22×C7311yescharacteristic
835#388C22×C7311yescharacteristic
836#388C22×C7311yescharacteristic
837#388C22×C7311yescharacteristic
838#388C22×C7311yescharacteristic
839#388C22×C7311yescharacteristic
840#388C22×C7311yescharacteristic
841#388C22×C7311yescharacteristic
842#388C22×C7311yescharacteristic
843#388C22×C7311yescharacteristic
844#388C22×C7311yescharacteristic
845#388C22×C7311yescharacteristic
846#388C22×C7311yescharacteristic
847#388C22×C7311yescharacteristic, complemented
848#388C22×C7311yescharacteristic, complemented
849#388C22×C7311yescharacteristic, complemented
850#388C22×C7311yescharacteristic, complemented
851#388C22×C7311yescharacteristic, complemented
852#388C22×C7311yescharacteristic, complemented
853#387C22×C7311yescharacteristic, complemented
854#387C22×C7311yescharacteristic, complemented
855#387C22×C7311yescharacteristic, complemented
856#387C22×C7311yescharacteristic, complemented
857#387C22×C7311yescharacteristic, complemented
858#387C22×C7311yescharacteristic, complemented
859#387C22×C7311yescharacteristic, complemented
860#387C22×C7311yescharacteristic, complemented
861#387C22×C7311yescharacteristic, complemented
862#387C22×C7311yescharacteristic, complemented
863#387C22×C7311yescharacteristic, complemented
864#387C22×C7311yescharacteristic, complemented
865#387C22×C7311yescharacteristic, complemented
866#387C22×C7311yescharacteristic, complemented
867#387C22×C7311yescharacteristic, complemented
868#387C22×C7311yescharacteristic, complemented
869#386C22×C7311yescharacteristic
870#386C22×C7311yescharacteristic
871#386C22×C7311yescharacteristic
872#386C22×C7311yescharacteristic
873#386C22×C7311yescharacteristic
874#386C22×C7311yescharacteristic
875#385C22×C7311yescharacteristic
876#385C22×C7311yescharacteristic
877#385C22×C7311yescharacteristic
878#385C22×C7311yescharacteristic
879#385C22×C7311yescharacteristic
880#385C22×C7311yescharacteristic, complemented
881#385C22×C7311yescharacteristic, complemented
882#385C22×C7311yescharacteristic, complemented
883#384C22×C7311yescharacteristic, complemented
884#383C22×C7311yescharacteristic, complemented
885#383C22×C7311yescharacteristic, complemented
886#383C22×C7311yescharacteristic, complemented
887#382C22×C7311yescharacteristic, complemented
888#381C22×C7311yescharacteristic
889#381C22×C7311yescharacteristic
890#380C22×C7311yescharacteristic
891#380C22×C7311yescharacteristic
892#380C22×C7311yescharacteristic
893#380C22×C7311yescharacteristic
894#380C22×C7311yescharacteristic
895#380C22×C7311yescharacteristic
896#380C22×C7311yescharacteristic, complemented
897#379C22×C7311yescharacteristic
898#379C22×C7311yescharacteristic
899#379C22×C7311yescharacteristic
900C4×C4⋊C4C22×C7311yescharacteristic, complemented
901C4×C4⋊C4C22×C7311yescharacteristic, complemented
902C4×C4⋊C4C22×C7311yescharacteristic, complemented
903C4×C4⋊C4C22×C7311yescharacteristic, complemented
904C4×C4⋊C4C22×C7311yescharacteristic, complemented
905C4×C4⋊C4C22×C7311yescharacteristic, complemented
906C4×C4⋊C4C22×C7311yescharacteristic, complemented
907C4×C4⋊C4C22×C7311yescharacteristic, complemented
908C4×C4⋊C4C22×C7311yescharacteristic, complemented
909C4×C4⋊C4C22×C7311yescharacteristic, complemented
910C4×C4⋊C4C22×C7311yescharacteristic, complemented
911C4×C4⋊C4C22×C7311yescharacteristic, complemented
912C4×C4⋊C4C22×C7311yescharacteristic, complemented
913C4×C22⋊C4C22×C7311yescharacteristic
914C4×C22⋊C4C22×C7311yescharacteristic
915C4×C22⋊C4C22×C7311yescharacteristic
916C4×C22⋊C4C22×C7311yescharacteristic
917C4×C22⋊C4C22×C7311yescharacteristic
918C4×C22⋊C4C22×C7311yescharacteristic
919C4×C22⋊C4C22×C7311yescharacteristic
920C4×C22⋊C4C22×C7311yescharacteristic
921C4×C22⋊C4C22×C7311yescharacteristic
922C4×C22⋊C4C22×C7311yescharacteristic
923C4×C22⋊C4C22×C7311yescharacteristic
924C4×C22⋊C4C22×C7311yescharacteristic, complemented
925C4×C22⋊C4C22×C7311yescharacteristic, complemented
926C4×C22⋊C4C22×C7311yescharacteristic, complemented
927C4×C22⋊C4C22×C7311yescharacteristic, complemented
928#376C22×C7311yescharacteristic, complemented
929C2×#95C22×C7311yescharacteristic, complemented
930C43C22×C7311yescharacteristic, complemented
931C25C23×C7311yescharacteristic
932C22×Q8C23×C7311yescharacteristic
933C22×D4C23×C7311yescharacteristic
934C22×D4C23×C7311yescharacteristic
935C22×D4C23×C7311yescharacteristic
936C23×C4C23×C7311yescharacteristic
937C23×C4C23×C7311yescharacteristic
938C23×C4C23×C7311yescharacteristic
939C23×C4C23×C7311yescharacteristic
940C23×C4C23×C7311yescharacteristic
941C23×C4C23×C7311yescharacteristic
942C23×C4C23×C7311yescharacteristic
943C23×C4C23×C7311yescharacteristic
944C23×C4C23×C7311yescharacteristic
945#126C2×C4×C7318yescomplemented
946#126C2×C4×C7318yescomplemented
947#124C2×C4×C7318yes—
948#123C2×C4×C7318yes—
949#123C2×C4×C7318yescomplemented
950#123C2×C4×C7318yescomplemented
951C22⋊Q8C2×C4×C7318yescomplemented
952C22⋊Q8C2×C4×C7318yescomplemented
953#120C2×C4×C7318yes—
954C4×Q8—42no—
955C4×D4—42no—
956C4×D4C2×C4×C7318yescomplemented
957C4×D4C2×C4×C7318yescomplemented
958#117—42no—
959#117—42no—
960#117—42no—
961#117C2×C4×C7318yescomplemented
962#117C2×C4×C7318yescomplemented
963C2×C4⋊C4C23×C7311yescharacteristic
964C2×C4⋊C4C23×C7311yescharacteristic
965C2×C4⋊C4C23×C7311yescharacteristic
966C2×C4⋊C4C23×C7311yescharacteristic
967C2×C4⋊C4C23×C7311yescharacteristic
968C2×C4⋊C4C23×C7311yescharacteristic
969C2×C4⋊C4C23×C7311yescharacteristic
970C2×C4⋊C4C23×C7311yescharacteristic
971C2×C4⋊C4C23×C7311yescharacteristic
972C2×C4⋊C4C23×C7311yescharacteristic
973C2×C4⋊C4C23×C7311yescharacteristic
974C2×C4⋊C4C23×C7311yescharacteristic
975C2×C4⋊C4C23×C7311yescharacteristic
976C2×C4⋊C4C23×C7311yescharacteristic
977C2×C4⋊C4C23×C7311yescharacteristic
978C2×C4⋊C4C23×C7311yescharacteristic
979C2×C4⋊C4C23×C7311yescharacteristic
980C2×C4⋊C4C23×C7311yescharacteristic
981C2×C4⋊C4C23×C7311yescharacteristic
982C2×C4⋊C4C23×C7311yescharacteristic
983C2×C4⋊C4C23×C7311yescharacteristic
984C2×C4⋊C4C23×C7311yescharacteristic
985C2×C4⋊C4C23×C7311yescharacteristic
986C2×C4⋊C4C23×C7311yescharacteristic
987C2×C4⋊C4C23×C7311yescharacteristic
988C2×C4⋊C4C23×C7311yescharacteristic
989C2×C4⋊C4C23×C7311yescharacteristic
990C2×C4⋊C4C23×C7311yescharacteristic
991C2×C4⋊C4C23×C7311yescharacteristic
992C2×C4⋊C4C23×C7311yescharacteristic
993C2×C22⋊C4—42no—
994C2×C22⋊C4C2×C4×C7318yescomplemented
995C2×C22⋊C4C2×C4×C7318yescomplemented
996C2×C22⋊C4C23×C7311yescharacteristic
997C2×C22⋊C4C23×C7311yescharacteristic
998C2×C22⋊C4C23×C7311yescharacteristic
999C2×C22⋊C4C23×C7311yescharacteristic
1000C2×C22⋊C4C23×C7311yescharacteristic
1001C2×C22⋊C4C23×C7311yescharacteristic
1002C2×C22⋊C4C23×C7311yescharacteristic
1003C2×C22⋊C4C23×C7311yescharacteristic
1004C2×C22⋊C4C23×C7311yescharacteristic
1005C2×C22⋊C4C23×C7311yescharacteristic
1006C2×C22⋊C4C23×C7311yescharacteristic
1007C2×C22⋊C4C23×C7311yescharacteristic
1008C2×C22⋊C4C23×C7311yescharacteristic
1009C2×C22⋊C4C23×C7311yescharacteristic
1010C2×C22⋊C4C23×C7311yescharacteristic
1011C2×C22⋊C4C23×C7311yescharacteristic
1012C2×C22⋊C4C23×C7311yescharacteristic
1013C2×C22⋊C4C23×C7311yescharacteristic
1014C2×C22⋊C4C23×C7311yescharacteristic
1015C2×C22⋊C4C23×C7311yescharacteristic
1016C2×C22⋊C4C23×C7311yescharacteristic
1017C2×C22⋊C4C23×C7311yescharacteristic
1018C2×C22⋊C4C23×C7311yescharacteristic
1019C2×C22⋊C4C23×C7311yescharacteristic
1020C2×C22⋊C4C23×C7311yescharacteristic
1021C2×C22⋊C4C23×C7311yescharacteristic
1022C2×C22⋊C4C23×C7311yescharacteristic
1023C2×C22⋊C4C23×C7311yescharacteristic
1024C2×C22⋊C4C23×C7311yescharacteristic
1025C2×C22⋊C4C23×C7311yescharacteristic
1026C2×C22⋊C4C23×C7311yescharacteristic
1027C2×C22⋊C4C23×C7311yescharacteristic
1028C2×C22⋊C4C23×C7311yescharacteristic
1029C2×C22⋊C4C23×C7311yescharacteristic
1030C2×C22⋊C4C23×C7311yescharacteristic
1031C2×C22⋊C4C23×C7311yescharacteristic
1032C2×C22⋊C4C23×C7311yescharacteristic
1033C2×C22⋊C4C23×C7311yescharacteristic
1034C2×C22⋊C4C23×C7311yescharacteristic
1035C2×C22⋊C4C23×C7311yescharacteristic
1036C2×C22⋊C4C23×C7311yescharacteristic
1037C2×C22⋊C4C23×C7311yescharacteristic
1038C2×C42C23×C7311yescharacteristic
1039C2×C42C23×C7311yescharacteristic
1040C2×C42C23×C7311yescharacteristic
1041C2×C42C23×C7311yescharacteristic
1042C2×C42C23×C7311yescharacteristic
1043C2×C42C23×C7311yescharacteristic
1044C2×C42C23×C7311yescharacteristic
1045C2×C42C23×C7311yescharacteristic
1046C2×C42C23×C7311yescharacteristic
1047C2×C42C23×C7311yescharacteristic
1048C2×C42C23×C7311yescharacteristic
1049C2×C42C23×C7311yescharacteristic
1050C2×C42C23×C7311yescharacteristic
1051C2×C42C23×C7311yescharacteristic
1052C2×C42C23×C7311yescharacteristic
1053C2×C42C23×C7311yescharacteristic
1054C2×C42C23×C7311yescharacteristic
1055C2×C42C23×C7311yescharacteristic
1056C2×C42C23×C7311yescharacteristic
1057C2×C42C23×C7311yescharacteristic
1058C2×C42C23×C7311yescharacteristic
1059C2×C42C23×C7311yescharacteristic
1060C2×C42C23×C7311yescharacteristic
1061C2×C42C23×C7311yescharacteristic
1062C2×C42C23×C7311yescharacteristic
1063#95C23×C7311yescharacteristic
1064#95C23×C7311yescharacteristic
1065#95C23×C7311yescharacteristic
1066#95C23×C7311yescharacteristic
1067#95C23×C7311yescharacteristic
1068#95C23×C7311yescharacteristic
1069#95C23×C7311yescharacteristic
1070#95C23×C7311yescharacteristic
1071#95C23×C7311yescharacteristic
1072#95C23×C7311yescharacteristic
1073#95C23×C7311yescharacteristic
1074#95C23×C7311yescharacteristic
1075#95C23×C7311yescharacteristic
1076#95C23×C7311yescharacteristic
1077#95C23×C7311yescharacteristic
1078#95C23×C7311yescharacteristic
1079#95C23×C7311yescharacteristic
1080#95C23×C7311yescharacteristic
1081#95C23×C7311yescharacteristic
1082#95C23×C7311yescharacteristic
1083#95C23×C7311yescharacteristic
1084#95C23×C7311yescharacteristic
1085#95C23×C7311yescharacteristic
1086#95C23×C7311yescharacteristic
1087#95C23×C7311yescharacteristic
1088#95C23×C7311yescharacteristic
1089#95C23×C7311yescharacteristic
1090#95C23×C7311yescharacteristic
1091#95C23×C7311yescharacteristic
1092#95C23×C7311yescharacteristic
1093#95C23×C7311yescharacteristic
1094#95C23×C7311yescharacteristic
1095#95C23×C7311yescharacteristic
1096#95C23×C7311yescharacteristic
1097#95C23×C7311yescharacteristic
1098#95C23×C7311yescharacteristic
1099#95C23×C7311yescharacteristic
1100#95C23×C7311yescharacteristic
1101#95C23×C7311yescharacteristic
1102#95C23×C7311yescharacteristic
1103#95C23×C7311yescharacteristic
1104#95C23×C7311yescharacteristic
1105#95C23×C7311yescharacteristic
1106#95C23×C7311yescharacteristic
1107C24—41no—
1108C24—41no—
1109C24—41no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24C22×C4×C7314yes—
1114C24C24×C7311yescharacteristic
1115C24C24×C7311yescharacteristic
1116C24C24×C7311yescharacteristic
1117C24C24×C7311yescharacteristic
1118C2×Q8—41no—
1119C2×Q8—41no—
1120C2×Q8C22×C4×C7314yes—
1121C2×D4—41no—
1122C2×D4—41no—
1123C2×D4—41no—
1124C2×D4—41no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4C22×C4×C7314yes—
1128C2×D4C22×C4×C7314yes—
1129C2×D4C22×C4×C7314yes—
1130C22×C4—22no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—41no—
1142C22×C4—41no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—41no—
1146C22×C4—41no—
1147C22×C4—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4C22×C4×C7314yes—
1153C22×C4C22×C4×C7314yes—
1154C22×C4C22×C4×C7314yes—
1155C22×C4C22×C4×C7314yes—
1156C22×C4C22×C4×C7314yes—
1157C22×C4C24×C7311yescharacteristic
1158C22×C4C24×C7311yescharacteristic
1159C22×C4C24×C7311yescharacteristic
1160C22×C4C24×C7311yescharacteristic
1161C22×C4C24×C7311yescharacteristic
1162C22×C4C24×C7311yescharacteristic
1163C22×C4C24×C7311yescharacteristic
1164C22×C4C24×C7311yescharacteristic
1165C22×C4C24×C7311yescharacteristic
1166C22×C4C24×C7311yescharacteristic
1167C22×C4C24×C7311yescharacteristic
1168C22×C4C24×C7311yescharacteristic
1169C22×C4C24×C7311yescharacteristic
1170C22×C4C24×C7311yescharacteristic
1171C22×C4C24×C7311yescharacteristic
1172C22×C4C24×C7311yescharacteristic
1173C22×C4C24×C7311yescharacteristic
1174C22×C4C24×C7311yescharacteristic
1175C22×C4C24×C7311yescharacteristic
1176C22×C4C24×C7311yescharacteristic
1177C22×C4C24×C7311yescharacteristic
1178C22×C4C24×C7311yescharacteristic
1179C22×C4C24×C7311yescharacteristic
1180C22×C4C24×C7311yescharacteristic
1181C22×C4C24×C7311yescharacteristic
1182C22×C4C24×C7311yescharacteristic
1183C22×C4C24×C7311yescharacteristic
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—22no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4C22×C4×C7314yes—
1207C4⋊C4C22×C4×C7314yes—
1208C4⋊C4C22×C4×C7314yes—
1209C4⋊C4C22×C4×C7314yes—
1210C4⋊C4C22×C4×C7314yes—
1211C4⋊C4C22×C4×C7314yes—
1212C4⋊C4C22×C4×C7314yes—
1213C4⋊C4C22×C4×C7314yes—
1214C22⋊C4—22no—
1215C22⋊C4—22no—
1216C22⋊C4—22no—
1217C22⋊C4—41no—
1218C22⋊C4—41no—
1219C22⋊C4—41no—
1220C22⋊C4—41no—
1221C22⋊C4—41no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—41no—
1232C22⋊C4—41no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4C22×C4×C7314yes—
1243C22⋊C4C22×C4×C7314yes—
1244C22⋊C4C22×C4×C7314yes—
1245C22⋊C4C22×C4×C7314yes—
1246C22⋊C4C22×C4×C7314yes—
1247C22⋊C4C22×C4×C7314yes—
1248C22⋊C4C22×C4×C7314yes—
1249C22⋊C4C22×C4×C7314yes—
1250C22⋊C4C22×C4×C7314yes—
1251C22⋊C4C22×C4×C7314yes—
1252C22⋊C4C22×C4×C7314yes—
1253C22⋊C4C22×C4×C7314yes—
1254C22⋊C4C22×C4×C7314yes—
1255C22⋊C4C22×C4×C7314yes—
1256C42—22no—
1257C42—22no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—41no—
1268C42—41no—
1269C42—41no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42C22×C4×C7314yes—
1279C42C22×C4×C7314yes—
1280C42C22×C4×C7314yes—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—44no—
1306C23—44no—
1307C23—44no—
1308C23—82no—
1309C23—82no—
1310C23—82no—
1311C23—82no—
1312C23C23×C4×C7312yes—
1313C23C23×C4×C7312yes—
1314C23C23×C4×C7312yes—
1315C23C23×C4×C7312yes—
1316C23C25×C7311yescharacteristic
1317Q8—44no—
1318D4—44no—
1319D4—44no—
1320D4—44no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—44no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4—44no—
1394C2×C4—44no—
1395C2×C4—82no—
1396C2×C4—82no—
1397C2×C4—82no—
1398C2×C4—82no—
1399C2×C4C23×C4×C7312yes—
1400C2×C4C23×C4×C7312yes—
1401C2×C4C23×C4×C7312yes—
1402C2×C4C23×C4×C7312yes—
1403C2×C4C23×C4×C7312yes—
1404C2×C4C23×C4×C7312yes—
1405C2×C4C23×C4×C7312yes—
1406C2×C4C23×C4×C7312yes—
1407C2×C4C23×C4×C7312yes—
1408C2×C4C23×C4×C7312yes—
1409C2×C4C23×C4×C7312yes—
1410C2×C4H(5,𝔽2)×C7312yes—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—88no—
1440C22C24×C4×C7311yescharacteristic
1441C22C2×H(5,𝔽2)×C7311yescharacteristic
1442C22#585×C7311yescharacteristic
1443C22#585×C7311yescharacteristic
1444C22#585×C7311yescharacteristic
1445C22#585×C7311yescharacteristic
1446C22#585×C7311yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C2—42no—
1475C2—42no—
1476C2—42no—
1477C2—42no—
1478C2C73×#342811yescharacteristic
1479C2C73×#342811yescharacteristic
1480C2C4×H(5,𝔽2)×C7311yescharacteristic
1481C2C73×#356011yescharacteristic
1482C2C73×#356211yescharacteristic
1483C2C73×#356611yescharacteristic
1484C2C73×#356811yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutatorC22C24×C4×C73
Frattini, cosocleC23C25×C73
prime radicalC2×#120×C73C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#2383C2semidirect
3. C73×#2378C2semidirect
4. C73×#2376C2semidirect
6. C73×#2374C2semidirect
7. C73×#2373C2semidirect
8. C73×#2367C2semidirect
9. C73×#2362C2semidirect
10. C73×#2359C2semidirect
11. C73×#2354C2semidirect
12. C73×#2353C2semidirect
13. C73×#2347C2semidirect
14. C73×#2347C2semidirect
15. C73×#2342C2semidirect
16. C73×#2342C2semidirect
17. C73×#2337C2semidirect
18. C73×#2335C2semidirect
19. C73×#2335C2semidirect
20. C73×#2335C2semidirect
21. C73×#2334C2semidirect
22. C73×#2332C2semidirect
23. C73×#2323C2semidirect
25. C73×#2318C2semidirect
26. C73×#2314C2semidirect
27. C73×#2312C2semidirect
28. C73×#2312C2semidirect
29. C4×#126×C73C2semidirect
30. C73×#2298C2semidirect
31. C73×#2293C2semidirect
32. #551×C73C4semidirect
42. C2×C4×Q8×C73C22semidirect
50. C2×#117×C73C22semidirect
54. #391×C73C22semidirect
55. #391×C73C22semidirect
56. #391×C73C22semidirect
62. #389×C73C22semidirect
63. #389×C73C22semidirect
64. #389×C73C22semidirect
65. #389×C73C22semidirect
66. #389×C73C22semidirect
67. #389×C73C22semidirect
68. #389×C73C22semidirect
69. #389×C73C22semidirect
104. #388×C73C22semidirect
105. #388×C73C22semidirect
106. #388×C73C22semidirect
107. #388×C73C22semidirect
108. #388×C73C22semidirect
109. #388×C73C22semidirect
110. #387×C73C22semidirect
111. #387×C73C22semidirect
112. #387×C73C22semidirect
113. #387×C73C22semidirect
114. #387×C73C22semidirect
115. #387×C73C22semidirect
116. #387×C73C22semidirect
117. #387×C73C22semidirect
118. #387×C73C22semidirect
119. #387×C73C22semidirect
120. #387×C73C22semidirect
121. #387×C73C22semidirect
122. #387×C73C22semidirect
123. #387×C73C22semidirect
124. #387×C73C22semidirect
125. #387×C73C22semidirect
137. #385×C73C22semidirect
138. #385×C73C22semidirect
139. #385×C73C22semidirect
140. #384×C73C22semidirect
141. #383×C73C22semidirect
142. #383×C73C22semidirect
143. #383×C73C22semidirect
144. #382×C73C22semidirect
153. #380×C73C22semidirect
157. C4×C4⋊C4×C73C22semidirect
158. C4×C4⋊C4×C73C22semidirect
159. C4×C4⋊C4×C73C22semidirect
160. C4×C4⋊C4×C73C22semidirect
161. C4×C4⋊C4×C73C22semidirect
162. C4×C4⋊C4×C73C22semidirect
163. C4×C4⋊C4×C73C22semidirect
164. C4×C4⋊C4×C73C22semidirect
165. C4×C4⋊C4×C73C22semidirect
166. C4×C4⋊C4×C73C22semidirect
167. C4×C4⋊C4×C73C22semidirect
168. C4×C4⋊C4×C73C22semidirect
169. C4×C4⋊C4×C73C22semidirect
181. C4×C22⋊C4×C73C22semidirect
182. C4×C22⋊C4×C73C22semidirect
183. C4×C22⋊C4×C73C22semidirect
184. C4×C22⋊C4×C73C22semidirect
185. #376×C73C22semidirect
186. C2×#95×C73C22semidirect
187. C43×C73C22semidirect
202. #126×C73C2×C4semidirect
203. #126×C73C2×C4semidirect
206. #123×C73C2×C4semidirect
207. #123×C73C2×C4semidirect
208. C22⋊Q8×C73C2×C4semidirect
209. C22⋊Q8×C73C2×C4semidirect
213. C4×D4×C73C2×C4semidirect
214. C4×D4×C73C2×C4semidirect
218. #117×C73C2×C4semidirect
219. #117×C73C2×C4semidirect
251. C2×C22⋊C4×C73C2×C4semidirect
252. C2×C22⋊C4×C73C2×C4semidirect
731. #34504C73direct (N × H)
744. #2383C2×C73semidirect
745. #2378C2×C73semidirect
746. #2376C2×C73semidirect
748. #2374C2×C73semidirect
749. #2373C2×C73semidirect
750. #2367C2×C73semidirect
751. #2362C2×C73semidirect
752. #2359C2×C73semidirect
753. #2354C2×C73semidirect
754. #2353C2×C73semidirect
755. #2347C2×C73semidirect
756. #2347C2×C73semidirect
757. #2342C2×C73semidirect
758. #2342C2×C73semidirect
759. #2337C2×C73semidirect
760. #2335C2×C73semidirect
761. #2335C2×C73semidirect
762. #2335C2×C73semidirect
763. #2334C2×C73semidirect
764. #2332C2×C73semidirect
765. #2323C2×C73semidirect
767. #2318C2×C73semidirect
768. #2314C2×C73semidirect
769. #2312C2×C73semidirect
770. #2312C2×C73semidirect
771. C4×#126C2×C73semidirect
772. #2298C2×C73semidirect
773. #2293C2×C73semidirect
774. C73#34504direct (N × H)
775. #551C4×C73semidirect
785. C2×C4×Q8C22×C73semidirect
793. C2×#117C22×C73semidirect
797. #391C22×C73semidirect
798. #391C22×C73semidirect
799. #391C22×C73semidirect
805. #389C22×C73semidirect
806. #389C22×C73semidirect
807. #389C22×C73semidirect
808. #389C22×C73semidirect
809. #389C22×C73semidirect
810. #389C22×C73semidirect
811. #389C22×C73semidirect
812. #389C22×C73semidirect
847. #388C22×C73semidirect
848. #388C22×C73semidirect
849. #388C22×C73semidirect
850. #388C22×C73semidirect
851. #388C22×C73semidirect
852. #388C22×C73semidirect
853. #387C22×C73semidirect
854. #387C22×C73semidirect
855. #387C22×C73semidirect
856. #387C22×C73semidirect
857. #387C22×C73semidirect
858. #387C22×C73semidirect
859. #387C22×C73semidirect
860. #387C22×C73semidirect
861. #387C22×C73semidirect
862. #387C22×C73semidirect
863. #387C22×C73semidirect
864. #387C22×C73semidirect
865. #387C22×C73semidirect
866. #387C22×C73semidirect
867. #387C22×C73semidirect
868. #387C22×C73semidirect
880. #385C22×C73semidirect
881. #385C22×C73semidirect
882. #385C22×C73semidirect
883. #384C22×C73semidirect
884. #383C22×C73semidirect
885. #383C22×C73semidirect
886. #383C22×C73semidirect
887. #382C22×C73semidirect
896. #380C22×C73semidirect
900. C4×C4⋊C4C22×C73semidirect
901. C4×C4⋊C4C22×C73semidirect
902. C4×C4⋊C4C22×C73semidirect
903. C4×C4⋊C4C22×C73semidirect
904. C4×C4⋊C4C22×C73semidirect
905. C4×C4⋊C4C22×C73semidirect
906. C4×C4⋊C4C22×C73semidirect
907. C4×C4⋊C4C22×C73semidirect
908. C4×C4⋊C4C22×C73semidirect
909. C4×C4⋊C4C22×C73semidirect
910. C4×C4⋊C4C22×C73semidirect
911. C4×C4⋊C4C22×C73semidirect
912. C4×C4⋊C4C22×C73semidirect
924. C4×C22⋊C4C22×C73semidirect
925. C4×C22⋊C4C22×C73semidirect
926. C4×C22⋊C4C22×C73semidirect
927. C4×C22⋊C4C22×C73semidirect
928. #376C22×C73semidirect
929. C2×#95C22×C73semidirect
930. C43C22×C73semidirect
945. #126C2×C4×C73semidirect
946. #126C2×C4×C73semidirect
949. #123C2×C4×C73semidirect
950. #123C2×C4×C73semidirect
951. C22⋊Q8C2×C4×C73semidirect
952. C22⋊Q8C2×C4×C73semidirect
956. C4×D4C2×C4×C73semidirect
957. C4×D4C2×C4×C73semidirect
961. #117C2×C4×C73semidirect
962. #117C2×C4×C73semidirect
994. C2×C22⋊C4C2×C4×C73semidirect
995. C2×C22⋊C4C2×C4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#551×C732
C73×#23832
C73×#23782
C73×#23762
C73×#23752
C73×#23742
C73×#23732
C73×#23672
C73×#23622
C73×#23592
C73×#23542
C73×#23532
C73×#23472
C73×#23422
C73×#23372
C73×#23352
C73×#23342
C73×#23322
C73×#23232
C73×#23212
C73×#23182
C73×#23142
C73×#23122
C4×#126×C732
C73×#22982
C73×#22932
#3450473