Finite Group Databasebeta

← C73×#34861 #32944265

Subgroups — C73×#34861 #32944265

Order 18688.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2605C211yesmaximal, characteristic, complemented
2C73×#2603C211yesmaximal, characteristic, complemented
3C73×#2601C211yesmaximal, characteristic, complemented
4C73×#2598C211yesmaximal, characteristic, complemented
5C73×#2597C211yesmaximal, characteristic, complemented
6C73×#2589C211yesmaximal, characteristic, complemented
7C73×#2576C211yesmaximal, characteristic, complemented
8C73×#2557C211yesmaximal, characteristic, complemented
9C73×#2531C211yesmaximal, characteristic, complemented
10C73×#2527C211yesmaximal, characteristic, complemented
11C73×#2520C211yesmaximal, characteristic, complemented
12C73×#2516C211yesmaximal, characteristic, complemented
13C73×#2477C211yesmaximal, characteristic, complemented
14C73×#2471C211yesmaximal, characteristic, complemented
15C73×#2461C211yesmaximal, characteristic, complemented
16C73×#2457C211yesmaximal, characteristic, complemented
17C73×#2401C211yesmaximal, characteristic, complemented
18C73×#2396C211yesmaximal, characteristic, complemented
19C73×#2395C211yesmaximal, characteristic, complemented
20C73×#2388C211yesmaximal, characteristic
21C4×#126×C73C211yesmaximal, characteristic, complemented
22C4×#124×C73C211yesmaximal, characteristic, complemented
23C4×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
24C4×#123×C73C211yesmaximal, characteristic, complemented
25C4×#123×C73C211yesmaximal, characteristic, complemented
26C73×#2298C211yesmaximal, characteristic, complemented
27C73×#2297C211yesmaximal, characteristic, complemented
28C73×#2297C211yesmaximal, characteristic, complemented
29C73×#2290C211yesmaximal, characteristic, complemented
30C42×D4×C73C211yesmaximal, characteristic, complemented
31C4×#117×C73C211yesmaximal, characteristic, complemented
32C22×#41×C73C2211yescharacteristic
33C2×#126×C73C2211yescharacteristic
34C2×#124×C73C2211yescharacteristic
35C2×#123×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic
37C2×C22⋊Q8×C73C2211yescharacteristic
38C2×C4×Q8×C73C2211yescharacteristic
39C2×C4×D4×C73C2211yescharacteristic
40C2×C4×D4×C73C2211yescharacteristic
41C2×C4×D4×C73C2211yescharacteristic
42C2×C4×D4×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C2×#117×C73C2211yescharacteristic
45C2×#117×C73C2211yescharacteristic
46C2×#117×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48C22×C42×C73C2211yescharacteristic
49C22×C42×C73C2211yescharacteristic
50C22×C42×C73C2211yescharacteristic
51#401×C73C2211yescharacteristic
52#400×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic
54#400×C73C2211yescharacteristic
55#400×C73C2211yescharacteristic
56#400×C73C2211yescharacteristic
57#399×C73C2211yescharacteristic
58#399×C73C2211yescharacteristic
59#398×C73C2211yescharacteristic
60#398×C73C2211yescharacteristic
61#398×C73C2211yescharacteristic
62#397×C73C2211yescharacteristic
63#397×C73C2211yescharacteristic
64#397×C73C2211yescharacteristic
65#397×C73C2211yescharacteristic
66#397×C73C2211yescharacteristic
67#397×C73C2211yescharacteristic
68#396×C73C2211yescharacteristic
69#396×C73C2211yescharacteristic
70#396×C73C2211yescharacteristic
71#395×C73C2211yescharacteristic
72#395×C73C2211yescharacteristic
73#394×C73C2211yescharacteristic
74#394×C73C2211yescharacteristic
75#394×C73C2211yescharacteristic
76#394×C73C2211yescharacteristic
77#394×C73C2211yescharacteristic
78#393×C73C2211yescharacteristic
79#393×C73C2211yescharacteristic
80#392×C73C2211yescharacteristic
81#392×C73C2211yescharacteristic
82#392×C73C2211yescharacteristic
83#391×C73C2211yescharacteristic
84#391×C73C2211yescharacteristic
85#391×C73C2211yescharacteristic
86#391×C73C2211yescharacteristic
87#391×C73C2211yescharacteristic
88#391×C73C2211yescharacteristic
89#390×C73C2211yescharacteristic
90#390×C73C2211yescharacteristic
91#390×C73C2211yescharacteristic
92#390×C73C2211yescharacteristic
93#390×C73C2211yescharacteristic
94#389×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
105#388×C73C2211yescharacteristic
106#388×C73C2211yescharacteristic
107#388×C73C2211yescharacteristic
108#388×C73C2211yescharacteristic
109#388×C73C2211yescharacteristic
110#388×C73C2211yescharacteristic
111#388×C73C2211yescharacteristic
112#387×C73C2211yescharacteristic
113#387×C73C2211yescharacteristic
114#387×C73C2211yescharacteristic
115#387×C73C2211yescharacteristic
116#387×C73C2211yescharacteristic
117#387×C73C2211yescharacteristic
118#387×C73C2211yescharacteristic
119#387×C73C2211yescharacteristic
120#387×C73C2211yescharacteristic
121#387×C73C2211yescharacteristic
122#387×C73C2211yescharacteristic
123#387×C73C2211yescharacteristic
124#387×C73C2211yescharacteristic
125#387×C73C2211yescharacteristic
126#387×C73C2211yescharacteristic
127#386×C73C2211yescharacteristic
128#386×C73C2211yescharacteristic
129#386×C73C2211yescharacteristic
130#386×C73C2211yescharacteristic
131#386×C73C2211yescharacteristic
132#386×C73C2211yescharacteristic
133#386×C73C2211yescharacteristic
134#386×C73C2211yescharacteristic
135#386×C73C2211yescharacteristic
136#386×C73C2211yescharacteristic
137#386×C73C2211yescharacteristic
138#386×C73C2211yescharacteristic
139#385×C73C2211yescharacteristic
140#385×C73C2211yescharacteristic
141#385×C73C2211yescharacteristic
142#385×C73C2211yescharacteristic
143#385×C73C2211yescharacteristic
144#385×C73C2211yescharacteristic
145#383×C73C2211yescharacteristic
146#382×C73C2211yescharacteristic
147#381×C73C2211yescharacteristic
148#381×C73C2211yescharacteristic
149#380×C73C2211yescharacteristic
150C4×C4⋊C4×C73C2211yescharacteristic
151C4×C4⋊C4×C73C2211yescharacteristic
152C4×C4⋊C4×C73C2211yescharacteristic
153C4×C4⋊C4×C73C2211yescharacteristic
154C4×C4⋊C4×C73C2211yescharacteristic
155C4×C4⋊C4×C73C2211yescharacteristic
156C4×C4⋊C4×C73C2211yescharacteristic
157C4×C4⋊C4×C73C2211yescharacteristic
158C4×C4⋊C4×C73C2211yescharacteristic
159C4×C4⋊C4×C73C2211yescharacteristic
160C4×C4⋊C4×C73C2211yescharacteristic
161C4×C4⋊C4×C73C2211yescharacteristic
162C4×C22⋊C4×C73C2211yescharacteristic
163C4×C22⋊C4×C73C2211yescharacteristic
164C4×C22⋊C4×C73C2211yescharacteristic
165C4×C22⋊C4×C73C2211yescharacteristic
166C4×C22⋊C4×C73C2211yescharacteristic
167C4×C22⋊C4×C73C2211yescharacteristic
168C4×C22⋊C4×C73C2211yescharacteristic
169C4×C22⋊C4×C73C2211yescharacteristic
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
182#376×C73C2211yescharacteristic
183#376×C73C2211yescharacteristic
184#376×C73C2211yescharacteristic
185C43×C73C2211yescharacteristic
186C43×C73C2211yescharacteristic
187C2×#41×C73—24no—
188C2×#41×C73—24no—
189C2×#41×C73—42no—
190C22×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C22×D4×C73C2311yescharacteristic
197C22×D4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208#126×C73—24no—
209#124×C73—24no—
210#123×C73—24no—
211#123×C73—24no—
212C22⋊Q8×C73—24no—
213C4×Q8×C73—42no—
214C4×D4×C73—24no—
215C4×D4×C73—24no—
216C4×D4×C73—24no—
217C4×D4×C73—24no—
218C4×D4×C73—42no—
219#117×C73—24no—
220#117×C73—24no—
221#117×C73—24no—
222#117×C73—42no—
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×C22⋊C4×C73C2311yescharacteristic
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73C2311yescharacteristic
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×C42×C73—24no—
288C2×C42×C73—42no—
289C2×C42×C73—42no—
290C2×C42×C73C2311yescharacteristic
291C2×C42×C73C2311yescharacteristic
292C2×C42×C73C2311yescharacteristic
293C2×C42×C73C2311yescharacteristic
294C2×C42×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
315#95×C73C2311yescharacteristic
316#95×C73C2311yescharacteristic
317#95×C73C2311yescharacteristic
318#95×C73C2311yescharacteristic
319#95×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
363C24×C73C2411yescharacteristic
364C24×C73C2411yescharacteristic
365C24×C73C2411yescharacteristic
366C24×C73C2411yescharacteristic
367#41×C73—416no—
368C2×Q8×C73—22no—
369C2×Q8×C73—22no—
370C2×Q8×C73—22no—
371C2×Q8×C73—22no—
372C2×Q8×C73—41no—
373C2×Q8×C73—41no—
374C2×D4×C73—22no—
375C2×D4×C73—22no—
376C2×D4×C73—22no—
377C2×D4×C73—22no—
378C2×D4×C73—22no—
379C2×D4×C73—22no—
380C2×D4×C73—22no—
381C2×D4×C73—22no—
382C2×D4×C73—22no—
383C2×D4×C73—22no—
384C2×D4×C73—22no—
385C2×D4×C73—22no—
386C2×D4×C73—22no—
387C2×D4×C73—41no—
388C2×D4×C73—41no—
389C2×D4×C73—41no—
390C2×D4×C73—41no—
391C2×D4×C73—41no—
392C22×C4×C73—22no—
393C22×C4×C73—22no—
394C22×C4×C73—22no—
395C22×C4×C73—22no—
396C22×C4×C73—22no—
397C22×C4×C73—22no—
398C22×C4×C73—22no—
399C22×C4×C73—22no—
400C22×C4×C73—22no—
401C22×C4×C73—22no—
402C22×C4×C73—22no—
403C22×C4×C73—22no—
404C22×C4×C73—22no—
405C22×C4×C73—22no—
406C22×C4×C73—22no—
407C22×C4×C73—22no—
408C22×C4×C73—22no—
409C22×C4×C73—22no—
410C22×C4×C73—22no—
411C22×C4×C73—22no—
412C22×C4×C73—22no—
413C22×C4×C73—41no—
414C22×C4×C73—41no—
415C22×C4×C73—41no—
416C22×C4×C73—41no—
417C22×C4×C73—41no—
418C22×C4×C73—41no—
419C22×C4×C73—41no—
420C22×C4×C73#4114yes—
421C22×C4×C73#4114yes—
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
441C22×C4×C73C2411yescharacteristic
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
444C22×C4×C73C2411yescharacteristic
445C22×C4×C73C2411yescharacteristic
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C4⋊C4×C73—22no—
450C4⋊C4×C73—22no—
451C4⋊C4×C73—22no—
452C4⋊C4×C73—22no—
453C4⋊C4×C73—22no—
454C4⋊C4×C73—22no—
455C4⋊C4×C73—22no—
456C4⋊C4×C73—22no—
457C4⋊C4×C73—22no—
458C4⋊C4×C73—22no—
459C4⋊C4×C73—22no—
460C4⋊C4×C73—22no—
461C4⋊C4×C73—22no—
462C4⋊C4×C73—22no—
463C4⋊C4×C73—22no—
464C4⋊C4×C73—22no—
465C4⋊C4×C73—22no—
466C4⋊C4×C73—41no—
467C4⋊C4×C73—41no—
468C4⋊C4×C73—41no—
469C4⋊C4×C73—41no—
470C4⋊C4×C73—41no—
471C4⋊C4×C73—41no—
472C4⋊C4×C73—41no—
473C4⋊C4×C73—41no—
474C4⋊C4×C73#4114yescomplemented
475C22⋊C4×C73—22no—
476C22⋊C4×C73—22no—
477C22⋊C4×C73—22no—
478C22⋊C4×C73—22no—
479C22⋊C4×C73—22no—
480C22⋊C4×C73—22no—
481C22⋊C4×C73—22no—
482C22⋊C4×C73—22no—
483C22⋊C4×C73—22no—
484C22⋊C4×C73—22no—
485C22⋊C4×C73—22no—
486C22⋊C4×C73—22no—
487C22⋊C4×C73—22no—
488C22⋊C4×C73—22no—
489C22⋊C4×C73—22no—
490C22⋊C4×C73—22no—
491C22⋊C4×C73—22no—
492C22⋊C4×C73—22no—
493C22⋊C4×C73—22no—
494C22⋊C4×C73—22no—
495C22⋊C4×C73—22no—
496C22⋊C4×C73—22no—
497C22⋊C4×C73—22no—
498C22⋊C4×C73—22no—
499C22⋊C4×C73—22no—
500C22⋊C4×C73—22no—
501C22⋊C4×C73—41no—
502C22⋊C4×C73—41no—
503C22⋊C4×C73—41no—
504C22⋊C4×C73—41no—
505C22⋊C4×C73—41no—
506C22⋊C4×C73—41no—
507C22⋊C4×C73—41no—
508C22⋊C4×C73—41no—
509C22⋊C4×C73—41no—
510C22⋊C4×C73—41no—
511C22⋊C4×C73—41no—
512C22⋊C4×C73#4114yescomplemented
513C42×C73—22no—
514C42×C73—22no—
515C42×C73—22no—
516C42×C73—22no—
517C42×C73—22no—
518C42×C73—22no—
519C42×C73—22no—
520C42×C73—22no—
521C42×C73—22no—
522C42×C73—22no—
523C42×C73—22no—
524C42×C73—22no—
525C42×C73—22no—
526C42×C73—22no—
527C42×C73—22no—
528C42×C73—22no—
529C42×C73—22no—
530C42×C73—22no—
531C42×C73—41no—
532C42×C73—41no—
533C42×C73—41no—
534C42×C73—41no—
535C42×C73—41no—
536C42×C73—41no—
537C42×C73#4114yescomplemented
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—21no—
563C23×C73C2×#4112yes—
564C23×C73C2×#4112yes—
565C23×C73C2×#4112yes—
566C23×C73C2511yescharacteristic
567Q8×C73—44no—
568Q8×C73—44no—
569D4×C73—28no—
570D4×C73—44no—
571D4×C73—44no—
572D4×C73—44no—
573D4×C73—44no—
574D4×C73—44no—
575C2×C4×C73—28no—
576C2×C4×C73—21no—
577C2×C4×C73—21no—
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—28no—
597C2×C4×C73—28no—
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—44no—
647C2×C4×C73—44no—
648C2×C4×C73—44no—
649C2×C4×C73—44no—
650C2×C4×C73—44no—
651C2×C4×C73—44no—
652C2×C4×C73—44no—
653C2×C4×C73C2×#4112yes—
654C2×C4×C73C2×#4112yes—
655C2×C4×C73C2×#4112yes—
656C2×C4×C73C2×#4112yes—
657C2×C4×C73C2×#4112yes—
658C2×C4×C73C2×#4112yes—
659C2×C4×C73C2×#4112yes—
660C2×C4×C73C2×#4112yes—
661C2×C4×C73C2×#4112yes—
662C2×C4×C73C2×#4112yes—
663C2×C4×C73C2×#4112yes—
664C2×C4×C73C2×#4112yes—
665C2×C4×C73H(5,𝔽2)12yes—
666C22×C73—22no—
667C22×C73—22no—
668C22×C73—22no—
669C22×C73—22no—
670C22×C73—22no—
671C22×C73—22no—
672C22×C73—22no—
673C22×C73—22no—
674C22×C73—22no—
675C22×C73—41no—
676C22×C73—41no—
677C22×C73—41no—
678C22×C73—41no—
679C22×C73—41no—
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×C73C22×#4111yescharacteristic
695C22×C73C22×#4111yescharacteristic
696C22×C73C22×#4111yescharacteristic
697C22×C73C22×#4111yescharacteristic
698C22×C73C22×#4111yescharacteristic
699C22×C73C2×H(5,𝔽2)11yescharacteristic
700C22×C73#58511yescharacteristic
701C4×C73—22no—
702C4×C73—22no—
703C4×C73—22no—
704C4×C73—22no—
705C4×C73—22no—
706C4×C73—22no—
707C4×C73—22no—
708C4×C73—22no—
709C4×C73—22no—
710C4×C73—22no—
711C4×C73—41no—
712C4×C73—41no—
713C4×C73—41no—
714C4×C73—41no—
715C4×C73—41no—
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#55114yes—
728#34861C7311yesmaximal, characteristic, direct product factor, Sylow
729C2×C73—42no—
730C2×C73—42no—
731C2×C73—42no—
732C2×C73—81no—
733C2×C73#344411yescharacteristic
734C2×C73#344411yescharacteristic
735C2×C73#346011yescharacteristic
736C2×C73C2×#55111yescharacteristic
737C2×C73#347511yescharacteristic
738C2×C73#348011yescharacteristic
739C2×C73#348111yescharacteristic
740#2605C2×C7311yescharacteristic, complemented
741#2603C2×C7311yescharacteristic, complemented
742#2601C2×C7311yescharacteristic, complemented
743#2598C2×C7311yescharacteristic, complemented
744#2597C2×C7311yescharacteristic, complemented
745#2589C2×C7311yescharacteristic, complemented
746#2576C2×C7311yescharacteristic, complemented
747#2557C2×C7311yescharacteristic, complemented
748#2531C2×C7311yescharacteristic, complemented
749#2527C2×C7311yescharacteristic, complemented
750#2520C2×C7311yescharacteristic, complemented
751#2516C2×C7311yescharacteristic, complemented
752#2477C2×C7311yescharacteristic, complemented
753#2471C2×C7311yescharacteristic, complemented
754#2461C2×C7311yescharacteristic, complemented
755#2457C2×C7311yescharacteristic, complemented
756#2401C2×C7311yescharacteristic, complemented
757#2396C2×C7311yescharacteristic, complemented
758#2395C2×C7311yescharacteristic, complemented
759#2388C2×C7311yescharacteristic
760C4×#126C2×C7311yescharacteristic, complemented
761C4×#124C2×C7311yescharacteristic, complemented
762C4×C22⋊Q8C2×C7311yescharacteristic, complemented
763C4×#123C2×C7311yescharacteristic, complemented
764C4×#123C2×C7311yescharacteristic, complemented
765#2298C2×C7311yescharacteristic, complemented
766#2297C2×C7311yescharacteristic, complemented
767#2297C2×C7311yescharacteristic, complemented
768#2290C2×C7311yescharacteristic, complemented
769C42×D4C2×C7311yescharacteristic, complemented
770C4×#117C2×C7311yescharacteristic, complemented
771C73#3486111yescharacteristic, direct product factor, Sylow
772C22×#41C22×C7311yescharacteristic
773C2×#126C22×C7311yescharacteristic
774C2×#124C22×C7311yescharacteristic
775C2×#123C22×C7311yescharacteristic
776C2×#123C22×C7311yescharacteristic
777C2×C22⋊Q8C22×C7311yescharacteristic
778C2×C4×Q8C22×C7311yescharacteristic
779C2×C4×D4C22×C7311yescharacteristic
780C2×C4×D4C22×C7311yescharacteristic
781C2×C4×D4C22×C7311yescharacteristic
782C2×C4×D4C22×C7311yescharacteristic
783C2×C4×D4C22×C7311yescharacteristic
784C2×#117C22×C7311yescharacteristic
785C2×#117C22×C7311yescharacteristic
786C2×#117C22×C7311yescharacteristic
787C2×#117C22×C7311yescharacteristic
788C22×C42C22×C7311yescharacteristic
789C22×C42C22×C7311yescharacteristic
790C22×C42C22×C7311yescharacteristic
791#401C22×C7311yescharacteristic
792#400C22×C7311yescharacteristic
793#400C22×C7311yescharacteristic
794#400C22×C7311yescharacteristic
795#400C22×C7311yescharacteristic
796#400C22×C7311yescharacteristic
797#399C22×C7311yescharacteristic
798#399C22×C7311yescharacteristic
799#398C22×C7311yescharacteristic
800#398C22×C7311yescharacteristic
801#398C22×C7311yescharacteristic
802#397C22×C7311yescharacteristic
803#397C22×C7311yescharacteristic
804#397C22×C7311yescharacteristic
805#397C22×C7311yescharacteristic
806#397C22×C7311yescharacteristic
807#397C22×C7311yescharacteristic
808#396C22×C7311yescharacteristic
809#396C22×C7311yescharacteristic
810#396C22×C7311yescharacteristic
811#395C22×C7311yescharacteristic
812#395C22×C7311yescharacteristic
813#394C22×C7311yescharacteristic
814#394C22×C7311yescharacteristic
815#394C22×C7311yescharacteristic
816#394C22×C7311yescharacteristic
817#394C22×C7311yescharacteristic
818#393C22×C7311yescharacteristic
819#393C22×C7311yescharacteristic
820#392C22×C7311yescharacteristic
821#392C22×C7311yescharacteristic
822#392C22×C7311yescharacteristic
823#391C22×C7311yescharacteristic
824#391C22×C7311yescharacteristic
825#391C22×C7311yescharacteristic
826#391C22×C7311yescharacteristic
827#391C22×C7311yescharacteristic
828#391C22×C7311yescharacteristic
829#390C22×C7311yescharacteristic
830#390C22×C7311yescharacteristic
831#390C22×C7311yescharacteristic
832#390C22×C7311yescharacteristic
833#390C22×C7311yescharacteristic
834#389C22×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
848#388C22×C7311yescharacteristic
849#388C22×C7311yescharacteristic
850#388C22×C7311yescharacteristic
851#388C22×C7311yescharacteristic
852#387C22×C7311yescharacteristic
853#387C22×C7311yescharacteristic
854#387C22×C7311yescharacteristic
855#387C22×C7311yescharacteristic
856#387C22×C7311yescharacteristic
857#387C22×C7311yescharacteristic
858#387C22×C7311yescharacteristic
859#387C22×C7311yescharacteristic
860#387C22×C7311yescharacteristic
861#387C22×C7311yescharacteristic
862#387C22×C7311yescharacteristic
863#387C22×C7311yescharacteristic
864#387C22×C7311yescharacteristic
865#387C22×C7311yescharacteristic
866#387C22×C7311yescharacteristic
867#386C22×C7311yescharacteristic
868#386C22×C7311yescharacteristic
869#386C22×C7311yescharacteristic
870#386C22×C7311yescharacteristic
871#386C22×C7311yescharacteristic
872#386C22×C7311yescharacteristic
873#386C22×C7311yescharacteristic
874#386C22×C7311yescharacteristic
875#386C22×C7311yescharacteristic
876#386C22×C7311yescharacteristic
877#386C22×C7311yescharacteristic
878#386C22×C7311yescharacteristic
879#385C22×C7311yescharacteristic
880#385C22×C7311yescharacteristic
881#385C22×C7311yescharacteristic
882#385C22×C7311yescharacteristic
883#385C22×C7311yescharacteristic
884#385C22×C7311yescharacteristic
885#383C22×C7311yescharacteristic
886#382C22×C7311yescharacteristic
887#381C22×C7311yescharacteristic
888#381C22×C7311yescharacteristic
889#380C22×C7311yescharacteristic
890C4×C4⋊C4C22×C7311yescharacteristic
891C4×C4⋊C4C22×C7311yescharacteristic
892C4×C4⋊C4C22×C7311yescharacteristic
893C4×C4⋊C4C22×C7311yescharacteristic
894C4×C4⋊C4C22×C7311yescharacteristic
895C4×C4⋊C4C22×C7311yescharacteristic
896C4×C4⋊C4C22×C7311yescharacteristic
897C4×C4⋊C4C22×C7311yescharacteristic
898C4×C4⋊C4C22×C7311yescharacteristic
899C4×C4⋊C4C22×C7311yescharacteristic
900C4×C4⋊C4C22×C7311yescharacteristic
901C4×C4⋊C4C22×C7311yescharacteristic
902C4×C22⋊C4C22×C7311yescharacteristic
903C4×C22⋊C4C22×C7311yescharacteristic
904C4×C22⋊C4C22×C7311yescharacteristic
905C4×C22⋊C4C22×C7311yescharacteristic
906C4×C22⋊C4C22×C7311yescharacteristic
907C4×C22⋊C4C22×C7311yescharacteristic
908C4×C22⋊C4C22×C7311yescharacteristic
909C4×C22⋊C4C22×C7311yescharacteristic
910C4×C22⋊C4C22×C7311yescharacteristic
911C4×C22⋊C4C22×C7311yescharacteristic
912C4×C22⋊C4C22×C7311yescharacteristic
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
922#376C22×C7311yescharacteristic
923#376C22×C7311yescharacteristic
924#376C22×C7311yescharacteristic
925C43C22×C7311yescharacteristic
926C43C22×C7311yescharacteristic
927C2×#41—24no—
928C2×#41—24no—
929C2×#41—42no—
930C22×Q8C23×C7311yescharacteristic
931C22×Q8C23×C7311yescharacteristic
932C22×D4C23×C7311yescharacteristic
933C22×D4C23×C7311yescharacteristic
934C22×D4C23×C7311yescharacteristic
935C22×D4C23×C7311yescharacteristic
936C22×D4C23×C7311yescharacteristic
937C22×D4C23×C7311yescharacteristic
938C23×C4C23×C7311yescharacteristic
939C23×C4C23×C7311yescharacteristic
940C23×C4C23×C7311yescharacteristic
941C23×C4C23×C7311yescharacteristic
942C23×C4C23×C7311yescharacteristic
943C23×C4C23×C7311yescharacteristic
944C23×C4C23×C7311yescharacteristic
945C23×C4C23×C7311yescharacteristic
946C23×C4C23×C7311yescharacteristic
947C23×C4C23×C7311yescharacteristic
948#126—24no—
949#124—24no—
950#123—24no—
951#123—24no—
952C22⋊Q8—24no—
953C4×Q8—42no—
954C4×D4—24no—
955C4×D4—24no—
956C4×D4—24no—
957C4×D4—24no—
958C4×D4—42no—
959#117—24no—
960#117—24no—
961#117—24no—
962#117—42no—
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×C22⋊C4C23×C7311yescharacteristic
990C2×C22⋊C4C23×C7311yescharacteristic
991C2×C22⋊C4C23×C7311yescharacteristic
992C2×C22⋊C4C23×C7311yescharacteristic
993C2×C22⋊C4C23×C7311yescharacteristic
994C2×C22⋊C4C23×C7311yescharacteristic
995C2×C22⋊C4C23×C7311yescharacteristic
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×C42—24no—
1028C2×C42—42no—
1029C2×C42—42no—
1030C2×C42C23×C7311yescharacteristic
1031C2×C42C23×C7311yescharacteristic
1032C2×C42C23×C7311yescharacteristic
1033C2×C42C23×C7311yescharacteristic
1034C2×C42C23×C7311yescharacteristic
1035C2×C42C23×C7311yescharacteristic
1036C2×C42C23×C7311yescharacteristic
1037C2×C42C23×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
1055#95C23×C7311yescharacteristic
1056#95C23×C7311yescharacteristic
1057#95C23×C7311yescharacteristic
1058#95C23×C7311yescharacteristic
1059#95C23×C7311yescharacteristic
1060#95C23×C7311yescharacteristic
1061#95C23×C7311yescharacteristic
1062#95C23×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
1103C24C24×C7311yescharacteristic
1104C24C24×C7311yescharacteristic
1105C24C24×C7311yescharacteristic
1106C24C24×C7311yescharacteristic
1107#41—416no—
1108C2×Q8—22no—
1109C2×Q8—22no—
1110C2×Q8—22no—
1111C2×Q8—22no—
1112C2×Q8—41no—
1113C2×Q8—41no—
1114C2×D4—22no—
1115C2×D4—22no—
1116C2×D4—22no—
1117C2×D4—22no—
1118C2×D4—22no—
1119C2×D4—22no—
1120C2×D4—22no—
1121C2×D4—22no—
1122C2×D4—22no—
1123C2×D4—22no—
1124C2×D4—22no—
1125C2×D4—22no—
1126C2×D4—22no—
1127C2×D4—41no—
1128C2×D4—41no—
1129C2×D4—41no—
1130C2×D4—41no—
1131C2×D4—41no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4#41×C7314yes—
1161C22×C4#41×C7314yes—
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
1184C22×C4C24×C7311yescharacteristic
1185C22×C4C24×C7311yescharacteristic
1186C22×C4C24×C7311yescharacteristic
1187C22×C4C24×C7311yescharacteristic
1188C22×C4C24×C7311yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4#41×C7314yescomplemented
1215C22⋊C4—22no—
1216C22⋊C4—22no—
1217C22⋊C4—22no—
1218C22⋊C4—22no—
1219C22⋊C4—22no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—22no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—22no—
1226C22⋊C4—22no—
1227C22⋊C4—22no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—22no—
1233C22⋊C4—22no—
1234C22⋊C4—22no—
1235C22⋊C4—22no—
1236C22⋊C4—22no—
1237C22⋊C4—22no—
1238C22⋊C4—22no—
1239C22⋊C4—22no—
1240C22⋊C4—22no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4—41no—
1246C22⋊C4—41no—
1247C22⋊C4—41no—
1248C22⋊C4—41no—
1249C22⋊C4—41no—
1250C22⋊C4—41no—
1251C22⋊C4—41no—
1252C22⋊C4#41×C7314yescomplemented
1253C42—22no—
1254C42—22no—
1255C42—22no—
1256C42—22no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—22no—
1261C42—22no—
1262C42—22no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42#41×C7314yescomplemented
1278C23—21no—
1279C23—21no—
1280C23—21no—
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—
1303C23C2×#41×C7312yes—
1304C23C2×#41×C7312yes—
1305C23C2×#41×C7312yes—
1306C23C25×C7311yescharacteristic
1307Q8—44no—
1308Q8—44no—
1309D4—28no—
1310D4—44no—
1311D4—44no—
1312D4—44no—
1313D4—44no—
1314D4—44no—
1315C2×C4—28no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
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—28no—
1337C2×C4—28no—
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—44no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—44no—
1390C2×C4—44no—
1391C2×C4—44no—
1392C2×C4—44no—
1393C2×C4C2×#41×C7312yes—
1394C2×C4C2×#41×C7312yes—
1395C2×C4C2×#41×C7312yes—
1396C2×C4C2×#41×C7312yes—
1397C2×C4C2×#41×C7312yes—
1398C2×C4C2×#41×C7312yes—
1399C2×C4C2×#41×C7312yes—
1400C2×C4C2×#41×C7312yes—
1401C2×C4C2×#41×C7312yes—
1402C2×C4C2×#41×C7312yes—
1403C2×C4C2×#41×C7312yes—
1404C2×C4C2×#41×C7312yes—
1405C2×C4H(5,𝔽2)×C7312yes—
1406C22—22no—
1407C22—22no—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—41no—
1416C22—41no—
1417C22—41no—
1418C22—41no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22C22×#41×C7311yescharacteristic
1435C22C22×#41×C7311yescharacteristic
1436C22C22×#41×C7311yescharacteristic
1437C22C22×#41×C7311yescharacteristic
1438C22C22×#41×C7311yescharacteristic
1439C22C2×H(5,𝔽2)×C7311yescharacteristic
1440C22#585×C7311yescharacteristic
1441C4—22no—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—41no—
1452C4—41no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4#551×C7314yes—
1468C2—42no—
1469C2—42no—
1470C2—42no—
1471C2—81no—
1472C2C73×#344411yescharacteristic
1473C2C73×#344411yescharacteristic
1474C2C73×#346011yescharacteristic
1475C2C2×#551×C7311yescharacteristic
1476C2C73×#347511yescharacteristic
1477C2C73×#348011yescharacteristic
1478C2C73×#348111yescharacteristic
subgroupG/H
centerC22×C4×C73C24
commutator, Frattini, cosocleC23C25×C73
socleC23×C73C25
prime radicalC73×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2605C2semidirect
2. C73×#2603C2semidirect
3. C73×#2601C2semidirect
4. C73×#2598C2semidirect
5. C73×#2597C2semidirect
6. C73×#2589C2semidirect
7. C73×#2576C2semidirect
8. C73×#2557C2semidirect
9. C73×#2531C2semidirect
10. C73×#2527C2semidirect
11. C73×#2520C2semidirect
12. C73×#2516C2semidirect
13. C73×#2477C2semidirect
14. C73×#2471C2semidirect
15. C73×#2461C2semidirect
16. C73×#2457C2semidirect
17. C73×#2401C2semidirect
18. C73×#2396C2semidirect
19. C73×#2395C2semidirect
21. C4×#126×C73C2semidirect
22. C4×#124×C73C2semidirect
23. C4×C22⋊Q8×C73C2semidirect
24. C4×#123×C73C2semidirect
25. C4×#123×C73C2semidirect
26. C73×#2298C2semidirect
27. C73×#2297C2semidirect
28. C73×#2297C2semidirect
29. C73×#2290C2semidirect
30. C42×D4×C73C2semidirect
31. C4×#117×C73C2semidirect
474. C4⋊C4×C73#41semidirect
512. C22⋊C4×C73#41semidirect
537. C42×C73#41semidirect
728. #34861C73direct (N × H)
740. #2605C2×C73semidirect
741. #2603C2×C73semidirect
742. #2601C2×C73semidirect
743. #2598C2×C73semidirect
744. #2597C2×C73semidirect
745. #2589C2×C73semidirect
746. #2576C2×C73semidirect
747. #2557C2×C73semidirect
748. #2531C2×C73semidirect
749. #2527C2×C73semidirect
750. #2520C2×C73semidirect
751. #2516C2×C73semidirect
752. #2477C2×C73semidirect
753. #2471C2×C73semidirect
754. #2461C2×C73semidirect
755. #2457C2×C73semidirect
756. #2401C2×C73semidirect
757. #2396C2×C73semidirect
758. #2395C2×C73semidirect
760. C4×#126C2×C73semidirect
761. C4×#124C2×C73semidirect
762. C4×C22⋊Q8C2×C73semidirect
763. C4×#123C2×C73semidirect
764. C4×#123C2×C73semidirect
765. #2298C2×C73semidirect
766. #2297C2×C73semidirect
767. #2297C2×C73semidirect
768. #2290C2×C73semidirect
769. C42×D4C2×C73semidirect
770. C4×#117C2×C73semidirect
771. C73#34861direct (N × H)
1214. C4⋊C4#41×C73semidirect
1252. C22⋊C4#41×C73semidirect
1277. C42#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#26052
C73×#26032
C73×#26012
C73×#25982
C73×#25972
C73×#25892
C73×#25762
C73×#25572
C73×#25312
C73×#25272
C73×#25202
C73×#25162
C73×#24772
C73×#24712
C73×#24612
C73×#24572
C73×#24012
C73×#23962
C73×#23952
C73×#23882
C4×#126×C732
C4×#124×C732
C4×C22⋊Q8×C732
C4×#123×C732
C73×#22982
C73×#22972
C73×#22902
C42×D4×C732
C4×#117×C732
#3486173