Finite Group Databasebeta

← C73×#59492 #32968896

Subgroups — C73×#59492 #32968896

Order 18688.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2781C211yesmaximal, characteristic, complemented
2C73×#2773C211yesmaximal, characteristic, complemented
3C73×#2770C211yesmaximal, characteristic, complemented
4C73×#2743C211yesmaximal, characteristic, complemented
5C73×#2604C211yesmaximal, characteristic, complemented
6C73×#2575C211yesmaximal, characteristic, complemented
7C73×#2558C211yesmaximal, characteristic, complemented
8C73×#2556C211yesmaximal, characteristic, complemented
9C73×#2536C211yesmaximal, characteristic, complemented
10C73×#2529C211yesmaximal, characteristic, complemented
11C73×#2525C211yesmaximal, characteristic, complemented
12C73×#2505C211yesmaximal, characteristic, complemented
13C73×#2505C211yesmaximal, characteristic, complemented
14C73×#2488C211yesmaximal, characteristic, complemented
15C73×#2480C211yesmaximal, characteristic, complemented
16C73×#2479C211yesmaximal, characteristic, complemented
17C73×#2470C211yesmaximal, characteristic, complemented
18C73×#2449C211yesmaximal, characteristic, complemented
19C73×#2442C211yesmaximal, characteristic, complemented
20C73×#2437C211yesmaximal, characteristic, complemented
21C73×#2418C211yesmaximal, characteristic
22C73×#2418C211yesmaximal, characteristic
23C73×#2359C211yesmaximal, characteristic, complemented
24C73×#2358C211yesmaximal, characteristic
25C73×#2353C211yesmaximal, characteristic, complemented
26C73×#2349C211yesmaximal, characteristic, complemented
27C73×#2346C211yesmaximal, characteristic, complemented
28C73×#2342C211yesmaximal, characteristic, complemented
29C4×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
30C73×#2290C211yesmaximal, characteristic, complemented
31C2×#388×C73C211yesmaximal, characteristic, complemented
32C2×#126×C73C2211yescharacteristic
33C2×#125×C73C2211yescharacteristic, complemented
34C2×#123×C73C2211yescharacteristic
35C2×#123×C73C2211yescharacteristic
36C2×C22⋊Q8×C73C2211yescharacteristic
37C2×C22⋊Q8×C73C2211yescharacteristic
38C2×C22⋊Q8×C73C2211yescharacteristic, complemented
39C2×#120×C73C2211yescharacteristic
40C2×C4×Q8×C73C2211yescharacteristic, complemented
41C2×C4×D4×C73C2211yescharacteristic
42C2×C4×D4×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C2×C4×D4×C73C2211yescharacteristic
45C2×#117×C73C2211yescharacteristic
46C2×#117×C73C2211yescharacteristic, complemented
47C22×C4⋊C4×C73C2211yescharacteristic
48C22×C22⋊C4×C73C2211yescharacteristic
49C22×C22⋊C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic, complemented
54#400×C73C2211yescharacteristic, complemented
55#400×C73C2211yescharacteristic, complemented
56#400×C73C2211yescharacteristic, complemented
57#400×C73C2211yescharacteristic, complemented
58#400×C73C2211yescharacteristic, complemented
59#400×C73C2211yescharacteristic, complemented
60#400×C73C2211yescharacteristic, complemented
61#399×C73C2211yescharacteristic
62#399×C73C2211yescharacteristic
63#399×C73C2211yescharacteristic
64#399×C73C2211yescharacteristic, complemented
65#398×C73C2211yescharacteristic, complemented
66#398×C73C2211yescharacteristic, complemented
67#398×C73C2211yescharacteristic, complemented
68#398×C73C2211yescharacteristic, complemented
69#398×C73C2211yescharacteristic, complemented
70#397×C73C2211yescharacteristic
71#397×C73C2211yescharacteristic
72#397×C73C2211yescharacteristic
73#397×C73C2211yescharacteristic
74#397×C73C2211yescharacteristic
75#396×C73C2211yescharacteristic
76#396×C73C2211yescharacteristic
77#396×C73C2211yescharacteristic
78#396×C73C2211yescharacteristic, complemented
79#395×C73C2211yescharacteristic, complemented
80#394×C73C2211yescharacteristic
81#394×C73C2211yescharacteristic
82#394×C73C2211yescharacteristic
83#394×C73C2211yescharacteristic
84#393×C73C2211yescharacteristic
85#391×C73C2211yescharacteristic, complemented
86#390×C73C2211yescharacteristic
87#389×C73C2211yescharacteristic, complemented
88#389×C73C2211yescharacteristic, complemented
89#389×C73C2211yescharacteristic, complemented
90#389×C73C2211yescharacteristic, complemented
91#389×C73C2211yescharacteristic, complemented
92#389×C73C2211yescharacteristic, complemented
93#389×C73C2211yescharacteristic, complemented
94#389×C73C2211yescharacteristic, complemented
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#388×C73C2211yescharacteristic
113#388×C73C2211yescharacteristic
114#388×C73C2211yescharacteristic
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic, complemented
117#388×C73C2211yescharacteristic, complemented
118#388×C73C2211yescharacteristic, complemented
119#388×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#387×C73C2211yescharacteristic, complemented
127#387×C73C2211yescharacteristic, complemented
128#387×C73C2211yescharacteristic, complemented
129#387×C73C2211yescharacteristic, complemented
130#387×C73C2211yescharacteristic, complemented
131#386×C73C2211yescharacteristic
132#386×C73C2211yescharacteristic
133#386×C73C2211yescharacteristic
134#386×C73C2211yescharacteristic
135#386×C73C2211yescharacteristic
136#386×C73C2211yescharacteristic
137#386×C73C2211yescharacteristic
138#385×C73C2211yescharacteristic
139#385×C73C2211yescharacteristic
140#385×C73C2211yescharacteristic
141#385×C73C2211yescharacteristic
142#385×C73C2211yescharacteristic
143#385×C73C2211yescharacteristic
144#385×C73C2211yescharacteristic
145#385×C73C2211yescharacteristic
146#385×C73C2211yescharacteristic
147#385×C73C2211yescharacteristic
148#385×C73C2211yescharacteristic
149#385×C73C2211yescharacteristic
150#385×C73C2211yescharacteristic, complemented
151#385×C73C2211yescharacteristic, complemented
152#385×C73C2211yescharacteristic, complemented
153#383×C73C2211yescharacteristic, complemented
154#382×C73C2211yescharacteristic, complemented
155#382×C73C2211yescharacteristic, complemented
156#382×C73C2211yescharacteristic, complemented
157#382×C73C2211yescharacteristic, complemented
158#381×C73C2211yescharacteristic
159#381×C73C2211yescharacteristic, complemented
160#380×C73C2211yescharacteristic
161#380×C73C2211yescharacteristic
162#380×C73C2211yescharacteristic
163#380×C73C2211yescharacteristic
164#380×C73C2211yescharacteristic
165#380×C73C2211yescharacteristic
166#380×C73C2211yescharacteristic, complemented
167#379×C73C2211yescharacteristic
168#379×C73C2211yescharacteristic
169C4×C4⋊C4×C73C2211yescharacteristic, complemented
170C4×C4⋊C4×C73C2211yescharacteristic, complemented
171C4×C4⋊C4×C73C2211yescharacteristic, complemented
172C4×C4⋊C4×C73C2211yescharacteristic, complemented
173C4×C4⋊C4×C73C2211yescharacteristic, complemented
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, complemented
181C4×C22⋊C4×C73C2211yescharacteristic, complemented
182#376×C73C2211yescharacteristic, complemented
183#376×C73C2211yescharacteristic, complemented
184C2×#95×C73C2211yescharacteristic
185C2×#95×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic, complemented
187C25×C73C2311yescharacteristic
188C22×Q8×C73C2311yescharacteristic
189C22×D4×C73C2311yescharacteristic
190C22×D4×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C23×C4×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
202C23×C4×C73C2311yescharacteristic
203#126×C73—42no—
204#125×C73—42no—
205#123×C73—24no—
206#123×C73—42no—
207C22⋊Q8×C73—24no—
208C22⋊Q8×C73—42no—
209C22⋊Q8×C73—42no—
210#120×C73—24no—
211C4×Q8×C73—42no—
212C4×D4×C73—24no—
213C4×D4×C73—24no—
214C4×D4×C73—24no—
215C4×D4×C73—42no—
216#117×C73—24no—
217#117×C73—42no—
218C2×C4⋊C4×C73—42no—
219C2×C4⋊C4×C73C2311yescharacteristic
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×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊C4×C73C2311yescharacteristic
253C2×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C22⋊C4×C73—24no—
256C2×C22⋊C4×C73—24no—
257C2×C22⋊C4×C73—42no—
258C2×C22⋊C4×C73—42no—
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×C22⋊C4×C73C2311yescharacteristic
296C2×C22⋊C4×C73C2311yescharacteristic
297C2×C22⋊C4×C73C2311yescharacteristic
298C2×C22⋊C4×C73C2311yescharacteristic
299C2×C42×C73—42no—
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×C73—22no—
364C24×C73—22no—
365C24×C73—22no—
366C24×C73—22no—
367C24×C73—41no—
368C24×C73—41no—
369C24×C73—41no—
370C24×C73C2411yescharacteristic
371C24×C73C2411yescharacteristic
372C24×C73C2411yescharacteristic
373C24×C73C2411yescharacteristic
374C2×Q8×C73—22no—
375C2×Q8×C73—22no—
376C2×Q8×C73—41no—
377C2×D4×C73—22no—
378C2×D4×C73—22no—
379C2×D4×C73—22no—
380C2×D4×C73—22no—
381C2×D4×C73—22no—
382C2×D4×C73—41no—
383C2×D4×C73—41no—
384C2×D4×C73—41no—
385C2×D4×C73#4114yes—
386C22×C4×C73—22no—
387C22×C4×C73—22no—
388C22×C4×C73—22no—
389C22×C4×C73—22no—
390C22×C4×C73—22no—
391C22×C4×C73—22no—
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—41no—
404C22×C4×C73—41no—
405C22×C4×C73—41no—
406C22×C4×C73—41no—
407C22×C4×C73—41no—
408C22×C4×C73—41no—
409C22×C4×C73—41no—
410C22×C4×C73—41no—
411C22×C4×C73—41no—
412C22×C4×C73—41no—
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×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
441C22×C4×C73C2411yescharacteristic
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
444C22×C4×C73C2411yescharacteristic
445C22×C4×C73C2411yescharacteristic
446C4⋊C4×C73—22no—
447C4⋊C4×C73—22no—
448C4⋊C4×C73—22no—
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—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73—41no—
464C4⋊C4×C73—41no—
465C4⋊C4×C73—41no—
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—41no—
475C4⋊C4×C73—41no—
476C4⋊C4×C73—41no—
477C4⋊C4×C73—41no—
478C4⋊C4×C73—41no—
479C4⋊C4×C73—41no—
480C4⋊C4×C73—41no—
481C4⋊C4×C73—41no—
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—22no—
502C22⋊C4×C73—22no—
503C22⋊C4×C73—22no—
504C22⋊C4×C73—22no—
505C22⋊C4×C73—22no—
506C22⋊C4×C73—22no—
507C22⋊C4×C73—41no—
508C22⋊C4×C73—41no—
509C22⋊C4×C73—41no—
510C22⋊C4×C73—41no—
511C22⋊C4×C73—41no—
512C22⋊C4×C73—41no—
513C22⋊C4×C73—41no—
514C22⋊C4×C73—41no—
515C22⋊C4×C73—41no—
516C22⋊C4×C73—41no—
517C22⋊C4×C73—41no—
518C22⋊C4×C73—41no—
519C22⋊C4×C73—41no—
520C22⋊C4×C73#4114yes—
521C22⋊C4×C73#4114yes—
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—
537C23×C73—21no—
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—44no—
561C23×C73—44no—
562C23×C73—44no—
563C23×C73—44no—
564C23×C73—82no—
565C23×C73—82no—
566C23×C73—82no—
567C23×C73C2×#4112yes—
568C23×C73C2×#4112yes—
569C23×C73C2×#4112yes—
570C23×C73C2×#4112yes—
571C23×C732−1+412yes—
572C23×C73C2511yescharacteristic
573Q8×C73—44no—
574D4×C73—28no—
575D4×C73—44no—
576D4×C73—82no—
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—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—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—44no—
652C2×C4×C73—44no—
653C2×C4×C73—44no—
654C2×C4×C73—44no—
655C2×C4×C73—44no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C2×C4×C73—82no—
659C2×C4×C73—82no—
660C2×C4×C73—82no—
661C2×C4×C73—82no—
662C2×C4×C73C2×#4112yes—
663C2×C4×C73C2×#4112yes—
664C2×C4×C73C2×#4112yes—
665C2×C4×C73C2×#4112yes—
666C2×C4×C73C2×#4112yes—
667C2×C4×C73H(5,𝔽2)12yes—
668C2×C4×C73H(5,𝔽2)12yes—
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—22no—
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×C73#55214yes—
698C22×C73C22×#4111yescharacteristic
699C22×C73C22×#4111yescharacteristic
700C22×C73C22×#4111yescharacteristic
701C22×C73C2×H(5,𝔽2)11yescharacteristic
702C22×C73C2×H(5,𝔽2)11yescharacteristic
703C22×C73C2×2−1+411yescharacteristic
704C22×C73#58511yescharacteristic
705C4×C73—22no—
706C4×C73—22no—
707C4×C73—22no—
708C4×C73—22no—
709C4×C73—22no—
710C4×C73—22no—
711C4×C73—22no—
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—41no—
728C4×C73—41no—
729C4×C73—41no—
730C4×C73—41no—
731C4×C73—41no—
732#59492C7311yesmaximal, characteristic, direct product factor, Sylow
733C2×C73—24no—
734C2×C73—42no—
735C2×C73—42no—
736C2×C73—81no—
737C2×C73C2×#55211yescharacteristic
738C2×C73#347511yescharacteristic
739C2×C73#348111yescharacteristic
740C2×C73#351411yescharacteristic
741C2×C73#351911yescharacteristic
742C2×C73#352011yescharacteristic
743C2×C73#353511yescharacteristic
744#2781C2×C7311yescharacteristic, complemented
745#2773C2×C7311yescharacteristic, complemented
746#2770C2×C7311yescharacteristic, complemented
747#2743C2×C7311yescharacteristic, complemented
748#2604C2×C7311yescharacteristic, complemented
749#2575C2×C7311yescharacteristic, complemented
750#2558C2×C7311yescharacteristic, complemented
751#2556C2×C7311yescharacteristic, complemented
752#2536C2×C7311yescharacteristic, complemented
753#2529C2×C7311yescharacteristic, complemented
754#2525C2×C7311yescharacteristic, complemented
755#2505C2×C7311yescharacteristic, complemented
756#2505C2×C7311yescharacteristic, complemented
757#2488C2×C7311yescharacteristic, complemented
758#2480C2×C7311yescharacteristic, complemented
759#2479C2×C7311yescharacteristic, complemented
760#2470C2×C7311yescharacteristic, complemented
761#2449C2×C7311yescharacteristic, complemented
762#2442C2×C7311yescharacteristic, complemented
763#2437C2×C7311yescharacteristic, complemented
764#2418C2×C7311yescharacteristic
765#2418C2×C7311yescharacteristic
766#2359C2×C7311yescharacteristic, complemented
767#2358C2×C7311yescharacteristic
768#2353C2×C7311yescharacteristic, complemented
769#2349C2×C7311yescharacteristic, complemented
770#2346C2×C7311yescharacteristic, complemented
771#2342C2×C7311yescharacteristic, complemented
772C4×C22⋊Q8C2×C7311yescharacteristic, complemented
773#2290C2×C7311yescharacteristic, complemented
774C2×#388C2×C7311yescharacteristic, complemented
775C73#5949211yescharacteristic, direct product factor, Sylow
776C2×#126C22×C7311yescharacteristic
777C2×#125C22×C7311yescharacteristic, complemented
778C2×#123C22×C7311yescharacteristic
779C2×#123C22×C7311yescharacteristic
780C2×C22⋊Q8C22×C7311yescharacteristic
781C2×C22⋊Q8C22×C7311yescharacteristic
782C2×C22⋊Q8C22×C7311yescharacteristic, complemented
783C2×#120C22×C7311yescharacteristic
784C2×C4×Q8C22×C7311yescharacteristic, complemented
785C2×C4×D4C22×C7311yescharacteristic
786C2×C4×D4C22×C7311yescharacteristic
787C2×C4×D4C22×C7311yescharacteristic
788C2×C4×D4C22×C7311yescharacteristic
789C2×#117C22×C7311yescharacteristic
790C2×#117C22×C7311yescharacteristic, complemented
791C22×C4⋊C4C22×C7311yescharacteristic
792C22×C22⋊C4C22×C7311yescharacteristic
793C22×C22⋊C4C22×C7311yescharacteristic
794C22×C22⋊C4C22×C7311yescharacteristic
795C22×C22⋊C4C22×C7311yescharacteristic
796C22×C42C22×C7311yescharacteristic
797#400C22×C7311yescharacteristic, complemented
798#400C22×C7311yescharacteristic, complemented
799#400C22×C7311yescharacteristic, complemented
800#400C22×C7311yescharacteristic, complemented
801#400C22×C7311yescharacteristic, complemented
802#400C22×C7311yescharacteristic, complemented
803#400C22×C7311yescharacteristic, complemented
804#400C22×C7311yescharacteristic, complemented
805#399C22×C7311yescharacteristic
806#399C22×C7311yescharacteristic
807#399C22×C7311yescharacteristic
808#399C22×C7311yescharacteristic, complemented
809#398C22×C7311yescharacteristic, complemented
810#398C22×C7311yescharacteristic, complemented
811#398C22×C7311yescharacteristic, complemented
812#398C22×C7311yescharacteristic, complemented
813#398C22×C7311yescharacteristic, complemented
814#397C22×C7311yescharacteristic
815#397C22×C7311yescharacteristic
816#397C22×C7311yescharacteristic
817#397C22×C7311yescharacteristic
818#397C22×C7311yescharacteristic
819#396C22×C7311yescharacteristic
820#396C22×C7311yescharacteristic
821#396C22×C7311yescharacteristic
822#396C22×C7311yescharacteristic, complemented
823#395C22×C7311yescharacteristic, complemented
824#394C22×C7311yescharacteristic
825#394C22×C7311yescharacteristic
826#394C22×C7311yescharacteristic
827#394C22×C7311yescharacteristic
828#393C22×C7311yescharacteristic
829#391C22×C7311yescharacteristic, complemented
830#390C22×C7311yescharacteristic
831#389C22×C7311yescharacteristic, complemented
832#389C22×C7311yescharacteristic, complemented
833#389C22×C7311yescharacteristic, complemented
834#389C22×C7311yescharacteristic, complemented
835#389C22×C7311yescharacteristic, complemented
836#389C22×C7311yescharacteristic, complemented
837#389C22×C7311yescharacteristic, complemented
838#389C22×C7311yescharacteristic, complemented
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#388C22×C7311yescharacteristic
853#388C22×C7311yescharacteristic
854#388C22×C7311yescharacteristic
855#388C22×C7311yescharacteristic
856#388C22×C7311yescharacteristic
857#388C22×C7311yescharacteristic
858#388C22×C7311yescharacteristic
859#388C22×C7311yescharacteristic
860#388C22×C7311yescharacteristic, complemented
861#388C22×C7311yescharacteristic, complemented
862#388C22×C7311yescharacteristic, complemented
863#388C22×C7311yescharacteristic, complemented
864#387C22×C7311yescharacteristic, complemented
865#387C22×C7311yescharacteristic, complemented
866#387C22×C7311yescharacteristic, complemented
867#387C22×C7311yescharacteristic, complemented
868#387C22×C7311yescharacteristic, complemented
869#387C22×C7311yescharacteristic, complemented
870#387C22×C7311yescharacteristic, complemented
871#387C22×C7311yescharacteristic, complemented
872#387C22×C7311yescharacteristic, complemented
873#387C22×C7311yescharacteristic, complemented
874#387C22×C7311yescharacteristic, complemented
875#386C22×C7311yescharacteristic
876#386C22×C7311yescharacteristic
877#386C22×C7311yescharacteristic
878#386C22×C7311yescharacteristic
879#386C22×C7311yescharacteristic
880#386C22×C7311yescharacteristic
881#386C22×C7311yescharacteristic
882#385C22×C7311yescharacteristic
883#385C22×C7311yescharacteristic
884#385C22×C7311yescharacteristic
885#385C22×C7311yescharacteristic
886#385C22×C7311yescharacteristic
887#385C22×C7311yescharacteristic
888#385C22×C7311yescharacteristic
889#385C22×C7311yescharacteristic
890#385C22×C7311yescharacteristic
891#385C22×C7311yescharacteristic
892#385C22×C7311yescharacteristic
893#385C22×C7311yescharacteristic
894#385C22×C7311yescharacteristic, complemented
895#385C22×C7311yescharacteristic, complemented
896#385C22×C7311yescharacteristic, complemented
897#383C22×C7311yescharacteristic, complemented
898#382C22×C7311yescharacteristic, complemented
899#382C22×C7311yescharacteristic, complemented
900#382C22×C7311yescharacteristic, complemented
901#382C22×C7311yescharacteristic, complemented
902#381C22×C7311yescharacteristic
903#381C22×C7311yescharacteristic, complemented
904#380C22×C7311yescharacteristic
905#380C22×C7311yescharacteristic
906#380C22×C7311yescharacteristic
907#380C22×C7311yescharacteristic
908#380C22×C7311yescharacteristic
909#380C22×C7311yescharacteristic
910#380C22×C7311yescharacteristic, complemented
911#379C22×C7311yescharacteristic
912#379C22×C7311yescharacteristic
913C4×C4⋊C4C22×C7311yescharacteristic, complemented
914C4×C4⋊C4C22×C7311yescharacteristic, complemented
915C4×C4⋊C4C22×C7311yescharacteristic, complemented
916C4×C4⋊C4C22×C7311yescharacteristic, complemented
917C4×C4⋊C4C22×C7311yescharacteristic, complemented
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
926#376C22×C7311yescharacteristic, complemented
927#376C22×C7311yescharacteristic, complemented
928C2×#95C22×C7311yescharacteristic
929C2×#95C22×C7311yescharacteristic
930C2×#95C22×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
945C23×C4C23×C7311yescharacteristic
946C23×C4C23×C7311yescharacteristic
947#126—42no—
948#125—42no—
949#123—24no—
950#123—42no—
951C22⋊Q8—24no—
952C22⋊Q8—42no—
953C22⋊Q8—42no—
954#120—24no—
955C4×Q8—42no—
956C4×D4—24no—
957C4×D4—24no—
958C4×D4—24no—
959C4×D4—42no—
960#117—24no—
961#117—42no—
962C2×C4⋊C4—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×C4⋊C4C23×C7311yescharacteristic
990C2×C4⋊C4C23×C7311yescharacteristic
991C2×C4⋊C4C23×C7311yescharacteristic
992C2×C4⋊C4C23×C7311yescharacteristic
993C2×C4⋊C4C23×C7311yescharacteristic
994C2×C4⋊C4C23×C7311yescharacteristic
995C2×C4⋊C4C23×C7311yescharacteristic
996C2×C4⋊C4C23×C7311yescharacteristic
997C2×C4⋊C4C23×C7311yescharacteristic
998C2×C4⋊C4C23×C7311yescharacteristic
999C2×C22⋊C4—24no—
1000C2×C22⋊C4—24no—
1001C2×C22⋊C4—42no—
1002C2×C22⋊C4—42no—
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×C22⋊C4C23×C7311yescharacteristic
1039C2×C22⋊C4C23×C7311yescharacteristic
1040C2×C22⋊C4C23×C7311yescharacteristic
1041C2×C22⋊C4C23×C7311yescharacteristic
1042C2×C22⋊C4C23×C7311yescharacteristic
1043C2×C42—42no—
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
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
1103#95C23×C7311yescharacteristic
1104#95C23×C7311yescharacteristic
1105#95C23×C7311yescharacteristic
1106#95C23×C7311yescharacteristic
1107C24—22no—
1108C24—22no—
1109C24—22no—
1110C24—22no—
1111C24—41no—
1112C24—41no—
1113C24—41no—
1114C24C24×C7311yescharacteristic
1115C24C24×C7311yescharacteristic
1116C24C24×C7311yescharacteristic
1117C24C24×C7311yescharacteristic
1118C2×Q8—22no—
1119C2×Q8—22no—
1120C2×Q8—41no—
1121C2×D4—22no—
1122C2×D4—22no—
1123C2×D4—22no—
1124C2×D4—22no—
1125C2×D4—22no—
1126C2×D4—41no—
1127C2×D4—41no—
1128C2×D4—41no—
1129C2×D4#41×C7314yes—
1130C22×C4—22no—
1131C22×C4—22no—
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—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
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
1189C22×C4C24×C7311yescharacteristic
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—41no—
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—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
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—22no—
1242C22⋊C4—22no—
1243C22⋊C4—22no—
1244C22⋊C4—22no—
1245C22⋊C4—22no—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—22no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4#41×C7314yes—
1265C22⋊C4#41×C7314yes—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
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—44no—
1305C23—44no—
1306C23—44no—
1307C23—44no—
1308C23—82no—
1309C23—82no—
1310C23—82no—
1311C23C2×#41×C7312yes—
1312C23C2×#41×C7312yes—
1313C23C2×#41×C7312yes—
1314C23C2×#41×C7312yes—
1315C232−1+4×C7312yes—
1316C23C25×C7311yescharacteristic
1317Q8—44no—
1318D4—28no—
1319D4—44no—
1320D4—82no—
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—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—44no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—44no—
1400C2×C4—44no—
1401C2×C4—82no—
1402C2×C4—82no—
1403C2×C4—82no—
1404C2×C4—82no—
1405C2×C4—82no—
1406C2×C4C2×#41×C7312yes—
1407C2×C4C2×#41×C7312yes—
1408C2×C4C2×#41×C7312yes—
1409C2×C4C2×#41×C7312yes—
1410C2×C4C2×#41×C7312yes—
1411C2×C4H(5,𝔽2)×C7312yes—
1412C2×C4H(5,𝔽2)×C7312yes—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—22no—
1424C22—22no—
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—41no—
1440C22—88no—
1441C22#552×C7314yes—
1442C22C22×#41×C7311yescharacteristic
1443C22C22×#41×C7311yescharacteristic
1444C22C22×#41×C7311yescharacteristic
1445C22C2×H(5,𝔽2)×C7311yescharacteristic
1446C22C2×H(5,𝔽2)×C7311yescharacteristic
1447C22C2×2−1+4×C7311yescharacteristic
1448C22#585×C7311yescharacteristic
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
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—
1474C4—41no—
1475C4—41no—
1476C2—24no—
1477C2—42no—
1478C2—42no—
1479C2—81no—
1480C2C2×#552×C7311yescharacteristic
1481C2C73×#347511yescharacteristic
1482C2C73×#348111yescharacteristic
1483C2C73×#351411yescharacteristic
1484C2C73×#351911yescharacteristic
1485C2C73×#352011yescharacteristic
1486C2C73×#353511yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC2×#120×C73C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2781C2semidirect
2. C73×#2773C2semidirect
3. C73×#2770C2semidirect
4. C73×#2743C2semidirect
5. C73×#2604C2semidirect
6. C73×#2575C2semidirect
7. C73×#2558C2semidirect
8. C73×#2556C2semidirect
9. C73×#2536C2semidirect
10. C73×#2529C2semidirect
11. C73×#2525C2semidirect
12. C73×#2505C2semidirect
13. C73×#2505C2semidirect
14. C73×#2488C2semidirect
15. C73×#2480C2semidirect
16. C73×#2479C2semidirect
17. C73×#2470C2semidirect
18. C73×#2449C2semidirect
19. C73×#2442C2semidirect
20. C73×#2437C2semidirect
23. C73×#2359C2semidirect
25. C73×#2353C2semidirect
26. C73×#2349C2semidirect
27. C73×#2346C2semidirect
28. C73×#2342C2semidirect
29. C4×C22⋊Q8×C73C2semidirect
30. C73×#2290C2semidirect
31. C2×#388×C73C2semidirect
33. C2×#125×C73C22semidirect
38. C2×C22⋊Q8×C73C22semidirect
40. C2×C4×Q8×C73C22semidirect
46. C2×#117×C73C22semidirect
53. #400×C73C22semidirect
54. #400×C73C22semidirect
55. #400×C73C22semidirect
56. #400×C73C22semidirect
57. #400×C73C22semidirect
58. #400×C73C22semidirect
59. #400×C73C22semidirect
60. #400×C73C22semidirect
64. #399×C73C22semidirect
65. #398×C73C22semidirect
66. #398×C73C22semidirect
67. #398×C73C22semidirect
68. #398×C73C22semidirect
69. #398×C73C22semidirect
78. #396×C73C22semidirect
79. #395×C73C22semidirect
85. #391×C73C22semidirect
87. #389×C73C22semidirect
88. #389×C73C22semidirect
89. #389×C73C22semidirect
90. #389×C73C22semidirect
91. #389×C73C22semidirect
92. #389×C73C22semidirect
93. #389×C73C22semidirect
94. #389×C73C22semidirect
116. #388×C73C22semidirect
117. #388×C73C22semidirect
118. #388×C73C22semidirect
119. #388×C73C22semidirect
120. #387×C73C22semidirect
121. #387×C73C22semidirect
122. #387×C73C22semidirect
123. #387×C73C22semidirect
124. #387×C73C22semidirect
125. #387×C73C22semidirect
126. #387×C73C22semidirect
127. #387×C73C22semidirect
128. #387×C73C22semidirect
129. #387×C73C22semidirect
130. #387×C73C22semidirect
150. #385×C73C22semidirect
151. #385×C73C22semidirect
152. #385×C73C22semidirect
153. #383×C73C22semidirect
154. #382×C73C22semidirect
155. #382×C73C22semidirect
156. #382×C73C22semidirect
157. #382×C73C22semidirect
159. #381×C73C22semidirect
166. #380×C73C22semidirect
169. C4×C4⋊C4×C73C22semidirect
170. C4×C4⋊C4×C73C22semidirect
171. C4×C4⋊C4×C73C22semidirect
172. C4×C4⋊C4×C73C22semidirect
173. C4×C4⋊C4×C73C22semidirect
180. C4×C22⋊C4×C73C22semidirect
181. C4×C22⋊C4×C73C22semidirect
182. #376×C73C22semidirect
183. #376×C73C22semidirect
186. C2×#95×C73C22semidirect
732. #59492C73direct (N × H)
744. #2781C2×C73semidirect
745. #2773C2×C73semidirect
746. #2770C2×C73semidirect
747. #2743C2×C73semidirect
748. #2604C2×C73semidirect
749. #2575C2×C73semidirect
750. #2558C2×C73semidirect
751. #2556C2×C73semidirect
752. #2536C2×C73semidirect
753. #2529C2×C73semidirect
754. #2525C2×C73semidirect
755. #2505C2×C73semidirect
756. #2505C2×C73semidirect
757. #2488C2×C73semidirect
758. #2480C2×C73semidirect
759. #2479C2×C73semidirect
760. #2470C2×C73semidirect
761. #2449C2×C73semidirect
762. #2442C2×C73semidirect
763. #2437C2×C73semidirect
766. #2359C2×C73semidirect
768. #2353C2×C73semidirect
769. #2349C2×C73semidirect
770. #2346C2×C73semidirect
771. #2342C2×C73semidirect
772. C4×C22⋊Q8C2×C73semidirect
773. #2290C2×C73semidirect
774. C2×#388C2×C73semidirect
775. C73#59492direct (N × H)
777. C2×#125C22×C73semidirect
782. C2×C22⋊Q8C22×C73semidirect
784. C2×C4×Q8C22×C73semidirect
790. C2×#117C22×C73semidirect
797. #400C22×C73semidirect
798. #400C22×C73semidirect
799. #400C22×C73semidirect
800. #400C22×C73semidirect
801. #400C22×C73semidirect
802. #400C22×C73semidirect
803. #400C22×C73semidirect
804. #400C22×C73semidirect
808. #399C22×C73semidirect
809. #398C22×C73semidirect
810. #398C22×C73semidirect
811. #398C22×C73semidirect
812. #398C22×C73semidirect
813. #398C22×C73semidirect
822. #396C22×C73semidirect
823. #395C22×C73semidirect
829. #391C22×C73semidirect
831. #389C22×C73semidirect
832. #389C22×C73semidirect
833. #389C22×C73semidirect
834. #389C22×C73semidirect
835. #389C22×C73semidirect
836. #389C22×C73semidirect
837. #389C22×C73semidirect
838. #389C22×C73semidirect
860. #388C22×C73semidirect
861. #388C22×C73semidirect
862. #388C22×C73semidirect
863. #388C22×C73semidirect
864. #387C22×C73semidirect
865. #387C22×C73semidirect
866. #387C22×C73semidirect
867. #387C22×C73semidirect
868. #387C22×C73semidirect
869. #387C22×C73semidirect
870. #387C22×C73semidirect
871. #387C22×C73semidirect
872. #387C22×C73semidirect
873. #387C22×C73semidirect
874. #387C22×C73semidirect
894. #385C22×C73semidirect
895. #385C22×C73semidirect
896. #385C22×C73semidirect
897. #383C22×C73semidirect
898. #382C22×C73semidirect
899. #382C22×C73semidirect
900. #382C22×C73semidirect
901. #382C22×C73semidirect
903. #381C22×C73semidirect
910. #380C22×C73semidirect
913. C4×C4⋊C4C22×C73semidirect
914. C4×C4⋊C4C22×C73semidirect
915. C4×C4⋊C4C22×C73semidirect
916. C4×C4⋊C4C22×C73semidirect
917. C4×C4⋊C4C22×C73semidirect
924. C4×C22⋊C4C22×C73semidirect
925. C4×C22⋊C4C22×C73semidirect
926. #376C22×C73semidirect
927. #376C22×C73semidirect
930. C2×#95C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#27812
C73×#27732
C73×#27702
C73×#27432
C73×#26042
C73×#25752
C73×#25582
C73×#25562
C73×#25362
C73×#25292
C73×#25252
C73×#25052
C73×#24882
C73×#24802
C73×#24792
C73×#24702
C73×#24492
C73×#24422
C73×#24372
C73×#24182
C73×#23592
C73×#23582
C73×#23532
C73×#23492
C73×#23462
C73×#23422
C4×C22⋊Q8×C732
C73×#22902
C2×#388×C732
#5949273