Finite Group Databasebeta

← #14216762

Subgroups — #14216762

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2493C211yesmaximal, characteristic, complemented
2#11735875C211yesmaximal, characteristic, complemented
3#11735875C211yesmaximal, characteristic, complemented
4#11735838C211yesmaximal, characteristic, complemented
5#11735760C211yesmaximal, characteristic, complemented
6#11735630C211yesmaximal, characteristic, complemented
7#11735621C211yesmaximal, characteristic, complemented
8#11735596C211yesmaximal, characteristic, complemented
9#11735585C211yesmaximal, characteristic, complemented
10#11732753C211yesmaximal, characteristic, complemented
11#11732524C211yesmaximal, characteristic, complemented
12#11732518C211yesmaximal, characteristic, complemented
13#11732469C211yesmaximal, characteristic, complemented
14#11732384C211yesmaximal, characteristic, complemented
15#11732384C211yesmaximal, characteristic, complemented
16#11732093C211yesmaximal, characteristic, complemented
17#11732042C211yesmaximal, characteristic, complemented
18#11731884C211yesmaximal, characteristic, complemented
19#11731883C211yesmaximal, characteristic, complemented
20#11731742C211yesmaximal, characteristic, complemented
21#11731719C211yesmaximal, characteristic, complemented
22#11731587C211yesmaximal, characteristic, complemented
23#11731568C211yesmaximal, characteristic, complemented
24#11731530C211yesmaximal, characteristic, complemented
25#11731514C211yesmaximal, characteristic
26#11731370C211yesmaximal, characteristic, complemented
27#11731349C211yesmaximal, characteristic
28#11731034C211yesmaximal, characteristic
29#11730885C211yesmaximal, characteristic, complemented
30#11730782C211yesmaximal, characteristic, complemented
31#11730781C211yesmaximal, characteristic, complemented
32C2×#6492C2211yescharacteristic
33C2×C4×C22⋊D7C2211yescharacteristic
34C2×C4×C22⋊D7C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C2×#6457C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6446C2211yescharacteristic
40C2×C4×D28C2211yescharacteristic
41C7×#401C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#400C2211yescharacteristic
44C7×#400C2211yescharacteristic
45C7×#387C2211yescharacteristic
46C7×#387C2211yescharacteristic
47C7×#387C2211yescharacteristic
48C7×#385C2211yescharacteristic
49C7×#385C2211yescharacteristic
50C7×#383C2211yescharacteristic
51C7×#381C2211yescharacteristic
52C7×#381C2211yescharacteristic
53C7×#380C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#89985C2211yescharacteristic
57#89985C2211yescharacteristic
58#89985C2211yescharacteristic
59#89984C2211yescharacteristic
60#89982C2211yescharacteristic
61C4×C22⋊Dic7C2211yescharacteristic
62C4×C22⋊Dic7C2211yescharacteristic
63C4×C22⋊Dic7C2211yescharacteristic
64#89766C2211yescharacteristic
65#89766C2211yescharacteristic
66#89766C2211yescharacteristic
67#89765C2211yescharacteristic
68#89762C2211yescharacteristic
69#89762C2211yescharacteristic
70#89762C2211yescharacteristic
71#89761C2211yescharacteristic
72#89757C2211yescharacteristic
73#89757C2211yescharacteristic
74#89754C2211yescharacteristic
75#89754C2211yescharacteristic
76#89753C2211yescharacteristic
77#89753C2211yescharacteristic
78#89748C2211yescharacteristic
79C4⋊C4×Dic7C2211yescharacteristic
80C4⋊C4×Dic7C2211yescharacteristic
81#89745C2211yescharacteristic
82#89744C2211yescharacteristic
83#89744C2211yescharacteristic
84#89744C2211yescharacteristic
85#89733C2211yescharacteristic
86#89732C2211yescharacteristic
87#89731C2211yescharacteristic
88#89728C2211yescharacteristic
89#89728C2211yescharacteristic
90#89728C2211yescharacteristic
91#89724C2211yescharacteristic
92#89723C2211yescharacteristic
93#89720C2211yescharacteristic
94#89720C2211yescharacteristic
95#89717C2211yescharacteristic
96#89717C2211yescharacteristic
97#89717C2211yescharacteristic
98#89716C2211yescharacteristic
99#89716C2211yescharacteristic
100#89712C2211yescharacteristic
101#89712C2211yescharacteristic
102#89705C2211yescharacteristic
103#89704C2211yescharacteristic
104C4×Dic7⋊C4C2211yescharacteristic
105C4×Dic7⋊C4C2211yescharacteristic
106C42×Dic7C2211yescharacteristic
107#89448C2211yescharacteristic
108#89447C2211yescharacteristic
109#89444C2211yescharacteristic
110#89442C2211yescharacteristic
111#89442C2211yescharacteristic
112#89442C2211yescharacteristic
113#89442C2211yescharacteristic
114#89441C2211yescharacteristic
115#89441C2211yescharacteristic
116#89441C2211yescharacteristic
117#89440C2211yescharacteristic
118#89440C2211yescharacteristic
119#89440C2211yescharacteristic
120#89440C2211yescharacteristic
121#89440C2211yescharacteristic
122#89439C2211yescharacteristic
123#89439C2211yescharacteristic
124#89439C2211yescharacteristic
125#89439C2211yescharacteristic
126#89438C2211yescharacteristic
127#89438C2211yescharacteristic
128#89438C2211yescharacteristic
129#89438C2211yescharacteristic
130#89438C2211yescharacteristic
131#89438C2211yescharacteristic
132#89438C2211yescharacteristic
133#89438C2211yescharacteristic
134#89437C2211yescharacteristic
135#89437C2211yescharacteristic
136#89437C2211yescharacteristic
137#89436C2211yescharacteristic
138#89436C2211yescharacteristic
139#89436C2211yescharacteristic
140#89436C2211yescharacteristic
141D7×#95C2211yescharacteristic
142D7×#95C2211yescharacteristic
143#89432C2211yescharacteristic
144#89432C2211yescharacteristic
145#89432C2211yescharacteristic
146#89432C2211yescharacteristic
147#89432C2211yescharacteristic
148#89431C2211yescharacteristic
149#89430C2211yescharacteristic
150#89430C2211yescharacteristic
151#89430C2211yescharacteristic
152#89430C2211yescharacteristic
153#89430C2211yescharacteristic
154#89430C2211yescharacteristic
155#89430C2211yescharacteristic
156#89427C2211yescharacteristic
157#89427C2211yescharacteristic
158#89427C2211yescharacteristic
159#89427C2211yescharacteristic
160#89427C2211yescharacteristic
161#89427C2211yescharacteristic
162#89426C2211yescharacteristic
163#89426C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89425C2211yescharacteristic
174#89424C2211yescharacteristic
175#89424C2211yescharacteristic
176#89424C2211yescharacteristic
177#89423C2211yescharacteristic
178#89423C2211yescharacteristic
179#89423C2211yescharacteristic
180#89421C2211yescharacteristic
181#89421C2211yescharacteristic
182#89420C2211yescharacteristic
183#89420C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#60026—71nomaximal, Sylow
188C23×C4×C7C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C22×C22⋊D7C2311yescharacteristic
192C22×C22⋊D7C2311yescharacteristic
193C22×D28C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C22×C4×D7C2311yescharacteristic
197C22×C4×D7C2311yescharacteristic
198C22×C4×D7C2311yescharacteristic
199C22×C4×D7C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2311yescharacteristic
212C2×C22⋊Dic7C2311yescharacteristic
213C2×C22⋊Dic7C2311yescharacteristic
214C2×C22⋊Dic7C2311yescharacteristic
215C2×C22⋊Dic7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218#6492—24no—
219C4×C22⋊D7—24no—
220C4×C22⋊D7—24no—
221C2×(C2×D7)⋊C4C2311yescharacteristic
222C2×(C2×D7)⋊C4C2311yescharacteristic
223C2×(C2×D7)⋊C4C2311yescharacteristic
224C2×(C2×D7)⋊C4C2311yescharacteristic
225C2×(C2×D7)⋊C4C2311yescharacteristic
226C2×(C2×D7)⋊C4C2311yescharacteristic
227C2×(C2×D7)⋊C4C2311yescharacteristic
228C2×(C2×D7)⋊C4C2311yescharacteristic
229C2×(C2×D7)⋊C4C2311yescharacteristic
230C2×(C2×D7)⋊C4C2311yescharacteristic
231C2×(C2×D7)⋊C4C2311yescharacteristic
232C2×(C2×D7)⋊C4C2311yescharacteristic
233C2×(C2×D7)⋊C4C2311yescharacteristic
234C2×(C2×D7)⋊C4C2311yescharacteristic
235C2×(C2×D7)⋊C4C2311yescharacteristic
236C2×(C2×D7)⋊C4C2311yescharacteristic
237C2×(C2×D7)⋊C4C2311yescharacteristic
238C2×(C2×D7)⋊C4C2311yescharacteristic
239C2×(C2×D7)⋊C4C2311yescharacteristic
240C2×(C2×D7)⋊C4C2311yescharacteristic
241#6489—24no—
242C2×C4⋊Dic7C2311yescharacteristic
243C2×C4⋊Dic7C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2311yescharacteristic
255C2×Dic7⋊C4C2311yescharacteristic
256C2×Dic7⋊C4C2311yescharacteristic
257C2×Dic7⋊C4C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
260C2×Dic7⋊C4C2311yescharacteristic
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×Dic7⋊C4C2311yescharacteristic
264C2×Dic7⋊C4C2311yescharacteristic
265C2×Dic7⋊C4C2311yescharacteristic
266C2×Dic7⋊C4C2311yescharacteristic
267C2×Dic7⋊C4C2311yescharacteristic
268C2×Dic7⋊C4C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285#6457—24no—
286#6455—24no—
287#6455—24no—
288#6446—24no—
289C4×D28—24no—
290C7×#95C2311yescharacteristic
291C7×#95C2311yescharacteristic
292C7×#95C2311yescharacteristic
293C7×#95C2311yescharacteristic
294C7×#95C2311yescharacteristic
295C7×#95C2311yescharacteristic
296C7×#95C2311yescharacteristic
297C7×#95C2311yescharacteristic
298C7×#95C2311yescharacteristic
299C7×#95C2311yescharacteristic
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7×#95C2311yescharacteristic
303C7×#95C2311yescharacteristic
304C7×#95C2311yescharacteristic
305C7×#95C2311yescharacteristic
306C7×#95C2311yescharacteristic
307C7×#95C2311yescharacteristic
308C7×#95C2311yescharacteristic
309C7×#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352#2810—71no—
353#2750—71no—
354#2750—71no—
355#2750—71no—
356#2573—71no—
357#2573—71no—
358#2573—71no—
359#2533—71no—
360#2533—71no—
361#2533—71no—
362#2497—71no—
363#2497—71no—
364#2497—71no—
365#2493—71no—
366#2493—71no—
367#2493D711yescharacteristic, complemented
368#2470—71no—
369#2470—71no—
370#2470—71no—
371#2457—71no—
372#2457—71no—
373#2457—71no—
374#2359—71no—
375#2359—71no—
376#2359—71no—
377#2353—71no—
378#2353—71no—
379#2353—71no—
380#2298—71no—
381#2298—71no—
382#2298—71no—
383C24×C7C2411yescharacteristic
384C23×D7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C22×C4×C7—22no—
387C22×C4×C7—22no—
388C22×C4×C7—22no—
389C22×C4×C7—22no—
390C22×C4×C7—41no—
391C22×C4×C7—41no—
392C22×C4×C7—41no—
393C22×C4×C7—41no—
394C22×C4×C7—41no—
395C22×C4×C7C2411yescharacteristic
396C22×C4×C7C2411yescharacteristic
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C2×C22⋊D7—22no—
410C2×C22⋊D7—22no—
411C2×C22⋊D7—22no—
412C2×C22⋊D7—22no—
413C2×C22⋊D7—41no—
414C2×C22⋊D7—41no—
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C2×D28—22no—
430C2×D28—22no—
431C2×D28—41no—
432C2×C4×D7—22no—
433C2×C4×D7—22no—
434C2×C4×D7—22no—
435C2×C4×D7—22no—
436C2×C4×D7—22no—
437C2×C4×D7—22no—
438C2×C4×D7—22no—
439C2×C4×D7—22no—
440C2×C4×D7—41no—
441C2×C4×D7—41no—
442C2×C4×D7—41no—
443C2×C4×D7—41no—
444C2×C4×D7—41no—
445C2×C4×D7—41no—
446C2×C4×D7—41no—
447C2×C4×D7—41no—
448C2×C4×D7—41no—
449C2×C4×D7—41no—
450C7×C4⋊C4—22no—
451C7×C4⋊C4—22no—
452C7×C4⋊C4—22no—
453C7×C4⋊C4—41no—
454C7×C4⋊C4—41no—
455C7×C4⋊C4—41no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4—41no—
459C7×C22⋊C4—41no—
460C42×C7—22no—
461C42×C7—41no—
462C22⋊Dic7—22no—
463C22⋊Dic7—22no—
464C22⋊Dic7—22no—
465C22⋊Dic7—41no—
466C22⋊Dic7—41no—
467C22⋊Dic7#4114yes—
468(C2×D7)⋊C4—22no—
469(C2×D7)⋊C4—22no—
470(C2×D7)⋊C4—22no—
471(C2×D7)⋊C4—22no—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—22no—
475(C2×D7)⋊C4—22no—
476(C2×D7)⋊C4—41no—
477(C2×D7)⋊C4—41no—
478(C2×D7)⋊C4—41no—
479(C2×D7)⋊C4—41no—
480(C2×D7)⋊C4—41no—
481(C2×D7)⋊C4—41no—
482(C2×D7)⋊C4—41no—
483(C2×D7)⋊C4—41no—
484(C2×D7)⋊C4—41no—
485(C2×D7)⋊C4—41no—
486(C2×D7)⋊C4#4114yes—
487(C2×D7)⋊C4#4114yes—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—22no—
491C4⋊Dic7—22no—
492C4⋊Dic7—22no—
493C4⋊Dic7—22no—
494C4⋊Dic7—41no—
495C4⋊Dic7—41no—
496C4⋊Dic7—41no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—22no—
503Dic7⋊C4—41no—
504Dic7⋊C4—41no—
505Dic7⋊C4—41no—
506Dic7⋊C4—41no—
507Dic7⋊C4—41no—
508Dic7⋊C4—41no—
509Dic7⋊C4—41no—
510Dic7⋊C4—41no—
511Dic7⋊C4—41no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4—41no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—41no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#123—71no—
532C2×#123—71no—
533C2×#123—71no—
534C2×C4×D4—71no—
535C2×C4×D4—71no—
536C2×C4×D4—71no—
537C2×#117—71no—
538C2×#117—71no—
539C2×#117—71no—
540#401C2×D711yescharacteristic
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#400—71no—
549#400—71no—
550#400—71no—
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400—71no—
556#400C2×D711yescharacteristic
557#400C2×D711yescharacteristic
558#400C2×D711yescharacteristic
559#397—71no—
560#397—71no—
561#397—71no—
562#396—71no—
563#396—71no—
564#396—71no—
565#396—71no—
566#396—71no—
567#396—71no—
568#394—71no—
569#394—71no—
570#394—71no—
571#392—71no—
572#389—71no—
573#389—71no—
574#389—71no—
575#389—71no—
576#389—71no—
577#389—71no—
578#389—71no—
579#389—71no—
580#389—71no—
581#388—71no—
582#388—71no—
583#388—71no—
584#388—71no—
585#388—71no—
586#388—71no—
587#388—71no—
588#388—71no—
589#388—71no—
590#388—71no—
591#388—71no—
592#388—71no—
593#388—71no—
594#388—71no—
595#388—71no—
596#388—71no—
597#388—71no—
598#388—71no—
599#387—71no—
600#387—71no—
601#387—71no—
602#387—71no—
603#387—71no—
604#387—71no—
605#387—71no—
606#387—71no—
607#387—71no—
608#387—71no—
609#387—71no—
610#387—71no—
611#387—71no—
612#387—71no—
613#387—71no—
614#387—71no—
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387—71no—
623#387C2×D711yescharacteristic
624#387C2×D711yescharacteristic
625#387C2×D711yescharacteristic
626#386—71no—
627#386—71no—
628#386—71no—
629#386—71no—
630#386—71no—
631#386—71no—
632#386—71no—
633#386—71no—
634#386—71no—
635#385—71no—
636#385—71no—
637#385—71no—
638#385—71no—
639#385—71no—
640#385—71no—
641#385—71no—
642#385C2×D711yescharacteristic
643#385C2×D711yescharacteristic
644#384—71no—
645#383—71no—
646#383—71no—
647#383—71no—
648#383C2×D711yescharacteristic
649#381—71no—
650#381—71no—
651#381—71no—
652#381—71no—
653#381C2×D711yescharacteristic
654#381C2×D711yescharacteristic
655#380—71no—
656#380—71no—
657#380—71no—
658#380—71no—
659#380—71no—
660#380C2×D711yescharacteristic
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C22⋊C4—71no—
668C4×C22⋊C4—71no—
669C4×C22⋊C4—71no—
670C4×C22⋊C4—71no—
671C4×C22⋊C4—71no—
672C4×C22⋊C4—71no—
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4—71no—
677C4×C22⋊C4—71no—
678C4×C22⋊C4C2×D711yescharacteristic
679#376—71no—
680#376—71no—
681#376—71no—
682C2×#95—71no—
683C2×#95—71no—
684C2×#95C2×D711yescharacteristic
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7C2×#4112yes—
693C23×C7C2511yescharacteristic
694C22×D7—21no—
695C22×D7—21no—
696C22×D7—21no—
697C22×D7—21no—
698C22×D7—21no—
699C22×D7—21no—
700C22×D7—21no—
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7C2×#4112yes—
707C22×D7C2×#4112yes—
708C2×C4×C7—21no—
709C2×C4×C7—21no—
710C2×C4×C7—21no—
711C2×C4×C7—21no—
712C2×C4×C7—21no—
713C2×C4×C7—21no—
714C2×C4×C7—21no—
715C2×C4×C7—21no—
716C2×C4×C7—21no—
717C2×C4×C7—21no—
718C2×C4×C7—21no—
719C2×C4×C7—21no—
720C2×C4×C7—21no—
721C2×C4×C7—21no—
722C2×C4×C7—21no—
723C2×C4×C7—21no—
724C2×C4×C7—21no—
725C2×C4×C7—21no—
726C2×C4×C7—21no—
727C2×C4×C7—21no—
728C2×C4×C7—21no—
729C2×C4×C7—21no—
730C2×C4×C7—21no—
731C2×C4×C7—21no—
732C2×C4×C7—21no—
733C2×C4×C7—21no—
734C2×C4×C7—21no—
735C2×C4×C7—21no—
736C2×C4×C7—21no—
737C2×C4×C7—21no—
738C2×C4×C7—21no—
739C2×C4×C7—21no—
740C2×C4×C7—21no—
741C2×C4×C7—21no—
742C2×C4×C7—21no—
743C2×C4×C7—21no—
744C2×C4×C7—21no—
745C2×C4×C7—21no—
746C2×C4×C7—21no—
747C2×C4×C7—21no—
748C2×C4×C7—44no—
749C2×C4×C7—82no—
750C2×C4×C7—82no—
751C2×C4×C7C2×#4112yes—
752C2×C4×C7C2×#4112yes—
753C22⋊D7—44no—
754C22⋊D7—44no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7—21no—
781C2×Dic7—21no—
782C2×Dic7—21no—
783C2×Dic7—21no—
784C2×Dic7—21no—
785C2×Dic7—21no—
786C2×Dic7—21no—
787C2×Dic7—21no—
788C2×Dic7—21no—
789C2×Dic7—21no—
790C2×Dic7—21no—
791C2×Dic7—21no—
792C2×Dic7—21no—
793C2×Dic7C2×#4112yes—
794C2×Dic7C2×#4112yes—
795C2×Dic7C2×#4112yes—
796C2×Dic7C2×#4112yes—
797D28—44no—
798C4×D7—44no—
799C4×D7—44no—
800C4×D7—82no—
801C4×D7—82no—
802C4×D7—82no—
803C4×D7—82no—
804C22×D4—71no—
805C22×D4—71no—
806C22×D4—71no—
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4—71no—
812C23×C4—71no—
813C23×C4C22×D711yescharacteristic
814C23×C4C22×D711yescharacteristic
815C23×C4C22×D711yescharacteristic
816#123—144no—
817#123—144no—
818#123—144no—
819C4×D4—144no—
820C4×D4—144no—
821C4×D4—144no—
822#117—144no—
823#117—144no—
824#117—144no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—71no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—71no—
839C2×C4⋊C4—71no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—71no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—71no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—71no—
850C2×C4⋊C4—71no—
851C2×C4⋊C4—71no—
852C2×C4⋊C4C22×D711yescharacteristic
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C22⋊C4—71no—
859C2×C22⋊C4—71no—
860C2×C22⋊C4—71no—
861C2×C22⋊C4—71no—
862C2×C22⋊C4—71no—
863C2×C22⋊C4—71no—
864C2×C22⋊C4—71no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4—71no—
867C2×C22⋊C4—71no—
868C2×C22⋊C4—71no—
869C2×C22⋊C4—71no—
870C2×C22⋊C4—71no—
871C2×C22⋊C4—71no—
872C2×C22⋊C4—71no—
873C2×C22⋊C4—71no—
874C2×C22⋊C4—71no—
875C2×C22⋊C4—71no—
876C2×C22⋊C4—71no—
877C2×C22⋊C4—71no—
878C2×C22⋊C4—71no—
879C2×C22⋊C4—71no—
880C2×C22⋊C4—71no—
881C2×C22⋊C4—71no—
882C2×C22⋊C4—71no—
883C2×C22⋊C4—71no—
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C42—71no—
889C2×C42—71no—
890C2×C42—71no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—71no—
894C2×C42—71no—
895C2×C42—71no—
896C2×C42—71no—
897C2×C42—71no—
898C2×C42—71no—
899C2×C42—71no—
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42C22×D711yescharacteristic
905C2×C42C22×D711yescharacteristic
906#95—71no—
907#95—71no—
908#95—71no—
909#95—71no—
910#95—71no—
911#95—71no—
912#95—71no—
913#95—71no—
914#95—71no—
915#95—71no—
916#95—71no—
917#95—71no—
918#95—71no—
919#95—71no—
920#95—71no—
921#95—71no—
922#95—71no—
923#95—71no—
924#95—71no—
925#95—71no—
926#95—71no—
927#95—71no—
928#95—71no—
929#95—71no—
930#95—71no—
931#95—71no—
932#95—71no—
933#95—71no—
934#95—71no—
935#95—71no—
936#95—71no—
937#95—71no—
938#95—71no—
939#95—71no—
940#95—71no—
941#95—71no—
942#95—71no—
943#95—71no—
944#95—71no—
945#95—71no—
946#95—71no—
947#95—71no—
948#95C22×D711yescharacteristic
949#95C22×D711yescharacteristic
950#95C22×D711yescharacteristic
951#95C22×D711yescharacteristic
952#95C22×D711yescharacteristic
953#95C22×D711yescharacteristic
954#95C22×D711yescharacteristic
955#95C22×D711yescharacteristic
956#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964#95C22×D711yescharacteristic
965#95C22×D711yescharacteristic
966#95C22×D711yescharacteristic
967#95C22×D711yescharacteristic
968C22×C7—22no—
969C22×C7—22no—
970C22×C7—22no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7C22×#4111yescharacteristic
976C22×C7C22×#4111yescharacteristic
977C22×C7C22×#4111yescharacteristic
978C22×C7#58511yescharacteristic
979C22×C7#58511yescharacteristic
980C22×C7#58511yescharacteristic
981C22×C7#58511yescharacteristic
982C2×D7—22no—
983C2×D7—22no—
984C2×D7—22no—
985C2×D7—22no—
986C2×D7—22no—
987C2×D7—22no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
993C2×D7—41no—
994C2×D7—41no—
995C2×D7—41no—
996C4×C7—22no—
997C4×C7—22no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006C4×C7—41no—
1007C4×C7—41no—
1008C4×C7—41no—
1009C4×C7—41no—
1010Dic7—22no—
1011Dic7—22no—
1012Dic7—22no—
1013Dic7—22no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022Dic7—41no—
1023Dic7—41no—
1024C24—71no—
1025C24—71no—
1026C24C23×D711yescharacteristic
1027C2×D4—142no—
1028C2×D4—142no—
1029C2×D4—142no—
1030C2×D4—142no—
1031C2×D4—142no—
1032C2×D4—142no—
1033C2×D4—281no—
1034C2×D4—281no—
1035C2×D4—281no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—71no—
1055C22×C4—71no—
1056C22×C4—71no—
1057C22×C4—71no—
1058C22×C4—71no—
1059C22×C4—142no—
1060C22×C4—142no—
1061C22×C4—142no—
1062C22×C4—142no—
1063C22×C4—142no—
1064C22×C4—142no—
1065C22×C4—142no—
1066C22×C4—142no—
1067C22×C4—281no—
1068C22×C4—281no—
1069C22×C4—281no—
1070C22×C4—281no—
1071C22×C4—281no—
1072C22×C4—281no—
1073C22×C4—281no—
1074C22×C4—281no—
1075C22×C4—281no—
1076C22×C4—281no—
1077C22×C4C23×D711yescharacteristic
1078C22×C4C23×D711yescharacteristic
1079C22×C4C23×D711yescharacteristic
1080C22×C4C23×D711yescharacteristic
1081C22×C4C23×D711yescharacteristic
1082C22×C4C23×D711yescharacteristic
1083C22×C4C23×D711yescharacteristic
1084C22×C4C23×D711yescharacteristic
1085C22×C4C23×D711yescharacteristic
1086C22×C4C23×D711yescharacteristic
1087C22×C4C23×D711yescharacteristic
1088C22×C4C23×D711yescharacteristic
1089C22×C4C23×D711yescharacteristic
1090C22×C4C23×D711yescharacteristic
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—142no—
1098C4⋊C4—142no—
1099C4⋊C4—142no—
1100C4⋊C4—142no—
1101C4⋊C4—142no—
1102C4⋊C4—142no—
1103C4⋊C4—142no—
1104C4⋊C4—142no—
1105C4⋊C4—142no—
1106C4⋊C4—142no—
1107C4⋊C4—142no—
1108C4⋊C4—142no—
1109C4⋊C4—281no—
1110C4⋊C4—281no—
1111C4⋊C4—281no—
1112C4⋊C4—281no—
1113C4⋊C4—281no—
1114C4⋊C4—281no—
1115C4⋊C4—281no—
1116C4⋊C4—281no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C22⋊C4—22no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—74no—
1129C22⋊C4—74no—
1130C22⋊C4—74no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—142no—
1137C22⋊C4—142no—
1138C22⋊C4—142no—
1139C22⋊C4—142no—
1140C22⋊C4—142no—
1141C22⋊C4—142no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C22⋊C4—281no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C42—22no—
1155C42—41no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—142no—
1163C42—142no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C42—281no—
1171C42—281no—
1172C2×C7—42no—
1173C2×C7#347511yescharacteristic
1174C2×C7#347511yescharacteristic
1175C2×C7#347511yescharacteristic
1176C2×C7#352111yescharacteristic
1177C2×C7#352111yescharacteristic
1178C2×C7#352111yescharacteristic
1179C2×C7#356711yescharacteristic
1180D7—42no—
1181D7—42no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—72no—
1189C23—72no—
1190C23—141no—
1191C23—141no—
1192C23—141no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23—141no—
1199C23—141no—
1200C23—141no—
1201C23—141no—
1202C23D7×#4112yes—
1203C23C24×D711yescharacteristic
1204D4—284no—
1205D4—284no—
1206D4—284no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—44no—
1248C2×C4—72no—
1249C2×C4—72no—
1250C2×C4—72no—
1251C2×C4—72no—
1252C2×C4—82no—
1253C2×C4—82no—
1254C2×C4—141no—
1255C2×C4—141no—
1256C2×C4—141no—
1257C2×C4—141no—
1258C2×C4—141no—
1259C2×C4—141no—
1260C2×C4—141no—
1261C2×C4—141no—
1262C2×C4—141no—
1263C2×C4—141no—
1264C2×C4—141no—
1265C2×C4—141no—
1266C2×C4—141no—
1267C2×C4—141no—
1268C2×C4—141no—
1269C2×C4—141no—
1270C2×C4—141no—
1271C2×C4—141no—
1272C2×C4—141no—
1273C2×C4—141no—
1274C2×C4—141no—
1275C2×C4—141no—
1276C2×C4—141no—
1277C2×C4—141no—
1278C2×C4—141no—
1279C2×C4—141no—
1280C2×C4—141no—
1281C2×C4—141no—
1282C2×C4—141no—
1283C2×C4—141no—
1284C2×C4—141no—
1285C2×C4—141no—
1286C2×C4—141no—
1287C2×C4—141no—
1288C2×C4—141no—
1289C2×C4—141no—
1290C2×C4—141no—
1291C2×C4—141no—
1292C2×C4—284no—
1293C2×C4—284no—
1294C2×C4—562no—
1295C2×C4—562no—
1296C2×C4—562no—
1297C2×C4—562no—
1298C2×C4D7×#4112yes—
1299C2×C4D7×#4112yes—
1300C7#6002611yescharacteristic, complemented, Sylow
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—142no—
1309C22—142no—
1310C22—142no—
1311C22—142no—
1312C22—142no—
1313C22—142no—
1314C22—281no—
1315C22—281no—
1316C22—281no—
1317C22—281no—
1318C22—281no—
1319C22—281no—
1320C22—281no—
1321C22—281no—
1322C22C2×D7×#4111yescharacteristic
1323C22C2×D7×#4111yescharacteristic
1324C22C2×D7×#4111yescharacteristic
1325C22#9061611yescharacteristic
1326C22#9061611yescharacteristic
1327C22#9061811yescharacteristic
1328C22#9062011yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—142no—
1344C4—142no—
1345C4—142no—
1346C4—142no—
1347C4—281no—
1348C4—281no—
1349C4—281no—
1350C4—281no—
1351C4—281no—
1352C4—281no—
1353C4—281no—
1354C4—281no—
1355C4—281no—
1356C4—281no—
1357C2—42no—
1358C2—282no—
1359C2—282no—
1360C2#1174318411yescharacteristic
1361C2#1174321911yescharacteristic
1362C2#1174351911yescharacteristic
1363C2#1174385811yescharacteristic
1364C2#1174386811yescharacteristic
1365C2#1174389511yescharacteristic
1366C2#1174390911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2493C2
prime radical#89732C22
hypercenter#2493D7
hypocenterC7#60026
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2493

Complements

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

NH ≅ G/Ntype
1. C7×#2493C2semidirect
2. #11735875C2semidirect
3. #11735875C2semidirect
4. #11735838C2semidirect
5. #11735760C2semidirect
6. #11735630C2semidirect
7. #11735621C2semidirect
8. #11735596C2semidirect
9. #11735585C2semidirect
10. #11732753C2semidirect
11. #11732524C2semidirect
12. #11732518C2semidirect
13. #11732469C2semidirect
14. #11732384C2semidirect
15. #11732384C2semidirect
16. #11732093C2semidirect
17. #11732042C2semidirect
18. #11731884C2semidirect
19. #11731883C2semidirect
20. #11731742C2semidirect
21. #11731719C2semidirect
22. #11731587C2semidirect
23. #11731568C2semidirect
24. #11731530C2semidirect
26. #11731370C2semidirect
29. #11730885C2semidirect
30. #11730782C2semidirect
31. #11730781C2semidirect
367. #2493D7semidirect
1300. C7#60026semidirect

Maximal subgroups

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

subgroupindex
C7×#24932
#117358752
#117358382
#117357602
#117356302
#117356212
#117355962
#117355852
#117327532
#117325242
#117325182
#117324692
#117323842
#117320932
#117320422
#117318842
#117318832
#117317422
#117317192
#117315872
#117315682
#117315302
#117315142
#117313702
#117313492
#117310342
#117308852
#117307822
#117307812
#600267