Finite Group Databasebeta

← #14216726

Subgroups — #14216726

Order 1792.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2460C211yesmaximal, characteristic, complemented
2#11740478C211yesmaximal, characteristic, complemented
3#11740471C211yesmaximal, characteristic, complemented
4#11739786C211yesmaximal, characteristic
5#11739780C211yesmaximal, characteristic, complemented
6#11734975C211yesmaximal, characteristic, complemented
7#11734940C211yesmaximal, characteristic, complemented
8#11734845C211yesmaximal, characteristic, complemented
9#11734758C211yesmaximal, characteristic, complemented
10#11734494C211yesmaximal, characteristic, complemented
11#11734382C211yesmaximal, characteristic, complemented
12#11734375C211yesmaximal, characteristic
13#11734375C211yesmaximal, characteristic
14#11733019C211yesmaximal, characteristic, complemented
15#11733002C211yesmaximal, characteristic, complemented
16#11732918C211yesmaximal, characteristic, complemented
17#11732896C211yesmaximal, characteristic, complemented
18#11732792C211yesmaximal, characteristic, complemented
19#11732651C211yesmaximal, characteristic, complemented
20#11732556C211yesmaximal, characteristic, complemented
21#11732540C211yesmaximal, characteristic, complemented
22#11732419C211yesmaximal, characteristic, complemented
23#11732384C211yesmaximal, characteristic, complemented
24#11731916C211yesmaximal, characteristic, complemented
25#11731913C211yesmaximal, characteristic, complemented
26#11731899C211yesmaximal, characteristic, complemented
27#11731896C211yesmaximal, characteristic, complemented
28#11731422C211yesmaximal, characteristic, complemented
29#11731323C211yesmaximal, characteristic, complemented
30#11730978C211yesmaximal, characteristic, complemented
31#11730885C211yesmaximal, characteristic, complemented
32C2×C7×#125C2211yescharacteristic
33C2×C4×C7×D4C2211yescharacteristic
34C2×#6501C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C2×#6461C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6440C2211yescharacteristic
40C2×#6440C2211yescharacteristic
41C7×#397C2211yescharacteristic
42C7×#396C2211yescharacteristic
43C7×#394C2211yescharacteristic
44C7×#394C2211yescharacteristic
45C7×#388C2211yescharacteristic
46C7×#388C2211yescharacteristic
47C7×#387C2211yescharacteristic
48C7×#387C2211yescharacteristic
49C7×#387C2211yescharacteristic
50C7×#385C2211yescharacteristic
51C7×#385C2211yescharacteristic
52C7×#380C2211yescharacteristic
53C4×C7×C22⋊C4C2211yescharacteristic
54#89993C2211yescharacteristic
55#89992C2211yescharacteristic
56#89992C2211yescharacteristic
57#89985C2211yescharacteristic
58#89985C2211yescharacteristic
59#89984C2211yescharacteristic
60#89984C2211yescharacteristic
61C4×C22⋊Dic7C2211yescharacteristic
62C4×C22⋊Dic7C2211yescharacteristic
63#89766C2211yescharacteristic
64#89765C2211yescharacteristic
65#89765C2211yescharacteristic
66#89762C2211yescharacteristic
67#89762C2211yescharacteristic
68#89761C2211yescharacteristic
69#89761C2211yescharacteristic
70#89758C2211yescharacteristic
71#89758C2211yescharacteristic
72#89757C2211yescharacteristic
73#89756C2211yescharacteristic
74#89755C2211yescharacteristic
75#89755C2211yescharacteristic
76#89753C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89753C2211yescharacteristic
80#89753C2211yescharacteristic
81#89753C2211yescharacteristic
82#89753C2211yescharacteristic
83#89753C2211yescharacteristic
84#89753C2211yescharacteristic
85#89750C2211yescharacteristic
86#89750C2211yescharacteristic
87#89749C2211yescharacteristic
88C4⋊C4×Dic7C2211yescharacteristic
89C4⋊C4×Dic7C2211yescharacteristic
90C4⋊C4×Dic7C2211yescharacteristic
91C4⋊C4×Dic7C2211yescharacteristic
92C4⋊C4×Dic7C2211yescharacteristic
93#89745C2211yescharacteristic
94#89745C2211yescharacteristic
95#89744C2211yescharacteristic
96#89744C2211yescharacteristic
97#89731C2211yescharacteristic
98#89731C2211yescharacteristic
99#89731C2211yescharacteristic
100#89731C2211yescharacteristic
101#89730C2211yescharacteristic
102#89730C2211yescharacteristic
103#89729C2211yescharacteristic
104#89729C2211yescharacteristic
105#89729C2211yescharacteristic
106#89729C2211yescharacteristic
107#89725C2211yescharacteristic
108#89725C2211yescharacteristic
109#89724C2211yescharacteristic
110#89723C2211yescharacteristic
111#89723C2211yescharacteristic
112#89723C2211yescharacteristic
113#89723C2211yescharacteristic
114#89723C2211yescharacteristic
115#89721C2211yescharacteristic
116#89721C2211yescharacteristic
117#89720C2211yescharacteristic
118#89717C2211yescharacteristic
119#89717C2211yescharacteristic
120#89717C2211yescharacteristic
121#89717C2211yescharacteristic
122#89717C2211yescharacteristic
123#89716C2211yescharacteristic
124#89716C2211yescharacteristic
125#89716C2211yescharacteristic
126#89716C2211yescharacteristic
127#89716C2211yescharacteristic
128#89716C2211yescharacteristic
129#89715C2211yescharacteristic
130#89715C2211yescharacteristic
131#89714C2211yescharacteristic
132C22⋊C4×Dic7C2211yescharacteristic
133C22⋊C4×Dic7C2211yescharacteristic
134C22⋊C4×Dic7C2211yescharacteristic
135#89712C2211yescharacteristic
136#89712C2211yescharacteristic
137C4×(C2×D7)⋊C4C2211yescharacteristic
138#89708C2211yescharacteristic
139C4×C4⋊Dic7C2211yescharacteristic
140#89705C2211yescharacteristic
141#89704C2211yescharacteristic
142#89704C2211yescharacteristic
143C4×Dic7⋊C4C2211yescharacteristic
144C4×Dic7⋊C4C2211yescharacteristic
145C42×Dic7C2211yescharacteristic
146#89700C2211yescharacteristic
147#89449C2211yescharacteristic
148#89447C2211yescharacteristic
149#89446C2211yescharacteristic
150#89442C2211yescharacteristic
151#89442C2211yescharacteristic
152#89442C2211yescharacteristic
153#89442C2211yescharacteristic
154#89441C2211yescharacteristic
155#89438C2211yescharacteristic
156#89438C2211yescharacteristic
157#89432C2211yescharacteristic
158#89432C2211yescharacteristic
159#89430C2211yescharacteristic
160#89430C2211yescharacteristic
161#89429C2211yescharacteristic
162#89429C2211yescharacteristic
163#89429C2211yescharacteristic
164#89427C2211yescharacteristic
165#89427C2211yescharacteristic
166#89426C2211yescharacteristic
167#89426C2211yescharacteristic
168#89426C2211yescharacteristic
169#89426C2211yescharacteristic
170#89426C2211yescharacteristic
171#89426C2211yescharacteristic
172#89426C2211yescharacteristic
173#89426C2211yescharacteristic
174#89425C2211yescharacteristic
175#89425C2211yescharacteristic
176#89425C2211yescharacteristic
177#89424C2211yescharacteristic
178#89424C2211yescharacteristic
179#89422C2211yescharacteristic
180#89421C2211yescharacteristic
181#89421C2211yescharacteristic
182#89421C2211yescharacteristic
183#89420C2211yescharacteristic
184#89420C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#60025—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C22×C22⋊D7C2311yescharacteristic
192C22×C22⋊D7C2311yescharacteristic
193C23×Dic7C2311yescharacteristic
194C23×Dic7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C7×#125—24no—
197C4×C7×D4—24no—
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4C2311yescharacteristic
213C2×C7×C22⋊C4C2311yescharacteristic
214C2×C7×C22⋊C4C2311yescharacteristic
215C2×C7×C22⋊C4C2311yescharacteristic
216C2×C7×C22⋊C4C2311yescharacteristic
217C2×C42×C7C2311yescharacteristic
218C2×C42×C7C2311yescharacteristic
219C2×C42×C7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C2×C22⋊Dic7C2311yescharacteristic
222C2×C22⋊Dic7C2311yescharacteristic
223C2×C22⋊Dic7C2311yescharacteristic
224C2×C22⋊Dic7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226C2×C22⋊Dic7C2311yescharacteristic
227C2×C22⋊Dic7C2311yescharacteristic
228C2×C22⋊Dic7C2311yescharacteristic
229C2×C22⋊Dic7C2311yescharacteristic
230C2×C22⋊Dic7C2311yescharacteristic
231C2×C22⋊Dic7C2311yescharacteristic
232#6501—24no—
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
241C2×(C2×D7)⋊C4C2311yescharacteristic
242C2×(C2×D7)⋊C4C2311yescharacteristic
243C2×(C2×D7)⋊C4C2311yescharacteristic
244C2×(C2×D7)⋊C4C2311yescharacteristic
245#6489—24no—
246C2×C4⋊Dic7—24no—
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
252C2×C4⋊Dic7C2311yescharacteristic
253C2×C4⋊Dic7C2311yescharacteristic
254C2×C4⋊Dic7C2311yescharacteristic
255C2×C4⋊Dic7C2311yescharacteristic
256C2×C4⋊Dic7C2311yescharacteristic
257C2×C4⋊Dic7C2311yescharacteristic
258C2×C4⋊Dic7C2311yescharacteristic
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×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
273C2×Dic7⋊C4C2311yescharacteristic
274C2×Dic7⋊C4C2311yescharacteristic
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
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291C2×C4×Dic7C2311yescharacteristic
292C2×C4×Dic7C2311yescharacteristic
293C2×C4×Dic7C2311yescharacteristic
294#6461—24no—
295#6455—24no—
296#6440—24no—
297#6440—24no—
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#2800—71no—
353#2767—71no—
354#2741—71no—
355#2740—71no—
356#2596—71no—
357#2590—71no—
358#2585—71no—
359#2531—71no—
360#2530—71no—
361#2529—71no—
362#2526—71no—
363#2522—71no—
364#2517—71no—
365#2516—71no—
366#2516—71no—
367#2513—71no—
368#2481—71no—
369#2479—71no—
370#2476—71no—
371#2476—71no—
372#2475—71no—
373#2460D711yescharacteristic, complemented
374#2373—71no—
375#2371—71no—
376#2363—71no—
377#2352—71no—
378#2346—71no—
379#2344—71no—
380#2298—71no—
381#2298—71no—
382#2298—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—22no—
388C2×C7×D4—41no—
389C22×C4×C7—22no—
390C22×C4×C7—22no—
391C22×C4×C7—22no—
392C22×C4×C7—22no—
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
408C2×C22⋊D7—22no—
409C2×C22⋊D7—22no—
410C2×C22⋊D7—41no—
411C2×C22⋊D7—41no—
412C2×C22⋊D7—41no—
413C2×C22⋊D7—41no—
414C22×Dic7—22no—
415C22×Dic7—22no—
416C22×Dic7—22no—
417C22×Dic7—22no—
418C22×Dic7—41no—
419C22×Dic7—41no—
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C22×Dic7C2411yescharacteristic
431C22×Dic7C2411yescharacteristic
432C22×Dic7C2411yescharacteristic
433C22×Dic7C2411yescharacteristic
434C22×Dic7C2411yescharacteristic
435C2×C4×D7—22no—
436C2×C4×D7—22no—
437C2×C4×D7—41no—
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—22no—
443C7×C4⋊C4—22no—
444C7×C4⋊C4—41no—
445C7×C4⋊C4—41no—
446C7×C4⋊C4#4114yes—
447C7×C22⋊C4—22no—
448C7×C22⋊C4—22no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—22no—
451C7×C22⋊C4—41no—
452C7×C22⋊C4—41no—
453C7×C22⋊C4—41no—
454C7×C22⋊C4—41no—
455C7×C22⋊C4—41no—
456C7×C22⋊C4—41no—
457C42×C7—22no—
458C42×C7—22no—
459C42×C7—41no—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—22no—
463C22⋊Dic7—41no—
464C22⋊Dic7—41no—
465C22⋊Dic7—41no—
466C22⋊Dic7—41no—
467C22⋊Dic7—41no—
468C22⋊Dic7—41no—
469C22⋊Dic7—41no—
470C22⋊Dic7—41no—
471C22⋊Dic7#4114yes—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—22no—
475(C2×D7)⋊C4—22no—
476(C2×D7)⋊C4—22no—
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—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—22no—
487C4⋊Dic7—22no—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—41no—
491C4⋊Dic7—41no—
492C4⋊Dic7—41no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
495C4⋊Dic7#4114yes—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—41no—
502Dic7⋊C4—41no—
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—
512C4×Dic7—22no—
513C4×Dic7—22no—
514C4×Dic7—22no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—41no—
522C4×Dic7—41no—
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×#126—71no—
532C2×#125C2×D711yescharacteristic
533C2×#121—71no—
534C2×C4×D4C2×D711yescharacteristic
535C2×#117—71no—
536C2×#117—71no—
537C2×#117—71no—
538C2×#117—71no—
539C22×C4⋊C4—71no—
540#400—71no—
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#399—71no—
547#399—71no—
548#399—71no—
549#398—71no—
550#398—71no—
551#398—71no—
552#398—71no—
553#398—71no—
554#398—71no—
555#397—71no—
556#397—71no—
557#397—71no—
558#397—71no—
559#397—71no—
560#397—71no—
561#397—71no—
562#397C2×D711yescharacteristic
563#396—71no—
564#396—71no—
565#396C2×D711yescharacteristic
566#394—71no—
567#394—71no—
568#394—71no—
569#394—71no—
570#394C2×D711yescharacteristic
571#394C2×D711yescharacteristic
572#390—71no—
573#390—71no—
574#390—71no—
575#390—71no—
576#390—71no—
577#389—71no—
578#389—71no—
579#389—71no—
580#389—71no—
581#389—71no—
582#389—71no—
583#389—71no—
584#389—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#388—71no—
600#388—71no—
601#388—71no—
602#388—71no—
603#388—71no—
604#388—71no—
605#388—71no—
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388C2×D711yescharacteristic
611#388C2×D711yescharacteristic
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#387—71no—
624#387—71no—
625#387—71no—
626#387—71no—
627#387—71no—
628#387—71no—
629#387—71no—
630#387—71no—
631#387—71no—
632#387—71no—
633#387—71no—
634#387—71no—
635#387—71no—
636#387—71no—
637#387—71no—
638#387—71no—
639#387C2×D711yescharacteristic
640#387C2×D711yescharacteristic
641#387C2×D711yescharacteristic
642#386—71no—
643#386—71no—
644#386—71no—
645#386—71no—
646#386—71no—
647#386—71no—
648#385—71no—
649#385—71no—
650#385C2×D711yescharacteristic
651#385C2×D711yescharacteristic
652#382—71no—
653#382—71no—
654#382—71no—
655#381—71no—
656#381—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×C4⋊C4—71no—
668C4×C4⋊C4—71no—
669C4×C4⋊C4—71no—
670C4×C4⋊C4—71no—
671C4×C4⋊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⋊C4—71no—
679C4×C22⋊C4—71no—
680C4×C22⋊C4C2×D711yescharacteristic
681#376—71no—
682#376—71no—
683#376—71no—
684#376—71no—
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7—21no—
697C23×C7—21no—
698C23×C7—21no—
699C23×C7C2×#4112yes—
700C23×C7C2511yescharacteristic
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7—21no—
707C22×D7—21no—
708C7×D4—44no—
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—44no—
745C2×C4×C7—44no—
746C2×C4×C7C2×#4112yes—
747C2×C4×C7C2×#4112yes—
748C2×C4×C7C2×#4112yes—
749C2×C4×C7C2×#4112yes—
750C22⋊D7—82no—
751C22⋊D7—82no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
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×Dic7—44no—
794C2×Dic7—44no—
795C2×Dic7C2×#4112yes—
796C2×Dic7C2×#4112yes—
797C2×Dic7C2×#4112yes—
798C2×Dic7C2×#4112yes—
799C4×D7—44no—
800C22×D4—71no—
801C22×D4—71no—
802C22×D4C22×D711yescharacteristic
803C23×C4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4C22×D711yescharacteristic
807C23×C4C22×D711yescharacteristic
808#126—144no—
809#125—24no—
810#121—144no—
811C4×D4—24no—
812#117—144no—
813#117—144no—
814#117—144no—
815#117—144no—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—71no—
818C2×C4⋊C4—71no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—71no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
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—144no—
845C2×C4⋊C4C22×D711yescharacteristic
846C2×C4⋊C4C22×D711yescharacteristic
847C2×C4⋊C4C22×D711yescharacteristic
848C2×C4⋊C4C22×D711yescharacteristic
849C2×C4⋊C4C22×D711yescharacteristic
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C4⋊C4C22×D711yescharacteristic
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C22⋊C4—71no—
855C2×C22⋊C4—71no—
856C2×C22⋊C4—71no—
857C2×C22⋊C4—71no—
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⋊C4C22×D711yescharacteristic
879C2×C22⋊C4C22×D711yescharacteristic
880C2×C22⋊C4C22×D711yescharacteristic
881C2×C22⋊C4C22×D711yescharacteristic
882C2×C22⋊C4C22×D711yescharacteristic
883C2×C22⋊C4C22×D711yescharacteristic
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×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
907C2×C42C22×D711yescharacteristic
908C2×C42C22×D711yescharacteristic
909C2×C42C22×D711yescharacteristic
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#95—71no—
949#95—71no—
950#95—71no—
951#95—71no—
952#95—71no—
953#95—71no—
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
964C22×C7—22no—
965C22×C7—22no—
966C22×C7—22no—
967C22×C7—41no—
968C22×C7—41no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7—41no—
978C22×C7C22×#4111yescharacteristic
979C22×C7C22×#4111yescharacteristic
980C22×C7C22×#4111yescharacteristic
981C22×C7#58511yescharacteristic
982C22×C7#58511yescharacteristic
983C22×C7#58511yescharacteristic
984C22×C7#58511yescharacteristic
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C4×C7—22no—
993C4×C7—22no—
994C4×C7—22no—
995C4×C7—22no—
996C4×C7—41no—
997C4×C7—41no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005Dic7—22no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020C24—71no—
1021C24C23×D711yescharacteristic
1022C24C23×D711yescharacteristic
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—41no—
1026C2×D4—142no—
1027C2×D4—142no—
1028C2×D4—281no—
1029C2×D4—281no—
1030C2×D4—281no—
1031C2×D4—281no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
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—142no—
1054C22×C4—142no—
1055C22×C4—142no—
1056C22×C4—142no—
1057C22×C4—142no—
1058C22×C4—142no—
1059C22×C4—281no—
1060C22×C4—281no—
1061C22×C4—281no—
1062C22×C4C23×D711yescharacteristic
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C22×C4C23×D711yescharacteristic
1068C22×C4C23×D711yescharacteristic
1069C22×C4C23×D711yescharacteristic
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—74no—
1084C4⋊C4—142no—
1085C4⋊C4—142no—
1086C4⋊C4—142no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—142no—
1090C4⋊C4—142no—
1091C4⋊C4—142no—
1092C4⋊C4—142no—
1093C4⋊C4—142no—
1094C4⋊C4—142no—
1095C4⋊C4—281no—
1096C4⋊C4—281no—
1097C4⋊C4—281no—
1098C4⋊C4—281no—
1099C4⋊C4—281no—
1100C4⋊C4—281no—
1101C4⋊C4—281no—
1102C4⋊C4—281no—
1103C4⋊C4—281no—
1104C4⋊C4—281no—
1105C4⋊C4—281no—
1106C4⋊C4—281no—
1107C4⋊C4—281no—
1108C4⋊C4—281no—
1109C4⋊C4—281no—
1110C4⋊C4—281no—
1111C4⋊C4#115914yes—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—74no—
1123C22⋊C4—142no—
1124C22⋊C4—142no—
1125C22⋊C4—142no—
1126C22⋊C4—142no—
1127C22⋊C4—142no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
1131C22⋊C4—281no—
1132C22⋊C4—281no—
1133C22⋊C4—281no—
1134C22⋊C4—281no—
1135C22⋊C4—281no—
1136C22⋊C4—281no—
1137C22⋊C4—281no—
1138C22⋊C4—281no—
1139C22⋊C4—281no—
1140C22⋊C4—281no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C42—22no—
1147C42—22no—
1148C42—41no—
1149C42—142no—
1150C42—142no—
1151C42—142no—
1152C42—142no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—281no—
1159C42—281no—
1160C42—281no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—42no—
1169C2×C7—81no—
1170C2×C7#347511yescharacteristic
1171C2×C7#347511yescharacteristic
1172C2×C7#347511yescharacteristic
1173C2×C7#352111yescharacteristic
1174C2×C7#352411yescharacteristic
1175C2×C7#352411yescharacteristic
1176C2×C7#356711yescharacteristic
1177D7—81no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—141no—
1192C23—141no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23D7×#4112yes—
1199C23C24×D711yescharacteristic
1200D4—44no—
1201D4—562no—
1202D4—562no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
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—44no—
1239C2×C4—44no—
1240C2×C4—72no—
1241C2×C4—72no—
1242C2×C4—72no—
1243C2×C4—72no—
1244C2×C4—141no—
1245C2×C4—141no—
1246C2×C4—141no—
1247C2×C4—141no—
1248C2×C4—141no—
1249C2×C4—141no—
1250C2×C4—141no—
1251C2×C4—141no—
1252C2×C4—141no—
1253C2×C4—141no—
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—284no—
1286C2×C4—284no—
1287C2×C4—284no—
1288C2×C4C2×#115912yes—
1289C2×C4C2×#115912yes—
1290C2×C4C2×#115912yes—
1291C2×C4D7×#4112yes—
1292C7#6002511yescharacteristic, complemented, Sylow
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—281no—
1308C22—281no—
1309C22—281no—
1310C22—281no—
1311C22—281no—
1312C22—281no—
1313C22—281no—
1314C22C22×#115911yescharacteristic
1315C22C2×D7×#4111yescharacteristic
1316C22C2×D7×#4111yescharacteristic
1317C22#9061611yescharacteristic
1318C22#9061611yescharacteristic
1319C22#9061811yescharacteristic
1320C22#9062011yescharacteristic
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—142no—
1335C4—142no—
1336C4—142no—
1337C4—142no—
1338C4—281no—
1339C4—281no—
1340C4—281no—
1341C4—281no—
1342C4—281no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C2—42no—
1350C2—81no—
1351C2—561no—
1352C2#1174308911yescharacteristic
1353C2#1174319811yescharacteristic
1354C2#1174351911yescharacteristic
1355C2#1174369511yescharacteristic
1356C2#1174379211yescharacteristic
1357C2#1174389411yescharacteristic
1358C2#1174395711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2460C2
prime radicalC2×#6501C22
hypercenter#2460D7
hypocenterC7#60025
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2460

Complements

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

NH ≅ G/Ntype
1. C7×#2460C2semidirect
2. #11740478C2semidirect
3. #11740471C2semidirect
5. #11739780C2semidirect
6. #11734975C2semidirect
7. #11734940C2semidirect
8. #11734845C2semidirect
9. #11734758C2semidirect
10. #11734494C2semidirect
11. #11734382C2semidirect
14. #11733019C2semidirect
15. #11733002C2semidirect
16. #11732918C2semidirect
17. #11732896C2semidirect
18. #11732792C2semidirect
19. #11732651C2semidirect
20. #11732556C2semidirect
21. #11732540C2semidirect
22. #11732419C2semidirect
23. #11732384C2semidirect
24. #11731916C2semidirect
25. #11731913C2semidirect
26. #11731899C2semidirect
27. #11731896C2semidirect
28. #11731422C2semidirect
29. #11731323C2semidirect
30. #11730978C2semidirect
31. #11730885C2semidirect
373. #2460D7semidirect
1292. C7#60025semidirect

Maximal subgroups

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

subgroupindex
C7×#24602
#117404782
#117404712
#117397862
#117397802
#117349752
#117349402
#117348452
#117347582
#117344942
#117343822
#117343752
#117330192
#117330022
#117329182
#117328962
#117327922
#117326512
#117325562
#117325402
#117324192
#117323842
#117319162
#117319132
#117318992
#117318962
#117314222
#117313232
#117309782
#117308852
#600257