Finite Group Databasebeta

← #13568282

Subgroups — #13568282

Order 1792.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2787C211yesmaximal, characteristic, complemented
2#11735866C211yesmaximal, characteristic, complemented
3#11735862C211yesmaximal, characteristic, complemented
4#11735815C211yesmaximal, characteristic, complemented
5#11735640C211yesmaximal, characteristic, complemented
6#11735422C211yesmaximal, characteristic, complemented
7#11735322C211yesmaximal, characteristic, complemented
8#11735275C211yesmaximal, characteristic, complemented
9#11735208C211yesmaximal, characteristic, complemented
10#11735080C211yesmaximal, characteristic, complemented
11#11735077C211yesmaximal, characteristic, complemented
12#11734979C211yesmaximal, characteristic
13#11734907C211yesmaximal, characteristic, complemented
14#11733719C211yesmaximal, characteristic, complemented
15#11733470C211yesmaximal, characteristic, complemented
16#11733180C211yesmaximal, characteristic
17#11733165C211yesmaximal, characteristic, complemented
18#11732909C211yesmaximal, characteristic, complemented
19#11732895C211yesmaximal, characteristic, complemented
20#11732852C211yesmaximal, characteristic, complemented
21#11732738C211yesmaximal, characteristic, complemented
22#11732737C211yesmaximal, characteristic, complemented
23#11732666C211yesmaximal, characteristic, complemented
24#11732640C211yesmaximal, characteristic, complemented
25#11732560C211yesmaximal, characteristic, complemented
26#11732025C211yesmaximal, characteristic
27#11731982C211yesmaximal, characteristic, complemented
28#11731859C211yesmaximal, characteristic, complemented
29#11731828C211yesmaximal, characteristic, complemented
30#11731410C211yesmaximal, characteristic, complemented
31#11731388C211yesmaximal, characteristic, complemented
32C2×#6487C2211yescharacteristic
33C2×#6461C2211yescharacteristic
34C2×#6461C2211yescharacteristic
35C2×#6459C2211yescharacteristic
36C2×#6455C2211yescharacteristic
37C2×(C22⋊D7)⋊C4C2211yescharacteristic
38C2×(C22⋊D7)⋊C4C2211yescharacteristic
39C2×#6441C2211yescharacteristic
40C2×#6440C2211yescharacteristic
41C7×#401C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#398C2211yescharacteristic
44C7×#398C2211yescharacteristic
45C7×#397C2211yescharacteristic
46C7×#397C2211yescharacteristic
47C7×#389C2211yescharacteristic
48C7×#388C2211yescharacteristic
49C7×#388C2211yescharacteristic
50C7×#387C2211yescharacteristic
51C7×#387C2211yescharacteristic
52C7×#387C2211yescharacteristic
53C7×#385C2211yescharacteristic
54C7×#385C2211yescharacteristic
55C7×#380C2211yescharacteristic
56#89985C2211yescharacteristic
57#89985C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89766C2211yescharacteristic
60#89766C2211yescharacteristic
61#89765C2211yescharacteristic
62#89765C2211yescharacteristic
63#89764C2211yescharacteristic
64#89764C2211yescharacteristic
65#89764C2211yescharacteristic
66#89762C2211yescharacteristic
67#89762C2211yescharacteristic
68#89762C2211yescharacteristic
69#89761C2211yescharacteristic
70#89761C2211yescharacteristic
71#89761C2211yescharacteristic
72#89760C2211yescharacteristic
73#89759C2211yescharacteristic
74#89758C2211yescharacteristic
75#89756C2211yescharacteristic
76#89754C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89752C2211yescharacteristic
80#89751C2211yescharacteristic
81#89751C2211yescharacteristic
82#89751C2211yescharacteristic
83#89750C2211yescharacteristic
84#89750C2211yescharacteristic
85#89750C2211yescharacteristic
86#89750C2211yescharacteristic
87#89750C2211yescharacteristic
88#89749C2211yescharacteristic
89#89746C2211yescharacteristic
90#89745C2211yescharacteristic
91#89744C2211yescharacteristic
92#89744C2211yescharacteristic
93#89744C2211yescharacteristic
94#89744C2211yescharacteristic
95#89733C2211yescharacteristic
96#89732C2211yescharacteristic
97#89731C2211yescharacteristic
98#89731C2211yescharacteristic
99#89731C2211yescharacteristic
100#89730C2211yescharacteristic
101#89730C2211yescharacteristic
102#89729C2211yescharacteristic
103#89729C2211yescharacteristic
104#89724C2211yescharacteristic
105#89723C2211yescharacteristic
106#89723C2211yescharacteristic
107#89722C2211yescharacteristic
108#89718C2211yescharacteristic
109#89717C2211yescharacteristic
110#89717C2211yescharacteristic
111#89715C2211yescharacteristic
112#89714C2211yescharacteristic
113#89714C2211yescharacteristic
114C22⋊C4×Dic7C2211yescharacteristic
115#89712C2211yescharacteristic
116#89712C2211yescharacteristic
117#89712C2211yescharacteristic
118#89712C2211yescharacteristic
119C4×C4⋊Dic7C2211yescharacteristic
120#89705C2211yescharacteristic
121#89705C2211yescharacteristic
122C42×Dic7C2211yescharacteristic
123#89447C2211yescharacteristic
124#89447C2211yescharacteristic
125#89447C2211yescharacteristic
126#89446C2211yescharacteristic
127#89446C2211yescharacteristic
128#89446C2211yescharacteristic
129#89445C2211yescharacteristic
130#89445C2211yescharacteristic
131#89445C2211yescharacteristic
132#89444C2211yescharacteristic
133#89444C2211yescharacteristic
134#89444C2211yescharacteristic
135#89442C2211yescharacteristic
136#89442C2211yescharacteristic
137#89442C2211yescharacteristic
138#89441C2211yescharacteristic
139#89441C2211yescharacteristic
140#89441C2211yescharacteristic
141#89441C2211yescharacteristic
142#89441C2211yescharacteristic
143#89441C2211yescharacteristic
144#89440C2211yescharacteristic
145#89439C2211yescharacteristic
146#89438C2211yescharacteristic
147#89437C2211yescharacteristic
148#89437C2211yescharacteristic
149#89436C2211yescharacteristic
150C7⋊#401C2211yescharacteristic
151#89433C2211yescharacteristic
152#89431C2211yescharacteristic
153#89430C2211yescharacteristic
154#89430C2211yescharacteristic
155#89430C2211yescharacteristic
156#89429C2211yescharacteristic
157#89429C2211yescharacteristic
158#89429C2211yescharacteristic
159#89429C2211yescharacteristic
160#89427C2211yescharacteristic
161#89427C2211yescharacteristic
162#89427C2211yescharacteristic
163#89427C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89425C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89424C2211yescharacteristic
170#89424C2211yescharacteristic
171#89424C2211yescharacteristic
172#89424C2211yescharacteristic
173#89424C2211yescharacteristic
174#89423C2211yescharacteristic
175#89422C2211yescharacteristic
176#89422C2211yescharacteristic
177#89421C2211yescharacteristic
178#89421C2211yescharacteristic
179#89419C2211yescharacteristic
180#89419C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#36996—71nomaximal, Sylow
188C23×C4×C7C2311yescharacteristic
189C22×C22⋊D7C2311yescharacteristic
190C22×C22⋊D7C2311yescharacteristic
191C23×Dic7C2311yescharacteristic
192C23×Dic7C2311yescharacteristic
193C22×D28C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C22×Dic14C2311yescharacteristic
197C22×Dic14C2311yescharacteristic
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×C4⋊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×C42×C7C2311yescharacteristic
215C2×C42×C7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
220C2×(C2×D7)⋊C4C2311yescharacteristic
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
241C2×(C2×D7)⋊C4C2311yescharacteristic
242C2×(C2×D7)⋊C4C2311yescharacteristic
243C2×(C2×D7)⋊C4C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251#6487—42no—
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×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
273C2×Dic7⋊C4C2311yescharacteristic
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
285C2×C4×Dic7C2311yescharacteristic
286#6461—42no—
287#6461—42no—
288#6459—42no—
289#6455—42no—
290(C22⋊D7)⋊C4—24no—
291(C22⋊D7)⋊C4—24no—
292#6441—24no—
293#6440—42no—
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#2865—71no—
353#2864—71no—
354#2797—71no—
355#2787—71no—
356#2787D711yescharacteristic, complemented
357#2786—71no—
358#2773—71no—
359#2766—71no—
360#2759—71no—
361#2755—71no—
362#2753—71no—
363#2742—71no—
364#2741—71no—
365#2740—71no—
366#2723—71no—
367#2702—71no—
368#2702—71no—
369#2698—71no—
370#2653—71no—
371#2652—71no—
372#2600—71no—
373#2594—71no—
374#2588—71no—
375#2564—71no—
376#2479—71no—
377#2478—71no—
378#2438—71no—
379#2415—71no—
380#2332—71no—
381#2318—71no—
382#2293—71no—
383C24×C7C2411yescharacteristic
384C23×D7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C22×C4×C7—41no—
387C22×C4×C7—41no—
388C22×C4×C7—41no—
389C22×C4×C7C2411yescharacteristic
390C22×C4×C7C2411yescharacteristic
391C22×C4×C7C2411yescharacteristic
392C22×C4×C7C2411yescharacteristic
393C22×C4×C7C2411yescharacteristic
394C22×C4×C7C2411yescharacteristic
395C22×C4×C7C2411yescharacteristic
396C22×C4×C7C2411yescharacteristic
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C2×C22⋊D7—22no—
404C2×C22⋊D7—22no—
405C2×C22⋊D7—22no—
406C2×C22⋊D7—41no—
407C2×C22⋊D7—41no—
408C2×C22⋊D7—41no—
409C22×Dic7—41no—
410C22×Dic7—41no—
411C22×Dic7—41no—
412C22×Dic7—41no—
413C22×Dic7—41no—
414C22×Dic7#4114yes—
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—41no—
430C2×D28—41no—
431C2×D28—41no—
432C2×C4×D7—22no—
433C2×C4×D7—22no—
434C2×C4×D7—41no—
435C2×C4×D7—41no—
436C2×C4×D7—41no—
437C2×C4×D7—41no—
438C2×Dic14—22no—
439C2×Dic14—41no—
440C2×Dic14—41no—
441C2×Dic14—41no—
442C2×Dic14—41no—
443C2×Dic14—41no—
444C7×C4⋊C4—41no—
445C7×C4⋊C4—41no—
446C7×C4⋊C4—41no—
447C7×C4⋊C4—41no—
448C7×C4⋊C4—41no—
449C7×C4⋊C4—41no—
450C7×C4⋊C4—41no—
451C7×C4⋊C4—41no—
452C7×C4⋊C4—41no—
453C7×C4⋊C4—41no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4—41no—
459C7×C22⋊C4—41no—
460C42×C7—41no—
461C42×C7—41no—
462C22⋊Dic7—22no—
463C22⋊Dic7—22no—
464C22⋊Dic7—41no—
465C22⋊Dic7—41no—
466(C2×D7)⋊C4—22no—
467(C2×D7)⋊C4—22no—
468(C2×D7)⋊C4—22no—
469(C2×D7)⋊C4—22no—
470(C2×D7)⋊C4—22no—
471(C2×D7)⋊C4—41no—
472(C2×D7)⋊C4—41no—
473(C2×D7)⋊C4—41no—
474(C2×D7)⋊C4—41no—
475(C2×D7)⋊C4—41no—
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—41no—
487(C2×D7)⋊C4—41no—
488(C2×D7)⋊C4—41no—
489(C2×D7)⋊C4—41no—
490C4⋊Dic7—22no—
491C4⋊Dic7—22no—
492C4⋊Dic7—22no—
493C4⋊Dic7—41no—
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—22no—
504Dic7⋊C4—22no—
505Dic7⋊C4—22no—
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—
515Dic7⋊C4—41no—
516Dic7⋊C4—41no—
517Dic7⋊C4—41no—
518Dic7⋊C4—41no—
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×#126—71no—
532C2×#126—71no—
533C2×C22⋊Q8—71no—
534C2×C22⋊Q8—71no—
535C2×C22⋊Q8—71no—
536C2×C4×D4—71no—
537C2×C4×D4—71no—
538C2×#117—71no—
539C2×#117—71no—
540#401—71no—
541#401C2×D711yescharacteristic
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#400C2×D711yescharacteristic
549#399—71no—
550#399—71no—
551#399—71no—
552#398—71no—
553#398—71no—
554#398—71no—
555#398—71no—
556#398—71no—
557#398—71no—
558#398—71no—
559#398C2×D711yescharacteristic
560#398C2×D711yescharacteristic
561#397—71no—
562#397—71no—
563#397—71no—
564#397—71no—
565#397—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397C2×D711yescharacteristic
571#397C2×D711yescharacteristic
572#396—71no—
573#396—71no—
574#395—71no—
575#395—71no—
576#395—71no—
577#394—71no—
578#394—71no—
579#394—71no—
580#394—71no—
581#394—71no—
582#394—71no—
583#394—71no—
584#393—71no—
585#393—71no—
586#393—71no—
587#392—71no—
588#391—71no—
589#391—71no—
590#391—71no—
591#391—71no—
592#391—71no—
593#390—71no—
594#390—71no—
595#390—71no—
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389C2×D711yescharacteristic
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388—71no—
611#388—71no—
612#388—71no—
613#388—71no—
614#388—71no—
615#388—71no—
616#388—71no—
617#388—71no—
618#388—71no—
619#388—71no—
620#388—71no—
621#388—71no—
622#388—71no—
623#388—71no—
624#388—71no—
625#388—71no—
626#388C2×D711yescharacteristic
627#388C2×D711yescharacteristic
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#387—71no—
640#387—71no—
641#387—71no—
642#387—71no—
643#387—71no—
644#387—71no—
645#387—71no—
646#387—71no—
647#387—71no—
648#387—71no—
649#387—71no—
650#387—71no—
651#387C2×D711yescharacteristic
652#387C2×D711yescharacteristic
653#387C2×D711yescharacteristic
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#386—71no—
659#386—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385C2×D711yescharacteristic
667#385C2×D711yescharacteristic
668#383—71no—
669#382—71no—
670#382—71no—
671#382—71no—
672#381—71no—
673#381—71no—
674#380—71no—
675#380—71no—
676#380—71no—
677#380—71no—
678#380C2×D711yescharacteristic
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C4⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C2×#95—71no—
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×D7—21no—
707C22×D7—21no—
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—21no—
749C2×C4×C7—21no—
750C2×C4×C7—82no—
751C22⋊D7—44no—
752C22⋊D7—44no—
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—44no—
792C2×Dic7—82no—
793C2×Dic7C2×#4112yes—
794C2×Dic7C2×#4112yes—
795C2×Dic7H(5,𝔽2)12yes—
796C2×Dic72−1+412yes—
797D28—82no—
798C4×D7—44no—
799C4×D7—82no—
800Dic14—82no—
801Dic14—82no—
802C22×Q8—71no—
803C22×Q8—71no—
804C22×D4—71no—
805C22×D4—71no—
806C22×D4—71no—
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4C22×D711yescharacteristic
812#126—282no—
813#126—282no—
814C22⋊Q8—144no—
815C22⋊Q8—282no—
816C22⋊Q8—282no—
817C4×D4—144no—
818C4×D4—144no—
819#117—282no—
820#117—282no—
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—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—71no—
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
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×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
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⋊C4—71no—
885C2×C22⋊C4—71no—
886C2×C22⋊C4—71no—
887C2×C22⋊C4—71no—
888C2×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
891C2×C22⋊C4C22×D711yescharacteristic
892C2×C22⋊C4C22×D711yescharacteristic
893C2×C22⋊C4C22×D711yescharacteristic
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×C42C22×D711yescharacteristic
907C2×C42C22×D711yescharacteristic
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#95—71no—
949#95—71no—
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
966C22×C7—22no—
967C22×C7—22no—
968C22×C7—22no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7C22×#4111yescharacteristic
974C22×C7C2×H(5,𝔽2)11yescharacteristic
975C22×C7C2×2−1+411yescharacteristic
976C22×C7#58511yescharacteristic
977C22×C7#58511yescharacteristic
978C22×C7#58511yescharacteristic
979C22×C7#58511yescharacteristic
980C2×D7—41no—
981C2×D7—41no—
982C2×D7—41no—
983C2×D7—41no—
984C2×D7—41no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
993C2×D7—41no—
994C4×C7—41no—
995C4×C7—41no—
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—
1005C4×C7—41no—
1006C4×C7—41no—
1007C4×C7—41no—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—22no—
1011Dic7—22no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022C24—71no—
1023C24—71no—
1024C24C23×D711yescharacteristic
1025C2×Q8—142no—
1026C2×Q8—281no—
1027C2×Q8—281no—
1028C2×Q8—281no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×D4—142no—
1032C2×D4—142no—
1033C2×D4—142no—
1034C2×D4—281no—
1035C2×D4—281no—
1036C2×D4—281no—
1037C2×D4—281no—
1038C2×D4—281no—
1039C2×D4—281no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—74no—
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—142no—
1059C22×C4—142no—
1060C22×C4—281no—
1061C22×C4—281no—
1062C22×C4—281no—
1063C22×C4—281no—
1064C22×C4—281no—
1065C22×C4—281no—
1066C22×C4—281no—
1067C22×C4—281no—
1068C22×C4—281no—
1069C22×C4C23×D711yescharacteristic
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C22×C4C23×D711yescharacteristic
1076C22×C4C23×D711yescharacteristic
1077C22×C4C23×D711yescharacteristic
1078C22×C4C23×D711yescharacteristic
1079C22×C4C23×D711yescharacteristic
1080C22×C4C23×D711yescharacteristic
1081C22×C4C23×D711yescharacteristic
1082C22×C4C23×D711yescharacteristic
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—142no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—142no—
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—281no—
1106C4⋊C4—281no—
1107C4⋊C4—281no—
1108C4⋊C4—281no—
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—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
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—
1146C22⋊C4—281no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C22⋊C4—281no—
1155C22⋊C4—281no—
1156C42—41no—
1157C42—41no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C2×C7—42no—
1171C2×C7#345511yescharacteristic
1172C2×C7#349511yescharacteristic
1173C2×C7#350511yescharacteristic
1174C2×C7#355711yescharacteristic
1175C2×C7#355911yescharacteristic
1176C2×C7#356211yescharacteristic
1177C2×C7#356811yescharacteristic
1178D7—81no—
1179D7—81no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—141no—
1187C23—141no—
1188C23—141no—
1189C23—141no—
1190C23—141no—
1191C23—141no—
1192C23—141no—
1193C23—141no—
1194C23—141no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23—141no—
1199C23—141no—
1200C23D7×#4112yes—
1201C23C24×D711yescharacteristic
1202Q8—562no—
1203Q8—562no—
1204D4—284no—
1205D4—284no—
1206D4—562no—
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—21no—
1248C2×C4—21no—
1249C2×C4—72no—
1250C2×C4—72no—
1251C2×C4—72no—
1252C2×C4—72no—
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—
1296C7#3699611yescharacteristic, complemented, Sylow
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—281no—
1305C22—281no—
1306C22—281no—
1307C22—281no—
1308C22—281no—
1309C22—281no—
1310C22—281no—
1311C22—281no—
1312C22—281no—
1313C22—281no—
1314C22—281no—
1315C22—281no—
1316C22—281no—
1317C22—281no—
1318C22C2×D7×#4111yescharacteristic
1319C22#9061611yescharacteristic
1320C22#9061611yescharacteristic
1321C22D7×H(5,𝔽2)11yescharacteristic
1322C22#9061811yescharacteristic
1323C22D7×2−1+411yescharacteristic
1324C22#9062011yescharacteristic
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—142no—
1340C4—142no—
1341C4—142no—
1342C4—142no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C4—281no—
1350C4—281no—
1351C4—281no—
1352C4—281no—
1353C2—42no—
1354C2—561no—
1355C2—561no—
1356C2#1174347511yescharacteristic
1357C2#1174349511yescharacteristic
1358C2#1174350911yescharacteristic
1359C2#1174389711yescharacteristic
1360C2#1174398011yescharacteristic
1361C2#1174407011yescharacteristic
1362C2#1174420211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2787C2
prime radical#89732C22
hypercenter#2787D7
hypocenterC7#36996
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2787

Complements

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

NH ≅ G/Ntype
1. C7×#2787C2semidirect
2. #11735866C2semidirect
3. #11735862C2semidirect
4. #11735815C2semidirect
5. #11735640C2semidirect
6. #11735422C2semidirect
7. #11735322C2semidirect
8. #11735275C2semidirect
9. #11735208C2semidirect
10. #11735080C2semidirect
11. #11735077C2semidirect
13. #11734907C2semidirect
14. #11733719C2semidirect
15. #11733470C2semidirect
17. #11733165C2semidirect
18. #11732909C2semidirect
19. #11732895C2semidirect
20. #11732852C2semidirect
21. #11732738C2semidirect
22. #11732737C2semidirect
23. #11732666C2semidirect
24. #11732640C2semidirect
25. #11732560C2semidirect
27. #11731982C2semidirect
28. #11731859C2semidirect
29. #11731828C2semidirect
30. #11731410C2semidirect
31. #11731388C2semidirect
356. #2787D7semidirect
1296. C7#36996semidirect

Maximal subgroups

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

subgroupindex
C7×#27872
#117358662
#117358622
#117358152
#117356402
#117354222
#117353222
#117352752
#117352082
#117350802
#117350772
#117349792
#117349072
#117337192
#117334702
#117331802
#117331652
#117329092
#117328952
#117328522
#117327382
#117327372
#117326662
#117326402
#117325602
#117320252
#117319822
#117318592
#117318282
#117314102
#117313882
#369967