Finite Group Databasebeta

← #14217049

Subgroups — #14217049

Order 1792.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2527C211yesmaximal, characteristic, complemented
2#11735860C211yesmaximal, characteristic, complemented
3#11735858C211yesmaximal, characteristic, complemented
4#11735743C211yesmaximal, characteristic, complemented
5#11735584C211yesmaximal, characteristic, complemented
6#11734963C211yesmaximal, characteristic
7#11734924C211yesmaximal, characteristic, complemented
8#11734268C211yesmaximal, characteristic, complemented
9#11734229C211yesmaximal, characteristic
10#11734015C211yesmaximal, characteristic, complemented
11#11733946C211yesmaximal, characteristic, complemented
12#11733937C211yesmaximal, characteristic, complemented
13#11733926C211yesmaximal, characteristic, complemented
14#11733039C211yesmaximal, characteristic
15#11732979C211yesmaximal, characteristic
16#11732930C211yesmaximal, characteristic, complemented
17#11732896C211yesmaximal, characteristic, complemented
18#11732794C211yesmaximal, characteristic, complemented
19#11732571C211yesmaximal, characteristic, complemented
20#11732557C211yesmaximal, characteristic, complemented
21#11732538C211yesmaximal, characteristic, complemented
22#11732483C211yesmaximal, characteristic, complemented
23#11732418C211yesmaximal, characteristic, complemented
24#11731978C211yesmaximal, characteristic
25#11731841C211yesmaximal, characteristic, complemented
26#11731531C211yesmaximal, characteristic, complemented
27#11731509C211yesmaximal, characteristic
28#11730923C211yesmaximal, characteristic
29#11730911C211yesmaximal, characteristic, complemented
30#11730851C211yesmaximal, characteristic, complemented
31#11730830C211yesmaximal, characteristic, complemented
32C2×Q8×Dic7C2211yescharacteristic
33C2×#6507C2211yescharacteristic
34C2×#6507C2211yescharacteristic
35C2×#6492C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C2×#6461C2211yescharacteristic
38C2×#6461C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6449C2211yescharacteristic
41C2×#6442C2211yescharacteristic
42C2×#6441C2211yescharacteristic
43C2×#6441C2211yescharacteristic
44C2×#6440C2211yescharacteristic
45C2×#6435C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#401C2211yescharacteristic
48C7×#400C2211yescharacteristic
49C7×#397C2211yescharacteristic
50C7×#393C2211yescharacteristic
51C7×#391C2211yescharacteristic
52C7×#391C2211yescharacteristic
53C7×#388C2211yescharacteristic
54C7×#388C2211yescharacteristic
55C7×#387C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C7×#387C2211yescharacteristic
58C7×#385C2211yescharacteristic
59C7×#381C2211yescharacteristic
60C4×C7×C22⋊C4C2211yescharacteristic
61C7×#376C2211yescharacteristic
62#90003C2211yescharacteristic
63#89982C2211yescharacteristic
64C4×C22⋊Dic7C2211yescharacteristic
65#89766C2211yescharacteristic
66#89764C2211yescharacteristic
67#89761C2211yescharacteristic
68#89756C2211yescharacteristic
69#89755C2211yescharacteristic
70#89753C2211yescharacteristic
71#89752C2211yescharacteristic
72#89750C2211yescharacteristic
73#89750C2211yescharacteristic
74#89748C2211yescharacteristic
75C4⋊C4×Dic7C2211yescharacteristic
76C4⋊C4×Dic7C2211yescharacteristic
77#89746C2211yescharacteristic
78#89745C2211yescharacteristic
79#89745C2211yescharacteristic
80#89744C2211yescharacteristic
81#89744C2211yescharacteristic
82#89733C2211yescharacteristic
83#89731C2211yescharacteristic
84#89730C2211yescharacteristic
85#89729C2211yescharacteristic
86#89728C2211yescharacteristic
87#89724C2211yescharacteristic
88#89723C2211yescharacteristic
89#89722C2211yescharacteristic
90#89721C2211yescharacteristic
91#89718C2211yescharacteristic
92#89718C2211yescharacteristic
93#89717C2211yescharacteristic
94#89717C2211yescharacteristic
95#89716C2211yescharacteristic
96#89716C2211yescharacteristic
97C22⋊C4×Dic7C2211yescharacteristic
98C22⋊C4×Dic7C2211yescharacteristic
99C22⋊C4×Dic7C2211yescharacteristic
100C22⋊C4×Dic7C2211yescharacteristic
101#89712C2211yescharacteristic
102C4×(C2×D7)⋊C4C2211yescharacteristic
103C4×(C2×D7)⋊C4C2211yescharacteristic
104#89708C2211yescharacteristic
105#89705C2211yescharacteristic
106#89705C2211yescharacteristic
107#89705C2211yescharacteristic
108#89704C2211yescharacteristic
109C4×Dic7⋊C4C2211yescharacteristic
110C4×Dic7⋊C4C2211yescharacteristic
111C4×Dic7⋊C4C2211yescharacteristic
112C42×Dic7C2211yescharacteristic
113#89701C2211yescharacteristic
114#89700C2211yescharacteristic
115#89448C2211yescharacteristic
116#89448C2211yescharacteristic
117#89447C2211yescharacteristic
118#89445C2211yescharacteristic
119#89445C2211yescharacteristic
120#89442C2211yescharacteristic
121#89442C2211yescharacteristic
122#89442C2211yescharacteristic
123#89442C2211yescharacteristic
124#89441C2211yescharacteristic
125#89441C2211yescharacteristic
126#89441C2211yescharacteristic
127#89441C2211yescharacteristic
128#89441C2211yescharacteristic
129#89441C2211yescharacteristic
130#89441C2211yescharacteristic
131#89439C2211yescharacteristic
132#89438C2211yescharacteristic
133#89433C2211yescharacteristic
134#89432C2211yescharacteristic
135#89432C2211yescharacteristic
136#89430C2211yescharacteristic
137#89430C2211yescharacteristic
138#89429C2211yescharacteristic
139#89429C2211yescharacteristic
140#89429C2211yescharacteristic
141#89429C2211yescharacteristic
142#89429C2211yescharacteristic
143#89429C2211yescharacteristic
144#89428C2211yescharacteristic
145#89428C2211yescharacteristic
146#89427C2211yescharacteristic
147#89427C2211yescharacteristic
148#89427C2211yescharacteristic
149#89427C2211yescharacteristic
150#89427C2211yescharacteristic
151#89427C2211yescharacteristic
152#89427C2211yescharacteristic
153#89426C2211yescharacteristic
154#89426C2211yescharacteristic
155#89426C2211yescharacteristic
156#89426C2211yescharacteristic
157#89425C2211yescharacteristic
158#89425C2211yescharacteristic
159#89424C2211yescharacteristic
160#89424C2211yescharacteristic
161#89424C2211yescharacteristic
162#89424C2211yescharacteristic
163#89424C2211yescharacteristic
164#89424C2211yescharacteristic
165#89424C2211yescharacteristic
166#89424C2211yescharacteristic
167#89424C2211yescharacteristic
168#89422C2211yescharacteristic
169#89421C2211yescharacteristic
170#89421C2211yescharacteristic
171#89421C2211yescharacteristic
172#89421C2211yescharacteristic
173#89421C2211yescharacteristic
174#89421C2211yescharacteristic
175#89421C2211yescharacteristic
176#89420C2211yescharacteristic
177#89419C2211yescharacteristic
178#89419C2211yescharacteristic
179#89419C2211yescharacteristic
180#89419C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#60041—71nomaximal, Sylow
188C22×C7×Q8C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C22×C22⋊D7C2311yescharacteristic
191C23×Dic7C2311yescharacteristic
192C23×Dic7C2311yescharacteristic
193C22×C4×D7C2311yescharacteristic
194C22×Dic14C2311yescharacteristic
195C22×Dic14C2311yescharacteristic
196C2×C7×C4⋊C4C2311yescharacteristic
197C2×C7×C4⋊C4C2311yescharacteristic
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C22⋊C4C2311yescharacteristic
202C2×C7×C22⋊C4C2311yescharacteristic
203C2×C7×C22⋊C4C2311yescharacteristic
204C2×C7×C22⋊C4C2311yescharacteristic
205C2×C7×C22⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C42×C7C2311yescharacteristic
208C2×C42×C7C2311yescharacteristic
209C2×C42×C7C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C22⋊Dic7C2311yescharacteristic
212C2×C22⋊Dic7C2311yescharacteristic
213C2×C22⋊Dic7C2311yescharacteristic
214C2×C22⋊Dic7C2311yescharacteristic
215C2×C22⋊Dic7C2311yescharacteristic
216Q8×Dic7—42no—
217#6507—24no—
218#6507—24no—
219#6492—24no—
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×C4⋊Dic7C2311yescharacteristic
234C2×C4⋊Dic7C2311yescharacteristic
235C2×C4⋊Dic7C2311yescharacteristic
236C2×C4⋊Dic7C2311yescharacteristic
237C2×C4⋊Dic7C2311yescharacteristic
238C2×C4⋊Dic7C2311yescharacteristic
239C2×C4⋊Dic7C2311yescharacteristic
240C2×C4⋊Dic7C2311yescharacteristic
241C2×C4⋊Dic7C2311yescharacteristic
242C2×C4⋊Dic7C2311yescharacteristic
243C2×Dic7⋊C4—42no—
244C2×Dic7⋊C4C2311yescharacteristic
245C2×Dic7⋊C4C2311yescharacteristic
246C2×Dic7⋊C4C2311yescharacteristic
247C2×Dic7⋊C4C2311yescharacteristic
248C2×Dic7⋊C4C2311yescharacteristic
249C2×Dic7⋊C4C2311yescharacteristic
250C2×Dic7⋊C4C2311yescharacteristic
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×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
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
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291C2×C4×Dic7C2311yescharacteristic
292#6461—24no—
293#6461—42no—
294#6450—42no—
295#6449—42no—
296#6442—24no—
297#6441—24no—
298#6441—24no—
299#6440—24no—
300#6435—24no—
301C4×Dic14—42no—
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
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356C7⋊#95C2311yescharacteristic
357C7⋊#95C2311yescharacteristic
358#2791—71no—
359#2718—71no—
360#2716—71no—
361#2677—71no—
362#2612—71no—
363#2604—71no—
364#2594—71no—
365#2590—71no—
366#2585—71no—
367#2575—71no—
368#2560—71no—
369#2553—71no—
370#2528—71no—
371#2527D711yescharacteristic, complemented
372#2522—71no—
373#2520—71no—
374#2478—71no—
375#2477—71no—
376#2469—71no—
377#2458—71no—
378#2439—71no—
379#2413—71no—
380#2374—71no—
381#2373—71no—
382#2373—71no—
383#2365—71no—
384#2360—71no—
385#2360—71no—
386C4×C4⋊Q8—71no—
387#2298—71no—
388#2298—71no—
389C24×C7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C2×C7×Q8—22no—
392C2×C7×Q8—22no—
393C2×C7×Q8—41no—
394C22×C4×C7—22no—
395C22×C4×C7—41no—
396C22×C4×C7—41no—
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
409C22×C4×C7C2411yescharacteristic
410C22×C4×C7C2411yescharacteristic
411C2×C22⋊D7—22no—
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—
438C2×Dic14—22no—
439C2×Dic14—22no—
440C2×Dic14—22no—
441C2×Dic14—22no—
442C2×Dic14—41no—
443C2×Dic14—41no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—41no—
447C7×C4⋊C4—41no—
448C7×C4⋊C4—41no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—22no—
451C7×C22⋊C4—22no—
452C7×C22⋊C4—22no—
453C7×C22⋊C4—22no—
454C7×C22⋊C4—41no—
455C42×C7—22no—
456C42×C7—22no—
457C42×C7—41no—
458C42×C7—41no—
459C22⋊Dic7—22no—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—22no—
463C22⋊Dic7#4114yes—
464(C2×D7)⋊C4—22no—
465(C2×D7)⋊C4—22no—
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—22no—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—41no—
474(C2×D7)⋊C4—41no—
475(C2×D7)⋊C4—41no—
476(C2×D7)⋊C4—41no—
477C4⋊Dic7—22no—
478C4⋊Dic7—22no—
479C4⋊Dic7—22no—
480C4⋊Dic7—22no—
481C4⋊Dic7—22no—
482C4⋊Dic7—22no—
483C4⋊Dic7—41no—
484C4⋊Dic7—41no—
485C4⋊Dic7—41no—
486C4⋊Dic7—41no—
487Dic7⋊C4—22no—
488Dic7⋊C4—22no—
489Dic7⋊C4—22no—
490Dic7⋊C4—22no—
491Dic7⋊C4—22no—
492Dic7⋊C4—22no—
493Dic7⋊C4—22no—
494Dic7⋊C4—22no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
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—22no—
507Dic7⋊C4—41no—
508Dic7⋊C4—41no—
509Dic7⋊C4—41no—
510Dic7⋊C4—41no—
511Dic7⋊C4—41no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4#4114yes—
515Dic7⋊C4#4114yes—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—22no—
525C4×Dic7—22no—
526C4×Dic7—22no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C4×Dic7—41no—
532C4×Dic7—41no—
533C4×Dic7—41no—
534C4×Dic7—41no—
535C2×C4⋊Q8—71no—
536C2×C4⋊Q8—71no—
537C2×#126—71no—
538C2×#126—71no—
539C2×#126—71no—
540C2×#123—71no—
541C2×#123—71no—
542C2×C22⋊Q8—71no—
543C2×C22⋊Q8—71no—
544C2×C4×Q8—71no—
545C2×C4×Q8—71no—
546C2×C4×Q8—71no—
547C2×#117—71no—
548C2×#117—71no—
549C22×C4⋊C4—71no—
550#401C2×D711yescharacteristic
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400C2×D711yescharacteristic
556#399—71no—
557#399—71no—
558#398—71no—
559#398—71no—
560#398—71no—
561#398—71no—
562#398—71no—
563#398—71no—
564#398—71no—
565#398—71no—
566#398—71no—
567#398—71no—
568#397—71no—
569#397—71no—
570#397C2×D711yescharacteristic
571#396—71no—
572#396—71no—
573#396—71no—
574#395—71no—
575#395—71no—
576#394—71no—
577#394—71no—
578#393—71no—
579#393—71no—
580#393—71no—
581#393C2×D711yescharacteristic
582#391—71no—
583#391—71no—
584#391—71no—
585#391—71no—
586#391C2×D711yescharacteristic
587#391C2×D711yescharacteristic
588#390—71no—
589#389—71no—
590#389—71no—
591#389—71no—
592#389—71no—
593#389—71no—
594#389—71no—
595#389—71no—
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—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#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#388C2×D711yescharacteristic
620#388C2×D711yescharacteristic
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#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#387C2×D711yescharacteristic
650#387C2×D711yescharacteristic
651#387C2×D711yescharacteristic
652#386—71no—
653#386—71no—
654#385—71no—
655#385—71no—
656#385—71no—
657#385—71no—
658#385—71no—
659#385C2×D711yescharacteristic
660#384—71no—
661#382—71no—
662#382—71no—
663#381C2×D711yescharacteristic
664#380—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×C4⋊C4—71no—
673C4×C4⋊C4—71no—
674C4×C4⋊C4—71no—
675C4×C4⋊C4—71no—
676C4×C4⋊C4—71no—
677C4×C22⋊C4—71no—
678C4×C22⋊C4—71no—
679C4×C22⋊C4—71no—
680C4×C22⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C4×C22⋊C4—71no—
685C4×C22⋊C4C2×D711yescharacteristic
686#376—71no—
687#376—71no—
688#376C2×D711yescharacteristic
689C43—71no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7C2×#4112yes—
697C23×C7C2511yescharacteristic
698C22×D7—21no—
699C22×D7—21no—
700C22×D7—21no—
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C7×Q8—44no—
706C2×C4×C7—21no—
707C2×C4×C7—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—82no—
746C2×C4×C7C2×#4112yes—
747C2×C4×C7C2×#4112yes—
748C2×C4×C72−1+412yes—
749C22⋊D7—82no—
750C2×Dic7—21no—
751C2×Dic7—21no—
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—44no—
788C2×Dic7—44no—
789C2×Dic7C2×#4112yes—
790C2×Dic7C2×#4112yes—
791C2×Dic7C2×#4112yes—
792C2×Dic7C2×#4112yes—
793C2×Dic7C2×#4112yes—
794C2×Dic7C2×#4112yes—
795C2×Dic7H(5,𝔽2)12yes—
796C2×Dic72−1+412yes—
797C4×D7—44no—
798Dic14—44no—
799Dic14—44no—
800C22×Q8—71no—
801C22×Q8—71no—
802C22×Q8C22×D711yescharacteristic
803C22×D4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4—71no—
807C23×C4C22×D711yescharacteristic
808C4⋊Q8—144no—
809C4⋊Q8—144no—
810#126—144no—
811#126—144no—
812#126—282no—
813#123—144no—
814#123—282no—
815C22⋊Q8—144no—
816C22⋊Q8—144no—
817C4×Q8—282no—
818C4×Q8—282no—
819C4×Q8—282no—
820#117—144no—
821#117—144no—
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⋊C4—71no—
851C2×C4⋊C4—71no—
852C2×C4⋊C4—71no—
853C2×C4⋊C4—71no—
854C2×C4⋊C4—71no—
855C2×C4⋊C4—71no—
856C2×C4⋊C4—71no—
857C2×C4⋊C4—71no—
858C2×C4⋊C4—71no—
859C2×C4⋊C4—71no—
860C2×C4⋊C4—71no—
861C2×C4⋊C4—282no—
862C2×C4⋊C4C22×D711yescharacteristic
863C2×C4⋊C4C22×D711yescharacteristic
864C2×C4⋊C4C22×D711yescharacteristic
865C2×C4⋊C4C22×D711yescharacteristic
866C2×C4⋊C4C22×D711yescharacteristic
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⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
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×C42—71no—
908C2×C42—71no—
909C2×C42—71no—
910C2×C42C22×D711yescharacteristic
911C2×C42C22×D711yescharacteristic
912C2×C42C22×D711yescharacteristic
913C2×C42C22×D711yescharacteristic
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#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
968#95C22×D711yescharacteristic
969#95C22×D711yescharacteristic
970C22×C7—22no—
971C22×C7—22no—
972C22×C7—22no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7C22×#4111yescharacteristic
978C22×C7C22×#4111yescharacteristic
979C22×C7C22×#4111yescharacteristic
980C22×C7C2×H(5,𝔽2)11yescharacteristic
981C22×C7C2×2−1+411yescharacteristic
982C22×C7C2×2−1+411yescharacteristic
983C22×C7#58511yescharacteristic
984C2×D7—41no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C4×C7—22no—
992C4×C7—22no—
993C4×C7—22no—
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—
1005Dic7—22no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—22no—
1011Dic7—22no—
1012Dic7—22no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020C24—71no—
1021C24C23×D711yescharacteristic
1022C2×Q8—22no—
1023C2×Q8—22no—
1024C2×Q8—41no—
1025C2×Q8—142no—
1026C2×Q8—142no—
1027C2×Q8—142no—
1028C2×Q8—142no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×D4—142no—
1032C2×D4—281no—
1033C2×D4—281no—
1034C22×C4—22no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—71no—
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—142no—
1053C22×C4—142no—
1054C22×C4—142no—
1055C22×C4—142no—
1056C22×C4—142no—
1057C22×C4—142no—
1058C22×C4—281no—
1059C22×C4—281no—
1060C22×C4—281no—
1061C22×C4C23×D711yescharacteristic
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—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—74no—
1081C4⋊C4—74no—
1082C4⋊C4—142no—
1083C4⋊C4—142no—
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—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—142no—
1106C4⋊C4—142no—
1107C4⋊C4—142no—
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—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—41no—
1125C22⋊C4—74no—
1126C22⋊C4—142no—
1127C22⋊C4—142no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
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—281no—
1140C22⋊C4—281no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C42—22no—
1144C42—22no—
1145C42—41no—
1146C42—41no—
1147C42—142no—
1148C42—142no—
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—
1166C2×C7—42no—
1167C2×C7#348111yescharacteristic
1168C2×C7#348211yescharacteristic
1169C2×C7#348211yescharacteristic
1170C2×C7#349411yescharacteristic
1171C2×C7#349511yescharacteristic
1172C2×C7#350711yescharacteristic
1173C2×C7#355211yescharacteristic
1174D7—81no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—141no—
1182C23—141no—
1183C23—141no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23D7×#4112yes—
1189C23C24×D711yescharacteristic
1190Q8—44no—
1191Q8—284no—
1192Q8—284no—
1193D4—562no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
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—72no—
1234C2×C4—72no—
1235C2×C4—72no—
1236C2×C4—72no—
1237C2×C4—72no—
1238C2×C4—72no—
1239C2×C4—72no—
1240C2×C4—72no—
1241C2×C4—82no—
1242C2×C4—141no—
1243C2×C4—141no—
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—284no—
1280C2×C4—284no—
1281C2×C4—284no—
1282C2×C4D7×#4112yes—
1283C2×C4D7×#4112yes—
1284C2×C4#655412yes—
1285C7#6004111yescharacteristic, complemented, Sylow
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—281no—
1294C22—281no—
1295C22—281no—
1296C22—281no—
1297C22—281no—
1298C22—281no—
1299C22—281no—
1300C22C2×D7×#4111yescharacteristic
1301C22C2×D7×#4111yescharacteristic
1302C22C2×D7×#4111yescharacteristic
1303C22C2×#655411yescharacteristic
1304C22#9061611yescharacteristic
1305C22D7×H(5,𝔽2)11yescharacteristic
1306C22D7×2−1+411yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—142no—
1322C4—142no—
1323C4—142no—
1324C4—142no—
1325C4—142no—
1326C4—142no—
1327C4—142no—
1328C4—142no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C4—281no—
1333C4—281no—
1334C4—281no—
1335C4—281no—
1336C2—42no—
1337C2—561no—
1338C2#1174322211yescharacteristic
1339C2#1174322511yescharacteristic
1340C2#1174363411yescharacteristic
1341C2#1174385911yescharacteristic
1342C2#1174386011yescharacteristic
1343C2#1174389611yescharacteristic
1344C2#1174407511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2527C2
prime radicalC22×C22⋊D7C23
hypercenter#2527D7
hypocenterC7#60041
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2527

Complements

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

NH ≅ G/Ntype
1. C7×#2527C2semidirect
2. #11735860C2semidirect
3. #11735858C2semidirect
4. #11735743C2semidirect
5. #11735584C2semidirect
7. #11734924C2semidirect
8. #11734268C2semidirect
10. #11734015C2semidirect
11. #11733946C2semidirect
12. #11733937C2semidirect
13. #11733926C2semidirect
16. #11732930C2semidirect
17. #11732896C2semidirect
18. #11732794C2semidirect
19. #11732571C2semidirect
20. #11732557C2semidirect
21. #11732538C2semidirect
22. #11732483C2semidirect
23. #11732418C2semidirect
25. #11731841C2semidirect
26. #11731531C2semidirect
29. #11730911C2semidirect
30. #11730851C2semidirect
31. #11730830C2semidirect
371. #2527D7semidirect
1285. C7#60041semidirect

Maximal subgroups

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

subgroupindex
C7×#25272
#117358602
#117358582
#117357432
#117355842
#117349632
#117349242
#117342682
#117342292
#117340152
#117339462
#117339372
#117339262
#117330392
#117329792
#117329302
#117328962
#117327942
#117325712
#117325572
#117325382
#117324832
#117324182
#117319782
#117318412
#117315312
#117315092
#117309232
#117309112
#117308512
#117308302
#600417