Finite Group Databasebeta

← #13527386

Subgroups — #13527386

Order 1792.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2577C211yesmaximal, characteristic, complemented
2#11735668C211yesmaximal, characteristic, complemented
3#11735598C211yesmaximal, characteristic, complemented
4#11735275C211yesmaximal, characteristic, complemented
5#11735193C211yesmaximal, characteristic, complemented
6#11734991C211yesmaximal, characteristic
7#11734991C211yesmaximal, characteristic
8#11734934C211yesmaximal, characteristic, complemented
9#11734909C211yesmaximal, characteristic, complemented
10#11732988C211yesmaximal, characteristic
11#11732941C211yesmaximal, characteristic
12#11732909C211yesmaximal, characteristic, complemented
13#11732908C211yesmaximal, characteristic, complemented
14#11732795C211yesmaximal, characteristic, complemented
15#11732737C211yesmaximal, characteristic, complemented
16#11732548C211yesmaximal, characteristic, complemented
17#11732470C211yesmaximal, characteristic, complemented
18#11732428C211yesmaximal, characteristic, complemented
19#11732405C211yesmaximal, characteristic, complemented
20#11732403C211yesmaximal, characteristic, complemented
21#11732386C211yesmaximal, characteristic, complemented
22#11732034C211yesmaximal, characteristic, complemented
23#11731875C211yesmaximal, characteristic
24#11731747C211yesmaximal, characteristic, complemented
25#11731738C211yesmaximal, characteristic, complemented
26#11731446C211yesmaximal, characteristic, complemented
27#11731350C211yesmaximal, characteristic
28#11731200C211yesmaximal, characteristic, complemented
29#11731177C211yesmaximal, characteristic, complemented
30#11730990C211yesmaximal, characteristic, complemented
31C4×(C22⋊D7)⋊C4C211yesmaximal, characteristic
32C2×C4×C22⋊D7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C2×#6459C2211yescharacteristic
35C2×#6453C2211yescharacteristic
36C2×#6452C2211yescharacteristic
37C2×#6451C2211yescharacteristic
38C2×#6450C2211yescharacteristic
39C2×(C22⋊D7)⋊C4C2211yescharacteristic
40C2×(C22⋊D7)⋊C4C2211yescharacteristic
41C2×#6441C2211yescharacteristic
42C2×#6441C2211yescharacteristic
43C2×#6441C2211yescharacteristic
44C2×#6435C2211yescharacteristic
45C2×#6435C2211yescharacteristic
46C2×C42×D7C2211yescharacteristic
47C7×#400C2211yescharacteristic
48C7×#398C2211yescharacteristic
49C7×#397C2211yescharacteristic
50C7×#397C2211yescharacteristic
51C7×#388C2211yescharacteristic
52C7×#388C2211yescharacteristic
53C7×#387C2211yescharacteristic
54C7×#387C2211yescharacteristic
55C7×#387C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C7×#385C2211yescharacteristic
58C7×#383C2211yescharacteristic
59C7×#380C2211yescharacteristic
60C4×C7×C4⋊C4C2211yescharacteristic
61C4×C7×C22⋊C4C2211yescharacteristic
62#89984C2211yescharacteristic
63#89982C2211yescharacteristic
64#89766C2211yescharacteristic
65#89766C2211yescharacteristic
66#89765C2211yescharacteristic
67#89765C2211yescharacteristic
68#89761C2211yescharacteristic
69#89761C2211yescharacteristic
70#89761C2211yescharacteristic
71#89758C2211yescharacteristic
72#89757C2211yescharacteristic
73#89754C2211yescharacteristic
74#89753C2211yescharacteristic
75#89753C2211yescharacteristic
76#89753C2211yescharacteristic
77#89751C2211yescharacteristic
78#89751C2211yescharacteristic
79#89750C2211yescharacteristic
80#89750C2211yescharacteristic
81#89750C2211yescharacteristic
82#89748C2211yescharacteristic
83C4⋊C4×Dic7C2211yescharacteristic
84#89746C2211yescharacteristic
85#89745C2211yescharacteristic
86#89744C2211yescharacteristic
87#89744C2211yescharacteristic
88#89744C2211yescharacteristic
89#89744C2211yescharacteristic
90#89744C2211yescharacteristic
91#89733C2211yescharacteristic
92#89733C2211yescharacteristic
93#89731C2211yescharacteristic
94#89731C2211yescharacteristic
95#89724C2211yescharacteristic
96#89724C2211yescharacteristic
97#89723C2211yescharacteristic
98#89723C2211yescharacteristic
99#89717C2211yescharacteristic
100#89717C2211yescharacteristic
101#89716C2211yescharacteristic
102#89716C2211yescharacteristic
103#89715C2211yescharacteristic
104#89715C2211yescharacteristic
105#89714C2211yescharacteristic
106#89714C2211yescharacteristic
107#89714C2211yescharacteristic
108C22⋊C4×Dic7C2211yescharacteristic
109C22⋊C4×Dic7C2211yescharacteristic
110C4×(C2×D7)⋊C4C2211yescharacteristic
111#89709C2211yescharacteristic
112C4×C4⋊Dic7C2211yescharacteristic
113#89705C2211yescharacteristic
114#89705C2211yescharacteristic
115#89705C2211yescharacteristic
116#89705C2211yescharacteristic
117C4×Dic7⋊C4C2211yescharacteristic
118C4×Dic7⋊C4C2211yescharacteristic
119C4×Dic7⋊C4C2211yescharacteristic
120C42×Dic7C2211yescharacteristic
121#89701C2211yescharacteristic
122#89700C2211yescharacteristic
123#89447C2211yescharacteristic
124#89447C2211yescharacteristic
125#89447C2211yescharacteristic
126#89447C2211yescharacteristic
127#89446C2211yescharacteristic
128#89446C2211yescharacteristic
129#89445C2211yescharacteristic
130#89445C2211yescharacteristic
131#89440C2211yescharacteristic
132#89440C2211yescharacteristic
133#89440C2211yescharacteristic
134#89439C2211yescharacteristic
135#89438C2211yescharacteristic
136#89438C2211yescharacteristic
137#89438C2211yescharacteristic
138#89438C2211yescharacteristic
139#89432C2211yescharacteristic
140#89431C2211yescharacteristic
141#89430C2211yescharacteristic
142#89429C2211yescharacteristic
143#89429C2211yescharacteristic
144#89429C2211yescharacteristic
145#89427C2211yescharacteristic
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#89425C2211yescharacteristic
160#89425C2211yescharacteristic
161#89424C2211yescharacteristic
162#89424C2211yescharacteristic
163#89424C2211yescharacteristic
164#89424C2211yescharacteristic
165#89423C2211yescharacteristic
166#89423C2211yescharacteristic
167#89422C2211yescharacteristic
168#89422C2211yescharacteristic
169#89421C2211yescharacteristic
170#89421C2211yescharacteristic
171#89421C2211yescharacteristic
172#89421C2211yescharacteristic
173#89419C2211yescharacteristic
174#89419C2211yescharacteristic
175#89419C2211yescharacteristic
176#89419C2211yescharacteristic
177#89419C2211yescharacteristic
178#89419C2211yescharacteristic
179#89418C2211yescharacteristic
180#89418C2211yescharacteristic
181#89418C2211yescharacteristic
182#89418C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#35039—71nomaximal, Sylow
188C23×C4×C7C2311yescharacteristic
189C22×C22⋊D7C2311yescharacteristic
190C23×Dic7C2311yescharacteristic
191C23×Dic7C2311yescharacteristic
192C22×C4×D7C2311yescharacteristic
193C22×C4×D7C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×Dic14C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C42×C7C2311yescharacteristic
215C2×C42×C7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C4×C22⋊D7—24no—
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×Dic7⋊C4C2311yescharacteristic
243C2×Dic7⋊C4C2311yescharacteristic
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×C4×Dic7—42no—
268C2×C4×Dic7C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285#6459—24no—
286#6453—24no—
287#6452—24no—
288#6451—42no—
289#6450—42no—
290(C22⋊D7)⋊C4—24no—
291(C22⋊D7)⋊C4—24no—
292#6441—24no—
293#6441—24no—
294#6441—42no—
295#6435—24no—
296#6435—42no—
297C42×D7—42no—
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
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356C7⋊#95C2311yescharacteristic
357C7⋊#95C2311yescharacteristic
358#2864—71no—
359#2863—71no—
360#2857—71no—
361#2855—71no—
362#2652—71no—
363#2652—71no—
364#2638—71no—
365#2638—71no—
366#2588—71no—
367#2588—71no—
368#2577—71no—
369#2577D711yescharacteristic, complemented
370#2523—71no—
371#2523—71no—
372#2506—71no—
373#2499—71no—
374#2495—71no—
375#2485—71no—
376#2460—71no—
377#2460—71no—
378#2451—71no—
379#2439—71no—
380#2421—71no—
381#2415—71no—
382#2336—71no—
383#2336—71no—
384#2332—71no—
385#2332—71no—
386C4×C22⋊Q8—71no—
387#2296—71no—
388C42×D4—71no—
389C24×C7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C22×C4×C7—22no—
392C22×C4×C7—22no—
393C22×C4×C7—41no—
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
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—22no—
411C22×Dic7—22no—
412C22×Dic7—22no—
413C22×Dic7—22no—
414C22×Dic7—41no—
415C22×Dic7—41no—
416C22×Dic7#4114yes—
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C22×Dic7C2411yescharacteristic
431C22×Dic7C2411yescharacteristic
432C2×C4×D7—22no—
433C2×C4×D7—22no—
434C2×C4×D7—22no—
435C2×C4×D7—22no—
436C2×C4×D7—22no—
437C2×C4×D7—41no—
438C2×C4×D7—41no—
439C2×C4×D7—41no—
440C2×C4×D7#4114yes—
441C2×Dic14—22no—
442C2×Dic14—22no—
443C2×Dic14—22no—
444C2×Dic14—22no—
445C2×Dic14—22no—
446C2×Dic14—41no—
447C2×Dic14—41no—
448C2×Dic14—41no—
449C2×Dic14—41no—
450C7×C4⋊C4—22no—
451C7×C4⋊C4—22no—
452C7×C4⋊C4—22no—
453C7×C4⋊C4—22no—
454C7×C4⋊C4—41no—
455C7×C4⋊C4—41no—
456C7×C4⋊C4—41no—
457C7×C4⋊C4—41no—
458C7×C22⋊C4—22no—
459C7×C22⋊C4—22no—
460C7×C22⋊C4—22no—
461C7×C22⋊C4—22no—
462C7×C22⋊C4—41no—
463C7×C22⋊C4—41no—
464C42×C7—22no—
465C42×C7—22no—
466C42×C7—41no—
467C42×C7—41no—
468C22⋊Dic7—22no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—41no—
472C22⋊Dic7—41no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—22no—
475(C2×D7)⋊C4—22no—
476(C2×D7)⋊C4—22no—
477(C2×D7)⋊C4—22no—
478(C2×D7)⋊C4—22no—
479(C2×D7)⋊C4—22no—
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—
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—22no—
508Dic7⋊C4—22no—
509Dic7⋊C4—22no—
510Dic7⋊C4—22no—
511Dic7⋊C4—22no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4—41no—
515Dic7⋊C4—41no—
516Dic7⋊C4—41no—
517Dic7⋊C4#4114yes—
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—22no—
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×#125—71no—
537C2×#125—71no—
538C2×C22⋊Q8—71no—
539C2×C22⋊Q8—71no—
540C2×C22⋊Q8—71no—
541C2×C22⋊Q8—71no—
542C2×C4×Q8—71no—
543C2×C4×D4—71no—
544C2×C4×D4—71no—
545C2×C4×D4—71no—
546C2×#117—71no—
547C2×#117—71no—
548C22×C42—71no—
549C22×C42—71no—
550#400—71no—
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400C2×D711yescharacteristic
556#398—71no—
557#398—71no—
558#398—71no—
559#398C2×D711yescharacteristic
560#397—71no—
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#394—71no—
577#394—71no—
578#394—71no—
579#394—71no—
580#393—71no—
581#393—71no—
582#391—71no—
583#391—71no—
584#391—71no—
585#391—71no—
586#391—71no—
587#391—71no—
588#391—71no—
589#391—71no—
590#391—71no—
591#391—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#389—71no—
603#389—71no—
604#389—71no—
605#389—71no—
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388—71no—
611#388—71no—
612#388C2×D711yescharacteristic
613#388C2×D711yescharacteristic
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#387—71no—
640#387—71no—
641#387—71no—
642#387—71no—
643#387—71no—
644#387C2×D711yescharacteristic
645#387C2×D711yescharacteristic
646#387C2×D711yescharacteristic
647#387C2×D711yescharacteristic
648#385—71no—
649#385—71no—
650#385—71no—
651#385—71no—
652#385—71no—
653#385—71no—
654#385—71no—
655#385C2×D711yescharacteristic
656#384—71no—
657#383—71no—
658#383—71no—
659#383—71no—
660#383C2×D711yescharacteristic
661#382—71no—
662#382—71no—
663#381—71no—
664#381—71no—
665#380—71no—
666#380—71no—
667#380—71no—
668#380—71no—
669#380—71no—
670#380C2×D711yescharacteristic
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×C4⋊C4—71no—
678C4×C4⋊C4—71no—
679C4×C4⋊C4—71no—
680C4×C4⋊C4C2×D711yescharacteristic
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C4×C22⋊C4—71no—
685C4×C22⋊C4—71no—
686C4×C22⋊C4—71no—
687C4×C22⋊C4—71no—
688C4×C22⋊C4C2×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×D7C2×#4112yes—
705C2×C4×C7—21no—
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—44no—
745C2×C4×C7C2×#4112yes—
746C2×C4×C7C2×#4112yes—
747C2×C4×C72−1+412yes—
748C22⋊D7—28no—
749C2×Dic7—21no—
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×Dic7H(5,𝔽2)12yes—
795C2×Dic72−1+412yes—
796C4×D7—28no—
797C4×D7—44no—
798C4×D7—44no—
799Dic14—44no—
800Dic14—82no—
801Dic14—82no—
802C22×Q8—71no—
803C22×Q8—71no—
804C22×Q8—71no—
805C22×D4—71no—
806C23×C4—71no—
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4C22×D711yescharacteristic
812C4⋊Q8—282no—
813#125—144no—
814#125—144no—
815C22⋊Q8—144no—
816C22⋊Q8—144no—
817C22⋊Q8—144no—
818C22⋊Q8—282no—
819C4×Q8—282no—
820C4×D4—144no—
821C4×D4—144no—
822C4×D4—144no—
823#117—144no—
824#117—282no—
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⋊C4C22×D711yescharacteristic
860C2×C4⋊C4C22×D711yescharacteristic
861C2×C4⋊C4C22×D711yescharacteristic
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⋊C4C22×D711yescharacteristic
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C22⋊C4C22×D711yescharacteristic
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—282no—
907C2×C42—282no—
908C2×C42C22×D711yescharacteristic
909C2×C42C22×D711yescharacteristic
910C2×C42C22×D711yescharacteristic
911C2×C42C22×D711yescharacteristic
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#95—71no—
955#95—71no—
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
970#95C22×D711yescharacteristic
971#95C22×D711yescharacteristic
972C22×C7—22no—
973C22×C7—22no—
974C22×C7—22no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7—41no—
978C22×C7—41no—
979C22×C7C22×#4111yescharacteristic
980C22×C7C22×#4111yescharacteristic
981C22×C7C22×#4111yescharacteristic
982C22×C7C2×H(5,𝔽2)11yescharacteristic
983C22×C7C2×2−1+411yescharacteristic
984C22×C7C2×2−1+411yescharacteristic
985C22×C7#58511yescharacteristic
986C2×D7—22no—
987C2×D7—22no—
988C2×D7—22no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
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—
1005C4×C7—41no—
1006C4×C7—41no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—22no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7#53914yes—
1022C24—71no—
1023C24C23×D711yescharacteristic
1024C2×Q8—142no—
1025C2×Q8—142no—
1026C2×Q8—142no—
1027C2×Q8—142no—
1028C2×Q8—142no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×Q8—281no—
1032C2×Q8—281no—
1033C2×D4—142no—
1034C2×D4—142no—
1035C2×D4—142no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—41no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—74no—
1045C22×C4—74no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—71no—
1055C22×C4—71no—
1056C22×C4—142no—
1057C22×C4—142no—
1058C22×C4—142no—
1059C22×C4—142no—
1060C22×C4—142no—
1061C22×C4—142no—
1062C22×C4—142no—
1063C22×C4—142no—
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—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—74no—
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—142no—
1109C4⋊C4—142no—
1110C4⋊C4—142no—
1111C4⋊C4—142no—
1112C4⋊C4—142no—
1113C4⋊C4—142no—
1114C4⋊C4—142no—
1115C4⋊C4—142no—
1116C4⋊C4—142no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C4⋊C4—281no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—142no—
1137C22⋊C4—142no—
1138C22⋊C4—142no—
1139C22⋊C4—142no—
1140C22⋊C4—142no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C22⋊C4—281no—
1147C42—22no—
1148C42—22no—
1149C42—41no—
1150C42—41no—
1151C42—142no—
1152C42—142no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—42no—
1169C2×C7#344411yescharacteristic
1170C2×C7C2×#53911yescharacteristic
1171C2×C7#346111yescharacteristic
1172C2×C7#350511yescharacteristic
1173C2×C7#350911yescharacteristic
1174C2×C7#351811yescharacteristic
1175C2×C7#352011yescharacteristic
1176D7—42no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—72no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23—141no—
1189C23—141no—
1190C23D7×#4112yes—
1191C23C24×D711yescharacteristic
1192Q8—284no—
1193Q8—562no—
1194Q8—562no—
1195D4—148no—
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—21no—
1234C2×C4—21no—
1235C2×C4—44no—
1236C2×C4—72no—
1237C2×C4—72no—
1238C2×C4—72no—
1239C2×C4—72no—
1240C2×C4—72no—
1241C2×C4—72no—
1242C2×C4—72no—
1243C2×C4—148no—
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—284no—
1283C2×C4—284no—
1284C2×C4—284no—
1285C2×C4—284no—
1286C2×C4D7×#4112yes—
1287C2×C4D7×#4112yes—
1288C2×C4#655412yes—
1289C7#3503911yescharacteristic, complemented, Sylow
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—142no—
1298C22—142no—
1299C22—142no—
1300C22—281no—
1301C22—281no—
1302C22—281no—
1303C22—281no—
1304C22C2×D7×#4111yescharacteristic
1305C22C2×D7×#4111yescharacteristic
1306C22C2×D7×#4111yescharacteristic
1307C22C2×#655411yescharacteristic
1308C22#9061611yescharacteristic
1309C22D7×H(5,𝔽2)11yescharacteristic
1310C22D7×2−1+411yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—74no—
1326C4—142no—
1327C4—142no—
1328C4—142no—
1329C4—142no—
1330C4—281no—
1331C4—281no—
1332C4—281no—
1333C4—281no—
1334C4—281no—
1335C4—281no—
1336C4—281no—
1337C4—281no—
1338C4—281no—
1339C4—281no—
1340C2—42no—
1341C2—282no—
1342C2#1174318711yescharacteristic
1343C2#1174321711yescharacteristic
1344C2D7×#53911yescharacteristic
1345C2#1174386611yescharacteristic
1346C2#1174390011yescharacteristic
1347C2#1174398011yescharacteristic
1348C2#1174405611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2577C2
prime radicalC22×C22⋊D7C23
hypercenter#2577D7
hypocenterC7#35039
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2577

Complements

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

NH ≅ G/Ntype
1. C7×#2577C2semidirect
2. #11735668C2semidirect
3. #11735598C2semidirect
4. #11735275C2semidirect
5. #11735193C2semidirect
8. #11734934C2semidirect
9. #11734909C2semidirect
12. #11732909C2semidirect
13. #11732908C2semidirect
14. #11732795C2semidirect
15. #11732737C2semidirect
16. #11732548C2semidirect
17. #11732470C2semidirect
18. #11732428C2semidirect
19. #11732405C2semidirect
20. #11732403C2semidirect
21. #11732386C2semidirect
22. #11732034C2semidirect
24. #11731747C2semidirect
25. #11731738C2semidirect
26. #11731446C2semidirect
28. #11731200C2semidirect
29. #11731177C2semidirect
30. #11730990C2semidirect
369. #2577D7semidirect
1289. C7#35039semidirect

Maximal subgroups

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

subgroupindex
C7×#25772
#117356682
#117355982
#117352752
#117351932
#117349912
#117349342
#117349092
#117329882
#117329412
#117329092
#117329082
#117327952
#117327372
#117325482
#117324702
#117324282
#117324052
#117324032
#117323862
#117320342
#117318752
#117317472
#117317382
#117314462
#117313502
#117312002
#117311772
#117309902
C4×(C22⋊D7)⋊C42
#350397