Finite Group Databasebeta

← #13563558

Subgroups — #13563558

Order 1792.

1602 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×#2329C211yesmaximal, characteristic, complemented
2#11740260C211yesmaximal, characteristic
3#11740230C211yesmaximal, characteristic, complemented
4#11734093C211yesmaximal, characteristic, complemented
5#11734025C211yesmaximal, characteristic, complemented
6#11734023C211yesmaximal, characteristic, complemented
7#11734011C211yesmaximal, characteristic, complemented
8#11733623C211yesmaximal, characteristic, complemented
9#11733619C211yesmaximal, characteristic, complemented
10#11733570C211yesmaximal, characteristic, complemented
11#11733567C211yesmaximal, characteristic, complemented
12#11732851C211yesmaximal, characteristic, complemented
13#11732675C211yesmaximal, characteristic, complemented
14#11732663C211yesmaximal, characteristic, complemented
15#11732649C211yesmaximal, characteristic, complemented
16#11732620C211yesmaximal, characteristic, complemented
17#11732618C211yesmaximal, characteristic, complemented
18#11732613C211yesmaximal, characteristic, complemented
19#11732612C211yesmaximal, characteristic, complemented
20#11732070C211yesmaximal, characteristic
21#11732032C211yesmaximal, characteristic
22#11732031C211yesmaximal, characteristic, complemented
23#11731949C211yesmaximal, characteristic, complemented
24#11731394C211yesmaximal, characteristic
25#11731346C211yesmaximal, characteristic, complemented
26#11730948C211yesmaximal, characteristic
27#11730948C211yesmaximal, characteristic
28#11730946C211yesmaximal, characteristic, complemented
29#11730946C211yesmaximal, characteristic, complemented
30#11730812C211yesmaximal, characteristic
31C2×#89419C211yesmaximal, characteristic, complemented
32C2×C7×C22⋊Q8C2211yescharacteristic
33C2×#6509C2211yescharacteristic
34C2×C4×C22⋊D7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6461C2211yescharacteristic
41C2×#6453C2211yescharacteristic
42C2×#6452C2211yescharacteristic
43C2×#6439C2211yescharacteristic
44C2×#6439C2211yescharacteristic
45C2×#6433C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47C7×#391C2211yescharacteristic
48C7×#391C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#389C2211yescharacteristic
51C7×#387C2211yescharacteristic
52C7×#387C2211yescharacteristic
53C7×#387C2211yescharacteristic
54C7×#387C2211yescharacteristic
55C7×#385C2211yescharacteristic
56C7×#385C2211yescharacteristic
57C7×#380C2211yescharacteristic
58C4×C7×C22⋊C4C2211yescharacteristic
59C4×C7×C22⋊C4C2211yescharacteristic
60C2×C7×#95C2211yescharacteristic
61#90002C2211yescharacteristic
62#90001C2211yescharacteristic
63#90001C2211yescharacteristic
64#89985C2211yescharacteristic
65#89985C2211yescharacteristic
66#89982C2211yescharacteristic
67#89982C2211yescharacteristic
68C4×C22⋊Dic7C2211yescharacteristic
69C2×C7⋊#95C2211yescharacteristic
70#89766C2211yescharacteristic
71#89766C2211yescharacteristic
72#89766C2211yescharacteristic
73#89766C2211yescharacteristic
74#89766C2211yescharacteristic
75#89765C2211yescharacteristic
76#89762C2211yescharacteristic
77#89759C2211yescharacteristic
78#89758C2211yescharacteristic
79#89757C2211yescharacteristic
80#89756C2211yescharacteristic
81#89756C2211yescharacteristic
82#89756C2211yescharacteristic
83#89755C2211yescharacteristic
84#89755C2211yescharacteristic
85#89755C2211yescharacteristic
86#89754C2211yescharacteristic
87#89754C2211yescharacteristic
88#89753C2211yescharacteristic
89#89753C2211yescharacteristic
90#89752C2211yescharacteristic
91#89752C2211yescharacteristic
92#89752C2211yescharacteristic
93#89750C2211yescharacteristic
94#89750C2211yescharacteristic
95#89749C2211yescharacteristic
96#89745C2211yescharacteristic
97#89745C2211yescharacteristic
98#89744C2211yescharacteristic
99#89744C2211yescharacteristic
100#89744C2211yescharacteristic
101#89744C2211yescharacteristic
102#89744C2211yescharacteristic
103#89730C2211yescharacteristic
104#89730C2211yescharacteristic
105#89730C2211yescharacteristic
106#89730C2211yescharacteristic
107#89722C2211yescharacteristic
108#89722C2211yescharacteristic
109#89722C2211yescharacteristic
110#89722C2211yescharacteristic
111#89718C2211yescharacteristic
112#89718C2211yescharacteristic
113#89718C2211yescharacteristic
114#89718C2211yescharacteristic
115#89714C2211yescharacteristic
116#89714C2211yescharacteristic
117#89714C2211yescharacteristic
118#89714C2211yescharacteristic
119#89712C2211yescharacteristic
120#89712C2211yescharacteristic
121#89705C2211yescharacteristic
122#89705C2211yescharacteristic
123#89705C2211yescharacteristic
124#89705C2211yescharacteristic
125#89705C2211yescharacteristic
126#89705C2211yescharacteristic
127#89705C2211yescharacteristic
128#89705C2211yescharacteristic
129#89700C2211yescharacteristic
130#89700C2211yescharacteristic
131#89448C2211yescharacteristic
132#89448C2211yescharacteristic
133#89447C2211yescharacteristic
134#89447C2211yescharacteristic
135#89447C2211yescharacteristic
136#89446C2211yescharacteristic
137#89442C2211yescharacteristic
138#89441C2211yescharacteristic
139#89441C2211yescharacteristic
140#89441C2211yescharacteristic
141#89440C2211yescharacteristic
142#89440C2211yescharacteristic
143#89439C2211yescharacteristic
144#89436C2211yescharacteristic
145C7⋊#401C2211yescharacteristic
146#89433C2211yescharacteristic
147#89433C2211yescharacteristic
148#89432C2211yescharacteristic
149#89432C2211yescharacteristic
150#89432C2211yescharacteristic
151#89432C2211yescharacteristic
152#89432C2211yescharacteristic
153#89431C2211yescharacteristic
154#89430C2211yescharacteristic
155#89430C2211yescharacteristic
156#89430C2211yescharacteristic
157#89430C2211yescharacteristic
158#89430C2211yescharacteristic
159#89430C2211yescharacteristic
160#89429C2211yescharacteristic
161#89429C2211yescharacteristic
162#89429C2211yescharacteristic
163#89429C2211yescharacteristic
164#89429C2211yescharacteristic
165#89429C2211yescharacteristic
166#89429C2211yescharacteristic
167#89426C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89424C2211yescharacteristic
172#89424C2211yescharacteristic
173#89424C2211yescharacteristic
174#89423C2211yescharacteristic
175#89423C2211yescharacteristic
176#89422C2211yescharacteristic
177#89422C2211yescharacteristic
178#89419C2211yescharacteristic
179#89419C2211yescharacteristic
180#89419C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#36825—71nomaximal, Sylow
188C22×C7×Q8C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C22×C22⋊D7C2311yescharacteristic
193C23×Dic7C2311yescharacteristic
194C23×Dic7C2311yescharacteristic
195C23×Dic7C2311yescharacteristic
196C23×Dic7C2311yescharacteristic
197C22×C4×D7C2311yescharacteristic
198C7×C22⋊Q8—24no—
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×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C42×C7C2311yescharacteristic
215C2×C42×C7C2311yescharacteristic
216C2×C22⋊Dic7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219#6509—42no—
220C4×C22⋊D7—24no—
221C2×(C2×D7)⋊C4C2311yescharacteristic
222C2×(C2×D7)⋊C4C2311yescharacteristic
223C2×(C2×D7)⋊C4C2311yescharacteristic
224C2×(C2×D7)⋊C4C2311yescharacteristic
225C2×(C2×D7)⋊C4C2311yescharacteristic
226C2×(C2×D7)⋊C4C2311yescharacteristic
227C2×(C2×D7)⋊C4C2311yescharacteristic
228C2×(C2×D7)⋊C4C2311yescharacteristic
229C2×(C2×D7)⋊C4C2311yescharacteristic
230C2×(C2×D7)⋊C4C2311yescharacteristic
231C2×(C2×D7)⋊C4C2311yescharacteristic
232C2×(C2×D7)⋊C4C2311yescharacteristic
233C2×(C2×D7)⋊C4C2311yescharacteristic
234C2×C4⋊Dic7—42no—
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×C4⋊Dic7C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×Dic7⋊C4—24no—
248C2×Dic7⋊C4—42no—
249C2×Dic7⋊C4—42no—
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×Dic7⋊C4C2311yescharacteristic
274C2×Dic7⋊C4C2311yescharacteristic
275C2×Dic7⋊C4C2311yescharacteristic
276C2×Dic7⋊C4C2311yescharacteristic
277C2×Dic7⋊C4C2311yescharacteristic
278C2×Dic7⋊C4C2311yescharacteristic
279C2×Dic7⋊C4C2311yescharacteristic
280C2×Dic7⋊C4C2311yescharacteristic
281C2×Dic7⋊C4C2311yescharacteristic
282C2×Dic7⋊C4C2311yescharacteristic
283C2×C4×Dic7—42no—
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291#6461—42no—
292#6453—42no—
293#6452—42no—
294#6439—42no—
295#6439—42no—
296#6433—42no—
297#6433—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#2852—71no—
359#2851—71no—
360#2802—71no—
361#2802—71no—
362#2776—71no—
363#2772—71no—
364#2766—71no—
365#2758—71no—
366#2755—71no—
367#2739—71no—
368#2725—71no—
369#2725—71no—
370#2725—71no—
371#2722—71no—
372#2719—71no—
373#2719—71no—
374#2704—71no—
375#2698—71no—
376#2646—71no—
377#2643—71no—
378#2583—71no—
379#2579—71no—
380#2481—71no—
381#2481—71no—
382#2473—71no—
383#2473—71no—
384#2442—71no—
385#2417—71no—
386#2329D711yescharacteristic, complemented
387#2318—71no—
388C2×#389—71no—
389C24×C7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C2×C7×Q8—22no—
392C2×C7×Q8—41no—
393C2×C7×Q8—41no—
394C22×C4×C7—22no—
395C22×C4×C7—22no—
396C22×C4×C7—41no—
397C22×C4×C7—41no—
398C22×C4×C7—41no—
399C22×C4×C7—41no—
400C22×C4×C7—41no—
401C22×C4×C7—41no—
402C22×C4×C7#4114yes—
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C22×C4×C7C2411yescharacteristic
410C22×C4×C7C2411yescharacteristic
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2411yescharacteristic
413C22×C4×C7C2411yescharacteristic
414C22×C4×C7C2411yescharacteristic
415C22×C4×C7C2411yescharacteristic
416C22×C4×C7C2411yescharacteristic
417C2×C22⋊D7—22no—
418C2×C22⋊D7—22no—
419C2×C22⋊D7—22no—
420C22×Dic7—22no—
421C22×Dic7—22no—
422C22×Dic7—22no—
423C22×Dic7—22no—
424C22×Dic7—22no—
425C22×Dic7—22no—
426C22×Dic7—22no—
427C22×Dic7—41no—
428C22×Dic7—41no—
429C22×Dic7—41no—
430C22×Dic7—41no—
431C22×Dic7—41no—
432C22×Dic7C2411yescharacteristic
433C22×Dic7C2411yescharacteristic
434C22×Dic7C2411yescharacteristic
435C22×Dic7C2411yescharacteristic
436C22×Dic7C2411yescharacteristic
437C22×Dic7C2411yescharacteristic
438C22×Dic7C2411yescharacteristic
439C22×Dic7C2411yescharacteristic
440C22×Dic7C2411yescharacteristic
441C22×Dic7C2411yescharacteristic
442C22×Dic7C2411yescharacteristic
443C22×Dic7C2411yescharacteristic
444C22×Dic7C2411yescharacteristic
445C22×Dic7C2411yescharacteristic
446C22×Dic7C2411yescharacteristic
447C2×C4×D7—22no—
448C2×C4×D7—41no—
449C2×C4×D7—41no—
450C7×C4⋊C4—22no—
451C7×C4⋊C4—22no—
452C7×C4⋊C4—22no—
453C7×C4⋊C4—41no—
454C7×C4⋊C4—41no—
455C7×C4⋊C4—41no—
456C7×C4⋊C4—41no—
457C7×C4⋊C4—41no—
458C7×C4⋊C4—41no—
459C7×C22⋊C4—22no—
460C7×C22⋊C4—22no—
461C7×C22⋊C4—22no—
462C7×C22⋊C4—22no—
463C42×C7—41no—
464C42×C7—41no—
465C42×C7—41no—
466C42×C7—41no—
467C22⋊Dic7—22no—
468C22⋊Dic7—22no—
469C22⋊Dic7—22no—
470(C2×D7)⋊C4—22no—
471(C2×D7)⋊C4—22no—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—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—
483C4⋊Dic7—22no—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—22no—
487C4⋊Dic7—22no—
488C4⋊Dic7—41no—
489C4⋊Dic7—41no—
490C4⋊Dic7—41no—
491C4⋊Dic7—41no—
492C4⋊Dic7—41no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
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—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—
519Dic7⋊C4—41no—
520Dic7⋊C4—41no—
521Dic7⋊C4—41no—
522Dic7⋊C4—41no—
523Dic7⋊C4—41no—
524Dic7⋊C4—41no—
525Dic7⋊C4—41no—
526Dic7⋊C4—41no—
527Dic7⋊C4—41no—
528C4×Dic7—22no—
529C4×Dic7—22no—
530C4×Dic7—22no—
531C4×Dic7—41no—
532C4×Dic7—41no—
533C4×Dic7—41no—
534C4×Dic7—41no—
535C2×#126—71no—
536C2×#126—71no—
537C2×#126—71no—
538C2×#125—71no—
539C2×#125—71no—
540C2×#125—71no—
541C2×#125—71no—
542C2×C22⋊Q8—71no—
543C2×C22⋊Q8C2×D711yescharacteristic
544C2×C4×D4—71no—
545C22×C4⋊C4—71no—
546C22×C4⋊C4—71no—
547C22×C4⋊C4—71no—
548C22×C4⋊C4—71no—
549C22×C42—71no—
550#401—71no—
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400—71no—
556#400—71no—
557#400—71no—
558#400—71no—
559#400—71no—
560#400—71no—
561#400—71no—
562#400—71no—
563#400—71no—
564#400—71no—
565#400—71no—
566#398—71no—
567#398—71no—
568#398—71no—
569#398—71no—
570#398—71no—
571#398—71no—
572#398—71no—
573#398—71no—
574#398—71no—
575#398—71no—
576#398—71no—
577#398—71no—
578#398—71no—
579#398—71no—
580#398—71no—
581#398—71no—
582#398—71no—
583#398—71no—
584#397—71no—
585#397—71no—
586#397—71no—
587#397—71no—
588#397—71no—
589#396—71no—
590#396—71no—
591#396—71no—
592#396—71no—
593#396—71no—
594#396—71no—
595#396—71no—
596#395—71no—
597#395—71no—
598#391—71no—
599#391C2×D711yescharacteristic
600#391C2×D711yescharacteristic
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389—71no—
606#389—71no—
607#389—71no—
608#389—71no—
609#389—71no—
610#389—71no—
611#389—71no—
612#389—71no—
613#389—71no—
614#389—71no—
615#389—71no—
616#389—71no—
617#389—71no—
618#389—71no—
619#389—71no—
620#389C2×D711yescharacteristic
621#389C2×D711yescharacteristic
622#388—71no—
623#388—71no—
624#388—71no—
625#388—71no—
626#388—71no—
627#388—71no—
628#388—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#387C2×D711yescharacteristic
649#387C2×D711yescharacteristic
650#387C2×D711yescharacteristic
651#387C2×D711yescharacteristic
652#386—71no—
653#386—71no—
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#385—71no—
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385—71no—
667#385—71no—
668#385—71no—
669#385—71no—
670#385C2×D711yescharacteristic
671#385C2×D711yescharacteristic
672#383—71no—
673#383—71no—
674#382—71no—
675#382—71no—
676#382—71no—
677#381—71no—
678#380—71no—
679#380—71no—
680#380—71no—
681#380—71no—
682#380—71no—
683#380—71no—
684#380C2×D711yescharacteristic
685C4×C22⋊C4—71no—
686C4×C22⋊C4C2×D711yescharacteristic
687C4×C22⋊C4C2×D711yescharacteristic
688C2×#95—71no—
689C2×#95C2×D711yescharacteristic
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7C2×#4112yes—
695C23×C72−1+412yes—
696C23×C72−1+412yes—
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—82no—
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—21no—
746C2×C4×C7—44no—
747C2×C4×C7—44no—
748C2×C4×C7—82no—
749C2×C4×C7C2×#4112yes—
750C2×C4×C7C2×#4112yes—
751C22⋊D7—44no—
752C2×Dic7—28no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7—21no—
781C2×Dic7—21no—
782C2×Dic7—21no—
783C2×Dic7—21no—
784C2×Dic7—21no—
785C2×Dic7—21no—
786C2×Dic7—21no—
787C2×Dic7—21no—
788C2×Dic7—21no—
789C2×Dic7—21no—
790C2×Dic7—21no—
791C2×Dic7—21no—
792C2×Dic7—21no—
793C2×Dic7—21no—
794C2×Dic7—21no—
795C2×Dic7—44no—
796C2×Dic7—44no—
797C2×Dic7—82no—
798C2×Dic7H(5,𝔽2)12yes—
799C2×Dic7H(5,𝔽2)12yes—
800C2×Dic72−1+412yes—
801C4×D7—82no—
802C22×Q8C22×D711yescharacteristic
803C22×D4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4—71no—
807C23×C4—71no—
808C23×C4—71no—
809C23×C4C22×D711yescharacteristic
810C23×C4C22×D711yescharacteristic
811C23×C4C22×D711yescharacteristic
812#126—282no—
813#126—282no—
814#126—282no—
815#125—282no—
816#125—282no—
817#125—282no—
818#125—282no—
819C22⋊Q8—24no—
820C22⋊Q8—282no—
821C4×D4—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—71no—
862C2×C4⋊C4—71no—
863C2×C4⋊C4—71no—
864C2×C4⋊C4—71no—
865C2×C4⋊C4—71no—
866C2×C4⋊C4—71no—
867C2×C4⋊C4—144no—
868C2×C4⋊C4—282no—
869C2×C4⋊C4—282no—
870C2×C4⋊C4—282no—
871C2×C4⋊C4C22×D711yescharacteristic
872C2×C4⋊C4C22×D711yescharacteristic
873C2×C4⋊C4C22×D711yescharacteristic
874C2×C4⋊C4C22×D711yescharacteristic
875C2×C4⋊C4C22×D711yescharacteristic
876C2×C4⋊C4C22×D711yescharacteristic
877C2×C4⋊C4C22×D711yescharacteristic
878C2×C4⋊C4C22×D711yescharacteristic
879C2×C4⋊C4C22×D711yescharacteristic
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⋊C4—71no—
889C2×C22⋊C4—71no—
890C2×C22⋊C4—71no—
891C2×C22⋊C4—71no—
892C2×C22⋊C4—71no—
893C2×C22⋊C4—71no—
894C2×C22⋊C4—71no—
895C2×C22⋊C4—71no—
896C2×C22⋊C4C22×D711yescharacteristic
897C2×C22⋊C4C22×D711yescharacteristic
898C2×C22⋊C4C22×D711yescharacteristic
899C2×C22⋊C4C22×D711yescharacteristic
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
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#95—71no—
957#95—71no—
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—22no—
976C22×C7—22no—
977C22×C7—22no—
978C22×C7#54114yes—
979C22×C7C22×#4111yescharacteristic
980C22×C7C2×H(5,𝔽2)11yescharacteristic
981C22×C7C2×H(5,𝔽2)11yescharacteristic
982C22×C7C2×2−1+411yescharacteristic
983C22×C7C2×2−1+411yescharacteristic
984C22×C7C2×2−1+411yescharacteristic
985C22×C7#58511yescharacteristic
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
993C4×C7—22no—
994C4×C7—22no—
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—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022C24—71no—
1023C24C23×D711yescharacteristic
1024C2×Q8—22no—
1025C2×Q8—41no—
1026C2×Q8—41no—
1027C2×D4—142no—
1028C2×D4—142no—
1029C2×D4—142no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—142no—
1054C22×C4—142no—
1055C22×C4—142no—
1056C22×C4—142no—
1057C22×C4—142no—
1058C22×C4—142no—
1059C22×C4—142no—
1060C22×C4—142no—
1061C22×C4—281no—
1062C22×C4—281no—
1063C22×C4—281no—
1064C22×C4—281no—
1065C22×C4—281no—
1066C22×C4—281no—
1067C22×C4—281no—
1068C22×C4#115714yes—
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—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
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—281no—
1113C4⋊C4—281no—
1114C4⋊C4—281no—
1115C4⋊C4—281no—
1116C4⋊C4—281no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C4⋊C4—281no—
1125C4⋊C4—281no—
1126C4⋊C4—281no—
1127C4⋊C4—281no—
1128C4⋊C4—281no—
1129C4⋊C4—281no—
1130C4⋊C4—281no—
1131C4⋊C4—281no—
1132C4⋊C4—281no—
1133C4⋊C4—281no—
1134C4⋊C4—281no—
1135C4⋊C4—281no—
1136C4⋊C4—281no—
1137C22⋊C4—22no—
1138C22⋊C4—22no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—142no—
1142C22⋊C4—142no—
1143C22⋊C4—142no—
1144C22⋊C4—142no—
1145C22⋊C4—142no—
1146C22⋊C4—142no—
1147C22⋊C4—142no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C22⋊C4—281no—
1155C22⋊C4—281no—
1156C22⋊C4—281no—
1157C42—41no—
1158C42—41no—
1159C42—41no—
1160C42—41no—
1161C42—142no—
1162C42—142no—
1163C42—142no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—24no—
1169C2×C7C2×#54111yescharacteristic
1170C2×C7#349211yescharacteristic
1171C2×C7#350511yescharacteristic
1172C2×C7#353611yescharacteristic
1173C2×C7#354111yescharacteristic
1174C2×C7#355211yescharacteristic
1175C2×C7#356311yescharacteristic
1176D7—81no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—141no—
1182C23—141no—
1183C23—141no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23C2×#115712yes—
1189C23#655112yes—
1190C23#655412yes—
1191C23C24×D711yescharacteristic
1192Q8—82no—
1193D4—284no—
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—21no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—72no—
1237C2×C4—72no—
1238C2×C4—72no—
1239C2×C4—82no—
1240C2×C4—148no—
1241C2×C4—141no—
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—141no—
1280C2×C4—141no—
1281C2×C4—141no—
1282C2×C4—141no—
1283C2×C4—284no—
1284C2×C4—284no—
1285C2×C4—562no—
1286C2×C4—562no—
1287C2×C4C2×#115712yes—
1288C2×C4C2×#115712yes—
1289C7#3682511yescharacteristic, complemented, Sylow
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—281no—
1297C22—281no—
1298C22—281no—
1299C22—281no—
1300C22—281no—
1301C22—281no—
1302C22—281no—
1303C22#9027414yes—
1304C22C22×#115711yescharacteristic
1305C22C2×#655111yescharacteristic
1306C22C2×#655411yescharacteristic
1307C22D7×H(5,𝔽2)11yescharacteristic
1308C22D7×H(5,𝔽2)11yescharacteristic
1309C22#9061811yescharacteristic
1310C22D7×2−1+411yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—142no—
1326C4—142no—
1327C4—142no—
1328C4—281no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C4—281no—
1333C4—281no—
1334C4—281no—
1335C4—281no—
1336C4—281no—
1337C4—281no—
1338C4—281no—
1339C4—281no—
1340C2—24no—
1341C2—561no—
1342C2C2×#9027411yescharacteristic
1343C2#1174292911yescharacteristic
1344C2#1174297011yescharacteristic
1345C2#1174346711yescharacteristic
1346C2#1174350611yescharacteristic
1347C2#1174364311yescharacteristic
1348C2#1174365911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2329C2
prime radicalC22×C22⋊D7C23
hypercenter#2329D7
hypocenterC7#36825
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2329

Complements

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

NH ≅ G/Ntype
1. C7×#2329C2semidirect
3. #11740230C2semidirect
4. #11734093C2semidirect
5. #11734025C2semidirect
6. #11734023C2semidirect
7. #11734011C2semidirect
8. #11733623C2semidirect
9. #11733619C2semidirect
10. #11733570C2semidirect
11. #11733567C2semidirect
12. #11732851C2semidirect
13. #11732675C2semidirect
14. #11732663C2semidirect
15. #11732649C2semidirect
16. #11732620C2semidirect
17. #11732618C2semidirect
18. #11732613C2semidirect
19. #11732612C2semidirect
22. #11732031C2semidirect
23. #11731949C2semidirect
25. #11731346C2semidirect
28. #11730946C2semidirect
29. #11730946C2semidirect
31. C2×#89419C2semidirect
386. #2329D7semidirect
1289. C7#36825semidirect

Maximal subgroups

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

subgroupindex
C7×#23292
#117402602
#117402302
#117340932
#117340252
#117340232
#117340112
#117336232
#117336192
#117335702
#117335672
#117328512
#117326752
#117326632
#117326492
#117326202
#117326182
#117326132
#117326122
#117320702
#117320322
#117320312
#117319492
#117313942
#117313462
#117309482
#117309462
#117308122
C2×#894192
#368257