Finite Group Databasebeta

← #11743700

Subgroups — #11743700

Order 896.

1540 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6554C211yesmaximal, characteristic, complemented
2C2×#6548C211yesmaximal, characteristic, complemented
3C7×#546C211yesmaximal, characteristic, complemented
4#90520C211yesmaximal, characteristic, complemented
5#90497C211yesmaximal, characteristic, complemented
6#90368C211yesmaximal, characteristic, complemented
7D7×#124C211yesmaximal, characteristic, complemented
8#90345C212yesmaximal, complemented
9#90339C212yesmaximal, complemented
10#90324C211yesmaximal, characteristic, complemented
11#90319C211yesmaximal, characteristic, complemented
12#90301C212yesmaximal, complemented
13#90298C211yesmaximal, characteristic, complemented
14#90289C211yesmaximal, characteristic, complemented
15#90287C212yesmaximal, complemented
16#90283C212yesmaximal, complemented
17#90282C212yesmaximal, complemented
18#90245C211yesmaximal, characteristic, complemented
19#90243C211yesmaximal, characteristic, complemented
20#90239C211yesmaximal, characteristic, complemented
21C4×#1159C211yesmaximal, characteristic, complemented
22C2×#6448C212yesmaximal, complemented
23#90181C212yesmaximal, complemented
24C2×C7×#41C2211yescharacteristic, complemented
25C22×C7×D4C2211yescharacteristic
26C22×C22⋊D7C2212yes—
27C22×C22⋊D7C2212yes—
28#6554—28no—
29C2×Q8×D7C2211yescharacteristic, complemented
30C2×Q8×D7C2211yescharacteristic, complemented
31#6548—28no—
32C2×#1159C2211yescharacteristic
33C2×#1159C2212yes—
34C2×#1159C2211yescharacteristic
35C2×#1159C2211yescharacteristic, complemented
36C2×#1159C2212yescomplemented
37C2×#1159C2212yescomplemented
38C2×D4×D7C2211yescharacteristic
39C2×D4×D7C2211yescharacteristic
40C2×D4×D7C2212yes—
41C2×#1157C2211yescharacteristic
42C2×#1157C2211yescharacteristic
43C2×#1157C2212yescomplemented
44C2×#1157C2211yescharacteristic, complemented
45C22×Dic14C2212yescomplemented
46C22×Dic14C2211yescharacteristic, complemented
47C7×#124C2211yescharacteristic, complemented
48C7×#123C2212yescomplemented
49C7×C22⋊Q8C2211yescharacteristic, complemented
50C7×#121C2212yescomplemented
51C7×#121C2211yescharacteristic, complemented
52C7×#120C2212yescomplemented
53C4×C7×D4C2211yescharacteristic, complemented
54C4×C7×D4C2211yescharacteristic, complemented
55C2×C7×C22⋊C4C2212yescomplemented
56#6516C2212yescomplemented
57C2×C22⋊Dic7C2212yescomplemented
58#6510C2211yescharacteristic, complemented
59#6509C2211yescharacteristic, complemented
60#6503C2211yescharacteristic, complemented
61#6503C2212yescomplemented
62#6502C2212yescomplemented
63#6502C2212yescomplemented
64#6502C2212yescomplemented
65#6502C2212yescomplemented
66#6501C2211yescharacteristic, complemented
67#6501C2211yescharacteristic, complemented
68#6500C2212yescomplemented
69#6500C2212yescomplemented
70#6499C2211yescharacteristic, complemented
71#6498C2212yescomplemented
72D4×Dic7C2211yescharacteristic, complemented
73D4×Dic7C2212yescomplemented
74#6493C2212yescomplemented
75#6493C2211yescharacteristic, complemented
76#6492C2212yescomplemented
77C4×C22⋊D7C2212yescomplemented
78C4×C22⋊D7C2211yescharacteristic, complemented
79C4×C22⋊D7C2211yescharacteristic, complemented
80C2×(C2×D7)⋊C4C2212yescomplemented
81C2×(C2×D7)⋊C4C2212yescomplemented
82#6487C2211yescharacteristic, complemented
83C2×C4×Dic7C2212yescomplemented
84#6460C2211yescharacteristic, complemented
85#6459C2212yescomplemented
86#6459C2212yescomplemented
87#6458C2211yescharacteristic, complemented
88#6458C2211yescharacteristic, complemented
89#6457C2212yescomplemented
90#6456C2212yescomplemented
91#6455C2211yescharacteristic, complemented
92#6451C2211yescharacteristic, complemented
93#6451C2212yescomplemented
94#6450C2211yescharacteristic, complemented
95#6449C2212yescomplemented
96#6448C2212yescomplemented
97#6448C2212yescomplemented
98#6448C2211yescharacteristic, complemented
99#6448C2212yescomplemented
100#6448C2212yescomplemented
101#6448C2212yescomplemented
102#6448C2212yescomplemented
103#6448C2212yescomplemented
104#6448C2211yescharacteristic, complemented
105#6448C2212yescomplemented
106#6447C2212yescomplemented
107#6447C2211yescharacteristic, complemented
108#6447C2212yescomplemented
109#6447C2211yescharacteristic, complemented
110#6446C2212yescomplemented
111#6445C2212yescomplemented
112#6445C2212yescomplemented
113(C22⋊D7)⋊C4C2212yescomplemented
114(C22⋊D7)⋊C4C2212yescomplemented
115(C22⋊D7)⋊C4C2212yescomplemented
116D7×C22⋊C4C2212yescomplemented
117D7×C22⋊C4C2212yescomplemented
118#6441C2212yescomplemented
119#6441C2212yescomplemented
120#6440C2212yescomplemented
121#6438C2211yescharacteristic, complemented
122C4×D28C2211yescharacteristic, complemented
123C42×D7C2211yescharacteristic, complemented
124C4×Dic14C2211yescharacteristic, complemented
125#3500—71nomaximal, Sylow
126C24×C7C2312yes—
127C23×D7C2312yes—
128C23×D7C2312yes—
129C7×#41—24no—
130C2×C7×Q8C2311yescharacteristic
131C2×C7×D4—24no—
132C2×C7×D4C2312yes—
133C2×C7×D4C2311yescharacteristic
134C2×C7×D4C2312yes—
135C2×C7×D4C2312yes—
136C2×C7×D4C2311yescharacteristic
137C2×C7×D4C2311yescharacteristic
138C22×C4×C7C2311yescharacteristic
139C22×C4×C7C2312yes—
140C22×C4×C7C2311yescharacteristic
141C22×C4×C7C2312yes—
142C2×C22⋊D7—28no—
143C2×C22⋊D7—28no—
144C2×C22⋊D7C2312yes—
145C2×C22⋊D7C2311yescharacteristic
146C2×C22⋊D7C2312yes—
147C2×C22⋊D7C2312yes—
148C2×C22⋊D7C2311yescharacteristic
149C2×C22⋊D7C2311yescharacteristic
150C2×C22⋊D7C2312yes—
151C2×C22⋊D7C2311yescharacteristic
152C2×C22⋊D7C2312yes—
153C2×C22⋊D7C2312yes—
154C2×C22⋊D7C2312yes—
155C2×C22⋊D7C2311yescharacteristic
156C2×C22⋊D7C2311yescharacteristic
157C2×C22⋊D7C2312yes—
158C22×Dic7C2312yes—
159C22×Dic7C2312yes—
160C22×Dic7C2312yes—
161C22×Dic7C2312yes—
162C22×Dic7C2312yes—
163Q8×D7—24no—
164Q8×D7—24no—
165#1159—24no—
166#1159—28no—
167#1159—28no—
168#1159—28no—
169#1159—24no—
170#1159D418yescomplemented
171D4×D7—24no—
172D4×D7—28no—
173D4×D7—24no—
174#1157—28no—
175#1157—24no—
176#1157—24no—
177#1157—24no—
178C2×D28C2311yescharacteristic
179C2×D28C2311yescharacteristic
180C2×D28C2311yescharacteristic
181C2×D28C2311yescharacteristic
182C2×D28C2312yes—
183C2×C4×D7C2311yescharacteristic
184C2×C4×D7C2311yescharacteristic
185C2×C4×D7C2312yes—
186C2×C4×D7C2312yes—
187C2×C4×D7C2312yes—
188C2×C4×D7C2311yescharacteristic
189C2×C4×D7C2311yescharacteristic
190C2×C4×D7C2311yescharacteristic
191C2×Dic14—28no—
192C2×Dic14—24no—
193C2×Dic14C2311yescharacteristic
194C2×Dic14C2312yes—
195C2×Dic14C2312yes—
196C2×Dic14C2311yescharacteristic
197C2×Dic14C2312yes—
198C2×Dic14C2311yescharacteristic
199C2×Dic14C2311yescharacteristic
200C7×C4⋊C4C2311yescharacteristic
201C7×C4⋊C4C2312yes—
202C7×C4⋊C4C2311yescharacteristic
203C7×C22⋊C4C2312yes—
204C7×C22⋊C4C2312yes—
205C7×C22⋊C4C2312yes—
206C7×C22⋊C4C2312yes—
207C7×C22⋊C4C2311yescharacteristic
208C7×C22⋊C4C2312yes—
209C7×C22⋊C4C2311yescharacteristic
210C42×C7C2311yescharacteristic
211C22⋊Dic7C2312yes—
212C22⋊Dic7C2312yes—
213C22⋊Dic7C2312yes—
214C22⋊Dic7C2312yes—
215C22⋊Dic7C2312yes—
216C22⋊Dic7C2311yescharacteristic
217C22⋊Dic7C2311yescharacteristic
218(C2×D7)⋊C4C2311yescharacteristic
219(C2×D7)⋊C4C2311yescharacteristic
220(C2×D7)⋊C4C2312yes—
221(C2×D7)⋊C4C2312yes—
222(C2×D7)⋊C4C2312yes—
223(C2×D7)⋊C4C2312yes—
224(C2×D7)⋊C4C2312yes—
225(C2×D7)⋊C4C2312yes—
226(C2×D7)⋊C4C2312yes—
227(C2×D7)⋊C4C2312yes—
228(C2×D7)⋊C4C2311yescharacteristic
229(C2×D7)⋊C4C2312yes—
230(C2×D7)⋊C4C2311yescharacteristic
231C4⋊Dic7C2311yescharacteristic
232C4⋊Dic7C2311yescharacteristic
233C4⋊Dic7C2312yes—
234Dic7⋊C4C2312yes—
235Dic7⋊C4C2312yes—
236Dic7⋊C4C2311yescharacteristic
237Dic7⋊C4C2312yes—
238Dic7⋊C4C2312yes—
239Dic7⋊C4C2311yescharacteristic
240C4×Dic7C2312yes—
241C4×Dic7C2311yescharacteristic
242C4×Dic7C2311yescharacteristic
243C4×Dic7C2311yescharacteristic
244C4×Dic7C2312yes—
245C4×Dic7C2312yes—
246C2×2−1+4—71no—
247C2×H(5,𝔽2)—71no—
248#548—71no—
249#548—71no—
250#548—71no—
251#548—71no—
252#546—71no—
253#546—71no—
254#546—72no—
255#546—72no—
256#546—72no—
257#546—71no—
258#546—72no—
259#546D711yescharacteristic, complemented
260#536—72no—
261#536—71no—
262#535—71no—
263#535—72no—
264#532—72no—
265#532—71no—
266C2×#124—71no—
267C2×#124—72no—
268C4×#41—71no—
269C23×C7—24no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7C2412yes—
273C23×C7C2411yescharacteristic
274C23×C7C2411yescharacteristic
275C23×C7C2412yes—
276C22×D7—24no—
277C22×D7—24no—
278C22×D7—42no—
279C22×D7—42no—
280C22×D7—42no—
281C22×D7—42no—
282C22×D7C2411yescharacteristic
283C22×D7C2412yes—
284C22×D7C2411yescharacteristic
285C22×D7C2411yescharacteristic
286C7×Q8—22no—
287C7×D4—24no—
288C7×D4—24no—
289C7×D4—22no—
290C7×D4—41no—
291C7×D4—42no—
292C7×D4C2×D414yes—
293C2×C4×C7—24no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—42no—
297C2×C4×C7C2411yescharacteristic
298C2×C4×C7C2412yes—
299C2×C4×C7C2411yescharacteristic
300C2×C4×C7C2411yescharacteristic
301C2×C4×C7C2411yescharacteristic
302C2×C4×C7C2412yes—
303C2×C4×C7C2411yescharacteristic
304C22⋊D7—24no—
305C22⋊D7—24no—
306C22⋊D7—22no—
307C22⋊D7—22no—
308C22⋊D7—22no—
309C22⋊D7—22no—
310C22⋊D7—24no—
311C22⋊D7—24no—
312C22⋊D7—24no—
313C22⋊D7—41no—
314C22⋊D7—41no—
315C22⋊D7—42no—
316C22⋊D7—42no—
317C22⋊D7C2×D418yes—
318C2×Dic7—24no—
319C2×Dic7—24no—
320C2×Dic7—24no—
321C2×Dic7—42no—
322C2×Dic7C2×D418yes—
323C2×Dic7C2411yescharacteristic
324C2×Dic7C2411yescharacteristic
325C2×Dic7C2412yes—
326C2×Dic7C2411yescharacteristic
327C2×Dic7C2412yes—
328C2×Dic7C2411yescharacteristic
329C2×Dic7C2411yescharacteristic
330C2×Dic7C2412yes—
331D28—22no—
332D28—22no—
333D28—22no—
334D28—41no—
335D28—42no—
336C4×D7—24no—
337C4×D7—22no—
338C4×D7—22no—
339C4×D7—24no—
340C4×D7—24no—
341C4×D7—41no—
342C4×D7—41no—
343C4×D7C2×D414yes—
344Dic14—22no—
345Dic14—22no—
346Dic14—24no—
347Dic14—24no—
348Dic14—24no—
349Dic14—22no—
350Dic14C2×D414yes—
3512−1+4—148no—
352H(5,𝔽2)—148no—
353C2×#41—71no—
354C2×#41—72no—
355C2×#41—72no—
356C2×#41—71no—
357C2×#41—72no—
358C2×#41—71no—
359C2×#41—71no—
360C2×#41—71no—
361C2×#41—72no—
362C2×#41—71no—
363C2×#41C2×D711yescharacteristic, complemented
364C22×Q8—71no—
365C22×Q8—71no—
366C22×Q8—72no—
367C22×Q8—71no—
368C22×D4—72no—
369C22×D4—72no—
370C22×D4—71no—
371C22×D4—72no—
372C22×D4—71no—
373C22×D4C2×D711yescharacteristic
374C4⋊Q8—72no—
375C4⋊Q8—71no—
376#127—72no—
377#127—71no—
378#124—71no—
379#124—71no—
380#124—72no—
381#124—71no—
382#124—72no—
383#124—72no—
384#124—72no—
385#124—72no—
386#124—72no—
387#124—72no—
388#124—72no—
389#124—71no—
390#124—71no—
391#124C2×D711yescharacteristic, complemented
392#123—72no—
393#123—72no—
394#123—72no—
395#123—72no—
396#123—72no—
397#123C2×D712yescomplemented
398C22⋊Q8—71no—
399C22⋊Q8—71no—
400C22⋊Q8—72no—
401C22⋊Q8—72no—
402C22⋊Q8—71no—
403C22⋊Q8—72no—
404C22⋊Q8—72no—
405C22⋊Q8C2×D711yescharacteristic, complemented
406#121—71no—
407#121—72no—
408#121—72no—
409#121—71no—
410#121—72no—
411#121—72no—
412#121—72no—
413#121—71no—
414#121—71no—
415#121—71no—
416#121—71no—
417#121—71no—
418#121—72no—
419#121—72no—
420#121C2×D712yescomplemented
421#121C2×D711yescharacteristic, complemented
422#120—72no—
423#120—72no—
424#120—72no—
425#120—72no—
426#120—72no—
427#120C2×D712yescomplemented
428C4×Q8—71no—
429C4×Q8—71no—
430C4×D4—71no—
431C4×D4—72no—
432C4×D4—72no—
433C4×D4—71no—
434C4×D4—71no—
435C4×D4—72no—
436C4×D4—72no—
437C4×D4—72no—
438C4×D4—72no—
439C4×D4—71no—
440C4×D4C2×D711yescharacteristic, complemented
441C4×D4C2×D711yescharacteristic, complemented
442#117—71no—
443#117—72no—
444C2×C22⋊C4—72no—
445C2×C22⋊C4—72no—
446C2×C22⋊C4—72no—
447C2×C22⋊C4—72no—
448C2×C22⋊C4—72no—
449C2×C22⋊C4C2×D712yescomplemented
450C2×C42—72no—
451C2×C42—71no—
452C22×C7—22no—
453C22×C7—22no—
454C22×C7—21no—
455C22×C7—22no—
456C22×C7—21no—
457C22×C7—21no—
458C22×C7—21no—
459C22×C7—22no—
460C22×C7—21no—
461C22×C7—22no—
462C22×C7—21no—
463C22×C7—84no—
464C22×C7C22×D414yes—
465C22×C7C2511yescharacteristic
466C2×D7—21no—
467C2×D7—21no—
468C2×D7—21no—
469C2×D7—21no—
470C2×D7—22no—
471C2×D7—21no—
472C2×D7—21no—
473C2×D7—21no—
474C2×D7—22no—
475C2×D7—22no—
476C2×D7—21no—
477C2×D7—84no—
478C2×D7—84no—
479C2×D7C22×D412yes—
480C4×C7—21no—
481C4×C7—22no—
482C4×C7—21no—
483C4×C7—21no—
484C4×C7—21no—
485C4×C7—22no—
486C4×C7C22×D412yes—
487Dic7—22no—
488Dic7—21no—
489Dic7—21no—
490Dic7—21no—
491Dic7—21no—
492Dic7—22no—
493Dic7C22×D412yes—
494Dic7C22×D414yes—
495C24—72no—
496C24—72no—
497C24C22×D712yes—
498#41—24no—
499#41—78no—
500#41—144no—
501#41—144no—
502#41—148no—
503#41—144no—
504#41—148no—
505#41—148no—
506#41—148no—
507#41—144no—
508#41—144no—
509C2×Q8—71no—
510C2×Q8—72no—
511C2×Q8—72no—
512C2×Q8—71no—
513C2×Q8—72no—
514C2×Q8—71no—
515C2×Q8—71no—
516C2×Q8—148no—
517C2×Q8—144no—
518C2×Q8—144no—
519C2×Q8—144no—
520C2×Q8C22×D711yescharacteristic
521C2×D4—24no—
522C2×D4—72no—
523C2×D4—71no—
524C2×D4—72no—
525C2×D4—71no—
526C2×D4—72no—
527C2×D4—72no—
528C2×D4—72no—
529C2×D4—72no—
530C2×D4—71no—
531C2×D4—71no—
532C2×D4—71no—
533C2×D4—72no—
534C2×D4—72no—
535C2×D4—71no—
536C2×D4—71no—
537C2×D4—71no—
538C2×D4—71no—
539C2×D4—72no—
540C2×D4—71no—
541C2×D4—144no—
542C2×D4—148no—
543C2×D4—148no—
544C2×D4—148no—
545C2×D4—144no—
546C2×D4C22×D712yes—
547C2×D4C22×D712yes—
548C2×D4C22×D711yescharacteristic
549C2×D4C22×D712yes—
550C2×D4C22×D711yescharacteristic
551C2×D4C22×D711yescharacteristic
552C22×C4—72no—
553C22×C4—71no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—71no—
561C22×C4—72no—
562C22×C4—71no—
563C22×C4—71no—
564C22×C4—71no—
565C22×C4C22×D712yes—
566C22×C4C22×D711yescharacteristic
567C22×C4C22×D711yescharacteristic
568C22×C4C22×D712yes—
569C4⋊C4—72no—
570C4⋊C4—72no—
571C4⋊C4—72no—
572C4⋊C4—71no—
573C4⋊C4—72no—
574C4⋊C4—71no—
575C4⋊C4—71no—
576C4⋊C4—72no—
577C4⋊C4—71no—
578C4⋊C4C22×D711yescharacteristic
579C4⋊C4C22×D712yes—
580C4⋊C4C22×D711yescharacteristic
581C22⋊C4—72no—
582C22⋊C4—71no—
583C22⋊C4—72no—
584C22⋊C4—72no—
585C22⋊C4—72no—
586C22⋊C4—72no—
587C22⋊C4—71no—
588C22⋊C4—72no—
589C22⋊C4—71no—
590C22⋊C4—71no—
591C22⋊C4—72no—
592C22⋊C4—72no—
593C22⋊C4—72no—
594C22⋊C4—72no—
595C22⋊C4—72no—
596C22⋊C4—72no—
597C22⋊C4—72no—
598C22⋊C4—72no—
599C22⋊C4—71no—
600C22⋊C4—71no—
601C22⋊C4C22×D712yes—
602C22⋊C4C22×D712yes—
603C22⋊C4C22×D711yescharacteristic
604C22⋊C4C22×D712yes—
605C22⋊C4C22×D712yes—
606C22⋊C4C22×D712yes—
607C22⋊C4C22×D711yescharacteristic
608C42—71no—
609C42—72no—
610C42—71no—
611C42—72no—
612C42—72no—
613C42—71no—
614C42C22×D711yescharacteristic
615C2×C7—24no—
616C2×C7—42no—
617C2×C7—41no—
618C2×C7—41no—
619C2×C7C23×D411yescharacteristic
620C2×C7#58511yescharacteristic
621C2×C7#58511yescharacteristic
622D7—22no—
623D7—41no—
624D7—42no—
625D7—41no—
626C23—24no—
627C23—42no—
628C23—42no—
629C23—71no—
630C23—72no—
631C23—71no—
632C23—71no—
633C23—144no—
634C23—144no—
635C23—282no—
636C23—282no—
637C23—282no—
638C23—282no—
639C23C23×D712yes—
640C23C23×D711yescharacteristic
641C23C23×D711yescharacteristic
642C23C23×D712yes—
643Q8—22no—
644Q8—74no—
645Q8—142no—
646Q8—144no—
647Q8—144no—
648Q8—144no—
649Q8—142no—
650Q8—142no—
651D4—24no—
652D4—24no—
653D4—22no—
654D4—41no—
655D4—42no—
656D4—78no—
657D4—142no—
658D4—142no—
659D4—142no—
660D4—144no—
661D4—144no—
662D4—144no—
663D4—142no—
664D4—142no—
665D4—142no—
666D4—144no—
667D4—144no—
668D4—142no—
669D4—281no—
670D4—282no—
671D4—282no—
672D4—282no—
673D4—281no—
674D4—281no—
675D4D4×D714yes—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—78no—
681C2×C4—71no—
682C2×C4—72no—
683C2×C4—74no—
684C2×C4—71no—
685C2×C4—72no—
686C2×C4—71no—
687C2×C4—71no—
688C2×C4—72no—
689C2×C4—71no—
690C2×C4—144no—
691C2×C4—144no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—144no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—281no—
699C2×C4—281no—
700C2×C4—282no—
701C2×C4C23×D711yescharacteristic
702C2×C4C23×D712yes—
703C2×C4C23×D711yescharacteristic
704C2×C4C23×D712yes—
705C2×C4C23×D711yescharacteristic
706C2×C4C23×D711yescharacteristic
707C2×C4C23×D711yescharacteristic
708C7#350011yescharacteristic, complemented, Sylow
709C22—22no—
710C22—22no—
711C22—21no—
712C22—21no—
713C22—22no—
714C22—21no—
715C22—21no—
716C22—22no—
717C22—21no—
718C22—22no—
719C22—21no—
720C22—72no—
721C22—84no—
722C22—141no—
723C22—141no—
724C22—141no—
725C22—142no—
726C22—141no—
727C22—141no—
728C22—141no—
729C22—142no—
730C22—141no—
731C22—142no—
732C22—141no—
733C22—564no—
734C22—564no—
735C22C2×D4×D714yes—
736C22C24×D711yescharacteristic
737C4—21no—
738C4—21no—
739C4—22no—
740C4—21no—
741C4—21no—
742C4—22no—
743C4—72no—
744C4—74no—
745C4—141no—
746C4—142no—
747C4—141no—
748C4—141no—
749C4—142no—
750C4—141no—
751C4C2×D4×D712yes—
752C2—24no—
753C2—41no—
754C2—42no—
755C2—41no—
756C2—142no—
757C2—281no—
758C2—282no—
759C2—281no—
760C2C22×D4×D711yescharacteristic
761C2#9061611yescharacteristic
762C2#9061811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D7
commutator, socle, cosocleC22×C7C25
FittingC7×#546C2
hypercenter#546D7
hypocenterC7#3500
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#6554C2semidirect
2. C2×#6548C2semidirect
3. C7×#546C2semidirect
4. #90520C2semidirect
5. #90497C2semidirect
6. #90368C2semidirect
7. D7×#124C2semidirect
8. #90345C2semidirect
9. #90339C2semidirect
10. #90324C2semidirect
11. #90319C2semidirect
12. #90301C2semidirect
13. #90298C2semidirect
14. #90289C2semidirect
15. #90287C2semidirect
16. #90283C2semidirect
17. #90282C2semidirect
18. #90245C2semidirect
19. #90243C2semidirect
20. #90239C2semidirect
21. C4×#1159C2semidirect
22. C2×#6448C2semidirect
23. #90181C2semidirect
24. C2×C7×#41C22semidirect
29. C2×Q8×D7C22semidirect
30. C2×Q8×D7C22semidirect
35. C2×#1159C22semidirect
36. C2×#1159C22semidirect
37. C2×#1159C22semidirect
43. C2×#1157C22semidirect
44. C2×#1157C22semidirect
45. C22×Dic14C22semidirect
46. C22×Dic14C22semidirect
47. C7×#124C22semidirect
48. C7×#123C22semidirect
49. C7×C22⋊Q8C22semidirect
50. C7×#121C22semidirect
51. C7×#121C22semidirect
52. C7×#120C22semidirect
53. C4×C7×D4C22semidirect
54. C4×C7×D4C22semidirect
55. C2×C7×C22⋊C4C22semidirect
56. #6516C22semidirect
57. C2×C22⋊Dic7C22semidirect
58. #6510C22semidirect
59. #6509C22semidirect
60. #6503C22semidirect
61. #6503C22semidirect
62. #6502C22semidirect
63. #6502C22semidirect
64. #6502C22semidirect
65. #6502C22semidirect
66. #6501C22semidirect
67. #6501C22semidirect
68. #6500C22semidirect
69. #6500C22semidirect
70. #6499C22semidirect
71. #6498C22semidirect
72. D4×Dic7C22semidirect
73. D4×Dic7C22semidirect
74. #6493C22semidirect
75. #6493C22semidirect
76. #6492C22semidirect
77. C4×C22⋊D7C22semidirect
78. C4×C22⋊D7C22semidirect
79. C4×C22⋊D7C22semidirect
80. C2×(C2×D7)⋊C4C22semidirect
81. C2×(C2×D7)⋊C4C22semidirect
82. #6487C22semidirect
83. C2×C4×Dic7C22semidirect
84. #6460C22semidirect
85. #6459C22semidirect
86. #6459C22semidirect
87. #6458C22semidirect
88. #6458C22semidirect
89. #6457C22semidirect
90. #6456C22semidirect
91. #6455C22semidirect
92. #6451C22semidirect
93. #6451C22semidirect
94. #6450C22semidirect
95. #6449C22semidirect
96. #6448C22semidirect
97. #6448C22semidirect
98. #6448C22semidirect
99. #6448C22semidirect
100. #6448C22semidirect
101. #6448C22semidirect
102. #6448C22semidirect
103. #6448C22semidirect
104. #6448C22semidirect
105. #6448C22semidirect
106. #6447C22semidirect
107. #6447C22semidirect
108. #6447C22semidirect
109. #6447C22semidirect
110. #6446C22semidirect
111. #6445C22semidirect
112. #6445C22semidirect
113. (C22⋊D7)⋊C4C22semidirect
114. (C22⋊D7)⋊C4C22semidirect
115. (C22⋊D7)⋊C4C22semidirect
116. D7×C22⋊C4C22semidirect
117. D7×C22⋊C4C22semidirect
118. #6441C22semidirect
119. #6441C22semidirect
120. #6440C22semidirect
121. #6438C22semidirect
122. C4×D28C22semidirect
123. C42×D7C22semidirect
124. C4×Dic14C22semidirect
170. #1159D4semidirect
259. #546D7semidirect
363. C2×#41C2×D7semidirect
391. #124C2×D7semidirect
397. #123C2×D7semidirect
405. C22⋊Q8C2×D7semidirect
420. #121C2×D7semidirect
421. #121C2×D7semidirect
427. #120C2×D7semidirect
440. C4×D4C2×D7semidirect
441. C4×D4C2×D7semidirect
449. C2×C22⋊C4C2×D7semidirect
708. C7#3500semidirect

Maximal subgroups

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

subgroupindex
C2×#65542
C2×#65482
C7×#5462
#905202
#904972
#903682
D7×#1242
#903452
#903392
#903242
#903192
#903012
#902982
#902892
#902872
#902832
#902822
#902452
#902432
#902392
C4×#11592
C2×#64482
#901812
#35007