Finite Group Databasebeta

← #15618321

Subgroups — #15618321

Order 2816.

1950 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081908C211yesmaximal, characteristic
2#13077632C214yesmaximal, complemented
3#13077626C214yesmaximal, complemented
4#13077615C214yesmaximal, complemented
5#13077613C214yesmaximal, complemented
6#13077549C211yesmaximal, characteristic, complemented
7#13077548C211yesmaximal, characteristic, complemented
8#13077326C211yesmaximal, characteristic, complemented
9#13077324C211yesmaximal, characteristic, complemented
10#13077320C211yesmaximal, characteristic, complemented
11#13077319C211yesmaximal, characteristic, complemented
12#13077315C211yesmaximal, characteristic, complemented
13#13077266C211yesmaximal, characteristic, complemented
14#13077263C211yesmaximal, characteristic, complemented
15#13077245C211yesmaximal, characteristic, complemented
16#13077043C211yesmaximal, characteristic, complemented
17#13077042C211yesmaximal, characteristic, complemented
18C2×M16×Dic11C211yesmaximal, characteristic, complemented
19C11×#2930C211yesmaximal, characteristic, complemented
20C2×C11×#131C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#525C2211yescharacteristic
23#10623363C2211yescharacteristic
24#41×Dic11C2211yescharacteristic
25C2×#67001C2211yescharacteristic
26#10623322C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C2×#66960C2211yescharacteristic
30C2×#66954C2211yescharacteristic
31#10623180C414yes—
32#10623155C412yes—
33#10623153C412yes—
34#10623131C412yes—
35#10623127C412yes—
36#10623117C414yes—
37#10623069C2214yes—
38C4×#4341C2214yes—
39#10623053C2211yescharacteristic
40#10623048C2211yescharacteristic
41C11×#436C2214yes—
42C11×#435C2214yes—
43C11×#424C2211yescharacteristic
44C11×#408C2211yescharacteristic
45C11×#407C2211yescharacteristic
46C11×#405C2211yescharacteristic
47#10622847C2211yescharacteristic
48#10622820C2211yescharacteristic
49#10622742C2211yescharacteristic
50#10622741C2214yes—
51#10622741C2214yescomplemented
52#10622740C2214yes—
53#10622735C2211yescharacteristic
54#10622735C2212yescomplemented
55#10622732C2211yescharacteristic
56#10622731C2211yescharacteristic
57#10622731C2211yescharacteristic
58M16×Dic11C2211yescharacteristic
59M16×Dic11C2211yescharacteristic
60M16×Dic11C2212yes—
61M16×Dic11C2212yes—
62M16×Dic11C2212yes—
63M16×Dic11C2212yes—
64M16×Dic11C2212yescomplemented
65#10622723C2211yescharacteristic
66C8×C22⋊D11C2214yescomplemented
67#10622715C2211yescharacteristic
68#10622714C2211yescharacteristic
69#10622714C2212yescomplemented
70C2×#66879C2211yescharacteristic
71C2×#66879C2211yescharacteristic
72C2×#66879C2212yescomplemented
73C2×C8×Dic11C2211yescharacteristic
74C2×C8×Dic11C2211yescharacteristic
75#10622625C2214yes—
76#10622624C2214yes—
77#10622612C2211yescharacteristic
78#10622610C2211yescharacteristic
79#10622453C2214yescomplemented
80#10622448C2214yescomplemented
81#10622443C2214yescomplemented
82#10622441C2214yescomplemented
83#10622342C2214yes—
84#10622342C2214yescomplemented
85#10622341C2214yes—
86(C22⋊D11)⋊C8C2214yescomplemented
87#10622333C2214yescomplemented
88#10622332C2214yes—
89#10622332C2214yescomplemented
90#10622331C2214yes—
91#10622321C2212yescomplemented
92D11×#97C2212yescomplemented
93#10622314C2214yescomplemented
94#10622302C2212yescomplemented
95C4×#4313C2212yescomplemented
96C8×Dic22C2214yescomplemented
97C2×C11×#41C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×Dic11C2×C412yes—
100C2×#4341C2×C414yes—
101C2×#4339C2311yescharacteristic
102C11×#131—24no—
103C2×C11×M16—24no—
104C2×C11×M16C2312yes—
105C2×C11×M16C2312yes—
106C2×C11×M16C2311yescharacteristic
107C2×C11×M16C2311yescharacteristic
108C2×C11×M16C2312yes—
109C22×C8×C11C2312yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#123C2×C412yes—
113C11×C22⋊Q8C2×C412yes—
114C11×#121C2×C412yes—
115C11×#120C2×C412yes—
116C4×D4×C11C2314yes—
117C11×#117C2311yescharacteristic
118#67006C2×C412yes—
119#67001—24no—
120#67000C2×C411yescharacteristic
121Q8×Dic11C2×C412yes—
122#66997C2×C411yescharacteristic
123#66993C2×C411yescharacteristic
124#66992C2×C414yes—
125#66992C2×C414yes—
126#66989C2×C411yescharacteristic
127#66988C2×C414yes—
128D4×Dic11C2×C414yes—
129D4×Dic11C2×C414yes—
130D4×Dic11C2×C412yes—
131#66983C2×C412yes—
132#66982C2×C412yes—
133C4×C22⋊D11C2314yes—
134C4×C22⋊D11C2314yes—
135#66979C2311yescharacteristic
136#66979C2312yes—
137#66977C2×C412yes—
138C2×C4×Dic11C2×C412yes—
139C2×C4×Dic11C2×C412yes—
140C2×C4×Dic11C2×C412yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×#4318—24no—
147C2×#4318C2311yescharacteristic
148C2×#4318C2312yes—
149C2×#4318C2312yes—
150C2×#4318C2311yescharacteristic
151C2×#4318C2312yes—
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2312yes—
154C22×C11⋊C8C2311yescharacteristic
155#66960—24no—
156#66954—24no—
157C2×#4313C2312yes—
158C2×#4313C2312yes—
159C2×C8×D11C2312yes—
160C2×C8×D11C2312yes—
161#66951C2×C414yes—
162#66946C2×C412yes—
163#66945C2×C414yes—
164#66943C2×C412yes—
165#66942C2×C414yes—
166#66941C2×C412yes—
167#66940C2×C412yes—
168#66940C2×C414yes—
169#66939C2×C414yes—
170#66938C2×C414yes—
171(C22⋊D11)⋊C4C2×C414yes—
172(C22⋊D11)⋊C4C2×C414yes—
173(C22⋊D11)⋊C4C2×C414yes—
174#66932C2×C414yes—
175#66931C2×C414yes—
176#66931C2×C414yes—
177#66930C2×C414yes—
178#66930C2×C414yes—
179#66925C2312yes—
180C42×D11C2312yes—
181C4×Dic22C2314yes—
182C11×C4⋊C8C2314yes—
183C11×C22⋊C8C2314yes—
184C11×C22⋊C8C2314yes—
185C11×#97C2312yes—
186C4×C8×C11C2312yes—
187C22⋊(C11⋊C8)C2314yes—
188C22⋊(C11⋊C8)C2314yes—
189(C2×D11)⋊C8C2314yes—
190(C2×D11)⋊C8C2314yes—
191#66879C2311yescharacteristic
192#66879C2311yescharacteristic
193#66879C2311yescharacteristic
194#66879C2311yescharacteristic
195#66879C2312yes—
196#66879C2312yes—
197#66879C2312yes—
198#66879C2312yes—
199#66879C2312yes—
200#66879C2312yes—
201Dic11⋊C8C2314yes—
202Dic11⋊C8C2314yes—
203Dic11⋊C8C2314yes—
204Dic11⋊C8C2314yes—
205C8×Dic11C2312yes—
206C8×Dic11C2312yes—
207C8×Dic11C2312yes—
208C8×Dic11C2312yes—
209C8×Dic11C2312yes—
210C8×Dic11C2312yes—
211C8×Dic11C2312yes—
212C8×Dic11C2312yes—
213C4⋊(C11⋊C8)C2314yes—
214#66867C2312yes—
215C4×C11⋊C8C2312yes—
216#60208—111nomaximal, Sylow
217C24×C11C22×C411yescharacteristic
218C11×#41—22no—
219C11×#41—22no—
220C2×Q8×C11C22×C411yescharacteristic
221C2×D4×C11C22×C411yescharacteristic
222C2×D4×C11C22×C412yes—
223C2×D4×C11C22×C414yes—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C411yescharacteristic
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11C22×C412yes—
232C2×C22⋊D11C22×C414yes—
233C2×C22⋊D11C22×C414yes—
234C22×Dic11—44no—
235C22×Dic11C22×C412yes—
236C22×Dic11C22×C412yes—
237C22×Dic11C22×C412yes—
238C22×Dic11C22×C414yes—
239C22×Dic11C22×C412yes—
240C22×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242#4341—48no—
243#4339—22no—
244#4339—22no—
245C2×D44C22×C411yescharacteristic
246C2×C4×D11C22×C414yes—
247C2×C4×D11C2412yes—
248C2×Dic22C22×C414yes—
249C2×Dic22C22×C411yescharacteristic
250C11×M16—24no—
251C11×M16—24no—
252C11×M16—24no—
253C11×M16—22no—
254C11×M16—22no—
255C2×C8×C11—24no—
256C2×C8×C11—22no—
257C2×C8×C11#4114yescomplemented
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C2×C8×C11C2411yescharacteristic
262C2×C8×C11C2411yescharacteristic
263C11×C4⋊C4C22×C412yes—
264C11×C4⋊C4C22×C414yes—
265C11×C22⋊C4C22×C414yes—
266C11×C22⋊C4C22×C414yes—
267C11×C22⋊C4C22×C412yes—
268C42×C11C2412yes—
269C22⋊Dic11C22×C414yes—
270C22⋊Dic11C22×C414yes—
271C22⋊Dic11C22×C412yes—
272C22⋊Dic11C22×C414yes—
273(C2×D11)⋊C4C22×C414yes—
274(C2×D11)⋊C4C22×C414yes—
275(C2×D11)⋊C4C22×C414yes—
276C4⋊Dic11C22×C414yes—
277C4⋊Dic11C22×C414yes—
278C4⋊Dic11C22×C412yes—
279Dic11⋊C4C22×C414yes—
280Dic11⋊C4C22×C414yes—
281Dic11⋊C4C22×C414yes—
282Dic11⋊C4C22×C414yes—
283Dic11⋊C4C22×C414yes—
284C4×Dic11C22×C414yes—
285C4×Dic11C22×C412yes—
286C4×Dic11C22×C414yes—
287C4×Dic11C22×C412yes—
288C4×Dic11C22×C412yes—
289C4×Dic11C22×C412yes—
290C4×Dic11C22×C412yes—
291C4×Dic11C22×C411yescharacteristic
292C4×Dic11C22×C411yescharacteristic
293C4×Dic11C2412yes—
294C4×Dic11C2411yescharacteristic
295C4×Dic11C2412yes—
296C4×Dic11C2411yescharacteristic
297#4318—24no—
298#4318—24no—
299#4318—24no—
300#4318—22no—
301#4318—22no—
302C2×C11⋊C8—24no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8#4114yescomplemented
305C2×C11⋊C8C2412yes—
306C2×C11⋊C8C2412yes—
307C2×C11⋊C8C2412yes—
308C2×C11⋊C8C2411yescharacteristic
309C2×C11⋊C8C2411yescharacteristic
310#4313—24no—
311#4313—24no—
312C8×D11—24no—
313C8×D11—24no—
314#3444—111no—
315#2971—114no—
316#2970—114no—
317#2969—114no—
318#2969—114no—
319#2960—111no—
320#2960—111no—
321#2931—111no—
322#2931—111no—
323#2930—111no—
324#2930—111no—
325#2930—111no—
326#2930D1111yescharacteristic, complemented
327#2923—111no—
328#2923—111no—
329#2920—111no—
330#2875—111no—
331#2875—111no—
332C2×C4×M16—111no—
333C23×C11—22no—
334C23×C11—42no—
335C23×C11C23×C412yes—
336C23×C11C23×C412yes—
337C23×C11C23×C411yescharacteristic
338C22×D11C23×C412yes—
339Q8×C11—22no—
340D4×C11—24no—
341D4×C11—22no—
342D4×C11—44no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C23×C414yes—
352C2×C4×C11C23×C411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11C2×#4112yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—24no—
357C22⋊D11—28no—
358C22⋊D11—44no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—44no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11C23×C412yes—
367C2×Dic11C23×C412yes—
368C2×Dic11C23×C412yes—
369C2×Dic11C23×C412yes—
370C2×Dic11C23×C414yes—
371C2×Dic11C23×C412yes—
372D44—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—44no—
376Dic22—22no—
377Dic22—28no—
378C8×C11—22no—
379C8×C11—22no—
380C8×C11—22no—
381C8×C11C2×#4112yes—
382C8×C11C2×#4112yes—
383C11⋊C8—22no—
384C11⋊C8—22no—
385C11⋊C8—22no—
386C11⋊C8C2×#4112yes—
387C11⋊C8C2×#4112yes—
388C2×#131—111no—
389C2×#131—111no—
390C2×#131—111no—
391C2×#131C2×D1111yescharacteristic
392C22×M16—111no—
393C22×M16C2×D1111yescharacteristic
394#533—112no—
395#533—111no—
396#532—111no—
397#532—112no—
398#529—114no—
399#529—112no—
400#529—112no—
401#529—114no—
402#525—111no—
403#525—114no—
404#525C2×D1111yescharacteristic
405C4×#41—111no—
406C4×#41—114no—
407C4×#41—111no—
408C22×C42—111no—
409#446—114no—
410#446—114no—
411C8×Q8—114no—
412C8×Q8—114no—
413#436—114no—
414#436—114no—
415#436—114no—
416#436—114no—
417#436—114no—
418#436C2×D1114yes—
419#435—114no—
420#435—114no—
421#435—114no—
422#435C2×D1114yes—
423C8×D4—114no—
424C8×D4—114no—
425#433—114no—
426#433—114no—
427#432—114no—
428#432—114no—
429#432—114no—
430#431—114no—
431#424—111no—
432#424—111no—
433#424—111no—
434#424C2×D1111yescharacteristic
435#423—111no—
436#423—111no—
437#408—111no—
438#408—111no—
439#408—111no—
440#408C2×D1111yescharacteristic
441#407—111no—
442#407C2×D1111yescharacteristic
443#405—111no—
444#405—112no—
445#405—111no—
446#405—112no—
447#405—111no—
448#405—112no—
449#405—112no—
450#405C2×D1111yescharacteristic
451C4×M16—112no—
452C4×M16—112no—
453C4×M16—112no—
454C4×M16—112no—
455C4×M16—111no—
456C4×M16—111no—
457C4×M16—112no—
458C4×M16—112no—
459C2×#97—111no—
460C2×#97—111no—
461C2×#97—112no—
462C2×#97—112no—
463C2×C4×C8—111no—
464C2×C4×C8—111no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—24no—
470C22×C11—22no—
471C22×C11—44no—
472C22×C11C4×#4112yes—
473C22×C11C24×C411yescharacteristic
474C2×D11—22no—
475C2×D11—24no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—24no—
479C4×C11C4×#4112yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C22×#4111yescharacteristic
482Dic11—22no—
483Dic11—24no—
484Dic11—22no—
485Dic11—22no—
486Dic11—22no—
487Dic11#56814yes—
488C2×#41—114no—
489C2×#41—111no—
490C2×#41C22×D1111yescharacteristic
491C23×C4—112no—
492C23×C4C22×D1111yescharacteristic
493#131—24no—
494#131—224no—
495#131—224no—
496#131—224no—
497C2×M16—24no—
498C2×M16—112no—
499C2×M16—112no—
500C2×M16—111no—
501C2×M16—111no—
502C2×M16—112no—
503C2×M16—112no—
504C2×M16—112no—
505C2×M16—224no—
506C2×M16C22×D1112yes—
507C2×M16C22×D1112yes—
508C2×M16C22×D1111yescharacteristic
509C2×M16C22×D1111yescharacteristic
510C2×M16C22×D1112yes—
511C22×C8—111no—
512C22×C8—111no—
513C22×C8—112no—
514C22×C8—112no—
515C22×C8—112no—
516C22×C8C22×D1111yescharacteristic
517C22×C8C22×D1112yes—
518C22×C8C22×D1111yescharacteristic
519C4⋊Q8—111no—
520C4⋊Q8—112no—
521#127—111no—
522#126—114no—
523#126—114no—
524#125—114no—
525#125—112no—
526#124—111no—
527#124—111no—
528#124—114no—
529#123—114no—
530#123—112no—
531#123—114no—
532#123C4×D1112yes—
533C22⋊Q8—112no—
534C22⋊Q8—114no—
535C22⋊Q8—114no—
536C22⋊Q8C4×D1112yes—
537#121—114no—
538#121—114no—
539#121—112no—
540#121C4×D1112yes—
541#120—112no—
542#120C4×D1112yes—
543C4×Q8—112no—
544C4×Q8—114no—
545C4×Q8—112no—
546C4×Q8—114no—
547C4×D4—114no—
548C4×D4—114no—
549C4×D4—112no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—112no—
553C4×D4—114no—
554C4×D4—114no—
555C4×D4—114no—
556C4×D4C22×D1114yes—
557#117—111no—
558#117—112no—
559#117—114no—
560#117—114no—
561#117—114no—
562#117—112no—
563#117C22×D1111yescharacteristic
564C2×C42—112no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42—111no—
569C2×C42—112no—
570C2×C42—112no—
571C2×C42—111no—
572C2×C42—112no—
573C4⋊C8—114no—
574C4⋊C8—114no—
575C4⋊C8—114no—
576C4⋊C8—114no—
577C4⋊C8—114no—
578C4⋊C8C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583C22⋊C8C22×D1114yes—
584C22⋊C8C22×D1114yes—
585#97—111no—
586#97—111no—
587#97—111no—
588#97—111no—
589#97—112no—
590#97—112no—
591#97—112no—
592#97—112no—
593#97—112no—
594#97—112no—
595#97—112no—
596#97C22×D1112yes—
597C4×C8—112no—
598C4×C8—112no—
599C4×C8—112no—
600C4×C8—112no—
601C4×C8—112no—
602C4×C8—112no—
603C4×C8—112no—
604C4×C8—112no—
605C4×C8—112no—
606C4×C8C22×D1112yes—
607C2×C11—22no—
608C2×C11—42no—
609C2×C11—42no—
610C2×C11C2×C4×#4111yescharacteristic
611C2×C11C2×#56812yes—
612D11—42no—
613C24C2×C4×D1111yescharacteristic
614#41—22no—
615#41—22no—
616#41—222no—
617#41—222no—
618#41—448no—
619C2×Q8—114no—
620C2×Q8—111no—
621C2×Q8C2×C4×D1111yescharacteristic
622C2×D4—112no—
623C2×D4—114no—
624C2×D4—114no—
625C2×D4—111no—
626C2×D4C2×C4×D1112yes—
627C2×D4C2×C4×D1111yescharacteristic
628C2×D4C2×C4×D1114yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—114no—
638C22×C4—112no—
639C22×C4—114no—
640C22×C4—444no—
641C22×C4C2×C4×D1112yes—
642C22×C4C2×C4×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1112yes—
645C22×C4C23×D1111yescharacteristic
646M16—22no—
647M16—22no—
648M16—24no—
649M16—24no—
650M16—24no—
651M16—224no—
652M16—224no—
653M16—224no—
654M16—224no—
655M16—222no—
656M16—222no—
657M16—224no—
658C2×C8—22no—
659C2×C8—24no—
660C2×C8—114no—
661C2×C8—111no—
662C2×C8—111no—
663C2×C8—112no—
664C2×C8—112no—
665C2×C8—112no—
666C2×C8—224no—
667C2×C8—224no—
668C2×C8—222no—
669C2×C8—224no—
670C2×C8#434114yescomplemented
671C2×C8C23×D1112yes—
672C2×C8C23×D1112yes—
673C2×C8C23×D1112yes—
674C2×C8C23×D1111yescharacteristic
675C2×C8C23×D1111yescharacteristic
676C4⋊C4—114no—
677C4⋊C4—114no—
678C4⋊C4—112no—
679C4⋊C4—114no—
680C4⋊C4—114no—
681C4⋊C4—114no—
682C4⋊C4—114no—
683C4⋊C4—114no—
684C4⋊C4C2×C4×D1114yes—
685C4⋊C4C2×C4×D1112yes—
686C22⋊C4—114no—
687C22⋊C4—112no—
688C22⋊C4—114no—
689C22⋊C4—114no—
690C22⋊C4—114no—
691C22⋊C4—114no—
692C22⋊C4—114no—
693C22⋊C4C2×C4×D1114yes—
694C22⋊C4C2×C4×D1114yes—
695C22⋊C4C2×C4×D1112yes—
696C42—112no—
697C42—112no—
698C42—112no—
699C42—112no—
700C42—111no—
701C42—112no—
702C42—111no—
703C42—114no—
704C42—114no—
705C42—111no—
706C42—112no—
707C42—112no—
708C42—111no—
709C42C23×D1112yes—
710C11#6020811yescharacteristic, complemented, Sylow
711C23—22no—
712C23—42no—
713C23—112no—
714C23C22×C4×D1112yes—
715C23C22×C4×D1112yes—
716C23C22×C4×D1111yescharacteristic
717Q8—22no—
718Q8—228no—
719Q8—222no—
720D4—24no—
721D4—22no—
722D4—44no—
723D4—228no—
724D4—224no—
725D4—222no—
726D4—444no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—114no—
738C2×C4—112no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—444no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—444no—
749C2×C4C22×C4×D1112yes—
750C2×C4C22×C4×D1112yes—
751C2×C4C22×C4×D1114yes—
752C2×C4C22×C4×D1111yescharacteristic
753C2×C4C2×#434112yes—
754C2×C4#41×D1112yes—
755C2×C4C24×D1111yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—112no—
760C8—112no—
761C8—222no—
762C8—222no—
763C8—222no—
764C8C2×#434112yes—
765C8C2×#434112yes—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—22no—
771C22—22no—
772C22—44no—
773C22—224no—
774C22—222no—
775C22C4×#434112yes—
776C22C23×C4×D1111yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—114no—
781C4—222no—
782C4—222no—
783C4—222no—
784C4—224no—
785C4—222no—
786C4C4×#434112yes—
787C4C22×#434111yescharacteristic
788C4C2×#41×D1111yescharacteristic
789C2—22no—
790C2—42no—
791C2—42no—
792C2—442no—
793C2C2×C4×#434111yescharacteristic
794C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2930C2
prime radical#13081908C2
cosocleC2×C4×C11C25
hypercenter#2930D11
hypocenterC11#60208
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #13077632C2semidirect
3. #13077626C2semidirect
4. #13077615C2semidirect
5. #13077613C2semidirect
6. #13077549C2semidirect
7. #13077548C2semidirect
8. #13077326C2semidirect
9. #13077324C2semidirect
10. #13077320C2semidirect
11. #13077319C2semidirect
12. #13077315C2semidirect
13. #13077266C2semidirect
14. #13077263C2semidirect
15. #13077245C2semidirect
16. #13077043C2semidirect
17. #13077042C2semidirect
18. C2×M16×Dic11C2semidirect
19. C11×#2930C2semidirect
51. #10622741C22semidirect
54. #10622735C22semidirect
64. M16×Dic11C22semidirect
66. C8×C22⋊D11C22semidirect
69. #10622714C22semidirect
72. C2×#66879C22semidirect
79. #10622453C22semidirect
80. #10622448C22semidirect
81. #10622443C22semidirect
82. #10622441C22semidirect
84. #10622342C22semidirect
86. (C22⋊D11)⋊C8C22semidirect
87. #10622333C22semidirect
89. #10622332C22semidirect
91. #10622321C22semidirect
92. D11×#97C22semidirect
93. #10622314C22semidirect
94. #10622302C22semidirect
95. C4×#4313C22semidirect
96. C8×Dic22C22semidirect
257. C2×C8×C11#41semidirect
304. C2×C11⋊C8#41semidirect
326. #2930D11semidirect
670. C2×C8#4341semidirect
710. C11#60208semidirect

Maximal subgroups

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

subgroupindex
#130819082
#130776322
#130776262
#130776152
#130776132
#130775492
#130775482
#130773262
#130773242
#130773202
#130773192
#130773152
#130772662
#130772632
#130772452
#130770432
#130770422
C2×M16×Dic112
C11×#29302
#6020811