Finite Group Databasebeta

← #15618812

Subgroups — #15618812

Order 2816.

1658 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic
2#13077720C214yesmaximal, complemented
3#13077717C212yesmaximal, complemented
4#13077710C212yesmaximal, complemented
5#13077708C214yesmaximal, complemented
6#13077703C212yesmaximal, complemented
7#13077699C212yesmaximal, complemented
8M16×Dic22C211yesmaximal, characteristic, complemented
9#13077563C211yesmaximal, characteristic, complemented
10#13077562C212yesmaximal, complemented
11#13077555C212yesmaximal, complemented
12#13077550C211yesmaximal, characteristic, complemented
13C2×#10622292C211yesmaximal, characteristic, complemented
14#13077282C211yesmaximal, characteristic
15#13077278C212yesmaximal
16#13077263C212yesmaximal
17C11×#2922C211yesmaximal, characteristic
18C4×C11×#41C2211yescharacteristic
19#41×Dic11C2212yes—
20#10623101C411yescharacteristic
21#10623100C412yes—
22Q8×Dic22C411yescharacteristic
23#10623074C411yescharacteristic
24#10623074C412yes—
25#10623070C412yes—
26#10623070C414yes—
27D4×Dic22C411yescharacteristic
28D4×Dic22C412yes—
29#10623048C2212yes—
30#10623048C2214yes—
31#10623001C2211yescharacteristic
32#10623001C2212yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×C4×Dic22C2212yes—
35C11×#433C2212yes—
36C11×#433C2212yes—
37C11×#431C2212yes—
38C11×#431C2212yes—
39C11×#424C2211yescharacteristic
40C11×#424C2211yescharacteristic
41C11×#408C2211yescharacteristic
42C11×#408C2211yescharacteristic
43C4×C11×M16C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45#10622847C2212yes—
46#10622735C2212yes—
47#10622732C2212yes—
48#10622731C2212yes—
49M16×Dic11C2212yes—
50#10622715C2212yes—
51#10622714C2212yes—
52C2×#66879C2212yes—
53C2×Dic11⋊C8C2212yes—
54#10622613C2214yes—
55#10622610C2212yes—
56#10622539C2212yes—
57#10622538C2212yes—
58#10622537C2211yescharacteristic
59C2×C4⋊(C11⋊C8)C2211yescharacteristic
60#10622444C2214yes—
61#10622444C2214yes—
62#10622444C2214yes—
63#10622443C2214yes—
64#10622441C2214yes—
65#10622441C2214yes—
66#10622441C2214yes—
67#10622441C2214yes—
68#10622333C2214yes—
69#10622333C2214yes—
70#10622333C2214yes—
71#10622333C2214yes—
72#10622332C2214yes—
73#10622332C2214yes—
74#10622332C2214yes—
75#10622331C2214yes—
76#10622314C2214yes—
77#10622314C2214yes—
78#10622292C2211yescharacteristic
79#10622292C2211yescharacteristic
80#10622292C2212yes—
81#10622292C2211yescharacteristic
82#10622292C2211yescharacteristic
83#10622292C2212yes—
84#10622292C2212yes—
85#10622292C2212yes—
86#10622292C2212yes—
87#10622292C2212yes—
88C8×Dic22C2212yes—
89C8×Dic22C2212yes—
90C8×Dic22C2212yes—
91C8×Dic22C2212yes—
92C2×C11×#41C2311yescharacteristic
93C22×Dic22C2×C411yescharacteristic
94C22×Dic22C2×C412yes—
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C4×Q8×C11C2×C411yescharacteristic
100C4×Q8×C11C2×C411yescharacteristic
101C4×D4×C11C2×C412yes—
102C4×D4×C11C2×C411yescharacteristic
103C4×D4×C11C2×C412yes—
104C4×D4×C11C2×C411yescharacteristic
105C11×#117C2311yescharacteristic
106C11×#117C2312yes—
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2312yes—
109Q8×Dic11C2×C412yes—
110Q8×Dic11C2×C412yes—
111D4×Dic11C2×C414yes—
112D4×Dic11C2×C412yes—
113D4×Dic11C2×C414yes—
114D4×Dic11C2×C412yes—
115#66979C2312yes—
116#66979C2314yes—
117C2×C4⋊Dic11C2×C411yescharacteristic
118C2×C4⋊Dic11C2×C412yes—
119#66977C2×C412yes—
120#66977C2×C412yes—
121#66977C2×C412yes—
122#66977C2×C412yes—
123#66977C2×C414yes—
124C2×Dic11⋊C4C2×C412yes—
125C2×Dic11⋊C4C2×C414yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×#4318C2312yes—
129C22×C11⋊C8C2312yes—
130#66943C2×C412yes—
131#66943C2×C414yes—
132#66943C2×C412yes—
133#66943C2×C414yes—
134#66941C2×C412yes—
135#66941C2×C414yes—
136#66941C2×C412yes—
137#66941C2×C414yes—
138#66931C2×C414yes—
139#66931C2×C414yes—
140#66931C2×C414yes—
141#66931C2×C414yes—
142#66931C2×C414yes—
143#66931C2×C414yes—
144#66923C2×C412yes—
145#66923C2×C414yes—
146#66922C2×C411yescharacteristic
147#66922C2×C412yes—
148#66922C2×C411yescharacteristic
149#66922C2×C412yes—
150C4×Dic22C2×C411yescharacteristic
151C4×Dic22C2×C412yes—
152C4×Dic22C2×C412yes—
153C4×Dic22C2×C414yes—
154C4×Dic22C2×C411yescharacteristic
155C4×Dic22C2×C412yes—
156C4×Dic22C2311yescharacteristic
157C4×Dic22C2311yescharacteristic
158C4×Dic22C2312yes—
159C4×Dic22C2312yes—
160C4×Dic22C2314yes—
161C4×Dic22C2312yes—
162C4×Dic22C2314yes—
163C11×C4⋊C8C2312yes—
164C11×C4⋊C8C2312yes—
165C11×C4⋊C8C2312yes—
166C11×C4⋊C8C2312yes—
167C11×C22⋊C8C2312yes—
168C11×C22⋊C8C2312yes—
169C11×C22⋊C8C2312yes—
170C11×C22⋊C8C2312yes—
171C11×#97C2312yes—
172C4×C8×C11C2311yescharacteristic
173C4×C8×C11C2311yescharacteristic
174C4×C8×C11C2312yes—
175C4×C8×C11C2311yescharacteristic
176C4×C8×C11C2311yescharacteristic
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179#66879C2314yes—
180#66879C2314yes—
181#66879C2312yes—
182#66879C2312yes—
183#66879C2314yes—
184#66879C2312yes—
185#66879C2312yes—
186Dic11⋊C8C2314yes—
187Dic11⋊C8C2314yes—
188Dic11⋊C8C2314yes—
189Dic11⋊C8C2314yes—
190Dic11⋊C8C2314yes—
191Dic11⋊C8C2314yes—
192Dic11⋊C8C2312yes—
193Dic11⋊C8C2312yes—
194Dic11⋊C8C2312yes—
195Dic11⋊C8C2312yes—
196C8×Dic11C2314yes—
197C8×Dic11C2314yes—
198C8×Dic11C2314yes—
199C4⋊(C11⋊C8)C2311yescharacteristic
200C4⋊(C11⋊C8)C2311yescharacteristic
201C4⋊(C11⋊C8)C2312yes—
202C4⋊(C11⋊C8)C2312yes—
203C4⋊(C11⋊C8)C2312yes—
204#66867C2314yes—
205C4×C11⋊C8C2314yes—
206#60254—111nomaximal, Sylow
207C11×#41—22no—
208C11×#41—22no—
209C2×Q8×C11C22×C411yescharacteristic
210C2×D4×C11C22×C412yes—
211C2×D4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C412yes—
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C412yes—
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C22×Dic11C22×C414yes—
219C22×Dic11C22×C412yes—
220C22×Dic11C22×C414yes—
221C22×Dic11C22×C412yes—
222C2×Dic22—42no—
223C2×Dic22—44no—
224C2×Dic22C22×C411yescharacteristic
225C2×Dic22C22×C411yescharacteristic
226C2×Dic22C22×C412yes—
227C2×Dic22C22×C412yes—
228C2×Dic22C22×C414yes—
229C2×Dic22C22×C412yes—
230C2×Dic22C22×C414yes—
231C11×M16—22no—
232C11×M16—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2411yescharacteristic
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2411yescharacteristic
239C2×C8×C11C2411yescharacteristic
240C2×C8×C11C2411yescharacteristic
241C11×C4⋊C4C22×C412yes—
242C11×C4⋊C4C22×C412yes—
243C11×C4⋊C4C22×C411yescharacteristic
244C11×C4⋊C4C22×C411yescharacteristic
245C11×C22⋊C4C22×C412yes—
246C11×C22⋊C4C22×C412yes—
247C11×C22⋊C4C22×C412yes—
248C42×C11C22×C412yes—
249C42×C11C22×C411yescharacteristic
250C42×C11C22×C412yes—
251C42×C11C22×C411yescharacteristic
252C42×C11C2412yes—
253C42×C11C2411yescharacteristic
254C42×C11C2411yescharacteristic
255C22⋊Dic11C22×C414yes—
256C22⋊Dic11C22×C414yes—
257C22⋊Dic11C22×C414yes—
258C4⋊Dic11C22×C411yescharacteristic
259C4⋊Dic11C22×C411yescharacteristic
260C4⋊Dic11C22×C412yes—
261C4⋊Dic11C22×C412yes—
262C4⋊Dic11C22×C414yes—
263C4⋊Dic11C22×C412yes—
264C4⋊Dic11C22×C414yes—
265C4⋊Dic11C22×C414yes—
266C4⋊Dic11C22×C414yes—
267C4⋊Dic11C22×C412yes—
268C4⋊Dic11C22×C412yes—
269Dic11⋊C4C22×C412yes—
270Dic11⋊C4C22×C412yes—
271Dic11⋊C4C22×C414yes—
272Dic11⋊C4C22×C412yes—
273Dic11⋊C4C22×C414yes—
274Dic11⋊C4C22×C412yes—
275Dic11⋊C4C22×C414yes—
276Dic11⋊C4C22×C414yes—
277Dic11⋊C4C22×C414yes—
278Dic11⋊C4C22×C414yes—
279C4×Dic11C22×C414yes—
280C4×Dic11C22×C412yes—
281C4×Dic11C22×C414yes—
282C4×Dic11C22×C412yes—
283C4×Dic11C2412yes—
284C4×Dic11C2414yes—
285C4×Dic11C2412yes—
286#4318—24no—
287C2×C11⋊C8—24no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2414yes—
290C2×C11⋊C8C2412yes—
291Q8×#41—111no—
292#2987—114no—
293#2986—112no—
294#2985—114no—
295#2985—112no—
296#2984—112no—
297#2983—112no—
298Q8×M16—111no—
299#2962—112no—
300#2962—111no—
301#2961—112no—
302#2960—111no—
303C2×#446—111no—
304#2925—112no—
305#2925—111no—
306#2923—112no—
307#2922D1111yescharacteristic
308C23×C11C23×C412yes—
309C23×C11C23×C411yescharacteristic
310Q8×C11—22no—
311D4×C11—24no—
312D4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11C23×C412yes—
320C2×C4×C11C23×C411yescharacteristic
321C2×C4×C11C23×C412yes—
322C2×C4×C11C23×C411yescharacteristic
323C2×C4×C11C23×C412yes—
324C2×C4×C11C23×C411yescharacteristic
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C23×C411yescharacteristic
327C2×C4×C112−1+412yes—
328C2×C4×C112−1+412yes—
329C2×C4×C11C2511yescharacteristic
330C2×Dic11—42no—
331C2×Dic11—44no—
332C2×Dic11—42no—
333C2×Dic11—44no—
334C2×Dic11C23×C412yes—
335C2×Dic11C23×C412yes—
336C2×Dic11C23×C414yes—
337C2×Dic11C23×C412yes—
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C412yes—
340Dic22—22no—
341Dic22—22no—
342Dic22—24no—
343Dic22—42no—
344Dic22—44no—
345Dic22—42no—
346Dic22—44no—
347C8×C11—21no—
348C8×C11—21no—
349C8×C11—21no—
350C8×C11—21no—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C11⋊C8—24no—
356Q82—111no—
357#557—112no—
358#557—111no—
359#554—114no—
360#554—112no—
361#554—112no—
362#554—111no—
363D4×Q8—111no—
364D4×Q8—112no—
365#533—112no—
366#533—114no—
367#533—111no—
368#533—112no—
369C4×#41—112no—
370C4×#41C2×D1111yescharacteristic
371C2×C4×Q8—111no—
372C2×C4×Q8—112no—
373#446—114no—
374#446—114no—
375#446—114no—
376#446—114no—
377#446—114no—
378#446—114no—
379#446—114no—
380#446—114no—
381#446—114no—
382#446—111no—
383#446—111no—
384#446—111no—
385#446—112no—
386#446—111no—
387#446—112no—
388#446—112no—
389#446—112no—
390#446—112no—
391#446—112no—
392C8×Q8—114no—
393C8×Q8—112no—
394C8×Q8—112no—
395C8×Q8—112no—
396C8×Q8—112no—
397#433—114no—
398#433—114no—
399#433—114no—
400#433—114no—
401#433—114no—
402#433C2×D1112yes—
403#433C2×D1112yes—
404#432—112no—
405#432—114no—
406#432—114no—
407#432—114no—
408#431—112no—
409#431—114no—
410#431C2×D1112yes—
411#431C2×D1112yes—
412#424—112no—
413#424—112no—
414#424C2×D1111yescharacteristic
415#424C2×D1111yescharacteristic
416#423—112no—
417#423—111no—
418C2×C4⋊C8—112no—
419C2×C4⋊C8—111no—
420#408—112no—
421#408C2×D1111yescharacteristic
422#408C2×D1111yescharacteristic
423#405—112no—
424#405—112no—
425#405—112no—
426C4×M16—112no—
427C4×M16C2×D1111yescharacteristic
428C2×#97—112no—
429C2×C4×C8C2×D1111yescharacteristic
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11#51912yes—
436C22×C11C24×C411yescharacteristic
437C4×C11—22no—
438C4×C11—21no—
439C4×C11—22no—
440C4×C11—21no—
441C4×C11—21no—
442C4×C11—22no—
443C4×C11#51912yes—
444C4×C11#56812yes—
445C4×C11C2×2−1+411yescharacteristic
446C4×C11C2×2−1+411yescharacteristic
447Dic11—22no—
448Dic11—22no—
449Dic11—24no—
450Dic11—22no—
451Dic11—24no—
452Dic11—22no—
453C2×#41C22×D1111yescharacteristic
454C22×Q8—111no—
455C22×Q8—112no—
456C2×M16—112no—
457C2×M16C22×D1111yescharacteristic
458C2×M16C22×D1111yescharacteristic
459C22×C8—112no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C4⋊Q8—112no—
463C4⋊Q8—114no—
464C4⋊Q8—112no—
465C4⋊Q8—114no—
466C4⋊Q8—111no—
467C4⋊Q8—112no—
468C4⋊Q8—111no—
469C4⋊Q8—112no—
470#125—112no—
471#125—114no—
472#125—112no—
473#125—114no—
474#125—112no—
475#125—114no—
476C22⋊Q8—112no—
477C22⋊Q8—112no—
478C22⋊Q8—112no—
479C22⋊Q8—112no—
480C22⋊Q8—114no—
481C22⋊Q8—114no—
482C22⋊Q8—114no—
483C22⋊Q8—114no—
484C22⋊Q8—114no—
485C22⋊Q8—114no—
486C22⋊Q8—114no—
487C4×Q8—112no—
488C4×Q8—112no—
489C4×Q8—111no—
490C4×Q8—112no—
491C4×Q8—111no—
492C4×Q8—112no—
493C4×Q8—112no—
494C4×Q8—114no—
495C4×Q8—111no—
496C4×Q8—111no—
497C4×Q8—112no—
498C4×Q8—114no—
499C4×Q8—112no—
500C4×Q8—114no—
501C4×Q8—112no—
502C4×Q8C4×D1111yescharacteristic
503C4×Q8C4×D1111yescharacteristic
504C4×D4—114no—
505C4×D4—112no—
506C4×D4—114no—
507C4×D4—112no—
508C4×D4C4×D1112yes—
509C4×D4C4×D1111yescharacteristic
510C4×D4C4×D1112yes—
511C4×D4C4×D1111yescharacteristic
512#117—112no—
513#117—114no—
514#117C22×D1111yescharacteristic
515#117C22×D1112yes—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—112no—
520C2×C42—112no—
521C2×C42—114no—
522C2×C42C22×D1111yescharacteristic
523C2×C42C22×D1112yes—
524C4⋊C8—112no—
525C4⋊C8—112no—
526C4⋊C8—112no—
527C4⋊C8—112no—
528C4⋊C8—114no—
529C4⋊C8—114no—
530C4⋊C8—114no—
531C4⋊C8—114no—
532C4⋊C8—114no—
533C4⋊C8—114no—
534C4⋊C8—111no—
535C4⋊C8—111no—
536C4⋊C8—112no—
537C4⋊C8—112no—
538C4⋊C8—112no—
539C4⋊C8C22×D1112yes—
540C4⋊C8C22×D1112yes—
541C4⋊C8C22×D1112yes—
542C4⋊C8C22×D1112yes—
543C22⋊C8—114no—
544C22⋊C8—114no—
545C22⋊C8C22×D1112yes—
546C22⋊C8C22×D1112yes—
547C22⋊C8C22×D1112yes—
548C22⋊C8C22×D1112yes—
549#97—112no—
550#97—112no—
551#97—112no—
552#97—112no—
553#97—114no—
554#97—114no—
555#97—114no—
556#97—114no—
557#97C22×D1112yes—
558C4×C8—114no—
559C4×C8—114no—
560C4×C8—114no—
561C4×C8—114no—
562C4×C8C22×D1111yescharacteristic
563C4×C8C22×D1111yescharacteristic
564C4×C8C22×D1111yescharacteristic
565C4×C8C22×D1111yescharacteristic
566C4×C8C22×D1112yes—
567C2×C11—22no—
568C2×C11—42no—
569C2×C11C2×#51911yescharacteristic
570C2×C11C2×#56811yescharacteristic
571C2×C11#357311yescharacteristic
572#41—22no—
573#41—22no—
574C2×Q8—111no—
575C2×Q8—111no—
576C2×Q8—112no—
577C2×Q8—114no—
578C2×Q8—112no—
579C2×Q8—114no—
580C2×Q8—112no—
581C2×Q8—442no—
582C2×Q8—444no—
583C2×Q8C2×C4×D1111yescharacteristic
584C2×D4C2×C4×D1112yes—
585C2×D4C2×C4×D1111yescharacteristic
586C22×C4—114no—
587C22×C4—112no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4C2×C4×D1112yes—
591C22×C4C2×C4×D1111yescharacteristic
592C22×C4C2×C4×D1112yes—
593C22×C4C2×C4×D1111yescharacteristic
594C22×C4C23×D1112yes—
595C22×C4C23×D1111yescharacteristic
596M16—22no—
597M16—22no—
598M16—224no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—114no—
602C2×C8—112no—
603C2×C8—112no—
604C2×C8—224no—
605C2×C8C23×D1111yescharacteristic
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C2×C8C23×D1111yescharacteristic
609C2×C8C23×D1111yescharacteristic
610C2×C8C23×D1111yescharacteristic
611C4⋊C4—112no—
612C4⋊C4—111no—
613C4⋊C4—114no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—114no—
617C4⋊C4—114no—
618C4⋊C4—112no—
619C4⋊C4—114no—
620C4⋊C4—112no—
621C4⋊C4—111no—
622C4⋊C4—112no—
623C4⋊C4—114no—
624C4⋊C4—114no—
625C4⋊C4—112no—
626C4⋊C4—112no—
627C4⋊C4—114no—
628C4⋊C4—114no—
629C4⋊C4—114no—
630C4⋊C4—114no—
631C4⋊C4—112no—
632C4⋊C4C2×C4×D1112yes—
633C4⋊C4C2×C4×D1112yes—
634C4⋊C4C2×C4×D1111yescharacteristic
635C4⋊C4C2×C4×D1111yescharacteristic
636C22⋊C4—114no—
637C22⋊C4—114no—
638C22⋊C4—114no—
639C22⋊C4C2×C4×D1112yes—
640C22⋊C4C2×C4×D1112yes—
641C22⋊C4C2×C4×D1112yes—
642C42—114no—
643C42—112no—
644C42—114no—
645C42—112no—
646C42—112no—
647C42—114no—
648C42—112no—
649C42C2×C4×D1112yes—
650C42C2×C4×D1111yescharacteristic
651C42C2×C4×D1112yes—
652C42C2×C4×D1111yescharacteristic
653C42C23×D1112yes—
654C42C23×D1111yescharacteristic
655C42C23×D1111yescharacteristic
656C11#6025411yescharacteristic, complemented, Sylow
657C23C22×C4×D1112yes—
658C23C22×C4×D1111yescharacteristic
659Q8—22no—
660Q8—222no—
661Q8—222no—
662Q8—224no—
663Q8—442no—
664Q8—444no—
665Q8—442no—
666Q8—444no—
667D4—24no—
668D4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—114no—
678C2×C4—112no—
679C2×C4—114no—
680C2×C4—112no—
681C2×C4—442no—
682C2×C4—444no—
683C2×C4—442no—
684C2×C4—444no—
685C2×C4C22×C4×D1112yes—
686C2×C4C22×C4×D1111yescharacteristic
687C2×C4C22×C4×D1112yes—
688C2×C4C22×C4×D1111yescharacteristic
689C2×C4C22×C4×D1112yes—
690C2×C4C22×C4×D1111yescharacteristic
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C22×C4×D1111yescharacteristic
693C2×C4#6704312yes—
694C2×C4#6704312yes—
695C2×C4C24×D1111yescharacteristic
696C8—21no—
697C8—21no—
698C8—21no—
699C8—21no—
700C8—22no—
701C8—22no—
702C8—222no—
703C8—222no—
704C8—224no—
705C22—21no—
706C22—21no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22#1062304712yes—
711C22C23×C4×D1111yescharacteristic
712C4—21no—
713C4—22no—
714C4—21no—
715C4—21no—
716C4—22no—
717C4—22no—
718C4—222no—
719C4—222no—
720C4—224no—
721C4—222no—
722C4—222no—
723C4—224no—
724C4#1062304712yes—
725C4#1062328112yes—
726C4C2×#6704311yescharacteristic
727C4C2×#6704311yescharacteristic
728C2—22no—
729C2—42no—
730C2C2×#1062304711yescharacteristic
731C2C2×#1062328111yescharacteristic
732C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2922C2
prime radicalC2×C11×#41C23
cosocleC2×C4×C11C25
hypercenter#2922D11
hypocenterC11#60254
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13077720C2semidirect
3. #13077717C2semidirect
4. #13077710C2semidirect
5. #13077708C2semidirect
6. #13077703C2semidirect
7. #13077699C2semidirect
8. M16×Dic22C2semidirect
9. #13077563C2semidirect
10. #13077562C2semidirect
11. #13077555C2semidirect
12. #13077550C2semidirect
13. C2×#10622292C2semidirect
656. C11#60254semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
#130777202
#130777172
#130777102
#130777082
#130777032
#130776992
M16×Dic222
#130775632
#130775622
#130775552
#130775502
C2×#106222922
#130772822
#130772782
#130772632
C11×#29222
#6025411