Finite Group Databasebeta

← #14800822

Subgroups — #14800822

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622665C211yesmaximal, characteristic, complemented
2C2×#10622663C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5#13071981C211yesmaximal, characteristic
6#13069994C211yesmaximal, characteristic, complemented
7#13069938C211yesmaximal, characteristic, complemented
8#13069812C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13069486C211yesmaximal, characteristic, complemented
11#13069305C211yesmaximal, characteristic, complemented
12#13069047C211yesmaximal, characteristic, complemented
13#13069040C211yesmaximal, characteristic, complemented
14#13068809C211yesmaximal, characteristic, complemented
15C11×#2417C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#398—21no—
28C11×#396—21no—
29C11×#391C2211yescharacteristic
30C11×#389C2211yescharacteristic
31C11×#386—21no—
32C11×#380—21no—
33C11×#380C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622833—21no—
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622665—24no—
41#10622663—24no—
42#10622624—24no—
43#10622592—21no—
44C2×#66874—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53#10622560—21no—
54#10622559—21no—
55#10622542C2211yescharacteristic
56#10622542C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—21no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22—22no—
73C22×Dic22—21no—
74C22×Dic22—41no—
75C22×Dic22—41no—
76C22×Dic22C2311yescharacteristic
77C22×Dic22C2311yescharacteristic
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—41no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—41no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×#4326—22no—
104C2×#4326—22no—
105C2×#4326—22no—
106C2×#4326—22no—
107C2×#4326—41no—
108C2×#4326—41no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113#66977—41no—
114#66977—41no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318—41no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131#66899—22no—
132#66899—41no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139C22⋊(C11⋊C8)D414yes—
140#66874—22no—
141#66874—22no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66874D414yescomplemented
146#66872—22no—
147#66872—41no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25126—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11#4112yes—
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C2×Dic22—28no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—44no—
205C2×Dic22—44no—
206C2×Dic22—42no—
207C2×Dic22—42no—
208C2×Dic22—44no—
209C2×Dic22—42no—
210C2×Dic22C2×D412yes—
211C2×Dic22#4112yes—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4C2×D412yes—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C42×C11—21no—
229C42×C11—21no—
230C22⋊Dic11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—42no—
233#4326—44no—
234#4326—44no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239Dic11⋊C4—42no—
240Dic11⋊C4—42no—
241#4318—44no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—44no—
252C2×C11⋊C8C2×D412yes—
253C2×C11⋊C8C2×D412yes—
254C2×C11⋊C8C2×D412yes—
255C2×#470—111no—
256C2×#451—111no—
257C2×#435—111no—
258C22×#103—111no—
259#2417D1111yescharacteristic
260#2409—111no—
261#2066—111no—
262#2056—111no—
263#2035—111no—
264#2001—111no—
265#1971—111no—
266#1935—111no—
267#1894—111no—
268#1892—111no—
269#1853—111no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11#12112yes—
282C23×C11#13712yes—
283C23×C11#13712yes—
284C23×C11C22×D411yescharacteristic
285Q8×C11—41no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
289D4×C11—44no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—84no—
322C2×C4×C11#12112yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—48no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342Dic22—22no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22—48no—
347Dic22—41no—
348Dic22—41no—
349Dic22—41no—
350Dic22—41no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—41no—
355C23×Q8—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×M16—111no—
359C23×C8—111no—
360C2×C22⋊Q8—111no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×C22⋊Q8C2×D1111yescharacteristic
364C2×C4×D4C2×D1111yescharacteristic
365C22×C4⋊C4C2×D1111yescharacteristic
366#470—224no—
367#451—224no—
368#435—224no—
369C2×#106—111no—
370C2×#106—111no—
371C2×C4⋊C8—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103—224no—
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×#97—111no—
384#398—21no—
385#396—21no—
386#395—221no—
387#393—221no—
388#391—111no—
389#391—111no—
390#391C2×D1111yescharacteristic
391#389C2×D1111yescharacteristic
392#386—21no—
393#386—221no—
394#385—221no—
395#380—21no—
396#380—111no—
397#380C2×D1111yescharacteristic
398#340—111no—
399#340—111no—
400#340—111no—
401#340—111no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11#47014yescomplemented
416C22×C11C2×#12111yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11C2×#13711yescharacteristic
420C22×C11C2×#13711yescharacteristic
421C22×C11#57711yescharacteristic
422C22×C11#57811yescharacteristic
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—42no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11#52511yescharacteristic
432C4×C11#53811yescharacteristic
433C4×C11D4211yescharacteristic
434C4×C11#54611yescharacteristic
435Dic11—42no—
436Dic11—42no—
437Dic11—81no—
438Dic11—81no—
439C22×Q8—111no—
440C22×Q8—111no—
441C22×Q8—222no—
442C22×Q8—222no—
443C22×Q8—221no—
444C22×Q8—222no—
445C22×Q8—222no—
446C22×Q8—441no—
447C22×Q8—441no—
448C22×Q8C22×D1111yescharacteristic
449C22×D4C22⋊D1111yescharacteristic
450C23×C4—21no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C2×Q16—222no—
455C2×Q16—222no—
456C2×Q16—222no—
457C2×Q16—222no—
458C2×Q16—441no—
459C2×Q16—441no—
460C2×M16—222no—
461C2×M16—222no—
462C2×M16—441no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—222no—
468C22×C8—222no—
469C22×C8—441no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—41no—
474C22⋊Q8—222no—
475C22⋊Q8—222no—
476C22⋊Q8—441no—
477C22⋊Q8—441no—
478C4×D4—22no—
479C4×D4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4C22⋊D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4C22⋊D1111yescharacteristic
501C2×C22⋊C4C22⋊D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503#106—222no—
504#106—441no—
505C4⋊C8—222no—
506#103—114no—
507#103—222no—
508#103—222no—
509#103—222no—
510#103—222no—
511#103—222no—
512#103—222no—
513#103—441no—
514C22⋊C8—114no—
515C22⋊C8—222no—
516#97—222no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—221no—
522#95—221no—
523#95—221no—
524#95—221no—
525#95—221no—
526C2×C11—24no—
527C2×C11—81no—
528C2×C11#242411yescharacteristic
529C2×C11C2×#47011yescharacteristic
530C2×C11#306311yescharacteristic
531C2×C11#326611yescharacteristic
532C2×C11#327011yescharacteristic
533C2×C11#331211yescharacteristic
534C2×C11#331611yescharacteristic
535C24C2×C22⋊D1111yescharacteristic
536C24C2×C22⋊D1111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—112no—
544C2×Q8—112no—
545C2×Q8—228no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—442no—
557C2×Q8—442no—
558C2×Q8—444no—
559C2×Q8—444no—
560C2×Q8—444no—
561C2×Q8—442no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—81no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—442no—
587C22×C4—442no—
588C22×C4—442no—
589C22×C4D4×D1112yes—
590C22×C4#434112yes—
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C23×D1111yescharacteristic
596Q16—444no—
597Q16—444no—
598M16—444no—
599C2×C8—112no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—444no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—81no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—442no—
627C4⋊C4—442no—
628C4⋊C4D4×D1112yes—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—442no—
635C22⋊C4—442no—
636C22⋊C4—442no—
637C42—21no—
638C42—21no—
639C11#2512611yescharacteristic, complemented, Sylow
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23#6699212yes—
652C23#6699512yes—
653C23#6700412yes—
654C23C22×C22⋊D1111yescharacteristic
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—222no—
660Q8—222no—
661Q8—222no—
662Q8—222no—
663Q8—448no—
664Q8—441no—
665Q8—441no—
666Q8—441no—
667Q8—441no—
668D4—44no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4#6699212yes—
715C2×C4C2×D4×D1111yescharacteristic
716C2×C4C2×D4×D1111yescharacteristic
717C2×C4C2×#434111yescharacteristic
718C2×C4#6703711yescharacteristic
719C2×C4#41×D1111yescharacteristic
720C2×C4#6704211yescharacteristic
721C8—222no—
722C8—222no—
723C8—222no—
724C8—441no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22#1062266514yescomplemented
739C22D4×C22⋊D1111yescharacteristic
740C22C2×#6699211yescharacteristic
741C22C2×#6699511yescharacteristic
742C22C2×#6700411yescharacteristic
743C22#1062336011yescharacteristic
744C22#1062336711yescharacteristic
745C22#1062336911yescharacteristic
746C4—22no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—442no—
755C4—442no—
756C4—881no—
757C4—881no—
758C4#1062313711yescharacteristic
759C4#1062314011yescharacteristic
760C4#1062314111yescharacteristic
761C4#1062314811yescharacteristic
762C2—24no—
763C2—81no—
764C2#1307215811yescharacteristic
765C2C2×#1062266511yescharacteristic
766C2#1307830911yescharacteristic
767C2#1308012211yescharacteristic
768C2#1308018711yescharacteristic
769C2#1308066111yescharacteristic
770C2#1308072111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2417C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2417D11
hypocenterC11#25126
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#10622665C2semidirect
2. C2×#10622663C2semidirect
4. C22×#66874C2semidirect
6. #13069994C2semidirect
7. #13069938C2semidirect
8. #13069812C2semidirect
9. #13069624C2semidirect
10. #13069486C2semidirect
11. #13069305C2semidirect
12. #13069047C2semidirect
13. #13069040C2semidirect
14. #13068809C2semidirect
145. #66874D4semidirect
415. C22×C11#470semidirect
639. C11#25126semidirect
738. C22#10622665semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×#106226632
C2×#106226242
C22×#668742
#130719812
#130699942
#130699382
#130698122
#130696242
#130694862
#130693052
#130690472
#130690402
#130688092
C11×#24172
#2512611