Finite Group Databasebeta

← #14800816

Subgroups — #14800816

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×#10622429C211yesmaximal, characteristic, complemented
2C2×#10622841C211yesmaximal, characteristic, complemented
3C2×#10622724C211yesmaximal, characteristic
4#13072061C211yesmaximal, characteristic
5#13071975C211yesmaximal, characteristic
6#13069993C211yesmaximal, characteristic, complemented
7#13069937C211yesmaximal, characteristic, complemented
8#13069810C211yesmaximal, characteristic, complemented
9#13069625C211yesmaximal, characteristic, complemented
10#13069484C211yesmaximal, characteristic, complemented
11#13069308C211yesmaximal, characteristic, complemented
12#13069046C211yesmaximal, characteristic, complemented
13#13069039C211yesmaximal, characteristic, complemented
14#13068809C211yesmaximal, characteristic, complemented
15C22×C11×#103C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C2×#66950C2211yescharacteristic
27C2×C11×#103—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32#10622844—21no—
33#10622843C2211yescharacteristic
34#10622843C2211yescharacteristic
35#10622842—21no—
36#10622841—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622826—21no—
40#10622826—21no—
41#10622825—21no—
42#10622825C2211yescharacteristic
43#10622823—21no—
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622724—24no—
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49C2×#66879C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51#10622607—21no—
52#10622600C2211yescharacteristic
53#10622598C2211yescharacteristic
54#10622596—21no—
55#10622587C2211yescharacteristic
56C2×#66872C2211yescharacteristic
57C2×#66872C2211yescharacteristic
58#10622429—24no—
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22C2311yescharacteristic
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11D411yescharacteristic
91#66999—22no—
92#66999—22no—
93#66999—41no—
94#66999—41no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—22no—
98C2×#4326—22no—
99C2×#4326—41no—
100C2×#4326—41no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4D411yescharacteristic
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977—22no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4D411yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C2×#4313—22no—
123C2×#4313—22no—
124C2×#4313—41no—
125#66950—22no—
126#66950—41no—
127C11×#103—22no—
128C11×#103—22no—
129C11×#103—22no—
130C11×#103D414yescomplemented
131#66899—22no—
132#66899—22no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)D414yes—
143(C2×D11)⋊C8—22no—
144#66880—22no—
145#66880—41no—
146#66879—22no—
147Dic11⋊C8—22no—
148#66872—22no—
149#66872—41no—
150#25126—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C23×D11C2×D411yescharacteristic
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—28no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—42no—
165C2×Q8×C11—42no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C2×Q8×C11—42no—
170C2×Q8×C11C2×D412yes—
171C2×Q8×C11#4112yes—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—44no—
218C2×C8×C11C2×D412yes—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—42no—
223C11×C4⋊C4C2×D412yes—
224C22⋊Dic11—22no—
225C22⋊Dic11—42no—
226C22⋊Dic11—42no—
227#4326—44no—
228#4326—44no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4—81no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—42no—
241C4⋊Dic11—81no—
242Dic11⋊C4—22no—
243Dic11⋊C4—42no—
244Dic11⋊C4—42no—
245Dic11⋊C4—42no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8C2×D412yes—
253C2×C11⋊C8C2×D412yes—
254#4313—44no—
255C2×#470—111no—
256C2×#451—111no—
257C2×#435—111no—
258C22×#103D1111yescharacteristic, complemented
259#2417—111no—
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#12112yes—
275C23×C11#13712yes—
276C23×C11#13712yes—
277C23×C11C22×D411yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—48no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—41no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—48no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
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—84no—
314C2×C4×C11#12112yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C22⋊D11—44no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—41no—
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—
342C2×Dic11—41no—
343C4×D11—41no—
344C4×D11—41no—
345C4×D11—41no—
346C4×D11—41no—
347Dic22—41no—
348Dic22—41no—
349Dic22—41no—
350Dic22—41no—
351C8×C11—22no—
352C8×C11—41no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8C2×D1111yescharacteristic
356C22×Q16—111no—
357C22×Q16—111no—
358C22×M16—111no—
359C23×C8C2×D1111yescharacteristic
360C2×C22⋊Q8—111no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—111no—
363C2×C22⋊Q8—111no—
364C2×C4×D4—111no—
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—24no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103C2×D1111yescharacteristic
378C2×#103C2×D1111yescharacteristic
379C2×#103C2×D1111yescharacteristic
380C2×#103C2×D1111yescharacteristic
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×#97—111no—
384#398—221no—
385#396—221no—
386#395—221no—
387#393—221no—
388#391—111no—
389#391—111no—
390#391—111no—
391#389—111no—
392#386—221no—
393#386—221no—
394#385—221no—
395#380—111no—
396#380—111no—
397#380—221no—
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#47014yescomplemented
409C22×C11C2×#12111yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11C2×#13711yescharacteristic
413C22×C11C2×#13711yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57811yescharacteristic
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—81no—
428C4×C11#52511yescharacteristic
429C4×C11#53811yescharacteristic
430C4×C11D4211yescharacteristic
431C4×C11#54611yescharacteristic
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—81no—
436Dic11—81no—
437Dic11—81no—
438Dic11—81no—
439C22×Q8—21no—
440C22×Q8—22no—
441C22×Q8—22no—
442C22×Q8—22no—
443C22×Q8—22no—
444C22×Q8—41no—
445C22×Q8—41no—
446C22×Q8—111no—
447C22×Q8C22×D1111yescharacteristic
448C22×Q8C22×D1111yescharacteristic
449C22×D4—111no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—111no—
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—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8C22×D1111yescharacteristic
469C22×C8C22×D1111yescharacteristic
470C22⋊Q8—222no—
471C22⋊Q8—222no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474C22⋊Q8—222no—
475C22⋊Q8—441no—
476C22⋊Q8—441no—
477C22⋊Q8—441no—
478C4×D4—222no—
479C4×D4—222no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C42—111no—
503#106—222no—
504#106—441no—
505C4⋊C8—222no—
506#103—22no—
507#103—22no—
508#103—22no—
509#103—222no—
510#103—222no—
511#103—222no—
512#103—441no—
513#103C22⋊D1114yescomplemented
514C22⋊C8—114no—
515C22⋊C8—222no—
516#97—222no—
517#95—221no—
518#95—221no—
519#95—221no—
520#95—221no—
521#95—221no—
522#95—221no—
523#95—221no—
524#95—221no—
525#95—221no—
526C2×C11—24no—
527C2×C11#242411yescharacteristic
528C2×C11C2×#47011yescharacteristic
529C2×C11#306311yescharacteristic
530C2×C11#326611yescharacteristic
531C2×C11#327011yescharacteristic
532C2×C11#331211yescharacteristic
533C2×C11#331611yescharacteristic
534D11—81no—
535C24—111no—
536C24D4×D1111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—28no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—44no—
553C2×Q8—42no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8—221no—
558C2×Q8—221no—
559C2×Q8—221no—
560C2×Q8#433912yes—
561C2×Q8C2×C22⋊D1112yes—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—222no—
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—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4#433912yes—
593C22×C4D4×D1111yescharacteristic
594C22×C4D4×D1112yes—
595C22×C4C23×D1111yescharacteristic
596Q16—444no—
597Q16—444no—
598M16—444no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—44no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8C2×C22⋊D1112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—222no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—442no—
624C4⋊C4—442no—
625C4⋊C4—442no—
626C4⋊C4—442no—
627C4⋊C4—881no—
628C4⋊C4C2×C22⋊D1112yes—
629C22⋊C4—222no—
630C22⋊C4—222no—
631C22⋊C4—442no—
632C22⋊C4—442no—
633C22⋊C4—442no—
634C22⋊C4—442no—
635C22⋊C4—442no—
636C22⋊C4—881no—
637C42—221no—
638C42—221no—
639C11#2512611yescharacteristic, complemented, Sylow
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23#6693712yes—
652C23#6696812yes—
653C23#6697112yes—
654C23C2×D4×D1111yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—48no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—441no—
665Q8—441no—
666Q8—441no—
667Q8—441no—
668D4—444no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
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#6693712yes—
715C2×C4C2×#433911yescharacteristic
716C2×C4C2×#433911yescharacteristic
717C2×C4C2×D4×D1111yescharacteristic
718C2×C4#6703711yescharacteristic
719C2×C4#6703711yescharacteristic
720C2×C4C22×C22⋊D1111yescharacteristic
721C8—22no—
722C8—41no—
723C8—222no—
724C8—222no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22#1062242914yescomplemented
739C22C2×#6693711yescharacteristic
740C22#1062302111yescharacteristic
741C22C2×#6696811yescharacteristic
742C22#1062329311yescharacteristic
743C22C2×#6697111yescharacteristic
744C22#1062329711yescharacteristic
745C22D4×C22⋊D1111yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—81no—
751C4—441no—
752C4—441no—
753C4—441no—
754C4—881no—
755C4—881no—
756C4—881no—
757C4—881no—
758C4#1062302111yescharacteristic
759C4#1062302511yescharacteristic
760C4#1062332211yescharacteristic
761C4D4×C22⋊D1111yescharacteristic
762C2—24no—
763C2—881no—
764C2#1307215211yescharacteristic
765C2C2×#1062242911yescharacteristic
766C2#1307830511yescharacteristic
767C2#1308012611yescharacteristic
768C2#1308018611yescharacteristic
769C2#1308066311yescharacteristic
770C2#1308072311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC22×#103D11
hypocenterC11#25126
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#10622429C2semidirect
2. C2×#10622841C2semidirect
6. #13069993C2semidirect
7. #13069937C2semidirect
8. #13069810C2semidirect
9. #13069625C2semidirect
10. #13069484C2semidirect
11. #13069308C2semidirect
12. #13069046C2semidirect
13. #13069039C2semidirect
14. #13068809C2semidirect
15. C22×C11×#103C2semidirect
130. C11×#103D4semidirect
258. C22×#103D11semidirect
408. C22×C11#470semidirect
513. #103C22⋊D11semidirect
639. C11#25126semidirect
738. C22#10622429semidirect

Maximal subgroups

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

subgroupindex
C2×#106224292
C2×#106228412
C2×#106227242
#130720612
#130719752
#130699932
#130699372
#130698102
#130696252
#130694842
#130693082
#130690462
#130690392
#130688092
C22×C11×#1032
#2512611