Finite Group Databasebeta

← #14769298

Subgroups — #14769298

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069544C211yesmaximal, characteristic, complemented
6#13069441C211yesmaximal, characteristic, complemented
7#13069055C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068939C211yesmaximal, characteristic, complemented
10#13068934C211yesmaximal, characteristic, complemented
11#13068631C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#550C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#550—24no—
19C11×#550C418yescomplemented
20C2×C11×#127—21no—
21C2×C11×#127C2211yescharacteristic
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33#10622846—24no—
34#10622845—24no—
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622833—21no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622624—24no—
53#10622594—21no—
54#10622564—21no—
55C22⋊C4×Dic11—21no—
56#10622549C2211yescharacteristic
57C4×C4⋊Dic11C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×#66867C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41C2×C414yes—
75C2×C11×#41C2×C414yescomplemented
76C22×Q8×C11C2311yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×Dic11—21no—
91C11×#127—28no—
92C11×#127—22no—
93C11×#127C2×C414yescomplemented
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—28no—
97C11×#121—28no—
98C11×#121C2×C414yes—
99C11×#121C2×C414yescomplemented
100C4×Q8×C11—22no—
101C4×Q8×C11C2×C414yescomplemented
102C4×D4×C11—28no—
103C4×D4×C11C2×C414yes—
104C4×D4×C11D414yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66979—22no—
118#66979—41no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—41no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8—22no—
133C22×C11⋊C8—41no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138#66899—22no—
139#66899—22no—
140#66899—22no—
141#66899D414yescomplemented
142#66896—22no—
143#66896—22no—
144#66896—22no—
145#66896—22no—
146#66896—41no—
147#66896—41no—
148#66896—41no—
149#66896—41no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154C11⋊#95—21no—
155C22⋊(C11⋊C8)—22no—
156C22⋊(C11⋊C8)—22no—
157C4⋊(C11⋊C8)—22no—
158#66867—22no—
159#22422—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C24×C11C2×D411yescharacteristic
164C11×#41—28no—
165C11×#41—28no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C11×#41—44no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C22×C412yes—
176C2×Q8×C11C2×D412yes—
177C2×Q8×C11#4112yes—
178C2×D4×C11—24no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—41no—
195C2×D4×C11—41no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11—81no—
203C2×D4×C11—81no—
204C2×D4×C11—81no—
205C2×D4×C11—81no—
206C2×D4×C11—81no—
207C2×D4×C11—81no—
208C2×D4×C11C22⋊C414yes—
209C2×D4×C11C22×C412yes—
210C2×D4×C11C22×C412yes—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—24no—
222C22×C4×C11—24no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2411yescharacteristic
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—81no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4C22⋊C414yes—
246C11×C4⋊C4C22×C412yes—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4C22⋊C414yes—
250C11×C22⋊C4C22⋊C414yes—
251C42×C11—24no—
252C42×C11C22×C412yes—
253C42×C11C2×D412yes—
254C22⋊Dic11—42no—
255C22⋊Dic11—42no—
256C22⋊Dic11—81no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—42no—
265C4⋊Dic11C2×D412yes—
266C4×Dic11—42no—
267C4×Dic11—81no—
268#4318—44no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—44no—
281C2×C11⋊C8C2×D412yes—
282C2×#550D1111yescharacteristic
283C2×#435—111no—
284C2×#417—111no—
285C2×#416—111no—
286#2352—111no—
287#1982—111no—
288#1961—111no—
289#1895—111no—
290#1893—111no—
291#1875—111no—
292#1874—111no—
293#1805—111no—
294#1788—111no—
295#1788—111no—
296#1763—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11C2×C22⋊C412yes—
324C23×C11C2×C22⋊C412yes—
325C23×C11C22×D411yescharacteristic
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11C4×D414yes—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—44no—
335D4×C11—48no—
336D4×C11—48no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—84no—
343D4×C11—84no—
344D4×C11—84no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—48no—
366C2×C4×C11—48no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11C2×C22⋊C412yes—
370C2×C4×C11C2×C22⋊C412yes—
371C2×C4×C11C2×C22⋊C412yes—
372C2×C4×C11C2×C22⋊C412yes—
373C2×C4×C11C23×C411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C2×Dic11—22no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—84no—
392C11⋊C8—22no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C11⋊C8—41no—
396C22×#41C2×D1111yescharacteristic
397C22×#41C2×D1111yescharacteristic
398C22×M16—111no—
399C23×C8—111no—
400#550—24no—
401#550Dic1118yescomplemented
402C2×#127—21no—
403C2×#127C2×D1111yescharacteristic
404C2×#121—21no—
405C2×#121—21no—
406C2×#121C2×D1111yescharacteristic
407C2×#121C2×D1111yescharacteristic
408C2×C4×Q8C2×D1111yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4C2×D1111yescharacteristic
411C2×#117—111no—
412C22×C4⋊C4—111no—
413#435—224no—
414C2×C4⋊C8—111no—
415#417—224no—
416#416—224no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×C22⋊C8—111no—
430C2×C22⋊C8—111no—
431C2×#97—111no—
432#388—221no—
433#387—221no—
434#386—221no—
435#382—111no—
436#380—111no—
437#380—111no—
438C4×C4⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#340—111no—
443#340—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11C22×C22⋊C411yescharacteristic
473C22×C11D4211yescharacteristic
474C22×C11#54611yescharacteristic
475C22×C11#57511yescharacteristic
476C22×C11#57511yescharacteristic
477C22×C11#57611yescharacteristic
478C22×C11#57711yescharacteristic
479C4×C11—22no—
480C4×C11—22no—
481C4×C11—24no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—42no—
485C4×C11C2×C4×D411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11D4211yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—42no—
490Dic11—81no—
491Dic11—81no—
492Dic11—81no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41C2×Dic1114yes—
504C2×#41C2×Dic1114yescomplemented
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C22⋊D1111yescharacteristic
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—221no—
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C2×M16—222no—
521C2×M16—222no—
522C2×M16—441no—
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—222no—
528C22×C8—222no—
529C22×C8—441no—
530#127—28no—
531#127—22no—
532#127C2×Dic1114yescomplemented
533#121—22no—
534#121—22no—
535#121—28no—
536#121—28no—
537#121C2×Dic1114yes—
538#121C2×Dic1114yescomplemented
539C4×Q8—22no—
540C4×Q8C2×Dic1114yescomplemented
541C4×D4—28no—
542C4×D4C2×Dic1114yes—
543C4×D4C22⋊D1114yes—
544#117—222no—
545#117—441no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4C22⋊D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4C22⋊D1111yescharacteristic
562C2×C22⋊C4C22⋊D1111yescharacteristic
563C2×C42—21no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567C4⋊C8—222no—
568#103—114no—
569#103—222no—
570#103—222no—
571#103—222no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581C22⋊C8—222no—
582#97—222no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588C2×C11—42no—
589C2×C11—42no—
590C2×C11—82no—
591C2×C11—82no—
592C2×C11D4×C22⋊C411yescharacteristic
593C2×C11#289611yescharacteristic
594C2×C11#289711yescharacteristic
595C2×C11#326811yescharacteristic
596C2×C11#327111yescharacteristic
597C2×C11#330911yescharacteristic
598C2×C11#331711yescharacteristic
599C24—21no—
600C24—21no—
601C24C2×C22⋊D1111yescharacteristic
602C24C2×C22⋊D1111yescharacteristic
603#41—28no—
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8D4×D1112yes—
615C2×Q8#434112yes—
616C2×Q8C22×Dic1112yes—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C22⋊Dic1114yes—
648C2×D4C22×Dic1112yes—
649C2×D4C22×Dic1112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—881no—
673C22×C4C22×Dic1112yes—
674C22×C4C22×Dic1112yes—
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1112yes—
680C22×C4C2×C22⋊D1112yes—
681C22×C4C23×D1111yescharacteristic
682M16—444no—
683C2×C8—112no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—444no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—112no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—442no—
707C4⋊C4C22⋊Dic1114yes—
708C4⋊C4C22×Dic1112yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—881no—
714C22⋊C4C22⋊Dic1114yes—
715C22⋊C4C22⋊Dic1114yes—
716C42—24no—
717C42—442no—
718C42—881no—
719C42C22×Dic1112yes—
720C42C2×C22⋊D1112yes—
721C11#2242211yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic1112yes—
749C23C2×C22⋊Dic1112yes—
750C23C22×C22⋊D1111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic1114yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—222no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—884no—
807C2×C4C2×C22⋊Dic1112yes—
808C2×C4C2×C22⋊Dic1112yes—
809C2×C4C2×C22⋊Dic1112yes—
810C2×C4C2×C22⋊Dic1112yes—
811C2×C4C2×D4×D1111yescharacteristic
812C2×C4C2×#434111yescharacteristic
813C2×C4#6703711yescharacteristic
814C2×C4#6703711yescharacteristic
815C2×C4C23×Dic1111yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C8—222no—
818C8—441no—
819C8—441no—
820C8—441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22D4×C22⋊D1111yescharacteristic
850C22#1062333711yescharacteristic
851C22#1062335311yescharacteristic
852C22#1062335311yescharacteristic
853C22#1062336611yescharacteristic
854C22#1062336711yescharacteristic
855C22C22×C22⋊Dic1111yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—442no—
863C4—881no—
864C4—881no—
865C4—881no—
866C4C2×D4×Dic1111yescharacteristic
867C4#1062332911yescharacteristic
868C4D4×C22⋊D1111yescharacteristic
869C4#1062333711yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic1111yescharacteristic
875C2#1307713511yescharacteristic
876C2#1307714211yescharacteristic
877C2#1308015711yescharacteristic
878C2#1308019711yescharacteristic
879C2#1308062211yescharacteristic
880C2#1308074211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#22422
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622846C2semidirect
4. #13071545C2semidirect
5. #13069544C2semidirect
6. #13069441C2semidirect
7. #13069055C2semidirect
8. #13069045C2semidirect
9. #13068939C2semidirect
10. #13068934C2semidirect
11. #13068631C2semidirect
12. #13068556C2semidirect
13. #13068556C2semidirect
14. #13068446C2semidirect
19. C11×#550C4semidirect
75. C2×C11×#41C2×C4semidirect
93. C11×#127C2×C4semidirect
99. C11×#121C2×C4semidirect
101. C4×Q8×C11C2×C4semidirect
141. #66899D4semidirect
401. #550Dic11semidirect
504. C2×#41C2×Dic11semidirect
532. #127C2×Dic11semidirect
538. #121C2×Dic11semidirect
540. C4×Q8C2×Dic11semidirect
721. C11#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228452
C2×#106228462
#130715452
#130695442
#130694412
#130690552
#130690452
#130689392
#130689342
#130686312
#130685562
#130684462
C2×C11×#5502
#2242211