Finite Group Databasebeta

← #14769219

Subgroups — #14769219

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623164C211yesmaximal, characteristic
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
3C2×#10622615C211yesmaximal, characteristic, complemented
4C2×D11×#103C211yesmaximal, characteristic, complemented
5#13071546C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069424C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13069040C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068630C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24#10623164—24no—
25#10623164C418yescomplemented
26C2×#66949—21no—
27C2×#66948C2211yescharacteristic
28C2×#66946—21no—
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×#66938—21no—
32C2×#66937—21no—
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622615—24no—
47#10622600C2211yescharacteristic
48#10622590C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54#10622569—21no—
55#10622558—21no—
56C4×(C2×D11)⋊C4—21no—
57#10622546—21no—
58D11×#103—24no—
59(C22⋊D11)⋊C8—24no—
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11D411yescharacteristic
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—41no—
72C2×Q8×D11—41no—
73C2×Q8×D11C2×C414yes—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—22no—
77C2×#4339—41no—
78C2×#4339—41no—
79C2×#4339C2×C414yescomplemented
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2×C414yescomplemented
92C11×#117—22no—
93C11×#117—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#67000—22no—
104#67000C2×C414yescomplemented
105C4×C22⋊D11C2×C414yes—
106C4×C22⋊D11D414yes—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4D411yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4D411yescharacteristic
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C2×C8×D11—22no—
126C2×C8×D11—22no—
127C2×C8×D11—41no—
128#66949—28no—
129#66948—22no—
130#66948C2×C414yes—
131#66946—28no—
132C4⋊C4×D11—22no—
133C4⋊C4×D11—41no—
134#66940—22no—
135#66940C2×C414yescomplemented
136#66938—28no—
137#66937—28no—
138C11×#103—22no—
139C11×#103—41no—
140C11×C22⋊C8—22no—
141#66899—22no—
142#66899—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—41no—
149#66885—41no—
150(C2×D11)⋊C8—22no—
151#66880—22no—
152#66880—22no—
153Dic11⋊C8—22no—
154C8×Dic11—22no—
155#66874—22no—
156#66874D414yescomplemented
157#66873—22no—
158#66873—22no—
159#22416—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11—21no—
162C23×D11C2×D411yescharacteristic
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11C22×C412yes—
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—21no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—42no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11C22⋊C414yes—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11C2×D411yescharacteristic
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193Q8×D11—28no—
194Q8×D11—44no—
195Q8×D11—44no—
196Q8×D11—44no—
197#4339—28no—
198#4339—44no—
199#4339—44no—
200#4339—44no—
201C2×D44—24no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—42no—
208C2×D44—42no—
209C2×D44C22×C412yes—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C4×D11—21no—
215C2×C4×D11—21no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—81no—
223C2×C4×D11C22×C412yes—
224C2×C4×D11C2×D412yes—
225C2×Dic22—24no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—42no—
230C2×Dic22—42no—
231C2×Dic22C22×C412yes—
232C2×Dic22C2×D412yes—
233C2×Dic22#4112yes—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4C22×C412yes—
246C11×C4⋊C4C2×D412yes—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—42no—
249C42×C11—42no—
250C22⋊Dic11—81no—
251C22⋊Dic11C22⋊C414yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4C22⋊C414yes—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261Dic11⋊C4—24no—
262Dic11⋊C4—42no—
263Dic11⋊C4C22⋊C414yes—
264C4×Dic11—24no—
265C4×Dic11—81no—
266C4×Dic11C22×C412yes—
267C4×Dic11C2×D412yes—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—44no—
274C2×C11⋊C8C2×D412yes—
275C8×D11—44no—
276C2×#548—111no—
277C2×C8×D4—111no—
278C2×#416—111no—
279C22×#103—111no—
280#2352—111no—
281#1983—111no—
282#1958—111no—
283#1893—111no—
284#1892—111no—
285#1874—111no—
286#1873D1111yescharacteristic, complemented
287#1805—111no—
288#1788—111no—
289#1787—111no—
290C4×#103—111no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11C2×C22⋊C412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—22no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11C2×C22⋊C412yes—
311C22×D11#13512yes—
312C22×D11#13512yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—41no—
316Q8×C11—41no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11C2×C22⋊C412yes—
336C2×C4×C11C23×C411yescharacteristic
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C22⋊D11—28no—
343C22⋊D11—48no—
344C2×Dic11—22no—
345C2×Dic11—21no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11C2×C22⋊C412yes—
360C2×Dic11C2×C22⋊C412yes—
361C2×Dic11C2×C22⋊C412yes—
362D44—22no—
363D44—22no—
364D44—48no—
365D44—41no—
366D44—41no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—48no—
372C4×D11—48no—
373C4×D11—84no—
374Dic22—22no—
375Dic22—22no—
376Dic22—22no—
377Dic22—48no—
378Dic22C4×D414yes—
379C8×C11—41no—
380C8×C11—41no—
381C11⋊C8—22no—
382C11⋊C8—41no—
383C22×#41—111no—
384C23×Q8—111no—
385C23×C8—111no—
386C23×C8—111no—
387#548—118no—
388#548—224no—
389C2×#124—111no—
390C2×#124—221no—
391C2×C22⋊Q8—221no—
392C2×C22⋊Q8C2×D1111yescharacteristic
393C2×#121—111no—
394C2×#121—221no—
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—221no—
398C2×#117C2×D1111yescharacteristic
399C22×C4⋊C4—111no—
400C8×D4—224no—
401C2×C4⋊C8—111no—
402#416—224no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—224no—
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×C22⋊C8—111no—
417C2×C22⋊C8C2×D1111yescharacteristic
418C2×C4×C8—111no—
419#388—221no—
420#387—221no—
421#386—221no—
422#382—111no—
423#380—111no—
424#380—111no—
425C4×C4⋊C4—111no—
426C4×C22⋊C4—221no—
427#340—111no—
428#340—111no—
429#340C2×D1111yescharacteristic
430#340C2×D1111yescharacteristic
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11C22×C22⋊C411yescharacteristic
439C22×C11D4211yescharacteristic
440C22×C11#54611yescharacteristic
441C22×C11C2×#13511yescharacteristic
442C22×C11C2×#13511yescharacteristic
443C22×C11#57711yescharacteristic
444C22×C11#57811yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—81no—
455C2×D11—81no—
456C2×D11—81no—
457C2×D11—81no—
458C2×D11#41614yescomplemented
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—81no—
464C4×C11C2×C4×D411yescharacteristic
465C4×C11#51811yescharacteristic
466C4×C11D4211yescharacteristic
467C4×C11#54611yescharacteristic
468Dic11—24no—
469Dic11—22no—
470Dic11—22no—
471Dic11—22no—
472Dic11—81no—
473Dic11—81no—
474C2×#41—114no—
475C2×#41—222no—
476C2×#41—222no—
477C2×#41—222no—
478C2×#41—441no—
479C2×#41—441no—
480C22×Q8—114no—
481C22×Q8—111no—
482C22×Q8—221no—
483C22×Q8—222no—
484C22×Q8—222no—
485C22×Q8—222no—
486C22×Q8—441no—
487C22×Q8—441no—
488C22×Q8C22×D1111yescharacteristic
489C22×D4—111no—
490C22×D4—111no—
491C22×D4—221no—
492C22×D4—221no—
493C23×C4—111no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C22×C8—111no—
499C22×C8—111no—
500C22×C8—222no—
501C22×C8—222no—
502C22×C8—222no—
503C22×C8—222no—
504C22×C8—441no—
505C22×C8—441no—
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508#124—114no—
509#124—222no—
510#124—228no—
511C22⋊Q8—22no—
512C22⋊Q8—228no—
513C22⋊Q8C4×D1114yescomplemented
514#121—114no—
515#121—228no—
516#121—222no—
517C4×Q8—114no—
518C4×Q8—222no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—228no—
522#117—22no—
523#117—41no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—441no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—111no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C42—21no—
545C2×C42—111no—
546C2×C42—221no—
547C2×C42—221no—
548C4⋊C8—222no—
549#103—22no—
550#103—41no—
551#103—114no—
552#103—222no—
553#103—222no—
554#103—222no—
555#103—222no—
556#103—441no—
557#102—222no—
558#102—222no—
559#102—441no—
560#102—441no—
561C22⋊C8—22no—
562C22⋊C8—222no—
563C4×C8—222no—
564#95—221no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—42no—
570C2×C11D4×C22⋊C411yescharacteristic
571C2×C11C2×#41611yescharacteristic
572C2×C11#289811yescharacteristic
573C2×C11#328211yescharacteristic
574C2×C11#328511yescharacteristic
575C2×C11#330011yescharacteristic
576C2×C11#330111yescharacteristic
577D11—24no—
578D11—82no—
579C24—111no—
580C24—221no—
581C24D4×D1111yescharacteristic
582#41—228no—
583#41—444no—
584#41—444no—
585#41—444no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—112no—
592C2×Q8—112no—
593C2×Q8—112no—
594C2×Q8—224no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8—228no—
599C2×Q8—442no—
600C2×Q8—442no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8C2×C4×D1112yes—
605C2×D4—114no—
606C2×D4—112no—
607C2×D4—224no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—224no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—442no—
617C2×D4—442no—
618C2×D4—442no—
619C2×D4—442no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—224no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—224no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4—881no—
649C22×C4C2×C4×D1112yes—
650C22×C4D4×D1111yescharacteristic
651C22×C4D4×D1112yes—
652C22×C4C23×D1111yescharacteristic
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—112no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—444no—
666C2×C8—444no—
667C4⋊C4—24no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—224no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—442no—
679C4⋊C4C2×C4×D1112yes—
680C4⋊C4D4×D1112yes—
681C22⋊C4—24no—
682C22⋊C4—42no—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—442no—
689C22⋊C4—881no—
690C42—42no—
691C42—112no—
692C42—112no—
693C42—224no—
694C42—881no—
695C11#2241611yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—112no—
703C23—112no—
704C23—112no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—221no—
709C23—222no—
710C23—441no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23—441no—
716C23C22⋊C4×D1112yes—
717C23C2×D4×D1111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—114no—
723Q8—222no—
724Q8—222no—
725Q8—222no—
726Q8—448no—
727D4—228no—
728D4—222no—
729D4—222no—
730D4—448no—
731D4—448no—
732D4—441no—
733D4—441no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—112no—
753C2×C4—112no—
754C2×C4—112no—
755C2×C4—222no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—222no—
762C2×C4—221no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—448no—
769C2×C4—448no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—884no—
777C2×C4C22⋊C4×D1112yes—
778C2×C4C22×C4×D1111yescharacteristic
779C2×C4C2×D4×D1111yescharacteristic
780C2×C4C2×D4×D1111yescharacteristic
781C2×C4#6703711yescharacteristic
782C2×C4#41×D1111yescharacteristic
783C2×C4#6704211yescharacteristic
784C8—41no—
785C8—41no—
786C8—222no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—114no—
796C22—222no—
797C22—222no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—881no—
806C22—881no—
807C22—881no—
808C22—881no—
809C22C2×C22⋊C4×D1111yescharacteristic
810C22#1062312111yescharacteristic
811C22#1062318511yescharacteristic
812C22D11×#13511yescharacteristic
813C22D11×#13511yescharacteristic
814C22#1062330911yescharacteristic
815C22#1062331011yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—222no—
822C4—224no—
823C4—222no—
824C4—222no—
825C4—881no—
826C4—881no—
827C4C4×D4×D1111yescharacteristic
828C4#1062307611yescharacteristic
829C4#1062314011yescharacteristic
830C4#1062314111yescharacteristic
831C2—42no—
832C2—224no—
833C2—882no—
834C2#1307143411yescharacteristic
835C2D11×#41611yescharacteristic
836C2#1307714811yescharacteristic
837C2#1308032111yescharacteristic
838C2#1308035511yescharacteristic
839C2#1308050611yescharacteristic
840C2#1308052111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#10623164C2
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#22416
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D11)⋊C8C2semidirect
3. C2×#10622615C2semidirect
4. C2×D11×#103C2semidirect
5. #13071546C2semidirect
6. #13069545C2semidirect
7. #13069424C2semidirect
8. #13069043C2semidirect
9. #13069040C2semidirect
10. #13068932C2semidirect
11. #13068630C2semidirect
12. #13068557C2semidirect
13. #13068549C2semidirect
14. #13068435C2semidirect
15. C11×#1873C2semidirect
25. #10623164C4semidirect
79. C2×#4339C2×C4semidirect
91. C11×C22⋊Q8C2×C4semidirect
104. #67000C2×C4semidirect
135. #66940C2×C4semidirect
156. #66874D4semidirect
286. #1873D11semidirect
458. C2×D11#416semidirect
513. C22⋊Q8C4×D11semidirect
695. C11#22416semidirect

Maximal subgroups

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

subgroupindex
C2×#106231642
C2×(C22⋊D11)⋊C82
C2×#106226152
C2×D11×#1032
#130715462
#130695452
#130694242
#130690432
#130690402
#130689322
#130686302
#130685572
#130685492
#130684352
C11×#18732
#2241611