Finite Group Databasebeta

← #14769342

Subgroups — #14769342

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic
2C2×#10622319C211yesmaximal, characteristic
3C2×#10622415C211yesmaximal, characteristic, complemented
4C2×D11×#103C211yesmaximal, characteristic, complemented
5#13071542C211yesmaximal, characteristic
6#13069540C211yesmaximal, characteristic, complemented
7#13069046C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068925C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068628C211yesmaximal, characteristic, complemented
12#13068549C211yesmaximal, characteristic, complemented
13#13068549C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1960C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623258—24no—
24#10623258C418yescomplemented
25C2×#66949—21no—
26C2×#66949—21no—
27C2×#66946—21no—
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66941—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C11×#382C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622415—24no—
54D11×#103—24no—
55#10622319—24no—
56#10622282—21no—
57#10622279—21no—
58#10622278—21no—
59#10622267—21no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—41no—
73C2×Q8×D11—41no—
74C2×Q8×D11—41no—
75C2×Q8×D11—41no—
76C2×Q8×D11C2×C414yes—
77C2×Q8×D11C2×C414yescomplemented
78C22×D44D411yescharacteristic
79C22×C4×D11—21no—
80C22×C4×D11—21no—
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×Dic22—21no—
85C22×Dic22—21no—
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×C4⋊Q8—22no—
90C11×C4⋊Q8C2×C414yescomplemented
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96#66999—22no—
97#66999—22no—
98#66999C2×C414yes—
99#66999C2×C414yescomplemented
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4D411yescharacteristic
106C2×(C2×D11)⋊C4D411yescharacteristic
107C2×C4⋊Dic11D411yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313—41no—
123C2×C8×D11—22no—
124C2×C8×D11—22no—
125C2×C8×D11—41no—
126#66949—28no—
127#66949—28no—
128#66946—28no—
129#66945—22no—
130#66945—41no—
131C4⋊C4×D11—22no—
132C4⋊C4×D11—41no—
133#66941—28no—
134C4×D44C2×C414yes—
135C4×D44D414yes—
136C4×Dic22—22no—
137C4×Dic22C2×C414yescomplemented
138C11×#103—22no—
139C11×#103—22no—
140C11×#103—41no—
141C11×#103—41no—
142C11×#97—22no—
143C11×#95—21no—
144C11×#95—21no—
145#66899—22no—
146#66899—22no—
147#66899—41no—
148#66899—41no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152(C2×D11)⋊C8—22no—
153(C2×D11)⋊C8—22no—
154#66880—22no—
155#66880D414yescomplemented
156#66874—22no—
157#66874—22no—
158C4⋊(C11⋊C8)—22no—
159#22425—111nomaximal, Sylow
160C23×D11C2×D411yescharacteristic
161C23×D11C2×D411yescharacteristic
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C22×C412yes—
173C2×Q8×C11C22×C412yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187Q8×D11—28no—
188Q8×D11—28no—
189Q8×D11—44no—
190Q8×D11—44no—
191Q8×D11—44no—
192Q8×D11—44no—
193Q8×D11—44no—
194Q8×D11—44no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44C22⋊C414yes—
198C2×C4×D11—24no—
199C2×C4×D11—24no—
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×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×C4×D11—81no—
215C2×C4×D11C22×C412yes—
216C2×C4×D11C22×C412yes—
217C2×C4×D11C2×D412yes—
218C2×C4×D11C2×D412yes—
219C2×Dic22—24no—
220C2×Dic22—24no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—42no—
225C2×Dic22—42no—
226C2×Dic22—42no—
227C2×Dic22—42no—
228C2×Dic22C22×C412yes—
229C2×Dic22C2×D412yes—
230C2×Dic22#4112yes—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11C2×D412yes—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C42×C11C22×C412yes—
244C42×C11C2×D412yes—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—42no—
249(C2×D11)⋊C4—81no—
250(C2×D11)⋊C4C22⋊C414yes—
251(C2×D11)⋊C4C22⋊C414yes—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C22⋊C414yes—
257C4⋊Dic11C22×C412yes—
258C4⋊Dic11C2×D412yes—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—42no—
263C4×Dic11—24no—
264C4×Dic11—42no—
265C4×Dic11—81no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272#4313—44no—
273C8×D11—44no—
274C2×D4×Q8—111no—
275C2×#435—111no—
276C2×#419—111no—
277C22×#103—111no—
278#2352—111no—
279#1981—111no—
280#1960D1111yescharacteristic, complemented
281#1894—111no—
282#1892—111no—
283#1873—111no—
284#1872—111no—
285#1805—111no—
286#1787—111no—
287#1787—111no—
288#1763—111no—
289C23×C11C22×D411yescharacteristic
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11C2×C22⋊C412yes—
301C22×D11C2×C22⋊C412yes—
302C22×D11#13712yes—
303C22×D11#13712yes—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—41no—
309Q8×C11—41no—
310Q8×C11—41no—
311Q8×C11—41no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11C2×C22⋊C412yes—
329C2×C4×C11C2×C22⋊C412yes—
330C2×C4×C11C23×C411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×Dic11—22no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11C2×C22⋊C412yes—
353C2×Dic11C2×C22⋊C412yes—
354D44—28no—
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—48no—
364C4×D11—48no—
365C4×D11—84no—
366Dic22—22no—
367Dic22—22no—
368Dic22—22no—
369Dic22—48no—
370Dic22—48no—
371Dic22C4×D414yes—
372C8×C11—22no—
373C8×C11—41no—
374C11⋊C8—41no—
375C11⋊C8—41no—
376C23×Q8—111no—
377C23×Q8—111no—
378C22×M16—111no—
379C23×C8—111no—
380D4×Q8—118no—
381D4×Q8—224no—
382C2×C4⋊Q8—221no—
383C2×C4⋊Q8C2×D1111yescharacteristic
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×C22⋊Q8—221no—
388C2×C4×Q8—111no—
389C2×C4×D4—111no—
390C2×C4×D4—221no—
391C2×#117—111no—
392C22×C4⋊C4—111no—
393#435—224no—
394C2×C4⋊C8—111no—
395#419—224no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—224no—
405C2×#103C2×D1111yescharacteristic
406C2×#103C2×D1111yescharacteristic
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×#97C2×D1111yescharacteristic
412#388—221no—
413#387—221no—
414#386—221no—
415#382C2×D1111yescharacteristic
416#380—111no—
417#380—111no—
418C4×C4⋊C4—111no—
419C4×C22⋊C4—221no—
420#340—111no—
421#340—111no—
422#340—111no—
423#340—111no—
424C22×C11C22×C22⋊C411yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11#54611yescharacteristic
427C22×C11C2×#13711yescharacteristic
428C22×C11C2×#13711yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57811yescharacteristic
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—41no—
441C2×D11—41no—
442C2×D11—41no—
443C2×D11—41no—
444C2×D11#41914yescomplemented
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—81no—
450C4×C11—81no—
451C4×C11C2×C4×D411yescharacteristic
452C4×C11#51811yescharacteristic
453C4×C11D4211yescharacteristic
454C4×C11#54611yescharacteristic
455Dic11—24no—
456Dic11—22no—
457Dic11—22no—
458Dic11—42no—
459Dic11—42no—
460Dic11—81no—
461C22×Q8—114no—
462C22×Q8—114no—
463C22×Q8—111no—
464C22×Q8—221no—
465C22×Q8—221no—
466C22×Q8—222no—
467C22×Q8—222no—
468C22×Q8—222no—
469C22×Q8—222no—
470C22×Q8—222no—
471C22×Q8—222no—
472C22×Q8—441no—
473C22×Q8—441no—
474C22×Q8—441no—
475C22×Q8—441no—
476C22×Q8C22×D1111yescharacteristic
477C22×Q8C22×D1111yescharacteristic
478C22×D4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C2×M16—222no—
485C2×M16—222no—
486C2×M16—441no—
487C22×C8—111no—
488C22×C8—111no—
489C22×C8—222no—
490C22×C8—222no—
491C22×C8—441no—
492C22×C8C22×D1111yescharacteristic
493C22×C8C22×D1111yescharacteristic
494C4⋊Q8—22no—
495C4⋊Q8—228no—
496C4⋊Q8C4×D1114yescomplemented
497C22⋊Q8—114no—
498C22⋊Q8—114no—
499C22⋊Q8—228no—
500C22⋊Q8—228no—
501C22⋊Q8—222no—
502C22⋊Q8—222no—
503C4×Q8—114no—
504C4×Q8—222no—
505C4×D4—114no—
506C4×D4—114no—
507C4×D4—228no—
508#117—222no—
509#117—441no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—441no—
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—111no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C42—221no—
532C2×C42—221no—
533C2×C42—221no—
534C2×C42C22×D1111yescharacteristic
535C4⋊C8—222no—
536#103—22no—
537#103—22no—
538#103—41no—
539#103—41no—
540#103—114no—
541#103—222no—
542#103—222no—
543#103—222no—
544#103—222no—
545#103—222no—
546#103—441no—
547#103—441no—
548C22⋊C8—222no—
549C22⋊C8—222no—
550#97—22no—
551#95—21no—
552#95—21no—
553#95—221no—
554#95—221no—
555#95—221no—
556C2×C11D4×C22⋊C411yescharacteristic
557C2×C11C2×#41911yescharacteristic
558C2×C11#289811yescharacteristic
559C2×C11#326611yescharacteristic
560C2×C11#327011yescharacteristic
561C2×C11#331211yescharacteristic
562C2×C11#332011yescharacteristic
563D11—24no—
564D11—42no—
565C24—111no—
566C24—111no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—112no—
578C2×Q8—112no—
579C2×Q8—112no—
580C2×Q8—224no—
581C2×Q8—224no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—228no—
586C2×Q8—228no—
587C2×Q8—442no—
588C2×Q8—442no—
589C2×Q8—442no—
590C2×Q8—442no—
591C2×Q8—444no—
592C2×Q8—444no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8—444no—
596C2×Q8—444no—
597C2×Q8C2×C4×D1112yes—
598C2×Q8C2×C4×D1112yes—
599C2×D4—114no—
600C2×D4—222no—
601C2×D4—222no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—442no—
627C22×C4—442no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4—881no—
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1111yescharacteristic
636M16—444no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—444no—
649C2×C8D4×D1112yes—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—114no—
657C4⋊C4—112no—
658C4⋊C4—112no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—221no—
663C4⋊C4—221no—
664C4⋊C4—221no—
665C4⋊C4—221no—
666C4⋊C4—442no—
667C22⋊C4—114no—
668C22⋊C4—114no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—442no—
672C22⋊C4—442no—
673C22⋊C4—881no—
674C42—224no—
675C42—442no—
676C42—881no—
677C42C2×C4×D1112yes—
678C42D4×D1112yes—
679C11#2242511yescharacteristic, complemented, Sylow
680C23—112no—
681C23—112no—
682C23—112no—
683C23—112no—
684C23—221no—
685C23—221no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23—221no—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—114no—
704Q8—222no—
705Q8—222no—
706Q8—222no—
707Q8—448no—
708Q8—448no—
709D4—228no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—448no—
746C2×C4—448no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—884no—
755C2×C4C22⋊C4×D1112yes—
756C2×C4C22⋊C4×D1112yes—
757C2×C4C22×C4×D1111yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4#6703711yescharacteristic
761C2×C4#41×D1111yescharacteristic
762C2×C4#6704211yescharacteristic
763C8—22no—
764C8—41no—
765C8—441no—
766C8—441no—
767C22—114no—
768C22—222no—
769C22—222no—
770C22—222no—
771C22—222no—
772C22—222no—
773C22—222no—
774C22—222no—
775C22—222no—
776C22—222no—
777C22—441no—
778C22—441no—
779C22—441no—
780C22—441no—
781C22C2×C22⋊C4×D1111yescharacteristic
782C22#1062320711yescharacteristic
783C22#1062324811yescharacteristic
784C22D11×#13711yescharacteristic
785C22D11×#13711yescharacteristic
786C22#1062330911yescharacteristic
787C22#1062331011yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—222no—
795C4—222no—
796C4—224no—
797C4—442no—
798C4—442no—
799C4—881no—
800C4C4×D4×D1111yescharacteristic
801C4#1062307611yescharacteristic
802C4#1062314011yescharacteristic
803C4#1062314311yescharacteristic
804C2—224no—
805C2—442no—
806C2#1307143711yescharacteristic
807C2D11×#41911yescharacteristic
808C2#1307714811yescharacteristic
809C2#1308012511yescharacteristic
810C2#1308018511yescharacteristic
811C2#1308066611yescharacteristic
812C2#1308078611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1960C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1960D11
hypocenterC11#22425
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
3. C2×#10622415C2semidirect
4. C2×D11×#103C2semidirect
6. #13069540C2semidirect
7. #13069046C2semidirect
8. #13069036C2semidirect
9. #13068925C2semidirect
10. #13068920C2semidirect
11. #13068628C2semidirect
12. #13068549C2semidirect
13. #13068549C2semidirect
14. #13068447C2semidirect
15. C11×#1960C2semidirect
24. #10623258C4semidirect
77. C2×Q8×D11C2×C4semidirect
90. C11×C4⋊Q8C2×C4semidirect
99. #66999C2×C4semidirect
137. C4×Dic22C2×C4semidirect
155. #66880D4semidirect
280. #1960D11semidirect
444. C2×D11#419semidirect
496. C4⋊Q8C4×D11semidirect
679. C11#22425semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106223192
C2×#106224152
C2×D11×#1032
#130715422
#130695402
#130690462
#130690362
#130689252
#130689202
#130686282
#130685492
#130684472
C11×#19602
#2242511