Finite Group Databasebeta

← #14769269

Subgroups — #14769269

Order 2816.

1478 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×#10623355C211yesmaximal, characteristic
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×#10622385C211yesmaximal, characteristic, complemented
4#13071541C211yesmaximal, characteristic, complemented
5#13069537C211yesmaximal, characteristic, complemented
6#13069434C211yesmaximal, characteristic, complemented
7#13069049C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068925C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068553C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C2×C11×#417C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623355—24no—
21#10623355C418yescomplemented
22C2×#66999C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C2×#66992—21no—
25C2×#66988—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×Dic11⋊C4—21no—
31C22×C8×D11C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C11×#417—24no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622826—21no—
43#10622825C2211yescharacteristic
44C4×C22⋊Dic11—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622740—24no—
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49C2×#66880C2211yescharacteristic
50C2×#66879C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
52#10622603—21no—
53#10622600C2211yescharacteristic
54#10622591—21no—
55#10622590C2211yescharacteristic
56C4⋊C4×Dic11C2211yescharacteristic
57C2×#66874C2211yescharacteristic
58C2×#66874C2211yescharacteristic
59#10622385—24no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yes—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11D411yescharacteristic
78C23×Dic11—21no—
79C23×Dic11—21no—
80C2×#4341—22no—
81C2×#4341—22no—
82C2×#4341—22no—
83C2×#4341—41no—
84C2×#4341—41no—
85C2×#4341C2×C414yescomplemented
86C22×C4×D11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C2×C11×M16—22no—
89C2×C11×M16—22no—
90C2×C11×M16—41no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#66999—22no—
103#66999C2×C414yescomplemented
104#66997—22no—
105#66997C2×C414yescomplemented
106#66992—28no—
107#66988—28no—
108D4×Dic11—22no—
109D4×Dic11C2×C414yescomplemented
110#66982—28no—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120#66977—22no—
121#66977C2×C414yes—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—28no—
127C2×Dic11⋊C4D411yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11—41no—
136#66945—22no—
137#66945—41no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#102—22no—
141C11×#102D414yescomplemented
142#66899—41no—
143#66899—41no—
144#66896—22no—
145#66896—22no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152(C2×D11)⋊C8—22no—
153#66880—22no—
154#66880—41no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66874—22no—
158#66874—41no—
159#22420—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C23×D11C2×D411yescharacteristic
163C11×#41—28no—
164C11×#41—44no—
165C11×#41—44no—
166C11×#41—44no—
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×D4×C11—24no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11C22×C412yes—
180C2×D4×C11C2×D412yes—
181C2×D4×C11#4112yes—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—81no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—41no—
201C2×C22⋊D11—41no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11C22⋊C414yes—
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—42no—
212C22×Dic11—42no—
213C22×Dic11—42no—
214C22×Dic11—42no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218#4341—28no—
219#4341—44no—
220#4341—44no—
221#4341—44no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11C22×C412yes—
227C2×C4×D11C2×D412yes—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22C22×C412yes—
234C11×M16—44no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11C2×D412yes—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—42no—
245C11×C4⋊C4C2×D412yes—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—42no—
249C22⋊Dic11C22⋊C414yes—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—81no—
253(C2×D11)⋊C4C22⋊C414yes—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C22×C412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4C22⋊C414yes—
265C4×Dic11—42no—
266C4×Dic11—81no—
267C4×Dic11C22×C412yes—
268C4×Dic11C2×D412yes—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C8×D11—44no—
276C2×#547—111no—
277C2×#435—111no—
278C2×#417D1111yescharacteristic, complemented
279C2×#416—111no—
280#2352—111no—
281#1981—111no—
282#1960—111no—
283#1894—111no—
284#1892—111no—
285#1873—111no—
286#1872—111no—
287#1804—111no—
288#1788—111no—
289#1788—111no—
290#1762—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11C2×C22⋊C412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11C2×C22⋊C412yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—41no—
316Q8×C11—41no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—48no—
321D4×C11C4×D414yes—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—48no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—84no—
339C2×C4×C11C2×C22⋊C412yes—
340C2×C4×C11C23×C411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—44no—
347C22⋊D11—48no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—48no—
357C2×Dic11—48no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11C2×C22⋊C412yes—
369C2×Dic11C2×C22⋊C412yes—
370C2×Dic11C2×C22⋊C412yes—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375Dic22—22no—
376Dic22—22no—
377Dic22—41no—
378Dic22—41no—
379C8×C11—22no—
380C8×C11—41no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C22×#41—111no—
384C22×#41C2×D1111yescharacteristic
385C22×M16C2×D1111yescharacteristic
386C23×C8—111no—
387#547—118no—
388#547—224no—
389C2×C4⋊Q8—111no—
390C2×#123—221no—
391C2×#123—221no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×#121—221no—
395C2×C4×D4—111no—
396C2×C4×D4—111no—
397C2×#117—111no—
398C22×C4⋊C4—221no—
399C22×C4⋊C4C2×D1111yescharacteristic
400#435—224no—
401C2×C4⋊C8—111no—
402#417—24no—
403#416—224no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×#102C2×D1111yescharacteristic
416C2×C22⋊C8—111no—
417C2×C22⋊C8—111no—
418C2×#97—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#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—24no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—41no—
440C22×C11—42no—
441C22×C11—41no—
442C22×C11—42no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11C22×C22⋊C411yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11#54611yescharacteristic
448C22×C11#57511yescharacteristic
449C22×C11#57511yescharacteristic
450C22×C11#57711yescharacteristic
451C22×C11#57811yescharacteristic
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—41no—
456C2×D11—41no—
457C2×D11—41no—
458C2×D11—41no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—81no—
463C4×C11C2×C4×D411yescharacteristic
464C4×C11#51811yescharacteristic
465C4×C11D4211yescharacteristic
466C4×C11#54611yescharacteristic
467Dic11—22no—
468Dic11—22no—
469Dic11—22no—
470Dic11—42no—
471Dic11—42no—
472Dic11—81no—
473Dic11—81no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—114no—
480C2×#41—222no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—441no—
484C2×#41—441no—
485C2×#41C4×D1114yes—
486C22×Q8—111no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—21no—
489C22×D4—111no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—222no—
504C22×C8—222no—
505C22×C8—441no—
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508C4⋊Q8—114no—
509C4⋊Q8—222no—
510#123—228no—
511#123—228no—
512C22⋊Q8—114no—
513C22⋊Q8—114no—
514C22⋊Q8—222no—
515C22⋊Q8—222no—
516#121—228no—
517C4×D4—114no—
518C4×D4—114no—
519C4×D4—114no—
520C4×D4—222no—
521#117—222no—
522#117—441no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—228no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
545C2×C42—111no—
546C2×C42—221no—
547C2×C42—221no—
548C4⋊C8—222no—
549#103—22no—
550#103—22no—
551#103—222no—
552#103—222no—
553#103—441no—
554#103—441no—
555#103—441no—
556#103—441no—
557#102—22no—
558#102—222no—
559#102—222no—
560#102C22⋊D1114yescomplemented
561C22⋊C8—222no—
562C22⋊C8—222no—
563#97—222no—
564#95—221no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—42no—
570C2×C11—44no—
571C2×C11D4×C22⋊C411yescharacteristic
572C2×C11#289611yescharacteristic
573C2×C11#289811yescharacteristic
574C2×C11#326711yescharacteristic
575C2×C11#326911yescharacteristic
576C2×C11#330711yescharacteristic
577C2×C11#331511yescharacteristic
578D11—42no—
579C24—21no—
580C24—111no—
581C24D4×D1111yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—228no—
587#41—444no—
588#41—444no—
589#41—444no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—112no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8—221no—
599C2×Q8—221no—
600C2×Q8—221no—
601C2×Q8C2×C4×D1112yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—114no—
609C2×D4—224no—
610C2×D4—441no—
611C2×D4—441no—
612C2×D4—442no—
613C2×D4—442no—
614C2×D4C2×C4×D1112yes—
615C2×D4#433912yes—
616C2×D4C2×C22⋊D1112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—81no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4—442no—
649C22×C4C2×C4×D1112yes—
650C22×C4D4×D1111yescharacteristic
651C22×C4D4×D1112yes—
652C22×C4C23×D1111yescharacteristic
653M16—44no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—444no—
666C2×C8C2×C22⋊D1112yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4C2×C22⋊D1112yes—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C22⋊C4—881no—
691C42—112no—
692C42—112no—
693C42—442no—
694C42—881no—
695C11#2242011yescharacteristic, complemented, Sylow
696C23—22no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—112no—
710C23—221no—
711C23—221no—
712C23—221no—
713C23—221no—
714C23—221no—
715C23—221no—
716C23C22⋊C4×D1112yes—
717C23C2×D4×D1111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—222no—
723Q8—222no—
724Q8—441no—
725Q8—441no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—444no—
731D4—448no—
732D4C4×C22⋊D1114yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4—112no—
751C2×C4—112no—
752C2×C4—112no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4C22⋊C4×D1112yes—
778C2×C4C22×C4×D1111yescharacteristic
779C2×C4C2×#433911yescharacteristic
780C2×C4C2×D4×D1111yescharacteristic
781C2×C4#6703711yescharacteristic
782C2×C4#6703711yescharacteristic
783C2×C4C22×C22⋊D1111yescharacteristic
784C8—22no—
785C8—41no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—441no—
806C22—441no—
807C22—441no—
808C22—441no—
809C22C2×C22⋊C4×D1111yescharacteristic
810C22#1062302111yescharacteristic
811C22#1062330411yescharacteristic
812C22#1062330611yescharacteristic
813C22#1062330811yescharacteristic
814C22#1062331011yescharacteristic
815C22D4×C22⋊D1111yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—81no—
820C4—222no—
821C4—222no—
822C4—222no—
823C4—442no—
824C4—442no—
825C4—881no—
826C4—881no—
827C4#1062301711yescharacteristic
828C4#1062302111yescharacteristic
829C4C2×C4×C22⋊D1111yescharacteristic
830C4D4×C22⋊D1111yescharacteristic
831C2—42no—
832C2—44no—
833C2—442no—
834C2C22⋊C4×C22⋊D1111yescharacteristic
835C2#1307713211yescharacteristic
836C2#1307714711yescharacteristic
837C2#1308013511yescharacteristic
838C2#1308016511yescharacteristic
839C2#1308059311yescharacteristic
840C2#1308071311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623355C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#22420
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10622740C2semidirect
3. C2×#10622385C2semidirect
4. #13071541C2semidirect
5. #13069537C2semidirect
6. #13069434C2semidirect
7. #13069049C2semidirect
8. #13069036C2semidirect
9. #13068925C2semidirect
10. #13068923C2semidirect
11. #13068624C2semidirect
12. #13068556C2semidirect
13. #13068553C2semidirect
14. #13068443C2semidirect
15. C2×C11×#417C2semidirect
21. #10623355C4semidirect
85. C2×#4341C2×C4semidirect
103. #66999C2×C4semidirect
105. #66997C2×C4semidirect
109. D4×Dic11C2×C4semidirect
141. C11×#102D4semidirect
278. C2×#417D11semidirect
560. #102C22⋊D11semidirect
695. C11#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#106233552
C2×#106227402
C2×#106223852
#130715412
#130695372
#130694342
#130690492
#130690362
#130689252
#130689232
#130686242
#130685562
#130685532
#130684432
C2×C11×#4172
#2242011