Finite Group Databasebeta

← #14769212

Subgroups — #14769212

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×#10623348C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4#13071541C211yesmaximal, characteristic, complemented
5#13069545C211yesmaximal, characteristic, complemented
6#13069424C211yesmaximal, characteristic, complemented
7#13069044C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068629C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068551C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C22×C11×#103C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623348—24no—
21#10623348C418yescomplemented
22C2×#67000—21no—
23C2×#67000C2211yescharacteristic
24C2×#66999—21no—
25C2×#66999C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66983—21no—
28C2×#66983C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C2×C11×#103—24no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42#10622826—21no—
43#10622825C2211yescharacteristic
44C4×C22⋊Dic11—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C8×C22⋊D11—24no—
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
51C2×C8×Dic11C2211yescharacteristic
52#10622603—21no—
53#10622600C2211yescharacteristic
54#10622591—21no—
55#10622590C2211yescharacteristic
56C4⋊C4×Dic11C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58C2×#66873C2211yescharacteristic
59#10622417—24no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yes—
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11D411yescharacteristic
78C2×#4343—22no—
79C2×#4343—22no—
80C2×#4343—22no—
81C2×#4343—41no—
82C2×#4343—41no—
83C2×#4343C2×C414yescomplemented
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×C8×C11—22no—
89C22×C8×C11—22no—
90C22×C8×C11—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⋊Dic11D411yescharacteristic
100#67000—28no—
101#67000—22no—
102#67000C2×C414yescomplemented
103#66999—22no—
104#66999—28no—
105#66999C2×C414yescomplemented
106Q8×Dic11—22no—
107Q8×Dic11C2×C414yescomplemented
108#66983—22no—
109#66983—28no—
110#66983C2×C414yes—
111C4×C22⋊D11—28no—
112C4×C22⋊D11C2×C414yes—
113C4×C22⋊D11D414yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
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×#103—22no—
141C11×#103D414yescomplemented
142#66899—22no—
143#66899—22no—
144#66899—41no—
145#66899—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152#66885—22no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155Dic11⋊C8—22no—
156C8×Dic11—22no—
157#66873—22no—
158#66873—41no—
159#22416—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11—21no—
162C23×D11C2×D411yescharacteristic
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—28no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—42no—
174C2×Q8×C11—42no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11C22×C412yes—
179C2×Q8×C11C22×C412yes—
180C2×Q8×C11C2×D412yes—
181C2×Q8×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—24no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—81no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11C22⋊C414yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212#4343—28no—
213#4343—44no—
214#4343—44no—
215#4343—44no—
216C2×D44—24no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—42no—
223C2×D44—42no—
224C2×D44C22×C412yes—
225C2×C4×D11—24no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11C22×C412yes—
233C2×C4×D11C2×D412yes—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—44no—
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—42no—
247C22⋊Dic11C22⋊C414yes—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—42no—
253(C2×D11)⋊C4—81no—
254(C2×D11)⋊C4C22⋊C414yes—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11C22×C412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4C22⋊C414yes—
264C4×Dic11—24no—
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×#548—111no—
277C2×C8×D4—111no—
278C2×#416—111no—
279C22×#103D1111yescharacteristic, complemented
280#2352—111no—
281#1983—111no—
282#1958—111no—
283#1893—111no—
284#1892—111no—
285#1874—111no—
286#1873—111no—
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×C11C2×C22⋊C412yes—
296C23×C11#13512yes—
297C23×C11#13512yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—22no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11C2×C22⋊C412yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—22no—
318Q8×C11—48no—
319Q8×C11—41no—
320Q8×C11—41no—
321Q8×C11C4×D414yes—
322C2×C4×C11—22no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—48no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—84no—
342C2×C4×C11C2×C22⋊C412yes—
343C2×C4×C11C23×C411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C22⋊D11—28no—
350C22⋊D11—48no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—22no—
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×Dic11C2×C22⋊C412yes—
367C2×Dic11C2×C22⋊C412yes—
368C2×Dic11C2×C22⋊C412yes—
369D44—22no—
370D44—22no—
371D44—48no—
372D44—41no—
373D44—41no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—48no—
379C8×C11—22no—
380C8×C11—41no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C22×#41—111no—
384C23×Q8C2×D1111yescharacteristic
385C23×C8—111no—
386C23×C8C2×D1111yescharacteristic
387#548—118no—
388#548—224no—
389C2×#124—111no—
390C2×#124—221no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—221no—
393C2×#121—111no—
394C2×#121—221no—
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—221no—
398C2×#117—111no—
399C22×C4⋊C4C2×D1111yescharacteristic
400C8×D4—224no—
401C2×C4⋊C8—111no—
402#416—224no—
403C2×#103—24no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103C2×D1111yescharacteristic
409C2×#103C2×D1111yescharacteristic
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×C22⋊C8—111no—
417C2×C22⋊C8—111no—
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#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11#41614yescomplemented
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—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—41no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—81no—
456C2×D11—81no—
457C2×D11—81no—
458C2×D11—81no—
459C4×C11—22no—
460C4×C11—24no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—81no—
464C4×C11C2×C4×D411yescharacteristic
465C4×C11#51811yescharacteristic
466C4×C11D4211yescharacteristic
467C4×C11#54611yescharacteristic
468Dic11—22no—
469Dic11—22no—
470Dic11—22no—
471Dic11—42no—
472Dic11—81no—
473Dic11—81no—
474C2×#41—114no—
475C2×#41—222no—
476C2×#41—222no—
477C2×#41—222no—
478C2×#41—441no—
479C2×#41—441no—
480C22×Q8—21no—
481C22×Q8—22no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—41no—
485C22×Q8—41no—
486C22×Q8C4×D1114yes—
487C22×Q8C22×D1111yescharacteristic
488C22×Q8C22×D1111yescharacteristic
489C22×D4—111no—
490C22×D4—111no—
491C22×D4—221no—
492C22×D4—221no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—111no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—41no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—222no—
504C22×C8—222no—
505C22×C8—441no—
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508#124—114no—
509#124—222no—
510#124—228no—
511C22⋊Q8—114no—
512C22⋊Q8—228no—
513C22⋊Q8—222no—
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—222no—
523#117—441no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C42—111no—
545C2×C42—221no—
546C2×C42—221no—
547C2×C42—221no—
548C4⋊C8—222no—
549#103—22no—
550#103—22no—
551#103—22no—
552#103—222no—
553#103—222no—
554#103—441no—
555#103—441no—
556#103C22⋊D1114yescomplemented
557#102—222no—
558#102—222no—
559#102—441no—
560#102—441no—
561C22⋊C8—222no—
562C22⋊C8—222no—
563C4×C8—222no—
564#95—221no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—24no—
570C2×C11D4×C22⋊C411yescharacteristic
571C2×C11C2×#41611yescharacteristic
572C2×C11#289811yescharacteristic
573C2×C11#328211yescharacteristic
574C2×C11#328511yescharacteristic
575C2×C11#330011yescharacteristic
576C2×C11#330111yescharacteristic
577D11—42no—
578D11—82no—
579C24—111no—
580C24—221no—
581C24D4×D1111yescharacteristic
582#41—228no—
583#41—444no—
584#41—444no—
585#41—444no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—28no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8C2×C4×D1112yes—
602C2×Q8C2×C4×D1112yes—
603C2×Q8#433912yes—
604C2×Q8C2×C22⋊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—24no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—81no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—442no—
648C22×C4—442no—
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—44no—
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—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4C2×C22⋊D1112yes—
681C22⋊C4—114no—
682C22⋊C4—114no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—442no—
688C22⋊C4—442no—
689C22⋊C4—881no—
690C42—112no—
691C42—112no—
692C42—224no—
693C42—442no—
694C42—881no—
695C11#2241611yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—112no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—222no—
708C23—441no—
709C23—441no—
710C23—441no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23C22⋊C4×D1112yes—
715C23#6696912yes—
716C23#6697212yes—
717C23C2×D4×D1111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8C4×C22⋊D1114yes—
727D4—228no—
728D4—222no—
729D4—222no—
730D4—448no—
731D4—448no—
732D4—441no—
733D4—441no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—84no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—221no—
762C2×C4—221no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—448no—
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—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—222no—
795C22—222no—
796C22—222no—
797C22—441no—
798C22—441no—
799C22—441no—
800C22—441no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—881no—
805C22—881no—
806C22—881no—
807C22—881no—
808C22#1062241714yescomplemented
809C22C2×C22⋊C4×D1111yescharacteristic
810C22#1062302111yescharacteristic
811C22C2×#6696911yescharacteristic
812C22#1062329311yescharacteristic
813C22C2×#6697211yescharacteristic
814C22#1062329711yescharacteristic
815C22D4×C22⋊D1111yescharacteristic
816C4—22no—
817C4—24no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—222no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—881no—
826C4—881no—
827C4#1062301711yescharacteristic
828C4#1062302111yescharacteristic
829C4C2×C4×C22⋊D1111yescharacteristic
830C4D4×C22⋊D1111yescharacteristic
831C2—24no—
832C2—442no—
833C2—882no—
834C2C22⋊C4×C22⋊D1111yescharacteristic
835C2C2×#1062241711yescharacteristic
836C2#1307714411yescharacteristic
837C2#1308032311yescharacteristic
838C2#1308035711yescharacteristic
839C2#1308049911yescharacteristic
840C2#1308051411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#10623348C2
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#22416
LCSG ▷ C2×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
2. C2×C8×C22⋊D11C2semidirect
3. C2×#10622417C2semidirect
4. #13071541C2semidirect
5. #13069545C2semidirect
6. #13069424C2semidirect
7. #13069044C2semidirect
8. #13069036C2semidirect
9. #13068933C2semidirect
10. #13068925C2semidirect
11. #13068629C2semidirect
12. #13068555C2semidirect
13. #13068551C2semidirect
14. #103×Dic11C2semidirect
15. C22×C11×#103C2semidirect
21. #10623348C4semidirect
83. C2×#4343C2×C4semidirect
102. #67000C2×C4semidirect
105. #66999C2×C4semidirect
107. Q8×Dic11C2×C4semidirect
141. C11×#103D4semidirect
279. C22×#103D11semidirect
437. C22×C11#416semidirect
556. #103C22⋊D11semidirect
695. C11#22416semidirect
808. C22#10622417semidirect

Maximal subgroups

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

subgroupindex
C2×#106233482
C2×C8×C22⋊D112
C2×#106224172
#130715412
#130695452
#130694242
#130690442
#130690362
#130689332
#130689252
#130686292
#130685552
#130685512
#103×Dic112
C22×C11×#1032
#2241611