Finite Group Databasebeta

← #14769299

Subgroups — #14769299

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×#10623365C211yesmaximal, characteristic
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4#13071541C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069438C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068935C211yesmaximal, characteristic, complemented
10#13068933C211yesmaximal, characteristic, complemented
11#13068629C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C2×C11×#417C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20#10623365—24no—
21#10623365C418yescomplemented
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66993—21no—
24C2×#66993C2211yescharacteristic
25C2×#66991—21no—
26C2×#66991C2211yescharacteristic
27C2×#66983—21no—
28C2×#66983C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
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×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×#66879C2211yescharacteristic
51C2×Dic11⋊C8C2211yescharacteristic
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
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⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11D411yescharacteristic
81C2×#4343—22no—
82C2×#4343—22no—
83C2×#4343—22no—
84C2×#4343—41no—
85C2×#4343—41no—
86C2×#4343C2×C414yescomplemented
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11C2311yescharacteristic
91C2×C11×M16—22no—
92C2×C11×M16—22no—
93C2×C11×M16—41no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104Q8×Dic11—22no—
105Q8×Dic11C2×C414yescomplemented
106#66993—28no—
107#66993—22no—
108#66993C2×C414yescomplemented
109#66991—22no—
110#66991—28no—
111#66991C2×C414yescomplemented
112#66983—22no—
113#66983—28no—
114#66983C2×C414yes—
115C4×C22⋊D11—28no—
116C4×C22⋊D11C2×C414yes—
117C4×C22⋊D11D414yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
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×#103D414yescomplemented
140C11×#102—22no—
141C11×#102—22no—
142#66899—22no—
143#66899—22no—
144#66896—41no—
145#66896—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—
155#66879—22no—
156Dic11⋊C8—22no—
157#66873—22no—
158#66873—41no—
159#22422—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11C2×D411yescharacteristic
164C11×#41—28no—
165C11×#41—44no—
166C11×#41—44no—
167C11×#41—44no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11C22×C412yes—
172C2×Q8×C11C2×D412yes—
173C2×Q8×C11#4112yes—
174C2×D4×C11—24no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—42no—
181C2×D4×C11—42no—
182C2×D4×C11C22×C412yes—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
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—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—41no—
205C2×C22⋊D11—41no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—81no—
209C2×C22⋊D11—81no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11—81no—
213C2×C22⋊D11—81no—
214C2×C22⋊D11C22⋊C414yes—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221#4343—28no—
222#4343—44no—
223#4343—44no—
224#4343—44no—
225C2×D44—24no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—42no—
232C2×D44—42no—
233C2×D44C22×C412yes—
234C2×C4×D11—24no—
235C2×C4×D11—21no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—42no—
240C2×C4×D11—42no—
241C2×C4×D11C22×C412yes—
242C2×C4×D11C2×D412yes—
243C11×M16—44no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11C2×D412yes—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—42no—
254C11×C4⋊C4C2×D412yes—
255C22⋊Dic11—24no—
256C22⋊Dic11—42no—
257C22⋊Dic11C22⋊C414yes—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4C22⋊C414yes—
262C4⋊Dic11—24no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C22×C412yes—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—24no—
271C4×Dic11—42no—
272C4×Dic11—81no—
273C4×Dic11C22×C412yes—
274C4×Dic11C2×D412yes—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C8×D11—44no—
282C2×#550—111no—
283C2×#435—111no—
284C2×#417D1111yescharacteristic, complemented
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—22no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—22no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11C2×C22⋊C412yes—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11C4×D414yes—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—48no—
333D4×C11—41no—
334D4×C11—41no—
335C2×C4×C11—22no—
336C2×C4×C11—21no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—21no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—48no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—84no—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—44no—
360C22⋊D11—48no—
361C22⋊D11—84no—
362C22⋊D11—84no—
363C22⋊D11—84no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—22no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11C2×C22⋊C412yes—
380C2×Dic11C2×C22⋊C412yes—
381C2×Dic11C2×C22⋊C412yes—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—41no—
386D44—41no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—48no—
392C8×C11—22no—
393C8×C11—41no—
394C11⋊C8—41no—
395C11⋊C8—41no—
396C22×#41—111no—
397C22×#41C2×D1111yescharacteristic
398C22×M16C2×D1111yescharacteristic
399C23×C8—111no—
400#550—118no—
401#550—224no—
402C2×#127—111no—
403C2×#127—221no—
404C2×#121—111no—
405C2×#121—111no—
406C2×#121—221no—
407C2×#121—221no—
408C2×C4×Q8—111no—
409C2×C4×D4—111no—
410C2×C4×D4—221no—
411C2×#117—111no—
412C22×C4⋊C4C2×D1111yescharacteristic
413#435—224no—
414C2×C4⋊C8—111no—
415#417—24no—
416#416—224no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103C2×D1111yescharacteristic
420C2×#103C2×D1111yescharacteristic
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102C2×D1111yescharacteristic
428C2×#102C2×D1111yescharacteristic
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—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11C22×C22⋊C411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11#54611yescharacteristic
461C22×C11#57511yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—41no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C4×C11—22no—
480C4×C11—24no—
481C4×C11—42no—
482C4×C11—81no—
483C4×C11C2×C4×D411yescharacteristic
484C4×C11#51811yescharacteristic
485C4×C11D4211yescharacteristic
486C4×C11#54611yescharacteristic
487Dic11—22no—
488Dic11—22no—
489Dic11—22no—
490Dic11—42no—
491Dic11—81no—
492Dic11—81no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—114no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—441no—
503C2×#41—441no—
504C2×#41C4×D1114yes—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—111no—
518C23×C4—221no—
519C23×C4C22×D1111yescharacteristic
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—41no—
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—222no—
526C22×C8—222no—
527C22×C8—441no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#127—114no—
531#127—222no—
532#127—228no—
533#121—114no—
534#121—114no—
535#121—228no—
536#121—228no—
537#121—222no—
538#121—222no—
539C4×Q8—114no—
540C4×Q8—222no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4—228no—
544#117—222no—
545#117—441no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C22⋊C4—111no—
557C2×C22⋊C4—111no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C42—111no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42—221no—
567C4⋊C8—222no—
568#103—22no—
569#103—222no—
570#103—222no—
571#103C22⋊D1114yescomplemented
572#102—22no—
573#102—22no—
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—82no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11#289611yescharacteristic
592C2×C11#289711yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327111yescharacteristic
595C2×C11#330911yescharacteristic
596C2×C11#331711yescharacteristic
597D11—42no—
598D11—82no—
599C24—21no—
600C24—111no—
601C24—221no—
602C24D4×D1111yescharacteristic
603#41—28no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—228no—
608#41—444no—
609#41—444no—
610#41—444no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C4×D1112yes—
615C2×Q8#433912yes—
616C2×Q8C2×C22⋊D1112yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—114no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—442no—
638C2×D4—442no—
639C2×D4—441no—
640C2×D4—441no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—881no—
644C2×D4—881no—
645C2×D4—881no—
646C2×D4—881no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—81no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—224no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4C2×C4×D1112yes—
679C22×C4D4×D1111yescharacteristic
680C22×C4D4×D1112yes—
681C22×C4C23×D1111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—444no—
695C2×C8C2×C22⋊D1112yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—114no—
701C4⋊C4—112no—
702C4⋊C4—224no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4C2×C22⋊D1112yes—
709C22⋊C4—114no—
710C22⋊C4—114no—
711C22⋊C4—224no—
712C22⋊C4—224no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—881no—
716C42—112no—
717C42—112no—
718C42—224no—
719C42—442no—
720C42—881no—
721C11#2242211yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—112no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—222no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23C22⋊C4×D1112yes—
750C23C2×D4×D1111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×C22⋊D1114yes—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—222no—
761D4—222no—
762D4—448no—
763D4—444no—
764D4—448no—
765D4—441no—
766D4—441no—
767D4—884no—
768D4—884no—
769D4—884no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—48no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4—112no—
788C2×C4—112no—
789C2×C4—112no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—448no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4C22⋊C4×D1112yes—
811C2×C4C22×C4×D1111yescharacteristic
812C2×C4C2×#433911yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4#6703711yescharacteristic
815C2×C4#6703711yescharacteristic
816C2×C4C22×C22⋊D1111yescharacteristic
817C8—22no—
818C8—41no—
819C8—441no—
820C8—441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—222no—
836C22—222no—
837C22—222no—
838C22—441no—
839C22—441no—
840C22—441no—
841C22—441no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—881no—
846C22—881no—
847C22—881no—
848C22—881no—
849C22C2×C22⋊C4×D1111yescharacteristic
850C22#1062302111yescharacteristic
851C22#1062330411yescharacteristic
852C22#1062330511yescharacteristic
853C22#1062330811yescharacteristic
854C22#1062330911yescharacteristic
855C22D4×C22⋊D1111yescharacteristic
856C4—22no—
857C4—24no—
858C4—42no—
859C4—81no—
860C4—222no—
861C4—222no—
862C4—222no—
863C4—442no—
864C4—881no—
865C4—881no—
866C4#1062301711yescharacteristic
867C4#1062302111yescharacteristic
868C4C2×C4×C22⋊D1111yescharacteristic
869C4D4×C22⋊D1111yescharacteristic
870C2—42no—
871C2—82no—
872C2—442no—
873C2—882no—
874C2C22⋊C4×C22⋊D1111yescharacteristic
875C2#1307713211yescharacteristic
876C2#1307714011yescharacteristic
877C2#1308015011yescharacteristic
878C2#1308019511yescharacteristic
879C2#1308062311yescharacteristic
880C2#1308074311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#22422
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×#10622417C2semidirect
4. #13071541C2semidirect
5. #13069541C2semidirect
6. #13069438C2semidirect
7. #13069054C2semidirect
8. #13069041C2semidirect
9. #13068935C2semidirect
10. #13068933C2semidirect
11. #13068629C2semidirect
12. #13068556C2semidirect
13. #13068555C2semidirect
14. #13068448C2semidirect
15. C2×C11×#417C2semidirect
21. #10623365C4semidirect
86. C2×#4343C2×C4semidirect
105. Q8×Dic11C2×C4semidirect
108. #66993C2×C4semidirect
111. #66991C2×C4semidirect
139. C11×#103D4semidirect
284. C2×#417D11semidirect
571. #103C22⋊D11semidirect
721. C11#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#106233652
C2×#106227402
C2×#106224172
#130715412
#130695412
#130694382
#130690542
#130690412
#130689352
#130689332
#130686292
#130685562
#130685552
#130684482
C2×C11×#4172
#2242211