Finite Group Databasebeta

← #14769238

Subgroups — #14769238

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623365C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4#13071566C211yesmaximal, characteristic, complemented
5#13069541C211yesmaximal, characteristic, complemented
6#13069420C211yesmaximal, characteristic, complemented
7#13069044C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068935C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#416C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
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×#416—24no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C8×C22⋊D11—24no—
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622570—21no—
56#10622557—21no—
57#10622553—21no—
58C4×Dic11⋊C4—21no—
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×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11D411yescharacteristic
80C2×#4343—22no—
81C2×#4343—22no—
82C2×#4343—22no—
83C2×#4343—41no—
84C2×#4343—41no—
85C2×#4343C2×C414yes—
86C22×D44—21no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#117—22no—
96C11×#117—41no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104Q8×Dic11—22no—
105Q8×Dic11C2×C414yes—
106#66993—28no—
107#66993—22no—
108#66993C2×C414yes—
109#66991—22no—
110#66991—28no—
111#66991C2×C414yes—
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⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×C8×D11—22no—
136C2×C8×D11—22no—
137C2×C8×D11—41no—
138#66945—22no—
139#66945—41no—
140C11×#103—22no—
141C11×#103D414yescomplemented
142C11×#102—22no—
143C11×#102—22no—
144#66899—22no—
145#66899—22no—
146#66896—41no—
147#66896—41no—
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#22418—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×C11C22×C412yes—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—22no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—81no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11—81no—
209C2×C22⋊D11—81no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11C22⋊C414yes—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218#4343—28no—
219#4343—44no—
220#4343—44no—
221#4343—44no—
222C2×D44—24no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—42no—
229C2×D44—42no—
230C2×D44C22×C412yes—
231C2×C4×D11—24no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C2×D412yes—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—44no—
246C2×C8×C11C2×D412yes—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2×D412yes—
251C11×C22⋊C4—42no—
252C42×C11—42no—
253C22⋊Dic11—24no—
254C22⋊Dic11—81no—
255C22⋊Dic11C22⋊C414yes—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—81no—
259(C2×D11)⋊C4C22⋊C414yes—
260C4⋊Dic11—24no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11C22×C412yes—
267Dic11⋊C4—42no—
268Dic11⋊C4—81no—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—24no—
271C4×Dic11—42no—
272C4×Dic11—42no—
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×C8×D4—111no—
284C2×#416—111no—
285C2×#416D1111yescharacteristic, complemented
286#2354—111no—
287#1982—111no—
288#1957—111no—
289#1893—111no—
290#1893—111no—
291#1875—111no—
292#1875—111no—
293#1803—111no—
294#1788—111no—
295#1788—111no—
296C4×#103—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×C11C2×C22⋊C412yes—
352C2×C4×C11C23×C411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C22⋊D11—28no—
359C22⋊D11—48no—
360C22⋊D11—84no—
361C22⋊D11—84no—
362C22⋊D11—84no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—22no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11C2×C22⋊C412yes—
377C2×Dic11C2×C22⋊C412yes—
378C2×Dic11C2×C22⋊C412yes—
379C2×Dic11#13512yes—
380C2×Dic11#13512yes—
381D44—22no—
382D44—22no—
383D44—48no—
384D44—41no—
385D44—41no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—48no—
391C8×C11—22no—
392C8×C11—41no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C22×#41—111no—
396C22×#41C2×D1111yescharacteristic
397C23×C8—111no—
398C23×C8C2×D1111yescharacteristic
399#550—118no—
400#550—224no—
401C2×#127—111no—
402C2×#127—221no—
403C2×#121—111no—
404C2×#121—111no—
405C2×#121—221no—
406C2×#121—221no—
407C2×C4×Q8—111no—
408C2×C4×D4—111no—
409C2×C4×D4—221no—
410C2×#117—111no—
411C2×#117C2×D1111yescharacteristic
412C8×D4—224no—
413C2×C4⋊C8—111no—
414#416—24no—
415#416—224no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103C2×D1111yescharacteristic
419C2×#103C2×D1111yescharacteristic
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102C2×D1111yescharacteristic
427C2×#102C2×D1111yescharacteristic
428C2×C22⋊C8—111no—
429C2×C22⋊C8—111no—
430C2×C4×C8—111no—
431#390—221no—
432#388—221no—
433#388—221no—
434#384—111no—
435#380—111no—
436#380—111no—
437C4×C4⋊C4—111no—
438C4×C4⋊C4—221no—
439#340—111no—
440#340—111no—
441#340—111no—
442#340—111no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11C22×C22⋊C411yescharacteristic
458C22×C11D4211yescharacteristic
459C22×C11#54611yescharacteristic
460C22×C11C2×#13511yescharacteristic
461C22×C11C2×#13511yescharacteristic
462C22×C11#57611yescharacteristic
463C22×C11#57711yescharacteristic
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—41no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—81no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C4×C11—22no—
479C4×C11—24no—
480C4×C11—42no—
481C4×C11—81no—
482C4×C11C2×C4×D411yescharacteristic
483C4×C11#51811yescharacteristic
484C4×C11D4211yescharacteristic
485C4×C11#54611yescharacteristic
486Dic11—22no—
487Dic11—22no—
488Dic11—42no—
489Dic11—81no—
490Dic11—81no—
491Dic11#41614yescomplemented
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—114no—
498C2×#41—222no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—441no—
502C2×#41—441no—
503C2×#41C4×D1114yes—
504C22×Q8C22×D1111yescharacteristic
505C22×D4—21no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4C22×D1111yescharacteristic
514C23×C4—21no—
515C23×C4—111no—
516C23×C4—221no—
517C23×C4C22×D1111yescharacteristic
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—41no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—222no—
524C22×C8—222no—
525C22×C8—441no—
526C22×C8C22×D1111yescharacteristic
527C22×C8C22×D1111yescharacteristic
528#127—114no—
529#127—222no—
530#127—228no—
531#121—114no—
532#121—114no—
533#121—228no—
534#121—228no—
535#121—222no—
536#121—222no—
537C4×Q8—114no—
538C4×Q8—222no—
539C4×D4—114no—
540C4×D4—114no—
541C4×D4—228no—
542#117—22no—
543#117—41no—
544#117—222no—
545#117—441no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C22⋊C4—21no—
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—21no—
564C2×C42—111no—
565C2×C42—221no—
566C2×C42—221no—
567C2×C42—221no—
568C4⋊C8—222no—
569#103—22no—
570#103—222no—
571#103—222no—
572#103C22⋊D1114yescomplemented
573#102—22no—
574#102—22no—
575#102—222no—
576#102—222no—
577#102—441no—
578#102—441no—
579#102—441no—
580#102—441no—
581C22⋊C8—222no—
582C22⋊C8—222no—
583C4×C8—222no—
584#95—221no—
585#95—221no—
586#95—221no—
587C2×C11—42no—
588C2×C11—82no—
589C2×C11D4×C22⋊C411yescharacteristic
590C2×C11C2×#41611yescharacteristic
591C2×C11#289711yescharacteristic
592C2×C11#328411yescharacteristic
593C2×C11#328711yescharacteristic
594C2×C11#330411yescharacteristic
595C2×C11#330511yescharacteristic
596D11—42no—
597D11—82no—
598C24—21no—
599C24—111no—
600C24—221no—
601C24D4×D1111yescharacteristic
602#41—28no—
603#41—44no—
604#41—44no—
605#41—44no—
606#41—228no—
607#41—444no—
608#41—444no—
609#41—444no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8C2×C4×D1112yes—
614C2×Q8#433912yes—
615C2×Q8C2×C22⋊D1112yes—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—114no—
625C2×D4—112no—
626C2×D4—224no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—442no—
639C2×D4—442no—
640C2×D4—442no—
641C2×D4—442no—
642C2×D4—881no—
643C2×D4—881no—
644C2×D4—881no—
645C2×D4—881no—
646C2×D4—881no—
647C2×D4—881no—
648C2×D4C2×C4×D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—224no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—442no—
673C22×C4—442no—
674C22×C4C2×C4×D1112yes—
675C22×C4D4×D1111yescharacteristic
676C22×C4D4×D1112yes—
677C22×C4C23×D1111yescharacteristic
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—44no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—444no—
691C2×C8C2×C22⋊D1112yes—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—114no—
696C4⋊C4—112no—
697C4⋊C4—224no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—442no—
704C4⋊C4—881no—
705C4⋊C4C2×C22⋊D1112yes—
706C22⋊C4—42no—
707C22⋊C4—114no—
708C22⋊C4—114no—
709C22⋊C4—224no—
710C22⋊C4—224no—
711C22⋊C4—442no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—42no—
715C42—112no—
716C42—112no—
717C42—224no—
718C42—442no—
719C42—442no—
720C11#2241811yescharacteristic, complemented, Sylow
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—112no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—222no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23C22⋊C4×D1112yes—
749C23C2×D4×D1111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8C4×C22⋊D1114yes—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—228no—
760D4—222no—
761D4—222no—
762D4—448no—
763D4—448no—
764D4—441no—
765D4—441no—
766D4—884no—
767D4—884no—
768D4—884no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—112no—
786C2×C4—112no—
787C2×C4—112no—
788C2×C4—112no—
789C2×C4—112no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—448no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4C22⋊C4×D1112yes—
809C2×C4C22×C4×D1111yescharacteristic
810C2×C4C2×#433911yescharacteristic
811C2×C4C2×D4×D1111yescharacteristic
812C2×C4#6703711yescharacteristic
813C2×C4#6703711yescharacteristic
814C2×C4C22×C22⋊D1111yescharacteristic
815C8—22no—
816C8—41no—
817C8—441no—
818C8—441no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—222no—
834C22—222no—
835C22—222no—
836C22—441no—
837C22—441no—
838C22—441no—
839C22—441no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—881no—
844C22—881no—
845C22—881no—
846C22—881no—
847C22C2×C22⋊C4×D1111yescharacteristic
848C22#1062302111yescharacteristic
849C22D11×#13511yescharacteristic
850C22D11×#13511yescharacteristic
851C22#1062330011yescharacteristic
852C22#1062330111yescharacteristic
853C22D4×C22⋊D1111yescharacteristic
854C4—22no—
855C4—24no—
856C4—42no—
857C4—81no—
858C4—114no—
859C4—222no—
860C4—222no—
861C4—442no—
862C4—881no—
863C4—881no—
864C4#1062301711yescharacteristic
865C4#1062302111yescharacteristic
866C4C2×C4×C22⋊D1111yescharacteristic
867C4D4×C22⋊D1111yescharacteristic
868C2—42no—
869C2—82no—
870C2—442no—
871C2—882no—
872C2C22⋊C4×C22⋊D1111yescharacteristic
873C2D11×#41611yescharacteristic
874C2#1307713811yescharacteristic
875C2#1308034011yescharacteristic
876C2#1308037011yescharacteristic
877C2#1308055111yescharacteristic
878C2#1308056211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#22418
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D11C2semidirect
3. C2×#10622417C2semidirect
4. #13071566C2semidirect
5. #13069541C2semidirect
6. #13069420C2semidirect
7. #13069044C2semidirect
8. #13069041C2semidirect
9. #13068938C2semidirect
10. #13068935C2semidirect
11. #13068619C2semidirect
12. #13068556C2semidirect
13. #13068555C2semidirect
14. #103×Dic11C2semidirect
15. C2×C11×#416C2semidirect
21. #10623365C4semidirect
141. C11×#103D4semidirect
285. C2×#416D11semidirect
491. Dic11#416semidirect
572. #103C22⋊D11semidirect
720. C11#22418semidirect

Maximal subgroups

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

subgroupindex
C2×#106233652
C2×C8×C22⋊D112
C2×#106224172
#130715662
#130695412
#130694202
#130690442
#130690412
#130689382
#130689352
#130686192
#130685562
#130685552
#103×Dic112
C2×C11×#4162
#2241811