Finite Group Databasebeta

← #14791394

Subgroups — #14791394

Order 2816.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622651C211yesmaximal, characteristic, complemented
2C2×#10622851C211yesmaximal, characteristic, complemented
3C2×#10622830C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic, complemented
6#13069852C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069693C211yesmaximal, characteristic, complemented
9#13069617C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068909C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C11×#546—24no—
19C11×#546—24no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4—21no—
29C22×#4325C2211yescharacteristic, complemented
30C22×#4323C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic, complemented
34C2×#66979C2211yescharacteristic, complemented
35C23×C11⋊C8C2211yescharacteristic, complemented
36#10622851—24no—
37#10622846—24no—
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66899C2211yescharacteristic, complemented
41#10622836—21no—
42#10622830—24no—
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622651—24no—
54#10622603—21no—
55C2×#66873C2211yescharacteristic, complemented
56C2×#66871C2211yescharacteristic, complemented
57#10622572—21no—
58#10622570—21no—
59#10622552C2211yescharacteristic, complemented
60#10622541C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C2×C11×#41D414yescomplemented
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—21no—
80C22×D4×C11—41no—
81C22×D4×C11—41no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×D44C2311yescharacteristic
92C11×#124—22no—
93C11×#124—22no—
94C11×#123—28no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×#121—28no—
98C11×#121—22no—
99C11×#121D414yescomplemented
100C11×#120—28no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—28no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×#4325—22no—
120C2×#4325—41no—
121C2×#4325—41no—
122C2×#4323—22no—
123C2×#4323—22no—
124C2×#4323—22no—
125C2×#4323—22no—
126C2×#4323—22no—
127C2×#4323—41no—
128#66983—22no—
129#66983—22no—
130#66983—22no—
131#66983—41no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136#66979—22no—
137#66979—41no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C22×C11⋊C8—22no—
144C22×C11⋊C8—22no—
145C22×C11⋊C8—41no—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150#66899—22no—
151#66899—22no—
152#66899—22no—
153#66896—22no—
154#66896—22no—
155#66896—22no—
156#66896—22no—
157#66896—41no—
158#66896D414yescomplemented
159C11⋊#95—21no—
160C11⋊#95—21no—
161C22⋊(C11⋊C8)—22no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—41no—
164#66873—22no—
165#66871—22no—
166#24428—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11—24no—
169C24×C11—21no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C23×D11—21no—
179C11×#41—28no—
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11C2×D412yes—
189C2×D4×C11—24no—
190C2×D4×C11—22no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—41no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11—44no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—44no—
211C2×D4×C11—81no—
212C2×D4×C11—81no—
213C2×D4×C11C2×D412yes—
214C2×D4×C11C2×D412yes—
215C2×D4×C11C2×D412yes—
216C2×D4×C11#4112yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—24no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—81no—
234C22×C4×C11—81no—
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—42no—
243C2×C22⋊D11—42no—
244C2×C22⋊D11—42no—
245C2×C22⋊D11—81no—
246C2×C22⋊D11—81no—
247C2×C22⋊D11—81no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C2×D44—21no—
252C2×D44—21no—
253C2×D44—21no—
254C2×D44—21no—
255C2×D44—21no—
256C2×D44—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4C2×D412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—24no—
268C42×C11—21no—
269C42×C11—21no—
270C22⋊Dic11—42no—
271C22⋊Dic11—81no—
272#4325—44no—
273#4323—44no—
274#4323—44no—
275(C2×D11)⋊C4—42no—
276(C2×D11)⋊C4—42no—
277(C2×D11)⋊C4—42no—
278(C2×D11)⋊C4—81no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11C2×D412yes—
285Dic11⋊C4—81no—
286C4×Dic11—42no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—21no—
294C2×C11⋊C8—21no—
295C2×C11⋊C8—21no—
296C2×C11⋊C8—21no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—44no—
299C2×C11⋊C8C2×D412yes—
300C2×#546D1111yescharacteristic, complemented
301C2×#466—111no—
302C2×#449—111no—
303C2×#447—111no—
304C2×#416—111no—
305#2414—111no—
306#2042—111no—
307#2036—111no—
308#2012—111no—
309#2000—111no—
310#1879—111no—
311#1875—111no—
312#1869—111no—
313#1862—111no—
314#1786—111no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—22no—
331C23×C11—48no—
332C23×C11—48no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—84no—
344C23×C11—84no—
345C23×C11—84no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11#12012yes—
349C23×C11#13512yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—41no—
361Q8×C11—41no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—44no—
368D4×C11—48no—
369D4×C11—48no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—84no—
373D4×C11#12114yes—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—48no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—84no—
401C2×C4×C11#12012yes—
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C2×#4111yescharacteristic
406C2×C4×C11H(5,𝔽2)11yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C22⋊D11—84no—
409C22⋊D11—84no—
410C2×Dic11—22no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419D44—41no—
420D44—41no—
421D44—41no—
422D44—41no—
423C11⋊C8—22no—
424C11⋊C8—41no—
425C11⋊C8—41no—
426C11⋊C8—41no—
427C22×#41C2×D1111yescharacteristic
428C23×D4C2×D1111yescharacteristic
429C22×SD16—111no—
430C22×D8—111no—
431C22×D8—111no—
432C23×C8—111no—
433#546—24no—
434#546—24no—
435C2×#124C2×D1111yescharacteristic
436C2×#123—21no—
437C2×C22⋊Q8C2×D1111yescharacteristic
438C2×#121—21no—
439C2×#121—111no—
440C2×#121—111no—
441C2×#121C2×D1111yescharacteristic
442C2×#120—21no—
443C2×C4×D4C2×D1111yescharacteristic
444C2×C4×D4C2×D1111yescharacteristic
445C2×#117—111no—
446C22×C22⋊C4—21no—
447#466—224no—
448#449—224no—
449#447—224no—
450C2×#107—111no—
451#416—224no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#103—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—111no—
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×C22⋊C8—111no—
465#394—221no—
466#392—221no—
467#390—111no—
468#390—221no—
469#389—111no—
470#388—221no—
471#380—111no—
472#340—111no—
473#340—111no—
474#336—111no—
475#336—111no—
476C22×C11—22no—
477C22×C11—24no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—816no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—81no—
505C22×C11C2×#12011yescharacteristic
506C22×C11D4211yescharacteristic
507C22×C11#54611yescharacteristic
508C22×C11C2×#13511yescharacteristic
509C22×C11#57511yescharacteristic
510C22×C11#57611yescharacteristic
511C22×C11#57611yescharacteristic
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C2×D11—81no—
519C4×C11—22no—
520C4×C11—41no—
521C4×C11—42no—
522C4×C11—41no—
523C4×C11—41no—
524C4×C11—42no—
525C4×C11C2×#12111yescharacteristic
526C4×C11#53411yescharacteristic
527C4×C11D4211yescharacteristic
528C4×C11#54611yescharacteristic
529Dic11—42no—
530Dic11—81no—
531Dic11—81no—
532C25—21no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—41no—
537C2×#41—41no—
538C2×#41C22⋊D1114yescomplemented
539C22×Q8C22×D1111yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—22no—
546C22×D4—21no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4—111no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4C22⋊D1111yescharacteristic
553C22×D4C22×D1111yescharacteristic
554C22×D4C22×D1111yescharacteristic
555C23×C4—21no—
556C23×C4—21no—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C2×SD16—222no—
560C2×SD16—441no—
561C2×SD16—441no—
562C2×D8—222no—
563C2×D8—222no—
564C2×D8—222no—
565C2×D8—222no—
566C2×D8—222no—
567C2×D8—441no—
568C22×C8—111no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—111no—
572C22×C8—222no—
573C22×C8—222no—
574C22×C8—441no—
575#124—22no—
576#124—22no—
577#123—28no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580#121—28no—
581#121—22no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—441no—
586#121C22⋊D1114yescomplemented
587#120—28no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592#117—222no—
593#117—441no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4C22⋊D1111yescharacteristic
600C2×C4⋊C4C22×D1111yescharacteristic
601C2×C22⋊C4—28no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4C22⋊D1111yescharacteristic
614C2×C22⋊C4C22⋊D1111yescharacteristic
615C2×C42—221no—
616C2×C42C22×D1111yescharacteristic
617#107—222no—
618#103—222no—
619#103—222no—
620#103—222no—
621#102—114no—
622#102—222no—
623#102—222no—
624#102—222no—
625#102—222no—
626#102—222no—
627#102—441no—
628C22⋊C8—222no—
629C22⋊C8—222no—
630C22⋊C8—441no—
631#95—221no—
632#95—221no—
633C2×C11—42no—
634C2×C11—42no—
635C2×C11—44no—
636C2×C11—82no—
637C2×C11#241011yescharacteristic
638C2×C11#300211yescharacteristic
639C2×C11#300811yescharacteristic
640C2×C11#326811yescharacteristic
641C2×C11#328011yescharacteristic
642C2×C11#329711yescharacteristic
643C2×C11#331911yescharacteristic
644D11—161no—
645C24—21no—
646C24—24no—
647C24—21no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—81no—
653C24—81no—
654C24—221no—
655C24C2×C22⋊D1111yescharacteristic
656C24C2×C22⋊D1111yescharacteristic
657#41—28no—
658#41—44no—
659#41—44no—
660#41—44no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8C2×C22⋊D1112yes—
667C2×D4—24no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—41no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—44no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—221no—
692C2×D4—221no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—221no—
696C2×D4—221no—
697C2×D4—442no—
698C2×D4—442no—
699C2×D4—442no—
700C2×D4—881no—
701C2×D4—881no—
702C2×D4—881no—
703C2×D4D4×D1112yes—
704C2×D4#434112yes—
705C2×D4C2×C22⋊D1112yes—
706C2×D4C2×C22⋊D1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—81no—
724C22×C4—81no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1112yes—
733C22×C4C2×C22⋊D1112yes—
734C22×C4C23×D1111yescharacteristic
735SD16—444no—
736D8—444no—
737D8—444no—
738C2×C8—112no—
739C2×C8—221no—
740C2×C8—221no—
741C2×C8—221no—
742C2×C8—221no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—221no—
749C2×C8—221no—
750C2×C8—444no—
751C4⋊C4—24no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—112no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—881no—
761C4⋊C4C2×C22⋊D1112yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—442no—
770C22⋊C4—442no—
771C22⋊C4—442no—
772C22⋊C4—442no—
773C22⋊C4—881no—
774C22⋊C4—881no—
775C42—21no—
776C42—21no—
777C42—442no—
778C11#2442811yescharacteristic, complemented, Sylow
779C23—21no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—22no—
795C23—48no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23#6700312yes—
820C23#6700612yes—
821C23C22×C22⋊D1111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—84no—
837D4—441no—
838D4—441no—
839D4—441no—
840D4—441no—
841D4—884no—
842D4—884no—
843D4#6699214yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—84no—
871C2×C4—222no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4#6700612yes—
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×#434111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#6703711yescharacteristic
885C2×C4C22×C22⋊D1111yescharacteristic
886C2×C4C22×C22⋊D1111yescharacteristic
887C8—222no—
888C8—441no—
889C8—441no—
890C8—441no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—881no—
921C22—881no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22—881no—
927C22D4×C22⋊D1111yescharacteristic
928C22#1062333711yescharacteristic
929C22C2×#6700311yescharacteristic
930C22#1062335311yescharacteristic
931C22#1062336611yescharacteristic
932C22#1062336611yescharacteristic
933C22C2×#6700611yescharacteristic
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—41no—
939C4—42no—
940C4—442no—
941C4—881no—
942C4—881no—
943C4D4×C22⋊D1111yescharacteristic
944C4C2×#6699211yescharacteristic
945C4#1062333511yescharacteristic
946C4#1062333711yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—1761no—
952C2#1307199011yescharacteristic
953C2#1307783411yescharacteristic
954C2#1307788411yescharacteristic
955C2#1308015211yescharacteristic
956C2#1308029711yescharacteristic
957C2#1308046611yescharacteristic
958C2#1308077211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#24428
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10622651C2semidirect
2. C2×#10622851C2semidirect
3. C2×#10622830C2semidirect
4. C2×#10622846C2semidirect
5. #13072034C2semidirect
6. #13069852C2semidirect
7. #13069816C2semidirect
8. #13069693C2semidirect
9. #13069617C2semidirect
10. #13068964C2semidirect
11. #13068939C2semidirect
12. #13068909C2semidirect
13. #13068863C2semidirect
14. #13068547C2semidirect
15. C2×C11×#546C2semidirect
29. C22×#4325C22semidirect
33. C2×#66983C22semidirect
34. C2×#66979C22semidirect
35. C23×C11⋊C8C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
40. C2×#66899C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
55. C2×#66873C22semidirect
56. C2×#66871C22semidirect
59. #10622552C22semidirect
60. #10622541C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
71. C2×C11×#41D4semidirect
99. C11×#121D4semidirect
158. #66896D4semidirect
300. C2×#546D11semidirect
538. C2×#41C22⋊D11semidirect
586. #121C22⋊D11semidirect
778. C11#24428semidirect

Maximal subgroups

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

subgroupindex
C2×#106226512
C2×#106228512
C2×#106228302
C2×#106228462
#130720342
#130698522
#130698162
#130696932
#130696172
#130689642
#130689392
#130689092
#130688632
#130685472
C2×C11×#5462
#2442811