Finite Group Databasebeta

← #14791364

Subgroups — #14791364

Order 2816.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622664C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622831C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5#13072067C211yesmaximal, characteristic, complemented
6#13069852C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069710C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic, complemented
12#13068909C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic
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×#4326C2211yescharacteristic, complemented
30C22×#4324C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic, complemented
35C23×C11⋊C8C2211yescharacteristic
36#10622852—24no—
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40#10622833—21no—
41#10622831—24no—
42C2×#66896—24no—
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic, complemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622664—24no—
54#10622597—21no—
55C2×#66874C2211yescharacteristic, complemented
56C2×#66871C2211yescharacteristic, complemented
57#10622561—21no—
58#10622555—21no—
59#10622542C2211yescharacteristic, 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—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—22no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11D414yes—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×Dic11—21no—
90C22×Dic22C2311yescharacteristic
91C11×#124—22no—
92C11×#124—22no—
93C11×#123—28no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D414yes—
96C11×#121—28no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#120—28no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—28no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×#4326—22no—
120C2×#4326—22no—
121C2×#4326—41no—
122C2×#4324—22no—
123C2×#4324—22no—
124C2×#4324—22no—
125C2×#4324—22no—
126C2×#4324—41no—
127C2×#4324—41no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134#66977—22no—
135#66977—22no—
136#66977—22no—
137#66977—41no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C22×C11⋊C8—22no—
142C22×C11⋊C8—22no—
143C22×C11⋊C8—41no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66899—22no—
149#66899—22no—
150#66899—41no—
151#66896—22no—
152#66896—22no—
153#66896—22no—
154#66896—22no—
155#66896—22no—
156#66896D414yescomplemented
157C11⋊#95—21no—
158C11⋊#95—21no—
159C11⋊#95—21no—
160C11⋊#95—21no—
161C22⋊(C11⋊C8)—22no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—41no—
164#66874—22no—
165#66871—22no—
166#24426—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—24no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—81no—
175C24×C11—81no—
176C24×C11C2×D411yescharacteristic
177C24×C11C2×D411yescharacteristic
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—28no—
189C2×D4×C11—24no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
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—21no—
203C2×D4×C11—44no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—81no—
211C2×D4×C11—81no—
212C2×D4×C11C2×D412yes—
213C2×D4×C11C2×D412yes—
214C2×D4×C11C2×D412yes—
215C2×D4×C11#4112yes—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—42no—
231C22×C4×C11—42no—
232C22×C4×C11—81no—
233C22×C4×C11—81no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2411yescharacteristic
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—42no—
246C22×Dic11—42no—
247C22×Dic11—81no—
248C2×Dic22—21no—
249C2×Dic22—21no—
250C2×Dic22—21no—
251C2×Dic22—21no—
252C2×Dic22—21no—
253C2×Dic22—21no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2×D412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—22no—
265C42×C11—21no—
266C42×C11—21no—
267C22⋊Dic11—42no—
268C22⋊Dic11—42no—
269C22⋊Dic11—81no—
270#4326—44no—
271#4324—44no—
272#4324—44no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—42no—
279C4⋊Dic11C2×D412yes—
280Dic11⋊C4—42no—
281Dic11⋊C4—42no—
282Dic11⋊C4—81no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
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—44no—
295C2×C11⋊C8C2×D412yes—
296C2×#546D1111yescharacteristic
297C2×#467—111no—
298C2×#452—111no—
299C2×#450—111no—
300C22×#102—111no—
301#2417—111no—
302#2042—111no—
303#2033—111no—
304#2015—111no—
305#2000—111no—
306#1877—111no—
307#1872—111no—
308#1869—111no—
309#1862—111no—
310#1788—111no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—48no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—48no—
338C23×C11—84no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11#12012yes—
344C23×C11#13512yes—
345C23×C11#13712yes—
346C23×C11C22×D411yescharacteristic
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—41no—
350Q8×C11—41no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—48no—
357D4×C11—48no—
358D4×C11—44no—
359D4×C11—41no—
360D4×C11—41no—
361D4×C11—84no—
362D4×C11#12114yes—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—48no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—84no—
390C2×C4×C11#12012yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C2×#4111yescharacteristic
395C2×C4×C11H(5,𝔽2)11yescharacteristic
396C2×C4×C11H(5,𝔽2)11yescharacteristic
397C2×Dic11—22no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—84no—
410Dic22—41no—
411Dic22—41no—
412Dic22—41no—
413Dic22—41no—
414C11⋊C8—22no—
415C11⋊C8—41no—
416C11⋊C8—41no—
417C11⋊C8—41no—
418C22×#41C2×D1111yescharacteristic
419C23×D4C2×D1111yescharacteristic
420C22×Q16—111no—
421C22×SD16—111no—
422C22×SD16—111no—
423C23×C8—111no—
424#546—24no—
425#546—24no—
426C2×#124C2×D1111yescharacteristic
427C2×#123—21no—
428C2×C22⋊Q8—111no—
429C2×C22⋊Q8—111no—
430C2×C22⋊Q8C2×D1111yescharacteristic
431C2×#121—21no—
432C2×#121C2×D1111yescharacteristic
433C2×#120—21no—
434C2×C4×D4C2×D1111yescharacteristic
435C2×C4×D4C2×D1111yescharacteristic
436C22×C4⋊C4—111no—
437C22×C22⋊C4—21no—
438#467—224no—
439#452—224no—
440#450—224no—
441C2×#107—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#103—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—224no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×C22⋊C8—111no—
456#398—221no—
457#396—221no—
458#391—111no—
459#389—111no—
460#386—221no—
461#380—111no—
462#380—221no—
463#340—111no—
464#340—111no—
465#336—111no—
466#336—111no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—24no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—42no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—42no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—816no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11#45214yescomplemented
496C22×C11C2×#12011yescharacteristic
497C22×C11D4211yescharacteristic
498C22×C11#54611yescharacteristic
499C22×C11C2×#13511yescharacteristic
500C22×C11C2×#13711yescharacteristic
501C22×C11#57611yescharacteristic
502C22×C11#57711yescharacteristic
503C4×C11—22no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—41no—
507C4×C11—41no—
508C4×C11—42no—
509C4×C11C2×#12111yescharacteristic
510C4×C11#53411yescharacteristic
511C4×C11D4211yescharacteristic
512C4×C11#54611yescharacteristic
513Dic11—42no—
514Dic11—81no—
515Dic11—81no—
516Dic11—81no—
517C25—21no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C22×Q8—111no—
525C22×Q8C22×D1111yescharacteristic
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—22no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C22⋊D1111yescharacteristic
535C22×D4C22⋊D1114yes—
536C22×D4C22×D1111yescharacteristic
537C22×D4C22×D1111yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—221no—
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C2×Q16—222no—
544C2×Q16—222no—
545C2×Q16—441no—
546C2×SD16—222no—
547C2×SD16—222no—
548C2×SD16—222no—
549C2×SD16—222no—
550C2×SD16—441no—
551C2×SD16—441no—
552C22×C8—111no—
553C22×C8—111no—
554C22×C8—111no—
555C22×C8—111no—
556C22×C8—222no—
557C22×C8—222no—
558C22×C8—441no—
559#124—22no—
560#124—22no—
561#123—28no—
562C22⋊Q8—22no—
563C22⋊Q8—222no—
564C22⋊Q8—222no—
565C22⋊Q8—222no—
566C22⋊Q8—441no—
567C22⋊Q8C22⋊D1114yes—
568#121—28no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4—441no—
586C2×C4⋊C4C22⋊D1111yescharacteristic
587C2×C4⋊C4C22×D1111yescharacteristic
588C2×C22⋊C4—28no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—221no—
595C2×C22⋊C4—221no—
596C2×C22⋊C4—221no—
597C2×C22⋊C4C22⋊D1111yescharacteristic
598C2×C22⋊C4C22⋊D1111yescharacteristic
599C2×C42C22×D1111yescharacteristic
600#107—222no—
601#103—222no—
602#103—222no—
603#103—222no—
604#103—441no—
605#102—114no—
606#102—222no—
607#102—222no—
608#102—222no—
609#102—222no—
610#102—222no—
611C22⋊C8—222no—
612C22⋊C8—222no—
613C22⋊C8—441no—
614#95—221no—
615#95—221no—
616#95—221no—
617#95—221no—
618C2×C11—24no—
619C2×C11—44no—
620C2×C11—81no—
621C2×C11—82no—
622C2×C11#241011yescharacteristic
623C2×C11C2×#45211yescharacteristic
624C2×C11#301211yescharacteristic
625C2×C11#326611yescharacteristic
626C2×C11#328011yescharacteristic
627C2×C11#329611yescharacteristic
628C2×C11#331411yescharacteristic
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—81no—
637C24—81no—
638C24C2×C22⋊D1111yescharacteristic
639C24C2×C22⋊D1111yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—221no—
650C2×Q8—221no—
651C2×Q8—221no—
652C2×Q8—221no—
653C2×Q8—221no—
654C2×Q8—221no—
655C2×Q8C2×C22⋊D1112yes—
656C2×D4—28no—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4D4×D1112yes—
681C2×D4#434112yes—
682C2×D4C2×C22⋊D1112yes—
683C2×D4C2×C22⋊D1112yes—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—442no—
707C22×C4—442no—
708C22×C4—881no—
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1112yes—
714C22×C4C2×C22⋊D1112yes—
715C22×C4C23×D1111yescharacteristic
716Q16—444no—
717SD16—444no—
718SD16—444no—
719C2×C8—112no—
720C2×C8—221no—
721C2×C8—221no—
722C2×C8—221no—
723C2×C8—221no—
724C2×C8—221no—
725C2×C8—221no—
726C2×C8—221no—
727C2×C8—221no—
728C2×C8—221no—
729C2×C8—221no—
730C2×C8—221no—
731C2×C8—444no—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—112no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—221no—
741C4⋊C4—442no—
742C4⋊C4—442no—
743C4⋊C4—442no—
744C4⋊C4—881no—
745C4⋊C4C2×C22⋊D1112yes—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—22no—
751C22⋊C4—24no—
752C22⋊C4—22no—
753C22⋊C4—442no—
754C22⋊C4—442no—
755C22⋊C4—881no—
756C42—21no—
757C42—21no—
758C11#2442611yescharacteristic, complemented, Sylow
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—48no—
784C23—41no—
785C23—41no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#6700312yes—
792C23#6700412yes—
793C23#6700612yes—
794C23C22×C22⋊D1111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—441no—
800Q8—441no—
801Q8—441no—
802Q8—441no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#6699214yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—48no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—84no—
842C2×C4—222no—
843C2×C4—441no—
844C2×C4—441no—
845C2×C4—441no—
846C2×C4—441no—
847C2×C4—441no—
848C2×C4—441no—
849C2×C4—441no—
850C2×C4—441no—
851C2×C4—441no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—884no—
855C2×C4#6700612yes—
856C2×C4C2×D4×D1111yescharacteristic
857C2×C4C2×#434111yescharacteristic
858C2×C4#6703711yescharacteristic
859C2×C4#6703711yescharacteristic
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1111yescharacteristic
862C8—222no—
863C8—441no—
864C8—441no—
865C8—441no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—41no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#1062285214yescomplemented
895C22D4×C22⋊D1111yescharacteristic
896C22#1062333711yescharacteristic
897C22C2×#6700311yescharacteristic
898C22C2×#6700411yescharacteristic
899C22#1062336611yescharacteristic
900C22#1062336711yescharacteristic
901C22C2×#6700611yescharacteristic
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—41no—
907C4—42no—
908C4—442no—
909C4—881no—
910C4—881no—
911C4—881no—
912C4D4×C22⋊D1111yescharacteristic
913C4C2×#6699211yescharacteristic
914C4#1062333511yescharacteristic
915C4#1062333711yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2#1307199011yescharacteristic
921C2C2×#1062285211yescharacteristic
922C2#1307792011yescharacteristic
923C2#1308012211yescharacteristic
924C2#1308029711yescharacteristic
925C2#1308045111yescharacteristic
926C2#1308069711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#24426
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×#10622664C2semidirect
2. C2×#10622852C2semidirect
3. C2×#10622831C2semidirect
4. C22×#66896C2semidirect
5. #13072067C2semidirect
6. #13069852C2semidirect
7. #13069795C2semidirect
8. #13069710C2semidirect
9. #13069619C2semidirect
10. #13068950C2semidirect
11. #13068924C2semidirect
12. #13068909C2semidirect
13. #13068863C2semidirect
14. #13068556C2semidirect
29. C22×#4326C22semidirect
34. C2×#66977C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
49. #10622825C22semidirect
51. C2×C22⋊(C11⋊C8)C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
55. C2×#66874C22semidirect
56. C2×#66871C22semidirect
59. #10622542C22semidirect
60. #10622541C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
156. #66896D4semidirect
495. C22×C11#452semidirect
758. C11#24426semidirect
894. C22#10622852semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
C2×#106228522
C2×#106228312
C22×#668962
#130720672
#130698522
#130697952
#130697102
#130696192
#130689502
#130689242
#130689092
#130688632
#130685562
C2×C11×#5462
#2442611