Finite Group Databasebeta

← #14765099

Subgroups — #14765099

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622851C211yesmaximal, characteristic
2#13071309C211yesmaximal, characteristic, complemented
3#13069500C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic, complemented
5#13069316C211yesmaximal, characteristic, complemented
6#13069295C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068933C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#2311C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#386—21no—
28C11×#386—21no—
29C11×#380—21no—
30C11×#380—21no—
31#10622851C418yescomplemented
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622603—21no—
42#10622602—21no—
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622570—21no—
48#10622569—21no—
49#10622552C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yescomplemented
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C11×#117—41no—
76C11×#117—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×#4325—41no—
94C2×#4325—41no—
95C2×#4325C2×C414yescomplemented
96C2×#4323—41no—
97C2×#4323—41no—
98C2×#4323C2×C414yescomplemented
99#66983—22no—
100#66983C2×C414yes—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C4×D44—41no—
115C4×D44—41no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#66899—41no—
121#66899—41no—
122#66899C2×C414yescomplemented
123#66896—41no—
124#66896—41no—
125#66896C2×C414yescomplemented
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)C2×C414yescomplemented
131#66873—41no—
132#66873—41no—
133#66871—41no—
134#66871—41no—
135#66867—41no—
136C4×C11⋊C8—41no—
137#22055—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11C22×C412yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—81no—
183C2×C22⋊D11—81no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44C22×C412yes—
193C2×C4×D11—42no—
194C2×C4×D11—81no—
195C2×C4×D11—81no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—42no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C22⋊Dic11—81no—
214#4325—44no—
215#4323—44no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—81no—
219(C2×D11)⋊C4—81no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11C22×C412yes—
226Dic11⋊C4—81no—
227C4×Dic11—81no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C22×C412yes—
239C2×C11⋊C8C22×C412yes—
240C2×#449—111no—
241#2324—111no—
242#2311D1111yescharacteristic, complemented
243#1973—111no—
244#1970—111no—
245#1936—111no—
246#1933—111no—
247#1928—111no—
248#1925—111no—
249#1879—111no—
250#1877—111no—
251#1874—111no—
252#1852—111no—
253#1788—111no—
254#1750—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C4×D412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—48no—
284D4×C11—41no—
285D4×C11—41no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—48no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—84no—
315C2×C4×C11C4×D412yes—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—84no—
323C2×Dic11—22no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332D44—22no—
333D44—22no—
334D44—41no—
335D44—41no—
336C4×D11—84no—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×#41C2×D1111yescharacteristic
342C22×SD16—111no—
343C22×D8—111no—
344C2×#121—111no—
345C2×C4×D4—111no—
346C2×#117C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348#449—118no—
349C2×#107—111no—
350C2×#107—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×#97—111no—
362C2×C4×C8—111no—
363#391C2×D1111yescharacteristic
364#391C2×D1111yescharacteristic
365#390—111no—
366#390—221no—
367#390C2×D1111yescharacteristic
368#390C2×D1111yescharacteristic
369#389—111no—
370#388—221no—
371#386—21no—
372#386—21no—
373#386—221no—
374#385—221no—
375#380—21no—
376#380—21no—
377#380—111no—
378C4×C4⋊C4—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#336—111no—
384#336—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11C2×C4×D411yescharacteristic
400C22×C11#53411yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#57611yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57811yescharacteristic
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C4×C11—22no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11#51811yescharacteristic
422C4×C11#51811yescharacteristic
423C4×C11#53811yescharacteristic
424C4×C11#53811yescharacteristic
425Dic11—42no—
426Dic11—81no—
427Dic11—81no—
428C2×#41—22no—
429C2×#41—41no—
430C2×#41—41no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C4×D1114yescomplemented
434C22×Q8C22×D1111yescharacteristic
435C22×D4—21no—
436C22×D4—111no—
437C22×D4—221no—
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—221no—
442C23×C4C22×D1111yescharacteristic
443C2×SD16—114no—
444C2×SD16—441no—
445C2×SD16—441no—
446C2×D8—114no—
447C2×D8—441no—
448C2×D8—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453#121—114no—
454#121—222no—
455C4×D4—441no—
456C4×D4—441no—
457#117—41no—
458#117—41no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4C22⋊D1111yescharacteristic
467C2×C4⋊C4C22⋊D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C22⋊C4C22⋊D1111yescharacteristic
481C2×C42—221no—
482C2×C42C22×D1111yescharacteristic
483C2×C42C22×D1111yescharacteristic
484#107—441no—
485#107—441no—
486#103—114no—
487#103—441no—
488#103—441no—
489#102—114no—
490#102—441no—
491#102—441no—
492#102—441no—
493#102—441no—
494C22⋊C8—114no—
495C22⋊C8—222no—
496#97—441no—
497C4×C8—441no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—221no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11—82no—
507C2×C11#232111yescharacteristic
508C2×C11#294611yescharacteristic
509C2×C11#295111yescharacteristic
510C2×C11#319811yescharacteristic
511C2×C11#320311yescharacteristic
512C2×C11#322011yescharacteristic
513C2×C11#322511yescharacteristic
514D11—82no—
515C24—21no—
516C24—221no—
517C24C2×C22⋊D1111yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C2×C4×D1112yes—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—112no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—881no—
544C2×D4—881no—
545C2×D4C2×C4×D1112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—442no—
563C22×C4—881no—
564C22×C4—881no—
565C22×C4C2×C4×D1112yes—
566C22×C4#433912yes—
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573SD16—444no—
574D8—444no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—42no—
594C4⋊C4—112no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—881no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—224no—
608C22⋊C4—442no—
609C22⋊C4—881no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—881no—
617C11#2205511yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—222no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23C4×C22⋊D1112yes—
639C23C22×C22⋊D1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—48no—
647D4—41no—
648D4—41no—
649D4—222no—
650D4—222no—
651D4—441no—
652D4—441no—
653D4—884no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—222no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—884no—
693C2×C4C4×C22⋊D1112yes—
694C2×C4C22×C4×D1111yescharacteristic
695C2×C4C2×#433911yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#6703711yescharacteristic
698C2×C4#6703711yescharacteristic
699C2×C4#6703711yescharacteristic
700C8—222no—
701C8—222no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—881no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22C2×C4×C22⋊D1111yescharacteristic
726C22#1062333511yescharacteristic
727C22#1062333611yescharacteristic
728C22#1062336611yescharacteristic
729C22#1062336611yescharacteristic
730C22#1062336811yescharacteristic
731C22#1062336911yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—442no—
741C4—881no—
742C4—881no—
743C4#1062301711yescharacteristic
744C4#1062301711yescharacteristic
745C4#1062302511yescharacteristic
746C4#1062302511yescharacteristic
747C2—42no—
748C2—82no—
749C2—882no—
750C2#1307127411yescharacteristic
751C2#1307744411yescharacteristic
752C2#1307748911yescharacteristic
753C2#1307946211yescharacteristic
754C2#1307951311yescharacteristic
755C2#1307966611yescharacteristic
756C2#1307972511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
cosocleC22×C4×C11C24
hypercenter#2311D11
hypocenterC11#22055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13071309C2semidirect
3. #13069500C2semidirect
4. #13069481C2semidirect
5. #13069316C2semidirect
6. #13069295C2semidirect
7. #13069254C2semidirect
8. #13069233C2semidirect
9. #13068967C2semidirect
10. #13068953C2semidirect
11. #13068933C2semidirect
12. #13068804C2semidirect
13. #13068556C2semidirect
14. #13068382C2semidirect
15. C11×#2311C2semidirect
31. #10622851C4semidirect
65. C2×C11×#41C2×C4semidirect
95. C2×#4325C2×C4semidirect
98. C2×#4323C2×C4semidirect
122. #66899C2×C4semidirect
125. #66896C2×C4semidirect
130. C22⋊(C11⋊C8)C2×C4semidirect
242. #2311D11semidirect
433. C2×#41C4×D11semidirect
617. C11#22055semidirect

Maximal subgroups

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

subgroupindex
C2×#106228512
#130713092
#130695002
#130694812
#130693162
#130692952
#130692542
#130692332
#130689672
#130689532
#130689332
#130688042
#130685562
#130683822
C11×#23112
#2205511