Finite Group Databasebeta

← #14753883

Subgroups — #14753883

Order 2816.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic, complemented
2#13071225C211yesmaximal, characteristic, complemented
3#13068706C211yesmaximal, characteristic, complemented
4#13068702C211yesmaximal, characteristic, complemented
5#13068631C211yesmaximal, characteristic, complemented
6#13068626C211yesmaximal, characteristic, complemented
7#13068621C211yesmaximal, characteristic, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068556C211yesmaximal, characteristic
10#13068556C211yesmaximal, characteristic
11#13068446C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13C4×#66899C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C2×C11×#520C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C11×#520—24no—
18C11×#520C418yescomplemented
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4—21no—
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622613—24no—
42#10622594—21no—
43#10622594—21no—
44#10622564—21no—
45#10622564—21no—
46#10622549C2211yescharacteristic
47#10622548C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41C2×C414yes—
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11C2×C414yes—
79C4×Q8×C11C2×C414yes—
80C4×D4×C11—28no—
81C4×D4×C11—28no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11C2×C414yes—
85C4×D4×C11C2×C414yes—
86C11×#117—28no—
87C11×#117C2×C414yes—
88C11×#117D414yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—28no—
94C2×C11×C4⋊C4C2×C414yes—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121#66899—22no—
122#66899—22no—
123#66899—22no—
124#66899—22no—
125#66896—22no—
126#66896—22no—
127#66896—22no—
128#66896—22no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C22⋊(C11⋊C8)—22no—
136C22⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138C4⋊(C11⋊C8)—22no—
139#66867—22no—
140C4×C11⋊C8—22no—
141#20746—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C11×#41—28no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—28no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C2×Q8×C11#4112yes—
153C2×Q8×C11#4112yes—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C22×C412yes—
161C2×D4×C11#4112yes—
162C2×D4×C11#4112yes—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C22⋊C414yes—
200C11×C4⋊C4C22⋊C414yes—
201C11×C4⋊C4C22×C412yes—
202C11×C4⋊C4C22×C412yes—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4C22⋊C414yes—
206C11×C22⋊C4C22⋊C414yes—
207C42×C11—24no—
208C42×C11—24no—
209C42×C11C22×C412yes—
210C42×C11C22×C412yes—
211C42×C11C2×D412yes—
212C42×C11C2×D412yes—
213C22⋊Dic11—81no—
214C22⋊Dic11—81no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—81no—
224C4⋊Dic11—81no—
225C4×Dic11—81no—
226C4×Dic11—81no—
227C2×C11⋊C8—21no—
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⋊C8—21no—
239C2×#520D1111yescharacteristic
240C2×#433—111no—
241#2314—111no—
242#1824—111no—
243#1823—111no—
244#1805—111no—
245#1804—111no—
246#1803—111no—
247#1802—111no—
248#1788—111no—
249#1788—111no—
250#1763—111no—
251#1762—111no—
252C4×#103—111no—
253C4×#102—111no—
254C23×C11—22no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11C2×C22⋊C412yes—
268C23×C11C22×D411yescharacteristic
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—22no—
272Q8×C11#11714yes—
273D4×C11—216no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—22no—
277D4×C11#11714yes—
278C2×C4×C11—216no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—84no—
303C2×C4×C11—84no—
304C2×C4×C11—84no—
305C2×C4×C11C2×C22⋊C412yes—
306C2×C4×C11C2×C22⋊C412yes—
307C2×C4×C11C2×C22⋊C412yes—
308C2×C4×C11C2×C22⋊C412yes—
309C2×C4×C11C2×C22⋊C412yes—
310C2×C4×C11C23×C411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C11⋊C8—41no—
332C22×#41C2×D1111yescharacteristic
333#520—24no—
334#520Dic1118yescomplemented
335C2×C4×Q8C2×D1111yescharacteristic
336C2×C4×Q8C2×D1111yescharacteristic
337C2×C4×D4—21no—
338C2×C4×D4—21no—
339C2×C4×D4C2×D1111yescharacteristic
340C2×C4×D4C2×D1111yescharacteristic
341C2×#117—21no—
342C2×#117C2×D1111yescharacteristic
343C22×C4⋊C4—21no—
344C22×C4⋊C4C2×D1111yescharacteristic
345#433—224no—
346C2×C4⋊C8—111no—
347C2×C4⋊C8—111no—
348C2×#103—111no—
349C2×#103—111no—
350C2×#103—111no—
351C2×#103—111no—
352C2×#102—111no—
353C2×#102—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×#97—111no—
359C2×C4×C8—111no—
360#388—221no—
361#388—221no—
362#387—221no—
363#387—221no—
364#384—111no—
365#382—111no—
366#380—111no—
367#380—111no—
368C4×C4⋊C4—111no—
369C4×C4⋊C4—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—24no—
382C22×C11—41no—
383C22×C11—42no—
384C22×C11—41no—
385C22×C11—42no—
386C22×C11—41no—
387C22×C11—42no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11C22×C22⋊C411yescharacteristic
393C22×C11#52511yescharacteristic
394C22×C11#52511yescharacteristic
395C22×C11#57611yescharacteristic
396C22×C11#57711yescharacteristic
397C22×C11#57711yescharacteristic
398C22×C11#57811yescharacteristic
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—22no—
404C4×C11—24no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11C2×#11711yescharacteristic
408C4×C11C2×#11711yescharacteristic
409C4×C11#52511yescharacteristic
410C4×C11#52511yescharacteristic
411Dic11—81no—
412Dic11—81no—
413Dic11—81no—
414Dic11—81no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41C2×Dic1114yes—
421C22×Q8C22×D1111yescharacteristic
422C22×D4—21no—
423C22×D4C22×D1111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4C22×D1111yescharacteristic
429C22×C8—111no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8C2×Dic1114yes—
436C4×Q8C2×Dic1114yes—
437C4×D4—28no—
438C4×D4—28no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4C2×Dic1114yes—
442C4×D4C2×Dic1114yes—
443#117—28no—
444#117C2×Dic1114yes—
445#117C22⋊D1114yes—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—28no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—221no—
456C2×C4⋊C4—221no—
457C2×C4⋊C4C2×Dic1114yes—
458C2×C4⋊C4C22⋊D1111yescharacteristic
459C2×C4⋊C4C22⋊D1111yescharacteristic
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—221no—
465C2×C22⋊C4—221no—
466C2×C22⋊C4C22⋊D1111yescharacteristic
467C2×C22⋊C4C22⋊D1111yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—221no—
471C2×C42—221no—
472C2×C42C22×D1111yescharacteristic
473C2×C42C22×D1111yescharacteristic
474C4⋊C8—222no—
475C4⋊C8—222no—
476#103—222no—
477#103—222no—
478#103—222no—
479#103—222no—
480#102—222no—
481#102—222no—
482#102—222no—
483#102—222no—
484C22⋊C8—222no—
485C22⋊C8—222no—
486#97—222no—
487C4×C8—222no—
488#95—221no—
489#95—221no—
490#95—221no—
491#95—221no—
492#95—221no—
493#95—221no—
494C2×C11—42no—
495C2×C11—44no—
496C2×C11#228011yescharacteristic
497C2×C11#289711yescharacteristic
498C2×C11#289811yescharacteristic
499C2×C11#311911yescharacteristic
500C2×C11#312011yescharacteristic
501C2×C11#312411yescharacteristic
502C2×C11#312511yescharacteristic
503C24—21no—
504C24C2×C22⋊D1111yescharacteristic
505#41—28no—
506#41—28no—
507#41—28no—
508#41—28no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8#433912yes—
513C2×Q8#433912yes—
514C2×Q8C22×Dic1112yes—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4#433912yes—
522C2×D4#433912yes—
523C2×D4C22×Dic1112yes—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4—221no—
547C22×C4C22×Dic1112yes—
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C2×C22⋊D1111yescharacteristic
552C22×C4C2×C22⋊D1111yescharacteristic
553C22×C4C2×C22⋊D1112yes—
554C22×C4C23×D1111yescharacteristic
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—881no—
581C4⋊C4—881no—
582C4⋊C4C22⋊Dic1114yes—
583C4⋊C4C22⋊Dic1114yes—
584C4⋊C4C22×Dic1112yes—
585C4⋊C4C22×Dic1112yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—881no—
589C22⋊C4—881no—
590C22⋊C4C22⋊Dic1114yes—
591C22⋊C4C22⋊Dic1114yes—
592C42—24no—
593C42—24no—
594C42—881no—
595C42—881no—
596C42C22×Dic1112yes—
597C42C22×Dic1112yes—
598C42C2×C22⋊D1112yes—
599C42C2×C22⋊D1112yes—
600C11#2074611yescharacteristic, complemented, Sylow
601C23—21no—
602C23—21no—
603C23—22no—
604C23—22no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C2×C22⋊Dic1112yes—
615C23C22×C22⋊D1111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#6697914yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#6697914yes—
625C2×C4—216no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4C2×C22⋊Dic1112yes—
665C2×C4C2×C22⋊Dic1112yes—
666C2×C4C2×C22⋊Dic1112yes—
667C2×C4C2×C22⋊Dic1112yes—
668C2×C4C2×C22⋊Dic1112yes—
669C2×C4C2×#433911yescharacteristic
670C2×C4C2×#433911yescharacteristic
671C2×C4C2×#433911yescharacteristic
672C2×C4C2×#433911yescharacteristic
673C2×C4C23×Dic1111yescharacteristic
674C2×C4C22×C22⋊D1111yescharacteristic
675C8—441no—
676C8—441no—
677C8—441no—
678C8—441no—
679C22—22no—
680C22—22no—
681C22—24no—
682C22—22no—
683C22—41no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22#1062332211yescharacteristic
694C22#1062332211yescharacteristic
695C22#1062336611yescharacteristic
696C22#1062336711yescharacteristic
697C22#1062336811yescharacteristic
698C22#1062336911yescharacteristic
699C22C22×C22⋊Dic1111yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—24no—
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—881no—
709C4—881no—
710C4—881no—
711C4—881no—
712C4C2×#6697911yescharacteristic
713C4C2×#6697911yescharacteristic
714C4#1062332211yescharacteristic
715C4#1062332211yescharacteristic
716C2—42no—
717C2—44no—
718C2#1307099911yescharacteristic
719C2#1307714211yescharacteristic
720C2#1307714911yescharacteristic
721C2#1307881511yescharacteristic
722C2#1307883011yescharacteristic
723C2#1307887811yescharacteristic
724C2#1307889311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20746
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#10622613C2semidirect
2. #13071225C2semidirect
3. #13068706C2semidirect
4. #13068702C2semidirect
5. #13068631C2semidirect
6. #13068626C2semidirect
7. #13068621C2semidirect
8. #13068616C2semidirect
11. #13068446C2semidirect
12. #13068441C2semidirect
13. C4×#66899C2semidirect
14. C4×#66896C2semidirect
18. C11×#520C4semidirect
334. #520Dic11semidirect
600. C11#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712252
#130687062
#130687022
#130686312
#130686262
#130686212
#130686162
#130685562
#130684462
#130684412
C4×#668992
C4×#668962
C2×C11×#5202
#2074611