Finite Group Databasebeta

← #14770151

Subgroups — #14770151

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic
2#13071545C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4#13069569C211yesmaximal, characteristic, complemented
5#13069050C211yesmaximal, characteristic, complemented
6#13069040C211yesmaximal, characteristic, complemented
7#13068929C211yesmaximal, characteristic, complemented
8#13068924C211yesmaximal, characteristic, complemented
9#13068706C211yesmaximal, characteristic, complemented
10#13068702C211yesmaximal, characteristic, complemented
11#13068631C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068335C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C2×C11×#554C211yesmaximal, characteristic
16C11×#554—24no—
17C11×#554C418yescomplemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#125—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622833—21no—
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622624—24no—
43#10622594—21no—
44#10622564—21no—
45C22⋊C4×Dic11—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11—21no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2×C414yescomplemented
72C11×#125—28no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8C2×C414yes—
78C11×C22⋊Q8C2×C414yescomplemented
79C4×Q8×C11—22no—
80C4×Q8×C11C2×C414yescomplemented
81C4×D4×C11—28no—
82C4×D4×C11C2×C414yes—
83C4×D4×C11D414yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2×C414yes—
93C2×C11×C4⋊C4C2×C414yescomplemented
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#66979—22no—
108#66979—41no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318—41no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—41no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66899—22no—
129#66899—22no—
130#66899—41no—
131#66899—41no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—22no—
140#66867—22no—
141#22497—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—81no—
151C2×Q8×C11—81no—
152C2×Q8×C11C22×C412yes—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11C22⋊C414yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2411yescharacteristic
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—42no—
188C22×Dic11—42no—
189C22×Dic11—81no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C22⋊C414yes—
200C11×C4⋊C4C22×C412yes—
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×C11C22×C412yes—
209C42×C11C2×D412yes—
210C22⋊Dic11—42no—
211C22⋊Dic11—42no—
212C22⋊Dic11—81no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—42no—
221C4⋊Dic11#4112yes—
222C4×Dic11—42no—
223C4×Dic11—81no—
224#4318—44no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
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—44no—
237C2×C11⋊C8#4112yes—
238C2×#554D1111yescharacteristic
239C2×#435—111no—
240#2352—111no—
241#1993—111no—
242#1988—111no—
243#1894—111no—
244#1892—111no—
245#1873—111no—
246#1872—111no—
247#1824—111no—
248#1823—111no—
249#1805—111no—
250#1763—111no—
251#1736—111no—
252C2×#340—111no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C2×C22⋊C412yes—
264C23×C11C2×C22⋊C412yes—
265C23×C11#13712yes—
266C23×C11#13712yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—84no—
273D4×C11—28no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
305C2×C4×C11C2×C22⋊C412yes—
306C2×C4×C11C2×C22⋊C412yes—
307C2×C4×C11C2×C22⋊C412yes—
308C2×C4×C11C23×C411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×C4×C112−1+411yescharacteristic
314C2×Dic11—22no—
315C2×Dic11—41no—
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—84no—
327C11⋊C8—22no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C22×M16—111no—
332C23×C8—111no—
333#554—24no—
334#554Dic1118yescomplemented
335C2×C4⋊Q8C2×D1111yescharacteristic
336C2×#125—21no—
337C2×C22⋊Q8—21no—
338C2×C22⋊Q8—21no—
339C2×C22⋊Q8C2×D1111yescharacteristic
340C2×C22⋊Q8C2×D1111yescharacteristic
341C2×C4×Q8C2×D1111yescharacteristic
342C2×C4×D4—21no—
343C2×C4×D4C2×D1111yescharacteristic
344C2×#117—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348#435—224no—
349C2×C4⋊C8—111no—
350C2×#103—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×C22⋊C8—111no—
355C2×C22⋊C8—111no—
356C2×#97—111no—
357#388—221no—
358#387—221no—
359#386—221no—
360#382—111no—
361#380—111no—
362#380—111no—
363C4×C4⋊C4—111no—
364C4×C22⋊C4—221no—
365#340—111no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11#41914yes—
391C22×C11C22×C22⋊C411yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11C2×#13711yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57611yescharacteristic
397C22×C11#57711yescharacteristic
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11C4×#4111yescharacteristic
407C4×C11#52011yescharacteristic
408C4×C11#54611yescharacteristic
409C4×C11#54711yescharacteristic
410Dic11—42no—
411Dic11—81no—
412Dic11—81no—
413Dic11—81no—
414C22×Q8—21no—
415C22×Q8C22×D1111yescharacteristic
416C22×D4C22⋊D1111yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—221no—
420C23×C4C22×D1111yescharacteristic
421C23×C4C22×D1111yescharacteristic
422C2×M16—222no—
423C2×M16—222no—
424C2×M16—441no—
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8—222no—
430C22×C8—222no—
431C22×C8—441no—
432C4⋊Q8—22no—
433C4⋊Q8C2×Dic1114yescomplemented
434#125—28no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439C22⋊Q8C2×Dic1114yes—
440C22⋊Q8C2×Dic1114yescomplemented
441C4×Q8—22no—
442C4×Q8C2×Dic1114yescomplemented
443C4×D4—28no—
444C4×D4C2×Dic1114yes—
445C4×D4C22⋊D1114yes—
446#117—222no—
447#117—441no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—441no—
463C2×C4⋊C4C2×Dic1114yes—
464C2×C4⋊C4C2×Dic1114yescomplemented
465C2×C4⋊C4C22⋊D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4C22⋊D1111yescharacteristic
475C2×C22⋊C4C22⋊D1111yescharacteristic
476C2×C42—21no—
477C2×C42—221no—
478C2×C42—221no—
479C2×C42C22×D1111yescharacteristic
480C4⋊C8—222no—
481#103—222no—
482#103—222no—
483#103—441no—
484#103—441no—
485C22⋊C8—222no—
486C22⋊C8—222no—
487#97—222no—
488#95—221no—
489#95—221no—
490#95—221no—
491#95—221no—
492#95—221no—
493C2×C11—24no—
494C2×C11—42no—
495C2×C11#233911yescharacteristic
496C2×C11C2×#41911yescharacteristic
497C2×C11#289711yescharacteristic
498C2×C11#331411yescharacteristic
499C2×C11#331611yescharacteristic
500C2×C11#334411yescharacteristic
501C2×C11#334611yescharacteristic
502C24C2×C22⋊D1111yescharacteristic
503C24C2×C22⋊D1111yescharacteristic
504C2×Q8—24no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—81no—
511C2×Q8—81no—
512C2×Q8C22×Dic1112yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4C22⋊Dic1114yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—442no—
539C22×C4—442no—
540C22×C4—881no—
541C22×C4C22×Dic1112yes—
542C22×C4C22×Dic1112yes—
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1112yes—
548C22×C4C2×C22⋊D1112yes—
549C22×C4C23×D1111yescharacteristic
550M16—444no—
551C2×C8—112no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
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—444no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—112no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—442no—
582C4⋊C4C22⋊Dic1114yes—
583C4⋊C4C22×Dic1112yes—
584C4⋊C4C22×Dic1112yes—
585C4⋊C4C22×Dic1112yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—442no—
589C22⋊C4—442no—
590C22⋊C4—881no—
591C22⋊C4C22⋊Dic1114yes—
592C22⋊C4C22⋊Dic1114yes—
593C42—24no—
594C42—442no—
595C42—881no—
596C42C22×Dic1112yes—
597C42C2×C22⋊D1112yes—
598C11#2249711yescharacteristic, complemented, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23#6699512yes—
610C23#6699512yes—
611C23C2×C22⋊Dic1112yes—
612C23C2×C22⋊Dic1112yes—
613C23C22×C22⋊D1111yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—222no—
651C2×C4—441no—
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—884no—
663C2×C4C2×C22⋊Dic1112yes—
664C2×C4C2×C22⋊Dic1112yes—
665C2×C4C2×C22⋊Dic1112yes—
666C2×C4C2×C22⋊Dic1112yes—
667C2×C4#41×D1111yescharacteristic
668C2×C4#41×D1111yescharacteristic
669C2×C4#6704211yescharacteristic
670C2×C4#6704311yescharacteristic
671C2×C4C23×Dic1111yescharacteristic
672C2×C4C22×C22⋊D1111yescharacteristic
673C8—222no—
674C8—441no—
675C8—441no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1062283814yes—
691C22C2×#6699511yescharacteristic
692C22C2×#6699511yescharacteristic
693C22#1062335511yescharacteristic
694C22#1062336011yescharacteristic
695C22#1062336611yescharacteristic
696C22#1062336711yescharacteristic
697C22C22×C22⋊Dic1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—442no—
707C4—881no—
708C4—881no—
709C4—881no—
710C4#1062335511yescharacteristic
711C4#41×Dic1111yescharacteristic
712C4#1062335811yescharacteristic
713C4#1062336011yescharacteristic
714C2—24no—
715C2—42no—
716C2#1307144611yescharacteristic
717C2C2×#1062283811yescharacteristic
718C2#1307714211yescharacteristic
719C2#1308069111yescharacteristic
720C2#1308072111yescharacteristic
721C2#1308106511yescharacteristic
722C2#1308109511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#554D11
hypocenterC11#22497
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. #13069569C2semidirect
5. #13069050C2semidirect
6. #13069040C2semidirect
7. #13068929C2semidirect
8. #13068924C2semidirect
9. #13068706C2semidirect
10. #13068702C2semidirect
11. #13068631C2semidirect
12. #13068446C2semidirect
13. #13068335C2semidirect
14. C2×#10622167C2semidirect
17. C11×#554C4semidirect
71. C11×C4⋊Q8C2×C4semidirect
78. C11×C22⋊Q8C2×C4semidirect
80. C4×Q8×C11C2×C4semidirect
93. C2×C11×C4⋊C4C2×C4semidirect
334. #554Dic11semidirect
433. C4⋊Q8C2×Dic11semidirect
440. C22⋊Q8C2×Dic11semidirect
442. C4×Q8C2×Dic11semidirect
464. C2×C4⋊C4C2×Dic11semidirect
598. C11#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
#130715452
#130695902
#130695692
#130690502
#130690402
#130689292
#130689242
#130687062
#130687022
#130686312
#130684462
#130683352
C2×#106221672
C2×C11×#5542
#2249711