Finite Group Databasebeta

← C11×#22507 #14599700

Subgroups — C11×#22507 #14599700

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3475C211yesmaximal, characteristic
2D4×C11×M16C211yesmaximal, characteristic, complemented
3C11×#2293C211yesmaximal, characteristic, complemented
4C11×#1994C211yesmaximal, characteristic, complemented
5C11×#1986C211yesmaximal, characteristic, complemented
6C11×#1897C212yesmaximal, complemented
7C11×#1871C212yesmaximal, complemented
8C11×#1826C212yesmaximal, complemented
9C11×#1806C211yesmaximal, characteristic, complemented
10C4×C11×#104C211yesmaximal, characteristic, complemented
11C11×#1733C212yesmaximal, complemented
12C22×C11×M16C2212yes—
13C11×#556C411yescharacteristic, complemented
14C11×#555C411yescharacteristic, complemented
15C11×#554C411yescharacteristic, complemented
16C11×#553C412yescomplemented
17C11×#552—21no—
18C11×#552C412yescomplemented
19C11×#551—22no—
20C11×#547C411yescharacteristic, complemented
21C11×#546—21no—
22C11×#533C2211yescharacteristic
23C11×#529—22no—
24C11×#529—21no—
25C11×#525C2212yes—
26C4×C11×#41—21no—
27C4×C11×#41C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2212yes—
30C2×C11×#117C2212yes—
31C11×#436—21no—
32C11×#435—22no—
33C8×D4×C11—21no—
34C11×#423C2211yescharacteristic
35C2×C11×#104C2211yescharacteristic
36C2×C11×#104C2211yescharacteristic
37C2×C11×#104C2212yes—
38C11×#407C2212yes—
39C4×C11×M16C2211yescharacteristic
40C11×#390—21no—
41C11×#389—21no—
42C11×#388—22no—
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4C2212yes—
45C43×C11C2211yescharacteristic
46C11×#339C2212yes—
47C11×#339C2212yes—
48C11×#339C2212yes—
49C11×#339C2212yes—
50C11×#339C2211yescharacteristic
51C11×#339C2212yes—
52C11×#339C2211yescharacteristic
53C2×C11×#41—21no—
54C2×C11×#41C2311yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11C2312yes—
57C2×C11×M16—22no—
58C2×C11×M16—24no—
59C2×C11×M16—42no—
60C2×C11×M16C2311yescharacteristic
61C2×C11×M16C2312yes—
62C2×C11×M16C2311yescharacteristic
63C22×C8×C11—22no—
64C11×C4⋊Q8C2×C411yescharacteristic
65C11×C4⋊Q8C2×C411yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—22no—
69C11×#125—22no—
70C11×#125—21no—
71C11×#125C2×C412yes—
72C11×#124—21no—
73C11×#124—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8C2×C412yes—
83C11×C22⋊Q8C2×C412yes—
84C11×#121—22no—
85C11×#121—21no—
86C11×#121C2×C412yes—
87C11×#121C2×C412yes—
88C11×#120—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11C2×C411yescharacteristic
93C4×Q8×C11C2×C411yescharacteristic
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11C2×C411yescharacteristic
101C4×D4×C11C2×C411yescharacteristic
102C4×D4×C11C2×C411yescharacteristic
103C4×D4×C11C2×C412yes—
104C4×D4×C11C2×C411yescharacteristic
105C4×D4×C11D411yescharacteristic
106C4×D4×C11D411yescharacteristic
107C4×D4×C11D412yes—
108C11×#117—22no—
109C11×#117—22no—
110C11×#117—21no—
111C11×#117—22no—
112C11×#117—21no—
113C11×#117—24no—
114C11×#117—42no—
115C11×#117C2×C412yes—
116C11×#117C2×C412yes—
117C11×#117C2311yescharacteristic
118C11×#117C2312yes—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2×C412yes—
122C2×C11×C4⋊C4C2×C412yes—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4D412yes—
128C2×C42×C11—22no—
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11—21no—
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2312yes—
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C11×C4⋊C8—21no—
137C11×C4⋊C8—21no—
138C11×#104—22no—
139C11×#104—22no—
140C11×#104—42no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C11×#95—22no—
146C11×#95—21no—
147#22507C1111yesmaximal, characteristic, direct product factor, Sylow
148C24×C11C2×D412yes—
149C11×#41—21no—
150C11×#41—21no—
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—44no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—42no—
161C2×D4×C11C22⋊C411yescharacteristic
162C2×D4×C11C22⋊C411yescharacteristic
163C2×D4×C11C22⋊C412yes—
164C2×D4×C11C22×C411yescharacteristic
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C11×M16—21no—
186C11×M16—22no—
187C11×M16—21no—
188C11×M16—22no—
189C11×M16—21no—
190C11×M16—44no—
191C11×M16#4112yescomplemented
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—22no—
195C2×C8×C11—44no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—44no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4C22⋊C411yescharacteristic
209C11×C4⋊C4C22⋊C411yescharacteristic
210C11×C4⋊C4C22⋊C412yes—
211C11×C4⋊C4C22×C411yescharacteristic
212C11×C4⋊C4C22×C411yescharacteristic
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C22×C412yes—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—44no—
226C11×C22⋊C4—44no—
227C11×C22⋊C4C22⋊C412yes—
228C11×C22⋊C4C22⋊C412yes—
229C11×C22⋊C4C22⋊C412yes—
230C11×C22⋊C4C22⋊C412yes—
231C42×C11—22no—
232C42×C11—21no—
233C42×C11—22no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—22no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—22no—
240C42×C11—22no—
241C42×C11—21no—
242C42×C11—42no—
243C42×C11—42no—
244C42×C11C22×C411yescharacteristic
245C42×C11C22×C411yescharacteristic
246C42×C11C2×D411yescharacteristic
247C42×C11C2×D411yescharacteristic
248C42×C11#4112yescomplemented
249#3475C2×C1111yescharacteristic
250D4×M16C2×C1111yescharacteristic, complemented
251#2293C2×C1111yescharacteristic, complemented
252#1994C2×C1111yescharacteristic, complemented
253#1986C2×C1111yescharacteristic, complemented
254#1897C2×C1112yescomplemented
255#1871C2×C1112yescomplemented
256#1826C2×C1112yescomplemented
257#1806C2×C1111yescharacteristic, complemented
258C4×#104C2×C1111yescharacteristic, complemented
259#1733C2×C1112yescomplemented
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11C2×C22⋊C412yes—
266C23×C11C2×C22⋊C412yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—21no—
269Q8×C11—21no—
270Q8×C11—42no—
271Q8×C11—81no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—42no—
277D4×C11—44no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—82no—
281C2×C4×C11—22no—
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—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—44no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—81no—
312C2×C4×C11—82no—
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C2×C22⋊C411yescharacteristic
315C2×C4×C11C2×C22⋊C411yescharacteristic
316C2×C4×C11C2×C22⋊C411yescharacteristic
317C2×C4×C11C2×C22⋊C412yes—
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C23×C411yescharacteristic
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C112−1+411yescharacteristic
325C8×C11—22no—
326C8×C11—42no—
327C8×C11—41no—
328C22×M16C22×C1112yes—
329#556C4×C1111yescharacteristic, complemented
330#555C4×C1111yescharacteristic, complemented
331#554C4×C1111yescharacteristic, complemented
332#553C4×C1112yescomplemented
333#552—21no—
334#552C4×C1112yescomplemented
335#551—22no—
336#547C4×C1111yescharacteristic, complemented
337#546—21no—
338#533C22×C1111yescharacteristic
339#529—22no—
340#529—21no—
341#525C22×C1112yes—
342C4×#41—21no—
343C4×#41C22×C1111yescharacteristic
344C2×C4×D4C22×C1111yescharacteristic
345C2×#117C22×C1112yes—
346C2×#117C22×C1112yes—
347#436—21no—
348#435—22no—
349C8×D4—21no—
350#423C22×C1111yescharacteristic
351C2×#104C22×C1111yescharacteristic
352C2×#104C22×C1111yescharacteristic
353C2×#104C22×C1112yes—
354#407C22×C1112yes—
355C4×M16C22×C1111yescharacteristic
356#390—21no—
357#389—21no—
358#388—22no—
359C4×C4⋊C4C22×C1111yescharacteristic
360C4×C22⋊C4C22×C1112yes—
361C43C22×C1111yescharacteristic
362#339C22×C1112yes—
363#339C22×C1111yescharacteristic
364#339C22×C1112yes—
365#339C22×C1112yes—
366#339C22×C1112yes—
367#339C22×C1112yes—
368#339C22×C1111yescharacteristic
369C22×C11—21no—
370C22×C11—21no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—82no—
381C22×C11—82no—
382C22×C11C22×C22⋊C411yescharacteristic
383C22×C11#54611yescharacteristic
384C22×C11#54711yescharacteristic
385C4×C11—22no—
386C4×C11—22no—
387C4×C11—21no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—82no—
398C4×C11#42112yes—
399C4×C11C4×#4111yescharacteristic
400C4×C11#52011yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#54711yescharacteristic
403C2×#41—21no—
404C2×#41C23×C1111yescharacteristic
405C22×D4D4×C1111yescharacteristic
406C23×C4C23×C1112yes—
407C2×M16—22no—
408C2×M16—24no—
409C2×M16—42no—
410C2×M16C23×C1112yes—
411C2×M16C23×C1111yescharacteristic
412C2×M16C23×C1111yescharacteristic
413C22×C8—22no—
414C4⋊Q8C2×C4×C1111yescharacteristic
415C4⋊Q8C2×C4×C1111yescharacteristic
416#126—22no—
417#126—22no—
418#126—22no—
419#125—22no—
420#125—21no—
421#125C2×C4×C1112yes—
422#124—21no—
423#124—22no—
424#123—22no—
425#123—22no—
426#123—22no—
427#123—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—22no—
432C22⋊Q8C2×C4×C1112yes—
433C22⋊Q8C2×C4×C1112yes—
434#121—22no—
435#121—21no—
436#121C2×C4×C1112yes—
437#121C2×C4×C1112yes—
438#120—22no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8C2×C4×C1111yescharacteristic
443C4×Q8C2×C4×C1111yescharacteristic
444C4×D4—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4C2×C4×C1111yescharacteristic
451C4×D4C2×C4×C1111yescharacteristic
452C4×D4C2×C4×C1111yescharacteristic
453C4×D4C2×C4×C1112yes—
454C4×D4C2×C4×C1111yescharacteristic
455C4×D4D4×C1111yescharacteristic
456C4×D4D4×C1111yescharacteristic
457C4×D4D4×C1112yes—
458#117—22no—
459#117—22no—
460#117—21no—
461#117—22no—
462#117—21no—
463#117—24no—
464#117—42no—
465#117C2×C4×C1112yes—
466#117C2×C4×C1112yes—
467#117C23×C1111yescharacteristic
468#117C23×C1112yes—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4C2×C4×C1112yes—
472C2×C4⋊C4C2×C4×C1112yes—
473C2×C4⋊C4D4×C1111yescharacteristic
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4D4×C1112yes—
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C1112yes—
483C2×C42C23×C1111yescharacteristic
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486C4⋊C8—21no—
487C4⋊C8—21no—
488#104—22no—
489#104—22no—
490#104—42no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—21no—
494C4×C8—21no—
495#95—22no—
496#95—21no—
497C2×C11—21no—
498C2×C11—21no—
499C2×C11—42no—
500C2×C11—42no—
501C2×C11—81no—
502C2×C11#233911yescharacteristic
503C2×C11C2×#42111yescharacteristic
504C2×C11#290111yescharacteristic
505C24C2×D4×C1112yes—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—44no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×C4×C1111yescharacteristic
514C2×D4—22no—
515C2×D4—21no—
516C2×D4—22no—
517C2×D4—42no—
518C2×D4C11×C22⋊C411yescharacteristic
519C2×D4C11×C22⋊C411yescharacteristic
520C2×D4C11×C22⋊C412yes—
521C2×D4C22×C4×C1111yescharacteristic
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4C22×C4×C1112yes—
535C22×C4C22×C4×C1112yes—
536C22×C4C2×D4×C1112yes—
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C2×D4×C1112yes—
539C22×C4C2×D4×C1112yes—
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C24×C1111yescharacteristic
542M16—21no—
543M16—21no—
544M16—22no—
545M16—22no—
546M16—21no—
547M16—44no—
548M16C11×#4112yescomplemented
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—22no—
552C2×C8—44no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—44no—
564C4⋊C4—42no—
565C4⋊C4C11×C22⋊C411yescharacteristic
566C4⋊C4C11×C22⋊C411yescharacteristic
567C4⋊C4C11×C22⋊C412yes—
568C4⋊C4C22×C4×C1111yescharacteristic
569C4⋊C4C22×C4×C1111yescharacteristic
570C4⋊C4C22×C4×C1112yes—
571C4⋊C4C22×C4×C1112yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—21no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—22no—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4C11×C22⋊C412yes—
585C22⋊C4C11×C22⋊C412yes—
586C22⋊C4C11×C22⋊C412yes—
587C22⋊C4C11×C22⋊C412yes—
588C42—22no—
589C42—21no—
590C42—22no—
591C42—21no—
592C42—21no—
593C42—22no—
594C42—21no—
595C42—21no—
596C42—22no—
597C42—22no—
598C42—21no—
599C42—42no—
600C42—42no—
601C42C22×C4×C1111yescharacteristic
602C42C22×C4×C1111yescharacteristic
603C42C2×D4×C1111yescharacteristic
604C42C2×D4×C1111yescharacteristic
605C42C11×#4112yescomplemented
606C11#2250711yescharacteristic, direct product factor, Sylow
607C23—22no—
608C23—22no—
609C23—21no—
610C23—42no—
611C23—42no—
612C23C2×C11×C22⋊C412yes—
613C23C2×C11×C22⋊C412yes—
614C23C22×D4×C1111yescharacteristic
615Q8—21no—
616Q8—21no—
617Q8—42no—
618Q8—81no—
619D4—21no—
620D4—21no—
621D4—22no—
622D4—22no—
623D4—42no—
624D4—44no—
625D4—41no—
626D4—41no—
627D4—82no—
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—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—44no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—81no—
659C2×C4—82no—
660C2×C4C2×C11×C22⋊C412yes—
661C2×C4C2×C11×C22⋊C411yescharacteristic
662C2×C4C2×C11×C22⋊C411yescharacteristic
663C2×C4C2×C11×C22⋊C411yescharacteristic
664C2×C4C2×C11×C22⋊C412yes—
665C2×C4C2×C11×C22⋊C411yescharacteristic
666C2×C4C23×C4×C1111yescharacteristic
667C2×C4C22×D4×C1111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C2×C11×#4111yescharacteristic
670C2×C4C11×H(5,𝔽2)11yescharacteristic
671C2×C4C11×2−1+411yescharacteristic
672C8—22no—
673C8—42no—
674C8—41no—
675C22—21no—
676C22—21no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—82no—
687C22—82no—
688C22C22×C11×C22⋊C411yescharacteristic
689C22C11×#54611yescharacteristic
690C22C11×#54711yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—41no—
699C4—42no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—82no—
704C4C11×#42112yes—
705C4C4×C11×#4111yescharacteristic
706C4C11×#52011yescharacteristic
707C4C11×#54611yescharacteristic
708C4C11×#54711yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—42no—
713C2—81no—
714C2C11×#233911yescharacteristic
715C2C2×C11×#42111yescharacteristic
716C2C11×#290111yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C22×C22⋊C4
prime radicalC11×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C11×M16C2semidirect
3. C11×#2293C2semidirect
4. C11×#1994C2semidirect
5. C11×#1986C2semidirect
6. C11×#1897C2semidirect
7. C11×#1871C2semidirect
8. C11×#1826C2semidirect
9. C11×#1806C2semidirect
10. C4×C11×#104C2semidirect
11. C11×#1733C2semidirect
13. C11×#556C4semidirect
14. C11×#555C4semidirect
15. C11×#554C4semidirect
16. C11×#553C4semidirect
18. C11×#552C4semidirect
20. C11×#547C4semidirect
147. #22507C11direct (N × H)
191. C11×M16#41semidirect
248. C42×C11#41semidirect
250. D4×M16C2×C11semidirect
251. #2293C2×C11semidirect
252. #1994C2×C11semidirect
253. #1986C2×C11semidirect
254. #1897C2×C11semidirect
255. #1871C2×C11semidirect
256. #1826C2×C11semidirect
257. #1806C2×C11semidirect
258. C4×#104C2×C11semidirect
259. #1733C2×C11semidirect
329. #556C4×C11semidirect
330. #555C4×C11semidirect
331. #554C4×C11semidirect
332. #553C4×C11semidirect
334. #552C4×C11semidirect
336. #547C4×C11semidirect
548. M16C11×#41semidirect
605. C42C11×#41semidirect
606. C11#22507direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34752
D4×C11×M162
C11×#22932
C11×#19942
C11×#19862
C11×#18972
C11×#18712
C11×#18262
C11×#18062
C4×C11×#1042
C11×#17332
#2250711