Finite Group Databasebeta

← C11×#18910 #14596103

Subgroups — C11×#18910 #14596103

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3247C211yesmaximal, characteristic, complemented
3C11×#3207C211yesmaximal, characteristic, complemented
4C11×#3106C211yesmaximal, characteristic, complemented
5C11×#1636C211yesmaximal, characteristic, complemented
6C11×#1635C211yesmaximal, characteristic, complemented
7C11×#1631C211yesmaximal, characteristic, complemented
8C11×#1631C211yesmaximal, characteristic, complemented
9C11×#1626C211yesmaximal, characteristic, complemented
10C11×#1625C211yesmaximal, characteristic, complemented
11C11×#1621C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic, complemented
13C11×#1540C211yesmaximal, characteristic, complemented
14C11×#1482C211yesmaximal, characteristic, complemented
15C11×#1477C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic
17C11×#553—22no—
18C11×#553—21no—
19C11×#550—21no—
20C11×#550—21no—
21C11×#550C2211yescharacteristic
22C11×#550C2211yescharacteristic
23C11×#547—21no—
24C11×#547C2211yescharacteristic
25C11×#540—22no—
26C11×#540—21no—
27C11×#532—21no—
28C11×#532C2211yescharacteristic
29C11×#532C2211yescharacteristic
30C11×#529—21no—
31C11×#529C2211yescharacteristic
32C11×#520—21no—
33C4×C11×#41C2211yescharacteristic
34C11×#493C2211yescharacteristic
35C11×#492C2211yescharacteristic
36C11×#487C2211yescharacteristic
37C11×#486C2211yescharacteristic
38C11×#482—21no—
39C11×#478—21no—
40C11×#477C2211yescharacteristic
41C11×#477C2211yescharacteristic
42C11×#476C2211yescharacteristic
43C11×#476C2211yescharacteristic
44C11×#466—21no—
45C11×#465—21no—
46C11×#463—21no—
47C11×#463—22no—
48C11×#460C2211yescharacteristic
49C11×#460C2211yescharacteristic
50C11×#459C2211yescharacteristic
51C11×#459C2211yescharacteristic
52C11×#449—21no—
53C11×#449—22no—
54C4×C11×SD16—21no—
55C4×C11×D8—21no—
56C11×#431C2211yescharacteristic
57C11×#431C2211yescharacteristic
58C2×C11×C4⋊C8C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×#331C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×Q8⋊C8C2211yescharacteristic
67C11×D4⋊C8C2211yescharacteristic
68C11×D4⋊C8C2211yescharacteristic
69C11×D4⋊C8C2211yescharacteristic
70C11×D4⋊C8C2211yescharacteristic
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41D411yescharacteristic
77C2×C11×SD16—21no—
78C2×C11×SD16—21no—
79C2×C11×SD16—22no—
80C2×C11×D8—21no—
81C2×C11×D8—22no—
82C2×C11×D8—21no—
83C22×C8×C11—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×#127—22no—
88C11×#127—21no—
89C11×#127—21no—
90C11×#127C2311yescharacteristic
91C11×#127C2311yescharacteristic
92C11×#126—22no—
93C11×#126—21no—
94C11×#125—22no—
95C11×#125—21no—
96C11×#125D411yescharacteristic
97C11×#124—21no—
98C11×#124—21no—
99C11×#124D411yescharacteristic
100C11×#123—22no—
101C11×#123—22no—
102C11×#123—22no—
103C11×#123—21no—
104C11×#123—22no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8D411yescharacteristic
107C11×#121—22no—
108C11×#121—22no—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—22no—
112C11×#121—21no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121D411yescharacteristic
121C11×#121D412yes—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11D411yescharacteristic
125C4×Q8×C11C2311yescharacteristic
126C4×Q8×C11C2311yescharacteristic
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11D411yescharacteristic
140C4×D4×C11D412yes—
141C4×D4×C11C2311yescharacteristic
142C4×D4×C11C2311yescharacteristic
143C11×#117—22no—
144C11×#117—21no—
145C11×#117—21no—
146C11×#117D411yescharacteristic
147C2×C11×C4⋊C4—22no—
148C2×C11×C4⋊C4—21no—
149C2×C42×C11—21no—
150C2×C42×C11C2311yescharacteristic
151C11×#107—21no—
152C11×#107—21no—
153C11×#106—21no—
154C11×#106—21no—
155C11×C4⋊C8—21no—
156C11×C4⋊C8—21no—
157C11×C4⋊C8C2311yescharacteristic
158C11×C4⋊C8C2311yescharacteristic
159C11×C4⋊C8C2311yescharacteristic
160C11×C4⋊C8C2311yescharacteristic
161C11×#103—21no—
162C11×#103—21no—
163C11×#103—22no—
164C11×#102—21no—
165C11×#102—21no—
166C11×#102—21no—
167C11×#102—21no—
168C11×#102—22no—
169C11×#102—21no—
170C11×#102—21no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8—21no—
173C4×C8×C11—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18910C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—22no—
178C11×#41—41no—
179C11×#41—42no—
180C11×#41—42no—
181C11×#41—81no—
182C11×#41—81no—
183C11×#41—81no—
184C11×#41—81no—
185C11×#41—81no—
186C11×#41—81no—
187C11×#41—82no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11C2×D411yescharacteristic
191C2×Q8×C11C2×D411yescharacteristic
192C2×D4×C11—22no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—41no—
206C2×D4×C11C2×D411yescharacteristic
207C2×D4×C11C2×D411yescharacteristic
208C2×D4×C11C2×D412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—22no—
217C22×C4×C11—41no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C11×SD16—42no—
222C11×SD16—81no—
223C11×SD16—82no—
224C11×D8—42no—
225C11×D8—81no—
226C11×D8—82no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—81no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4C2×D412yes—
248C11×C4⋊C4C2×D411yescharacteristic
249C11×C4⋊C4C2×D411yescharacteristic
250C11×C4⋊C4C2×D411yescharacteristic
251C11×C4⋊C4C2×D411yescharacteristic
252C11×C22⋊C4—22no—
253C11×C22⋊C4—22no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—41no—
266C11×C22⋊C4—41no—
267C42×C11—22no—
268C42×C11—21no—
269C42×C11—21no—
270C42×C11—21no—
271C42×C11—21no—
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2411yescharacteristic
276#3517C2×C1111yescharacteristic, complemented
277#3247C2×C1111yescharacteristic, complemented
278#3207C2×C1111yescharacteristic, complemented
279#3106C2×C1111yescharacteristic, complemented
280#1636C2×C1111yescharacteristic, complemented
281#1635C2×C1111yescharacteristic, complemented
282#1631C2×C1111yescharacteristic, complemented
283#1631C2×C1111yescharacteristic, complemented
284#1626C2×C1111yescharacteristic, complemented
285#1625C2×C1111yescharacteristic, complemented
286#1621C2×C1111yescharacteristic, complemented
287#1621C2×C1111yescharacteristic, complemented
288#1540C2×C1111yescharacteristic, complemented
289#1482C2×C1111yescharacteristic, complemented
290#1477C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—22no—
294C23×C11—41no—
295C23×C11#12011yescharacteristic
296Q8×C11—21no—
297Q8×C11—21no—
298Q8×C11—21no—
299Q8×C11—42no—
300Q8×C11—41no—
301Q8×C11—41no—
302Q8×C11#13512yes—
303D4×C11—21no—
304D4×C11—21no—
305D4×C11—21no—
306D4×C11—21no—
307D4×C11—42no—
308D4×C11—42no—
309D4×C11—44no—
310D4×C11—42no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11—41no—
318D4×C11—41no—
319D4×C11—81no—
320D4×C11—82no—
321D4×C11—82no—
322D4×C11—82no—
323D4×C11—82no—
324D4×C11—82no—
325D4×C11—82no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—21no—
337C2×C4×C11—41no—
338C2×C4×C11—42no—
339C2×C4×C11—44no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—81no—
346C2×C4×C11—82no—
347C2×C4×C11—82no—
348C2×C4×C11—82no—
349C2×C4×C11—82no—
350C2×C4×C11#12011yescharacteristic
351C2×C4×C11#12011yescharacteristic
352C2×C4×C11#12011yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C8×C11—41no—
361C8×C11—41no—
362#557C22×C1111yescharacteristic
363#553—22no—
364#553—21no—
365#550—21no—
366#550—21no—
367#550C22×C1111yescharacteristic
368#550C22×C1111yescharacteristic
369#547—21no—
370#547C22×C1111yescharacteristic
371#540—22no—
372#540—21no—
373#532—21no—
374#532C22×C1111yescharacteristic
375#532C22×C1111yescharacteristic
376#529—21no—
377#529C22×C1111yescharacteristic
378#520—21no—
379C4×#41C22×C1111yescharacteristic
380#493C22×C1111yescharacteristic
381#492C22×C1111yescharacteristic
382#487C22×C1111yescharacteristic
383#486C22×C1111yescharacteristic
384#482—21no—
385#478—21no—
386#477C22×C1111yescharacteristic
387#477C22×C1111yescharacteristic
388#476C22×C1111yescharacteristic
389#476C22×C1111yescharacteristic
390#466—21no—
391#465—21no—
392#463—21no—
393#463—22no—
394#460C22×C1111yescharacteristic
395#460C22×C1111yescharacteristic
396#459C22×C1111yescharacteristic
397#459C22×C1111yescharacteristic
398#449—21no—
399#449—22no—
400C4×SD16—21no—
401C4×D8—21no—
402#431C22×C1111yescharacteristic
403#431C22×C1111yescharacteristic
404C2×C4⋊C8C22×C1111yescharacteristic
405#332C22×C1111yescharacteristic
406#332C22×C1111yescharacteristic
407#331C22×C1111yescharacteristic
408#331C22×C1111yescharacteristic
409Q8⋊C8C22×C1111yescharacteristic
410Q8⋊C8C22×C1111yescharacteristic
411Q8⋊C8C22×C1111yescharacteristic
412Q8⋊C8C22×C1111yescharacteristic
413D4⋊C8C22×C1111yescharacteristic
414D4⋊C8C22×C1111yescharacteristic
415D4⋊C8C22×C1111yescharacteristic
416D4⋊C8C22×C1111yescharacteristic
417C22×C11—21no—
418C22×C11—21no—
419C22×C11—21no—
420C22×C11—41no—
421C22×C11—42no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—42no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11C2×#12011yescharacteristic
433C4×C11—21no—
434C4×C11—22no—
435C4×C11—21no—
436C4×C11—21no—
437C4×C11—21no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—42no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—81no—
445C4×C11C2×#13511yescharacteristic
446C4×C11#57511yescharacteristic
447C4×C11#57611yescharacteristic
448C4×C11#57711yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41D4×C1111yescharacteristic
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—22no—
458C2×D8—21no—
459C2×D8—22no—
460C2×D8—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8C23×C1111yescharacteristic
464C4⋊Q8C23×C1111yescharacteristic
465#127—22no—
466#127—21no—
467#127—21no—
468#127C23×C1111yescharacteristic
469#127C23×C1111yescharacteristic
470#126—22no—
471#126—21no—
472#125—22no—
473#125—21no—
474#125D4×C1111yescharacteristic
475#124—21no—
476#124—21no—
477#124D4×C1111yescharacteristic
478#123—22no—
479#123—22no—
480#123—22no—
481#123—21no—
482#123—22no—
483C22⋊Q8—21no—
484C22⋊Q8D4×C1111yescharacteristic
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—21no—
491#121—22no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121D4×C1111yescharacteristic
499#121D4×C1112yes—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8D4×C1111yescharacteristic
503C4×Q8C23×C1111yescharacteristic
504C4×Q8C23×C1111yescharacteristic
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4D4×C1111yescharacteristic
518C4×D4D4×C1112yes—
519C4×D4C23×C1111yescharacteristic
520C4×D4C23×C1111yescharacteristic
521#117—22no—
522#117—21no—
523#117—21no—
524#117D4×C1111yescharacteristic
525C2×C4⋊C4—22no—
526C2×C4⋊C4—21no—
527C2×C42—21no—
528C2×C42C23×C1111yescharacteristic
529#107—21no—
530#107—21no—
531#106—21no—
532#106—21no—
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C1111yescharacteristic
536C4⋊C8C23×C1111yescharacteristic
537C4⋊C8C23×C1111yescharacteristic
538C4⋊C8C23×C1111yescharacteristic
539#103—21no—
540#103—21no—
541#103—22no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—22no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C4×C8—21no—
552C4×C8C23×C1111yescharacteristic
553C4×C8C23×C1111yescharacteristic
554C2×C11—41no—
555C2×C11—81no—
556C2×C11—81no—
557C2×C11—82no—
558C2×C11—161no—
559C2×C11#300211yescharacteristic
560C2×C11#301211yescharacteristic
561C2×C11#302111yescharacteristic
562#41—22no—
563#41—41no—
564#41—42no—
565#41—42no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—82no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C2×D4×C1111yescharacteristic
576C2×Q8C2×D4×C1111yescharacteristic
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4C2×D4×C1111yescharacteristic
592C2×D4C2×D4×C1111yescharacteristic
593C2×D4C2×D4×C1112yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—41no—
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1111yescharacteristic
606SD16—42no—
607SD16—81no—
608SD16—82no—
609D8—42no—
610D8—81no—
611D8—82no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4C2×D4×C1112yes—
633C4⋊C4C2×D4×C1111yescharacteristic
634C4⋊C4C2×D4×C1111yescharacteristic
635C4⋊C4C2×D4×C1111yescharacteristic
636C4⋊C4C2×D4×C1111yescharacteristic
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—22no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42C2×D4×C1111yescharacteristic
658C42C2×D4×C1111yescharacteristic
659C42C2×D4×C1111yescharacteristic
660C42C24×C1111yescharacteristic
661C11#1891011yescharacteristic, direct product factor, Sylow
662C23—21no—
663C23—21no—
664C23—22no—
665C23—41no—
666C23C11×#12011yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—42no—
671Q8—41no—
672Q8—41no—
673Q8C11×#13512yes—
674D4—21no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—42no—
679D4—42no—
680D4—44no—
681D4—42no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—81no—
691D4—82no—
692D4—82no—
693D4—82no—
694D4—82no—
695D4—82no—
696D4—82no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4C11×#12011yescharacteristic
722C2×C4C11×#12011yescharacteristic
723C2×C4C11×#12011yescharacteristic
724C2×C4C22×D4×C1111yescharacteristic
725C2×C4C22×D4×C1111yescharacteristic
726C2×C4C22×D4×C1111yescharacteristic
727C8—41no—
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—41no—
737C22—42no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22C2×C11×#12011yescharacteristic
749C4—21no—
750C4—22no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—41no—
759C4—41no—
760C4—81no—
761C4C2×C11×#13511yescharacteristic
762C4C11×#57511yescharacteristic
763C4C11×#57611yescharacteristic
764C4C11×#57711yescharacteristic
765C2—41no—
766C2—81no—
767C2—81no—
768C2—82no—
769C2—161no—
770C2C11×#300211yescharacteristic
771C2C11×#301211yescharacteristic
772C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3517C2semidirect
2. C11×#3247C2semidirect
3. C11×#3207C2semidirect
4. C11×#3106C2semidirect
5. C11×#1636C2semidirect
6. C11×#1635C2semidirect
7. C11×#1631C2semidirect
8. C11×#1631C2semidirect
9. C11×#1626C2semidirect
10. C11×#1625C2semidirect
11. C11×#1621C2semidirect
12. C11×#1621C2semidirect
13. C11×#1540C2semidirect
14. C11×#1482C2semidirect
15. C11×#1477C2semidirect
176. #18910C11direct (N × H)
276. #3517C2×C11semidirect
277. #3247C2×C11semidirect
278. #3207C2×C11semidirect
279. #3106C2×C11semidirect
280. #1636C2×C11semidirect
281. #1635C2×C11semidirect
282. #1631C2×C11semidirect
283. #1631C2×C11semidirect
284. #1626C2×C11semidirect
285. #1625C2×C11semidirect
286. #1621C2×C11semidirect
287. #1621C2×C11semidirect
288. #1540C2×C11semidirect
289. #1482C2×C11semidirect
290. #1477C2×C11semidirect
661. C11#18910direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35172
C11×#32472
C11×#32072
C11×#31062
C11×#16362
C11×#16352
C11×#16312
C11×#16262
C11×#16252
C11×#16212
C11×#15402
C11×#14822
C11×#14772
#1891011