Finite Group Databasebeta

← C11×#18920 #14596113

Subgroups — C11×#18920 #14596113

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic
2C11×#3248C211yesmaximal, characteristic, complemented
3C11×#3228C211yesmaximal, characteristic, complemented
4C11×#3107C211yesmaximal, characteristic, complemented
5C11×#1654C211yesmaximal, characteristic, complemented
6C11×#1653C211yesmaximal, characteristic, complemented
7C11×#1648C211yesmaximal, characteristic, complemented
8C11×#1647C211yesmaximal, characteristic, complemented
9C11×#1642C211yesmaximal, characteristic, complemented
10C11×#1642C211yesmaximal, characteristic, complemented
11C11×#1641C211yesmaximal, characteristic, complemented
12C11×#1641C211yesmaximal, 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×#533C2211yescharacteristic
28C11×#532—21no—
29C11×#532C2211yescharacteristic
30C11×#529—21no—
31C11×#529C2211yescharacteristic
32C11×#520—21no—
33C4×C11×#41C2211yescharacteristic
34C11×#500C2211yescharacteristic
35C11×#498C2211yescharacteristic
36C11×#486C2211yescharacteristic
37C11×#486C2211yescharacteristic
38C11×#485—21no—
39C11×#482—22no—
40C11×#479—21no—
41C11×#478—22no—
42C11×#475C2211yescharacteristic
43C11×#475C2211yescharacteristic
44C11×#474C2211yescharacteristic
45C11×#474C2211yescharacteristic
46C11×#467—21no—
47C11×#465—21no—
48C11×#464—21no—
49C11×#462C2211yescharacteristic
50C11×#462C2211yescharacteristic
51C11×#461C2211yescharacteristic
52C11×#461C2211yescharacteristic
53C11×#452—21no—
54C4×C11×Q16—21no—
55C4×C11×SD16—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×#41D411yescharacteristic
76C2×C11×Q16—21no—
77C2×C11×Q16—21no—
78C2×C11×SD16—21no—
79C2×C11×SD16—21no—
80C22×C8×C11—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×#127—22no—
86C11×#127—21no—
87C11×#127—21no—
88C11×#127C2311yescharacteristic
89C11×#126—22no—
90C11×#126—21no—
91C11×#125—22no—
92C11×#125—21no—
93C11×#125—21no—
94C11×#125D411yescharacteristic
95C11×#124—21no—
96C11×#124D411yescharacteristic
97C11×#123—22no—
98C11×#123—22no—
99C11×#123—22no—
100C11×#123—21no—
101C11×#123—22no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8D411yescharacteristic
106C11×#121—22no—
107C11×#121—22no—
108C11×#121—22no—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—21no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121—21no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121D411yescharacteristic
118C11×#121D412yes—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11D411yescharacteristic
124C4×Q8×C11C2311yescharacteristic
125C4×Q8×C11C2311yescharacteristic
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11D411yescharacteristic
137C4×D4×C11D412yes—
138C4×D4×C11C2311yescharacteristic
139C4×D4×C11C2311yescharacteristic
140C11×#117—22no—
141C11×#117—21no—
142C11×#117—21no—
143C11×#117—21no—
144C11×#117D411yescharacteristic
145C2×C11×C4⋊C4—22no—
146C2×C11×C4⋊C4—21no—
147C2×C42×C11—21no—
148C2×C42×C11C2311yescharacteristic
149C11×#107—22no—
150C11×#107—21no—
151C11×#107—21no—
152C11×#106—22no—
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—21no—
164C11×#103—21no—
165C11×#103—21no—
166C11×#103—21no—
167C11×#102—21no—
168C11×#102—21no—
169C11×#102—22no—
170C11×#102—22no—
171C11×C22⋊C8—21no—
172C11×C22⋊C8—21no—
173C4×C8×C11—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18920C1111yesmaximal, 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—
187C2×Q8×C11—21no—
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×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C2×D4×C11C2×D412yes—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—22no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C11×Q16—42no—
217C11×Q16—81no—
218C11×SD16—42no—
219C11×SD16—81no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—81no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—41no—
243C11×C4⋊C4—41no—
244C11×C4⋊C4C2×D411yescharacteristic
245C11×C4⋊C4C2×D411yescharacteristic
246C11×C4⋊C4C2×D411yescharacteristic
247C11×C4⋊C4C2×D411yescharacteristic
248C11×C4⋊C4C2×D412yes—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—22no—
251C11×C22⋊C4—22no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—41no—
263C42×C11—22no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—21no—
268C42×C11—41no—
269C42×C11C2×D411yescharacteristic
270C42×C11C2×D411yescharacteristic
271C42×C11C2×D411yescharacteristic
272C42×C11C2411yescharacteristic
273#3517C2×C1111yescharacteristic
274#3248C2×C1111yescharacteristic, complemented
275#3228C2×C1111yescharacteristic, complemented
276#3107C2×C1111yescharacteristic, complemented
277#1654C2×C1111yescharacteristic, complemented
278#1653C2×C1111yescharacteristic, complemented
279#1648C2×C1111yescharacteristic, complemented
280#1647C2×C1111yescharacteristic, complemented
281#1642C2×C1111yescharacteristic, complemented
282#1642C2×C1111yescharacteristic, complemented
283#1641C2×C1111yescharacteristic, complemented
284#1641C2×C1111yescharacteristic, complemented
285#1540C2×C1111yescharacteristic, complemented
286#1482C2×C1111yescharacteristic, complemented
287#1477C2×C1111yescharacteristic, complemented
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—22no—
291C23×C11#12011yescharacteristic
292Q8×C11—21no—
293Q8×C11—21no—
294Q8×C11—21no—
295Q8×C11—41no—
296Q8×C11—41no—
297Q8×C11—41no—
298Q8×C11—41no—
299Q8×C11—41no—
300Q8×C11—41no—
301Q8×C11#13512yes—
302D4×C11—21no—
303D4×C11—21no—
304D4×C11—21no—
305D4×C11—21no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—44no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—81no—
314D4×C11—82no—
315D4×C11—82no—
316D4×C11—82no—
317D4×C11—82no—
318D4×C11—82no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—41no—
331C2×C4×C11—42no—
332C2×C4×C11—44no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—81no—
340C2×C4×C11—82no—
341C2×C4×C11—82no—
342C2×C4×C11—82no—
343C2×C4×C11#12011yescharacteristic
344C2×C4×C11#12011yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C8×C11—41no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355#557C22×C1111yescharacteristic
356#553—22no—
357#553—21no—
358#550—21no—
359#550—21no—
360#550C22×C1111yescharacteristic
361#550C22×C1111yescharacteristic
362#547—21no—
363#547C22×C1111yescharacteristic
364#540—22no—
365#540—21no—
366#533C22×C1111yescharacteristic
367#532—21no—
368#532C22×C1111yescharacteristic
369#529—21no—
370#529C22×C1111yescharacteristic
371#520—21no—
372C4×#41C22×C1111yescharacteristic
373#500C22×C1111yescharacteristic
374#498C22×C1111yescharacteristic
375#486C22×C1111yescharacteristic
376#486C22×C1111yescharacteristic
377#485—21no—
378#482—22no—
379#479—21no—
380#478—22no—
381#475C22×C1111yescharacteristic
382#475C22×C1111yescharacteristic
383#474C22×C1111yescharacteristic
384#474C22×C1111yescharacteristic
385#467—21no—
386#465—21no—
387#464—21no—
388#462C22×C1111yescharacteristic
389#462C22×C1111yescharacteristic
390#461C22×C1111yescharacteristic
391#461C22×C1111yescharacteristic
392#452—21no—
393C4×Q16—21no—
394C4×SD16—21no—
395#431C22×C1111yescharacteristic
396#431C22×C1111yescharacteristic
397C2×C4⋊C8C22×C1111yescharacteristic
398#332C22×C1111yescharacteristic
399#332C22×C1111yescharacteristic
400#331C22×C1111yescharacteristic
401#331C22×C1111yescharacteristic
402Q8⋊C8C22×C1111yescharacteristic
403Q8⋊C8C22×C1111yescharacteristic
404Q8⋊C8C22×C1111yescharacteristic
405Q8⋊C8C22×C1111yescharacteristic
406D4⋊C8C22×C1111yescharacteristic
407D4⋊C8C22×C1111yescharacteristic
408D4⋊C8C22×C1111yescharacteristic
409D4⋊C8C22×C1111yescharacteristic
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—42no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11C2×#12011yescharacteristic
423C4×C11—21no—
424C4×C11—22no—
425C4×C11—21no—
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—42no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11C2×#13511yescharacteristic
437C4×C11#57511yescharacteristic
438C4×C11#57611yescharacteristic
439C4×C11#57711yescharacteristic
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41D4×C1111yescharacteristic
445C2×Q16—21no—
446C2×Q16—21no—
447C2×SD16—21no—
448C2×SD16—21no—
449C22×C8—21no—
450C4⋊Q8—21no—
451C4⋊Q8C23×C1111yescharacteristic
452C4⋊Q8C23×C1111yescharacteristic
453C4⋊Q8C23×C1111yescharacteristic
454#127—22no—
455#127—21no—
456#127—21no—
457#127C23×C1111yescharacteristic
458#126—22no—
459#126—21no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125D4×C1111yescharacteristic
464#124—21no—
465#124D4×C1111yescharacteristic
466#123—22no—
467#123—22no—
468#123—22no—
469#123—21no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8D4×C1111yescharacteristic
475#121—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121D4×C1111yescharacteristic
487#121D4×C1112yes—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8D4×C1111yescharacteristic
493C4×Q8C23×C1111yescharacteristic
494C4×Q8C23×C1111yescharacteristic
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4D4×C1111yescharacteristic
506C4×D4D4×C1112yes—
507C4×D4C23×C1111yescharacteristic
508C4×D4C23×C1111yescharacteristic
509#117—22no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C1111yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—21no—
516C2×C42—21no—
517C2×C42C23×C1111yescharacteristic
518#107—21no—
519#107—21no—
520#107—22no—
521#106—21no—
522#106—21no—
523#106—22no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8C23×C1111yescharacteristic
527C4⋊C8C23×C1111yescharacteristic
528C4⋊C8C23×C1111yescharacteristic
529C4⋊C8C23×C1111yescharacteristic
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—21no—
535#103—21no—
536#102—21no—
537#102—21no—
538#102—22no—
539#102—22no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C4×C8—21no—
543C4×C8C23×C1111yescharacteristic
544C4×C8C23×C1111yescharacteristic
545C2×C11—41no—
546C2×C11—81no—
547C2×C11—81no—
548C2×C11—82no—
549C2×C11#300211yescharacteristic
550C2×C11#301211yescharacteristic
551C2×C11#302211yescharacteristic
552#41—22no—
553#41—41no—
554#41—42no—
555#41—42no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560#41—81no—
561#41—81no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C2×D4×C1111yescharacteristic
566C2×Q8C2×D4×C1111yescharacteristic
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4C2×D4×C1111yescharacteristic
578C2×D4C2×D4×C1111yescharacteristic
579C2×D4C2×D4×C1112yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1111yescharacteristic
591Q16—42no—
592Q16—81no—
593SD16—42no—
594SD16—81no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—81no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4C2×D4×C1111yescharacteristic
620C4⋊C4C2×D4×C1111yescharacteristic
621C4⋊C4C2×D4×C1111yescharacteristic
622C4⋊C4C2×D4×C1111yescharacteristic
623C4⋊C4C2×D4×C1112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—41no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—41no—
644C42C2×D4×C1111yescharacteristic
645C42C2×D4×C1111yescharacteristic
646C42C2×D4×C1111yescharacteristic
647C42C24×C1111yescharacteristic
648C11#1892011yescharacteristic, direct product factor, Sylow
649C23—21no—
650C23—21no—
651C23—22no—
652C23C11×#12011yescharacteristic
653Q8—21no—
654Q8—21no—
655Q8—21no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8C11×#13512yes—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—81no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4C11×#12011yescharacteristic
705C2×C4C11×#12011yescharacteristic
706C2×C4C11×#12011yescharacteristic
707C2×C4C22×D4×C1111yescharacteristic
708C2×C4C22×D4×C1111yescharacteristic
709C2×C4C22×D4×C1111yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22C2×C11×#12011yescharacteristic
729C4—21no—
730C4—22no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4C2×C11×#13511yescharacteristic
743C4C11×#57511yescharacteristic
744C4C11×#57611yescharacteristic
745C4C11×#57711yescharacteristic
746C2—41no—
747C2—81no—
748C2—81no—
749C2—82no—
750C2C11×#300211yescharacteristic
751C2C11×#301211yescharacteristic
752C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3517C2
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
2. C11×#3248C2semidirect
3. C11×#3228C2semidirect
4. C11×#3107C2semidirect
5. C11×#1654C2semidirect
6. C11×#1653C2semidirect
7. C11×#1648C2semidirect
8. C11×#1647C2semidirect
9. C11×#1642C2semidirect
10. C11×#1642C2semidirect
11. C11×#1641C2semidirect
12. C11×#1641C2semidirect
13. C11×#1540C2semidirect
14. C11×#1482C2semidirect
15. C11×#1477C2semidirect
176. #18920C11direct (N × H)
274. #3248C2×C11semidirect
275. #3228C2×C11semidirect
276. #3107C2×C11semidirect
277. #1654C2×C11semidirect
278. #1653C2×C11semidirect
279. #1648C2×C11semidirect
280. #1647C2×C11semidirect
281. #1642C2×C11semidirect
282. #1642C2×C11semidirect
283. #1641C2×C11semidirect
284. #1641C2×C11semidirect
285. #1540C2×C11semidirect
286. #1482C2×C11semidirect
287. #1477C2×C11semidirect
648. C11#18920direct (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×#32482
C11×#32282
C11×#31072
C11×#16542
C11×#16532
C11×#16482
C11×#16472
C11×#16422
C11×#16412
C11×#15402
C11×#14822
C11×#14772
#1892011