Finite Group Databasebeta

← C11×#18921 #14596114

Subgroups — C11×#18921 #14596114

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3518C211yesmaximal, characteristic
2C11×#3248C211yesmaximal, characteristic, complemented
3C11×#3231C211yesmaximal, characteristic, complemented
4C11×#3107C211yesmaximal, characteristic, complemented
5C11×#1652C211yesmaximal, characteristic, complemented
6C11×#1651C211yesmaximal, characteristic, complemented
7C11×#1650C211yesmaximal, characteristic, complemented
8C11×#1649C211yesmaximal, characteristic, complemented
9C11×#1646C211yesmaximal, characteristic, complemented
10C11×#1646C211yesmaximal, characteristic, complemented
11C11×#1645C211yesmaximal, characteristic, complemented
12C11×#1645C211yesmaximal, characteristic, complemented
13C11×#1542C211yesmaximal, characteristic, complemented
14C11×#1482C211yesmaximal, characteristic, complemented
15C11×#1477C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#556—21no—
18C11×#556—22no—
19C11×#556—21no—
20C11×#556C2211yescharacteristic
21C11×#555—21no—
22C11×#555C2211yescharacteristic
23D4×Q8×C11C2211yescharacteristic
24C11×#548—21no—
25C11×#542—22no—
26C11×#542—21no—
27C11×#533—21no—
28C11×#533C2211yescharacteristic
29C11×#533C2211yescharacteristic
30C11×#529—21no—
31C11×#529C2211yescharacteristic
32C11×#519—21no—
33C4×C11×#41C2211yescharacteristic
34C11×#500C2211yescharacteristic
35C11×#498C2211yescharacteristic
36C11×#487C2211yescharacteristic
37C11×#487C2211yescharacteristic
38C11×#485—22no—
39C11×#485—21no—
40C11×#479—21no—
41C11×#479—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×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
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×#41D411yescharacteristic
72C22×Q8×C11—21no—
73C2×C11×Q16—21no—
74C2×C11×Q16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C22×C8×C11—21no—
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#126—22no—
87C11×#126—22no—
88C11×#126—22no—
89C11×#126—22no—
90C11×#126—21no—
91C11×#125—21no—
92C11×#125—21no—
93C11×#125D411yescharacteristic
94C11×#124—22no—
95C11×#124—22no—
96C11×#124—22no—
97C11×#124—22no—
98C11×#124—21no—
99C11×#124D411yescharacteristic
100C11×#123—22no—
101C11×#123—21no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8D411yescharacteristic
111C11×C22⋊Q8D412yes—
112C11×#121—22no—
113C11×#121—21no—
114C11×#121—21no—
115C11×#121D411yescharacteristic
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×Q8×C11—22no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11D411yescharacteristic
126C4×Q8×C11D412yes—
127C4×Q8×C11C2311yescharacteristic
128C4×Q8×C11C2311yescharacteristic
129C4×D4×C11—22no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11D411yescharacteristic
135C4×D4×C11C2311yescharacteristic
136C4×D4×C11C2311yescharacteristic
137C11×#117—22no—
138C11×#117—22no—
139C11×#117—21no—
140C11×#117—21no—
141C11×#117—21no—
142C11×#117—21no—
143C11×#117—21no—
144C11×#117—21no—
145C11×#117—21no—
146C11×#117D411yescharacteristic
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—22no—
164C11×#103—22no—
165C11×#103—21no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#103—21no—
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#18921C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—22no—
178C11×#41—41no—
179C2×Q8×C11—22no—
180C2×Q8×C11—22no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—42no—
185C2×Q8×C11—42no—
186C2×Q8×C11C2×D411yescharacteristic
187C2×Q8×C11C2×D411yescharacteristic
188C2×Q8×C11C2×D412yes—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11C2×D411yescharacteristic
193C2×D4×C11C2×D411yescharacteristic
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C11×Q16—42no—
203C11×Q16—81no—
204C11×SD16—42no—
205C11×SD16—81no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—81no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—41no—
233C11×C4⋊C4—41no—
234C11×C4⋊C4C2×D411yescharacteristic
235C11×C4⋊C4C2×D411yescharacteristic
236C11×C4⋊C4C2×D411yescharacteristic
237C11×C4⋊C4C2×D411yescharacteristic
238C11×C4⋊C4C2×D412yes—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—41no—
254C42×C11—22no—
255C42×C11—22no—
256C42×C11—22no—
257C42×C11—21no—
258C42×C11—21no—
259C42×C11—22no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—41no—
263C42×C11C2×D411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2411yescharacteristic
267#3518C2×C1111yescharacteristic
268#3248C2×C1111yescharacteristic, complemented
269#3231C2×C1111yescharacteristic, complemented
270#3107C2×C1111yescharacteristic, complemented
271#1652C2×C1111yescharacteristic, complemented
272#1651C2×C1111yescharacteristic, complemented
273#1650C2×C1111yescharacteristic, complemented
274#1649C2×C1111yescharacteristic, complemented
275#1646C2×C1111yescharacteristic, complemented
276#1646C2×C1111yescharacteristic, complemented
277#1645C2×C1111yescharacteristic, complemented
278#1645C2×C1111yescharacteristic, complemented
279#1542C2×C1111yescharacteristic, complemented
280#1482C2×C1111yescharacteristic, complemented
281#1477C2×C1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—21no—
284C23×C11#12011yescharacteristic
285Q8×C11—21no—
286Q8×C11—21no—
287Q8×C11—21no—
288Q8×C11—42no—
289Q8×C11—44no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11—41no—
294Q8×C11—41no—
295Q8×C11—41no—
296Q8×C11—82no—
297Q8×C11#13512yes—
298D4×C11—21no—
299D4×C11—21no—
300D4×C11—21no—
301D4×C11—21no—
302D4×C11—42no—
303D4×C11—81no—
304D4×C11—82no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—44no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—81no—
327C2×C4×C11#12011yescharacteristic
328C2×C4×C11#12011yescharacteristic
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C8×C11—41no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339Q82C22×C1111yescharacteristic
340#556—21no—
341#556—22no—
342#556—21no—
343#556C22×C1111yescharacteristic
344#555—21no—
345#555C22×C1111yescharacteristic
346D4×Q8C22×C1111yescharacteristic
347#548—21no—
348#542—22no—
349#542—21no—
350#533—21no—
351#533C22×C1111yescharacteristic
352#533C22×C1111yescharacteristic
353#529—21no—
354#529C22×C1111yescharacteristic
355#519—21no—
356C4×#41C22×C1111yescharacteristic
357#500C22×C1111yescharacteristic
358#498C22×C1111yescharacteristic
359#487C22×C1111yescharacteristic
360#487C22×C1111yescharacteristic
361#485—22no—
362#485—21no—
363#479—21no—
364#479—22no—
365#475C22×C1111yescharacteristic
366#475C22×C1111yescharacteristic
367#474C22×C1111yescharacteristic
368#474C22×C1111yescharacteristic
369#467—21no—
370#465—21no—
371#464—21no—
372#462C22×C1111yescharacteristic
373#462C22×C1111yescharacteristic
374#461C22×C1111yescharacteristic
375#461C22×C1111yescharacteristic
376#452—21no—
377C4×Q16—21no—
378C4×SD16—21no—
379#431C22×C1111yescharacteristic
380#431C22×C1111yescharacteristic
381C2×C4⋊C8C22×C1111yescharacteristic
382#333C22×C1111yescharacteristic
383#333C22×C1111yescharacteristic
384#332C22×C1111yescharacteristic
385#332C22×C1111yescharacteristic
386Q8⋊C8C22×C1111yescharacteristic
387Q8⋊C8C22×C1111yescharacteristic
388Q8⋊C8C22×C1111yescharacteristic
389Q8⋊C8C22×C1111yescharacteristic
390D4⋊C8C22×C1111yescharacteristic
391D4⋊C8C22×C1111yescharacteristic
392D4⋊C8C22×C1111yescharacteristic
393D4⋊C8C22×C1111yescharacteristic
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11C2×#12011yescharacteristic
404C4×C11—21no—
405C4×C11—22no—
406C4×C11—21no—
407C4×C11—21no—
408C4×C11—21no—
409C4×C11—42no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11C2×#13511yescharacteristic
419C4×C11#57511yescharacteristic
420C4×C11#57711yescharacteristic
421C4×C11#57811yescharacteristic
422C2×#41D4×C1111yescharacteristic
423C22×Q8—21no—
424C2×Q16—21no—
425C2×Q16—21no—
426C2×SD16—21no—
427C2×SD16—21no—
428C22×C8—21no—
429C4⋊Q8—22no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8—21no—
433C4⋊Q8C23×C1111yescharacteristic
434C4⋊Q8C23×C1111yescharacteristic
435C4⋊Q8C23×C1111yescharacteristic
436C4⋊Q8C23×C1111yescharacteristic
437#126—22no—
438#126—22no—
439#126—22no—
440#126—22no—
441#126—21no—
442#125—21no—
443#125—21no—
444#125D4×C1111yescharacteristic
445#124—22no—
446#124—22no—
447#124—22no—
448#124—22no—
449#124—21no—
450#124D4×C1111yescharacteristic
451#123—22no—
452#123—21no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8D4×C1111yescharacteristic
462C22⋊Q8D4×C1112yes—
463#121—22no—
464#121—21no—
465#121—21no—
466#121D4×C1111yescharacteristic
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8D4×C1111yescharacteristic
477C4×Q8D4×C1112yes—
478C4×Q8C23×C1111yescharacteristic
479C4×Q8C23×C1111yescharacteristic
480C4×D4—22no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4D4×C1111yescharacteristic
486C4×D4C23×C1111yescharacteristic
487C4×D4C23×C1111yescharacteristic
488#117—22no—
489#117—22no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117D4×C1111yescharacteristic
498C2×C42—21no—
499C2×C42C23×C1111yescharacteristic
500#107—21no—
501#107—21no—
502#107—22no—
503#106—21no—
504#106—21no—
505#106—22no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8C23×C1111yescharacteristic
509C4⋊C8C23×C1111yescharacteristic
510C4⋊C8C23×C1111yescharacteristic
511C4⋊C8C23×C1111yescharacteristic
512#103—21no—
513#103—21no—
514#103—22no—
515#103—22no—
516#103—21no—
517#103—21no—
518#103—21no—
519#103—21no—
520#102—21no—
521#102—21no—
522C22⋊C8—21no—
523C22⋊C8—21no—
524C4×C8—21no—
525C4×C8C23×C1111yescharacteristic
526C4×C8C23×C1111yescharacteristic
527C2×C11—41no—
528C2×C11—81no—
529C2×C11—81no—
530C2×C11#300211yescharacteristic
531C2×C11#301311yescharacteristic
532C2×C11#302211yescharacteristic
533#41—22no—
534#41—41no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—42no—
541C2×Q8—42no—
542C2×Q8C2×D4×C1111yescharacteristic
543C2×Q8C2×D4×C1111yescharacteristic
544C2×Q8C2×D4×C1112yes—
545C2×D4—21no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4C2×D4×C1111yescharacteristic
549C2×D4C2×D4×C1111yescharacteristic
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C2×D4×C1111yescharacteristic
558Q16—42no—
559Q16—81no—
560SD16—42no—
561SD16—81no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—81no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4C2×D4×C1111yescharacteristic
591C4⋊C4C2×D4×C1111yescharacteristic
592C4⋊C4C2×D4×C1111yescharacteristic
593C4⋊C4C2×D4×C1111yescharacteristic
594C4⋊C4C2×D4×C1112yes—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—41no—
619C42C2×D4×C1111yescharacteristic
620C42C2×D4×C1111yescharacteristic
621C42C2×D4×C1111yescharacteristic
622C42C24×C1111yescharacteristic
623C11#1892111yescharacteristic, direct product factor, Sylow
624C23—21no—
625C23—21no—
626C23C11×#12011yescharacteristic
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—42no—
631Q8—44no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—82no—
639Q8C11×#13512yes—
640D4—21no—
641D4—21no—
642D4—21no—
643D4—21no—
644D4—42no—
645D4—81no—
646D4—82no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—81no—
669C2×C4C11×#12011yescharacteristic
670C2×C4C11×#12011yescharacteristic
671C2×C4C11×#12011yescharacteristic
672C2×C4C22×D4×C1111yescharacteristic
673C2×C4C22×D4×C1111yescharacteristic
674C2×C4C22×D4×C1111yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×C11×#12011yescharacteristic
691C4—21no—
692C4—22no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4C2×C11×#13511yescharacteristic
706C4C11×#57511yescharacteristic
707C4C11×#57711yescharacteristic
708C4C11×#57811yescharacteristic
709C2—41no—
710C2—81no—
711C2—81no—
712C2C11×#300211yescharacteristic
713C2C11×#301311yescharacteristic
714C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3518C2
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×#3231C2semidirect
4. C11×#3107C2semidirect
5. C11×#1652C2semidirect
6. C11×#1651C2semidirect
7. C11×#1650C2semidirect
8. C11×#1649C2semidirect
9. C11×#1646C2semidirect
10. C11×#1646C2semidirect
11. C11×#1645C2semidirect
12. C11×#1645C2semidirect
13. C11×#1542C2semidirect
14. C11×#1482C2semidirect
15. C11×#1477C2semidirect
176. #18921C11direct (N × H)
268. #3248C2×C11semidirect
269. #3231C2×C11semidirect
270. #3107C2×C11semidirect
271. #1652C2×C11semidirect
272. #1651C2×C11semidirect
273. #1650C2×C11semidirect
274. #1649C2×C11semidirect
275. #1646C2×C11semidirect
276. #1646C2×C11semidirect
277. #1645C2×C11semidirect
278. #1645C2×C11semidirect
279. #1542C2×C11semidirect
280. #1482C2×C11semidirect
281. #1477C2×C11semidirect
623. C11#18921direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35182
C11×#32482
C11×#32312
C11×#31072
C11×#16522
C11×#16512
C11×#16502
C11×#16492
C11×#16462
C11×#16452
C11×#15422
C11×#14822
C11×#14772
#1892111