Finite Group Databasebeta

← C11×#18963 #14596156

Subgroups — C11×#18963 #14596156

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3555C211yesmaximal, characteristic, complemented
2C11×#3254C211yesmaximal, characteristic, complemented
3C11×#3247C211yesmaximal, characteristic
4C11×#3210C211yesmaximal, characteristic, complemented
5C11×#1638C211yesmaximal, characteristic, complemented
6C11×#1636C211yesmaximal, characteristic, complemented
7C11×#1633C211yesmaximal, characteristic, complemented
8C11×#1632C211yesmaximal, characteristic, complemented
9C11×#1628C211yesmaximal, characteristic, complemented
10C11×#1626C211yesmaximal, characteristic, complemented
11C11×#1623C211yesmaximal, characteristic, complemented
12C11×#1622C211yesmaximal, characteristic, complemented
13C11×#1550C211yesmaximal, characteristic, complemented
14C11×#1495C211yesmaximal, characteristic, complemented
15C11×#1481C211yesmaximal, characteristic, complemented
16C11×#563—22no—
17Q82×C11C2211yescharacteristic
18C11×#557—21no—
19C11×#557C2211yescharacteristic
20C11×#556—21no—
21C11×#556—21no—
22C11×#556C2211yescharacteristic
23C11×#554C2211yescharacteristic
24C11×#552—21no—
25C11×#544—21no—
26C11×#542—21no—
27C11×#541—21no—
28C11×#541—21no—
29C11×#541—22no—
30C11×#533C2211yescharacteristic
31C11×#533C2211yescharacteristic
32C11×#532C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C11×#494C2211yescharacteristic
35C11×#492C2211yescharacteristic
36C11×#487C2211yescharacteristic
37C11×#486C2211yescharacteristic
38C11×#478—21no—
39C11×#477C2211yescharacteristic
40C11×#477C2211yescharacteristic
41C11×#477C2211yescharacteristic
42C11×#476C2211yescharacteristic
43C11×#474—21no—
44C11×#468—21no—
45C11×#468—21no—
46C11×#466—21no—
47C11×#465—21no—
48C11×#464—22no—
49C11×#463—21no—
50C11×#461—21no—
51C11×#460C2211yescharacteristic
52C11×#460C2211yescharacteristic
53C11×#460C2211yescharacteristic
54C11×#459C2211yescharacteristic
55C11×#452—22no—
56C11×#431C2211yescharacteristic
57C11×#423C2211yescharacteristic
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×Q8⋊C8C2211yescharacteristic
68C11×Q8⋊C8C2211yescharacteristic
69C11×D4⋊C8C2211yescharacteristic
70C11×D4⋊C8C2211yescharacteristic
71C2×C11×#41—21no—
72C2×C11×Q16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×D8—21no—
78C2×C11×M16—21no—
79C22×C8×C11—21no—
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8D411yescharacteristic
86C11×C4⋊Q8D411yescharacteristic
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×C4⋊Q8C2311yescharacteristic
90C11×#127C2311yescharacteristic
91C11×#126—22no—
92C11×#126—22no—
93C11×#126—22no—
94C11×#126—22no—
95C11×#126—22no—
96C11×#126—22no—
97C11×#126—21no—
98C11×#125—22no—
99C11×#125—22no—
100C11×#125—22no—
101C11×#125—22no—
102C11×#125—21no—
103C11×#125—22no—
104C11×#125—21no—
105C11×#125—21no—
106C11×#125—21no—
107C11×#125D411yescharacteristic
108C11×#124—22no—
109C11×#124—21no—
110C11×#124—21no—
111C11×#124D411yescharacteristic
112C11×#123—22no—
113C11×#123—21no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8D411yescharacteristic
122C11×C22⋊Q8D411yescharacteristic
123C11×C22⋊Q8D411yescharacteristic
124C11×C22⋊Q8D412yes—
125C11×#121—21no—
126C11×#121—21no—
127C11×#121D411yescharacteristic
128C4×Q8×C11—22no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11—21no—
134C4×Q8×C11—21no—
135C4×Q8×C11—21no—
136C4×Q8×C11D412yes—
137C4×Q8×C11C2311yescharacteristic
138C4×Q8×C11C2311yescharacteristic
139C4×Q8×C11C2311yescharacteristic
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11C2311yescharacteristic
145C11×#117—22no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117—21no—
150C2×C11×C4⋊C4—21no—
151C2×C42×C11C2311yescharacteristic
152C11×#107—21no—
153C11×#107—21no—
154C11×#107—21no—
155C11×#106—21no—
156C11×C4⋊C8—21no—
157C11×C4⋊C8—21no—
158C11×C4⋊C8—21no—
159C11×C4⋊C8C2311yescharacteristic
160C11×C4⋊C8C2311yescharacteristic
161C11×C4⋊C8C2311yescharacteristic
162C11×C4⋊C8C2311yescharacteristic
163C11×#103—21no—
164C11×#103—21no—
165C11×#103—21no—
166C11×#103—22no—
167C11×#102—21no—
168C11×#102—22no—
169C11×#102—21no—
170C11×#102—21no—
171C11×#102—21no—
172C11×#102—21no—
173C11×C22⋊C8—21no—
174C4×C8×C11C2311yescharacteristic
175C4×C8×C11C2311yescharacteristic
176#18963C1111yesmaximal, characteristic, direct product factor, Sylow
177C11×#41—82no—
178C2×Q8×C11—22no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11C2×D411yescharacteristic
183C2×Q8×C11C2×D411yescharacteristic
184C2×Q8×C11C2×D411yescharacteristic
185C2×Q8×C11C2×D412yes—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—41no—
191C2×D4×C11C2×D411yescharacteristic
192C22×C4×C11—22no—
193C22×C4×C11—21no—
194C22×C4×C11—41no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C11×Q16—82no—
199C11×SD16—81no—
200C11×SD16—81no—
201C11×SD16—81no—
202C11×SD16—82no—
203C11×D8—81no—
204C11×M16—81no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—81no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
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⋊C4C2×D412yes—
239C11×C4⋊C4C2×D411yescharacteristic
240C11×C4⋊C4C2×D411yescharacteristic
241C11×C4⋊C4C2×D411yescharacteristic
242C11×C4⋊C4C2×D411yescharacteristic
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—41no—
255C11×C22⋊C4—41no—
256C42×C11—22no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11—22no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11C2×D411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2411yescharacteristic
267#3555C2×C1111yescharacteristic, complemented
268#3254C2×C1111yescharacteristic, complemented
269#3247C2×C1111yescharacteristic
270#3210C2×C1111yescharacteristic, complemented
271#1638C2×C1111yescharacteristic, complemented
272#1636C2×C1111yescharacteristic, complemented
273#1633C2×C1111yescharacteristic, complemented
274#1632C2×C1111yescharacteristic, complemented
275#1628C2×C1111yescharacteristic, complemented
276#1626C2×C1111yescharacteristic, complemented
277#1623C2×C1111yescharacteristic, complemented
278#1622C2×C1111yescharacteristic, complemented
279#1550C2×C1111yescharacteristic, complemented
280#1495C2×C1111yescharacteristic, complemented
281#1481C2×C1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—41no—
284C23×C11#12011yescharacteristic
285Q8×C11—21no—
286Q8×C11—21no—
287Q8×C11—21no—
288Q8×C11—21no—
289Q8×C11—21no—
290Q8×C11—21no—
291Q8×C11—42no—
292Q8×C11—42no—
293Q8×C11—41no—
294Q8×C11—41no—
295Q8×C11—81no—
296Q8×C11—82no—
297D4×C11—21no—
298D4×C11—21no—
299D4×C11—42no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—81no—
305D4×C11—82no—
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—21no—
313C2×C4×C11—22no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—82no—
324C2×C4×C11—82no—
325C2×C4×C11#12011yescharacteristic
326C2×C4×C11#12011yescharacteristic
327C2×C4×C11#12011yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C8×C11—41no—
332C8×C11—41no—
333C8×C11—41no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337#563—22no—
338Q82C22×C1111yescharacteristic
339#557—21no—
340#557C22×C1111yescharacteristic
341#556—21no—
342#556—21no—
343#556C22×C1111yescharacteristic
344#554C22×C1111yescharacteristic
345#552—21no—
346#544—21no—
347#542—21no—
348#541—21no—
349#541—21no—
350#541—22no—
351#533C22×C1111yescharacteristic
352#533C22×C1111yescharacteristic
353#532C22×C1111yescharacteristic
354#529C22×C1111yescharacteristic
355#494C22×C1111yescharacteristic
356#492C22×C1111yescharacteristic
357#487C22×C1111yescharacteristic
358#486C22×C1111yescharacteristic
359#478—21no—
360#477C22×C1111yescharacteristic
361#477C22×C1111yescharacteristic
362#477C22×C1111yescharacteristic
363#476C22×C1111yescharacteristic
364#474—21no—
365#468—21no—
366#468—21no—
367#466—21no—
368#465—21no—
369#464—22no—
370#463—21no—
371#461—21no—
372#460C22×C1111yescharacteristic
373#460C22×C1111yescharacteristic
374#460C22×C1111yescharacteristic
375#459C22×C1111yescharacteristic
376#452—22no—
377#431C22×C1111yescharacteristic
378#423C22×C1111yescharacteristic
379C2×C4⋊C8C22×C1111yescharacteristic
380#333C22×C1111yescharacteristic
381#333C22×C1111yescharacteristic
382#332C22×C1111yescharacteristic
383#332C22×C1111yescharacteristic
384Q8⋊C8C22×C1111yescharacteristic
385Q8⋊C8C22×C1111yescharacteristic
386Q8⋊C8C22×C1111yescharacteristic
387Q8⋊C8C22×C1111yescharacteristic
388Q8⋊C8C22×C1111yescharacteristic
389Q8⋊C8C22×C1111yescharacteristic
390D4⋊C8C22×C1111yescharacteristic
391D4⋊C8C22×C1111yescharacteristic
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11C2×#12011yescharacteristic
402C4×C11—21no—
403C4×C11—21no—
404C4×C11—21no—
405C4×C11—21no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11—42no—
411C4×C11—41no—
412C4×C11—42no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—81no—
416C4×C11#57711yescharacteristic
417C4×C11#57711yescharacteristic
418C4×C11#57811yescharacteristic
419C4×C11#57811yescharacteristic
420C2×#41—21no—
421C2×Q16—22no—
422C2×SD16—22no—
423C2×SD16—21no—
424C2×SD16—21no—
425C2×SD16—21no—
426C2×D8—21no—
427C2×M16—21no—
428C22×C8—21no—
429C4⋊Q8—22no—
430C4⋊Q8—21no—
431C4⋊Q8—22no—
432C4⋊Q8—21no—
433C4⋊Q8—21no—
434C4⋊Q8D4×C1111yescharacteristic
435C4⋊Q8D4×C1111yescharacteristic
436C4⋊Q8C23×C1111yescharacteristic
437C4⋊Q8C23×C1111yescharacteristic
438C4⋊Q8C23×C1111yescharacteristic
439#127C23×C1111yescharacteristic
440#126—22no—
441#126—22no—
442#126—22no—
443#126—22no—
444#126—22no—
445#126—22no—
446#126—21no—
447#125—22no—
448#125—22no—
449#125—22no—
450#125—22no—
451#125—21no—
452#125—22no—
453#125—21no—
454#125—21no—
455#125—21no—
456#125D4×C1111yescharacteristic
457#124—22no—
458#124—21no—
459#124—21no—
460#124D4×C1111yescharacteristic
461#123—22no—
462#123—21no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—22no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8D4×C1111yescharacteristic
471C22⋊Q8D4×C1111yescharacteristic
472C22⋊Q8D4×C1111yescharacteristic
473C22⋊Q8D4×C1112yes—
474#121—21no—
475#121—21no—
476#121D4×C1111yescharacteristic
477C4×Q8—22no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8D4×C1112yes—
486C4×Q8C23×C1111yescharacteristic
487C4×Q8C23×C1111yescharacteristic
488C4×Q8C23×C1111yescharacteristic
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4C23×C1111yescharacteristic
494#117—22no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499C2×C4⋊C4—21no—
500C2×C42C23×C1111yescharacteristic
501#107—21no—
502#107—21no—
503#107—21no—
504#106—21no—
505C4⋊C8—21no—
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—21no—
515#103—22no—
516#102—21no—
517#102—22no—
518#102—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522C22⋊C8—21no—
523C4×C8C23×C1111yescharacteristic
524C4×C8C23×C1111yescharacteristic
525C2×C11—41no—
526C2×C11—81no—
527C2×C11—161no—
528C2×C11#301311yescharacteristic
529C2×C11#301311yescharacteristic
530C2×C11#302111yescharacteristic
531#41—82no—
532C2×Q8—22no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8C2×D4×C1111yescharacteristic
537C2×Q8C2×D4×C1111yescharacteristic
538C2×Q8C2×D4×C1111yescharacteristic
539C2×Q8C2×D4×C1112yes—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4C2×D4×C1111yescharacteristic
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—41no—
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552Q16—82no—
553SD16—81no—
554SD16—81no—
555SD16—81no—
556SD16—82no—
557D8—81no—
558M16—81no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—81no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C1112yes—
593C4⋊C4C2×D4×C1111yescharacteristic
594C4⋊C4C2×D4×C1111yescharacteristic
595C4⋊C4C2×D4×C1111yescharacteristic
596C4⋊C4C2×D4×C1111yescharacteristic
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—22no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C1111yescharacteristic
618C42C2×D4×C1111yescharacteristic
619C42C2×D4×C1111yescharacteristic
620C42C24×C1111yescharacteristic
621C11#1896311yescharacteristic, direct product factor, Sylow
622C23—21no—
623C23—41no—
624C23C11×#12011yescharacteristic
625Q8—21no—
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—42no—
633Q8—41no—
634Q8—41no—
635Q8—81no—
636Q8—82no—
637D4—21no—
638D4—21no—
639D4—42no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—81no—
645D4—82no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4C11×#12011yescharacteristic
666C2×C4C11×#12011yescharacteristic
667C2×C4C11×#12011yescharacteristic
668C2×C4C22×D4×C1111yescharacteristic
669C2×C4C22×D4×C1111yescharacteristic
670C2×C4C22×D4×C1111yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22C2×C11×#12011yescharacteristic
687C4—21no—
688C4—21no—
689C4—21no—
690C4—21no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4C11×#57711yescharacteristic
702C4C11×#57711yescharacteristic
703C4C11×#57811yescharacteristic
704C4C11×#57811yescharacteristic
705C2—41no—
706C2—81no—
707C2—161no—
708C2C11×#301311yescharacteristic
709C2C11×#301311yescharacteristic
710C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3247C2
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×#3555C2semidirect
2. C11×#3254C2semidirect
4. C11×#3210C2semidirect
5. C11×#1638C2semidirect
6. C11×#1636C2semidirect
7. C11×#1633C2semidirect
8. C11×#1632C2semidirect
9. C11×#1628C2semidirect
10. C11×#1626C2semidirect
11. C11×#1623C2semidirect
12. C11×#1622C2semidirect
13. C11×#1550C2semidirect
14. C11×#1495C2semidirect
15. C11×#1481C2semidirect
176. #18963C11direct (N × H)
267. #3555C2×C11semidirect
268. #3254C2×C11semidirect
270. #3210C2×C11semidirect
271. #1638C2×C11semidirect
272. #1636C2×C11semidirect
273. #1633C2×C11semidirect
274. #1632C2×C11semidirect
275. #1628C2×C11semidirect
276. #1626C2×C11semidirect
277. #1623C2×C11semidirect
278. #1622C2×C11semidirect
279. #1550C2×C11semidirect
280. #1495C2×C11semidirect
281. #1481C2×C11semidirect
621. C11#18963direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35552
C11×#32542
C11×#32472
C11×#32102
C11×#16382
C11×#16362
C11×#16332
C11×#16322
C11×#16282
C11×#16262
C11×#16232
C11×#16222
C11×#15502
C11×#14952
C11×#14812
#1896311