Finite Group Databasebeta

← C11×#61976 #14639169

Subgroups — C11×#61976 #14639169

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3482C211yesmaximal, characteristic, complemented
3C11×#3398C211yesmaximal, characteristic, complemented
4C11×#3397C211yesmaximal, characteristic, complemented
5C11×#3374C211yesmaximal, characteristic, complemented
6C11×#3368C211yesmaximal, characteristic, complemented
7C11×#3332C211yesmaximal, characteristic, complemented
8C11×#3330C211yesmaximal, characteristic, complemented
9C11×#3317C212yesmaximal, complemented
10C11×#3315C212yesmaximal, complemented
11C11×#3278C211yesmaximal, characteristic, complemented
12C11×#3276C211yesmaximal, characteristic, complemented
13C11×#3271C212yesmaximal, complemented
14C11×#3269C212yesmaximal, complemented
15C11×#3256C212yesmaximal, complemented
16C11×#3248C211yesmaximal, characteristic, complemented
17C11×#3219C212yesmaximal, complemented
18C11×#3210C211yesmaximal, characteristic, complemented
19C11×#3117C212yesmaximal, complemented
20C11×#3102C211yesmaximal, characteristic, complemented
21C11×#3037C212yesmaximal, complemented
22C11×#3035C211yesmaximal, characteristic, complemented
23C11×#2989C211yesmaximal, characteristic, complemented
24C2×C11×#137C2212yes—
25C2×C11×#137C2212yes—
26C2×C11×#135C2212yes—
27C11×#557C2211yescharacteristic
28C11×#557C2211yescharacteristic
29C11×#556—21no—
30C11×#556C2211yescharacteristic
31C11×#553—22no—
32C11×#553—21no—
33C11×#552—22no—
34C11×#552C2212yes—
35C11×#550—21no—
36C11×#550C2212yes—
37C11×#550C2211yescharacteristic
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40C11×#548C2212yes—
41C11×#547—21no—
42C11×#547C2212yes—
43C11×#547C2211yescharacteristic
44C11×#547C2211yescharacteristic
45C11×#540—21no—
46C11×#540—22no—
47C11×#533—21no—
48C11×#533C2211yescharacteristic
49C11×#532C2211yescharacteristic
50C11×#532C2212yes—
51C11×#529—22no—
52C11×#529C2212yes—
53C11×#529C2211yescharacteristic
54C11×#529C2212yes—
55C11×#520—21no—
56C4×C11×#41—21no—
57C4×C11×#41C2211yescharacteristic
58C4×C11×#41C2211yescharacteristic
59C2×C4×Q8×C11C2212yes—
60C11×#497C2212yes—
61C11×#496C2212yes—
62C11×#494C2211yescharacteristic
63C11×#492C2211yescharacteristic
64C11×#491C2212yes—
65C11×#490C2212yes—
66C11×#487C2211yescharacteristic
67C11×#486C2211yescharacteristic
68C11×#485C2211yescharacteristic
69C11×#484C2212yes—
70C11×#482C2211yescharacteristic
71C11×#481C2212yes—
72C11×#479C2212yes—
73C11×#479C2212yes—
74C11×#479C2211yescharacteristic
75C11×#478C2211yescharacteristic
76C11×#478C2212yes—
77C11×#475C2211yescharacteristic
78C11×#474C2211yescharacteristic
79C11×#470C2212yes—
80C11×#469C2212yes—
81C11×#468C2212yes—
82C11×#468C2212yes—
83C11×#467C2212yes—
84C11×#465C2212yes—
85C11×#464C2212yes—
86C11×#464C2212yes—
87C11×#464C2212yes—
88C11×#464C2212yes—
89C11×#464C2212yes—
90C11×#464C2211yescharacteristic
91C11×#463C2211yescharacteristic
92C11×#463C2212yes—
93C11×#463C2212yes—
94C11×#462C2211yescharacteristic
95C11×#462C2212yes—
96C11×#462C2211yescharacteristic
97C11×#462C2212yes—
98C11×#461C2211yescharacteristic
99C11×#461C2211yescharacteristic
100C11×#460C2212yes—
101C11×#460C2211yescharacteristic
102C11×#460C2212yes—
103C11×#459C2211yescharacteristic
104C11×#452C2212yes—
105C11×#452C2212yes—
106C11×#452C2212yes—
107C11×#452C2212yes—
108C11×#452C2211yescharacteristic
109C11×#451C2212yes—
110C11×#449C2212yes—
111C11×#449C2212yes—
112C11×#449C2211yescharacteristic
113C11×#448C2212yes—
114C11×#446C2211yescharacteristic
115C11×#446C2211yescharacteristic
116C11×#441C2212yes—
117C11×#441C2212yes—
118C11×#440C2212yes—
119C11×#440C2212yes—
120C4×C11×Q16C2211yescharacteristic
121C4×C11×SD16C2211yescharacteristic
122C4×C11×SD16C2211yescharacteristic
123C4×C11×D8C2211yescharacteristic
124C11×#436C2211yescharacteristic
125C11×#436C2211yescharacteristic
126C11×#435C2212yes—
127C11×#435C2212yes—
128C11×#432C2212yes—
129C11×#431C2211yescharacteristic
130C11×#423C2212yes—
131C2×C11×C4⋊C8C2211yescharacteristic
132C11×#417C2212yes—
133C11×#417C2212yes—
134C11×#416C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41D411yescharacteristic
138C2×C11×#41C2311yescharacteristic
139C2×C11×#41C2312yes—
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C22×Q8×C11C2312yes—
143C11×#137—44no—
144C11×#137—44no—
145C11×#135—44no—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2311yescharacteristic
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2312yes—
150C2×C11×Q16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2311yescharacteristic
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2311yescharacteristic
157C2×C11×SD16C2312yes—
158C2×C11×D8C2311yescharacteristic
159C2×C11×D8C2312yes—
160C2×C11×M16C2312yes—
161C2×C11×M16C2312yes—
162C22×C8×C11C2312yes—
163C11×C4⋊Q8—21no—
164C11×C4⋊Q8—21no—
165C11×C4⋊Q8C2312yes—
166C11×C4⋊Q8C2311yescharacteristic
167C11×C4⋊Q8C2311yescharacteristic
168C11×C4⋊Q8C2311yescharacteristic
169C11×#127—21no—
170C11×#127—22no—
171C11×#127C2312yes—
172C11×#127C2311yescharacteristic
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—22no—
176C11×#126—21no—
177C11×#126—22no—
178C11×#125—22no—
179C11×#125—22no—
180C11×#125—21no—
181C11×#125—22no—
182C11×#125—21no—
183C11×#125C2312yes—
184C11×#125C2311yescharacteristic
185C11×#124—22no—
186C11×#124C2312yes—
187C11×#124C2311yescharacteristic
188C11×#124C2312yes—
189C11×#123—22no—
190C11×#123—22no—
191C11×#123—21no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×C22⋊Q8—21no—
198C11×C22⋊Q8—21no—
199C11×C22⋊Q8—21no—
200C11×C22⋊Q8—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2311yescharacteristic
204C11×C22⋊Q8C2312yes—
205C11×C22⋊Q8C2312yes—
206C11×#121—22no—
207C11×#121—21no—
208C11×#121—22no—
209C11×#121—22no—
210C11×#121—21no—
211C11×#121—21no—
212C11×#121—22no—
213C11×#121—21no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121—22no—
218C11×#121C2312yes—
219C11×#121C2312yes—
220C11×#121C2311yescharacteristic
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11—22no—
224C4×Q8×C11—22no—
225C4×Q8×C11—21no—
226C4×Q8×C11D411yescharacteristic
227C4×Q8×C11C2311yescharacteristic
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2312yes—
230C4×Q8×C11C2312yes—
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2311yescharacteristic
235C4×D4×C11—21no—
236C4×D4×C11—22no—
237C4×D4×C11—21no—
238C4×D4×C11—21no—
239C4×D4×C11—21no—
240C4×D4×C11—22no—
241C4×D4×C11—22no—
242C4×D4×C11—21no—
243C4×D4×C11—22no—
244C4×D4×C11—21no—
245C4×D4×C11—22no—
246C4×D4×C11—21no—
247C4×D4×C11—22no—
248C4×D4×C11D411yescharacteristic
249C4×D4×C11D412yes—
250C4×D4×C11C2311yescharacteristic
251C4×D4×C11C2311yescharacteristic
252C4×D4×C11C2311yescharacteristic
253C4×D4×C11C2312yes—
254C4×D4×C11C2311yescharacteristic
255C4×D4×C11C2312yes—
256C11×#117—21no—
257C11×#117—21no—
258C11×#117—22no—
259C11×#117—21no—
260C11×#117—21no—
261C11×#117—22no—
262C11×#117—22no—
263C11×#117D412yes—
264C11×#117D411yescharacteristic
265C11×#117C2311yescharacteristic
266C2×C11×C4⋊C4—22no—
267C2×C11×C4⋊C4—22no—
268C2×C11×C4⋊C4—21no—
269C2×C11×C4⋊C4C2312yes—
270C2×C42×C11—22no—
271C2×C42×C11—21no—
272C2×C42×C11C2312yes—
273C2×C42×C11C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#107C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2311yescharacteristic
283C11×C4⋊C8C2311yescharacteristic
284C11×C4⋊C8C2312yes—
285C11×C4⋊C8C2312yes—
286C11×C4⋊C8C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2312yes—
297C11×#103C2312yes—
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2312yes—
305C11×#102C2311yescharacteristic
306C11×#102C2311yescharacteristic
307C11×C22⋊C8C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2312yes—
310C11×C22⋊C8C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2311yescharacteristic
314C4×C8×C11C2311yescharacteristic
315#61976C1111yesmaximal, characteristic, direct product factor, Sylow
316C11×#41—22no—
317C11×#41—42no—
318C11×#41—41no—
319C11×#41—42no—
320C11×#41—42no—
321C11×#41—42no—
322C11×#41—42no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—44no—
326C11×#41—44no—
327C2×Q8×C11—22no—
328C2×Q8×C11—21no—
329C2×Q8×C11—24no—
330C2×Q8×C11—42no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2412yes—
335C2×Q8×C11C2411yescharacteristic
336C2×D4×C11—21no—
337C2×D4×C11—22no—
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—22no—
346C2×D4×C11—21no—
347C2×D4×C11C2×D411yescharacteristic
348C2×D4×C11C2×D412yes—
349C2×D4×C11C2412yes—
350C2×D4×C11C2411yescharacteristic
351C2×D4×C11C2411yescharacteristic
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11—21no—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—22no—
358C22×C4×C11—21no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D412yes—
364C22×C4×C11C2×D412yes—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2412yes—
367C22×C4×C11C2411yescharacteristic
368C11×Q16—24no—
369C11×Q16—22no—
370C11×Q16—42no—
371C11×Q16—42no—
372C11×Q16—42no—
373C11×SD16—24no—
374C11×SD16—22no—
375C11×SD16—41no—
376C11×SD16—42no—
377C11×SD16—42no—
378C11×SD16—42no—
379C11×SD16—42no—
380C11×D8—41no—
381C11×D8—42no—
382C11×M16—42no—
383C11×M16—42no—
384C2×C8×C11—42no—
385C2×C8×C11C2411yescharacteristic
386C2×C8×C11C2411yescharacteristic
387C2×C8×C11C2411yescharacteristic
388C2×C8×C11C2411yescharacteristic
389C2×C8×C11C2412yes—
390C2×C8×C11C2412yes—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—21no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—21no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4C2×D412yes—
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2×D412yes—
418C11×C4⋊C4C2411yescharacteristic
419C11×C4⋊C4C2412yes—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C4⋊C4C2411yescharacteristic
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—21no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—22no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4C2×D412yes—
442C11×C22⋊C4C2×D412yes—
443C11×C22⋊C4C2×D412yes—
444C42×C11—21no—
445C42×C11—21no—
446C42×C11—22no—
447C42×C11—22no—
448C42×C11—21no—
449C42×C11—22no—
450C42×C11—22no—
451C42×C11—21no—
452C42×C11C2×D411yescharacteristic
453C42×C11C2×D412yes—
454C42×C11C2×D411yescharacteristic
455C42×C11C2×D412yes—
456C42×C11C2411yescharacteristic
457C42×C11C2412yes—
458C42×C11C2411yescharacteristic
459#3517C2×C1111yescharacteristic, complemented
460#3482C2×C1111yescharacteristic, complemented
461#3398C2×C1111yescharacteristic, complemented
462#3397C2×C1111yescharacteristic, complemented
463#3374C2×C1111yescharacteristic, complemented
464#3368C2×C1111yescharacteristic, complemented
465#3332C2×C1111yescharacteristic, complemented
466#3330C2×C1111yescharacteristic, complemented
467#3317C2×C1112yescomplemented
468#3315C2×C1112yescomplemented
469#3278C2×C1111yescharacteristic, complemented
470#3276C2×C1111yescharacteristic, complemented
471#3271C2×C1112yescomplemented
472#3269C2×C1112yescomplemented
473#3256C2×C1112yescomplemented
474#3248C2×C1111yescharacteristic, complemented
475#3219C2×C1112yescomplemented
476#3210C2×C1111yescharacteristic, complemented
477#3117C2×C1112yescomplemented
478#3102C2×C1111yescharacteristic, complemented
479#3037C2×C1112yescomplemented
480#3035C2×C1111yescharacteristic, complemented
481#2989C2×C1111yescharacteristic, complemented
482C23×C11—21no—
483C23×C11—22no—
484C23×C11—21no—
485C23×C11C22×D411yescharacteristic
486C23×C11C22×D412yes—
487Q8×C11—22no—
488Q8×C11—21no—
489Q8×C11—22no—
490Q8×C11—22no—
491Q8×C11—21no—
492Q8×C11—22no—
493Q8×C11—21no—
494Q8×C11—22no—
495Q8×C11—44no—
496Q8×C11—42no—
497Q8×C11H(5,𝔽2)12yes—
498D4×C11—22no—
499D4×C11—21no—
500D4×C11—22no—
501D4×C11—21no—
502D4×C11—21no—
503D4×C11—21no—
504D4×C11—22no—
505D4×C11—42no—
506D4×C11—42no—
507D4×C11—44no—
508D4×C11—44no—
509D4×C11—42no—
510D4×C11—82no—
511D4×C11—81no—
512D4×C11—81no—
513D4×C11—82no—
514D4×C11—82no—
515D4×C11—82no—
516D4×C11—82no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—42no—
532C2×C4×C11—41no—
533C2×C4×C11—42no—
534C2×C4×C11—42no—
535C2×C4×C11—44no—
536C2×C4×C11—42no—
537C2×C4×C11—44no—
538C2×C4×C11—44no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—82no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D412yes—
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C22×D412yes—
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2511yescharacteristic
553C8×C11—22no—
554C8×C11—22no—
555C8×C11—21no—
556C8×C11—21no—
557C8×C11—21no—
558C8×C11—21no—
559C2×#137C22×C1112yes—
560C2×#137C22×C1112yes—
561C2×#135C22×C1112yes—
562#557C22×C1111yescharacteristic
563#557C22×C1111yescharacteristic
564#556—21no—
565#556C22×C1111yescharacteristic
566#553—22no—
567#553—21no—
568#552—22no—
569#552C22×C1112yes—
570#550—21no—
571#550C22×C1111yescharacteristic
572#550C22×C1112yes—
573#550C22×C1111yescharacteristic
574D4×Q8C22×C1111yescharacteristic
575#548C22×C1112yes—
576#547—21no—
577#547C22×C1111yescharacteristic
578#547C22×C1112yes—
579#547C22×C1111yescharacteristic
580#540—21no—
581#540—22no—
582#533—21no—
583#533C22×C1111yescharacteristic
584#532C22×C1111yescharacteristic
585#532C22×C1112yes—
586#529—22no—
587#529C22×C1111yescharacteristic
588#529C22×C1112yes—
589#529C22×C1112yes—
590#520—21no—
591C4×#41—21no—
592C4×#41C22×C1111yescharacteristic
593C4×#41C22×C1111yescharacteristic
594C2×C4×Q8C22×C1112yes—
595#497C22×C1112yes—
596#496C22×C1112yes—
597#494C22×C1111yescharacteristic
598#492C22×C1111yescharacteristic
599#491C22×C1112yes—
600#490C22×C1112yes—
601#487C22×C1111yescharacteristic
602#486C22×C1111yescharacteristic
603#485C22×C1111yescharacteristic
604#484C22×C1112yes—
605#482C22×C1111yescharacteristic
606#481C22×C1112yes—
607#479C22×C1111yescharacteristic
608#479C22×C1112yes—
609#479C22×C1112yes—
610#478C22×C1111yescharacteristic
611#478C22×C1112yes—
612#475C22×C1111yescharacteristic
613#474C22×C1111yescharacteristic
614#470C22×C1112yes—
615#469C22×C1112yes—
616#468C22×C1112yes—
617#468C22×C1112yes—
618#467C22×C1112yes—
619#465C22×C1112yes—
620#464C22×C1111yescharacteristic
621#464C22×C1112yes—
622#464C22×C1112yes—
623#464C22×C1112yes—
624#464C22×C1112yes—
625#464C22×C1112yes—
626#463C22×C1111yescharacteristic
627#463C22×C1112yes—
628#463C22×C1112yes—
629#462C22×C1112yes—
630#462C22×C1111yescharacteristic
631#462C22×C1111yescharacteristic
632#462C22×C1112yes—
633#461C22×C1111yescharacteristic
634#461C22×C1111yescharacteristic
635#460C22×C1112yes—
636#460C22×C1111yescharacteristic
637#460C22×C1112yes—
638#459C22×C1111yescharacteristic
639#452C22×C1111yescharacteristic
640#452C22×C1112yes—
641#452C22×C1112yes—
642#452C22×C1112yes—
643#452C22×C1112yes—
644#451C22×C1112yes—
645#449C22×C1112yes—
646#449C22×C1112yes—
647#449C22×C1111yescharacteristic
648#448C22×C1112yes—
649#446C22×C1111yescharacteristic
650#446C22×C1111yescharacteristic
651#441C22×C1112yes—
652#441C22×C1112yes—
653#440C22×C1112yes—
654#440C22×C1112yes—
655C4×Q16C22×C1111yescharacteristic
656C4×SD16C22×C1111yescharacteristic
657C4×SD16C22×C1111yescharacteristic
658C4×D8C22×C1111yescharacteristic
659#436C22×C1111yescharacteristic
660#436C22×C1111yescharacteristic
661#435C22×C1112yes—
662#435C22×C1112yes—
663#432C22×C1112yes—
664#431C22×C1111yescharacteristic
665#423C22×C1112yes—
666C2×C4⋊C8C22×C1111yescharacteristic
667#417C22×C1112yes—
668#417C22×C1112yes—
669#416C22×C1112yes—
670C22×C11—21no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—21no—
674C22×C11—21no—
675C22×C11—22no—
676C22×C11—41no—
677C22×C11—42no—
678C22×C11—41no—
679C22×C11—41no—
680C22×C11—42no—
681C22×C11—41no—
682C22×C11—42no—
683C22×C11—41no—
684C22×C11—41no—
685C22×C11C23×D411yescharacteristic
686C4×C11—21no—
687C4×C11—22no—
688C4×C11—21no—
689C4×C11—21no—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11—21no—
693C4×C11—22no—
694C4×C11—41no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—42no—
698C4×C11—41no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11#57512yes—
703C4×C11C2×H(5,𝔽2)11yescharacteristic
704C4×C11#58511yescharacteristic
705C2×#41—21no—
706C2×#41—21no—
707C2×#41D4×C1111yescharacteristic
708C2×#41C23×C1111yescharacteristic
709C2×#41C23×C1112yes—
710C2×#41C23×C1112yes—
711C2×#41C23×C1112yes—
712C22×Q8C23×C1112yes—
713#137—44no—
714#137—44no—
715#135—44no—
716C2×Q16C23×C1112yes—
717C2×Q16C23×C1111yescharacteristic
718C2×Q16C23×C1112yes—
719C2×Q16C23×C1112yes—
720C2×Q16C23×C1112yes—
721C2×SD16C23×C1112yes—
722C2×SD16C23×C1111yescharacteristic
723C2×SD16C23×C1112yes—
724C2×SD16C23×C1112yes—
725C2×SD16C23×C1112yes—
726C2×SD16C23×C1111yescharacteristic
727C2×SD16C23×C1112yes—
728C2×D8C23×C1112yes—
729C2×D8C23×C1111yescharacteristic
730C2×M16C23×C1112yes—
731C2×M16C23×C1112yes—
732C22×C8C23×C1112yes—
733C4⋊Q8—21no—
734C4⋊Q8—21no—
735C4⋊Q8C23×C1111yescharacteristic
736C4⋊Q8C23×C1112yes—
737C4⋊Q8C23×C1111yescharacteristic
738C4⋊Q8C23×C1111yescharacteristic
739#127—21no—
740#127—22no—
741#127C23×C1111yescharacteristic
742#127C23×C1112yes—
743#126—22no—
744#126—22no—
745#126—22no—
746#126—21no—
747#126—22no—
748#125—22no—
749#125—22no—
750#125—21no—
751#125—22no—
752#125—21no—
753#125C23×C1111yescharacteristic
754#125C23×C1112yes—
755#124—22no—
756#124C23×C1111yescharacteristic
757#124C23×C1112yes—
758#124C23×C1112yes—
759#123—22no—
760#123—22no—
761#123—21no—
762#123—22no—
763#123—22no—
764#123—22no—
765#123—22no—
766#123—22no—
767C22⋊Q8—21no—
768C22⋊Q8—21no—
769C22⋊Q8—21no—
770C22⋊Q8—22no—
771C22⋊Q8—22no—
772C22⋊Q8C23×C1112yes—
773C22⋊Q8C23×C1111yescharacteristic
774C22⋊Q8C23×C1112yes—
775C22⋊Q8C23×C1112yes—
776#121—22no—
777#121—21no—
778#121—22no—
779#121—22no—
780#121—21no—
781#121—21no—
782#121—22no—
783#121—21no—
784#121—22no—
785#121—22no—
786#121—22no—
787#121—22no—
788#121C23×C1112yes—
789#121C23×C1112yes—
790#121C23×C1111yescharacteristic
791C4×Q8—21no—
792C4×Q8—21no—
793C4×Q8—22no—
794C4×Q8—22no—
795C4×Q8—21no—
796C4×Q8D4×C1111yescharacteristic
797C4×Q8C23×C1111yescharacteristic
798C4×Q8C23×C1112yes—
799C4×Q8C23×C1112yes—
800C4×Q8C23×C1112yes—
801C4×Q8C23×C1111yescharacteristic
802C4×Q8C23×C1111yescharacteristic
803C4×Q8C23×C1112yes—
804C4×Q8C23×C1111yescharacteristic
805C4×D4—21no—
806C4×D4—22no—
807C4×D4—21no—
808C4×D4—21no—
809C4×D4—21no—
810C4×D4—22no—
811C4×D4—22no—
812C4×D4—21no—
813C4×D4—22no—
814C4×D4—21no—
815C4×D4—22no—
816C4×D4—21no—
817C4×D4—22no—
818C4×D4D4×C1111yescharacteristic
819C4×D4D4×C1112yes—
820C4×D4C23×C1111yescharacteristic
821C4×D4C23×C1111yescharacteristic
822C4×D4C23×C1111yescharacteristic
823C4×D4C23×C1112yes—
824C4×D4C23×C1111yescharacteristic
825C4×D4C23×C1112yes—
826#117—21no—
827#117—21no—
828#117—22no—
829#117—21no—
830#117—21no—
831#117—22no—
832#117—22no—
833#117D4×C1112yes—
834#117D4×C1111yescharacteristic
835#117C23×C1111yescharacteristic
836C2×C4⋊C4—22no—
837C2×C4⋊C4—22no—
838C2×C4⋊C4—21no—
839C2×C4⋊C4C23×C1112yes—
840C2×C42—22no—
841C2×C42—21no—
842C2×C42C23×C1112yes—
843C2×C42C23×C1111yescharacteristic
844#107C23×C1111yescharacteristic
845#107C23×C1111yescharacteristic
846#107C23×C1112yes—
847#106C23×C1111yescharacteristic
848#106C23×C1111yescharacteristic
849#106C23×C1112yes—
850C4⋊C8C23×C1112yes—
851C4⋊C8C23×C1111yescharacteristic
852C4⋊C8C23×C1111yescharacteristic
853C4⋊C8C23×C1111yescharacteristic
854C4⋊C8C23×C1112yes—
855C4⋊C8C23×C1112yes—
856C4⋊C8C23×C1111yescharacteristic
857#103C23×C1112yes—
858#103C23×C1112yes—
859#103C23×C1111yescharacteristic
860#103C23×C1112yes—
861#103C23×C1112yes—
862#103C23×C1111yescharacteristic
863#103C23×C1111yescharacteristic
864#103C23×C1111yescharacteristic
865#103C23×C1112yes—
866#103C23×C1112yes—
867#103C23×C1112yes—
868#102C23×C1112yes—
869#102C23×C1112yes—
870#102C23×C1111yescharacteristic
871#102C23×C1112yes—
872#102C23×C1112yes—
873#102C23×C1111yescharacteristic
874#102C23×C1111yescharacteristic
875#102C23×C1111yescharacteristic
876#102C23×C1112yes—
877C22⋊C8C23×C1111yescharacteristic
878C22⋊C8C23×C1111yescharacteristic
879C22⋊C8C23×C1112yes—
880C22⋊C8C23×C1112yes—
881#97C23×C1112yes—
882#97C23×C1112yes—
883C4×C8C23×C1111yescharacteristic
884C4×C8C23×C1111yescharacteristic
885C2×C11—42no—
886C2×C11—41no—
887C2×C11—81no—
888C2×C11—82no—
889C2×C11—81no—
890C2×C11#348811yescharacteristic
891C2×C11C2×#57511yescharacteristic
892C2×C11#358611yescharacteristic
893#41—22no—
894#41—42no—
895#41—41no—
896#41—42no—
897#41—42no—
898#41—42no—
899#41—42no—
900#41—42no—
901#41—42no—
902#41—44no—
903#41—44no—
904C2×Q8—22no—
905C2×Q8—21no—
906C2×Q8—24no—
907C2×Q8—42no—
908C2×Q8C2×D4×C1111yescharacteristic
909C2×Q8C24×C1112yes—
910C2×Q8C24×C1111yescharacteristic
911C2×Q8C24×C1112yes—
912C2×Q8C24×C1111yescharacteristic
913C2×D4—21no—
914C2×D4—22no—
915C2×D4—21no—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—22no—
923C2×D4—21no—
924C2×D4C2×D4×C1111yescharacteristic
925C2×D4C2×D4×C1112yes—
926C2×D4C24×C1112yes—
927C2×D4C24×C1111yescharacteristic
928C2×D4C24×C1111yescharacteristic
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—22no—
935C22×C4—21no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4C2×D4×C1111yescharacteristic
940C22×C4C2×D4×C1112yes—
941C22×C4C2×D4×C1112yes—
942C22×C4C2×D4×C1111yescharacteristic
943C22×C4C24×C1112yes—
944C22×C4C24×C1111yescharacteristic
945Q16—24no—
946Q16—22no—
947Q16—42no—
948Q16—42no—
949Q16—42no—
950SD16—24no—
951SD16—22no—
952SD16—42no—
953SD16—42no—
954SD16—42no—
955SD16—42no—
956SD16—41no—
957D8—42no—
958D8—41no—
959M16—42no—
960M16—42no—
961C2×C8—42no—
962C2×C8C24×C1111yescharacteristic
963C2×C8C24×C1111yescharacteristic
964C2×C8C24×C1111yescharacteristic
965C2×C8C24×C1111yescharacteristic
966C2×C8C24×C1112yes—
967C2×C8C24×C1112yes—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—22no—
984C4⋊C4—21no—
985C4⋊C4—22no—
986C4⋊C4—21no—
987C4⋊C4—22no—
988C4⋊C4—21no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4C2×D4×C1112yes—
992C4⋊C4C2×D4×C1111yescharacteristic
993C4⋊C4C2×D4×C1111yescharacteristic
994C4⋊C4C2×D4×C1112yes—
995C4⋊C4C24×C1111yescharacteristic
996C4⋊C4C24×C1112yes—
997C4⋊C4C24×C1111yescharacteristic
998C4⋊C4C24×C1111yescharacteristic
999C4⋊C4C24×C1111yescharacteristic
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—21no—
1003C22⋊C4—21no—
1004C22⋊C4—22no—
1005C22⋊C4—21no—
1006C22⋊C4—22no—
1007C22⋊C4—21no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—21no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—21no—
1018C22⋊C4C2×D4×C1112yes—
1019C22⋊C4C2×D4×C1112yes—
1020C22⋊C4C2×D4×C1112yes—
1021C42—21no—
1022C42—21no—
1023C42—22no—
1024C42—22no—
1025C42—21no—
1026C42—22no—
1027C42—22no—
1028C42—21no—
1029C42C2×D4×C1111yescharacteristic
1030C42C2×D4×C1112yes—
1031C42C2×D4×C1111yescharacteristic
1032C42C2×D4×C1112yes—
1033C42C24×C1111yescharacteristic
1034C42C24×C1112yes—
1035C42C24×C1111yescharacteristic
1036C11#6197611yescharacteristic, direct product factor, Sylow
1037C23—21no—
1038C23—22no—
1039C23—21no—
1040C23C22×D4×C1111yescharacteristic
1041C23C22×D4×C1112yes—
1042Q8—22no—
1043Q8—21no—
1044Q8—22no—
1045Q8—22no—
1046Q8—21no—
1047Q8—22no—
1048Q8—21no—
1049Q8—22no—
1050Q8—44no—
1051Q8—42no—
1052Q8C11×H(5,𝔽2)12yes—
1053D4—22no—
1054D4—21no—
1055D4—22no—
1056D4—21no—
1057D4—21no—
1058D4—21no—
1059D4—22no—
1060D4—42no—
1061D4—42no—
1062D4—44no—
1063D4—44no—
1064D4—42no—
1065D4—82no—
1066D4—81no—
1067D4—81no—
1068D4—82no—
1069D4—82no—
1070D4—82no—
1071D4—82no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—42no—
1087C2×C4—41no—
1088C2×C4—42no—
1089C2×C4—42no—
1090C2×C4—44no—
1091C2×C4—42no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4C22×D4×C1111yescharacteristic
1100C2×C4C22×D4×C1112yes—
1101C2×C4C22×D4×C1111yescharacteristic
1102C2×C4C22×D4×C1112yes—
1103C2×C4C22×D4×C1111yescharacteristic
1104C2×C4C22×D4×C1112yes—
1105C2×C4C22×D4×C1111yescharacteristic
1106C2×C4C22×D4×C1111yescharacteristic
1107C2×C4C25×C1111yescharacteristic
1108C8—22no—
1109C8—22no—
1110C8—21no—
1111C8—21no—
1112C8—21no—
1113C8—21no—
1114C22—22no—
1115C22—21no—
1116C22—21no—
1117C22—22no—
1118C22—21no—
1119C22—22no—
1120C22—41no—
1121C22—42no—
1122C22—41no—
1123C22—42no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22C23×D4×C1111yescharacteristic
1130C4—21no—
1131C4—22no—
1132C4—22no—
1133C4—21no—
1134C4—22no—
1135C4—21no—
1136C4—22no—
1137C4—21no—
1138C4—42no—
1139C4—42no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4C11×#57512yes—
1147C4C2×C11×H(5,𝔽2)11yescharacteristic
1148C4C11×#58511yescharacteristic
1149C2—42no—
1150C2—41no—
1151C2—81no—
1152C2—82no—
1153C2—81no—
1154C2C11×#348811yescharacteristic
1155C2C2×C11×#57511yescharacteristic
1156C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3517C2semidirect
2. C11×#3482C2semidirect
3. C11×#3398C2semidirect
4. C11×#3397C2semidirect
5. C11×#3374C2semidirect
6. C11×#3368C2semidirect
7. C11×#3332C2semidirect
8. C11×#3330C2semidirect
9. C11×#3317C2semidirect
10. C11×#3315C2semidirect
11. C11×#3278C2semidirect
12. C11×#3276C2semidirect
13. C11×#3271C2semidirect
14. C11×#3269C2semidirect
15. C11×#3256C2semidirect
16. C11×#3248C2semidirect
17. C11×#3219C2semidirect
18. C11×#3210C2semidirect
19. C11×#3117C2semidirect
20. C11×#3102C2semidirect
21. C11×#3037C2semidirect
22. C11×#3035C2semidirect
23. C11×#2989C2semidirect
315. #61976C11direct (N × H)
459. #3517C2×C11semidirect
460. #3482C2×C11semidirect
461. #3398C2×C11semidirect
462. #3397C2×C11semidirect
463. #3374C2×C11semidirect
464. #3368C2×C11semidirect
465. #3332C2×C11semidirect
466. #3330C2×C11semidirect
467. #3317C2×C11semidirect
468. #3315C2×C11semidirect
469. #3278C2×C11semidirect
470. #3276C2×C11semidirect
471. #3271C2×C11semidirect
472. #3269C2×C11semidirect
473. #3256C2×C11semidirect
474. #3248C2×C11semidirect
475. #3219C2×C11semidirect
476. #3210C2×C11semidirect
477. #3117C2×C11semidirect
478. #3102C2×C11semidirect
479. #3037C2×C11semidirect
480. #3035C2×C11semidirect
481. #2989C2×C11semidirect
1036. C11#61976direct (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×#34822
C11×#33982
C11×#33972
C11×#33742
C11×#33682
C11×#33322
C11×#33302
C11×#33172
C11×#33152
C11×#32782
C11×#32762
C11×#32712
C11×#32692
C11×#32562
C11×#32482
C11×#32192
C11×#32102
C11×#31172
C11×#31022
C11×#30372
C11×#30352
C11×#29892
#6197611