Finite Group Databasebeta

← C11×#61993 #14639186

Subgroups — C11×#61993 #14639186

Order 2816.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3475C211yesmaximal, characteristic, complemented
3C11×#3398C211yesmaximal, characteristic, complemented
4C11×#3397C211yesmaximal, characteristic, complemented
5C11×#3372C211yesmaximal, characteristic, complemented
6C11×#3366C211yesmaximal, characteristic, complemented
7C11×#3317C212yesmaximal, complemented
8C11×#3315C212yesmaximal, complemented
9C11×#3305C211yesmaximal, characteristic, complemented
10C11×#3303C211yesmaximal, characteristic, complemented
11C11×#3284C211yesmaximal, characteristic, complemented
12C11×#3283C211yesmaximal, characteristic, complemented
13C11×#3268C212yesmaximal, complemented
14C11×#3267C212yesmaximal, complemented
15C11×#3252C211yesmaximal, characteristic, complemented
16C11×#3250C212yesmaximal, complemented
17C11×#3219C212yesmaximal, complemented
18C11×#3210C211yesmaximal, characteristic, complemented
19C11×#3111C212yesmaximal, complemented
20C11×#3105C211yesmaximal, characteristic, complemented
21C11×#3036C211yesmaximal, characteristic, complemented
22C11×#3035C212yesmaximal, complemented
23C11×#2990C211yesmaximal, characteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2212yes—
25C2×C11×#135C2212yes—
26C2×C11×#135C2212yes—
27C11×#557C2211yescharacteristic, complemented
28C11×#556C2211yescharacteristic
29C11×#555C2211yescharacteristic
30C11×#554C2211yescharacteristic
31C11×#553—21no—
32C11×#553—22no—
33C11×#553—21no—
34C11×#552—21no—
35C11×#552C2212yes—
36C11×#551—22no—
37C11×#550—21no—
38C11×#550C2212yes—
39C11×#550C2211yescharacteristic, complemented
40C11×#550C2211yescharacteristic, complemented
41C11×#547C2211yescharacteristic
42C11×#547C2212yes—
43C11×#547C2211yescharacteristic, complemented
44C11×#546C2212yes—
45C11×#540—21no—
46C11×#540—22no—
47C11×#533C2211yescharacteristic
48C11×#532C2211yescharacteristic
49C11×#532C2212yescomplemented
50C11×#529—22no—
51C11×#529C2212yes—
52C11×#529C2211yescharacteristic
53C11×#529C2212yescomplemented
54C11×#525—21no—
55C11×#520—21no—
56C4×C11×#41C2212yes—
57C4×C11×#41C2211yescharacteristic
58C2×C4×D4×C11C2211yescharacteristic
59C2×C11×#117—21no—
60C11×#497C2212yes—
61C11×#496C2212yes—
62C11×#494C2211yescharacteristic, complemented
63C11×#492C2211yescharacteristic, complemented
64C11×#491C2212yescomplemented
65C11×#490C2212yescomplemented
66C11×#487C2211yescharacteristic, complemented
67C11×#486C2211yescharacteristic, complemented
68C11×#485C2212yescomplemented
69C11×#484C2211yescharacteristic
70C11×#482C2212yescomplemented
71C11×#481C2211yescharacteristic
72C11×#479C2212yescomplemented
73C11×#479C2212yescomplemented
74C11×#478C2211yescharacteristic
75C11×#478C2211yescharacteristic
76C11×#478C2212yescomplemented
77C11×#477C2211yescharacteristic, complemented
78C11×#476C2211yescharacteristic, complemented
79C11×#470C2212yes—
80C11×#468C2212yes—
81C11×#467C2212yescomplemented
82C11×#466C2212yes—
83C11×#465C2212yes—
84C11×#465C2212yescomplemented
85C11×#464C2212yes—
86C11×#464C2212yescomplemented
87C11×#464C2212yescomplemented
88C11×#464C2212yescomplemented
89C11×#463C2211yescharacteristic
90C11×#463C2212yes—
91C11×#463C2212yes—
92C11×#463C2211yescharacteristic
93C11×#463C2212yes—
94C11×#462C2211yescharacteristic, complemented
95C11×#462C2212yescomplemented
96C11×#461C2212yes—
97C11×#461C2211yescharacteristic
98C11×#461C2211yescharacteristic
99C11×#461C2211yescharacteristic, complemented
100C11×#460C2212yescomplemented
101C11×#459C2212yes—
102C11×#459C2211yescharacteristic
103C11×#459C2211yescharacteristic
104C11×#452C2212yes—
105C11×#452C2212yes—
106C11×#452C2212yes—
107C11×#452C2212yescomplemented
108C11×#452C2212yescomplemented
109C11×#450C2211yescharacteristic
110C11×#449C2212yes—
111C11×#449C2212yes—
112C11×#449C2212yes—
113C11×#447C2211yescharacteristic
114C11×#446C2211yescharacteristic, complemented
115C11×#446C2211yescharacteristic, complemented
116C11×#442C2212yes—
117C11×#441C2212yescomplemented
118C11×#440C2212yes—
119C11×#440C2212yescomplemented
120C4×C11×SD16C2211yescharacteristic
121C4×C11×SD16C2211yescharacteristic
122C4×C11×D8C2211yescharacteristic
123C4×C11×D8C2211yescharacteristic
124C11×#435C2212yes—
125C11×#435C2212yes—
126C8×D4×C11C2211yescharacteristic, complemented
127C8×D4×C11C2211yescharacteristic, complemented
128C11×#432C2212yescomplemented
129C11×#431C2211yescharacteristic
130C11×#423C2211yescharacteristic
131C2×C11×C4⋊C8C2212yescomplemented
132C11×#417C2212yes—
133C11×#416C2212yescomplemented
134C11×#416C2212yescomplemented
135C2×C11×#41—21no—
136C2×C11×#41D411yescharacteristic
137C2×C11×#41C2312yes—
138C2×C11×#41C2312yes—
139C2×C11×#41C2312yes—
140C2×C11×#41C2312yes—
141C22×D4×C11C2311yescharacteristic
142C23×C4×C11—21no—
143C11×AGL(1,ℤ/8)—44no—
144C11×#135—44no—
145C11×#135—44no—
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×SD16C2311yescharacteristic
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2311yescharacteristic
155C2×C11×SD16C2312yes—
156C2×C11×D8C2311yescharacteristic
157C2×C11×D8C2312yes—
158C2×C11×D8C2311yescharacteristic
159C2×C11×D8C2312yes—
160C2×C11×M16C2312yes—
161C22×C8×C11C2312yes—
162C22×C8×C11C2312yes—
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2311yescharacteristic
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2311yescharacteristic
167C11×#127—22no—
168C11×#127—21no—
169C11×#127C2312yes—
170C11×#127C2311yescharacteristic
171C11×#126—22no—
172C11×#126—22no—
173C11×#126—22no—
174C11×#126—21no—
175C11×#126—22no—
176C11×#125—22no—
177C11×#125—21no—
178C11×#125—22no—
179C11×#125—21no—
180C11×#125C2312yes—
181C11×#125C2311yescharacteristic
182C11×#124—22no—
183C11×#124C2312yes—
184C11×#124C2311yescharacteristic
185C11×#124C2312yes—
186C11×#123—22no—
187C11×#123—21no—
188C11×#123—22no—
189C11×#123—22no—
190C11×#123—22no—
191C11×#123—22no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×C22⋊Q8—21no—
196C11×C22⋊Q8—21no—
197C11×C22⋊Q8—21no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8C2311yescharacteristic
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2312yes—
202C11×C22⋊Q8C2312yes—
203C11×#121—21no—
204C11×#121—21no—
205C11×#121—22no—
206C11×#121—21no—
207C11×#121—21no—
208C11×#121—21no—
209C11×#121—22no—
210C11×#121—22no—
211C11×#121—21no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121C2312yes—
218C11×#121C2311yescharacteristic
219C11×#121C2312yes—
220C11×#120—22no—
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11D411yescharacteristic
224C4×Q8×C11C2312yes—
225C4×Q8×C11C2312yes—
226C4×Q8×C11C2311yescharacteristic
227C4×Q8×C11C2312yes—
228C4×Q8×C11C2311yescharacteristic
229C4×D4×C11—22no—
230C4×D4×C11—22no—
231C4×D4×C11—22no—
232C4×D4×C11—21no—
233C4×D4×C11—22no—
234C4×D4×C11—22no—
235C4×D4×C11—21no—
236C4×D4×C11—21no—
237C4×D4×C11—21no—
238C4×D4×C11—21no—
239C4×D4×C11—22no—
240C4×D4×C11—21no—
241C4×D4×C11—22no—
242C4×D4×C11D412yes—
243C4×D4×C11D411yescharacteristic
244C4×D4×C11C2311yescharacteristic
245C4×D4×C11C2311yescharacteristic
246C4×D4×C11C2311yescharacteristic
247C4×D4×C11C2311yescharacteristic
248C4×D4×C11C2312yes—
249C4×D4×C11C2311yescharacteristic
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2311yescharacteristic
253C11×#117—21no—
254C11×#117—21no—
255C11×#117—21no—
256C11×#117—22no—
257C11×#117—22no—
258C11×#117—22no—
259C11×#117—21no—
260C11×#117—22no—
261C11×#117D411yescharacteristic
262C11×#117D412yes—
263C11×#117C2312yes—
264C2×C11×C4⋊C4—21no—
265C2×C11×C4⋊C4—21no—
266C2×C11×C4⋊C4—22no—
267C2×C11×C4⋊C4—21no—
268C2×C11×C4⋊C4C2311yescharacteristic
269C2×C11×C22⋊C4—21no—
270C2×C11×C22⋊C4—22no—
271C2×C42×C11—22no—
272C2×C42×C11C2311yescharacteristic
273C2×C42×C11C2312yes—
274C11×#107C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#107C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2312yes—
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×C4⋊C8C2311yescharacteristic
285C11×C4⋊C8C2311yescharacteristic
286C11×C4⋊C8C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2311yescharacteristic
292C11×#103C2312yes—
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#102C2311yescharacteristic
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2311yescharacteristic
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#61993C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—21no—
317C11×#41—24no—
318C11×#41—42no—
319C11×#41—42no—
320C11×#41—42no—
321C11×#41—42no—
322C11×#41—42no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—42no—
326C11×#41—44no—
327C2×Q8×C11—21no—
328C2×Q8×C11C2×D411yescharacteristic
329C2×Q8×C11C2412yes—
330C2×Q8×C11C2411yescharacteristic
331C2×Q8×C11C2412yes—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—21no—
336C2×D4×C11—22no—
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—22no—
342C2×D4×C11—21no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—41no—
346C2×D4×C11C2×D411yescharacteristic
347C2×D4×C11C2×D412yes—
348C2×D4×C11C2412yes—
349C2×D4×C11C2411yescharacteristic
350C2×D4×C11C2411yescharacteristic
351C2×D4×C11C2411yescharacteristic
352C22×C4×C11—21no—
353C22×C4×C11—21no—
354C22×C4×C11—22no—
355C22×C4×C11—21no—
356C22×C4×C11—22no—
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11—22no—
363C22×C4×C11—22no—
364C22×C4×C11—44no—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2×D411yescharacteristic
367C22×C4×C11C2×D412yes—
368C22×C4×C11C2×D412yes—
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2412yes—
371C11×Q16—42no—
372C11×Q16—42no—
373C11×Q16—42no—
374C11×SD16—22no—
375C11×SD16—24no—
376C11×SD16—41no—
377C11×SD16—42no—
378C11×SD16—42no—
379C11×SD16—42no—
380C11×SD16—42no—
381C11×D8—22no—
382C11×D8—24no—
383C11×D8—41no—
384C11×D8—42no—
385C11×M16—42no—
386C2×C8×C11—42no—
387C2×C8×C11—42no—
388C2×C8×C11C2411yescharacteristic
389C2×C8×C11C2411yescharacteristic
390C2×C8×C11C2411yescharacteristic
391C2×C8×C11C2411yescharacteristic
392C2×C8×C11C2412yes—
393C2×C8×C11C2412yes—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—21no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4C2×D411yescharacteristic
415C11×C4⋊C4C2×D411yescharacteristic
416C11×C4⋊C4C2×D412yes—
417C11×C4⋊C4C2×D412yes—
418C11×C4⋊C4C2411yescharacteristic
419C11×C4⋊C4C2411yescharacteristic
420C11×C4⋊C4C2412yes—
421C11×C4⋊C4C2411yescharacteristic
422C11×C4⋊C4C2411yescharacteristic
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—21no—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—22no—
443C11×C22⋊C4—21no—
444C11×C22⋊C4C2×D412yes—
445C11×C22⋊C4C2×D412yes—
446C11×C22⋊C4C2×D412yes—
447C42×C11—22no—
448C42×C11—22no—
449C42×C11—22no—
450C42×C11—22no—
451C42×C11—21no—
452C42×C11C2×D412yes—
453C42×C11C2×D412yes—
454C42×C11C2×D411yescharacteristic
455C42×C11C2×D411yescharacteristic
456C42×C11C2411yescharacteristic
457C42×C11C2412yes—
458C42×C11C2411yescharacteristic
459#3517C2×C1111yescharacteristic, complemented
460#3475C2×C1111yescharacteristic, complemented
461#3398C2×C1111yescharacteristic, complemented
462#3397C2×C1111yescharacteristic, complemented
463#3372C2×C1111yescharacteristic, complemented
464#3366C2×C1111yescharacteristic, complemented
465#3317C2×C1112yescomplemented
466#3315C2×C1112yescomplemented
467#3305C2×C1111yescharacteristic, complemented
468#3303C2×C1111yescharacteristic, complemented
469#3284C2×C1111yescharacteristic, complemented
470#3283C2×C1111yescharacteristic, complemented
471#3268C2×C1112yescomplemented
472#3267C2×C1112yescomplemented
473#3252C2×C1111yescharacteristic, complemented
474#3250C2×C1112yescomplemented
475#3219C2×C1112yescomplemented
476#3210C2×C1111yescharacteristic, complemented
477#3111C2×C1112yescomplemented
478#3105C2×C1111yescharacteristic, complemented
479#3036C2×C1111yescharacteristic, complemented
480#3035C2×C1112yescomplemented
481#2990C2×C1111yescharacteristic, complemented
482C23×C11—21no—
483C23×C11—21no—
484C23×C11—22no—
485C23×C11—21no—
486C23×C11—42no—
487C23×C11—42no—
488C23×C11—81no—
489C23×C11C22×D411yescharacteristic
490C23×C11C22×D412yes—
491Q8×C11—22no—
492Q8×C11—22no—
493Q8×C11—21no—
494Q8×C11—22no—
495Q8×C11—22no—
496Q8×C11—21no—
497Q8×C11—22no—
498Q8×C11—81no—
499D4×C11—22no—
500D4×C11—22no—
501D4×C11—21no—
502D4×C11—21no—
503D4×C11—21no—
504D4×C11—21no—
505D4×C11—21no—
506D4×C11—22no—
507D4×C11—42no—
508D4×C11—42no—
509D4×C11—44no—
510D4×C11—44no—
511D4×C11—42no—
512D4×C11—82no—
513D4×C11—81no—
514D4×C11—82no—
515D4×C11—82no—
516D4×C11—81no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11—82no—
520D4×C11H(5,𝔽2)12yes—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—42no—
535C2×C4×C11—41no—
536C2×C4×C11—42no—
537C2×C4×C11—44no—
538C2×C4×C11—42no—
539C2×C4×C11—42no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—42no—
544C2×C4×C11—42no—
545C2×C4×C11—82no—
546C2×C4×C11—82no—
547C2×C4×C11—82no—
548C2×C4×C11—82no—
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D412yes—
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C2511yescharacteristic
558C8×C11—21no—
559C8×C11—21no—
560C8×C11—22no—
561C8×C11—22no—
562C8×C11—21no—
563C8×C11—21no—
564C2×AGL(1,ℤ/8)C22×C1112yes—
565C2×#135C22×C1112yes—
566C2×#135C22×C1112yes—
567#557C22×C1111yescharacteristic, complemented
568#556C22×C1111yescharacteristic
569#555C22×C1111yescharacteristic
570#554C22×C1111yescharacteristic
571#553—21no—
572#553—22no—
573#553—21no—
574#552—21no—
575#552C22×C1112yes—
576#551—22no—
577#550—21no—
578#550C22×C1112yes—
579#550C22×C1111yescharacteristic, complemented
580#550C22×C1111yescharacteristic, complemented
581#547C22×C1111yescharacteristic
582#547C22×C1112yes—
583#547C22×C1111yescharacteristic, complemented
584#546C22×C1112yes—
585#540—21no—
586#540—22no—
587#533C22×C1111yescharacteristic
588#532C22×C1111yescharacteristic
589#532C22×C1112yescomplemented
590#529—22no—
591#529C22×C1111yescharacteristic
592#529C22×C1112yes—
593#529C22×C1112yescomplemented
594#525—21no—
595#520—21no—
596C4×#41C22×C1112yes—
597C4×#41C22×C1111yescharacteristic
598C2×C4×D4C22×C1111yescharacteristic
599C2×#117—21no—
600#497C22×C1112yes—
601#496C22×C1112yes—
602#494C22×C1111yescharacteristic, complemented
603#492C22×C1111yescharacteristic, complemented
604#491C22×C1112yescomplemented
605#490C22×C1112yescomplemented
606#487C22×C1111yescharacteristic, complemented
607#486C22×C1111yescharacteristic, complemented
608#485C22×C1112yescomplemented
609#484C22×C1111yescharacteristic
610#482C22×C1112yescomplemented
611#481C22×C1111yescharacteristic
612#479C22×C1112yescomplemented
613#479C22×C1112yescomplemented
614#478C22×C1111yescharacteristic
615#478C22×C1111yescharacteristic
616#478C22×C1112yescomplemented
617#477C22×C1111yescharacteristic, complemented
618#476C22×C1111yescharacteristic, complemented
619#470C22×C1112yes—
620#468C22×C1112yes—
621#467C22×C1112yescomplemented
622#466C22×C1112yes—
623#465C22×C1112yes—
624#465C22×C1112yescomplemented
625#464C22×C1112yes—
626#464C22×C1112yescomplemented
627#464C22×C1112yescomplemented
628#464C22×C1112yescomplemented
629#463C22×C1111yescharacteristic
630#463C22×C1111yescharacteristic
631#463C22×C1112yes—
632#463C22×C1112yes—
633#463C22×C1112yes—
634#462C22×C1111yescharacteristic, complemented
635#462C22×C1112yescomplemented
636#461C22×C1112yes—
637#461C22×C1111yescharacteristic
638#461C22×C1111yescharacteristic
639#461C22×C1111yescharacteristic, complemented
640#460C22×C1112yescomplemented
641#459C22×C1112yes—
642#459C22×C1111yescharacteristic
643#459C22×C1111yescharacteristic
644#452C22×C1112yes—
645#452C22×C1112yes—
646#452C22×C1112yes—
647#452C22×C1112yescomplemented
648#452C22×C1112yescomplemented
649#450C22×C1111yescharacteristic
650#449C22×C1112yes—
651#449C22×C1112yes—
652#449C22×C1112yes—
653#447C22×C1111yescharacteristic
654#446C22×C1111yescharacteristic, complemented
655#446C22×C1111yescharacteristic, complemented
656#442C22×C1112yes—
657#441C22×C1112yescomplemented
658#440C22×C1112yes—
659#440C22×C1112yescomplemented
660C4×SD16C22×C1111yescharacteristic
661C4×SD16C22×C1111yescharacteristic
662C4×D8C22×C1111yescharacteristic
663C4×D8C22×C1111yescharacteristic
664#435C22×C1112yes—
665#435C22×C1112yes—
666C8×D4C22×C1111yescharacteristic, complemented
667C8×D4C22×C1111yescharacteristic, complemented
668#432C22×C1112yescomplemented
669#431C22×C1111yescharacteristic
670#423C22×C1111yescharacteristic
671C2×C4⋊C8C22×C1112yescomplemented
672#417C22×C1112yes—
673#416C22×C1112yescomplemented
674#416C22×C1112yescomplemented
675C22×C11—22no—
676C22×C11—21no—
677C22×C11—22no—
678C22×C11—21no—
679C22×C11—22no—
680C22×C11—21no—
681C22×C11—22no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11—41no—
685C22×C11—42no—
686C22×C11—41no—
687C22×C11—42no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—42no—
692C22×C11—41no—
693C22×C11—84no—
694C22×C11C23×D411yescharacteristic
695C4×C11—21no—
696C4×C11—22no—
697C4×C11—21no—
698C4×C11—22no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11—42no—
703C4×C11—41no—
704C4×C11—42no—
705C4×C11—42no—
706C4×C11—41no—
707C4×C11—41no—
708C4×C11—41no—
709C4×C11—41no—
710C4×C11#57512yes—
711C4×C11C2×H(5,𝔽2)11yescharacteristic
712C4×C11#58511yescharacteristic
713C2×#41—21no—
714C2×#41D4×C1111yescharacteristic
715C2×#41C23×C1112yes—
716C2×#41C23×C1112yes—
717C2×#41C23×C1112yes—
718C2×#41C23×C1112yes—
719C22×D4C23×C1111yescharacteristic
720C23×C4—21no—
721AGL(1,ℤ/8)—44no—
722#135—44no—
723#135—44no—
724C2×Q16C23×C1112yes—
725C2×Q16C23×C1112yes—
726C2×Q16C23×C1112yes—
727C2×SD16C23×C1111yescharacteristic
728C2×SD16C23×C1112yes—
729C2×SD16C23×C1112yes—
730C2×SD16C23×C1112yes—
731C2×SD16C23×C1112yes—
732C2×SD16C23×C1111yescharacteristic
733C2×SD16C23×C1112yes—
734C2×D8C23×C1111yescharacteristic
735C2×D8C23×C1112yes—
736C2×D8C23×C1112yes—
737C2×D8C23×C1111yescharacteristic
738C2×M16C23×C1112yes—
739C22×C8C23×C1112yes—
740C22×C8C23×C1112yes—
741C4⋊Q8C23×C1111yescharacteristic
742C4⋊Q8C23×C1112yes—
743C4⋊Q8C23×C1111yescharacteristic
744C4⋊Q8C23×C1111yescharacteristic
745#127—22no—
746#127—21no—
747#127C23×C1111yescharacteristic
748#127C23×C1112yes—
749#126—22no—
750#126—22no—
751#126—22no—
752#126—21no—
753#126—22no—
754#125—22no—
755#125—21no—
756#125—22no—
757#125—21no—
758#125C23×C1111yescharacteristic
759#125C23×C1112yes—
760#124—22no—
761#124C23×C1111yescharacteristic
762#124C23×C1112yes—
763#124C23×C1112yes—
764#123—22no—
765#123—21no—
766#123—22no—
767#123—22no—
768#123—22no—
769#123—22no—
770#123—22no—
771#123—22no—
772#123—22no—
773C22⋊Q8—21no—
774C22⋊Q8—21no—
775C22⋊Q8—21no—
776C22⋊Q8—22no—
777C22⋊Q8C23×C1111yescharacteristic
778C22⋊Q8C23×C1112yes—
779C22⋊Q8C23×C1112yes—
780C22⋊Q8C23×C1112yes—
781#121—21no—
782#121—21no—
783#121—22no—
784#121—21no—
785#121—21no—
786#121—21no—
787#121—22no—
788#121—22no—
789#121—21no—
790#121—22no—
791#121—22no—
792#121—22no—
793#121—22no—
794#121—22no—
795#121C23×C1112yes—
796#121C23×C1111yescharacteristic
797#121C23×C1112yes—
798#120—22no—
799C4×Q8—21no—
800C4×Q8—21no—
801C4×Q8D4×C1111yescharacteristic
802C4×Q8C23×C1112yes—
803C4×Q8C23×C1112yes—
804C4×Q8C23×C1111yescharacteristic
805C4×Q8C23×C1112yes—
806C4×Q8C23×C1111yescharacteristic
807C4×D4—22no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—21no—
811C4×D4—22no—
812C4×D4—22no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—22no—
818C4×D4—21no—
819C4×D4—22no—
820C4×D4D4×C1112yes—
821C4×D4D4×C1111yescharacteristic
822C4×D4C23×C1111yescharacteristic
823C4×D4C23×C1111yescharacteristic
824C4×D4C23×C1111yescharacteristic
825C4×D4C23×C1111yescharacteristic
826C4×D4C23×C1112yes—
827C4×D4C23×C1111yescharacteristic
828C4×D4C23×C1112yes—
829C4×D4C23×C1112yes—
830C4×D4C23×C1111yescharacteristic
831#117—21no—
832#117—21no—
833#117—21no—
834#117—22no—
835#117—22no—
836#117—22no—
837#117—21no—
838#117—22no—
839#117D4×C1111yescharacteristic
840#117D4×C1112yes—
841#117C23×C1112yes—
842C2×C4⋊C4—21no—
843C2×C4⋊C4—21no—
844C2×C4⋊C4—22no—
845C2×C4⋊C4—21no—
846C2×C4⋊C4C23×C1111yescharacteristic
847C2×C22⋊C4—21no—
848C2×C22⋊C4—22no—
849C2×C42—22no—
850C2×C42C23×C1111yescharacteristic
851C2×C42C23×C1112yes—
852#107C23×C1111yescharacteristic
853#107C23×C1111yescharacteristic
854#107C23×C1112yes—
855#106C23×C1111yescharacteristic
856#106C23×C1111yescharacteristic
857#106C23×C1112yes—
858C4⋊C8C23×C1111yescharacteristic
859C4⋊C8C23×C1112yes—
860C4⋊C8C23×C1112yes—
861C4⋊C8C23×C1112yes—
862C4⋊C8C23×C1111yescharacteristic
863C4⋊C8C23×C1111yescharacteristic
864C4⋊C8C23×C1111yescharacteristic
865#103C23×C1111yescharacteristic
866#103C23×C1112yes—
867#103C23×C1112yes—
868#103C23×C1112yes—
869#103C23×C1112yes—
870#103C23×C1111yescharacteristic
871#103C23×C1112yes—
872#103C23×C1112yes—
873#103C23×C1112yes—
874#102C23×C1111yescharacteristic
875#102C23×C1112yes—
876#102C23×C1112yes—
877#102C23×C1112yes—
878#102C23×C1112yes—
879#102C23×C1111yescharacteristic
880#102C23×C1111yescharacteristic
881#102C23×C1111yescharacteristic
882#102C23×C1111yescharacteristic
883#102C23×C1111yescharacteristic
884#102C23×C1112yes—
885C22⋊C8C23×C1111yescharacteristic
886C22⋊C8C23×C1111yescharacteristic
887C22⋊C8C23×C1112yes—
888C22⋊C8C23×C1112yes—
889#97C23×C1112yes—
890#97C23×C1112yes—
891C4×C8C23×C1111yescharacteristic
892C4×C8C23×C1111yescharacteristic
893C2×C11—42no—
894C2×C11—41no—
895C2×C11—42no—
896C2×C11—82no—
897C2×C11—81no—
898C2×C11—81no—
899C2×C11#348811yescharacteristic
900C2×C11C2×#57511yescharacteristic
901C2×C11#358411yescharacteristic
902C24—21no—
903#41—24no—
904#41—42no—
905#41—42no—
906#41—42no—
907#41—42no—
908#41—42no—
909#41—42no—
910#41—42no—
911#41—42no—
912#41—44no—
913C2×Q8—21no—
914C2×Q8C2×D4×C1111yescharacteristic
915C2×Q8C24×C1112yes—
916C2×Q8C24×C1111yescharacteristic
917C2×Q8C24×C1112yes—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—21no—
927C2×D4—22no—
928C2×D4—21no—
929C2×D4—22no—
930C2×D4—21no—
931C2×D4—41no—
932C2×D4C2×D4×C1111yescharacteristic
933C2×D4C2×D4×C1112yes—
934C2×D4C24×C1112yes—
935C2×D4C24×C1111yescharacteristic
936C2×D4C24×C1111yescharacteristic
937C2×D4C24×C1111yescharacteristic
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—22no—
941C22×C4—21no—
942C22×C4—22no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—44no—
951C22×C4C2×D4×C1111yescharacteristic
952C22×C4C2×D4×C1111yescharacteristic
953C22×C4C2×D4×C1112yes—
954C22×C4C2×D4×C1112yes—
955C22×C4C24×C1111yescharacteristic
956C22×C4C24×C1112yes—
957Q16—42no—
958Q16—42no—
959Q16—42no—
960SD16—22no—
961SD16—24no—
962SD16—42no—
963SD16—42no—
964SD16—42no—
965SD16—42no—
966SD16—41no—
967D8—22no—
968D8—24no—
969D8—42no—
970D8—41no—
971M16—42no—
972C2×C8—42no—
973C2×C8—42no—
974C2×C8C24×C1111yescharacteristic
975C2×C8C24×C1111yescharacteristic
976C2×C8C24×C1111yescharacteristic
977C2×C8C24×C1111yescharacteristic
978C2×C8C24×C1112yes—
979C2×C8C24×C1112yes—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—22no—
994C4⋊C4—21no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—22no—
999C4⋊C4—21no—
1000C4⋊C4C2×D4×C1111yescharacteristic
1001C4⋊C4C2×D4×C1111yescharacteristic
1002C4⋊C4C2×D4×C1112yes—
1003C4⋊C4C2×D4×C1112yes—
1004C4⋊C4C24×C1111yescharacteristic
1005C4⋊C4C24×C1111yescharacteristic
1006C4⋊C4C24×C1112yes—
1007C4⋊C4C24×C1111yescharacteristic
1008C4⋊C4C24×C1111yescharacteristic
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—21no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—21no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—22no—
1021C22⋊C4—21no—
1022C22⋊C4—21no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—21no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—21no—
1030C22⋊C4C2×D4×C1112yes—
1031C22⋊C4C2×D4×C1112yes—
1032C22⋊C4C2×D4×C1112yes—
1033C42—22no—
1034C42—22no—
1035C42—22no—
1036C42—22no—
1037C42—21no—
1038C42C2×D4×C1112yes—
1039C42C2×D4×C1112yes—
1040C42C2×D4×C1111yescharacteristic
1041C42C2×D4×C1111yescharacteristic
1042C42C24×C1111yescharacteristic
1043C42C24×C1112yes—
1044C42C24×C1111yescharacteristic
1045C11#6199311yescharacteristic, direct product factor, Sylow
1046C23—21no—
1047C23—21no—
1048C23—22no—
1049C23—21no—
1050C23—42no—
1051C23—42no—
1052C23—81no—
1053C23C22×D4×C1111yescharacteristic
1054C23C22×D4×C1112yes—
1055Q8—22no—
1056Q8—22no—
1057Q8—21no—
1058Q8—22no—
1059Q8—22no—
1060Q8—21no—
1061Q8—22no—
1062Q8—81no—
1063D4—22no—
1064D4—22no—
1065D4—21no—
1066D4—21no—
1067D4—21no—
1068D4—21no—
1069D4—21no—
1070D4—22no—
1071D4—42no—
1072D4—42no—
1073D4—44no—
1074D4—44no—
1075D4—42no—
1076D4—82no—
1077D4—81no—
1078D4—82no—
1079D4—82no—
1080D4—81no—
1081D4—82no—
1082D4—82no—
1083D4—82no—
1084D4C11×H(5,𝔽2)12yes—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—44no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—44no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—82no—
1112C2×C4—82no—
1113C2×C4C22×D4×C1111yescharacteristic
1114C2×C4C22×D4×C1112yes—
1115C2×C4C22×D4×C1112yes—
1116C2×C4C22×D4×C1112yes—
1117C2×C4C22×D4×C1111yescharacteristic
1118C2×C4C22×D4×C1111yescharacteristic
1119C2×C4C22×D4×C1111yescharacteristic
1120C2×C4C22×D4×C1111yescharacteristic
1121C2×C4C25×C1111yescharacteristic
1122C8—21no—
1123C8—21no—
1124C8—22no—
1125C8—22no—
1126C8—21no—
1127C8—21no—
1128C22—22no—
1129C22—21no—
1130C22—22no—
1131C22—21no—
1132C22—22no—
1133C22—22no—
1134C22—21no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—42no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—41no—
1146C22—84no—
1147C22C23×D4×C1111yescharacteristic
1148C4—22no—
1149C4—21no—
1150C4—21no—
1151C4—22no—
1152C4—21no—
1153C4—22no—
1154C4—21no—
1155C4—42no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—42no—
1162C4—41no—
1163C4C11×#57512yes—
1164C4C2×C11×H(5,𝔽2)11yescharacteristic
1165C4C11×#58511yescharacteristic
1166C2—41no—
1167C2—42no—
1168C2—42no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C11×#348811yescharacteristic
1173C2C2×C11×#57511yescharacteristic
1174C2C11×#358411yescharacteristic
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×#3475C2semidirect
3. C11×#3398C2semidirect
4. C11×#3397C2semidirect
5. C11×#3372C2semidirect
6. C11×#3366C2semidirect
7. C11×#3317C2semidirect
8. C11×#3315C2semidirect
9. C11×#3305C2semidirect
10. C11×#3303C2semidirect
11. C11×#3284C2semidirect
12. C11×#3283C2semidirect
13. C11×#3268C2semidirect
14. C11×#3267C2semidirect
15. C11×#3252C2semidirect
16. C11×#3250C2semidirect
17. C11×#3219C2semidirect
18. C11×#3210C2semidirect
19. C11×#3111C2semidirect
20. C11×#3105C2semidirect
21. C11×#3036C2semidirect
22. C11×#3035C2semidirect
23. C11×#2990C2semidirect
27. C11×#557C22semidirect
39. C11×#550C22semidirect
40. C11×#550C22semidirect
43. C11×#547C22semidirect
49. C11×#532C22semidirect
53. C11×#529C22semidirect
62. C11×#494C22semidirect
63. C11×#492C22semidirect
64. C11×#491C22semidirect
65. C11×#490C22semidirect
66. C11×#487C22semidirect
67. C11×#486C22semidirect
68. C11×#485C22semidirect
70. C11×#482C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
76. C11×#478C22semidirect
77. C11×#477C22semidirect
78. C11×#476C22semidirect
81. C11×#467C22semidirect
84. C11×#465C22semidirect
86. C11×#464C22semidirect
87. C11×#464C22semidirect
88. C11×#464C22semidirect
94. C11×#462C22semidirect
95. C11×#462C22semidirect
99. C11×#461C22semidirect
100. C11×#460C22semidirect
107. C11×#452C22semidirect
108. C11×#452C22semidirect
114. C11×#446C22semidirect
115. C11×#446C22semidirect
117. C11×#441C22semidirect
119. C11×#440C22semidirect
126. C8×D4×C11C22semidirect
127. C8×D4×C11C22semidirect
128. C11×#432C22semidirect
131. C2×C11×C4⋊C8C22semidirect
133. C11×#416C22semidirect
134. C11×#416C22semidirect
315. #61993C11direct (N × H)
459. #3517C2×C11semidirect
460. #3475C2×C11semidirect
461. #3398C2×C11semidirect
462. #3397C2×C11semidirect
463. #3372C2×C11semidirect
464. #3366C2×C11semidirect
465. #3317C2×C11semidirect
466. #3315C2×C11semidirect
467. #3305C2×C11semidirect
468. #3303C2×C11semidirect
469. #3284C2×C11semidirect
470. #3283C2×C11semidirect
471. #3268C2×C11semidirect
472. #3267C2×C11semidirect
473. #3252C2×C11semidirect
474. #3250C2×C11semidirect
475. #3219C2×C11semidirect
476. #3210C2×C11semidirect
477. #3111C2×C11semidirect
478. #3105C2×C11semidirect
479. #3036C2×C11semidirect
480. #3035C2×C11semidirect
481. #2990C2×C11semidirect
567. #557C22×C11semidirect
579. #550C22×C11semidirect
580. #550C22×C11semidirect
583. #547C22×C11semidirect
589. #532C22×C11semidirect
593. #529C22×C11semidirect
602. #494C22×C11semidirect
603. #492C22×C11semidirect
604. #491C22×C11semidirect
605. #490C22×C11semidirect
606. #487C22×C11semidirect
607. #486C22×C11semidirect
608. #485C22×C11semidirect
610. #482C22×C11semidirect
612. #479C22×C11semidirect
613. #479C22×C11semidirect
616. #478C22×C11semidirect
617. #477C22×C11semidirect
618. #476C22×C11semidirect
621. #467C22×C11semidirect
624. #465C22×C11semidirect
626. #464C22×C11semidirect
627. #464C22×C11semidirect
628. #464C22×C11semidirect
634. #462C22×C11semidirect
635. #462C22×C11semidirect
639. #461C22×C11semidirect
640. #460C22×C11semidirect
647. #452C22×C11semidirect
648. #452C22×C11semidirect
654. #446C22×C11semidirect
655. #446C22×C11semidirect
657. #441C22×C11semidirect
659. #440C22×C11semidirect
666. C8×D4C22×C11semidirect
667. C8×D4C22×C11semidirect
668. #432C22×C11semidirect
671. C2×C4⋊C8C22×C11semidirect
673. #416C22×C11semidirect
674. #416C22×C11semidirect
1045. C11#61993direct (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×#34752
C11×#33982
C11×#33972
C11×#33722
C11×#33662
C11×#33172
C11×#33152
C11×#33052
C11×#33032
C11×#32842
C11×#32832
C11×#32682
C11×#32672
C11×#32522
C11×#32502
C11×#32192
C11×#32102
C11×#31112
C11×#31052
C11×#30362
C11×#30352
C11×#29902
#6199311