Finite Group Databasebeta

← C11×#61994 #14639187

Subgroups — C11×#61994 #14639187

Order 2816.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3480C211yesmaximal, characteristic, complemented
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3399C211yesmaximal, characteristic, complemented
5C11×#3374C211yesmaximal, characteristic, complemented
6C11×#3368C211yesmaximal, characteristic, complemented
7C11×#3309C212yesmaximal, complemented
8C11×#3307C212yesmaximal, complemented
9C11×#3304C211yesmaximal, characteristic, complemented
10C11×#3302C211yesmaximal, characteristic, complemented
11C11×#3287C211yesmaximal, characteristic, complemented
12C11×#3284C211yesmaximal, characteristic, complemented
13C11×#3271C212yesmaximal, complemented
14C11×#3269C212yesmaximal, complemented
15C11×#3251C211yesmaximal, characteristic, complemented
16C11×#3250C212yesmaximal, complemented
17C11×#3219C212yesmaximal, complemented
18C11×#3207C211yesmaximal, characteristic, complemented
19C11×#3111C212yesmaximal, complemented
20C11×#3108C211yesmaximal, characteristic, complemented
21C11×#3037C211yesmaximal, characteristic, complemented
22C11×#3035C212yesmaximal, complemented
23C11×#2990C211yesmaximal, characteristic, complemented
24C2×C11×#137C2212yes—
25C2×C11×#135C2212yes—
26C2×C11×#135C2212yes—
27C11×#559—21no—
28C11×#559C2211yescharacteristic
29C11×#557C2211yescharacteristic
30C11×#557C2211yescharacteristic
31C11×#556—21no—
32C11×#556C2211yescharacteristic
33C11×#553—22no—
34C11×#553—21no—
35C11×#553—22no—
36C11×#553C2212yes—
37C11×#550—21no—
38C11×#550C2211yescharacteristic
39C11×#550C2212yes—
40C11×#550C2211yescharacteristic
41C11×#550C2211yescharacteristic
42C11×#548C2212yes—
43C11×#547C2212yes—
44C11×#547C2211yescharacteristic
45C11×#540—22no—
46C11×#540—21no—
47C11×#532—21no—
48C11×#532C2211yescharacteristic
49C11×#532C2212yes—
50C11×#532C2211yescharacteristic
51C11×#529—22no—
52C11×#529C2212yes—
53C11×#529C2212yes—
54C11×#529C2211yescharacteristic
55C11×#520—21no—
56C4×C11×#41—21no—
57C4×C11×#41C2212yes—
58C4×C11×#41C2211yescharacteristic
59C2×C4×Q8×C11C2211yescharacteristic
60C11×#497C2212yes—
61C11×#496C2212yes—
62C11×#493C2211yescharacteristic
63C11×#492C2211yescharacteristic
64C11×#491C2212yes—
65C11×#490C2212yes—
66C11×#487C2211yescharacteristic
67C11×#486C2211yescharacteristic
68C11×#485C2212yes—
69C11×#483C2211yescharacteristic
70C11×#482C2212yes—
71C11×#480C2211yescharacteristic
72C11×#479C2211yescharacteristic
73C11×#479C2212yes—
74C11×#479C2211yescharacteristic
75C11×#478C2212yes—
76C11×#478C2212yes—
77C11×#475C2211yescharacteristic
78C11×#474C2211yescharacteristic
79C11×#469C2212yes—
80C11×#468C2212yes—
81C11×#467C2212yes—
82C11×#466C2212yes—
83C11×#465C2212yes—
84C11×#465C2212yes—
85C11×#464C2211yescharacteristic
86C11×#464C2212yes—
87C11×#464C2212yes—
88C11×#464C2211yescharacteristic
89C11×#464C2212yes—
90C11×#463C2212yes—
91C11×#463C2212yes—
92C11×#463C2212yes—
93C11×#463C2212yes—
94C11×#462C2212yes—
95C11×#462C2211yescharacteristic
96C11×#462C2211yescharacteristic
97C11×#461C2212yes—
98C11×#460C2211yescharacteristic
99C11×#460C2212yes—
100C11×#460C2211yescharacteristic
101C11×#460C2211yescharacteristic
102C11×#459C2211yescharacteristic
103C11×#459C2212yes—
104C11×#452C2212yes—
105C11×#452C2212yes—
106C11×#452C2212yes—
107C11×#451C2211yescharacteristic
108C11×#449C2212yes—
109C11×#449C2212yes—
110C11×#449C2212yes—
111C11×#449C2212yes—
112C11×#449C2212yes—
113C11×#448C2211yescharacteristic
114C11×#446C2211yescharacteristic
115C11×#446C2211yescharacteristic
116C11×#442C2212yes—
117C11×#441C2212yes—
118C11×#440C2212yes—
119C11×#440C2212yes—
120C4×C11×Q16C2211yescharacteristic
121C4×C11×Q16C2211yescharacteristic
122C4×C11×SD16C2211yescharacteristic
123C4×C11×SD16C2211yescharacteristic
124C11×#435C2212yes—
125C11×#435C2212yes—
126C8×D4×C11C2211yescharacteristic
127C8×D4×C11C2211yescharacteristic
128C11×#432C2212yes—
129C11×#431C2211yescharacteristic
130C11×#423C2211yescharacteristic
131C2×C11×C4⋊C8C2212yes—
132C11×#417C2212yes—
133C11×#416C2212yes—
134C11×#416C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41D411yescharacteristic
138C2×C11×#41C2312yes—
139C2×C11×#41C2312yes—
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C22×Q8×C11C2311yescharacteristic
143C11×#137—44no—
144C11×#135—44no—
145C11×#135—44no—
146C2×C11×Q16C2311yescharacteristic
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2311yescharacteristic
149C2×C11×Q16C2312yes—
150C2×C11×SD16C2311yescharacteristic
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2311yescharacteristic
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×D8C2312yes—
158C2×C11×D8C2312yes—
159C2×C11×D8C2312yes—
160C2×C11×M16C2312yes—
161C22×C8×C11C2312yes—
162C22×C8×C11C2312yes—
163C11×C4⋊Q8—21no—
164C11×C4⋊Q8C2312yes—
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2311yescharacteristic
167C11×#127—21no—
168C11×#127—21no—
169C11×#127—22no—
170C11×#127C2312yes—
171C11×#127C2311yescharacteristic
172C11×#127C2311yescharacteristic
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—22no—
176C11×#126—21no—
177C11×#126—22no—
178C11×#125—22no—
179C11×#125—21no—
180C11×#125—22no—
181C11×#125C2312yes—
182C11×#125C2311yescharacteristic
183C11×#124—21no—
184C11×#124—21no—
185C11×#124—22no—
186C11×#124—21no—
187C11×#124C2312yes—
188C11×#124C2312yes—
189C11×#124C2311yescharacteristic
190C11×#123—21no—
191C11×#123—22no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8C2311yescharacteristic
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2312yes—
202C11×#121—22no—
203C11×#121—22no—
204C11×#121—21no—
205C11×#121—22no—
206C11×#121—21no—
207C11×#121—22no—
208C11×#121—21no—
209C11×#121—22no—
210C11×#121—21no—
211C11×#121—21no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121C2311yescharacteristic
218C11×#121C2312yes—
219C11×#121C2312yes—
220C11×#121C2312yes—
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11—21no—
224C4×Q8×C11—21no—
225C4×Q8×C11—21no—
226C4×Q8×C11D411yescharacteristic
227C4×Q8×C11C2311yescharacteristic
228C4×Q8×C11C2311yescharacteristic
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2312yes—
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2311yescharacteristic
235C4×D4×C11—22no—
236C4×D4×C11—22no—
237C4×D4×C11—22no—
238C4×D4×C11—21no—
239C4×D4×C11—22no—
240C4×D4×C11—21no—
241C4×D4×C11—21no—
242C4×D4×C11—21no—
243C4×D4×C11—22no—
244C4×D4×C11—22no—
245C4×D4×C11—22no—
246C4×D4×C11—22no—
247C4×D4×C11—21no—
248C4×D4×C11—21no—
249C4×D4×C11—22no—
250C4×D4×C11—21no—
251C4×D4×C11D412yes—
252C4×D4×C11D411yescharacteristic
253C4×D4×C11C2312yes—
254C4×D4×C11C2312yes—
255C4×D4×C11C2311yescharacteristic
256C4×D4×C11C2312yes—
257C4×D4×C11C2312yes—
258C4×D4×C11C2311yescharacteristic
259C11×#117—22no—
260C11×#117—22no—
261C11×#117—22no—
262C11×#117—21no—
263C11×#117D411yescharacteristic
264C11×#117D412yes—
265C11×#117C2312yes—
266C2×C11×C4⋊C4—21no—
267C2×C11×C4⋊C4—21no—
268C2×C11×C4⋊C4—22no—
269C2×C11×C4⋊C4C2311yescharacteristic
270C2×C42×C11—21no—
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×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2311yescharacteristic
297C11×#103C2311yescharacteristic
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2311yescharacteristic
303C11×#102C2312yes—
304C11×#102C2312yes—
305C11×#102C2312yes—
306C11×#102C2312yes—
307C11×C22⋊C8C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2312yes—
310C11×C22⋊C8C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2311yescharacteristic
314C4×C8×C11C2311yescharacteristic
315#61994C1111yesmaximal, characteristic, direct product factor, Sylow
316C11×#41—24no—
317C11×#41—42no—
318C11×#41—42no—
319C11×#41—44no—
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×C11—21no—
329C2×Q8×C11—22no—
330C2×Q8×C11—41no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2411yescharacteristic
333C2×Q8×C11C2412yes—
334C2×Q8×C11C2411yescharacteristic
335C2×Q8×C11C2411yescharacteristic
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—22no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11—21no—
346C2×D4×C11—21no—
347C2×D4×C11—22no—
348C2×D4×C11—21no—
349C2×D4×C11—21no—
350C2×D4×C11C2×D411yescharacteristic
351C2×D4×C11C2×D412yes—
352C2×D4×C11C2411yescharacteristic
353C2×D4×C11C2412yes—
354C2×D4×C11C2412yes—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—22no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—21no—
361C22×C4×C11—22no—
362C22×C4×C11—22no—
363C22×C4×C11—22no—
364C22×C4×C11—22no—
365C22×C4×C11C2×D411yescharacteristic
366C22×C4×C11C2×D411yescharacteristic
367C22×C4×C11C2×D412yes—
368C22×C4×C11C2×D412yes—
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2412yes—
371C11×Q16—22no—
372C11×Q16—24no—
373C11×Q16—41no—
374C11×Q16—42no—
375C11×SD16—22no—
376C11×SD16—24no—
377C11×SD16—42no—
378C11×SD16—41no—
379C11×SD16—42no—
380C11×SD16—42no—
381C11×SD16—42no—
382C11×D8—42no—
383C11×D8—42no—
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—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4—21no—
411C11×C4⋊C4—22no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4C2×D411yescharacteristic
415C11×C4⋊C4C2×D412yes—
416C11×C4⋊C4C2×D411yescharacteristic
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—21no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
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—21no—
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#3480C2×C1111yescharacteristic, complemented
461#3400C2×C1111yescharacteristic, complemented
462#3399C2×C1111yescharacteristic, complemented
463#3374C2×C1111yescharacteristic, complemented
464#3368C2×C1111yescharacteristic, complemented
465#3309C2×C1112yescomplemented
466#3307C2×C1112yescomplemented
467#3304C2×C1111yescharacteristic, complemented
468#3302C2×C1111yescharacteristic, complemented
469#3287C2×C1111yescharacteristic, complemented
470#3284C2×C1111yescharacteristic, complemented
471#3271C2×C1112yescomplemented
472#3269C2×C1112yescomplemented
473#3251C2×C1111yescharacteristic, complemented
474#3250C2×C1112yescomplemented
475#3219C2×C1112yescomplemented
476#3207C2×C1111yescharacteristic, complemented
477#3111C2×C1112yescomplemented
478#3108C2×C1111yescharacteristic, complemented
479#3037C2×C1111yescharacteristic, complemented
480#3035C2×C1112yescomplemented
481#2990C2×C1111yescharacteristic, complemented
482C23×C11—22no—
483C23×C11—21no—
484C23×C11—22no—
485C23×C11C22×D412yes—
486C23×C11C22×D411yescharacteristic
487Q8×C11—22no—
488Q8×C11—21no—
489Q8×C11—21no—
490Q8×C11—21no—
491Q8×C11—22no—
492Q8×C11—21no—
493Q8×C11—22no—
494Q8×C11—21no—
495Q8×C11—42no—
496Q8×C11—42no—
497Q8×C11H(5,𝔽2)12yes—
498D4×C11—22no—
499D4×C11—21no—
500D4×C11—22no—
501D4×C11—22no—
502D4×C11—22no—
503D4×C11—22no—
504D4×C11—21no—
505D4×C11—42no—
506D4×C11—44no—
507D4×C11—44no—
508D4×C11—44no—
509D4×C11—42no—
510D4×C11—42no—
511D4×C11—82no—
512D4×C11—81no—
513D4×C11—81no—
514D4×C11—82no—
515D4×C11—81no—
516D4×C11—82no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11—82no—
520C2×C4×C11—21no—
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—21no—
529C2×C4×C11—22no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—22no—
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—44no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11—82no—
545C2×C4×C11—82no—
546C2×C4×C11—81no—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D412yes—
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C2511yescharacteristic
556C8×C11—21no—
557C8×C11—21no—
558C8×C11—22no—
559C8×C11—22no—
560C8×C11—21no—
561C8×C11—21no—
562C2×#137C22×C1112yes—
563C2×#135C22×C1112yes—
564C2×#135C22×C1112yes—
565#559—21no—
566#559C22×C1111yescharacteristic
567#557C22×C1111yescharacteristic
568#557C22×C1111yescharacteristic
569#556—21no—
570#556C22×C1111yescharacteristic
571#553—22no—
572#553—21no—
573#553—22no—
574#553C22×C1112yes—
575#550—21no—
576#550C22×C1111yescharacteristic
577#550C22×C1112yes—
578#550C22×C1111yescharacteristic
579#550C22×C1111yescharacteristic
580#548C22×C1112yes—
581#547C22×C1112yes—
582#547C22×C1111yescharacteristic
583#540—22no—
584#540—21no—
585#532—21no—
586#532C22×C1111yescharacteristic
587#532C22×C1112yes—
588#532C22×C1111yescharacteristic
589#529—22no—
590#529C22×C1111yescharacteristic
591#529C22×C1112yes—
592#529C22×C1112yes—
593#520—21no—
594C4×#41—21no—
595C4×#41C22×C1112yes—
596C4×#41C22×C1111yescharacteristic
597C2×C4×Q8C22×C1111yescharacteristic
598#497C22×C1112yes—
599#496C22×C1112yes—
600#493C22×C1111yescharacteristic
601#492C22×C1111yescharacteristic
602#491C22×C1112yes—
603#490C22×C1112yes—
604#487C22×C1111yescharacteristic
605#486C22×C1111yescharacteristic
606#485C22×C1112yes—
607#483C22×C1111yescharacteristic
608#482C22×C1112yes—
609#480C22×C1111yescharacteristic
610#479C22×C1111yescharacteristic
611#479C22×C1111yescharacteristic
612#479C22×C1112yes—
613#478C22×C1112yes—
614#478C22×C1112yes—
615#475C22×C1111yescharacteristic
616#474C22×C1111yescharacteristic
617#469C22×C1112yes—
618#468C22×C1112yes—
619#467C22×C1112yes—
620#466C22×C1112yes—
621#465C22×C1112yes—
622#465C22×C1112yes—
623#464C22×C1111yescharacteristic
624#464C22×C1111yescharacteristic
625#464C22×C1112yes—
626#464C22×C1112yes—
627#464C22×C1112yes—
628#463C22×C1112yes—
629#463C22×C1112yes—
630#463C22×C1112yes—
631#463C22×C1112yes—
632#462C22×C1112yes—
633#462C22×C1111yescharacteristic
634#462C22×C1111yescharacteristic
635#461C22×C1112yes—
636#460C22×C1112yes—
637#460C22×C1111yescharacteristic
638#460C22×C1111yescharacteristic
639#460C22×C1111yescharacteristic
640#459C22×C1111yescharacteristic
641#459C22×C1112yes—
642#452C22×C1112yes—
643#452C22×C1112yes—
644#452C22×C1112yes—
645#451C22×C1111yescharacteristic
646#449C22×C1112yes—
647#449C22×C1112yes—
648#449C22×C1112yes—
649#449C22×C1112yes—
650#449C22×C1112yes—
651#448C22×C1111yescharacteristic
652#446C22×C1111yescharacteristic
653#446C22×C1111yescharacteristic
654#442C22×C1112yes—
655#441C22×C1112yes—
656#440C22×C1112yes—
657#440C22×C1112yes—
658C4×Q16C22×C1111yescharacteristic
659C4×Q16C22×C1111yescharacteristic
660C4×SD16C22×C1111yescharacteristic
661C4×SD16C22×C1111yescharacteristic
662#435C22×C1112yes—
663#435C22×C1112yes—
664C8×D4C22×C1111yescharacteristic
665C8×D4C22×C1111yescharacteristic
666#432C22×C1112yes—
667#431C22×C1111yescharacteristic
668#423C22×C1111yescharacteristic
669C2×C4⋊C8C22×C1112yes—
670#417C22×C1112yes—
671#416C22×C1112yes—
672#416C22×C1112yes—
673C22×C11—21no—
674C22×C11—22no—
675C22×C11—21no—
676C22×C11—22no—
677C22×C11—21no—
678C22×C11—22no—
679C22×C11—42no—
680C22×C11—41no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—41no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—42no—
687C22×C11—41no—
688C22×C11C23×D411yescharacteristic
689C4×C11—21no—
690C4×C11—22no—
691C4×C11—21no—
692C4×C11—22no—
693C4×C11—21no—
694C4×C11—22no—
695C4×C11—21no—
696C4×C11—22no—
697C4×C11—41no—
698C4×C11—41no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—41no—
702C4×C11—42no—
703C4×C11—41no—
704C4×C11—42no—
705C4×C11#57512yes—
706C4×C11C2×H(5,𝔽2)11yescharacteristic
707C4×C11#58511yescharacteristic
708C2×#41—21no—
709C2×#41—21no—
710C2×#41D4×C1111yescharacteristic
711C2×#41C23×C1112yes—
712C2×#41C23×C1112yes—
713C2×#41C23×C1112yes—
714C2×#41C23×C1112yes—
715C22×Q8C23×C1111yescharacteristic
716#137—44no—
717#135—44no—
718#135—44no—
719C2×Q16C23×C1111yescharacteristic
720C2×Q16C23×C1112yes—
721C2×Q16C23×C1112yes—
722C2×Q16C23×C1111yescharacteristic
723C2×SD16C23×C1111yescharacteristic
724C2×SD16C23×C1112yes—
725C2×SD16C23×C1112yes—
726C2×SD16C23×C1112yes—
727C2×SD16C23×C1112yes—
728C2×SD16C23×C1111yescharacteristic
729C2×SD16C23×C1112yes—
730C2×D8C23×C1112yes—
731C2×D8C23×C1112yes—
732C2×D8C23×C1112yes—
733C2×M16C23×C1112yes—
734C22×C8C23×C1112yes—
735C22×C8C23×C1112yes—
736C4⋊Q8—21no—
737C4⋊Q8C23×C1112yes—
738C4⋊Q8C23×C1111yescharacteristic
739C4⋊Q8C23×C1111yescharacteristic
740#127—21no—
741#127—21no—
742#127—22no—
743#127C23×C1112yes—
744#127C23×C1111yescharacteristic
745#127C23×C1111yescharacteristic
746#126—22no—
747#126—22no—
748#126—22no—
749#126—21no—
750#126—22no—
751#125—22no—
752#125—21no—
753#125—22no—
754#125C23×C1111yescharacteristic
755#125C23×C1112yes—
756#124—21no—
757#124—21no—
758#124—22no—
759#124—21no—
760#124C23×C1111yescharacteristic
761#124C23×C1112yes—
762#124C23×C1112yes—
763#123—21no—
764#123—22no—
765#123—22no—
766#123—22no—
767#123—22no—
768#123—22no—
769#123—22no—
770#123—22no—
771C22⋊Q8—22no—
772C22⋊Q8C23×C1111yescharacteristic
773C22⋊Q8C23×C1112yes—
774C22⋊Q8C23×C1112yes—
775#121—22no—
776#121—22no—
777#121—21no—
778#121—22no—
779#121—21no—
780#121—22no—
781#121—21no—
782#121—22no—
783#121—21no—
784#121—21no—
785#121—22no—
786#121—22no—
787#121—22no—
788#121—22no—
789#121—22no—
790#121C23×C1111yescharacteristic
791#121C23×C1112yes—
792#121C23×C1112yes—
793#121C23×C1112yes—
794C4×Q8—21no—
795C4×Q8—21no—
796C4×Q8—21no—
797C4×Q8—21no—
798C4×Q8—21no—
799C4×Q8D4×C1111yescharacteristic
800C4×Q8C23×C1111yescharacteristic
801C4×Q8C23×C1111yescharacteristic
802C4×Q8C23×C1111yescharacteristic
803C4×Q8C23×C1111yescharacteristic
804C4×Q8C23×C1112yes—
805C4×Q8C23×C1111yescharacteristic
806C4×Q8C23×C1112yes—
807C4×Q8C23×C1111yescharacteristic
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—21no—
812C4×D4—22no—
813C4×D4—21no—
814C4×D4—21no—
815C4×D4—21no—
816C4×D4—22no—
817C4×D4—22no—
818C4×D4—22no—
819C4×D4—22no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4—22no—
823C4×D4—21no—
824C4×D4D4×C1112yes—
825C4×D4D4×C1111yescharacteristic
826C4×D4C23×C1112yes—
827C4×D4C23×C1112yes—
828C4×D4C23×C1111yescharacteristic
829C4×D4C23×C1112yes—
830C4×D4C23×C1112yes—
831C4×D4C23×C1111yescharacteristic
832#117—22no—
833#117—22no—
834#117—22no—
835#117—21no—
836#117D4×C1111yescharacteristic
837#117D4×C1112yes—
838#117C23×C1112yes—
839C2×C4⋊C4—21no—
840C2×C4⋊C4—21no—
841C2×C4⋊C4—22no—
842C2×C4⋊C4C23×C1111yescharacteristic
843C2×C42—21no—
844C2×C42—22no—
845C2×C42C23×C1111yescharacteristic
846C2×C42C23×C1112yes—
847#107C23×C1111yescharacteristic
848#107C23×C1111yescharacteristic
849#107C23×C1112yes—
850#106C23×C1111yescharacteristic
851#106C23×C1111yescharacteristic
852#106C23×C1112yes—
853C4⋊C8C23×C1111yescharacteristic
854C4⋊C8C23×C1112yes—
855C4⋊C8C23×C1112yes—
856C4⋊C8C23×C1112yes—
857C4⋊C8C23×C1111yescharacteristic
858C4⋊C8C23×C1111yescharacteristic
859C4⋊C8C23×C1111yescharacteristic
860#103C23×C1111yescharacteristic
861#103C23×C1112yes—
862#103C23×C1112yes—
863#103C23×C1112yes—
864#103C23×C1112yes—
865#103C23×C1111yescharacteristic
866#103C23×C1111yescharacteristic
867#103C23×C1111yescharacteristic
868#103C23×C1111yescharacteristic
869#103C23×C1111yescharacteristic
870#103C23×C1112yes—
871#102C23×C1111yescharacteristic
872#102C23×C1112yes—
873#102C23×C1112yes—
874#102C23×C1112yes—
875#102C23×C1112yes—
876#102C23×C1111yescharacteristic
877#102C23×C1112yes—
878#102C23×C1112yes—
879#102C23×C1112yes—
880C22⋊C8C23×C1111yescharacteristic
881C22⋊C8C23×C1111yescharacteristic
882C22⋊C8C23×C1112yes—
883C22⋊C8C23×C1112yes—
884#97C23×C1112yes—
885#97C23×C1112yes—
886C4×C8C23×C1111yescharacteristic
887C4×C8C23×C1111yescharacteristic
888C2×C11—41no—
889C2×C11—42no—
890C2×C11—82no—
891C2×C11—81no—
892C2×C11—82no—
893C2×C11#348811yescharacteristic
894C2×C11C2×#57511yescharacteristic
895C2×C11#358411yescharacteristic
896#41—24no—
897#41—42no—
898#41—42no—
899#41—44no—
900#41—42no—
901#41—42no—
902#41—42no—
903#41—42no—
904#41—42no—
905#41—42no—
906#41—44no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—22no—
910C2×Q8—41no—
911C2×Q8C2×D4×C1111yescharacteristic
912C2×Q8C24×C1111yescharacteristic
913C2×Q8C24×C1112yes—
914C2×Q8C24×C1111yescharacteristic
915C2×Q8C24×C1111yescharacteristic
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—21no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—22no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4C2×D4×C1111yescharacteristic
931C2×D4C2×D4×C1112yes—
932C2×D4C24×C1111yescharacteristic
933C2×D4C24×C1112yes—
934C2×D4C24×C1112yes—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—21no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4C2×D4×C1111yescharacteristic
946C22×C4C2×D4×C1111yescharacteristic
947C22×C4C2×D4×C1112yes—
948C22×C4C2×D4×C1112yes—
949C22×C4C24×C1111yescharacteristic
950C22×C4C24×C1112yes—
951Q16—22no—
952Q16—24no—
953Q16—42no—
954Q16—41no—
955SD16—22no—
956SD16—24no—
957SD16—42no—
958SD16—42no—
959SD16—42no—
960SD16—41no—
961SD16—42no—
962D8—42no—
963D8—42no—
964D8—42no—
965M16—42no—
966C2×C8—42no—
967C2×C8—42no—
968C2×C8C24×C1111yescharacteristic
969C2×C8C24×C1111yescharacteristic
970C2×C8C24×C1111yescharacteristic
971C2×C8C24×C1111yescharacteristic
972C2×C8C24×C1112yes—
973C2×C8C24×C1112yes—
974C4⋊C4—22no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—21no—
988C4⋊C4—22no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4C2×D4×C1111yescharacteristic
995C4⋊C4C2×D4×C1112yes—
996C4⋊C4C2×D4×C1111yescharacteristic
997C4⋊C4C2×D4×C1112yes—
998C4⋊C4C24×C1111yescharacteristic
999C4⋊C4C24×C1111yescharacteristic
1000C4⋊C4C24×C1112yes—
1001C4⋊C4C24×C1111yescharacteristic
1002C4⋊C4C24×C1111yescharacteristic
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—21no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—21no—
1009C22⋊C4—22no—
1010C22⋊C4—21no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—21no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—21no—
1021C22⋊C4C2×D4×C1112yes—
1022C22⋊C4C2×D4×C1112yes—
1023C22⋊C4C2×D4×C1112yes—
1024C42—21no—
1025C42—21no—
1026C42—22no—
1027C42—22no—
1028C42—21no—
1029C42—21no—
1030C42—22no—
1031C42—21no—
1032C42C2×D4×C1112yes—
1033C42C2×D4×C1112yes—
1034C42C2×D4×C1111yescharacteristic
1035C42C2×D4×C1111yescharacteristic
1036C42C24×C1111yescharacteristic
1037C42C24×C1112yes—
1038C42C24×C1111yescharacteristic
1039C11#6199411yescharacteristic, direct product factor, Sylow
1040C23—22no—
1041C23—21no—
1042C23—22no—
1043C23C22×D4×C1112yes—
1044C23C22×D4×C1111yescharacteristic
1045Q8—22no—
1046Q8—21no—
1047Q8—21no—
1048Q8—21no—
1049Q8—22no—
1050Q8—21no—
1051Q8—22no—
1052Q8—21no—
1053Q8—42no—
1054Q8—42no—
1055Q8C11×H(5,𝔽2)12yes—
1056D4—22no—
1057D4—21no—
1058D4—22no—
1059D4—22no—
1060D4—22no—
1061D4—22no—
1062D4—21no—
1063D4—42no—
1064D4—44no—
1065D4—44no—
1066D4—44no—
1067D4—42no—
1068D4—42no—
1069D4—82no—
1070D4—81no—
1071D4—81no—
1072D4—82no—
1073D4—81no—
1074D4—82no—
1075D4—82no—
1076D4—82no—
1077D4—82no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—42no—
1093C2×C4—41no—
1094C2×C4—42no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—42no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—82no—
1103C2×C4—82no—
1104C2×C4—81no—
1105C2×C4C22×D4×C1111yescharacteristic
1106C2×C4C22×D4×C1112yes—
1107C2×C4C22×D4×C1112yes—
1108C2×C4C22×D4×C1112yes—
1109C2×C4C22×D4×C1111yescharacteristic
1110C2×C4C22×D4×C1111yescharacteristic
1111C2×C4C22×D4×C1111yescharacteristic
1112C2×C4C22×D4×C1111yescharacteristic
1113C2×C4C25×C1111yescharacteristic
1114C8—21no—
1115C8—21no—
1116C8—22no—
1117C8—22no—
1118C8—21no—
1119C8—21no—
1120C22—21no—
1121C22—22no—
1122C22—21no—
1123C22—22no—
1124C22—21no—
1125C22—22no—
1126C22—42no—
1127C22—41no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—42no—
1133C22—41no—
1134C22—42no—
1135C22C23×D4×C1111yescharacteristic
1136C4—22no—
1137C4—21no—
1138C4—22no—
1139C4—21no—
1140C4—22no—
1141C4—21no—
1142C4—22no—
1143C4—21no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4C11×#57512yes—
1153C4C2×C11×H(5,𝔽2)11yescharacteristic
1154C4C11×#58511yescharacteristic
1155C2—41no—
1156C2—42no—
1157C2—82no—
1158C2—81no—
1159C2—82no—
1160C2C11×#348811yescharacteristic
1161C2C2×C11×#57511yescharacteristic
1162C2C11×#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×#3480C2semidirect
3. C11×#3400C2semidirect
4. C11×#3399C2semidirect
5. C11×#3374C2semidirect
6. C11×#3368C2semidirect
7. C11×#3309C2semidirect
8. C11×#3307C2semidirect
9. C11×#3304C2semidirect
10. C11×#3302C2semidirect
11. C11×#3287C2semidirect
12. C11×#3284C2semidirect
13. C11×#3271C2semidirect
14. C11×#3269C2semidirect
15. C11×#3251C2semidirect
16. C11×#3250C2semidirect
17. C11×#3219C2semidirect
18. C11×#3207C2semidirect
19. C11×#3111C2semidirect
20. C11×#3108C2semidirect
21. C11×#3037C2semidirect
22. C11×#3035C2semidirect
23. C11×#2990C2semidirect
315. #61994C11direct (N × H)
459. #3517C2×C11semidirect
460. #3480C2×C11semidirect
461. #3400C2×C11semidirect
462. #3399C2×C11semidirect
463. #3374C2×C11semidirect
464. #3368C2×C11semidirect
465. #3309C2×C11semidirect
466. #3307C2×C11semidirect
467. #3304C2×C11semidirect
468. #3302C2×C11semidirect
469. #3287C2×C11semidirect
470. #3284C2×C11semidirect
471. #3271C2×C11semidirect
472. #3269C2×C11semidirect
473. #3251C2×C11semidirect
474. #3250C2×C11semidirect
475. #3219C2×C11semidirect
476. #3207C2×C11semidirect
477. #3111C2×C11semidirect
478. #3108C2×C11semidirect
479. #3037C2×C11semidirect
480. #3035C2×C11semidirect
481. #2990C2×C11semidirect
1039. C11#61994direct (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×#34802
C11×#34002
C11×#33992
C11×#33742
C11×#33682
C11×#33092
C11×#33072
C11×#33042
C11×#33022
C11×#32872
C11×#32842
C11×#32712
C11×#32692
C11×#32512
C11×#32502
C11×#32192
C11×#32072
C11×#31112
C11×#31082
C11×#30372
C11×#30352
C11×#29902
#6199411