Finite Group Databasebeta

← C11×#61923 #14639116

Subgroups — C11×#61923 #14639116

Order 2816.

1696 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic, complemented
2C11×#3509C211yesmaximal, characteristic, complemented
3C11×#3401C212yesmaximal, complemented
4C11×#3400C211yesmaximal, characteristic, complemented
5C11×#3400C212yesmaximal, complemented
6C11×#3397C211yesmaximal, characteristic, complemented
7C11×#3394C211yesmaximal, characteristic, complemented
8C11×#3392C211yesmaximal, characteristic, complemented
9C11×#3376C212yesmaximal, complemented
10C11×#3374C211yesmaximal, characteristic, complemented
11C11×#3372C212yesmaximal, complemented
12C11×#3367C211yesmaximal, characteristic, complemented
13C11×#3364C211yesmaximal, characteristic, complemented
14C11×#3359C211yesmaximal, characteristic, complemented
15C11×#3225C212yesmaximal, complemented
16C11×#3221C212yesmaximal, complemented
17C11×#3218C211yesmaximal, characteristic, complemented
18C11×#3206C211yesmaximal, characteristic, complemented
19C11×#3126C212yesmaximal, complemented
20C11×#3121C212yesmaximal, complemented
21C11×#3115C211yesmaximal, characteristic, complemented
22C11×#3102C211yesmaximal, characteristic, complemented
23C11×#2985C211yesmaximal, characteristic, complemented
24C11×#562—22no—
25C11×#559C2211yescharacteristic
26C11×#559C2212yes—
27C11×#557C2211yescharacteristic
28C11×#557C2212yes—
29C11×#557C2211yescharacteristic
30C11×#557C2211yescharacteristic
31C11×#556C2211yescharacteristic
32C11×#556C2211yescharacteristic
33C11×#556C2212yes—
34C11×#554C2212yes—
35C11×#552—21no—
36C11×#552—21no—
37C11×#552—22no—
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40C11×#548—21no—
41C11×#547—21no—
42C11×#542—21no—
43C11×#542C2212yes—
44C11×#541—22no—
45C11×#540C2212yes—
46C11×#539—22no—
47C11×#536—21no—
48C11×#536C2212yes—
49C11×#533—21no—
50C11×#533—21no—
51C11×#533C2211yescharacteristic
52C11×#532C2211yescharacteristic
53C2×C11×C4⋊Q8C2211yescharacteristic
54C11×#529C2211yescharacteristic
55C11×#519C2212yes—
56C4×C11×#41C2211yescharacteristic
57C11×#497C2212yes—
58C11×#497C2212yes—
59C11×#496C2212yes—
60C11×#495C2212yes—
61C11×#492C2211yescharacteristic
62C11×#492C2211yescharacteristic
63C11×#492C2212yes—
64C11×#491C2212yes—
65C11×#491C2212yes—
66C11×#489C2212yes—
67C11×#488C2212yes—
68C11×#487C2211yescharacteristic
69C11×#487C2211yescharacteristic
70C11×#487C2212yes—
71C11×#485C2211yescharacteristic
72C11×#482C2211yescharacteristic
73C11×#482C2212yes—
74C11×#479C2211yescharacteristic
75C11×#479C2212yes—
76C11×#479C2212yes—
77C11×#478C2211yescharacteristic
78C11×#477C2212yes—
79C11×#475C2211yescharacteristic
80C11×#475C2212yes—
81C11×#474C2211yescharacteristic
82C11×#464C2212yes—
83C11×#464C2211yescharacteristic
84C11×#464C2212yes—
85C11×#464C2212yes—
86C11×#463C2212yes—
87C11×#463C2212yes—
88C11×#463C2212yes—
89C11×#463C2211yescharacteristic
90C11×#462C2211yescharacteristic
91C11×#462C2211yescharacteristic
92C11×#462C2212yes—
93C11×#461C2212yes—
94C11×#461C2212yes—
95C11×#461C2211yescharacteristic
96C11×#461C2211yescharacteristic
97C11×#461C2212yes—
98C11×#461C2212yes—
99C11×#461C2212yes—
100C11×#460C2211yescharacteristic
101C11×#460C2212yes—
102C11×#460C2212yes—
103C11×#459C2211yescharacteristic
104C11×#452C2211yescharacteristic
105C11×#451C2212yes—
106C11×#449C2211yescharacteristic
107C11×#449C2212yes—
108C11×#448C2212yes—
109C11×#448C2212yes—
110C11×#448C2212yes—
111C11×#446C2211yescharacteristic
112C11×#446C2212yes—
113C11×#446C2211yescharacteristic
114C11×#446C2212yes—
115C8×Q8×C11C2211yescharacteristic
116C8×Q8×C11C2211yescharacteristic
117C11×#442C2212yes—
118C11×#441C2212yes—
119C11×#440C2212yes—
120C11×#440C2212yes—
121C11×#440C2212yes—
122C11×#440C2212yes—
123C4×C11×Q16C2211yescharacteristic
124C4×C11×Q16C2212yes—
125C4×C11×SD16C2211yescharacteristic
126C4×C11×SD16C2211yescharacteristic
127C4×C11×SD16C2212yes—
128C4×C11×SD16C2212yes—
129C4×C11×SD16C2212yes—
130C4×C11×D8C2211yescharacteristic
131C11×#433C2212yes—
132C11×#433C2212yes—
133C11×#432C2211yescharacteristic
134C11×#431C2211yescharacteristic
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41C2311yescharacteristic
138C22×Q8×C11—21no—
139C22×Q8×C11C2312yes—
140C2×C11×Q16C2312yes—
141C2×C11×Q16C2312yes—
142C2×C11×Q16C2311yescharacteristic
143C2×C11×SD16C2312yes—
144C2×C11×SD16C2311yescharacteristic
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2311yescharacteristic
151C2×C11×SD16C2312yes—
152C2×C11×D8C2312yes—
153C2×C11×D8C2311yescharacteristic
154C11×C4⋊Q8—21no—
155C11×C4⋊Q8—21no—
156C11×C4⋊Q8—21no—
157C11×C4⋊Q8D411yescharacteristic
158C11×C4⋊Q8D411yescharacteristic
159C11×C4⋊Q8C2312yes—
160C11×C4⋊Q8C2312yes—
161C11×C4⋊Q8C2311yescharacteristic
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2312yes—
165C11×C4⋊Q8C2311yescharacteristic
166C11×#127C2311yescharacteristic
167C11×#127C2312yes—
168C11×#126—22no—
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#126—21no—
174C11×#125—21no—
175C11×#125—21no—
176C11×#125—22no—
177C11×#125—22no—
178C11×#125—22no—
179C11×#125—22no—
180C11×#125—22no—
181C11×#125—22no—
182C11×#125D412yes—
183C11×#125C2311yescharacteristic
184C11×#125C2312yes—
185C11×#124—21no—
186C11×#124—22no—
187C11×#124—22no—
188C11×#124—21no—
189C11×#124C2312yes—
190C11×#124C2312yes—
191C11×#124C2312yes—
192C11×#124C2311yescharacteristic
193C11×#123—21no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123—22no—
198C11×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×#123—22no—
202C11×C22⋊Q8—21no—
203C11×C22⋊Q8—21no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8—22no—
207C11×C22⋊Q8—22no—
208C11×C22⋊Q8—22no—
209C11×C22⋊Q8—22no—
210C11×C22⋊Q8—22no—
211C11×C22⋊Q8—22no—
212C11×C22⋊Q8—21no—
213C11×C22⋊Q8D411yescharacteristic
214C11×C22⋊Q8D411yescharacteristic
215C11×C22⋊Q8D412yes—
216C11×C22⋊Q8C2311yescharacteristic
217C11×#121—21no—
218C11×#121—22no—
219C11×#121—21no—
220C11×#121—22no—
221C11×#121—22no—
222C11×#121C2311yescharacteristic
223C11×#121C2312yes—
224C4×Q8×C11—21no—
225C4×Q8×C11—21no—
226C4×Q8×C11—22no—
227C4×Q8×C11—22no—
228C4×Q8×C11—22no—
229C4×Q8×C11—21no—
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2312yes—
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2312yes—
235C4×Q8×C11C2312yes—
236C4×Q8×C11C2311yescharacteristic
237C4×Q8×C11C2312yes—
238C4×Q8×C11C2311yescharacteristic
239C4×Q8×C11C2311yescharacteristic
240C4×Q8×C11C2312yes—
241C4×D4×C11—21no—
242C4×D4×C11—21no—
243C4×D4×C11—21no—
244C4×D4×C11—22no—
245C4×D4×C11—21no—
246C4×D4×C11—21no—
247C4×D4×C11C2311yescharacteristic
248C4×D4×C11C2311yescharacteristic
249C4×D4×C11C2311yescharacteristic
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2312yes—
254C11×#117—21no—
255C11×#117—21no—
256C11×#117—22no—
257C11×#117—22no—
258C11×#117—22no—
259C11×#117—21no—
260C11×#117—21no—
261C11×#117C2311yescharacteristic
262C11×#117C2312yes—
263C2×C11×C4⋊C4—21no—
264C2×C11×C4⋊C4—21no—
265C2×C11×C4⋊C4—22no—
266C2×C42×C11—21no—
267C2×C42×C11C2311yescharacteristic
268C11×#107C2311yescharacteristic
269C11×#107C2312yes—
270C11×#107C2311yescharacteristic
271C11×#106C2311yescharacteristic
272C11×#106C2311yescharacteristic
273C11×#106C2312yes—
274C11×C4⋊C8C2311yescharacteristic
275C11×C4⋊C8C2311yescharacteristic
276C11×C4⋊C8C2311yescharacteristic
277C11×C4⋊C8C2311yescharacteristic
278C11×C4⋊C8C2312yes—
279C11×C4⋊C8C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2312yes—
282C11×#103C2312yes—
283C11×#103C2312yes—
284C11×#103C2312yes—
285C11×#103C2311yescharacteristic
286C11×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#103C2312yes—
295C11×#102C2311yescharacteristic
296C11×#102C2312yes—
297C11×#102C2311yescharacteristic
298C11×#102C2311yescharacteristic
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2311yescharacteristic
302C11×C22⋊C8C2311yescharacteristic
303C11×C22⋊C8C2311yescharacteristic
304C11×C22⋊C8C2312yes—
305C11×#97C2312yes—
306C11×#97C2312yes—
307C11×#97C2312yes—
308C4×C8×C11C2311yescharacteristic
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2312yes—
311C4×C8×C11C2312yes—
312#61923C1111yesmaximal, characteristic, direct product factor, Sylow
313C11×#41—41no—
314C11×#41—41no—
315C11×#41—82no—
316C11×#41—82no—
317C2×Q8×C11—22no—
318C2×Q8×C11—21no—
319C2×Q8×C11—22no—
320C2×Q8×C11—42no—
321C2×Q8×C11—42no—
322C2×Q8×C11—82no—
323C2×Q8×C11C2×D411yescharacteristic
324C2×Q8×C11C2×D411yescharacteristic
325C2×Q8×C11C2×D412yes—
326C2×Q8×C11C2412yes—
327C2×Q8×C11C2412yes—
328C2×Q8×C11C2411yescharacteristic
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—21no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11C2411yescharacteristic
338C2×D4×C11C2411yescharacteristic
339C2×D4×C11C2412yes—
340C22×C4×C11—22no—
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—21no—
344C22×C4×C11—21no—
345C22×C4×C11—22no—
346C22×C4×C11—22no—
347C22×C4×C11—22no—
348C22×C4×C11—22no—
349C22×C4×C11C2×D411yescharacteristic
350C22×C4×C11C2×D411yescharacteristic
351C22×C4×C11C2411yescharacteristic
352C11×Q16—42no—
353C11×Q16—42no—
354C11×Q16—41no—
355C11×SD16—42no—
356C11×SD16—42no—
357C11×SD16—42no—
358C11×SD16—41no—
359C11×SD16—42no—
360C11×SD16—42no—
361C11×SD16—42no—
362C11×SD16—42no—
363C11×SD16—41no—
364C11×D8—42no—
365C11×D8—41no—
366C2×C8×C11C2411yescharacteristic
367C2×C8×C11C2411yescharacteristic
368C2×C8×C11C2411yescharacteristic
369C2×C8×C11C2412yes—
370C2×C8×C11C2412yes—
371C2×C8×C11C2411yescharacteristic
372C11×C4⋊C4—21no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—21no—
375C11×C4⋊C4—21no—
376C11×C4⋊C4—22no—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—21no—
379C11×C4⋊C4—21no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—21no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4C2×D412yes—
398C11×C4⋊C4C2×D411yescharacteristic
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D412yes—
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—21no—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—22no—
436C42×C11—22no—
437C42×C11—22no—
438C42×C11—22no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11C2×D411yescharacteristic
442C42×C11C2×D411yescharacteristic
443C42×C11C2411yescharacteristic
444C42×C11C2412yes—
445C42×C11C2412yes—
446C42×C11C2411yescharacteristic
447#3554C2×C1111yescharacteristic, complemented
448#3509C2×C1111yescharacteristic, complemented
449#3401C2×C1112yescomplemented
450#3400C2×C1111yescharacteristic, complemented
451#3400C2×C1112yescomplemented
452#3397C2×C1111yescharacteristic, complemented
453#3394C2×C1111yescharacteristic, complemented
454#3392C2×C1111yescharacteristic, complemented
455#3376C2×C1112yescomplemented
456#3374C2×C1111yescharacteristic, complemented
457#3372C2×C1112yescomplemented
458#3367C2×C1111yescharacteristic, complemented
459#3364C2×C1111yescharacteristic, complemented
460#3359C2×C1111yescharacteristic, complemented
461#3225C2×C1112yescomplemented
462#3221C2×C1112yescomplemented
463#3218C2×C1111yescharacteristic, complemented
464#3206C2×C1111yescharacteristic, complemented
465#3126C2×C1112yescomplemented
466#3121C2×C1112yescomplemented
467#3115C2×C1111yescharacteristic, complemented
468#3102C2×C1111yescharacteristic, complemented
469#2985C2×C1111yescharacteristic, complemented
470C23×C11—21no—
471C23×C11—22no—
472C23×C11—21no—
473C23×C11C22×D411yescharacteristic
474Q8×C11—22no—
475Q8×C11—22no—
476Q8×C11—22no—
477Q8×C11—22no—
478Q8×C11—21no—
479Q8×C11—21no—
480Q8×C11—22no—
481Q8×C11—22no—
482Q8×C11—21no—
483Q8×C11—21no—
484Q8×C11—42no—
485Q8×C11—44no—
486Q8×C11—42no—
487Q8×C11—82no—
488D4×C11—21no—
489D4×C11—22no—
490D4×C11—21no—
491D4×C11—21no—
492D4×C11—21no—
493D4×C11—22no—
494D4×C11—42no—
495D4×C11—42no—
496D4×C11—81no—
497D4×C11—82no—
498D4×C11—82no—
499D4×C11—81no—
500D4×C11—82no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—22no—
512C2×C4×C11—21no—
513C2×C4×C11—41no—
514C2×C4×C11—42no—
515C2×C4×C11—42no—
516C2×C4×C11—44no—
517C2×C4×C11—42no—
518C2×C4×C11—42no—
519C2×C4×C11—82no—
520C2×C4×C11—82no—
521C2×C4×C11—82no—
522C2×C4×C11—82no—
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D411yescharacteristic
525C2×C4×C11C22×D411yescharacteristic
526C2×C4×C11C22×D412yes—
527C2×C4×C11C22×D412yes—
528C2×C4×C11C22×D412yes—
529C2×C4×C11C22×D411yescharacteristic
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C2511yescharacteristic
533C8×C11—21no—
534C8×C11—22no—
535C8×C11—21no—
536C8×C11—21no—
537C8×C11—21no—
538C8×C11—22no—
539#562—22no—
540#559C22×C1111yescharacteristic
541#559C22×C1112yes—
542#557C22×C1111yescharacteristic
543#557C22×C1112yes—
544#557C22×C1111yescharacteristic
545#557C22×C1111yescharacteristic
546#556C22×C1111yescharacteristic
547#556C22×C1111yescharacteristic
548#556C22×C1112yes—
549#554C22×C1112yes—
550#552—21no—
551#552—21no—
552#552—22no—
553#550C22×C1111yescharacteristic
554D4×Q8C22×C1111yescharacteristic
555#548—21no—
556#547—21no—
557#542—21no—
558#542C22×C1112yes—
559#541—22no—
560#540C22×C1112yes—
561#539—22no—
562#536—21no—
563#536C22×C1112yes—
564#533—21no—
565#533—21no—
566#533C22×C1111yescharacteristic
567#532C22×C1111yescharacteristic
568C2×C4⋊Q8C22×C1111yescharacteristic
569#529C22×C1111yescharacteristic
570#519C22×C1112yes—
571C4×#41C22×C1111yescharacteristic
572#497C22×C1112yes—
573#497C22×C1112yes—
574#496C22×C1112yes—
575#495C22×C1112yes—
576#492C22×C1111yescharacteristic
577#492C22×C1112yes—
578#492C22×C1111yescharacteristic
579#491C22×C1112yes—
580#491C22×C1112yes—
581#489C22×C1112yes—
582#488C22×C1112yes—
583#487C22×C1111yescharacteristic
584#487C22×C1112yes—
585#487C22×C1111yescharacteristic
586#485C22×C1111yescharacteristic
587#482C22×C1111yescharacteristic
588#482C22×C1112yes—
589#479C22×C1111yescharacteristic
590#479C22×C1112yes—
591#479C22×C1112yes—
592#478C22×C1111yescharacteristic
593#477C22×C1112yes—
594#475C22×C1111yescharacteristic
595#475C22×C1112yes—
596#474C22×C1111yescharacteristic
597#464C22×C1111yescharacteristic
598#464C22×C1112yes—
599#464C22×C1112yes—
600#464C22×C1112yes—
601#463C22×C1111yescharacteristic
602#463C22×C1112yes—
603#463C22×C1112yes—
604#463C22×C1112yes—
605#462C22×C1111yescharacteristic
606#462C22×C1111yescharacteristic
607#462C22×C1112yes—
608#461C22×C1111yescharacteristic
609#461C22×C1112yes—
610#461C22×C1111yescharacteristic
611#461C22×C1112yes—
612#461C22×C1112yes—
613#461C22×C1112yes—
614#461C22×C1112yes—
615#460C22×C1111yescharacteristic
616#460C22×C1112yes—
617#460C22×C1112yes—
618#459C22×C1111yescharacteristic
619#452C22×C1111yescharacteristic
620#451C22×C1112yes—
621#449C22×C1111yescharacteristic
622#449C22×C1112yes—
623#448C22×C1112yes—
624#448C22×C1112yes—
625#448C22×C1112yes—
626#446C22×C1111yescharacteristic
627#446C22×C1112yes—
628#446C22×C1111yescharacteristic
629#446C22×C1112yes—
630C8×Q8C22×C1111yescharacteristic
631C8×Q8C22×C1111yescharacteristic
632#442C22×C1112yes—
633#441C22×C1112yes—
634#440C22×C1112yes—
635#440C22×C1112yes—
636#440C22×C1112yes—
637#440C22×C1112yes—
638C4×Q16C22×C1111yescharacteristic
639C4×Q16C22×C1112yes—
640C4×SD16C22×C1111yescharacteristic
641C4×SD16C22×C1111yescharacteristic
642C4×SD16C22×C1112yes—
643C4×SD16C22×C1112yes—
644C4×SD16C22×C1112yes—
645C4×D8C22×C1111yescharacteristic
646#433C22×C1112yes—
647#433C22×C1112yes—
648#432C22×C1111yescharacteristic
649#431C22×C1111yescharacteristic
650C22×C11—21no—
651C22×C11—21no—
652C22×C11—21no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11C23×D411yescharacteristic
663C4×C11—21no—
664C4×C11—21no—
665C4×C11—22no—
666C4×C11—22no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—41no—
672C4×C11—41no—
673C4×C11—41no—
674C4×C11—42no—
675C4×C11—42no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11—41no—
679C4×C11—42no—
680C4×C11#57712yes—
681C4×C11#58511yescharacteristic
682C4×C11#58511yescharacteristic
683C2×#41—21no—
684C2×#41—21no—
685C2×#41C23×C1111yescharacteristic
686C22×Q8—21no—
687C22×Q8C23×C1112yes—
688C2×Q16C23×C1112yes—
689C2×Q16C23×C1111yescharacteristic
690C2×Q16C23×C1112yes—
691C2×SD16C23×C1112yes—
692C2×SD16C23×C1112yes—
693C2×SD16C23×C1112yes—
694C2×SD16C23×C1111yescharacteristic
695C2×SD16C23×C1111yescharacteristic
696C2×SD16C23×C1112yes—
697C2×SD16C23×C1112yes—
698C2×SD16C23×C1112yes—
699C2×SD16C23×C1112yes—
700C2×D8C23×C1111yescharacteristic
701C2×D8C23×C1112yes—
702C4⋊Q8—21no—
703C4⋊Q8—21no—
704C4⋊Q8—21no—
705C4⋊Q8D4×C1111yescharacteristic
706C4⋊Q8D4×C1111yescharacteristic
707C4⋊Q8C23×C1112yes—
708C4⋊Q8C23×C1111yescharacteristic
709C4⋊Q8C23×C1111yescharacteristic
710C4⋊Q8C23×C1112yes—
711C4⋊Q8C23×C1112yes—
712C4⋊Q8C23×C1111yescharacteristic
713C4⋊Q8C23×C1112yes—
714#127C23×C1111yescharacteristic
715#127C23×C1112yes—
716#126—22no—
717#126—22no—
718#126—22no—
719#126—22no—
720#126—22no—
721#126—21no—
722#125—21no—
723#125—21no—
724#125—22no—
725#125—22no—
726#125—22no—
727#125—22no—
728#125—22no—
729#125—22no—
730#125D4×C1112yes—
731#125C23×C1111yescharacteristic
732#125C23×C1112yes—
733#124—21no—
734#124—22no—
735#124—22no—
736#124—21no—
737#124C23×C1111yescharacteristic
738#124C23×C1112yes—
739#124C23×C1112yes—
740#124C23×C1112yes—
741#123—21no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123—22no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—21no—
761C22⋊Q8D4×C1111yescharacteristic
762C22⋊Q8D4×C1111yescharacteristic
763C22⋊Q8D4×C1112yes—
764C22⋊Q8C23×C1111yescharacteristic
765#121—21no—
766#121—22no—
767#121—21no—
768#121—22no—
769#121—22no—
770#121C23×C1111yescharacteristic
771#121C23×C1112yes—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—22no—
775C4×Q8—22no—
776C4×Q8—22no—
777C4×Q8—21no—
778C4×Q8C23×C1111yescharacteristic
779C4×Q8C23×C1111yescharacteristic
780C4×Q8C23×C1112yes—
781C4×Q8C23×C1112yes—
782C4×Q8C23×C1112yes—
783C4×Q8C23×C1112yes—
784C4×Q8C23×C1111yescharacteristic
785C4×Q8C23×C1112yes—
786C4×Q8C23×C1111yescharacteristic
787C4×Q8C23×C1111yescharacteristic
788C4×Q8C23×C1112yes—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—22no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4C23×C1111yescharacteristic
796C4×D4C23×C1111yescharacteristic
797C4×D4C23×C1111yescharacteristic
798C4×D4C23×C1112yes—
799C4×D4C23×C1112yes—
800C4×D4C23×C1112yes—
801C4×D4C23×C1112yes—
802#117—21no—
803#117—21no—
804#117—22no—
805#117—22no—
806#117—22no—
807#117—21no—
808#117—21no—
809#117C23×C1111yescharacteristic
810#117C23×C1112yes—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—22no—
814C2×C42—21no—
815C2×C42C23×C1111yescharacteristic
816#107C23×C1111yescharacteristic
817#107C23×C1112yes—
818#107C23×C1111yescharacteristic
819#106C23×C1111yescharacteristic
820#106C23×C1111yescharacteristic
821#106C23×C1112yes—
822C4⋊C8C23×C1111yescharacteristic
823C4⋊C8C23×C1111yescharacteristic
824C4⋊C8C23×C1111yescharacteristic
825C4⋊C8C23×C1111yescharacteristic
826C4⋊C8C23×C1112yes—
827C4⋊C8C23×C1112yes—
828C4⋊C8C23×C1112yes—
829C4⋊C8C23×C1112yes—
830#103C23×C1111yescharacteristic
831#103C23×C1112yes—
832#103C23×C1112yes—
833#103C23×C1112yes—
834#103C23×C1111yescharacteristic
835#103C23×C1111yescharacteristic
836#103C23×C1112yes—
837#103C23×C1111yescharacteristic
838#103C23×C1112yes—
839#103C23×C1112yes—
840#103C23×C1112yes—
841#103C23×C1112yes—
842#103C23×C1112yes—
843#102C23×C1111yescharacteristic
844#102C23×C1111yescharacteristic
845#102C23×C1111yescharacteristic
846#102C23×C1112yes—
847#102C23×C1112yes—
848#102C23×C1111yescharacteristic
849#102C23×C1112yes—
850C22⋊C8C23×C1111yescharacteristic
851C22⋊C8C23×C1111yescharacteristic
852C22⋊C8C23×C1112yes—
853#97C23×C1112yes—
854#97C23×C1112yes—
855#97C23×C1112yes—
856C4×C8C23×C1111yescharacteristic
857C4×C8C23×C1111yescharacteristic
858C4×C8C23×C1112yes—
859C4×C8C23×C1112yes—
860C2×C11—41no—
861C2×C11—81no—
862C2×C11—82no—
863C2×C11—81no—
864C2×C11#348711yescharacteristic
865C2×C11C2×#57711yescharacteristic
866C2×C11#358611yescharacteristic
867#41—41no—
868#41—41no—
869#41—82no—
870#41—82no—
871C2×Q8—22no—
872C2×Q8—21no—
873C2×Q8—22no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—82no—
877C2×Q8C2×D4×C1111yescharacteristic
878C2×Q8C2×D4×C1111yescharacteristic
879C2×Q8C2×D4×C1112yes—
880C2×Q8C24×C1112yes—
881C2×Q8C24×C1112yes—
882C2×Q8C24×C1111yescharacteristic
883C2×Q8C24×C1111yescharacteristic
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—22no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4C24×C1111yescharacteristic
892C2×D4C24×C1111yescharacteristic
893C2×D4C24×C1112yes—
894C22×C4—22no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4C2×D4×C1111yescharacteristic
904C22×C4C2×D4×C1111yescharacteristic
905C22×C4C24×C1111yescharacteristic
906Q16—42no—
907Q16—42no—
908Q16—41no—
909SD16—42no—
910SD16—42no—
911SD16—42no—
912SD16—41no—
913SD16—42no—
914SD16—41no—
915SD16—42no—
916SD16—42no—
917SD16—42no—
918D8—41no—
919D8—42no—
920C2×C8C24×C1111yescharacteristic
921C2×C8C24×C1111yescharacteristic
922C2×C8C24×C1111yescharacteristic
923C2×C8C24×C1112yes—
924C2×C8C24×C1112yes—
925C2×C8C24×C1111yescharacteristic
926C4⋊C4—21no—
927C4⋊C4—22no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—22no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4C2×D4×C1112yes—
952C4⋊C4C2×D4×C1111yescharacteristic
953C4⋊C4C2×D4×C1111yescharacteristic
954C4⋊C4C2×D4×C1112yes—
955C4⋊C4C2×D4×C1112yes—
956C4⋊C4C2×D4×C1112yes—
957C4⋊C4C2×D4×C1112yes—
958C4⋊C4C2×D4×C1112yes—
959C4⋊C4C2×D4×C1112yes—
960C4⋊C4C24×C1111yescharacteristic
961C4⋊C4C24×C1111yescharacteristic
962C4⋊C4C24×C1111yescharacteristic
963C4⋊C4C24×C1111yescharacteristic
964C4⋊C4C24×C1112yes—
965C22⋊C4—21no—
966C22⋊C4—21no—
967C22⋊C4—21no—
968C22⋊C4—21no—
969C22⋊C4—21no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—21no—
975C22⋊C4—21no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4C2×D4×C1112yes—
985C22⋊C4C2×D4×C1112yes—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—22no—
990C42—22no—
991C42—22no—
992C42—22no—
993C42—21no—
994C42—22no—
995C42C2×D4×C1111yescharacteristic
996C42C2×D4×C1111yescharacteristic
997C42C24×C1111yescharacteristic
998C42C24×C1112yes—
999C42C24×C1112yes—
1000C42C24×C1111yescharacteristic
1001C11#6192311yescharacteristic, direct product factor, Sylow
1002C23—21no—
1003C23—21no—
1004C23—22no—
1005C23C22×D4×C1111yescharacteristic
1006Q8—22no—
1007Q8—22no—
1008Q8—22no—
1009Q8—22no—
1010Q8—21no—
1011Q8—21no—
1012Q8—22no—
1013Q8—22no—
1014Q8—21no—
1015Q8—21no—
1016Q8—42no—
1017Q8—44no—
1018Q8—42no—
1019Q8—82no—
1020D4—21no—
1021D4—21no—
1022D4—22no—
1023D4—21no—
1024D4—22no—
1025D4—21no—
1026D4—42no—
1027D4—42no—
1028D4—81no—
1029D4—82no—
1030D4—82no—
1031D4—81no—
1032D4—82no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—41no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—44no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—82no—
1052C2×C4—82no—
1053C2×C4—82no—
1054C2×C4—82no—
1055C2×C4C22×D4×C1112yes—
1056C2×C4C22×D4×C1111yescharacteristic
1057C2×C4C22×D4×C1111yescharacteristic
1058C2×C4C22×D4×C1112yes—
1059C2×C4C22×D4×C1112yes—
1060C2×C4C22×D4×C1112yes—
1061C2×C4C22×D4×C1111yescharacteristic
1062C2×C4C22×D4×C1111yescharacteristic
1063C2×C4C22×D4×C1111yescharacteristic
1064C2×C4C25×C1111yescharacteristic
1065C8—21no—
1066C8—22no—
1067C8—21no—
1068C8—21no—
1069C8—22no—
1070C8—21no—
1071C22—21no—
1072C22—21no—
1073C22—21no—
1074C22—41no—
1075C22—41no—
1076C22—42no—
1077C22—41no—
1078C22—41no—
1079C22—42no—
1080C22—41no—
1081C22—42no—
1082C22—41no—
1083C22C23×D4×C1111yescharacteristic
1084C4—21no—
1085C4—21no—
1086C4—22no—
1087C4—22no—
1088C4—21no—
1089C4—21no—
1090C4—22no—
1091C4—22no—
1092C4—41no—
1093C4—42no—
1094C4—42no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—42no—
1099C4—41no—
1100C4—41no—
1101C4C11×#57712yes—
1102C4C11×#58511yescharacteristic
1103C4C11×#58511yescharacteristic
1104C2—41no—
1105C2—81no—
1106C2—81no—
1107C2—82no—
1108C2C11×#348711yescharacteristic
1109C2C2×C11×#57711yescharacteristic
1110C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3554C2semidirect
2. C11×#3509C2semidirect
3. C11×#3401C2semidirect
4. C11×#3400C2semidirect
5. C11×#3400C2semidirect
6. C11×#3397C2semidirect
7. C11×#3394C2semidirect
8. C11×#3392C2semidirect
9. C11×#3376C2semidirect
10. C11×#3374C2semidirect
11. C11×#3372C2semidirect
12. C11×#3367C2semidirect
13. C11×#3364C2semidirect
14. C11×#3359C2semidirect
15. C11×#3225C2semidirect
16. C11×#3221C2semidirect
17. C11×#3218C2semidirect
18. C11×#3206C2semidirect
19. C11×#3126C2semidirect
20. C11×#3121C2semidirect
21. C11×#3115C2semidirect
22. C11×#3102C2semidirect
23. C11×#2985C2semidirect
312. #61923C11direct (N × H)
447. #3554C2×C11semidirect
448. #3509C2×C11semidirect
449. #3401C2×C11semidirect
450. #3400C2×C11semidirect
451. #3400C2×C11semidirect
452. #3397C2×C11semidirect
453. #3394C2×C11semidirect
454. #3392C2×C11semidirect
455. #3376C2×C11semidirect
456. #3374C2×C11semidirect
457. #3372C2×C11semidirect
458. #3367C2×C11semidirect
459. #3364C2×C11semidirect
460. #3359C2×C11semidirect
461. #3225C2×C11semidirect
462. #3221C2×C11semidirect
463. #3218C2×C11semidirect
464. #3206C2×C11semidirect
465. #3126C2×C11semidirect
466. #3121C2×C11semidirect
467. #3115C2×C11semidirect
468. #3102C2×C11semidirect
469. #2985C2×C11semidirect
1001. C11#61923direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#35092
C11×#34012
C11×#34002
C11×#33972
C11×#33942
C11×#33922
C11×#33762
C11×#33742
C11×#33722
C11×#33672
C11×#33642
C11×#33592
C11×#32252
C11×#32212
C11×#32182
C11×#32062
C11×#31262
C11×#31212
C11×#31152
C11×#31022
C11×#29852
#6192311