Finite Group Databasebeta

← C11×#61460 #14638653

Subgroups — C11×#61460 #14638653

Order 2816.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C211yesmaximal, characteristic, complemented
2C11×#3480C211yesmaximal, characteristic, complemented
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3386C211yesmaximal, characteristic, complemented
5C11×#3374C211yesmaximal, characteristic, complemented
6C11×#3373C211yesmaximal, characteristic, complemented
7C11×#3350C212yesmaximal, complemented
8C11×#3342C211yesmaximal, characteristic, complemented
9C11×#3313C212yesmaximal, complemented
10C11×#3307C212yesmaximal, complemented
11C11×#3304C211yesmaximal, characteristic, complemented
12C11×#3302C211yesmaximal, characteristic, complemented
13C11×#3284C211yesmaximal, characteristic, complemented
14C11×#3269C212yesmaximal, complemented
15C11×#3182C211yesmaximal, characteristic, complemented
16C11×#3181C212yesmaximal, complemented
17C11×#3116C212yesmaximal, complemented
18C11×#3115C211yesmaximal, characteristic, complemented
19C11×#3113C211yesmaximal, characteristic, complemented
20C11×#3111C212yesmaximal, complemented
21C11×#2970C211yesmaximal, characteristic, complemented
22C4×C11×#137C211yesmaximal, characteristic, complemented
23C11×#2943C212yesmaximal, complemented
24C2×C11×#137C2211yescharacteristic
25C2×C11×#135C2212yes—
26C11×#559—21no—
27C11×#559C2211yescharacteristic
28C11×#557C2211yescharacteristic
29C11×#557C2211yescharacteristic
30C11×#556—21no—
31C11×#556C2211yescharacteristic
32C11×#556C2211yescharacteristic
33C11×#556C2212yes—
34C11×#553—22no—
35C11×#553C2212yes—
36C11×#552—21no—
37C11×#552—22no—
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2211yescharacteristic
40C11×#548—21no—
41C11×#548C2212yes—
42C11×#547C2212yes—
43C11×#547C2211yescharacteristic
44C11×#533C2212yes—
45C11×#533C2211yescharacteristic
46C11×#532—21no—
47C11×#532C2211yescharacteristic
48C11×#529—22no—
49C11×#529—21no—
50C11×#529—22no—
51C11×#529C2212yes—
52C4×C11×#41—21no—
53C4×C11×#41C2212yes—
54C4×C11×#41C2212yes—
55C4×C11×#41C2211yescharacteristic
56C4×C11×#41C2211yescharacteristic
57C2×C4×Q8×C11—21no—
58C2×C4×Q8×C11C2211yescharacteristic
59C11×#501C2212yes—
60C11×#500C2211yescharacteristic
61C11×#497C2212yes—
62C11×#492C2211yescharacteristic
63C11×#491C2212yes—
64C11×#489C2212yes—
65C11×#487C2211yescharacteristic
66C11×#486C2211yescharacteristic
67C11×#485C2212yes—
68C11×#485C2212yes—
69C11×#485C2212yes—
70C11×#483C2212yes—
71C11×#482C2212yes—
72C11×#482C2212yes—
73C11×#479C2212yes—
74C11×#478C2212yes—
75C11×#477C2212yes—
76C11×#476C2212yes—
77C11×#475C2211yescharacteristic
78C11×#475C2211yescharacteristic
79C11×#475C2211yescharacteristic
80C11×#474C2211yescharacteristic
81C11×#468C2212yes—
82C11×#468C2212yes—
83C11×#467C2212yes—
84C11×#467C2212yes—
85C11×#465C2212yes—
86C11×#465C2212yes—
87C11×#464C2212yes—
88C11×#463C2212yes—
89C11×#462C2212yes—
90C11×#462C2211yescharacteristic
91C11×#462C2211yescharacteristic
92C11×#461C2212yes—
93C11×#460C2211yescharacteristic
94C11×#459C2211yescharacteristic
95C11×#452C2212yes—
96C11×#452C2212yes—
97C11×#452C2212yes—
98C11×#451C2212yes—
99C11×#449C2212yes—
100C11×#449C2212yes—
101C11×#446C2211yescharacteristic
102C11×#446C2211yescharacteristic
103C11×#442C2212yes—
104C11×#442C2212yes—
105C11×#441C2211yescharacteristic
106C11×#441C2212yes—
107C11×#441C2212yes—
108C11×#441C2212yes—
109C11×#441C2211yescharacteristic
110C11×#440C2212yes—
111C11×#440C2212yes—
112C11×#440C2212yes—
113C11×#440C2211yescharacteristic
114C11×#440C2212yes—
115C11×#440C2212yes—
116C11×#440C2211yescharacteristic
117C4×C11×Q16C2211yescharacteristic
118C4×C11×Q16C2211yescharacteristic
119C4×C11×SD16C2211yescharacteristic
120C4×C11×SD16C2211yescharacteristic
121C11×#435C2212yes—
122C11×#435C2212yes—
123C8×D4×C11C2211yescharacteristic
124C8×D4×C11C2211yescharacteristic
125C11×#432C2212yes—
126C11×#432C2211yescharacteristic
127C11×#428C2211yescharacteristic
128C11×#427C2212yes—
129C11×#419C2211yescharacteristic
130C11×#417C2211yescharacteristic
131C11×#416C2212yes—
132C11×#416C2212yes—
133C4×C11×M16C2211yescharacteristic
134C2×C11×#97C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41D411yescharacteristic
137C2×C11×#41C2312yes—
138C2×C11×#41C2311yescharacteristic
139C2×C11×#41C2312yes—
140C22×Q8×C11—21no—
141C22×Q8×C11C2311yescharacteristic
142C11×#137—24no—
143C11×#135—28no—
144C2×C11×Q16C2311yescharacteristic
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2311yescharacteristic
147C2×C11×Q16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2311yescharacteristic
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2311yescharacteristic
153C2×C11×D8C2312yes—
154C2×C11×M16C2311yescharacteristic
155C2×C11×M16C2311yescharacteristic
156C22×C8×C11C2312yes—
157C22×C8×C11C2312yes—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8C2312yes—
160C11×C4⋊Q8C2311yescharacteristic
161C11×C4⋊Q8C2312yes—
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2311yescharacteristic
164C11×#127—21no—
165C11×#127C2311yescharacteristic
166C11×#126—22no—
167C11×#126—22no—
168C11×#126—22no—
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#125—21no—
173C11×#125—22no—
174C11×#125—22no—
175C11×#125—22no—
176C11×#125—21no—
177C11×#125C2312yes—
178C11×#124—21no—
179C11×#124—21no—
180C11×#124—22no—
181C11×#124—21no—
182C11×#124—22no—
183C11×#124—21no—
184C11×#124C2312yes—
185C11×#123—22no—
186C11×#123—22no—
187C11×#123—22no—
188C11×#123—22no—
189C11×#123—22no—
190C11×#123—22no—
191C11×C22⋊Q8—21no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—21no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×#121—21no—
201C11×#121—22no—
202C11×#121—22no—
203C11×#121—22no—
204C11×#121—21no—
205C11×#121—22no—
206C11×#121C2312yes—
207C11×#121C2312yes—
208C4×Q8×C11—21no—
209C4×Q8×C11—21no—
210C4×Q8×C11—22no—
211C4×Q8×C11—21no—
212C4×Q8×C11—21no—
213C4×Q8×C11—22no—
214C4×Q8×C11—21no—
215C4×Q8×C11—21no—
216C4×Q8×C11—21no—
217C4×Q8×C11D411yescharacteristic
218C4×Q8×C11C2311yescharacteristic
219C4×Q8×C11C2311yescharacteristic
220C4×Q8×C11C2311yescharacteristic
221C4×Q8×C11C2311yescharacteristic
222C4×Q8×C11C2312yes—
223C4×Q8×C11C2311yescharacteristic
224C4×Q8×C11C2312yes—
225C4×Q8×C11C2311yescharacteristic
226C4×Q8×C11C2312yes—
227C4×Q8×C11C2311yescharacteristic
228C4×D4×C11—21no—
229C4×D4×C11—22no—
230C4×D4×C11—22no—
231C4×D4×C11—21no—
232C4×D4×C11—22no—
233C4×D4×C11—22no—
234C4×D4×C11—22no—
235C4×D4×C11—21no—
236C4×D4×C11—21no—
237C4×D4×C11—22no—
238C4×D4×C11—22no—
239C4×D4×C11—21no—
240C4×D4×C11D412yes—
241C4×D4×C11D411yescharacteristic
242C4×D4×C11C2311yescharacteristic
243C4×D4×C11C2312yes—
244C4×D4×C11C2311yescharacteristic
245C4×D4×C11C2312yes—
246C4×D4×C11C2312yes—
247C4×D4×C11C2312yes—
248C4×D4×C11C2311yescharacteristic
249C11×#117—21no—
250C11×#117—22no—
251C11×#117—22no—
252C11×#117—22no—
253C11×#117—21no—
254C11×#117—22no—
255C11×#117D411yescharacteristic
256C11×#117D412yes—
257C11×#117C2312yes—
258C11×#117C2312yes—
259C11×#117C2311yescharacteristic
260C2×C11×C4⋊C4—21no—
261C2×C11×C4⋊C4—21no—
262C2×C11×C4⋊C4—22no—
263C2×C11×C4⋊C4C2311yescharacteristic
264C2×C42×C11—21no—
265C2×C42×C11—22no—
266C2×C42×C11—21no—
267C2×C42×C11—22no—
268C2×C42×C11C2311yescharacteristic
269C2×C42×C11C2312yes—
270C11×#107C2312yes—
271C11×#107C2312yes—
272C11×#107C2312yes—
273C11×#107C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#106C2311yescharacteristic
276C11×#106C2312yes—
277C11×#106C2312yes—
278C11×#106C2312yes—
279C11×#106C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2312yes—
286C11×#103C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2312yes—
292C11×#103C2312yes—
293C11×#103C2311yescharacteristic
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#103C2312yes—
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2311yescharacteristic
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2311yescharacteristic
303C11×#102C2312yes—
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C11×#97C2311yescharacteristic
310C11×#97C2312yes—
311C11×#97C2311yescharacteristic
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2311yescharacteristic
314#61460C1111yesmaximal, characteristic, direct product factor, Sylow
315C11×#41—24no—
316C11×#41—24no—
317C11×#41—22no—
318C11×#41—42no—
319C11×#41—42no—
320C11×#41—42no—
321C11×#41—41no—
322C11×#41—44no—
323C2×Q8×C11—21no—
324C2×Q8×C11—22no—
325C2×Q8×C11—21no—
326C2×Q8×C11—21no—
327C2×Q8×C11—22no—
328C2×Q8×C11—41no—
329C2×Q8×C11—44no—
330C2×Q8×C11C2×D411yescharacteristic
331C2×Q8×C11C2411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2411yescharacteristic
335C2×D4×C11—22no—
336C2×D4×C11—22no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11C2×D411yescharacteristic
343C2×D4×C11C2×D412yes—
344C2×D4×C11C2412yes—
345C2×D4×C11C2411yescharacteristic
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11—21no—
349C22×C4×C11—22no—
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—21no—
353C22×C4×C11—22no—
354C22×C4×C11—22no—
355C22×C4×C11—22no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D412yes—
359C22×C4×C11C2×D412yes—
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2412yes—
362C11×Q16—22no—
363C11×Q16—24no—
364C11×Q16—22no—
365C11×Q16—42no—
366C11×SD16—24no—
367C11×SD16—22no—
368C11×SD16—42no—
369C11×SD16—42no—
370C11×SD16#4114yescomplemented
371C11×D8—24no—
372C11×M16—22no—
373C11×M16—41no—
374C2×C8×C11—24no—
375C2×C8×C11—42no—
376C2×C8×C11C2411yescharacteristic
377C2×C8×C11C2411yescharacteristic
378C2×C8×C11C2411yescharacteristic
379C2×C8×C11C2412yes—
380C2×C8×C11C2412yes—
381C2×C8×C11C2411yescharacteristic
382C11×C4⋊C4—21no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—22no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—21no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4—21no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4C2×D411yescharacteristic
406C11×C4⋊C4C2×D412yes—
407C11×C4⋊C4C2×D411yescharacteristic
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2412yes—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—21no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—21no—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—21no—
435C42×C11—21no—
436C42×C11—22no—
437C42×C11—21no—
438C42×C11—22no—
439C42×C11—22no—
440C42×C11—21no—
441C42×C11—22no—
442C42×C11—21no—
443C42×C11—22no—
444C42×C11—21no—
445C42×C11—21no—
446C42×C11C2×D412yes—
447C42×C11C2×D412yes—
448C42×C11C2×D411yescharacteristic
449C42×C11C2×D411yescharacteristic
450C42×C11C2411yescharacteristic
451C42×C11C2411yescharacteristic
452C42×C11C2412yes—
453#3482C2×C1111yescharacteristic, complemented
454#3480C2×C1111yescharacteristic, complemented
455#3400C2×C1111yescharacteristic, complemented
456#3386C2×C1111yescharacteristic, complemented
457#3374C2×C1111yescharacteristic, complemented
458#3373C2×C1111yescharacteristic, complemented
459#3350C2×C1112yescomplemented
460#3342C2×C1111yescharacteristic, complemented
461#3313C2×C1112yescomplemented
462#3307C2×C1112yescomplemented
463#3304C2×C1111yescharacteristic, complemented
464#3302C2×C1111yescharacteristic, complemented
465#3284C2×C1111yescharacteristic, complemented
466#3269C2×C1112yescomplemented
467#3182C2×C1111yescharacteristic, complemented
468#3181C2×C1112yescomplemented
469#3116C2×C1112yescomplemented
470#3115C2×C1111yescharacteristic, complemented
471#3113C2×C1111yescharacteristic, complemented
472#3111C2×C1112yescomplemented
473#2970C2×C1111yescharacteristic, complemented
474C4×#137C2×C1111yescharacteristic, complemented
475#2943C2×C1112yescomplemented
476C23×C11—21no—
477C23×C11—22no—
478C23×C11C22×D412yes—
479C23×C11C22×D411yescharacteristic
480Q8×C11—22no—
481Q8×C11—21no—
482Q8×C11—21no—
483Q8×C11—22no—
484Q8×C11—21no—
485Q8×C11—21no—
486Q8×C11—22no—
487Q8×C11—21no—
488Q8×C11—42no—
489Q8×C11—44no—
490Q8×C11—42no—
491Q8×C11—42no—
492Q8×C11C2×#4112yes—
493D4×C11—22no—
494D4×C11—22no—
495D4×C11—21no—
496D4×C11—22no—
497D4×C11—42no—
498D4×C11—44no—
499D4×C11—42no—
500D4×C11—44no—
501D4×C11—44no—
502D4×C11—42no—
503D4×C11—81no—
504D4×C11—82no—
505D4×C11C2×#4112yes—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—42no—
522C2×C4×C11—41no—
523C2×C4×C11—42no—
524C2×C4×C11—44no—
525C2×C4×C11—42no—
526C2×C4×C11—44no—
527C2×C4×C11—42no—
528C2×C4×C11—42no—
529C2×C4×C11—44no—
530C2×C4×C11—44no—
531C2×C4×C11—42no—
532C2×C4×C11—82no—
533C2×C4×C11—81no—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D412yes—
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C22×D412yes—
539C2×C4×C11C22×D412yes—
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C2511yescharacteristic
543C8×C11—22no—
544C8×C11—21no—
545C8×C11—21no—
546C8×C11—22no—
547C8×C11—21no—
548C8×C11C2×#4112yes—
549C2×#137C22×C1111yescharacteristic
550C2×#135C22×C1112yes—
551#559—21no—
552#559C22×C1111yescharacteristic
553#557C22×C1111yescharacteristic
554#557C22×C1111yescharacteristic
555#556—21no—
556#556C22×C1111yescharacteristic
557#556C22×C1111yescharacteristic
558#556C22×C1112yes—
559#553—22no—
560#553C22×C1112yes—
561#552—21no—
562#552—22no—
563#550C22×C1111yescharacteristic
564D4×Q8C22×C1111yescharacteristic
565#548—21no—
566#548C22×C1112yes—
567#547C22×C1112yes—
568#547C22×C1111yescharacteristic
569#533C22×C1111yescharacteristic
570#533C22×C1112yes—
571#532—21no—
572#532C22×C1111yescharacteristic
573#529—22no—
574#529—21no—
575#529—22no—
576#529C22×C1112yes—
577C4×#41—21no—
578C4×#41C22×C1112yes—
579C4×#41C22×C1111yescharacteristic
580C4×#41C22×C1112yes—
581C4×#41C22×C1111yescharacteristic
582C2×C4×Q8—21no—
583C2×C4×Q8C22×C1111yescharacteristic
584#501C22×C1112yes—
585#500C22×C1111yescharacteristic
586#497C22×C1112yes—
587#492C22×C1111yescharacteristic
588#491C22×C1112yes—
589#489C22×C1112yes—
590#487C22×C1111yescharacteristic
591#486C22×C1111yescharacteristic
592#485C22×C1112yes—
593#485C22×C1112yes—
594#485C22×C1112yes—
595#483C22×C1112yes—
596#482C22×C1112yes—
597#482C22×C1112yes—
598#479C22×C1112yes—
599#478C22×C1112yes—
600#477C22×C1112yes—
601#476C22×C1112yes—
602#475C22×C1111yescharacteristic
603#475C22×C1111yescharacteristic
604#475C22×C1111yescharacteristic
605#474C22×C1111yescharacteristic
606#468C22×C1112yes—
607#468C22×C1112yes—
608#467C22×C1112yes—
609#467C22×C1112yes—
610#465C22×C1112yes—
611#465C22×C1112yes—
612#464C22×C1112yes—
613#463C22×C1112yes—
614#462C22×C1111yescharacteristic
615#462C22×C1111yescharacteristic
616#462C22×C1112yes—
617#461C22×C1112yes—
618#460C22×C1111yescharacteristic
619#459C22×C1111yescharacteristic
620#452C22×C1112yes—
621#452C22×C1112yes—
622#452C22×C1112yes—
623#451C22×C1112yes—
624#449C22×C1112yes—
625#449C22×C1112yes—
626#446C22×C1111yescharacteristic
627#446C22×C1111yescharacteristic
628#442C22×C1112yes—
629#442C22×C1112yes—
630#441C22×C1112yes—
631#441C22×C1112yes—
632#441C22×C1111yescharacteristic
633#441C22×C1112yes—
634#441C22×C1111yescharacteristic
635#440C22×C1112yes—
636#440C22×C1111yescharacteristic
637#440C22×C1112yes—
638#440C22×C1112yes—
639#440C22×C1112yes—
640#440C22×C1112yes—
641#440C22×C1111yescharacteristic
642C4×Q16C22×C1111yescharacteristic
643C4×Q16C22×C1111yescharacteristic
644C4×SD16C22×C1111yescharacteristic
645C4×SD16C22×C1111yescharacteristic
646#435C22×C1112yes—
647#435C22×C1112yes—
648C8×D4C22×C1111yescharacteristic
649C8×D4C22×C1111yescharacteristic
650#432C22×C1112yes—
651#432C22×C1111yescharacteristic
652#428C22×C1111yescharacteristic
653#427C22×C1112yes—
654#419C22×C1111yescharacteristic
655#417C22×C1111yescharacteristic
656#416C22×C1112yes—
657#416C22×C1112yes—
658C4×M16C22×C1111yescharacteristic
659C2×#97C22×C1112yes—
660C22×C11—21no—
661C22×C11—22no—
662C22×C11—21no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—21no—
666C22×C11—22no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11C23×D411yescharacteristic
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—21no—
676C4×C11—22no—
677C4×C11—21no—
678C4×C11—22no—
679C4×C11—21no—
680C4×C11—22no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—41no—
684C4×C11—42no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—42no—
688C4×C11—42no—
689C4×C11—41no—
690C4×C11#57512yes—
691C4×C11C22×#4111yescharacteristic
692C4×C11#58511yescharacteristic
693C2×#41—21no—
694C2×#41D4×C1111yescharacteristic
695C2×#41C23×C1112yes—
696C2×#41C23×C1111yescharacteristic
697C2×#41C23×C1112yes—
698C22×Q8—21no—
699C22×Q8C23×C1111yescharacteristic
700#137—24no—
701#135—28no—
702C2×Q16C23×C1112yes—
703C2×Q16C23×C1111yescharacteristic
704C2×Q16C23×C1111yescharacteristic
705C2×Q16C23×C1112yes—
706C2×SD16C23×C1112yes—
707C2×SD16C23×C1111yescharacteristic
708C2×SD16C23×C1112yes—
709C2×SD16C23×C1112yes—
710C2×SD16C23×C1111yescharacteristic
711C2×D8C23×C1112yes—
712C2×M16C23×C1111yescharacteristic
713C2×M16C23×C1111yescharacteristic
714C22×C8C23×C1112yes—
715C22×C8C23×C1112yes—
716C4⋊Q8—21no—
717C4⋊Q8C23×C1112yes—
718C4⋊Q8C23×C1111yescharacteristic
719C4⋊Q8C23×C1111yescharacteristic
720C4⋊Q8C23×C1111yescharacteristic
721C4⋊Q8C23×C1112yes—
722#127—21no—
723#127C23×C1111yescharacteristic
724#126—22no—
725#126—22no—
726#126—22no—
727#126—22no—
728#126—22no—
729#126—22no—
730#125—21no—
731#125—22no—
732#125—22no—
733#125—22no—
734#125—21no—
735#125C23×C1112yes—
736#124—21no—
737#124—21no—
738#124—22no—
739#124—21no—
740#124—22no—
741#124—21no—
742#124C23×C1112yes—
743#123—22no—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749C22⋊Q8—21no—
750C22⋊Q8—22no—
751C22⋊Q8—22no—
752C22⋊Q8—21no—
753C22⋊Q8—22no—
754C22⋊Q8C23×C1112yes—
755C22⋊Q8C23×C1112yes—
756C22⋊Q8C23×C1112yes—
757C22⋊Q8C23×C1112yes—
758#121—21no—
759#121—22no—
760#121—22no—
761#121—22no—
762#121—21no—
763#121—22no—
764#121C23×C1112yes—
765#121C23×C1112yes—
766C4×Q8—21no—
767C4×Q8—21no—
768C4×Q8—22no—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×Q8—22no—
772C4×Q8—21no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8D4×C1111yescharacteristic
776C4×Q8C23×C1111yescharacteristic
777C4×Q8C23×C1111yescharacteristic
778C4×Q8C23×C1111yescharacteristic
779C4×Q8C23×C1111yescharacteristic
780C4×Q8C23×C1112yes—
781C4×Q8C23×C1111yescharacteristic
782C4×Q8C23×C1112yes—
783C4×Q8C23×C1111yescharacteristic
784C4×Q8C23×C1112yes—
785C4×Q8C23×C1111yescharacteristic
786C4×D4—21no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—21no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—21no—
798C4×D4D4×C1112yes—
799C4×D4D4×C1111yescharacteristic
800C4×D4C23×C1111yescharacteristic
801C4×D4C23×C1112yes—
802C4×D4C23×C1111yescharacteristic
803C4×D4C23×C1112yes—
804C4×D4C23×C1112yes—
805C4×D4C23×C1112yes—
806C4×D4C23×C1111yescharacteristic
807#117—21no—
808#117—22no—
809#117—22no—
810#117—22no—
811#117—21no—
812#117—22no—
813#117D4×C1111yescharacteristic
814#117D4×C1112yes—
815#117C23×C1112yes—
816#117C23×C1112yes—
817#117C23×C1111yescharacteristic
818C2×C4⋊C4—21no—
819C2×C4⋊C4—21no—
820C2×C4⋊C4—22no—
821C2×C4⋊C4C23×C1111yescharacteristic
822C2×C42—21no—
823C2×C42—22no—
824C2×C42—21no—
825C2×C42—22no—
826C2×C42C23×C1111yescharacteristic
827C2×C42C23×C1112yes—
828#107C23×C1111yescharacteristic
829#107C23×C1112yes—
830#107C23×C1111yescharacteristic
831#107C23×C1112yes—
832#107C23×C1112yes—
833#106C23×C1112yes—
834#106C23×C1112yes—
835#106C23×C1111yescharacteristic
836#106C23×C1111yescharacteristic
837#106C23×C1112yes—
838C4⋊C8C23×C1111yescharacteristic
839C4⋊C8C23×C1111yescharacteristic
840C4⋊C8C23×C1112yes—
841C4⋊C8C23×C1112yes—
842#103C23×C1111yescharacteristic
843#103C23×C1112yes—
844#103C23×C1112yes—
845#103C23×C1112yes—
846#103C23×C1111yescharacteristic
847#103C23×C1111yescharacteristic
848#103C23×C1111yescharacteristic
849#103C23×C1111yescharacteristic
850#103C23×C1111yescharacteristic
851#103C23×C1112yes—
852#103C23×C1112yes—
853#103C23×C1112yes—
854#103C23×C1112yes—
855#102C23×C1111yescharacteristic
856#102C23×C1112yes—
857#102C23×C1112yes—
858#102C23×C1112yes—
859#102C23×C1111yescharacteristic
860#102C23×C1112yes—
861#102C23×C1112yes—
862C22⋊C8C23×C1112yes—
863C22⋊C8C23×C1112yes—
864C22⋊C8C23×C1112yes—
865#97C23×C1111yescharacteristic
866#97C23×C1112yes—
867#97C23×C1112yes—
868#97C23×C1112yes—
869#97C23×C1111yescharacteristic
870C4×C8C23×C1111yescharacteristic
871C4×C8C23×C1111yescharacteristic
872C2×C11—41no—
873C2×C11—42no—
874C2×C11—42no—
875C2×C11—82no—
876C2×C11D4×#4111yescharacteristic
877C2×C11C2×#57511yescharacteristic
878C2×C11#358611yescharacteristic
879#41—24no—
880#41—24no—
881#41—22no—
882#41—42no—
883#41—42no—
884#41—42no—
885#41—41no—
886#41—44no—
887C2×Q8—21no—
888C2×Q8—22no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—41no—
893C2×Q8—44no—
894C2×Q8C2×D4×C1111yescharacteristic
895C2×Q8C24×C1111yescharacteristic
896C2×Q8C24×C1112yes—
897C2×Q8C24×C1111yescharacteristic
898C2×Q8C24×C1111yescharacteristic
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4C2×D4×C1111yescharacteristic
907C2×D4C2×D4×C1112yes—
908C2×D4C24×C1112yes—
909C2×D4C24×C1111yescharacteristic
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4C2×D4×C1111yescharacteristic
921C22×C4C2×D4×C1111yescharacteristic
922C22×C4C2×D4×C1112yes—
923C22×C4C2×D4×C1112yes—
924C22×C4C24×C1111yescharacteristic
925C22×C4C24×C1112yes—
926Q16—24no—
927Q16—22no—
928Q16—22no—
929Q16—42no—
930SD16—22no—
931SD16—24no—
932SD16—42no—
933SD16—42no—
934SD16C11×#4114yescomplemented
935D8—24no—
936M16—22no—
937M16—41no—
938C2×C8—24no—
939C2×C8—42no—
940C2×C8C24×C1111yescharacteristic
941C2×C8C24×C1111yescharacteristic
942C2×C8C24×C1111yescharacteristic
943C2×C8C24×C1112yes—
944C2×C8C24×C1112yes—
945C2×C8C24×C1111yescharacteristic
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—22no—
969C4⋊C4C2×D4×C1111yescharacteristic
970C4⋊C4C2×D4×C1112yes—
971C4⋊C4C2×D4×C1111yescharacteristic
972C4⋊C4C2×D4×C1112yes—
973C4⋊C4C24×C1111yescharacteristic
974C4⋊C4C24×C1112yes—
975C4⋊C4C24×C1111yescharacteristic
976C4⋊C4C24×C1111yescharacteristic
977C4⋊C4C24×C1111yescharacteristic
978C4⋊C4C24×C1112yes—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—21no—
985C22⋊C4—22no—
986C22⋊C4—21no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—21no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4C2×D4×C1112yes—
996C22⋊C4C2×D4×C1112yes—
997C22⋊C4C2×D4×C1112yes—
998C42—21no—
999C42—21no—
1000C42—22no—
1001C42—21no—
1002C42—22no—
1003C42—22no—
1004C42—21no—
1005C42—22no—
1006C42—21no—
1007C42—22no—
1008C42—21no—
1009C42—21no—
1010C42C2×D4×C1112yes—
1011C42C2×D4×C1112yes—
1012C42C2×D4×C1111yescharacteristic
1013C42C2×D4×C1111yescharacteristic
1014C42C24×C1111yescharacteristic
1015C42C24×C1111yescharacteristic
1016C42C24×C1112yes—
1017C11#6146011yescharacteristic, direct product factor, Sylow
1018C23—21no—
1019C23—22no—
1020C23C22×D4×C1112yes—
1021C23C22×D4×C1111yescharacteristic
1022Q8—22no—
1023Q8—21no—
1024Q8—21no—
1025Q8—22no—
1026Q8—21no—
1027Q8—21no—
1028Q8—22no—
1029Q8—21no—
1030Q8—42no—
1031Q8—44no—
1032Q8—42no—
1033Q8—42no—
1034Q8C2×C11×#4112yes—
1035D4—22no—
1036D4—22no—
1037D4—21no—
1038D4—22no—
1039D4—42no—
1040D4—44no—
1041D4—42no—
1042D4—44no—
1043D4—44no—
1044D4—42no—
1045D4—81no—
1046D4—82no—
1047D4C2×C11×#4112yes—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—42no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—44no—
1067C2×C4—42no—
1068C2×C4—44no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—42no—
1074C2×C4—82no—
1075C2×C4—81no—
1076C2×C4C22×D4×C1111yescharacteristic
1077C2×C4C22×D4×C1111yescharacteristic
1078C2×C4C22×D4×C1112yes—
1079C2×C4C22×D4×C1111yescharacteristic
1080C2×C4C22×D4×C1112yes—
1081C2×C4C22×D4×C1112yes—
1082C2×C4C22×D4×C1111yescharacteristic
1083C2×C4C22×D4×C1111yescharacteristic
1084C2×C4C25×C1111yescharacteristic
1085C8—22no—
1086C8—21no—
1087C8—21no—
1088C8—22no—
1089C8—21no—
1090C8C2×C11×#4112yes—
1091C22—21no—
1092C22—22no—
1093C22—22no—
1094C22—21no—
1095C22—22no—
1096C22—21no—
1097C22—22no—
1098C22—41no—
1099C22—41no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22C23×D4×C1111yescharacteristic
1104C4—22no—
1105C4—21no—
1106C4—22no—
1107C4—21no—
1108C4—22no—
1109C4—21no—
1110C4—22no—
1111C4—21no—
1112C4—42no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—42no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—41no—
1121C4C11×#57512yes—
1122C4C22×C11×#4111yescharacteristic
1123C4C11×#58511yescharacteristic
1124C2—41no—
1125C2—42no—
1126C2—42no—
1127C2—82no—
1128C2D4×C11×#4111yescharacteristic
1129C2C2×C11×#57511yescharacteristic
1130C2C11×#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×#3482C2semidirect
2. C11×#3480C2semidirect
3. C11×#3400C2semidirect
4. C11×#3386C2semidirect
5. C11×#3374C2semidirect
6. C11×#3373C2semidirect
7. C11×#3350C2semidirect
8. C11×#3342C2semidirect
9. C11×#3313C2semidirect
10. C11×#3307C2semidirect
11. C11×#3304C2semidirect
12. C11×#3302C2semidirect
13. C11×#3284C2semidirect
14. C11×#3269C2semidirect
15. C11×#3182C2semidirect
16. C11×#3181C2semidirect
17. C11×#3116C2semidirect
18. C11×#3115C2semidirect
19. C11×#3113C2semidirect
20. C11×#3111C2semidirect
21. C11×#2970C2semidirect
22. C4×C11×#137C2semidirect
23. C11×#2943C2semidirect
314. #61460C11direct (N × H)
370. C11×SD16#41semidirect
453. #3482C2×C11semidirect
454. #3480C2×C11semidirect
455. #3400C2×C11semidirect
456. #3386C2×C11semidirect
457. #3374C2×C11semidirect
458. #3373C2×C11semidirect
459. #3350C2×C11semidirect
460. #3342C2×C11semidirect
461. #3313C2×C11semidirect
462. #3307C2×C11semidirect
463. #3304C2×C11semidirect
464. #3302C2×C11semidirect
465. #3284C2×C11semidirect
466. #3269C2×C11semidirect
467. #3182C2×C11semidirect
468. #3181C2×C11semidirect
469. #3116C2×C11semidirect
470. #3115C2×C11semidirect
471. #3113C2×C11semidirect
472. #3111C2×C11semidirect
473. #2970C2×C11semidirect
474. C4×#137C2×C11semidirect
475. #2943C2×C11semidirect
934. SD16C11×#41semidirect
1017. C11#61460direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34822
C11×#34802
C11×#34002
C11×#33862
C11×#33742
C11×#33732
C11×#33502
C11×#33422
C11×#33132
C11×#33072
C11×#33042
C11×#33022
C11×#32842
C11×#32692
C11×#31822
C11×#31812
C11×#31162
C11×#31152
C11×#31132
C11×#31112
C11×#29702
C4×C11×#1372
C11×#29432
#6146011