Finite Group Databasebeta

← C11×#61703 #14638896

Subgroups — C11×#61703 #14638896

Order 2816.

1780 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×#3520C211yesmaximal, characteristic, complemented
2C11×#3475C211yesmaximal, characteristic, complemented
3C11×#3342C211yesmaximal, characteristic, complemented
4C11×#3340C211yesmaximal, characteristic, complemented
5C11×#3337C212yesmaximal, complemented
6C11×#3336C212yesmaximal, complemented
7C11×#3335C211yesmaximal, characteristic, complemented
8C11×#3334C211yesmaximal, characteristic, complemented
9C11×#3303C211yesmaximal, characteristic, complemented
10C11×#3302C211yesmaximal, characteristic, complemented
11C11×#3301C212yesmaximal, complemented
12C11×#3300C212yesmaximal, complemented
13C11×#3299C211yesmaximal, characteristic, complemented
14C11×#3298C211yesmaximal, characteristic, complemented
15C11×#3233C211yesmaximal, characteristic, complemented
16C11×#3231C211yesmaximal, characteristic, complemented
17C11×#3191C212yesmaximal, complemented
18C11×#3190C212yesmaximal, complemented
19C11×#3107C211yesmaximal, characteristic, complemented
20C11×#3102C211yesmaximal, characteristic, complemented
21C11×#3091C212yesmaximal, complemented
22C2×C11×#485C212yesmaximal, complemented
23C11×#2972C211yesmaximal, characteristic, complemented
24C11×#556C2211yescharacteristic
25C11×#556C2211yescharacteristic
26C11×#555C2211yescharacteristic
27C11×#554—21no—
28C11×#554C2211yescharacteristic
29C11×#553C2212yes—
30C11×#552—21no—
31C11×#552C2212yes—
32C11×#552C2212yes—
33C11×#551—22no—
34C11×#551—22no—
35D4×Q8×C11C2211yescharacteristic
36C11×#548C2212yes—
37C11×#547C2211yescharacteristic
38C11×#547C2211yescharacteristic
39C11×#547C2211yescharacteristic
40C11×#546—21no—
41C11×#546—21no—
42C11×#542—21no—
43C11×#539—22no—
44C11×#533C2211yescharacteristic
45C11×#533C2211yescharacteristic
46C11×#529—22no—
47C11×#529—21no—
48C11×#529C2211yescharacteristic
49C11×#525C2212yes—
50C11×#525C2212yes—
51C2×C11×C22⋊Q8C2212yes—
52C11×#520—21no—
53C4×C11×#41—21no—
54C4×C11×#41C2211yescharacteristic
55C2×C4×D4×C11C2211yescharacteristic
56C2×C11×#117C2212yes—
57C11×#500C2211yescharacteristic, complemented
58C11×#499C2212yescomplemented
59C11×#498C2211yescharacteristic, complemented
60C11×#488C2212yescomplemented
61C11×#487C2211yescharacteristic, complemented
62C11×#487C2211yescharacteristic, complemented
63C11×#485C2212yes—
64C11×#485C2212yes—
65C11×#485C2212yes—
66C11×#485C2211yescharacteristic
67C11×#485C2212yes—
68C11×#485C2212yescomplemented
69C11×#485C2212yescomplemented
70C11×#485C2212yescomplemented
71C11×#485C2212yescomplemented
72C11×#485C2212yescomplemented
73C11×#484C2212yescomplemented
74C11×#483C2212yescomplemented
75C11×#483C2212yescomplemented
76C11×#482C2212yes—
77C11×#482C2211yescharacteristic
78C11×#482C2212yescomplemented
79C11×#481C2212yescomplemented
80C11×#480C2212yescomplemented
81C11×#480C2212yescomplemented
82C11×#479C2212yescomplemented
83C11×#479C2212yescomplemented
84C11×#479C2211yescharacteristic, complemented
85C11×#478C2211yescharacteristic, complemented
86C11×#477C2211yescharacteristic, complemented
87C11×#476C2211yescharacteristic, complemented
88C11×#475C2211yescharacteristic, complemented
89C11×#475C2211yescharacteristic, complemented
90C11×#474C2211yescharacteristic, complemented
91C11×#474C2211yescharacteristic, complemented
92C11×#467C2212yescomplemented
93C11×#467C2212yescomplemented
94C11×#467C2212yescomplemented
95C11×#466C2212yescomplemented
96C11×#465C2212yescomplemented
97C11×#465C2212yescomplemented
98C11×#465C2212yescomplemented
99C11×#465C2212yescomplemented
100C11×#464C2211yescharacteristic, complemented
101C11×#463C2211yescharacteristic, complemented
102C11×#462C2211yescharacteristic, complemented
103C11×#461C2211yescharacteristic, complemented
104C11×#452C2211yescharacteristic
105C11×#452C2212yes—
106C11×#452C2212yescomplemented
107C11×#451C2212yescomplemented
108C11×#449C2211yescharacteristic
109C11×#449C2212yescomplemented
110C11×#448C2212yescomplemented
111C4×C11×Q16C2211yescharacteristic, complemented
112C4×C11×Q16C2212yescomplemented
113C4×C11×SD16C2211yescharacteristic, complemented
114C4×C11×SD16C2212yescomplemented
115C4×C11×SD16C2211yescharacteristic, complemented
116C4×C11×D8C2211yescharacteristic, complemented
117C8×D4×C11C2211yescharacteristic
118C8×D4×C11C2211yescharacteristic
119C8×D4×C11C2212yes—
120C8×D4×C11C2212yes—
121C8×D4×C11C2211yescharacteristic
122C8×D4×C11C2211yescharacteristic
123C11×#431C2211yescharacteristic
124C11×#431C2211yescharacteristic
125C11×#427C2212yescomplemented
126C11×#427C2212yescomplemented
127C2×C11×#107C2212yescomplemented
128C2×C11×#106C2212yescomplemented
129C11×#416C2212yescomplemented
130C11×#416C2212yescomplemented
131C2×C11×#103C2212yescomplemented
132C2×C11×#103C2212yescomplemented
133C2×C11×C22⋊C8C2212yes—
134C2×C11×C22⋊C8C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41C2311yescharacteristic
138C2×C11×#41C2312yes—
139C22×Q8×C11C2312yes—
140C22×D4×C11D411yescharacteristic
141C23×C4×C11C2312yes—
142C2×C11×Q16C2311yescharacteristic
143C2×C11×Q16C2312yes—
144C2×C11×SD16C2311yescharacteristic
145C2×C11×SD16C2312yes—
146C2×C11×SD16C2311yescharacteristic
147C2×C11×D8C2311yescharacteristic
148C22×C8×C11C2312yes—
149C22×C8×C11C2312yes—
150C22×C8×C11C2312yes—
151C22×C8×C11C2312yes—
152C11×C4⋊Q8—21no—
153C11×C4⋊Q8C2311yescharacteristic
154C11×C4⋊Q8C2311yescharacteristic
155C11×C4⋊Q8C2311yescharacteristic
156C11×C4⋊Q8C2311yescharacteristic
157C11×#126—22no—
158C11×#126—22no—
159C11×#126—22no—
160C11×#126—22no—
161C11×#126—22no—
162C11×#126—21no—
163C11×#125—22no—
164C11×#125—21no—
165C11×#125—22no—
166C11×#125—21no—
167C11×#125C2311yescharacteristic
168C11×#125C2312yes—
169C11×#124—21no—
170C11×#124—21no—
171C11×#124—22no—
172C11×#124—22no—
173C11×#124C2311yescharacteristic
174C11×#123—22no—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—21no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123—22no—
182C11×#123—22no—
183C11×C22⋊Q8—22no—
184C11×C22⋊Q8—22no—
185C11×C22⋊Q8—21no—
186C11×C22⋊Q8—21no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—22no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8C2311yescharacteristic
194C11×C22⋊Q8C2312yes—
195C11×C22⋊Q8C2312yes—
196C11×C22⋊Q8C2312yes—
197C11×C22⋊Q8C2312yes—
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×#121—22no—
201C11×#121—21no—
202C11×#121—22no—
203C11×#121—21no—
204C11×#121C2311yescharacteristic
205C11×#121C2312yes—
206C11×#121C2312yes—
207C11×#121C2312yes—
208C11×#120—22no—
209C11×#120—22no—
210C4×Q8×C11—21no—
211C4×Q8×C11—21no—
212C4×Q8×C11—21no—
213C4×Q8×C11—21no—
214C4×Q8×C11—21no—
215C4×Q8×C11C2311yescharacteristic
216C4×Q8×C11C2311yescharacteristic
217C4×Q8×C11C2311yescharacteristic
218C4×Q8×C11C2312yes—
219C4×D4×C11—21no—
220C4×D4×C11—21no—
221C4×D4×C11—22no—
222C4×D4×C11—21no—
223C4×D4×C11—21no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11—22no—
227C4×D4×C11—21no—
228C4×D4×C11—22no—
229C4×D4×C11—22no—
230C4×D4×C11D411yescharacteristic
231C4×D4×C11D412yes—
232C4×D4×C11D411yescharacteristic
233C4×D4×C11C2311yescharacteristic
234C4×D4×C11C2311yescharacteristic
235C4×D4×C11C2311yescharacteristic
236C4×D4×C11C2311yescharacteristic
237C4×D4×C11C2311yescharacteristic
238C4×D4×C11C2312yes—
239C11×#117—22no—
240C11×#117—22no—
241C11×#117—21no—
242C11×#117—21no—
243C11×#117—22no—
244C11×#117—22no—
245C11×#117—21no—
246C11×#117—21no—
247C11×#117C2311yescharacteristic
248C11×#117C2312yes—
249C11×#117C2312yes—
250C11×#117C2312yes—
251C11×#117C2312yes—
252C2×C11×C4⋊C4—22no—
253C2×C11×C4⋊C4—21no—
254C2×C11×C4⋊C4D411yescharacteristic
255C2×C11×C4⋊C4C2312yes—
256C2×C11×C4⋊C4C2312yes—
257C2×C11×C4⋊C4C2312yes—
258C2×C11×C22⋊C4—22no—
259C2×C11×C22⋊C4—22no—
260C2×C11×C22⋊C4D412yes—
261C2×C42×C11—22no—
262C2×C42×C11—21no—
263C2×C42×C11C2311yescharacteristic
264C11×#107C2312yes—
265C11×#107C2312yes—
266C11×#107C2312yes—
267C11×#107C2312yes—
268C11×#107C2311yescharacteristic
269C11×#107C2312yes—
270C11×#107C2311yescharacteristic
271C11×#106C2312yes—
272C11×#106C2312yes—
273C11×#106C2312yes—
274C11×#106C2312yes—
275C11×#106C2311yescharacteristic
276C11×#106C2312yes—
277C11×#106C2311yescharacteristic
278C11×C4⋊C8C2311yescharacteristic
279C11×C4⋊C8C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×#103C2311yescharacteristic
283C11×#103C2311yescharacteristic
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#103C2312yes—
295C11×#102C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2311yescharacteristic
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
302C11×C22⋊C8C2311yescharacteristic
303C11×C22⋊C8C2311yescharacteristic
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×C22⋊C8C2312yes—
308C11×C22⋊C8C2312yes—
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2312yes—
311C4×C8×C11C2311yescharacteristic
312#61703C1111yesmaximal, characteristic, direct product factor, Sylow
313C24×C11C2×D412yes—
314C11×#41—41no—
315C11×#41—41no—
316C11×#41—42no—
317C11×#41—42no—
318C11×#41—44no—
319C11×#41—44no—
320C2×Q8×C11—21no—
321C2×Q8×C11—21no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—42no—
325C2×Q8×C11—42no—
326C2×Q8×C11C2411yescharacteristic
327C2×Q8×C11C2412yes—
328C2×Q8×C11C2411yescharacteristic
329C2×D4×C11—24no—
330C2×D4×C11—21no—
331C2×D4×C11—21no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—22no—
336C2×D4×C11C2×D412yes—
337C2×D4×C11C2×D411yescharacteristic
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2411yescharacteristic
340C2×D4×C11C2411yescharacteristic
341C22×C4×C11—22no—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11—21no—
349C22×C4×C11—22no—
350C22×C4×C11—42no—
351C22×C4×C11—42no—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D412yes—
354C22×C4×C11C2×D411yescharacteristic
355C22×C4×C11C2×D412yes—
356C22×C4×C11C2×D412yes—
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2412yes—
359C22×C4×C11C2412yes—
360C11×Q16—41no—
361C11×Q16—42no—
362C11×SD16—41no—
363C11×SD16—42no—
364C11×SD16—41no—
365C11×D8—41no—
366C2×C8×C11—42no—
367C2×C8×C11—42no—
368C2×C8×C11—42no—
369C2×C8×C11—42no—
370C2×C8×C11C2412yes—
371C2×C8×C11C2411yescharacteristic
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2412yes—
375C2×C8×C11C2411yescharacteristic
376C11×C4⋊C4—21no—
377C11×C4⋊C4—22no—
378C11×C4⋊C4—21no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—22no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
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—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2411yescharacteristic
403C11×C4⋊C4C2412yes—
404C11×C4⋊C4C2411yescharacteristic
405C11×C4⋊C4C2412yes—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2412yes—
408C11×C4⋊C4C2411yescharacteristic
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—21no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—21no—
435C42×C11—22no—
436C42×C11—21no—
437C42×C11—22no—
438C42×C11—22no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11—22no—
442C42×C11—21no—
443C42×C11C2×D411yescharacteristic
444C42×C11C2×D411yescharacteristic
445C42×C11C2411yescharacteristic
446C42×C11C2411yescharacteristic
447#3520C2×C1111yescharacteristic, complemented
448#3475C2×C1111yescharacteristic, complemented
449#3342C2×C1111yescharacteristic, complemented
450#3340C2×C1111yescharacteristic, complemented
451#3337C2×C1112yescomplemented
452#3336C2×C1112yescomplemented
453#3335C2×C1111yescharacteristic, complemented
454#3334C2×C1111yescharacteristic, complemented
455#3303C2×C1111yescharacteristic, complemented
456#3302C2×C1111yescharacteristic, complemented
457#3301C2×C1112yescomplemented
458#3300C2×C1112yescomplemented
459#3299C2×C1111yescharacteristic, complemented
460#3298C2×C1111yescharacteristic, complemented
461#3233C2×C1111yescharacteristic, complemented
462#3231C2×C1111yescharacteristic, complemented
463#3191C2×C1112yescomplemented
464#3190C2×C1112yescomplemented
465#3107C2×C1111yescharacteristic, complemented
466#3102C2×C1111yescharacteristic, complemented
467#3091C2×C1112yescomplemented
468C2×#485C2×C1112yescomplemented
469#2972C2×C1111yescharacteristic, complemented
470C23×C11—24no—
471C23×C11—21no—
472C23×C11—21no—
473C23×C11—42no—
474C23×C11—42no—
475C23×C11C22×D412yes—
476C23×C11C22×D411yescharacteristic
477C23×C11C22×D412yes—
478Q8×C11—21no—
479Q8×C11—21no—
480Q8×C11—22no—
481Q8×C11—21no—
482Q8×C11—21no—
483Q8×C11—22no—
484Q8×C11—42no—
485Q8×C11—42no—
486Q8×C11—81no—
487Q8×C11—82no—
488D4×C11—24no—
489D4×C11—22no—
490D4×C11—21no—
491D4×C11—21no—
492D4×C11—21no—
493D4×C11—21no—
494D4×C11—42no—
495D4×C11—42no—
496D4×C11—44no—
497D4×C11—44no—
498D4×C11—82no—
499D4×C11—82no—
500D4×C11#13514yes—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—21no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—42no—
519C2×C4×C11—42no—
520C2×C4×C11—42no—
521C2×C4×C11—41no—
522C2×C4×C11—42no—
523C2×C4×C11—44no—
524C2×C4×C11—44no—
525C2×C4×C11—42no—
526C2×C4×C11—42no—
527C2×C4×C11—81no—
528C2×C4×C11—82no—
529C2×C4×C11—82no—
530C2×C4×C11—82no—
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D412yes—
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D412yes—
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C2511yescharacteristic
539C8×C11—21no—
540C8×C11—21no—
541C8×C11—21no—
542C8×C11—22no—
543C8×C11—22no—
544C8×C11—21no—
545#556C22×C1111yescharacteristic
546#556C22×C1111yescharacteristic
547#555C22×C1111yescharacteristic
548#554—21no—
549#554C22×C1111yescharacteristic
550#553C22×C1112yes—
551#552—21no—
552#552C22×C1112yes—
553#552C22×C1112yes—
554#551—22no—
555#551—22no—
556D4×Q8C22×C1111yescharacteristic
557#548C22×C1112yes—
558#547C22×C1111yescharacteristic
559#547C22×C1111yescharacteristic
560#547C22×C1111yescharacteristic
561#546—21no—
562#546—21no—
563#542—21no—
564#539—22no—
565#533C22×C1111yescharacteristic
566#533C22×C1111yescharacteristic
567#529—22no—
568#529—21no—
569#529C22×C1111yescharacteristic
570#525C22×C1112yes—
571#525C22×C1112yes—
572C2×C22⋊Q8C22×C1112yes—
573#520—21no—
574C4×#41—21no—
575C4×#41C22×C1111yescharacteristic
576C2×C4×D4C22×C1111yescharacteristic
577C2×#117C22×C1112yes—
578#500C22×C1111yescharacteristic, complemented
579#499C22×C1112yescomplemented
580#498C22×C1111yescharacteristic, complemented
581#488C22×C1112yescomplemented
582#487C22×C1111yescharacteristic, complemented
583#487C22×C1111yescharacteristic, complemented
584#485C22×C1111yescharacteristic
585#485C22×C1112yes—
586#485C22×C1112yes—
587#485C22×C1112yes—
588#485C22×C1112yes—
589#485C22×C1112yescomplemented
590#485C22×C1112yescomplemented
591#485C22×C1112yescomplemented
592#485C22×C1112yescomplemented
593#485C22×C1112yescomplemented
594#484C22×C1112yescomplemented
595#483C22×C1112yescomplemented
596#483C22×C1112yescomplemented
597#482C22×C1111yescharacteristic
598#482C22×C1112yes—
599#482C22×C1112yescomplemented
600#481C22×C1112yescomplemented
601#480C22×C1112yescomplemented
602#480C22×C1112yescomplemented
603#479C22×C1111yescharacteristic, complemented
604#479C22×C1112yescomplemented
605#479C22×C1112yescomplemented
606#478C22×C1111yescharacteristic, complemented
607#477C22×C1111yescharacteristic, complemented
608#476C22×C1111yescharacteristic, complemented
609#475C22×C1111yescharacteristic, complemented
610#475C22×C1111yescharacteristic, complemented
611#474C22×C1111yescharacteristic, complemented
612#474C22×C1111yescharacteristic, complemented
613#467C22×C1112yescomplemented
614#467C22×C1112yescomplemented
615#467C22×C1112yescomplemented
616#466C22×C1112yescomplemented
617#465C22×C1112yescomplemented
618#465C22×C1112yescomplemented
619#465C22×C1112yescomplemented
620#465C22×C1112yescomplemented
621#464C22×C1111yescharacteristic, complemented
622#463C22×C1111yescharacteristic, complemented
623#462C22×C1111yescharacteristic, complemented
624#461C22×C1111yescharacteristic, complemented
625#452C22×C1111yescharacteristic
626#452C22×C1112yes—
627#452C22×C1112yescomplemented
628#451C22×C1112yescomplemented
629#449C22×C1111yescharacteristic
630#449C22×C1112yescomplemented
631#448C22×C1112yescomplemented
632C4×Q16C22×C1112yescomplemented
633C4×Q16C22×C1111yescharacteristic, complemented
634C4×SD16C22×C1111yescharacteristic, complemented
635C4×SD16C22×C1112yescomplemented
636C4×SD16C22×C1111yescharacteristic, complemented
637C4×D8C22×C1111yescharacteristic, complemented
638C8×D4C22×C1111yescharacteristic
639C8×D4C22×C1111yescharacteristic
640C8×D4C22×C1112yes—
641C8×D4C22×C1112yes—
642C8×D4C22×C1111yescharacteristic
643C8×D4C22×C1111yescharacteristic
644#431C22×C1111yescharacteristic
645#431C22×C1111yescharacteristic
646#427C22×C1112yescomplemented
647#427C22×C1112yescomplemented
648C2×#107C22×C1112yescomplemented
649C2×#106C22×C1112yescomplemented
650#416C22×C1112yescomplemented
651#416C22×C1112yescomplemented
652C2×#103C22×C1112yescomplemented
653C2×#103C22×C1112yescomplemented
654C2×C22⋊C8C22×C1112yes—
655C2×C22⋊C8C22×C1112yes—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—21no—
659C22×C11—22no—
660C22×C11—21no—
661C22×C11—22no—
662C22×C11—21no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—41no—
670C22×C11—84no—
671C22×C11C2×#13514yes—
672C22×C11C23×D411yescharacteristic
673C4×C11—21no—
674C4×C11—21no—
675C4×C11—21no—
676C4×C11—22no—
677C4×C11—22no—
678C4×C11—21no—
679C4×C11—41no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11—41no—
685C4×C11—41no—
686C4×C11—41no—
687C4×C11—42no—
688C4×C11—42no—
689C4×C11C2×#13512yes—
690C4×C11#58511yescharacteristic
691C4×C11#58511yescharacteristic
692C2×#41—21no—
693C2×#41—21no—
694C2×#41C23×C1111yescharacteristic
695C2×#41C23×C1112yes—
696C22×Q8C23×C1112yes—
697C22×D4D4×C1111yescharacteristic
698C23×C4C23×C1112yes—
699C2×Q16C23×C1111yescharacteristic
700C2×Q16C23×C1112yes—
701C2×SD16C23×C1111yescharacteristic
702C2×SD16C23×C1112yes—
703C2×SD16C23×C1111yescharacteristic
704C2×D8C23×C1111yescharacteristic
705C22×C8C23×C1112yes—
706C22×C8C23×C1112yes—
707C22×C8C23×C1112yes—
708C22×C8C23×C1112yes—
709C4⋊Q8—21no—
710C4⋊Q8C23×C1111yescharacteristic
711C4⋊Q8C23×C1111yescharacteristic
712C4⋊Q8C23×C1111yescharacteristic
713C4⋊Q8C23×C1111yescharacteristic
714#126—22no—
715#126—22no—
716#126—22no—
717#126—22no—
718#126—22no—
719#126—21no—
720#125—22no—
721#125—21no—
722#125—22no—
723#125—21no—
724#125C23×C1111yescharacteristic
725#125C23×C1112yes—
726#124—21no—
727#124—21no—
728#124—22no—
729#124—22no—
730#124C23×C1111yescharacteristic
731#123—22no—
732#123—22no—
733#123—22no—
734#123—22no—
735#123—21no—
736#123—22no—
737#123—22no—
738#123—22no—
739#123—22no—
740C22⋊Q8—22no—
741C22⋊Q8—22no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—22no—
747C22⋊Q8—21no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8C23×C1111yescharacteristic
751C22⋊Q8C23×C1112yes—
752C22⋊Q8C23×C1112yes—
753C22⋊Q8C23×C1112yes—
754C22⋊Q8C23×C1112yes—
755C22⋊Q8C23×C1112yes—
756C22⋊Q8C23×C1112yes—
757#121—22no—
758#121—21no—
759#121—22no—
760#121—21no—
761#121C23×C1111yescharacteristic
762#121C23×C1112yes—
763#121C23×C1112yes—
764#121C23×C1112yes—
765#120—22no—
766#120—22no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×Q8—21no—
772C4×Q8C23×C1111yescharacteristic
773C4×Q8C23×C1111yescharacteristic
774C4×Q8C23×C1111yescharacteristic
775C4×Q8C23×C1112yes—
776C4×D4—21no—
777C4×D4—21no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—21no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4D4×C1111yescharacteristic
788C4×D4D4×C1112yes—
789C4×D4D4×C1111yescharacteristic
790C4×D4C23×C1111yescharacteristic
791C4×D4C23×C1111yescharacteristic
792C4×D4C23×C1111yescharacteristic
793C4×D4C23×C1111yescharacteristic
794C4×D4C23×C1111yescharacteristic
795C4×D4C23×C1112yes—
796#117—22no—
797#117—22no—
798#117—21no—
799#117—21no—
800#117—22no—
801#117—22no—
802#117—21no—
803#117—21no—
804#117C23×C1111yescharacteristic
805#117C23×C1112yes—
806#117C23×C1112yes—
807#117C23×C1112yes—
808#117C23×C1112yes—
809C2×C4⋊C4—22no—
810C2×C4⋊C4—21no—
811C2×C4⋊C4D4×C1111yescharacteristic
812C2×C4⋊C4C23×C1112yes—
813C2×C4⋊C4C23×C1112yes—
814C2×C4⋊C4C23×C1112yes—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4D4×C1112yes—
818C2×C42—22no—
819C2×C42—21no—
820C2×C42C23×C1111yescharacteristic
821#107C23×C1111yescharacteristic
822#107C23×C1112yes—
823#107C23×C1112yes—
824#107C23×C1112yes—
825#107C23×C1111yescharacteristic
826#107C23×C1112yes—
827#107C23×C1112yes—
828#106C23×C1111yescharacteristic
829#106C23×C1112yes—
830#106C23×C1112yes—
831#106C23×C1112yes—
832#106C23×C1111yescharacteristic
833#106C23×C1112yes—
834#106C23×C1112yes—
835C4⋊C8C23×C1111yescharacteristic
836C4⋊C8C23×C1111yescharacteristic
837C4⋊C8C23×C1111yescharacteristic
838C4⋊C8C23×C1111yescharacteristic
839#103C23×C1111yescharacteristic
840#103C23×C1111yescharacteristic
841#103C23×C1112yes—
842#103C23×C1112yes—
843#103C23×C1112yes—
844#103C23×C1112yes—
845#103C23×C1112yes—
846#103C23×C1112yes—
847#103C23×C1112yes—
848#103C23×C1112yes—
849#103C23×C1111yescharacteristic
850#103C23×C1111yescharacteristic
851#103C23×C1112yes—
852#102C23×C1111yescharacteristic
853#102C23×C1111yescharacteristic
854#102C23×C1112yes—
855#102C23×C1112yes—
856#102C23×C1111yescharacteristic
857#102C23×C1111yescharacteristic
858#102C23×C1112yes—
859C22⋊C8C23×C1111yescharacteristic
860C22⋊C8C23×C1112yes—
861C22⋊C8C23×C1111yescharacteristic
862C22⋊C8C23×C1112yes—
863C22⋊C8C23×C1112yes—
864C22⋊C8C23×C1112yes—
865C22⋊C8C23×C1112yes—
866C4×C8C23×C1111yescharacteristic
867C4×C8C23×C1111yescharacteristic
868C4×C8C23×C1112yes—
869C2×C11—24no—
870C2×C11—42no—
871C2×C11—41no—
872C2×C11—81no—
873C2×C11—81no—
874C2×C11#348511yescharacteristic
875C2×C11C22×#13511yescharacteristic
876C2×C11#358611yescharacteristic
877C24C2×D4×C1112yes—
878#41—41no—
879#41—41no—
880#41—42no—
881#41—42no—
882#41—44no—
883#41—44no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—22no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8C24×C1111yescharacteristic
891C2×Q8C24×C1112yes—
892C2×Q8C24×C1111yescharacteristic
893C2×D4—24no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4C2×D4×C1112yes—
901C2×D4C2×D4×C1111yescharacteristic
902C2×D4C2×D4×C1111yescharacteristic
903C2×D4C24×C1111yescharacteristic
904C2×D4C24×C1111yescharacteristic
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4C2×D4×C1111yescharacteristic
917C22×C4C2×D4×C1112yes—
918C22×C4C2×D4×C1111yescharacteristic
919C22×C4C2×D4×C1112yes—
920C22×C4C2×D4×C1112yes—
921C22×C4C24×C1111yescharacteristic
922C22×C4C24×C1112yes—
923C22×C4C24×C1112yes—
924Q16—41no—
925Q16—42no—
926SD16—41no—
927SD16—42no—
928SD16—41no—
929D8—41no—
930C2×C8—42no—
931C2×C8—42no—
932C2×C8—42no—
933C2×C8—42no—
934C2×C8C24×C1111yescharacteristic
935C2×C8C24×C1112yes—
936C2×C8C24×C1111yescharacteristic
937C2×C8C24×C1111yescharacteristic
938C2×C8C24×C1112yes—
939C2×C8C24×C1111yescharacteristic
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
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—21no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4C2×D4×C1111yescharacteristic
964C4⋊C4C2×D4×C1111yescharacteristic
965C4⋊C4C2×D4×C1112yes—
966C4⋊C4C24×C1111yescharacteristic
967C4⋊C4C24×C1112yes—
968C4⋊C4C24×C1111yescharacteristic
969C4⋊C4C24×C1112yes—
970C4⋊C4C24×C1111yescharacteristic
971C4⋊C4C24×C1112yes—
972C4⋊C4C24×C1111yescharacteristic
973C22⋊C4—21no—
974C22⋊C4—21no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—21no—
986C22⋊C4—22no—
987C22⋊C4—21no—
988C22⋊C4—21no—
989C22⋊C4—21no—
990C22⋊C4—21no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—21no—
994C22⋊C4C2×D4×C1112yes—
995C22⋊C4C2×D4×C1112yes—
996C22⋊C4C2×D4×C1112yes—
997C22⋊C4C2×D4×C1112yes—
998C42—21no—
999C42—22no—
1000C42—21no—
1001C42—22no—
1002C42—22no—
1003C42—21no—
1004C42—22no—
1005C42—22no—
1006C42—21no—
1007C42C2×D4×C1111yescharacteristic
1008C42C2×D4×C1111yescharacteristic
1009C42C24×C1111yescharacteristic
1010C42C24×C1111yescharacteristic
1011C11#6170311yescharacteristic, direct product factor, Sylow
1012C23—24no—
1013C23—21no—
1014C23—21no—
1015C23—42no—
1016C23—42no—
1017C23C22×D4×C1112yes—
1018C23C22×D4×C1111yescharacteristic
1019C23C22×D4×C1112yes—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—21no—
1025Q8—22no—
1026Q8—42no—
1027Q8—42no—
1028Q8—81no—
1029Q8—82no—
1030D4—24no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—21no—
1036D4—42no—
1037D4—42no—
1038D4—44no—
1039D4—44no—
1040D4—82no—
1041D4—82no—
1042D4C11×#13514yes—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—41no—
1064C2×C4—42no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—81no—
1070C2×C4—82no—
1071C2×C4—82no—
1072C2×C4—82no—
1073C2×C4C22×D4×C1111yescharacteristic
1074C2×C4C22×D4×C1111yescharacteristic
1075C2×C4C22×D4×C1112yes—
1076C2×C4C22×D4×C1111yescharacteristic
1077C2×C4C22×D4×C1111yescharacteristic
1078C2×C4C22×D4×C1112yes—
1079C2×C4C22×D4×C1111yescharacteristic
1080C2×C4C25×C1111yescharacteristic
1081C8—21no—
1082C8—21no—
1083C8—21no—
1084C8—22no—
1085C8—22no—
1086C8—21no—
1087C22—22no—
1088C22—22no—
1089C22—21no—
1090C22—22no—
1091C22—21no—
1092C22—22no—
1093C22—21no—
1094C22—22no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—84no—
1102C22C2×C11×#13514yes—
1103C22C23×D4×C1111yescharacteristic
1104C4—21no—
1105C4—22no—
1106C4—22no—
1107C4—21no—
1108C4—21no—
1109C4—21no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4C2×C11×#13512yes—
1121C4C11×#58511yescharacteristic
1122C4C11×#58511yescharacteristic
1123C2—24no—
1124C2—41no—
1125C2—42no—
1126C2—81no—
1127C2—81no—
1128C2C11×#348511yescharacteristic
1129C2C22×C11×#13511yescharacteristic
1130C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3520C2semidirect
2. C11×#3475C2semidirect
3. C11×#3342C2semidirect
4. C11×#3340C2semidirect
5. C11×#3337C2semidirect
6. C11×#3336C2semidirect
7. C11×#3335C2semidirect
8. C11×#3334C2semidirect
9. C11×#3303C2semidirect
10. C11×#3302C2semidirect
11. C11×#3301C2semidirect
12. C11×#3300C2semidirect
13. C11×#3299C2semidirect
14. C11×#3298C2semidirect
15. C11×#3233C2semidirect
16. C11×#3231C2semidirect
17. C11×#3191C2semidirect
18. C11×#3190C2semidirect
19. C11×#3107C2semidirect
20. C11×#3102C2semidirect
21. C11×#3091C2semidirect
22. C2×C11×#485C2semidirect
23. C11×#2972C2semidirect
57. C11×#500C22semidirect
58. C11×#499C22semidirect
59. C11×#498C22semidirect
60. C11×#488C22semidirect
61. C11×#487C22semidirect
62. C11×#487C22semidirect
68. C11×#485C22semidirect
69. C11×#485C22semidirect
70. C11×#485C22semidirect
71. C11×#485C22semidirect
72. C11×#485C22semidirect
73. C11×#484C22semidirect
74. C11×#483C22semidirect
75. C11×#483C22semidirect
78. C11×#482C22semidirect
79. C11×#481C22semidirect
80. C11×#480C22semidirect
81. C11×#480C22semidirect
82. C11×#479C22semidirect
83. C11×#479C22semidirect
84. C11×#479C22semidirect
85. C11×#478C22semidirect
86. C11×#477C22semidirect
87. C11×#476C22semidirect
88. C11×#475C22semidirect
89. C11×#475C22semidirect
90. C11×#474C22semidirect
91. C11×#474C22semidirect
92. C11×#467C22semidirect
93. C11×#467C22semidirect
94. C11×#467C22semidirect
95. C11×#466C22semidirect
96. C11×#465C22semidirect
97. C11×#465C22semidirect
98. C11×#465C22semidirect
99. C11×#465C22semidirect
100. C11×#464C22semidirect
101. C11×#463C22semidirect
102. C11×#462C22semidirect
103. C11×#461C22semidirect
106. C11×#452C22semidirect
107. C11×#451C22semidirect
109. C11×#449C22semidirect
110. C11×#448C22semidirect
111. C4×C11×Q16C22semidirect
112. C4×C11×Q16C22semidirect
113. C4×C11×SD16C22semidirect
114. C4×C11×SD16C22semidirect
115. C4×C11×SD16C22semidirect
116. C4×C11×D8C22semidirect
125. C11×#427C22semidirect
126. C11×#427C22semidirect
127. C2×C11×#107C22semidirect
128. C2×C11×#106C22semidirect
129. C11×#416C22semidirect
130. C11×#416C22semidirect
131. C2×C11×#103C22semidirect
132. C2×C11×#103C22semidirect
312. #61703C11direct (N × H)
447. #3520C2×C11semidirect
448. #3475C2×C11semidirect
449. #3342C2×C11semidirect
450. #3340C2×C11semidirect
451. #3337C2×C11semidirect
452. #3336C2×C11semidirect
453. #3335C2×C11semidirect
454. #3334C2×C11semidirect
455. #3303C2×C11semidirect
456. #3302C2×C11semidirect
457. #3301C2×C11semidirect
458. #3300C2×C11semidirect
459. #3299C2×C11semidirect
460. #3298C2×C11semidirect
461. #3233C2×C11semidirect
462. #3231C2×C11semidirect
463. #3191C2×C11semidirect
464. #3190C2×C11semidirect
465. #3107C2×C11semidirect
466. #3102C2×C11semidirect
467. #3091C2×C11semidirect
468. C2×#485C2×C11semidirect
469. #2972C2×C11semidirect
578. #500C22×C11semidirect
579. #499C22×C11semidirect
580. #498C22×C11semidirect
581. #488C22×C11semidirect
582. #487C22×C11semidirect
583. #487C22×C11semidirect
589. #485C22×C11semidirect
590. #485C22×C11semidirect
591. #485C22×C11semidirect
592. #485C22×C11semidirect
593. #485C22×C11semidirect
594. #484C22×C11semidirect
595. #483C22×C11semidirect
596. #483C22×C11semidirect
599. #482C22×C11semidirect
600. #481C22×C11semidirect
601. #480C22×C11semidirect
602. #480C22×C11semidirect
603. #479C22×C11semidirect
604. #479C22×C11semidirect
605. #479C22×C11semidirect
606. #478C22×C11semidirect
607. #477C22×C11semidirect
608. #476C22×C11semidirect
609. #475C22×C11semidirect
610. #475C22×C11semidirect
611. #474C22×C11semidirect
612. #474C22×C11semidirect
613. #467C22×C11semidirect
614. #467C22×C11semidirect
615. #467C22×C11semidirect
616. #466C22×C11semidirect
617. #465C22×C11semidirect
618. #465C22×C11semidirect
619. #465C22×C11semidirect
620. #465C22×C11semidirect
621. #464C22×C11semidirect
622. #463C22×C11semidirect
623. #462C22×C11semidirect
624. #461C22×C11semidirect
627. #452C22×C11semidirect
628. #451C22×C11semidirect
630. #449C22×C11semidirect
631. #448C22×C11semidirect
632. C4×Q16C22×C11semidirect
633. C4×Q16C22×C11semidirect
634. C4×SD16C22×C11semidirect
635. C4×SD16C22×C11semidirect
636. C4×SD16C22×C11semidirect
637. C4×D8C22×C11semidirect
646. #427C22×C11semidirect
647. #427C22×C11semidirect
648. C2×#107C22×C11semidirect
649. C2×#106C22×C11semidirect
650. #416C22×C11semidirect
651. #416C22×C11semidirect
652. C2×#103C22×C11semidirect
653. C2×#103C22×C11semidirect
1011. C11#61703direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35202
C11×#34752
C11×#33422
C11×#33402
C11×#33372
C11×#33362
C11×#33352
C11×#33342
C11×#33032
C11×#33022
C11×#33012
C11×#33002
C11×#32992
C11×#32982
C11×#32332
C11×#32312
C11×#31912
C11×#31902
C11×#31072
C11×#31022
C11×#30912
C2×C11×#4852
C11×#29722
#6170311