Finite Group Databasebeta

← C11×#61920 #14639113

Subgroups — C11×#61920 #14639113

Order 2816.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic, complemented
2C11×#3508C211yesmaximal, characteristic, complemented
3C11×#3403C212yesmaximal, complemented
4C11×#3399C211yesmaximal, characteristic, complemented
5C11×#3399C211yesmaximal, characteristic, complemented
6C11×#3399C212yesmaximal, complemented
7C11×#3396C211yesmaximal, characteristic, complemented
8C11×#3391C211yesmaximal, characteristic, complemented
9C11×#3373C211yesmaximal, characteristic, complemented
10C11×#3370C212yesmaximal, complemented
11C11×#3368C211yesmaximal, characteristic, complemented
12C11×#3366C212yesmaximal, complemented
13C11×#3365C211yesmaximal, characteristic, complemented
14C11×#3358C211yesmaximal, characteristic, complemented
15C11×#3224C212yesmaximal, complemented
16C11×#3220C212yesmaximal, complemented
17C11×#3217C211yesmaximal, characteristic, complemented
18C11×#3205C211yesmaximal, characteristic, complemented
19C11×#3122C212yesmaximal, complemented
20C11×#3118C212yesmaximal, complemented
21C11×#3115C211yesmaximal, characteristic, complemented
22C11×#3102C211yesmaximal, characteristic, complemented
23C11×#2985C211yesmaximal, characteristic, complemented
24C11×#562—22no—
25C11×#559C2212yes—
26C11×#559C2211yescharacteristic
27C11×#559C2211yescharacteristic
28C11×#559C2212yescomplemented
29C11×#559C2211yescharacteristic, complemented
30C11×#557C2211yescharacteristic, complemented
31C11×#554C2212yescomplemented
32C11×#550C2211yescharacteristic
33C11×#550C2212yes—
34C11×#550C2211yescharacteristic
35C11×#550C2211yescharacteristic, complemented
36D4×Q8×C11C2211yescharacteristic, complemented
37C11×#548—21no—
38C11×#547—21no—
39C11×#546—21no—
40C11×#546—21no—
41C11×#546—22no—
42C11×#542—21no—
43C11×#542C2212yes—
44C11×#540—22no—
45C11×#540C2212yes—
46C11×#539—22no—
47C11×#536—21no—
48C11×#535C2212yes—
49C11×#533C2211yescharacteristic
50C11×#532—21no—
51C11×#532—21no—
52C11×#532C2211yescharacteristic
53C2×C11×#127C2211yescharacteristic
54C11×#529C2211yescharacteristic
55C11×#518C2212yes—
56C4×C11×#41C2211yescharacteristic
57C11×#496C2212yes—
58C11×#496C2212yescomplemented
59C11×#496C2212yescomplemented
60C11×#495C2212yescomplemented
61C11×#493C2211yescharacteristic
62C11×#493C2211yescharacteristic
63C11×#493C2212yescomplemented
64C11×#490C2212yes—
65C11×#490C2212yescomplemented
66C11×#489C2212yescomplemented
67C11×#488C2212yescomplemented
68C11×#486C2211yescharacteristic
69C11×#486C2211yescharacteristic
70C11×#486C2212yescomplemented
71C11×#485C2211yescharacteristic
72C11×#482C2211yescharacteristic
73C11×#482C2212yes—
74C11×#479C2211yescharacteristic, complemented
75C11×#478C2211yescharacteristic, complemented
76C11×#478C2212yescomplemented
77C11×#478C2212yescomplemented
78C11×#476C2212yescomplemented
79C11×#475C2211yescharacteristic, complemented
80C11×#474C2211yescharacteristic, complemented
81C11×#474C2212yescomplemented
82C11×#464C2211yescharacteristic, complemented
83C11×#464C2212yescomplemented
84C11×#463C2212yescomplemented
85C11×#463C2212yescomplemented
86C11×#463C2212yescomplemented
87C11×#463C2212yescomplemented
88C11×#463C2211yescharacteristic, complemented
89C11×#463C2212yescomplemented
90C11×#460C2211yescharacteristic
91C11×#460C2211yescharacteristic
92C11×#460C2212yescomplemented
93C11×#460C2211yescharacteristic, complemented
94C11×#459C2212yes—
95C11×#459C2212yes—
96C11×#459C2211yescharacteristic
97C11×#459C2211yescharacteristic
98C11×#459C2212yescomplemented
99C11×#459C2212yescomplemented
100C11×#459C2212yescomplemented
101C11×#459C2212yescomplemented
102C11×#459C2211yescharacteristic, complemented
103C11×#459C2212yescomplemented
104C11×#452C2211yescharacteristic
105C11×#450C2212yes—
106C11×#449C2211yescharacteristic
107C11×#449C2212yes—
108C11×#447C2212yes—
109C11×#447C2212yes—
110C11×#447C2212yes—
111C11×#446C2212yescomplemented
112C11×#446C2211yescharacteristic, complemented
113C11×#446C2212yescomplemented
114C11×#446C2211yescharacteristic, complemented
115C8×Q8×C11C2211yescharacteristic, complemented
116C8×Q8×C11C2211yescharacteristic, complemented
117C11×#442C2212yescomplemented
118C11×#442C2212yescomplemented
119C11×#442C2212yescomplemented
120C11×#442C2212yescomplemented
121C11×#440C2212yescomplemented
122C11×#440C2212yescomplemented
123C4×C11×Q16C2211yescharacteristic, complemented
124C4×C11×SD16C2211yescharacteristic, complemented
125C4×C11×SD16C2211yescharacteristic, complemented
126C4×C11×SD16C2212yescomplemented
127C4×C11×D8C2212yescomplemented
128C4×C11×D8C2211yescharacteristic, complemented
129C4×C11×D8C2212yescomplemented
130C4×C11×D8C2212yescomplemented
131C11×#433C2212yes—
132C11×#433C2212yes—
133C11×#432C2211yescharacteristic
134C11×#431C2211yescharacteristic
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—22no—
138C2×C11×#41—21no—
139C2×C11×#41—21no—
140C2×C11×#41C2311yescharacteristic
141C22×Q8×C11—21no—
142C22×D4×C11—21no—
143C22×D4×C11—21no—
144C22×D4×C11C2312yes—
145C2×C11×Q16C2311yescharacteristic
146C2×C11×SD16C2312yes—
147C2×C11×SD16C2312yes—
148C2×C11×SD16C2312yes—
149C2×C11×SD16C2311yescharacteristic
150C2×C11×SD16C2311yescharacteristic
151C2×C11×D8C2312yes—
152C2×C11×D8C2312yes—
153C2×C11×D8C2312yes—
154C2×C11×D8C2312yes—
155C2×C11×D8C2311yescharacteristic
156C2×C11×D8C2312yes—
157C2×C11×D8C2312yes—
158C2×C11×D8C2312yes—
159C11×C4⋊Q8—21no—
160C11×C4⋊Q8D411yescharacteristic
161C11×C4⋊Q8D411yescharacteristic
162C11×C4⋊Q8C2312yes—
163C11×C4⋊Q8C2311yescharacteristic
164C11×#127—21no—
165C11×#127—21no—
166C11×#127C2312yes—
167C11×#127C2312yes—
168C11×#127C2311yescharacteristic
169C11×#127C2311yescharacteristic
170C11×#127C2311yescharacteristic
171C11×#127C2312yes—
172C11×#127C2312yes—
173C11×#126—22no—
174C11×#126—21no—
175C11×#125—22no—
176C11×#125D412yes—
177C11×#125C2311yescharacteristic
178C11×#125C2312yes—
179C11×#124—21no—
180C11×#124—21no—
181C11×#124—22no—
182C11×#124—21no—
183C11×#124—22no—
184C11×#124—22no—
185C11×#124—21no—
186C11×#124C2312yes—
187C11×#124C2312yes—
188C11×#124C2311yescharacteristic
189C11×#124C2312yes—
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×#123—22no—
199C11×#123—22no—
200C11×#123—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8—21no—
207C11×C22⋊Q8D411yescharacteristic
208C11×C22⋊Q8D411yescharacteristic
209C11×C22⋊Q8D412yes—
210C11×C22⋊Q8C2311yescharacteristic
211C11×#121—21no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—21no—
215C11×#121—21no—
216C11×#121—22no—
217C11×#121—22no—
218C11×#121—22no—
219C11×#121—22no—
220C11×#121—22no—
221C11×#121—22no—
222C11×#121—21no—
223C11×#121—22no—
224C11×#121—22no—
225C11×#121C2311yescharacteristic
226C11×#121C2312yes—
227C11×#120—22no—
228C11×#120—22no—
229C4×Q8×C11—21no—
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2312yes—
234C4×Q8×C11C2311yescharacteristic
235C4×Q8×C11C2311yescharacteristic
236C4×Q8×C11C2312yes—
237C4×D4×C11—21no—
238C4×D4×C11—21no—
239C4×D4×C11—21no—
240C4×D4×C11—22no—
241C4×D4×C11—22no—
242C4×D4×C11—21no—
243C4×D4×C11—21no—
244C4×D4×C11—22no—
245C4×D4×C11—22no—
246C4×D4×C11—21no—
247C4×D4×C11—21no—
248C4×D4×C11C2311yescharacteristic
249C4×D4×C11C2311yescharacteristic
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2312yes—
254C4×D4×C11C2311yescharacteristic
255C4×D4×C11C2312yes—
256C4×D4×C11C2312yes—
257C4×D4×C11C2312yes—
258C4×D4×C11C2312yes—
259C11×#117—21no—
260C11×#117—21no—
261C11×#117C2311yescharacteristic
262C11×#117C2312yes—
263C2×C11×C4⋊C4—22no—
264C2×C11×C22⋊C4—22no—
265C2×C11×C22⋊C4—22no—
266C2×C42×C11—21no—
267C2×C42×C11C2311yescharacteristic
268C11×#107C2311yescharacteristic
269C11×#107C2311yescharacteristic
270C11×#107C2312yes—
271C11×#106C2312yes—
272C11×#106C2311yescharacteristic
273C11×#106C2311yescharacteristic
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×#103C2311yescharacteristic
283C11×#103C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2311yescharacteristic
287C11×#102C2312yes—
288C11×#102C2312yes—
289C11×#102C2312yes—
290C11×#102C2312yes—
291C11×#102C2312yes—
292C11×#102C2311yescharacteristic
293C11×#102C2312yes—
294C11×#102C2312yes—
295C11×#102C2311yescharacteristic
296C11×#102C2312yes—
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2311yescharacteristic
300C11×#102C2311yescharacteristic
301C11×#102C2312yes—
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#61920C1111yesmaximal, characteristic, direct product factor, Sylow
313C24×C11—22no—
314C11×#41—41no—
315C11×#41—41no—
316C11×#41—82no—
317C11×#41—82no—
318C11×#41—82no—
319C11×#41—82no—
320C11×#41—84no—
321C2×Q8×C11—21no—
322C2×Q8×C11—22no—
323C2×Q8×C11—82no—
324C2×Q8×C11C2×D411yescharacteristic
325C2×Q8×C11C2×D411yescharacteristic
326C2×Q8×C11C2×D412yes—
327C2×Q8×C11C2411yescharacteristic
328C2×Q8×C11C2411yescharacteristic
329C2×D4×C11—21no—
330C2×D4×C11—21no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—21no—
334C2×D4×C11—22no—
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11—21no—
346C2×D4×C11—22no—
347C2×D4×C11—42no—
348C2×D4×C11—42no—
349C2×D4×C11—82no—
350C2×D4×C11—82no—
351C2×D4×C11C2412yes—
352C2×D4×C11C2412yes—
353C2×D4×C11C2411yescharacteristic
354C2×D4×C11C2411yescharacteristic
355C2×D4×C11C2412yes—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11—22no—
363C22×C4×C11—22no—
364C22×C4×C11—22no—
365C22×C4×C11—22no—
366C22×C4×C11—22no—
367C22×C4×C11—22no—
368C22×C4×C11C2×D411yescharacteristic
369C22×C4×C11C2×D411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C11×Q16—41no—
372C11×SD16—42no—
373C11×SD16—41no—
374C11×SD16—42no—
375C11×SD16—42no—
376C11×SD16—41no—
377C11×D8—42no—
378C11×D8—42no—
379C11×D8—42no—
380C11×D8—42no—
381C11×D8—41no—
382C11×D8—42no—
383C11×D8—42no—
384C11×D8—42no—
385C2×C8×C11C2411yescharacteristic
386C2×C8×C11C2411yescharacteristic
387C2×C8×C11C2412yes—
388C2×C8×C11C2411yescharacteristic
389C2×C8×C11C2411yescharacteristic
390C2×C8×C11C2412yes—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2×D412yes—
405C11×C4⋊C4C2×D411yescharacteristic
406C11×C4⋊C4C2×D411yescharacteristic
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D412yes—
409C11×C4⋊C4C2×D412yes—
410C11×C4⋊C4C2×D412yes—
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2412yes—
414C11×C4⋊C4C2411yescharacteristic
415C11×C4⋊C4C2411yescharacteristic
416C11×C22⋊C4—21no—
417C11×C22⋊C4—21no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—21no—
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—22no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—22no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—22no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4C2×D412yes—
440C11×C22⋊C4C2×D412yes—
441C42×C11—21no—
442C42×C11—21no—
443C42×C11—21no—
444C42×C11—21no—
445C42×C11—22no—
446C42×C11C2×D411yescharacteristic
447C42×C11C2×D411yescharacteristic
448C42×C11C2411yescharacteristic
449C42×C11C2412yes—
450C42×C11C2412yes—
451C42×C11C2411yescharacteristic
452#3554C2×C1111yescharacteristic, complemented
453#3508C2×C1111yescharacteristic, complemented
454#3403C2×C1112yescomplemented
455#3399C2×C1112yescomplemented
456#3399C2×C1111yescharacteristic, complemented
457#3399C2×C1111yescharacteristic, complemented
458#3396C2×C1111yescharacteristic, complemented
459#3391C2×C1111yescharacteristic, complemented
460#3373C2×C1111yescharacteristic, complemented
461#3370C2×C1112yescomplemented
462#3368C2×C1111yescharacteristic, complemented
463#3366C2×C1112yescomplemented
464#3365C2×C1111yescharacteristic, complemented
465#3358C2×C1111yescharacteristic, complemented
466#3224C2×C1112yescomplemented
467#3220C2×C1112yescomplemented
468#3217C2×C1111yescharacteristic, complemented
469#3205C2×C1111yescharacteristic, complemented
470#3122C2×C1112yescomplemented
471#3118C2×C1112yescomplemented
472#3115C2×C1111yescharacteristic, complemented
473#3102C2×C1111yescharacteristic, complemented
474#2985C2×C1111yescharacteristic, complemented
475C23×C11—22no—
476C23×C11—21no—
477C23×C11—22no—
478C23×C11—22no—
479C23×C11—21no—
480C23×C11—44no—
481C23×C11—82no—
482C23×C11—82no—
483C23×C11C22×D411yescharacteristic
484Q8×C11—22no—
485Q8×C11—22no—
486Q8×C11—21no—
487Q8×C11—21no—
488Q8×C11—21no—
489Q8×C11—21no—
490Q8×C11—42no—
491Q8×C11—42no—
492Q8×C11—82no—
493D4×C11—22no—
494D4×C11—21no—
495D4×C11—21no—
496D4×C11—22no—
497D4×C11—22no—
498D4×C11—22no—
499D4×C11—21no—
500D4×C11—22no—
501D4×C11—22no—
502D4×C11—21no—
503D4×C11—44no—
504D4×C11—44no—
505D4×C11—42no—
506D4×C11—42no—
507D4×C11—42no—
508D4×C11—42no—
509D4×C11—81no—
510D4×C11—82no—
511D4×C11—81no—
512D4×C11—81no—
513D4×C11—82no—
514D4×C11—82no—
515D4×C11—82no—
516D4×C11—82no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11—81no—
520D4×C11—82no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—22no—
530C2×C4×C11—21no—
531C2×C4×C11—41no—
532C2×C4×C11—42no—
533C2×C4×C11—42no—
534C2×C4×C11—42no—
535C2×C4×C11—42no—
536C2×C4×C11—82no—
537C2×C4×C11—82no—
538C2×C4×C11—82no—
539C2×C4×C11—82no—
540C2×C4×C11—82no—
541C2×C4×C11—82no—
542C2×C4×C11—82no—
543C2×C4×C11—82no—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C2511yescharacteristic
554C8×C11—21no—
555C8×C11—21no—
556C8×C11—22no—
557C8×C11—21no—
558C8×C11—21no—
559C8×C11—22no—
560#562—22no—
561#559C22×C1111yescharacteristic
562#559C22×C1112yes—
563#559C22×C1111yescharacteristic
564#559C22×C1111yescharacteristic, complemented
565#559C22×C1112yescomplemented
566#557C22×C1111yescharacteristic, complemented
567#554C22×C1112yescomplemented
568#550C22×C1111yescharacteristic
569#550C22×C1112yes—
570#550C22×C1111yescharacteristic
571#550C22×C1111yescharacteristic, complemented
572D4×Q8C22×C1111yescharacteristic, complemented
573#548—21no—
574#547—21no—
575#546—21no—
576#546—21no—
577#546—22no—
578#542—21no—
579#542C22×C1112yes—
580#540—22no—
581#540C22×C1112yes—
582#539—22no—
583#536—21no—
584#535C22×C1112yes—
585#533C22×C1111yescharacteristic
586#532—21no—
587#532—21no—
588#532C22×C1111yescharacteristic
589C2×#127C22×C1111yescharacteristic
590#529C22×C1111yescharacteristic
591#518C22×C1112yes—
592C4×#41C22×C1111yescharacteristic
593#496C22×C1112yes—
594#496C22×C1112yescomplemented
595#496C22×C1112yescomplemented
596#495C22×C1112yescomplemented
597#493C22×C1111yescharacteristic
598#493C22×C1111yescharacteristic
599#493C22×C1112yescomplemented
600#490C22×C1112yes—
601#490C22×C1112yescomplemented
602#489C22×C1112yescomplemented
603#488C22×C1112yescomplemented
604#486C22×C1111yescharacteristic
605#486C22×C1111yescharacteristic
606#486C22×C1112yescomplemented
607#485C22×C1111yescharacteristic
608#482C22×C1111yescharacteristic
609#482C22×C1112yes—
610#479C22×C1111yescharacteristic, complemented
611#478C22×C1111yescharacteristic, complemented
612#478C22×C1112yescomplemented
613#478C22×C1112yescomplemented
614#476C22×C1112yescomplemented
615#475C22×C1111yescharacteristic, complemented
616#474C22×C1111yescharacteristic, complemented
617#474C22×C1112yescomplemented
618#464C22×C1111yescharacteristic, complemented
619#464C22×C1112yescomplemented
620#463C22×C1111yescharacteristic, complemented
621#463C22×C1112yescomplemented
622#463C22×C1112yescomplemented
623#463C22×C1112yescomplemented
624#463C22×C1112yescomplemented
625#463C22×C1112yescomplemented
626#460C22×C1111yescharacteristic
627#460C22×C1111yescharacteristic
628#460C22×C1112yescomplemented
629#460C22×C1111yescharacteristic, complemented
630#459C22×C1111yescharacteristic
631#459C22×C1112yes—
632#459C22×C1112yes—
633#459C22×C1111yescharacteristic
634#459C22×C1112yescomplemented
635#459C22×C1112yescomplemented
636#459C22×C1112yescomplemented
637#459C22×C1111yescharacteristic, complemented
638#459C22×C1112yescomplemented
639#459C22×C1112yescomplemented
640#452C22×C1111yescharacteristic
641#450C22×C1112yes—
642#449C22×C1111yescharacteristic
643#449C22×C1112yes—
644#447C22×C1112yes—
645#447C22×C1112yes—
646#447C22×C1112yes—
647#446C22×C1112yescomplemented
648#446C22×C1111yescharacteristic, complemented
649#446C22×C1112yescomplemented
650#446C22×C1111yescharacteristic, complemented
651C8×Q8C22×C1111yescharacteristic, complemented
652C8×Q8C22×C1111yescharacteristic, complemented
653#442C22×C1112yescomplemented
654#442C22×C1112yescomplemented
655#442C22×C1112yescomplemented
656#442C22×C1112yescomplemented
657#440C22×C1112yescomplemented
658#440C22×C1112yescomplemented
659C4×Q16C22×C1111yescharacteristic, complemented
660C4×SD16C22×C1111yescharacteristic, complemented
661C4×SD16C22×C1111yescharacteristic, complemented
662C4×SD16C22×C1112yescomplemented
663C4×D8C22×C1111yescharacteristic, complemented
664C4×D8C22×C1112yescomplemented
665C4×D8C22×C1112yescomplemented
666C4×D8C22×C1112yescomplemented
667#433C22×C1112yes—
668#433C22×C1112yes—
669#432C22×C1111yescharacteristic
670#431C22×C1111yescharacteristic
671C22×C11—21no—
672C22×C11—21no—
673C22×C11—21no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—41no—
679C22×C11—41no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—41no—
684C22×C11—41no—
685C22×C11—41no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—42no—
689C22×C11—164no—
690C22×C11C23×D411yescharacteristic
691C4×C11—21no—
692C4×C11—21no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—41no—
702C4×C11—41no—
703C4×C11—41no—
704C4×C11—41no—
705C4×C11—42no—
706C4×C11#57612yes—
707C4×C11#58511yescharacteristic
708C4×C11#58511yescharacteristic
709C2×#41—21no—
710C2×#41—21no—
711C2×#41—22no—
712C2×#41—21no—
713C2×#41—21no—
714C2×#41C23×C1111yescharacteristic
715C22×Q8—21no—
716C22×D4—21no—
717C22×D4—21no—
718C22×D4C23×C1112yes—
719C2×Q16C23×C1111yescharacteristic
720C2×SD16C23×C1111yescharacteristic
721C2×SD16C23×C1112yes—
722C2×SD16C23×C1111yescharacteristic
723C2×SD16C23×C1112yes—
724C2×SD16C23×C1112yes—
725C2×D8C23×C1112yes—
726C2×D8C23×C1112yes—
727C2×D8C23×C1112yes—
728C2×D8C23×C1111yescharacteristic
729C2×D8C23×C1112yes—
730C2×D8C23×C1112yes—
731C2×D8C23×C1112yes—
732C2×D8C23×C1112yes—
733C4⋊Q8—21no—
734C4⋊Q8D4×C1111yescharacteristic
735C4⋊Q8D4×C1111yescharacteristic
736C4⋊Q8C23×C1111yescharacteristic
737C4⋊Q8C23×C1112yes—
738#127—21no—
739#127—21no—
740#127C23×C1112yes—
741#127C23×C1111yescharacteristic
742#127C23×C1111yescharacteristic
743#127C23×C1111yescharacteristic
744#127C23×C1112yes—
745#127C23×C1112yes—
746#127C23×C1112yes—
747#126—22no—
748#126—21no—
749#125—22no—
750#125D4×C1112yes—
751#125C23×C1111yescharacteristic
752#125C23×C1112yes—
753#124—21no—
754#124—21no—
755#124—22no—
756#124—21no—
757#124—22no—
758#124—22no—
759#124—21no—
760#124C23×C1111yescharacteristic
761#124C23×C1112yes—
762#124C23×C1112yes—
763#124C23×C1112yes—
764#123—21no—
765#123—22no—
766#123—22no—
767#123—22no—
768#123—22no—
769#123—22no—
770#123—22no—
771#123—22no—
772#123—22no—
773#123—22no—
774#123—22no—
775C22⋊Q8—22no—
776C22⋊Q8—22no—
777C22⋊Q8—22no—
778C22⋊Q8—22no—
779C22⋊Q8—22no—
780C22⋊Q8—21no—
781C22⋊Q8D4×C1111yescharacteristic
782C22⋊Q8D4×C1111yescharacteristic
783C22⋊Q8D4×C1112yes—
784C22⋊Q8C23×C1111yescharacteristic
785#121—21no—
786#121—22no—
787#121—22no—
788#121—21no—
789#121—21no—
790#121—22no—
791#121—22no—
792#121—22no—
793#121—22no—
794#121—22no—
795#121—22no—
796#121—21no—
797#121—22no—
798#121—22no—
799#121C23×C1111yescharacteristic
800#121C23×C1112yes—
801#120—22no—
802#120—22no—
803C4×Q8—21no—
804C4×Q8C23×C1111yescharacteristic
805C4×Q8C23×C1111yescharacteristic
806C4×Q8C23×C1111yescharacteristic
807C4×Q8C23×C1112yes—
808C4×Q8C23×C1111yescharacteristic
809C4×Q8C23×C1111yescharacteristic
810C4×Q8C23×C1112yes—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—21no—
814C4×D4—22no—
815C4×D4—22no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—22no—
819C4×D4—22no—
820C4×D4—21no—
821C4×D4—21no—
822C4×D4C23×C1111yescharacteristic
823C4×D4C23×C1111yescharacteristic
824C4×D4C23×C1112yes—
825C4×D4C23×C1112yes—
826C4×D4C23×C1112yes—
827C4×D4C23×C1112yes—
828C4×D4C23×C1111yescharacteristic
829C4×D4C23×C1112yes—
830C4×D4C23×C1112yes—
831C4×D4C23×C1112yes—
832C4×D4C23×C1112yes—
833#117—21no—
834#117—21no—
835#117C23×C1111yescharacteristic
836#117C23×C1112yes—
837C2×C4⋊C4—22no—
838C2×C22⋊C4—22no—
839C2×C22⋊C4—22no—
840C2×C42—21no—
841C2×C42C23×C1111yescharacteristic
842#107C23×C1111yescharacteristic
843#107C23×C1111yescharacteristic
844#107C23×C1112yes—
845#106C23×C1112yes—
846#106C23×C1111yescharacteristic
847#106C23×C1111yescharacteristic
848C4⋊C8C23×C1111yescharacteristic
849C4⋊C8C23×C1111yescharacteristic
850C4⋊C8C23×C1111yescharacteristic
851C4⋊C8C23×C1111yescharacteristic
852C4⋊C8C23×C1112yes—
853C4⋊C8C23×C1112yes—
854C4⋊C8C23×C1112yes—
855C4⋊C8C23×C1112yes—
856#103C23×C1111yescharacteristic
857#103C23×C1111yescharacteristic
858#103C23×C1111yescharacteristic
859#103C23×C1111yescharacteristic
860#103C23×C1112yes—
861#102C23×C1111yescharacteristic
862#102C23×C1112yes—
863#102C23×C1112yes—
864#102C23×C1112yes—
865#102C23×C1112yes—
866#102C23×C1112yes—
867#102C23×C1111yescharacteristic
868#102C23×C1111yescharacteristic
869#102C23×C1112yes—
870#102C23×C1111yescharacteristic
871#102C23×C1112yes—
872#102C23×C1112yes—
873#102C23×C1112yes—
874#102C23×C1112yes—
875#102C23×C1112yes—
876C22⋊C8C23×C1111yescharacteristic
877C22⋊C8C23×C1111yescharacteristic
878C22⋊C8C23×C1112yes—
879#97C23×C1112yes—
880#97C23×C1112yes—
881#97C23×C1112yes—
882C4×C8C23×C1111yescharacteristic
883C4×C8C23×C1111yescharacteristic
884C4×C8C23×C1112yes—
885C4×C8C23×C1112yes—
886C2×C11—41no—
887C2×C11—81no—
888C2×C11—82no—
889C2×C11—81no—
890C2×C11—82no—
891C2×C11—82no—
892C2×C11#348711yescharacteristic
893C2×C11C2×#57611yescharacteristic
894C2×C11#358511yescharacteristic
895C24—22no—
896#41—41no—
897#41—41no—
898#41—82no—
899#41—82no—
900#41—82no—
901#41—82no—
902#41—84no—
903C2×Q8—21no—
904C2×Q8—22no—
905C2×Q8—82no—
906C2×Q8C2×D4×C1111yescharacteristic
907C2×Q8C2×D4×C1111yescharacteristic
908C2×Q8C2×D4×C1112yes—
909C2×Q8C24×C1111yescharacteristic
910C2×Q8C24×C1111yescharacteristic
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—22no—
914C2×D4—22no—
915C2×D4—21no—
916C2×D4—22no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—22no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—82no—
932C2×D4—82no—
933C2×D4C24×C1112yes—
934C2×D4C24×C1112yes—
935C2×D4C24×C1111yescharacteristic
936C2×D4C24×C1111yescharacteristic
937C2×D4C24×C1112yes—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4C2×D4×C1111yescharacteristic
951C22×C4C2×D4×C1111yescharacteristic
952C22×C4C24×C1111yescharacteristic
953Q16—41no—
954SD16—41no—
955SD16—42no—
956SD16—41no—
957SD16—42no—
958SD16—42no—
959D8—41no—
960D8—42no—
961D8—42no—
962D8—42no—
963D8—42no—
964D8—42no—
965D8—42no—
966D8—42no—
967C2×C8C24×C1111yescharacteristic
968C2×C8C24×C1111yescharacteristic
969C2×C8C24×C1112yes—
970C2×C8C24×C1111yescharacteristic
971C2×C8C24×C1111yescharacteristic
972C2×C8C24×C1112yes—
973C4⋊C4—21no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—21no—
984C4⋊C4C2×D4×C1112yes—
985C4⋊C4C2×D4×C1112yes—
986C4⋊C4C2×D4×C1112yes—
987C4⋊C4C2×D4×C1111yescharacteristic
988C4⋊C4C2×D4×C1111yescharacteristic
989C4⋊C4C2×D4×C1112yes—
990C4⋊C4C2×D4×C1112yes—
991C4⋊C4C2×D4×C1112yes—
992C4⋊C4C2×D4×C1112yes—
993C4⋊C4C24×C1111yescharacteristic
994C4⋊C4C24×C1111yescharacteristic
995C4⋊C4C24×C1112yes—
996C4⋊C4C24×C1111yescharacteristic
997C4⋊C4C24×C1111yescharacteristic
998C22⋊C4—21no—
999C22⋊C4—21no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—21no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4C2×D4×C1112yes—
1022C22⋊C4C2×D4×C1112yes—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—22no—
1028C42C2×D4×C1111yescharacteristic
1029C42C2×D4×C1111yescharacteristic
1030C42C24×C1111yescharacteristic
1031C42C24×C1112yes—
1032C42C24×C1112yes—
1033C42C24×C1111yescharacteristic
1034C11#6192011yescharacteristic, direct product factor, Sylow
1035C23—21no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—21no—
1040C23—44no—
1041C23—82no—
1042C23—82no—
1043C23C22×D4×C1111yescharacteristic
1044Q8—22no—
1045Q8—22no—
1046Q8—21no—
1047Q8—21no—
1048Q8—21no—
1049Q8—21no—
1050Q8—42no—
1051Q8—42no—
1052Q8—82no—
1053D4—21no—
1054D4—22no—
1055D4—22no—
1056D4—21no—
1057D4—22no—
1058D4—22no—
1059D4—21no—
1060D4—22no—
1061D4—22no—
1062D4—21no—
1063D4—44no—
1064D4—44no—
1065D4—42no—
1066D4—42no—
1067D4—42no—
1068D4—42no—
1069D4—81no—
1070D4—82no—
1071D4—82no—
1072D4—81no—
1073D4—81no—
1074D4—82no—
1075D4—82no—
1076D4—82no—
1077D4—82no—
1078D4—82no—
1079D4—81no—
1080D4—82no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—41no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—82no—
1103C2×C4—82no—
1104C2×C4C22×D4×C1111yescharacteristic
1105C2×C4C22×D4×C1111yescharacteristic
1106C2×C4C22×D4×C1112yes—
1107C2×C4C22×D4×C1111yescharacteristic
1108C2×C4C22×D4×C1111yescharacteristic
1109C2×C4C22×D4×C1112yes—
1110C2×C4C22×D4×C1112yes—
1111C2×C4C22×D4×C1112yes—
1112C2×C4C22×D4×C1111yescharacteristic
1113C2×C4C25×C1111yescharacteristic
1114C8—21no—
1115C8—21no—
1116C8—21no—
1117C8—22no—
1118C8—21no—
1119C8—22no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—41no—
1124C22—42no—
1125C22—42no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—41no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—41no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—41no—
1138C22—164no—
1139C22C23×D4×C1111yescharacteristic
1140C4—21no—
1141C4—21no—
1142C4—22no—
1143C4—22no—
1144C4—21no—
1145C4—21no—
1146C4—22no—
1147C4—22no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—42no—
1153C4—41no—
1154C4—41no—
1155C4C11×#57612yes—
1156C4C11×#58511yescharacteristic
1157C4C11×#58511yescharacteristic
1158C2—41no—
1159C2—82no—
1160C2—82no—
1161C2—81no—
1162C2—81no—
1163C2—82no—
1164C2C11×#348711yescharacteristic
1165C2C2×C11×#57611yescharacteristic
1166C2C11×#358511yescharacteristic
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×#3508C2semidirect
3. C11×#3403C2semidirect
4. C11×#3399C2semidirect
5. C11×#3399C2semidirect
6. C11×#3399C2semidirect
7. C11×#3396C2semidirect
8. C11×#3391C2semidirect
9. C11×#3373C2semidirect
10. C11×#3370C2semidirect
11. C11×#3368C2semidirect
12. C11×#3366C2semidirect
13. C11×#3365C2semidirect
14. C11×#3358C2semidirect
15. C11×#3224C2semidirect
16. C11×#3220C2semidirect
17. C11×#3217C2semidirect
18. C11×#3205C2semidirect
19. C11×#3122C2semidirect
20. C11×#3118C2semidirect
21. C11×#3115C2semidirect
22. C11×#3102C2semidirect
23. C11×#2985C2semidirect
28. C11×#559C22semidirect
29. C11×#559C22semidirect
30. C11×#557C22semidirect
31. C11×#554C22semidirect
35. C11×#550C22semidirect
36. D4×Q8×C11C22semidirect
58. C11×#496C22semidirect
59. C11×#496C22semidirect
60. C11×#495C22semidirect
63. C11×#493C22semidirect
65. C11×#490C22semidirect
66. C11×#489C22semidirect
67. C11×#488C22semidirect
70. C11×#486C22semidirect
74. C11×#479C22semidirect
75. C11×#478C22semidirect
76. C11×#478C22semidirect
77. C11×#478C22semidirect
78. C11×#476C22semidirect
79. C11×#475C22semidirect
80. C11×#474C22semidirect
81. C11×#474C22semidirect
82. C11×#464C22semidirect
83. C11×#464C22semidirect
84. C11×#463C22semidirect
85. C11×#463C22semidirect
86. C11×#463C22semidirect
87. C11×#463C22semidirect
88. C11×#463C22semidirect
89. C11×#463C22semidirect
92. C11×#460C22semidirect
93. C11×#460C22semidirect
98. C11×#459C22semidirect
99. C11×#459C22semidirect
100. C11×#459C22semidirect
101. C11×#459C22semidirect
102. C11×#459C22semidirect
103. C11×#459C22semidirect
111. C11×#446C22semidirect
112. C11×#446C22semidirect
113. C11×#446C22semidirect
114. C11×#446C22semidirect
115. C8×Q8×C11C22semidirect
116. C8×Q8×C11C22semidirect
117. C11×#442C22semidirect
118. C11×#442C22semidirect
119. C11×#442C22semidirect
120. C11×#442C22semidirect
121. C11×#440C22semidirect
122. C11×#440C22semidirect
123. C4×C11×Q16C22semidirect
124. C4×C11×SD16C22semidirect
125. C4×C11×SD16C22semidirect
126. C4×C11×SD16C22semidirect
127. C4×C11×D8C22semidirect
128. C4×C11×D8C22semidirect
129. C4×C11×D8C22semidirect
130. C4×C11×D8C22semidirect
312. #61920C11direct (N × H)
452. #3554C2×C11semidirect
453. #3508C2×C11semidirect
454. #3403C2×C11semidirect
455. #3399C2×C11semidirect
456. #3399C2×C11semidirect
457. #3399C2×C11semidirect
458. #3396C2×C11semidirect
459. #3391C2×C11semidirect
460. #3373C2×C11semidirect
461. #3370C2×C11semidirect
462. #3368C2×C11semidirect
463. #3366C2×C11semidirect
464. #3365C2×C11semidirect
465. #3358C2×C11semidirect
466. #3224C2×C11semidirect
467. #3220C2×C11semidirect
468. #3217C2×C11semidirect
469. #3205C2×C11semidirect
470. #3122C2×C11semidirect
471. #3118C2×C11semidirect
472. #3115C2×C11semidirect
473. #3102C2×C11semidirect
474. #2985C2×C11semidirect
564. #559C22×C11semidirect
565. #559C22×C11semidirect
566. #557C22×C11semidirect
567. #554C22×C11semidirect
571. #550C22×C11semidirect
572. D4×Q8C22×C11semidirect
594. #496C22×C11semidirect
595. #496C22×C11semidirect
596. #495C22×C11semidirect
599. #493C22×C11semidirect
601. #490C22×C11semidirect
602. #489C22×C11semidirect
603. #488C22×C11semidirect
606. #486C22×C11semidirect
610. #479C22×C11semidirect
611. #478C22×C11semidirect
612. #478C22×C11semidirect
613. #478C22×C11semidirect
614. #476C22×C11semidirect
615. #475C22×C11semidirect
616. #474C22×C11semidirect
617. #474C22×C11semidirect
618. #464C22×C11semidirect
619. #464C22×C11semidirect
620. #463C22×C11semidirect
621. #463C22×C11semidirect
622. #463C22×C11semidirect
623. #463C22×C11semidirect
624. #463C22×C11semidirect
625. #463C22×C11semidirect
628. #460C22×C11semidirect
629. #460C22×C11semidirect
634. #459C22×C11semidirect
635. #459C22×C11semidirect
636. #459C22×C11semidirect
637. #459C22×C11semidirect
638. #459C22×C11semidirect
639. #459C22×C11semidirect
647. #446C22×C11semidirect
648. #446C22×C11semidirect
649. #446C22×C11semidirect
650. #446C22×C11semidirect
651. C8×Q8C22×C11semidirect
652. C8×Q8C22×C11semidirect
653. #442C22×C11semidirect
654. #442C22×C11semidirect
655. #442C22×C11semidirect
656. #442C22×C11semidirect
657. #440C22×C11semidirect
658. #440C22×C11semidirect
659. C4×Q16C22×C11semidirect
660. C4×SD16C22×C11semidirect
661. C4×SD16C22×C11semidirect
662. C4×SD16C22×C11semidirect
663. C4×D8C22×C11semidirect
664. C4×D8C22×C11semidirect
665. C4×D8C22×C11semidirect
666. C4×D8C22×C11semidirect
1034. C11#61920direct (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×#35082
C11×#34032
C11×#33992
C11×#33962
C11×#33912
C11×#33732
C11×#33702
C11×#33682
C11×#33662
C11×#33652
C11×#33582
C11×#32242
C11×#32202
C11×#32172
C11×#32052
C11×#31222
C11×#31182
C11×#31152
C11×#31022
C11×#29852
#6192011