Finite Group Databasebeta

← C11×#61974 #14639167

Subgroups — C11×#61974 #14639167

Order 2816.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3481C211yesmaximal, characteristic, complemented
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3399C211yesmaximal, characteristic, complemented
5C11×#3372C211yesmaximal, characteristic, complemented
6C11×#3366C211yesmaximal, characteristic, complemented
7C11×#3333C211yesmaximal, characteristic, complemented
8C11×#3331C211yesmaximal, characteristic, complemented
9C11×#3309C212yesmaximal, complemented
10C11×#3307C212yesmaximal, complemented
11C11×#3274C211yesmaximal, characteristic, complemented
12C11×#3272C211yesmaximal, characteristic, complemented
13C11×#3268C212yesmaximal, complemented
14C11×#3267C212yesmaximal, complemented
15C11×#3256C212yesmaximal, complemented
16C11×#3247C211yesmaximal, characteristic, complemented
17C11×#3219C212yesmaximal, complemented
18C11×#3207C211yesmaximal, characteristic, complemented
19C11×#3114C212yesmaximal, complemented
20C11×#3102C211yesmaximal, characteristic, complemented
21C11×#3036C212yesmaximal, complemented
22C11×#3035C211yesmaximal, characteristic, complemented
23C11×#2989C211yesmaximal, characteristic, complemented
24C2×C11×AGL(1,ℤ/8)C2212yes—
25C2×C11×AGL(1,ℤ/8)C2212yes—
26C2×C11×#135C2212yes—
27C11×#559C2211yescharacteristic
28C11×#557C2211yescharacteristic, complemented
29C11×#554C2211yescharacteristic
30C11×#554C2211yescharacteristic
31C11×#553—21no—
32C11×#553—21no—
33C11×#553—22no—
34C11×#553C2212yes—
35C11×#551—22no—
36C11×#550—21no—
37C11×#550C2211yescharacteristic
38C11×#550C2212yescomplemented
39C11×#550C2211yescharacteristic, complemented
40C11×#547C2211yescharacteristic
41C11×#547C2212yescomplemented
42C11×#546—21no—
43C11×#546C2212yes—
44D42×C11C2211yescharacteristic
45C11×#540—21no—
46C11×#540—22no—
47C11×#532C2211yescharacteristic
48C11×#532C2211yescharacteristic, complemented
49C11×#532C2212yescomplemented
50C11×#529—21no—
51C11×#529C2212yes—
52C11×#529C2211yescharacteristic, complemented
53C11×#529C2212yescomplemented
54C11×#525—22no—
55C11×#520—21no—
56C4×C11×#41C2211yescharacteristic
57C4×C11×#41C2211yescharacteristic
58C2×C4×D4×C11—21no—
59C2×C4×D4×C11C2212yes—
60C11×#497C2212yescomplemented
61C11×#496C2212yescomplemented
62C11×#493C2211yescharacteristic
63C11×#492C2211yescharacteristic
64C11×#491C2212yescomplemented
65C11×#490C2212yescomplemented
66C11×#487C2211yescharacteristic, complemented
67C11×#486C2211yescharacteristic, complemented
68C11×#485C2211yescharacteristic, complemented
69C11×#483C2212yescomplemented
70C11×#482C2211yescharacteristic, complemented
71C11×#480C2212yescomplemented
72C11×#479C2211yescharacteristic, complemented
73C11×#479C2212yescomplemented
74C11×#478C2211yescharacteristic
75C11×#478C2212yescomplemented
76C11×#478C2212yescomplemented
77C11×#477C2211yescharacteristic, complemented
78C11×#476C2211yescharacteristic, complemented
79C11×#470C2212yescomplemented
80C11×#469C2212yes—
81C11×#468C2212yes—
82C11×#468C2212yescomplemented
83C11×#466C2212yescomplemented
84C11×#465C2212yescomplemented
85C11×#464C2211yescharacteristic, complemented
86C11×#464C2212yescomplemented
87C11×#464C2212yescomplemented
88C11×#463C2212yes—
89C11×#463C2211yescharacteristic
90C11×#463C2212yescomplemented
91C11×#463C2212yescomplemented
92C11×#463C2212yescomplemented
93C11×#463C2212yescomplemented
94C11×#462C2211yescharacteristic, complemented
95C11×#461C2212yes—
96C11×#461C2211yescharacteristic
97C11×#461C2212yescomplemented
98C11×#460C2211yescharacteristic
99C11×#460C2211yescharacteristic, complemented
100C11×#459C2211yescharacteristic
101C11×#459C2212yes—
102C11×#459C2211yescharacteristic
103C11×#459C2212yescomplemented
104C11×#452C2211yescharacteristic
105C11×#452C2212yescomplemented
106C11×#452C2212yescomplemented
107C11×#450C2212yes—
108C11×#449C2212yes—
109C11×#449C2212yes—
110C11×#449C2211yescharacteristic
111C11×#449C2212yescomplemented
112C11×#449C2212yescomplemented
113C11×#447C2212yes—
114C11×#446C2211yescharacteristic, complemented
115C11×#446C2211yescharacteristic, complemented
116C11×#442C2212yes—
117C11×#442C2212yescomplemented
118C11×#440C2212yes—
119C11×#440C2212yescomplemented
120C4×C11×Q16C2211yescharacteristic, complemented
121C4×C11×SD16C2211yescharacteristic
122C4×C11×SD16C2211yescharacteristic, complemented
123C4×C11×D8C2211yescharacteristic
124C11×#436C2211yescharacteristic
125C11×#436C2211yescharacteristic
126C11×#435C2212yescomplemented
127C11×#435C2212yescomplemented
128C11×#432C2212yescomplemented
129C11×#431C2211yescharacteristic, complemented
130C11×#423C2212yescomplemented
131C2×C11×C4⋊C8C2211yescharacteristic, complemented
132C11×#417C2212yescomplemented
133C11×#417C2212yescomplemented
134C11×#416C2212yescomplemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41D411yescharacteristic
138C2×C11×#41C2311yescharacteristic
139C2×C11×#41C2312yes—
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C22×D4×C11—21no—
143C22×D4×C11C2312yes—
144C23×C4×C11—22no—
145C11×AGL(1,ℤ/8)—44no—
146C11×AGL(1,ℤ/8)—44no—
147C11×#135—44no—
148C2×C11×Q16C2311yescharacteristic
149C2×C11×Q16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2311yescharacteristic
152C2×C11×SD16C2312yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2311yescharacteristic
155C2×C11×SD16C2312yes—
156C2×C11×SD16C2312yes—
157C2×C11×D8C2312yes—
158C2×C11×D8C2311yescharacteristic
159C2×C11×D8C2312yes—
160C2×C11×D8C2312yes—
161C2×C11×D8C2312yes—
162C2×C11×M16C2312yes—
163C2×C11×M16C2312yes—
164C22×C8×C11C2312yes—
165C11×C4⋊Q8C2312yes—
166C11×C4⋊Q8C2311yescharacteristic
167C11×C4⋊Q8C2311yescharacteristic
168C11×#127—21no—
169C11×#127—22no—
170C11×#127C2312yes—
171C11×#127C2311yescharacteristic
172C11×#127C2311yescharacteristic
173C11×#126—22no—
174C11×#126—22no—
175C11×#126—21no—
176C11×#126—22no—
177C11×#125—21no—
178C11×#125—21no—
179C11×#125—22no—
180C11×#125C2312yes—
181C11×#125C2311yescharacteristic
182C11×#124—21no—
183C11×#124—21no—
184C11×#124C2312yes—
185C11×#124C2311yescharacteristic
186C11×#124C2312yes—
187C11×#123—22no—
188C11×#123—22no—
189C11×#123—21no—
190C11×#123—22no—
191C11×#123—22no—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×C22⋊Q8—21no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2311yescharacteristic
202C11×#121—22no—
203C11×#121—21no—
204C11×#121—22no—
205C11×#121—21no—
206C11×#121—22no—
207C11×#121—21no—
208C11×#121—21no—
209C11×#121—22no—
210C11×#121—21no—
211C11×#121—21no—
212C11×#121—22no—
213C11×#121—22no—
214C11×#121—22no—
215C11×#121—22no—
216C11×#121—22no—
217C11×#121C2312yes—
218C11×#121C2312yes—
219C11×#121C2311yescharacteristic
220C11×#121C2312yes—
221C11×#120—22no—
222C11×#120—22no—
223C4×Q8×C11—21no—
224C4×Q8×C11D411yescharacteristic
225C4×Q8×C11C2311yescharacteristic
226C4×Q8×C11C2311yescharacteristic
227C4×Q8×C11C2311yescharacteristic
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2311yescharacteristic
230C4×D4×C11—21no—
231C4×D4×C11—22no—
232C4×D4×C11—21no—
233C4×D4×C11—21no—
234C4×D4×C11—21no—
235C4×D4×C11—22no—
236C4×D4×C11—21no—
237C4×D4×C11—21no—
238C4×D4×C11—22no—
239C4×D4×C11—22no—
240C4×D4×C11—21no—
241C4×D4×C11—22no—
242C4×D4×C11—22no—
243C4×D4×C11—21no—
244C4×D4×C11—22no—
245C4×D4×C11—21no—
246C4×D4×C11—22no—
247C4×D4×C11D411yescharacteristic
248C4×D4×C11D412yes—
249C4×D4×C11C2311yescharacteristic
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2311yescharacteristic
254C4×D4×C11C2311yescharacteristic
255C4×D4×C11C2312yes—
256C4×D4×C11C2311yescharacteristic
257C4×D4×C11C2312yes—
258C11×#117—21no—
259C11×#117—21no—
260C11×#117—22no—
261C11×#117—22no—
262C11×#117D412yes—
263C11×#117D411yescharacteristic
264C11×#117C2311yescharacteristic
265C2×C11×C4⋊C4—21no—
266C2×C11×C4⋊C4—21no—
267C2×C11×C4⋊C4—22no—
268C2×C11×C4⋊C4C2312yes—
269C2×C11×C22⋊C4—22no—
270C2×C11×C22⋊C4—22no—
271C2×C42×C11—21no—
272C2×C42×C11C2312yes—
273C2×C42×C11C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2311yescharacteristic
276C11×#107C2312yes—
277C11×#106C2311yescharacteristic
278C11×#106C2311yescharacteristic
279C11×#106C2312yes—
280C11×C4⋊C8C2312yes—
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2311yescharacteristic
283C11×C4⋊C8C2311yescharacteristic
284C11×C4⋊C8C2312yes—
285C11×C4⋊C8C2312yes—
286C11×C4⋊C8C2311yescharacteristic
287C11×#103C2311yescharacteristic
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2312yes—
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2311yescharacteristic
295C11×#103C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2312yes—
298C11×#102C2312yes—
299C11×#102C2312yes—
300C11×#102C2312yes—
301C11×#102C2311yescharacteristic
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×#102C2311yescharacteristic
305C11×#102C2312yes—
306C11×#102C2312yes—
307C11×C22⋊C8C2311yescharacteristic
308C11×C22⋊C8C2311yescharacteristic
309C11×C22⋊C8C2312yes—
310C11×C22⋊C8C2312yes—
311C11×#97C2312yes—
312C11×#97C2312yes—
313C4×C8×C11C2311yescharacteristic
314C4×C8×C11C2311yescharacteristic
315#61974C1111yesmaximal, characteristic, direct product factor, Sylow
316C24×C11—22no—
317C11×#41—22no—
318C11×#41—42no—
319C11×#41—41no—
320C11×#41—42no—
321C11×#41—42no—
322C11×#41—42no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—42no—
326C11×#41—44no—
327C11×#41—82no—
328C2×Q8×C11—21no—
329C2×Q8×C11C2×D411yescharacteristic
330C2×Q8×C11C2411yescharacteristic
331C2×Q8×C11C2412yes—
332C2×Q8×C11C2411yescharacteristic
333C2×D4×C11—24no—
334C2×D4×C11—21no—
335C2×D4×C11—22no—
336C2×D4×C11—22no—
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—21no—
344C2×D4×C11—22no—
345C2×D4×C11—21no—
346C2×D4×C11—22no—
347C2×D4×C11—21no—
348C2×D4×C11—21no—
349C2×D4×C11—42no—
350C2×D4×C11—44no—
351C2×D4×C11C2×D411yescharacteristic
352C2×D4×C11C2×D412yes—
353C2×D4×C11C2411yescharacteristic
354C2×D4×C11C2412yes—
355C2×D4×C11C2412yes—
356C2×D4×C11C2411yescharacteristic
357C22×C4×C11—22no—
358C22×C4×C11—21no—
359C22×C4×C11—21no—
360C22×C4×C11—21no—
361C22×C4×C11—22no—
362C22×C4×C11—21no—
363C22×C4×C11—22no—
364C22×C4×C11—22no—
365C22×C4×C11—22no—
366C22×C4×C11—22no—
367C22×C4×C11—22no—
368C22×C4×C11—22no—
369C22×C4×C11—84no—
370C22×C4×C11C2×D411yescharacteristic
371C22×C4×C11C2×D412yes—
372C22×C4×C11C2×D412yes—
373C22×C4×C11C2×D411yescharacteristic
374C22×C4×C11C2412yes—
375C22×C4×C11C2411yescharacteristic
376C11×Q16—41no—
377C11×Q16—42no—
378C11×SD16—24no—
379C11×SD16—22no—
380C11×SD16—42no—
381C11×SD16—41no—
382C11×SD16—42no—
383C11×SD16—42no—
384C11×SD16—42no—
385C11×D8—24no—
386C11×D8—22no—
387C11×D8—42no—
388C11×D8—42no—
389C11×D8—42no—
390C11×M16—42no—
391C11×M16—42no—
392C2×C8×C11—42no—
393C2×C8×C11C2411yescharacteristic
394C2×C8×C11C2411yescharacteristic
395C2×C8×C11C2411yescharacteristic
396C2×C8×C11C2411yescharacteristic
397C2×C8×C11C2412yes—
398C2×C8×C11C2412yes—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—22no—
411C11×C4⋊C4—21no—
412C11×C4⋊C4—22no—
413C11×C4⋊C4—21no—
414C11×C4⋊C4—22no—
415C11×C4⋊C4—21no—
416C11×C4⋊C4C2×D411yescharacteristic
417C11×C4⋊C4C2×D411yescharacteristic
418C11×C4⋊C4C2×D412yes—
419C11×C4⋊C4C2×D412yes—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2412yes—
422C11×C4⋊C4C2411yescharacteristic
423C11×C4⋊C4C2411yescharacteristic
424C11×C4⋊C4C2411yescharacteristic
425C11×C22⋊C4—22no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—21no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4—22no—
432C11×C22⋊C4—22no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—22no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—22no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—21no—
443C11×C22⋊C4—22no—
444C11×C22⋊C4—22no—
445C11×C22⋊C4—21no—
446C11×C22⋊C4C2×D412yes—
447C11×C22⋊C4C2×D412yes—
448C11×C22⋊C4C2×D412yes—
449C42×C11—21no—
450C42×C11—21no—
451C42×C11—21no—
452C42×C11—22no—
453C42×C11—21no—
454C42×C11C2×D411yescharacteristic
455C42×C11C2×D412yes—
456C42×C11C2×D411yescharacteristic
457C42×C11C2×D412yes—
458C42×C11C2411yescharacteristic
459C42×C11C2412yes—
460C42×C11C2411yescharacteristic
461#3517C2×C1111yescharacteristic, complemented
462#3481C2×C1111yescharacteristic, complemented
463#3400C2×C1111yescharacteristic, complemented
464#3399C2×C1111yescharacteristic, complemented
465#3372C2×C1111yescharacteristic, complemented
466#3366C2×C1111yescharacteristic, complemented
467#3333C2×C1111yescharacteristic, complemented
468#3331C2×C1111yescharacteristic, complemented
469#3309C2×C1112yescomplemented
470#3307C2×C1112yescomplemented
471#3274C2×C1111yescharacteristic, complemented
472#3272C2×C1111yescharacteristic, complemented
473#3268C2×C1112yescomplemented
474#3267C2×C1112yescomplemented
475#3256C2×C1112yescomplemented
476#3247C2×C1111yescharacteristic, complemented
477#3219C2×C1112yescomplemented
478#3207C2×C1111yescharacteristic, complemented
479#3114C2×C1112yescomplemented
480#3102C2×C1111yescharacteristic, complemented
481#3036C2×C1112yescomplemented
482#3035C2×C1111yescharacteristic, complemented
483#2989C2×C1111yescharacteristic, complemented
484C23×C11—21no—
485C23×C11—22no—
486C23×C11—21no—
487C23×C11—22no—
488C23×C11—44no—
489C23×C11—44no—
490C23×C11—82no—
491C23×C11C22×D412yes—
492C23×C11C22×D411yescharacteristic
493Q8×C11—22no—
494Q8×C11—21no—
495Q8×C11—22no—
496Q8×C11—21no—
497Q8×C11—21no—
498Q8×C11—22no—
499Q8×C11—21no—
500Q8×C11—81no—
501D4×C11—22no—
502D4×C11—21no—
503D4×C11—22no—
504D4×C11—22no—
505D4×C11—21no—
506D4×C11—22no—
507D4×C11—22no—
508D4×C11—21no—
509D4×C11—42no—
510D4×C11—44no—
511D4×C11—44no—
512D4×C11—42no—
513D4×C11—44no—
514D4×C11—42no—
515D4×C11—42no—
516D4×C11—82no—
517D4×C11—81no—
518D4×C11—81no—
519D4×C11—82no—
520D4×C11—81no—
521D4×C11—82no—
522D4×C11—82no—
523D4×C11—82no—
524D4×C11—82no—
525D4×C11H(5,𝔽2)12yes—
526C2×C4×C11—22no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—41no—
542C2×C4×C11—42no—
543C2×C4×C11—42no—
544C2×C4×C11—44no—
545C2×C4×C11—44no—
546C2×C4×C11—42no—
547C2×C4×C11—42no—
548C2×C4×C11—82no—
549C2×C4×C11—82no—
550C2×C4×C11—82no—
551C2×C4×C11—82no—
552C2×C4×C11—82no—
553C2×C4×C11—82no—
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C22×D412yes—
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D412yes—
559C2×C4×C11C22×D412yes—
560C2×C4×C11C22×D411yescharacteristic
561C2×C4×C11C22×D411yescharacteristic
562C2×C4×C11C2511yescharacteristic
563C8×C11—22no—
564C8×C11—22no—
565C8×C11—21no—
566C8×C11—21no—
567C8×C11—21no—
568C8×C11—21no—
569C2×AGL(1,ℤ/8)C22×C1112yes—
570C2×AGL(1,ℤ/8)C22×C1112yes—
571C2×#135C22×C1112yes—
572#559C22×C1111yescharacteristic
573#557C22×C1111yescharacteristic, complemented
574#554C22×C1111yescharacteristic
575#554C22×C1111yescharacteristic
576#553—21no—
577#553—21no—
578#553—22no—
579#553C22×C1112yes—
580#551—22no—
581#550—21no—
582#550C22×C1111yescharacteristic
583#550C22×C1112yescomplemented
584#550C22×C1111yescharacteristic, complemented
585#547C22×C1111yescharacteristic
586#547C22×C1112yescomplemented
587#546—21no—
588#546C22×C1112yes—
589D42C22×C1111yescharacteristic
590#540—21no—
591#540—22no—
592#532C22×C1111yescharacteristic
593#532C22×C1111yescharacteristic, complemented
594#532C22×C1112yescomplemented
595#529—21no—
596#529C22×C1112yes—
597#529C22×C1111yescharacteristic, complemented
598#529C22×C1112yescomplemented
599#525—22no—
600#520—21no—
601C4×#41C22×C1111yescharacteristic
602C4×#41C22×C1111yescharacteristic
603C2×C4×D4—21no—
604C2×C4×D4C22×C1112yes—
605#497C22×C1112yescomplemented
606#496C22×C1112yescomplemented
607#493C22×C1111yescharacteristic
608#492C22×C1111yescharacteristic
609#491C22×C1112yescomplemented
610#490C22×C1112yescomplemented
611#487C22×C1111yescharacteristic, complemented
612#486C22×C1111yescharacteristic, complemented
613#485C22×C1111yescharacteristic, complemented
614#483C22×C1112yescomplemented
615#482C22×C1111yescharacteristic, complemented
616#480C22×C1112yescomplemented
617#479C22×C1111yescharacteristic, complemented
618#479C22×C1112yescomplemented
619#478C22×C1111yescharacteristic
620#478C22×C1112yescomplemented
621#478C22×C1112yescomplemented
622#477C22×C1111yescharacteristic, complemented
623#476C22×C1111yescharacteristic, complemented
624#470C22×C1112yescomplemented
625#469C22×C1112yes—
626#468C22×C1112yes—
627#468C22×C1112yescomplemented
628#466C22×C1112yescomplemented
629#465C22×C1112yescomplemented
630#464C22×C1111yescharacteristic, complemented
631#464C22×C1112yescomplemented
632#464C22×C1112yescomplemented
633#463C22×C1111yescharacteristic
634#463C22×C1112yes—
635#463C22×C1112yescomplemented
636#463C22×C1112yescomplemented
637#463C22×C1112yescomplemented
638#463C22×C1112yescomplemented
639#462C22×C1111yescharacteristic, complemented
640#461C22×C1112yes—
641#461C22×C1111yescharacteristic
642#461C22×C1112yescomplemented
643#460C22×C1111yescharacteristic
644#460C22×C1111yescharacteristic, complemented
645#459C22×C1112yes—
646#459C22×C1111yescharacteristic
647#459C22×C1111yescharacteristic
648#459C22×C1112yescomplemented
649#452C22×C1111yescharacteristic
650#452C22×C1112yescomplemented
651#452C22×C1112yescomplemented
652#450C22×C1112yes—
653#449C22×C1111yescharacteristic
654#449C22×C1112yes—
655#449C22×C1112yes—
656#449C22×C1112yescomplemented
657#449C22×C1112yescomplemented
658#447C22×C1112yes—
659#446C22×C1111yescharacteristic, complemented
660#446C22×C1111yescharacteristic, complemented
661#442C22×C1112yes—
662#442C22×C1112yescomplemented
663#440C22×C1112yes—
664#440C22×C1112yescomplemented
665C4×Q16C22×C1111yescharacteristic, complemented
666C4×SD16C22×C1111yescharacteristic
667C4×SD16C22×C1111yescharacteristic, complemented
668C4×D8C22×C1111yescharacteristic
669#436C22×C1111yescharacteristic
670#436C22×C1111yescharacteristic
671#435C22×C1112yescomplemented
672#435C22×C1112yescomplemented
673#432C22×C1112yescomplemented
674#431C22×C1111yescharacteristic, complemented
675#423C22×C1112yescomplemented
676C2×C4⋊C8C22×C1111yescharacteristic, complemented
677#417C22×C1112yescomplemented
678#417C22×C1112yescomplemented
679#416C22×C1112yescomplemented
680C22×C11—22no—
681C22×C11—21no—
682C22×C11—21no—
683C22×C11—22no—
684C22×C11—22no—
685C22×C11—21no—
686C22×C11—22no—
687C22×C11—41no—
688C22×C11—41no—
689C22×C11—42no—
690C22×C11—41no—
691C22×C11—42no—
692C22×C11—41no—
693C22×C11—42no—
694C22×C11—42no—
695C22×C11—42no—
696C22×C11—41no—
697C22×C11—42no—
698C22×C11—88no—
699C22×C11C23×D411yescharacteristic
700C4×C11—21no—
701C4×C11—22no—
702C4×C11—21no—
703C4×C11—21no—
704C4×C11—22no—
705C4×C11—21no—
706C4×C11—22no—
707C4×C11—41no—
708C4×C11—42no—
709C4×C11—41no—
710C4×C11—41no—
711C4×C11—41no—
712C4×C11—42no—
713C4×C11—41no—
714C4×C11—41no—
715C4×C11#57512yes—
716C4×C11C2×H(5,𝔽2)11yescharacteristic
717C4×C11#58511yescharacteristic
718C2×#41—21no—
719C2×#41—21no—
720C2×#41D4×C1111yescharacteristic
721C2×#41C23×C1111yescharacteristic
722C2×#41C23×C1112yes—
723C2×#41C23×C1112yes—
724C2×#41C23×C1112yes—
725C22×D4—21no—
726C22×D4C23×C1112yes—
727C23×C4—22no—
728AGL(1,ℤ/8)—44no—
729AGL(1,ℤ/8)—44no—
730#135—44no—
731C2×Q16C23×C1112yes—
732C2×Q16C23×C1111yescharacteristic
733C2×SD16C23×C1112yes—
734C2×SD16C23×C1111yescharacteristic
735C2×SD16C23×C1112yes—
736C2×SD16C23×C1112yes—
737C2×SD16C23×C1112yes—
738C2×SD16C23×C1111yescharacteristic
739C2×SD16C23×C1112yes—
740C2×D8C23×C1112yes—
741C2×D8C23×C1111yescharacteristic
742C2×D8C23×C1112yes—
743C2×D8C23×C1112yes—
744C2×D8C23×C1112yes—
745C2×M16C23×C1112yes—
746C2×M16C23×C1112yes—
747C22×C8C23×C1112yes—
748C4⋊Q8C23×C1111yescharacteristic
749C4⋊Q8C23×C1112yes—
750C4⋊Q8C23×C1111yescharacteristic
751#127—21no—
752#127—22no—
753#127C23×C1111yescharacteristic
754#127C23×C1111yescharacteristic
755#127C23×C1112yes—
756#126—22no—
757#126—22no—
758#126—21no—
759#126—22no—
760#125—21no—
761#125—21no—
762#125—22no—
763#125C23×C1112yes—
764#125C23×C1111yescharacteristic
765#124—21no—
766#124—21no—
767#124C23×C1112yes—
768#124C23×C1111yescharacteristic
769#124C23×C1112yes—
770#123—22no—
771#123—22no—
772#123—21no—
773#123—22no—
774#123—22no—
775#123—22no—
776#123—22no—
777#123—22no—
778#123—22no—
779C22⋊Q8—21no—
780C22⋊Q8—22no—
781C22⋊Q8—22no—
782C22⋊Q8C23×C1112yes—
783C22⋊Q8C23×C1112yes—
784C22⋊Q8C23×C1111yescharacteristic
785#121—22no—
786#121—21no—
787#121—22no—
788#121—21no—
789#121—22no—
790#121—21no—
791#121—21no—
792#121—22no—
793#121—21no—
794#121—21no—
795#121—22no—
796#121—22no—
797#121—22no—
798#121—22no—
799#121—22no—
800#121C23×C1112yes—
801#121C23×C1112yes—
802#121C23×C1111yescharacteristic
803#121C23×C1112yes—
804#120—22no—
805#120—22no—
806C4×Q8—21no—
807C4×Q8D4×C1111yescharacteristic
808C4×Q8C23×C1111yescharacteristic
809C4×Q8C23×C1111yescharacteristic
810C4×Q8C23×C1111yescharacteristic
811C4×Q8C23×C1112yes—
812C4×Q8C23×C1111yescharacteristic
813C4×D4—21no—
814C4×D4—22no—
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—22no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—22no—
822C4×D4—22no—
823C4×D4—21no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—21no—
827C4×D4—22no—
828C4×D4—21no—
829C4×D4—22no—
830C4×D4D4×C1111yescharacteristic
831C4×D4D4×C1112yes—
832C4×D4C23×C1111yescharacteristic
833C4×D4C23×C1112yes—
834C4×D4C23×C1112yes—
835C4×D4C23×C1112yes—
836C4×D4C23×C1111yescharacteristic
837C4×D4C23×C1111yescharacteristic
838C4×D4C23×C1112yes—
839C4×D4C23×C1111yescharacteristic
840C4×D4C23×C1112yes—
841#117—21no—
842#117—21no—
843#117—22no—
844#117—22no—
845#117D4×C1112yes—
846#117D4×C1111yescharacteristic
847#117C23×C1111yescharacteristic
848C2×C4⋊C4—21no—
849C2×C4⋊C4—21no—
850C2×C4⋊C4—22no—
851C2×C4⋊C4C23×C1112yes—
852C2×C22⋊C4—22no—
853C2×C22⋊C4—22no—
854C2×C42—21no—
855C2×C42C23×C1112yes—
856C2×C42C23×C1111yescharacteristic
857#107C23×C1111yescharacteristic
858#107C23×C1111yescharacteristic
859#107C23×C1112yes—
860#106C23×C1111yescharacteristic
861#106C23×C1111yescharacteristic
862#106C23×C1112yes—
863C4⋊C8C23×C1112yes—
864C4⋊C8C23×C1111yescharacteristic
865C4⋊C8C23×C1111yescharacteristic
866C4⋊C8C23×C1111yescharacteristic
867C4⋊C8C23×C1112yes—
868C4⋊C8C23×C1112yes—
869C4⋊C8C23×C1111yescharacteristic
870#103C23×C1112yes—
871#103C23×C1112yes—
872#103C23×C1111yescharacteristic
873#103C23×C1112yes—
874#103C23×C1112yes—
875#103C23×C1111yescharacteristic
876#103C23×C1111yescharacteristic
877#103C23×C1111yescharacteristic
878#103C23×C1112yes—
879#102C23×C1112yes—
880#102C23×C1112yes—
881#102C23×C1111yescharacteristic
882#102C23×C1112yes—
883#102C23×C1112yes—
884#102C23×C1111yescharacteristic
885#102C23×C1111yescharacteristic
886#102C23×C1111yescharacteristic
887#102C23×C1112yes—
888#102C23×C1112yes—
889#102C23×C1112yes—
890C22⋊C8C23×C1111yescharacteristic
891C22⋊C8C23×C1111yescharacteristic
892C22⋊C8C23×C1112yes—
893C22⋊C8C23×C1112yes—
894#97C23×C1112yes—
895#97C23×C1112yes—
896C4×C8C23×C1111yescharacteristic
897C4×C8C23×C1111yescharacteristic
898C2×C11—41no—
899C2×C11—42no—
900C2×C11—42no—
901C2×C11—81no—
902C2×C11—82no—
903C2×C11—82no—
904C2×C11#348811yescharacteristic
905C2×C11C2×#57511yescharacteristic
906C2×C11#358511yescharacteristic
907C24—22no—
908#41—22no—
909#41—42no—
910#41—41no—
911#41—42no—
912#41—42no—
913#41—42no—
914#41—42no—
915#41—42no—
916#41—42no—
917#41—44no—
918#41—82no—
919C2×Q8—21no—
920C2×Q8C2×D4×C1111yescharacteristic
921C2×Q8C24×C1111yescharacteristic
922C2×Q8C24×C1112yes—
923C2×Q8C24×C1111yescharacteristic
924C2×D4—24no—
925C2×D4—21no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—21no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—21no—
935C2×D4—22no—
936C2×D4—21no—
937C2×D4—22no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4C2×D4×C1111yescharacteristic
943C2×D4C2×D4×C1112yes—
944C2×D4C24×C1111yescharacteristic
945C2×D4C24×C1112yes—
946C2×D4C24×C1112yes—
947C2×D4C24×C1111yescharacteristic
948C22×C4—22no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—22no—
953C22×C4—21no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—84no—
961C22×C4C2×D4×C1111yescharacteristic
962C22×C4C2×D4×C1112yes—
963C22×C4C2×D4×C1112yes—
964C22×C4C2×D4×C1111yescharacteristic
965C22×C4C24×C1112yes—
966C22×C4C24×C1111yescharacteristic
967Q16—42no—
968Q16—41no—
969SD16—24no—
970SD16—22no—
971SD16—42no—
972SD16—42no—
973SD16—42no—
974SD16—41no—
975SD16—42no—
976D8—24no—
977D8—22no—
978D8—42no—
979D8—42no—
980D8—42no—
981M16—42no—
982M16—42no—
983C2×C8—42no—
984C2×C8C24×C1111yescharacteristic
985C2×C8C24×C1111yescharacteristic
986C2×C8C24×C1111yescharacteristic
987C2×C8C24×C1111yescharacteristic
988C2×C8C24×C1112yes—
989C2×C8C24×C1112yes—
990C4⋊C4—21no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—21no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—21no—
1003C4⋊C4—22no—
1004C4⋊C4—21no—
1005C4⋊C4—22no—
1006C4⋊C4—21no—
1007C4⋊C4C2×D4×C1111yescharacteristic
1008C4⋊C4C2×D4×C1111yescharacteristic
1009C4⋊C4C2×D4×C1112yes—
1010C4⋊C4C2×D4×C1112yes—
1011C4⋊C4C24×C1111yescharacteristic
1012C4⋊C4C24×C1112yes—
1013C4⋊C4C24×C1111yescharacteristic
1014C4⋊C4C24×C1111yescharacteristic
1015C4⋊C4C24×C1111yescharacteristic
1016C22⋊C4—22no—
1017C22⋊C4—21no—
1018C22⋊C4—22no—
1019C22⋊C4—21no—
1020C22⋊C4—21no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—21no—
1027C22⋊C4—22no—
1028C22⋊C4—21no—
1029C22⋊C4—22no—
1030C22⋊C4—21no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—21no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—21no—
1037C22⋊C4C2×D4×C1112yes—
1038C22⋊C4C2×D4×C1112yes—
1039C22⋊C4C2×D4×C1112yes—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—22no—
1044C42—21no—
1045C42C2×D4×C1111yescharacteristic
1046C42C2×D4×C1112yes—
1047C42C2×D4×C1111yescharacteristic
1048C42C2×D4×C1112yes—
1049C42C24×C1111yescharacteristic
1050C42C24×C1112yes—
1051C42C24×C1111yescharacteristic
1052C11#6197411yescharacteristic, direct product factor, Sylow
1053C23—21no—
1054C23—22no—
1055C23—21no—
1056C23—22no—
1057C23—44no—
1058C23—44no—
1059C23—82no—
1060C23C22×D4×C1112yes—
1061C23C22×D4×C1111yescharacteristic
1062Q8—22no—
1063Q8—21no—
1064Q8—22no—
1065Q8—21no—
1066Q8—21no—
1067Q8—22no—
1068Q8—21no—
1069Q8—81no—
1070D4—22no—
1071D4—21no—
1072D4—22no—
1073D4—22no—
1074D4—21no—
1075D4—22no—
1076D4—22no—
1077D4—21no—
1078D4—42no—
1079D4—44no—
1080D4—44no—
1081D4—42no—
1082D4—44no—
1083D4—42no—
1084D4—42no—
1085D4—82no—
1086D4—81no—
1087D4—81no—
1088D4—82no—
1089D4—81no—
1090D4—82no—
1091D4—82no—
1092D4—82no—
1093D4—82no—
1094D4C11×H(5,𝔽2)12yes—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4C22×D4×C1111yescharacteristic
1124C2×C4C22×D4×C1111yescharacteristic
1125C2×C4C22×D4×C1112yes—
1126C2×C4C22×D4×C1111yescharacteristic
1127C2×C4C22×D4×C1112yes—
1128C2×C4C22×D4×C1112yes—
1129C2×C4C22×D4×C1111yescharacteristic
1130C2×C4C22×D4×C1111yescharacteristic
1131C2×C4C25×C1111yescharacteristic
1132C8—22no—
1133C8—22no—
1134C8—21no—
1135C8—21no—
1136C8—21no—
1137C8—21no—
1138C22—21no—
1139C22—22no—
1140C22—22no—
1141C22—21no—
1142C22—22no—
1143C22—22no—
1144C22—21no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—41no—
1152C22—42no—
1153C22—42no—
1154C22—41no—
1155C22—42no—
1156C22—88no—
1157C22C23×D4×C1111yescharacteristic
1158C4—21no—
1159C4—22no—
1160C4—21no—
1161C4—22no—
1162C4—21no—
1163C4—22no—
1164C4—21no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—41no—
1173C4C11×#57512yes—
1174C4C2×C11×H(5,𝔽2)11yescharacteristic
1175C4C11×#58511yescharacteristic
1176C2—42no—
1177C2—41no—
1178C2—42no—
1179C2—82no—
1180C2—81no—
1181C2—82no—
1182C2C11×#348811yescharacteristic
1183C2C2×C11×#57511yescharacteristic
1184C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3517C2semidirect
2. C11×#3481C2semidirect
3. C11×#3400C2semidirect
4. C11×#3399C2semidirect
5. C11×#3372C2semidirect
6. C11×#3366C2semidirect
7. C11×#3333C2semidirect
8. C11×#3331C2semidirect
9. C11×#3309C2semidirect
10. C11×#3307C2semidirect
11. C11×#3274C2semidirect
12. C11×#3272C2semidirect
13. C11×#3268C2semidirect
14. C11×#3267C2semidirect
15. C11×#3256C2semidirect
16. C11×#3247C2semidirect
17. C11×#3219C2semidirect
18. C11×#3207C2semidirect
19. C11×#3114C2semidirect
20. C11×#3102C2semidirect
21. C11×#3036C2semidirect
22. C11×#3035C2semidirect
23. C11×#2989C2semidirect
28. C11×#557C22semidirect
38. C11×#550C22semidirect
39. C11×#550C22semidirect
41. C11×#547C22semidirect
48. C11×#532C22semidirect
49. C11×#532C22semidirect
52. C11×#529C22semidirect
53. C11×#529C22semidirect
60. C11×#497C22semidirect
61. C11×#496C22semidirect
64. C11×#491C22semidirect
65. C11×#490C22semidirect
66. C11×#487C22semidirect
67. C11×#486C22semidirect
68. C11×#485C22semidirect
69. C11×#483C22semidirect
70. C11×#482C22semidirect
71. C11×#480C22semidirect
72. C11×#479C22semidirect
73. C11×#479C22semidirect
75. C11×#478C22semidirect
76. C11×#478C22semidirect
77. C11×#477C22semidirect
78. C11×#476C22semidirect
79. C11×#470C22semidirect
82. C11×#468C22semidirect
83. C11×#466C22semidirect
84. C11×#465C22semidirect
85. C11×#464C22semidirect
86. C11×#464C22semidirect
87. C11×#464C22semidirect
90. C11×#463C22semidirect
91. C11×#463C22semidirect
92. C11×#463C22semidirect
93. C11×#463C22semidirect
94. C11×#462C22semidirect
97. C11×#461C22semidirect
99. C11×#460C22semidirect
103. C11×#459C22semidirect
105. C11×#452C22semidirect
106. C11×#452C22semidirect
111. C11×#449C22semidirect
112. C11×#449C22semidirect
114. C11×#446C22semidirect
115. C11×#446C22semidirect
117. C11×#442C22semidirect
119. C11×#440C22semidirect
120. C4×C11×Q16C22semidirect
122. C4×C11×SD16C22semidirect
126. C11×#435C22semidirect
127. C11×#435C22semidirect
128. C11×#432C22semidirect
129. C11×#431C22semidirect
130. C11×#423C22semidirect
131. C2×C11×C4⋊C8C22semidirect
132. C11×#417C22semidirect
133. C11×#417C22semidirect
134. C11×#416C22semidirect
315. #61974C11direct (N × H)
461. #3517C2×C11semidirect
462. #3481C2×C11semidirect
463. #3400C2×C11semidirect
464. #3399C2×C11semidirect
465. #3372C2×C11semidirect
466. #3366C2×C11semidirect
467. #3333C2×C11semidirect
468. #3331C2×C11semidirect
469. #3309C2×C11semidirect
470. #3307C2×C11semidirect
471. #3274C2×C11semidirect
472. #3272C2×C11semidirect
473. #3268C2×C11semidirect
474. #3267C2×C11semidirect
475. #3256C2×C11semidirect
476. #3247C2×C11semidirect
477. #3219C2×C11semidirect
478. #3207C2×C11semidirect
479. #3114C2×C11semidirect
480. #3102C2×C11semidirect
481. #3036C2×C11semidirect
482. #3035C2×C11semidirect
483. #2989C2×C11semidirect
573. #557C22×C11semidirect
583. #550C22×C11semidirect
584. #550C22×C11semidirect
586. #547C22×C11semidirect
593. #532C22×C11semidirect
594. #532C22×C11semidirect
597. #529C22×C11semidirect
598. #529C22×C11semidirect
605. #497C22×C11semidirect
606. #496C22×C11semidirect
609. #491C22×C11semidirect
610. #490C22×C11semidirect
611. #487C22×C11semidirect
612. #486C22×C11semidirect
613. #485C22×C11semidirect
614. #483C22×C11semidirect
615. #482C22×C11semidirect
616. #480C22×C11semidirect
617. #479C22×C11semidirect
618. #479C22×C11semidirect
620. #478C22×C11semidirect
621. #478C22×C11semidirect
622. #477C22×C11semidirect
623. #476C22×C11semidirect
624. #470C22×C11semidirect
627. #468C22×C11semidirect
628. #466C22×C11semidirect
629. #465C22×C11semidirect
630. #464C22×C11semidirect
631. #464C22×C11semidirect
632. #464C22×C11semidirect
635. #463C22×C11semidirect
636. #463C22×C11semidirect
637. #463C22×C11semidirect
638. #463C22×C11semidirect
639. #462C22×C11semidirect
642. #461C22×C11semidirect
644. #460C22×C11semidirect
648. #459C22×C11semidirect
650. #452C22×C11semidirect
651. #452C22×C11semidirect
656. #449C22×C11semidirect
657. #449C22×C11semidirect
659. #446C22×C11semidirect
660. #446C22×C11semidirect
662. #442C22×C11semidirect
664. #440C22×C11semidirect
665. C4×Q16C22×C11semidirect
667. C4×SD16C22×C11semidirect
671. #435C22×C11semidirect
672. #435C22×C11semidirect
673. #432C22×C11semidirect
674. #431C22×C11semidirect
675. #423C22×C11semidirect
676. C2×C4⋊C8C22×C11semidirect
677. #417C22×C11semidirect
678. #417C22×C11semidirect
679. #416C22×C11semidirect
1052. C11#61974direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35172
C11×#34812
C11×#34002
C11×#33992
C11×#33722
C11×#33662
C11×#33332
C11×#33312
C11×#33092
C11×#33072
C11×#32742
C11×#32722
C11×#32682
C11×#32672
C11×#32562
C11×#32472
C11×#32192
C11×#32072
C11×#31142
C11×#31022
C11×#30362
C11×#30352
C11×#29892
#6197411