Finite Group Databasebeta

← C11×#19418 #14596611

Subgroups — C11×#19418 #14596611

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3231C211yesmaximal, characteristic, complemented
2C11×#3116C211yesmaximal, characteristic
3C11×#3107C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic
5C11×#1684C211yesmaximal, characteristic, complemented
6C11×#1683C211yesmaximal, characteristic, complemented
7C11×#1680C211yesmaximal, characteristic, complemented
8C11×#1679C211yesmaximal, characteristic, complemented
9C11×#1674C211yesmaximal, characteristic, complemented
10C11×#1673C211yesmaximal, characteristic, complemented
11C11×#1672C211yesmaximal, characteristic, complemented
12C11×#1671C211yesmaximal, characteristic, complemented
13C11×#1572C211yesmaximal, characteristic, complemented
14C11×#1552C211yesmaximal, characteristic, complemented
15C11×#1542C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#485—21no—
24C11×#485—21no—
25C11×#485—21no—
26C11×#485—21no—
27C11×#479—21no—
28C11×#479—21no—
29C11×#477C2211yescharacteristic
30C11×#476C2211yescharacteristic
31C11×#475C2211yescharacteristic
32C11×#474C2211yescharacteristic
33C11×#462C2211yescharacteristic
34C11×#462C2211yescharacteristic
35C11×#461C2211yescharacteristic
36C11×#461C2211yescharacteristic
37C11×#452—21no—
38C11×#452—21no—
39C8×Q8×C11C2211yescharacteristic
40C8×Q8×C11C2211yescharacteristic
41C11×#441—21no—
42C11×#440—21no—
43C4×C11×Q16—21no—
44C4×C11×SD16—21no—
45C8×D4×C11—21no—
46C8×D4×C11—21no—
47C8×D4×C11C2211yescharacteristic
48C8×D4×C11C2211yescharacteristic
49C11×#432C2211yescharacteristic
50C11×#431—21no—
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C2×C11×C4⋊C8—21no—
54C2×C11×C4⋊C8C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#332C2211yescharacteristic
64C11×#332C2211yescharacteristic
65C11×#332C2211yescharacteristic
66C11×#332C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×C4⋊Q8C2311yescharacteristic
78C11×C4⋊Q8C2311yescharacteristic
79C11×#125—21no—
80C11×#125—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11D411yescharacteristic
90C4×Q8×C11C2311yescharacteristic
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11D411yescharacteristic
94C4×D4×C11C2311yescharacteristic
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—21no—
98C11×#117D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8D411yescharacteristic
137C11×C22⋊C8D411yescharacteristic
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19418C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×Q16—42no—
161C11×Q16—42no—
162C11×SD16—42no—
163C11×SD16—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—81no—
171C2×C8×C11—81no—
172C2×C8×C11—81no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—41no—
202C42×C11—41no—
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11#4111yescharacteristic
206C42×C11C2411yescharacteristic
207#3231C2×C1111yescharacteristic, complemented
208#3116C2×C1111yescharacteristic
209#3107C2×C1111yescharacteristic
210#2988C2×C1111yescharacteristic
211#1684C2×C1111yescharacteristic, complemented
212#1683C2×C1111yescharacteristic, complemented
213#1680C2×C1111yescharacteristic, complemented
214#1679C2×C1111yescharacteristic, complemented
215#1674C2×C1111yescharacteristic, complemented
216#1673C2×C1111yescharacteristic, complemented
217#1672C2×C1111yescharacteristic, complemented
218#1671C2×C1111yescharacteristic, complemented
219#1572C2×C1111yescharacteristic, complemented
220#1552C2×C1111yescharacteristic, complemented
221#1542C2×C1111yescharacteristic, complemented
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—81no—
232Q8×C11#13512yes—
233D4×C11—24no—
234D4×C11—21no—
235D4×C11#13512yes—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—81no—
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268#533C22×C1111yescharacteristic
269#533C22×C1111yescharacteristic
270C4×#41C22×C1111yescharacteristic
271#500C22×C1111yescharacteristic
272#498C22×C1111yescharacteristic
273#487C22×C1111yescharacteristic
274#487C22×C1111yescharacteristic
275#485—21no—
276#485—21no—
277#485—21no—
278#485—21no—
279#479—21no—
280#479—21no—
281#477C22×C1111yescharacteristic
282#476C22×C1111yescharacteristic
283#475C22×C1111yescharacteristic
284#474C22×C1111yescharacteristic
285#462C22×C1111yescharacteristic
286#462C22×C1111yescharacteristic
287#461C22×C1111yescharacteristic
288#461C22×C1111yescharacteristic
289#452—21no—
290#452—21no—
291C8×Q8C22×C1111yescharacteristic
292C8×Q8C22×C1111yescharacteristic
293#441—21no—
294#440—21no—
295C4×Q16—21no—
296C4×SD16—21no—
297C8×D4—21no—
298C8×D4—21no—
299C8×D4C22×C1111yescharacteristic
300C8×D4C22×C1111yescharacteristic
301#432C22×C1111yescharacteristic
302#431—21no—
303#431C22×C1111yescharacteristic
304#431C22×C1111yescharacteristic
305C2×C4⋊C8—21no—
306C2×C4⋊C8C22×C1111yescharacteristic
307#335C22×C1111yescharacteristic
308#335C22×C1111yescharacteristic
309#334C22×C1111yescharacteristic
310#334C22×C1111yescharacteristic
311#333C22×C1111yescharacteristic
312#333C22×C1111yescharacteristic
313#332C22×C1111yescharacteristic
314#332C22×C1111yescharacteristic
315#332C22×C1111yescharacteristic
316#332C22×C1111yescharacteristic
317#332C22×C1111yescharacteristic
318#332C22×C1111yescharacteristic
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—21no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11C2×#13511yescharacteristic
338C4×C11C2×#13511yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57811yescharacteristic
341C2×#41D4×C1111yescharacteristic
342C2×Q16—21no—
343C2×Q16—21no—
344C2×SD16—21no—
345C2×SD16—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8C23×C1111yescharacteristic
350C4⋊Q8C23×C1111yescharacteristic
351C4⋊Q8C23×C1111yescharacteristic
352C4⋊Q8C23×C1111yescharacteristic
353#125—21no—
354#125—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8D4×C1111yescharacteristic
364C4×Q8C23×C1111yescharacteristic
365C4×D4—21no—
366C4×D4—21no—
367C4×D4D4×C1111yescharacteristic
368C4×D4C23×C1111yescharacteristic
369#117—21no—
370#117—21no—
371#117—21no—
372#117D4×C1111yescharacteristic
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8D4×C1111yescharacteristic
387C4⋊C8D4×C1111yescharacteristic
388C4⋊C8C23×C1111yescharacteristic
389C4⋊C8C23×C1111yescharacteristic
390C4⋊C8C23×C1111yescharacteristic
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#102—21no—
405#102—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8D4×C1111yescharacteristic
411C22⋊C8D4×C1111yescharacteristic
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C2×C11—41no—
419C2×C11—42no—
420C2×C11#304611yescharacteristic
421C2×C11#305011yescharacteristic
422C2×C11#306911yescharacteristic
423#41—22no—
424#41—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×D4×C1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×D4×C1111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C11×#4111yescharacteristic
438Q16—42no—
439Q16—42no—
440SD16—42no—
441SD16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—81no—
451C2×C8C2×D4×C1111yescharacteristic
452C2×C8C2×D4×C1111yescharacteristic
453C2×C8C2×D4×C1111yescharacteristic
454C2×C8C2×D4×C1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C1111yescharacteristic
470C4⋊C4C2×D4×C1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42—41no—
481C42C2×D4×C1111yescharacteristic
482C42C2×D4×C1111yescharacteristic
483C42C11×#4111yescharacteristic
484C42C24×C1111yescharacteristic
485C11#1941811yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23C11×#12111yescharacteristic
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8C11×#13512yes—
497D4—24no—
498D4—21no—
499D4C11×#13512yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4C11×#12111yescharacteristic
517C2×C4C11×#12111yescharacteristic
518C2×C4C11×#12111yescharacteristic
519C2×C4C22×D4×C1111yescharacteristic
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22C2×C11×#12111yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C2×C11×#13511yescharacteristic
551C4C2×C11×#13511yescharacteristic
552C4C11×#57711yescharacteristic
553C4C11×#57811yescharacteristic
554C2—41no—
555C2—42no—
556C2C11×#304611yescharacteristic
557C2C11×#305011yescharacteristic
558C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3231C2semidirect
5. C11×#1684C2semidirect
6. C11×#1683C2semidirect
7. C11×#1680C2semidirect
8. C11×#1679C2semidirect
9. C11×#1674C2semidirect
10. C11×#1673C2semidirect
11. C11×#1672C2semidirect
12. C11×#1671C2semidirect
13. C11×#1572C2semidirect
14. C11×#1552C2semidirect
15. C11×#1542C2semidirect
144. #19418C11direct (N × H)
207. #3231C2×C11semidirect
211. #1684C2×C11semidirect
212. #1683C2×C11semidirect
213. #1680C2×C11semidirect
214. #1679C2×C11semidirect
215. #1674C2×C11semidirect
216. #1673C2×C11semidirect
217. #1672C2×C11semidirect
218. #1671C2×C11semidirect
219. #1572C2×C11semidirect
220. #1552C2×C11semidirect
221. #1542C2×C11semidirect
485. C11#19418direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32312
C11×#31162
C11×#31072
C11×#29882
C11×#16842
C11×#16832
C11×#16802
C11×#16792
C11×#16742
C11×#16732
C11×#16722
C11×#16712
C11×#15722
C11×#15522
C11×#15422
#1941811