Finite Group Databasebeta

← C11×#19181 #14596374

Subgroups — C11×#19181 #14596374

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3185C211yesmaximal, characteristic, complemented
2C11×#3107C211yesmaximal, characteristic
3C11×#3076C211yesmaximal, characteristic
4C11×#2970C211yesmaximal, characteristic
5C11×#1704C211yesmaximal, characteristic, complemented
6C11×#1700C211yesmaximal, characteristic, complemented
7C11×#1692C211yesmaximal, characteristic, complemented
8C11×#1690C211yesmaximal, characteristic, complemented
9C11×#1683C211yesmaximal, characteristic, complemented
10C11×#1679C211yesmaximal, characteristic, complemented
11C11×#1671C211yesmaximal, characteristic, complemented
12C11×#1669C211yesmaximal, characteristic, complemented
13C11×#1565C211yesmaximal, characteristic, complemented
14C11×#1554C211yesmaximal, characteristic, complemented
15C11×#1552C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#494C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#485—21no—
24C11×#479—21no—
25C11×#478—21no—
26C11×#477C2211yescharacteristic
27C11×#476C2211yescharacteristic
28C11×#475C2211yescharacteristic
29C11×#475C2211yescharacteristic
30C11×#474C2211yescharacteristic
31C11×#474C2211yescharacteristic
32C11×#470—21no—
33C11×#470—21no—
34C11×#462C2211yescharacteristic
35C11×#461C2211yescharacteristic
36C11×#452—21no—
37C11×#446C2211yescharacteristic
38C11×#446C2211yescharacteristic
39C11×#441—21no—
40C11×#441—21no—
41C4×C11×Q16—21no—
42C4×C11×SD16—21no—
43C11×#435—21no—
44C11×#435—21no—
45C8×D4×C11C2211yescharacteristic
46C8×D4×C11C2211yescharacteristic
47C11×#432—21no—
48C11×#432C2211yescharacteristic
49C11×#431C2211yescharacteristic
50C11×#427—21no—
51C2×C11×C4⋊C8C2211yescharacteristic
52C11×#416—21no—
53C4×C11×M16C2211yescharacteristic
54C2×C11×#97—21no—
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×Q16—21no—
71C2×C11×SD16—21no—
72C2×C11×M16D411yescharacteristic
73C2×C11×M16D411yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C11×C4⋊Q8C2311yescharacteristic
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#125—21no—
82C11×#125—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11C2311yescharacteristic
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11D411yescharacteristic
96C4×D4×C11C2311yescharacteristic
97C11×#117—21no—
98C11×#117—21no—
99C11×#117—21no—
100C11×#117D411yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
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×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×#97—21no—
137C11×#97—21no—
138C11×#97—21no—
139C11×#97D411yescharacteristic
140C11×#97D411yescharacteristic
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19181C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—41no—
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×Q16—42no—
163C11×SD16—42no—
164C11×M16—22no—
165C11×M16—41no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C2×C8×C11—42no—
174C2×C8×C11—42no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
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—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—41no—
204C42×C11—41no—
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11#4111yescharacteristic
208C42×C11C2411yescharacteristic
209#3185C2×C1111yescharacteristic, complemented
210#3107C2×C1111yescharacteristic
211#3076C2×C1111yescharacteristic
212#2970C2×C1111yescharacteristic
213#1704C2×C1111yescharacteristic, complemented
214#1700C2×C1111yescharacteristic, complemented
215#1692C2×C1111yescharacteristic, complemented
216#1690C2×C1111yescharacteristic, complemented
217#1683C2×C1111yescharacteristic, complemented
218#1679C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1669C2×C1111yescharacteristic, complemented
221#1565C2×C1111yescharacteristic, complemented
222#1554C2×C1111yescharacteristic, complemented
223#1552C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11#12111yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—81no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11#13712yes—
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—21no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—81no—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11#13512yes—
270#533C22×C1111yescharacteristic
271#533C22×C1111yescharacteristic
272C4×#41C22×C1111yescharacteristic
273#498C22×C1111yescharacteristic
274#494C22×C1111yescharacteristic
275#487C22×C1111yescharacteristic
276#487C22×C1111yescharacteristic
277#485—21no—
278#479—21no—
279#478—21no—
280#477C22×C1111yescharacteristic
281#476C22×C1111yescharacteristic
282#475C22×C1111yescharacteristic
283#475C22×C1111yescharacteristic
284#474C22×C1111yescharacteristic
285#474C22×C1111yescharacteristic
286#470—21no—
287#470—21no—
288#462C22×C1111yescharacteristic
289#461C22×C1111yescharacteristic
290#452—21no—
291#446C22×C1111yescharacteristic
292#446C22×C1111yescharacteristic
293#441—21no—
294#441—21no—
295C4×Q16—21no—
296C4×SD16—21no—
297#435—21no—
298#435—21no—
299C8×D4C22×C1111yescharacteristic
300C8×D4C22×C1111yescharacteristic
301#432—21no—
302#432C22×C1111yescharacteristic
303#431C22×C1111yescharacteristic
304#427—21no—
305C2×C4⋊C8C22×C1111yescharacteristic
306#416—21no—
307C4×M16C22×C1111yescharacteristic
308C2×#97—21no—
309#335C22×C1111yescharacteristic
310#335C22×C1111yescharacteristic
311#334C22×C1111yescharacteristic
312#334C22×C1111yescharacteristic
313#333C22×C1111yescharacteristic
314#333C22×C1111yescharacteristic
315#332C22×C1111yescharacteristic
316#332C22×C1111yescharacteristic
317#332C22×C1111yescharacteristic
318#332C22×C1111yescharacteristic
319#332C22×C1111yescharacteristic
320#332C22×C1111yescharacteristic
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—22no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×#12111yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#13511yescharacteristic
340C4×C11C2×#13711yescharacteristic
341C4×C11#57511yescharacteristic
342C4×C11#57511yescharacteristic
343C2×#41D4×C1111yescharacteristic
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×M16D4×C1111yescharacteristic
349C2×M16D4×C1111yescharacteristic
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—21no—
353C4⋊Q8C23×C1111yescharacteristic
354C4⋊Q8C23×C1111yescharacteristic
355C4⋊Q8C23×C1111yescharacteristic
356C4⋊Q8C23×C1111yescharacteristic
357#125—21no—
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8D4×C1111yescharacteristic
368C4×Q8C23×C1111yescharacteristic
369C4×D4—21no—
370C4×D4—21no—
371C4×D4D4×C1111yescharacteristic
372C4×D4C23×C1111yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117D4×C1111yescharacteristic
377C2×C42—21no—
378C2×C42C23×C1111yescharacteristic
379#107—21no—
380#107—21no—
381#107—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8C23×C1111yescharacteristic
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
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#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412#97—21no—
413#97—21no—
414#97—21no—
415#97D4×C1111yescharacteristic
416#97D4×C1111yescharacteristic
417C4×C8—21no—
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C2×C11—41no—
421C2×C11—42no—
422C2×C11#303511yescharacteristic
423C2×C11#305611yescharacteristic
424C2×C11#306911yescharacteristic
425#41—22no—
426#41—41no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C2×D4×C1111yescharacteristic
432C2×D4—21no—
433C2×D4C2×D4×C1111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C11×#4111yescharacteristic
440Q16—42no—
441Q16—42no—
442Q16—42no—
443SD16—42no—
444M16—22no—
445M16—41no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8C2×D4×C1111yescharacteristic
456C2×C8C2×D4×C1111yescharacteristic
457C2×C8C2×D4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C1111yescharacteristic
474C4⋊C4C2×D4×C1111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42C2×D4×C1111yescharacteristic
486C42C2×D4×C1111yescharacteristic
487C42C11×#4111yescharacteristic
488C42C24×C1111yescharacteristic
489C11#1918111yescharacteristic, direct product factor, Sylow
490C23—21no—
491C23C11×#12111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501D4—21no—
502D4—42no—
503D4C11×#13712yes—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4C11×#12111yescharacteristic
521C2×C4C11×#12111yescharacteristic
522C2×C4C11×#12111yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8C11×#13512yes—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×C11×#12111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4C2×C11×#13511yescharacteristic
555C4C2×C11×#13711yescharacteristic
556C4C11×#57511yescharacteristic
557C4C11×#57511yescharacteristic
558C2—41no—
559C2—42no—
560C2C11×#303511yescharacteristic
561C2C11×#305611yescharacteristic
562C2C11×#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×#3185C2semidirect
5. C11×#1704C2semidirect
6. C11×#1700C2semidirect
7. C11×#1692C2semidirect
8. C11×#1690C2semidirect
9. C11×#1683C2semidirect
10. C11×#1679C2semidirect
11. C11×#1671C2semidirect
12. C11×#1669C2semidirect
13. C11×#1565C2semidirect
14. C11×#1554C2semidirect
15. C11×#1552C2semidirect
144. #19181C11direct (N × H)
209. #3185C2×C11semidirect
213. #1704C2×C11semidirect
214. #1700C2×C11semidirect
215. #1692C2×C11semidirect
216. #1690C2×C11semidirect
217. #1683C2×C11semidirect
218. #1679C2×C11semidirect
219. #1671C2×C11semidirect
220. #1669C2×C11semidirect
221. #1565C2×C11semidirect
222. #1554C2×C11semidirect
223. #1552C2×C11semidirect
489. C11#19181direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31852
C11×#31072
C11×#30762
C11×#29702
C11×#17042
C11×#17002
C11×#16922
C11×#16902
C11×#16832
C11×#16792
C11×#16712
C11×#16692
C11×#15652
C11×#15542
C11×#15522
#1918111