Finite Group Databasebeta

← C11×#36708 #14613901

Subgroups — C11×#36708 #14613901

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊Q8C211yesmaximal, characteristic
3C11×#2848C212yesmaximal
4C11×#2690C218yesmaximal, complemented
5C11×#2677C218yesmaximal, complemented
6C11×#2627C212yesmaximal, complemented
7C11×#2561C212yesmaximal
8C11×#2484C212yesmaximal, complemented
9C11×#2482C212yesmaximal
10C11×#2434C212yesmaximal, complemented
11C11×#2313C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C11×#544—28no—
15C2×C11×C4⋊Q8C2214yescomplemented
16C2×C11×C4⋊Q8C2214yescomplemented
17C2×C11×#125C2214yescomplemented
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2218yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2214yes—
23C2×C11×#117C2212yes—
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C11×#400C2214yescomplemented
30C11×#400C2214yescomplemented
31C11×#399C2214yes—
32C11×#398C2214yescomplemented
33C11×#398C2218yescomplemented
34C11×#397C2214yes—
35C11×#397C2214yes—
36C11×#395C2214yescomplemented
37C11×#395C2218yescomplemented
38C11×#393C2214yes—
39C11×#391C2214yescomplemented
40C11×#388C2218yes—
41C11×#388C2218yes—
42C11×#387C2218yescomplemented
43C11×#387C2218yescomplemented
44C11×#385C2218yes—
45C11×#385C2214yes—
46C11×#385C2214yes—
47C11×#381C2212yes—
48C11×#381C2214yes—
49C11×#380C2214yes—
50C11×#380C2212yes—
51C11×#379C2214yes—
52C4×C11×C22⋊C4C2212yes—
53C25×C11C2311yescharacteristic
54C22×Q8×C11—24no—
55C22×Q8×C11—44no—
56C22×Q8×C11C2314yes—
57C22×Q8×C11C2312yes—
58C22×Q8×C11C2312yes—
59C23×C4×C11—24no—
60C23×C4×C11—44no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C11×C4⋊Q8—216no—
69C11×C4⋊Q8—48no—
70C11×#125—216no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—232no—
74C11×C22⋊Q8—48no—
75C11×#117—28no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4D418yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2318yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C11×C22⋊C4C2318yes—
99C2×C42×C11C2314yes—
100C2×C42×C11C2314yes—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2318yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C11×#95C2318yes—
109#36708C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—42no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C2×Q8×C11—28no—
117C2×Q8×C11—24no—
118C2×Q8×C11—24no—
119C2×Q8×C11—28no—
120C2×Q8×C11—44no—
121C2×Q8×C11—44no—
122C2×Q8×C11—44no—
123C2×Q8×C11—416no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—28no—
131C22×C4×C11—28no—
132C22×C4×C11—42no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—416no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2418yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—216no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—48no—
160C11×C4⋊C4C2×D4116yes—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—216no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—48no—
167C42×C11—28no—
168C42×C11—44no—
169C2×#544C2×C1111yescharacteristic, complemented
170C22×C22⋊Q8C2×C1111yescharacteristic
171#2848C2×C1112yes—
172#2690C2×C1118yescomplemented
173#2677C2×C1118yescomplemented
174#2627C2×C1112yescomplemented
175#2561C2×C1112yes—
176#2484C2×C1112yescomplemented
177#2482C2×C1112yes—
178#2434C2×C1112yescomplemented
179#2313C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—28no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—416no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11C22×D412yes—
191C23×C112−1+414yes—
192C23×C112−1+414yes—
193C23×C11C2511yescharacteristic
194Q8×C11—416no—
195Q8×C11—84no—
196Q8×C11—84no—
197C2×C4×C11—28no—
198C2×C4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—28no—
209C2×C4×C11—28no—
210C2×C4×C11—24no—
211C2×C4×C11—28no—
212C2×C4×C11—28no—
213C2×C4×C11—28no—
214C2×C4×C11—24no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—416no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11H(5,𝔽2)14yes—
224C23×Q8C22×C1111yescharacteristic
225C24×C4C22×C1111yescharacteristic
226#544—28no—
227C2×C4⋊Q8C22×C1114yescomplemented
228C2×C4⋊Q8C22×C1114yescomplemented
229C2×#125C22×C1114yescomplemented
230C2×C22⋊Q8—28no—
231C2×C22⋊Q8C22×C1112yes—
232C2×C22⋊Q8C22×C1112yes—
233C2×C22⋊Q8C22×C1118yes—
234C2×C22⋊Q8C22×C1114yes—
235C2×#117C22×C1112yes—
236C22×C4⋊C4C22×C1111yescharacteristic
237C22×C4⋊C4C22×C1111yescharacteristic
238C22×C4⋊C4C22×C1111yescharacteristic
239C22×C22⋊C4C22×C1111yescharacteristic
240C22×C22⋊C4C22×C1111yescharacteristic
241#400C22×C1114yescomplemented
242#400C22×C1114yescomplemented
243#399C22×C1114yes—
244#398C22×C1118yescomplemented
245#398C22×C1114yescomplemented
246#397C22×C1114yes—
247#397C22×C1114yes—
248#395C22×C1114yescomplemented
249#395C22×C1118yescomplemented
250#393C22×C1114yes—
251#391C22×C1114yescomplemented
252#388C22×C1118yes—
253#388C22×C1118yes—
254#387C22×C1118yescomplemented
255#387C22×C1118yescomplemented
256#385C22×C1118yes—
257#385C22×C1114yes—
258#385C22×C1114yes—
259#381C22×C1114yes—
260#381C22×C1112yes—
261#380C22×C1112yes—
262#380C22×C1114yes—
263#379C22×C1114yes—
264C4×C22⋊C4C22×C1112yes—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—28no—
268C22×C11—24no—
269C22×C11—28no—
270C22×C11—416no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—44no—
274C22×C11#53614yes—
275C22×C11C23×D411yescharacteristic
276C22×C11C2×H(5,𝔽2)12yes—
277C22×C11C2×2−1+412yes—
278C22×C11C2×2−1+412yes—
279C4×C11—24no—
280C4×C11—24no—
281C4×C11—24no—
282C4×C11—24no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—44no—
286C4×C11—44no—
287C4×C11—48no—
288C25C23×C1111yescharacteristic
289C22×Q8—24no—
290C22×Q8—44no—
291C22×Q8C23×C1114yes—
292C22×Q8C23×C1112yes—
293C22×Q8C23×C1112yes—
294C23×C4—24no—
295C23×C4—44no—
296C23×C4C23×C1111yescharacteristic
297C23×C4C23×C1111yescharacteristic
298C23×C4C23×C1114yes—
299C23×C4C23×C1111yescharacteristic
300C23×C4C23×C1111yescharacteristic
301C23×C4C23×C1111yescharacteristic
302C23×C4C23×C1111yescharacteristic
303C4⋊Q8—216no—
304C4⋊Q8—48no—
305#125—216no—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308C22⋊Q8—232no—
309C22⋊Q8—48no—
310#117—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4D4×C1118yes—
314C2×C4⋊C4C23×C1114yes—
315C2×C4⋊C4C23×C1114yes—
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1112yes—
320C2×C4⋊C4C23×C1114yes—
321C2×C4⋊C4C23×C1114yes—
322C2×C4⋊C4C23×C1118yes—
323C2×C4⋊C4C23×C1114yes—
324C2×C4⋊C4C23×C1118yes—
325C2×C4⋊C4C23×C1114yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4C23×C1114yes—
329C2×C22⋊C4C23×C1114yes—
330C2×C22⋊C4C23×C1114yes—
331C2×C22⋊C4C23×C1114yes—
332C2×C22⋊C4C23×C1118yes—
333C2×C22⋊C4C23×C1118yes—
334C2×C42C23×C1114yes—
335C2×C42C23×C1114yes—
336#95C23×C1114yes—
337#95C23×C1114yes—
338#95C23×C1118yes—
339#95C23×C1114yes—
340#95C23×C1114yes—
341#95C23×C1118yes—
342#95C23×C1118yes—
343#95C23×C1118yes—
344C2×C11—24no—
345C2×C11—44no—
346C2×C11C2×#53611yescharacteristic
347C2×C11#348411yescharacteristic
348C2×C11#348611yescharacteristic
349C2×C11#353814yes—
350C24—22no—
351C24—24no—
352C24—24no—
353C24—42no—
354C24C24×C1112yes—
355C24C24×C1111yescharacteristic
356C2×Q8—28no—
357C2×Q8—24no—
358C2×Q8—24no—
359C2×Q8—28no—
360C2×Q8—44no—
361C2×Q8—44no—
362C2×Q8—44no—
363C2×Q8—416no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—28no—
371C22×C4—28no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—416no—
377C22×C4C2×D4×C1114yes—
378C22×C4C2×D4×C1114yes—
379C22×C4C2×D4×C1114yes—
380C22×C4C24×C1118yes—
381C22×C4C24×C1112yes—
382C22×C4C24×C1114yes—
383C22×C4C24×C1112yes—
384C22×C4C24×C1114yes—
385C22×C4C24×C1112yes—
386C22×C4C24×C1112yes—
387C22×C4C24×C1112yes—
388C22×C4C24×C1112yes—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—28no—
396C4⋊C4—28no—
397C4⋊C4—216no—
398C4⋊C4—44no—
399C4⋊C4—48no—
400C4⋊C4C2×D4×C11116yes—
401C22⋊C4—28no—
402C22⋊C4—216no—
403C22⋊C4—28no—
404C22⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—48no—
407C42—28no—
408C42—44no—
409C11#3670811yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—22no—
412C23—28no—
413C23—22no—
414C23—24no—
415C23—22no—
416C23—24no—
417C23—416no—
418C23—44no—
419C23—44no—
420C23C22×D4×C1112yes—
421C23C11×2−1+414yes—
422C23C11×2−1+414yes—
423C23C25×C1111yescharacteristic
424Q8—416no—
425Q8—84no—
426Q8—84no—
427C2×C4—28no—
428C2×C4—28no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—28no—
439C2×C4—28no—
440C2×C4—24no—
441C2×C4—28no—
442C2×C4—28no—
443C2×C4—28no—
444C2×C4—24no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—416no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4C22×D4×C1114yes—
451C2×C4C22×D4×C1114yes—
452C2×C4C22×D4×C1114yes—
453C2×C4C11×H(5,𝔽2)14yes—
454C22—22no—
455C22—22no—
456C22—28no—
457C22—24no—
458C22—28no—
459C22—416no—
460C22—42no—
461C22—42no—
462C22—44no—
463C22C11×#53614yes—
464C22C23×D4×C1111yescharacteristic
465C22C2×C11×H(5,𝔽2)12yes—
466C22C2×C11×2−1+412yes—
467C22C2×C11×2−1+412yes—
468C4—24no—
469C4—24no—
470C4—24no—
471C4—24no—
472C4—42no—
473C4—42no—
474C4—44no—
475C4—44no—
476C4—48no—
477C2—24no—
478C2—44no—
479C2C2×C11×#53611yescharacteristic
480C2C11×#348411yescharacteristic
481C2C11×#348611yescharacteristic
482C2C11×#353814yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#544C2semidirect
4. C11×#2690C2semidirect
5. C11×#2677C2semidirect
6. C11×#2627C2semidirect
8. C11×#2484C2semidirect
10. C11×#2434C2semidirect
11. C11×#2313C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
16. C2×C11×C4⋊Q8C22semidirect
17. C2×C11×#125C22semidirect
29. C11×#400C22semidirect
30. C11×#400C22semidirect
32. C11×#398C22semidirect
33. C11×#398C22semidirect
36. C11×#395C22semidirect
37. C11×#395C22semidirect
39. C11×#391C22semidirect
42. C11×#387C22semidirect
43. C11×#387C22semidirect
109. #36708C11direct (N × H)
169. C2×#544C2×C11semidirect
172. #2690C2×C11semidirect
173. #2677C2×C11semidirect
174. #2627C2×C11semidirect
176. #2484C2×C11semidirect
178. #2434C2×C11semidirect
179. #2313C2×C11semidirect
227. C2×C4⋊Q8C22×C11semidirect
228. C2×C4⋊Q8C22×C11semidirect
229. C2×#125C22×C11semidirect
241. #400C22×C11semidirect
242. #400C22×C11semidirect
244. #398C22×C11semidirect
245. #398C22×C11semidirect
248. #395C22×C11semidirect
249. #395C22×C11semidirect
251. #391C22×C11semidirect
254. #387C22×C11semidirect
255. #387C22×C11semidirect
409. C11#36708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C22×C11×C22⋊Q82
C11×#28482
C11×#26902
C11×#26772
C11×#26272
C11×#25612
C11×#24842
C11×#24822
C11×#24342
C11×#23132
#3670811