Subgroups — C₁₁×#3458 #13066296

Order 1408.

996 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#544	C₂	1	12	yes	maximal, complemented
2	C₁₁×#543	C₂	1	4	yes	maximal
3	C₁₁×#533	C₂	1	12	yes	maximal, complemented
4	C₂×C₁₁×#117	C₂	1	3	yes	maximal
5	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×C₄⋊Q₈	C₂²	1	24	yes	complemented
7	C₁₁×#125	C₂²	1	24	yes	complemented
8	C₁₁×C₂²⋊Q₈	C₂²	1	48	yes	—
9	C₄×Q₈×C₁₁	C₂²	1	16	yes	complemented
10	C₁₁×#117	C₂²	1	12	yes	—
11	C₁₁×#117	C₂²	1	12	yes	—
12	C₂×C₁₁×C₄⋊C₄	C₂²	1	6	yes	—
13	C₂×C₁₁×C₂²⋊C₄	C₂²	1	6	yes	—
14	C₂×C₄²×C₁₁	C₂²	1	6	yes	—
15	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×Q₈×C₁₁	C₂³	1	16	yes	—
17	C₂²×C₄×C₁₁	Q₈	1	8	yes	complemented
18	C₂²×C₄×C₁₁	C₂³	1	12	yes	—
19	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
20	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
21	C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
22	C₁₁×C₄⋊C₄	C₂³	1	48	yes	—
23	C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
24	C₄²×C₁₁	C₂³	1	12	yes	—
25	C₄²×C₁₁	C₂³	1	12	yes	—
26	#3458	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₁₁	—	4	2	no	—
28	C₂³×C₁₁	C₂×Q₈	1	4	yes	—
29	C₂³×C₁₁	C₂⁴	1	3	yes	—
30	Q₈×C₁₁	—	4	16	no	—
31	C₂×C₄×C₁₁	—	4	12	no	—
32	C₂×C₄×C₁₁	C₂×Q₈	1	12	yes	—
33	C₂×C₄×C₁₁	C₂×Q₈	1	12	yes	—
34	C₂×C₄×C₁₁	C₂⁴	1	24	yes	—
35	C₂×C₄×C₁₁	C₂⁴	1	3	yes	—
36	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
37	#544	C₂×C₁₁	1	12	yes	complemented
38	#543	C₂×C₁₁	1	4	yes	—
39	#533	C₂×C₁₁	1	12	yes	complemented
40	C₂×#117	C₂×C₁₁	1	3	yes	—
41	C₂²×C₁₁	—	2	6	no	—
42	C₂²×C₁₁	—	4	4	no	—
43	C₂²×C₁₁	C₂²×Q₈	1	6	yes	—
44	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
45	C₄×C₁₁	—	2	24	no	—
46	C₄×C₁₁	C₂²×Q₈	1	6	yes	—
47	C₄×C₁₁	C₂²×Q₈	1	2	yes	—
48	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic
49	C₄⋊Q₈	C₂²×C₁₁	1	24	yes	complemented
50	#125	C₂²×C₁₁	1	24	yes	complemented
51	C₂²⋊Q₈	C₂²×C₁₁	1	48	yes	—
52	C₄×Q₈	C₂²×C₁₁	1	16	yes	complemented
53	#117	C₂²×C₁₁	1	12	yes	—
54	#117	C₂²×C₁₁	1	12	yes	—
55	C₂×C₄⋊C₄	C₂²×C₁₁	1	6	yes	—
56	C₂×C₂²⋊C₄	C₂²×C₁₁	1	6	yes	—
57	C₂×C₄²	C₂²×C₁₁	1	6	yes	—
58	C₂×C₁₁	—	2	6	no	—
59	C₂×C₁₁	C₂³×Q₈	1	1	yes	characteristic
60	C₂×C₁₁	#585	1	2	yes	—
61	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
62	C₂×Q₈	C₂³×C₁₁	1	16	yes	—
63	C₂²×C₄	Q₈×C₁₁	1	8	yes	complemented
64	C₂²×C₄	C₂³×C₁₁	1	12	yes	—
65	C₂²×C₄	C₂³×C₁₁	1	3	yes	—
66	C₂²×C₄	C₂³×C₁₁	1	3	yes	—
67	C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
68	C₄⋊C₄	C₂³×C₁₁	1	48	yes	—
69	C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
70	C₄²	C₂³×C₁₁	1	12	yes	—
71	C₄²	C₂³×C₁₁	1	12	yes	—
72	C₁₁	#3458	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³	—	4	2	no	—
74	C₂³	C₂×Q₈×C₁₁	1	4	yes	—
75	C₂³	C₂⁴×C₁₁	1	3	yes	—
76	Q₈	—	4	16	no	—
77	C₂×C₄	—	4	12	no	—
78	C₂×C₄	C₂×Q₈×C₁₁	1	12	yes	—
79	C₂×C₄	C₂×Q₈×C₁₁	1	12	yes	—
80	C₂×C₄	C₂⁴×C₁₁	1	24	yes	—
81	C₂×C₄	C₂⁴×C₁₁	1	3	yes	—
82	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
83	C₂²	—	2	6	no	—
84	C₂²	—	4	4	no	—
85	C₂²	C₂²×Q₈×C₁₁	1	6	yes	—
86	C₂²	C₂⁵×C₁₁	1	1	yes	characteristic
87	C₄	—	2	24	no	—
88	C₄	C₂²×Q₈×C₁₁	1	6	yes	—
89	C₄	C₂²×Q₈×C₁₁	1	2	yes	—
90	C₂	—	2	6	no	—
91	C₂	C₂³×Q₈×C₁₁	1	1	yes	characteristic
92	C₂	C₁₁×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁵
prime radical	C₂⁴×C₁₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#544	C₂	semidirect
3. C₁₁×#533	C₂	semidirect
6. C₁₁×C₄⋊Q₈	C₂²	semidirect
7. C₁₁×#125	C₂²	semidirect
9. C₄×Q₈×C₁₁	C₂²	semidirect
17. C₂²×C₄×C₁₁	Q₈	semidirect
26. #3458	C₁₁	direct (N × H)
37. #544	C₂×C₁₁	semidirect
39. #533	C₂×C₁₁	semidirect
49. C₄⋊Q₈	C₂²×C₁₁	semidirect
50. #125	C₂²×C₁₁	semidirect
52. C₄×Q₈	C₂²×C₁₁	semidirect
63. C₂²×C₄	Q₈×C₁₁	semidirect
72. C₁₁	#3458	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#544	2
C₁₁×#543	2
C₁₁×#533	2
C₂×C₁₁×#117	2
#3458	11

Subgroups — C11×#3458 #13066296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3458 #13066296