Subgroups — C₁₁×#541 #10623402

Order 704.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#126	C₂	1	4	yes	maximal
3	C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#125	C₂	1	4	yes	maximal, complemented
5	C₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal
6	C₄×Q₈×C₁₁	C₂	1	2	yes	maximal, complemented
7	C₁₁×#117	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₁₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
11	C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
12	C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
13	C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
14	C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
15	C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
16	C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₄²×C₁₁	C₂²	1	1	yes	characteristic
19	C₄²×C₁₁	C₂²	1	1	yes	characteristic
20	C₄²×C₁₁	C₂²	1	4	yes	—
21	C₂³×C₁₁	C₂³	1	1	yes	characteristic
22	Q₈×C₁₁	—	2	4	no	—
23	C₂×C₄×C₁₁	—	2	2	no	—
24	C₂×C₄×C₁₁	C₂³	1	2	yes	—
25	C₂×C₄×C₁₁	C₂³	1	2	yes	—
26	C₂×C₄×C₁₁	C₂³	1	4	yes	—
27	C₂×C₄×C₁₁	C₂³	1	4	yes	—
28	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
30	#541	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₁₁	—	2	1	no	—
32	C₂²×C₁₁	—	2	2	no	—
33	C₂²×C₁₁	C₂⁴	1	1	yes	characteristic
34	C₄×C₁₁	—	2	1	no	—
35	C₄×C₁₁	—	2	4	no	—
36	C₄×C₁₁	—	2	2	no	—
37	C₄×C₁₁	—	2	2	no	—
38	C₄×C₁₁	—	2	4	no	—
39	C₄×C₁₁	#41	1	2	yes	—
40	C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
41	#126	C₂×C₁₁	1	4	yes	—
42	#125	C₂×C₁₁	1	1	yes	characteristic, complemented
43	#125	C₂×C₁₁	1	4	yes	complemented
44	C₂²⋊Q₈	C₂×C₁₁	1	2	yes	—
45	C₄×Q₈	C₂×C₁₁	1	2	yes	complemented
46	#117	C₂×C₁₁	1	1	yes	characteristic
47	C₂×C₁₁	—	4	1	no	—
48	C₂×C₁₁	C₂×#41	1	1	yes	characteristic
49	C₂×C₁₁	2₋¹⁺⁴	1	2	yes	—
50	C₂×Q₈	C₂²×C₁₁	1	2	yes	—
51	C₂²×C₄	C₂²×C₁₁	1	1	yes	characteristic
52	C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
53	C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
54	C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
55	C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
56	C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
57	C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
58	C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
59	C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
60	C₄²	C₂²×C₁₁	1	1	yes	characteristic
61	C₄²	C₂²×C₁₁	1	1	yes	characteristic
62	C₄²	C₂²×C₁₁	1	4	yes	—
63	C₁₁	#541	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³	C₂³×C₁₁	1	1	yes	characteristic
65	Q₈	—	2	4	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	C₂³×C₁₁	1	2	yes	—
68	C₂×C₄	C₂³×C₁₁	1	2	yes	—
69	C₂×C₄	C₂³×C₁₁	1	4	yes	—
70	C₂×C₄	C₂³×C₁₁	1	4	yes	—
71	C₂×C₄	C₂³×C₁₁	1	1	yes	characteristic
72	C₂×C₄	C₂³×C₁₁	1	1	yes	characteristic
73	C₂²	—	2	1	no	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂⁴×C₁₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	4	no	—
78	C₄	—	2	2	no	—
79	C₄	—	2	2	no	—
80	C₄	—	2	4	no	—
81	C₄	C₁₁×#41	1	2	yes	—
82	C₂	—	4	1	no	—
83	C₂	C₂×C₁₁×#41	1	1	yes	characteristic
84	C₂	C₁₁×2₋¹⁺⁴	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₄⋊Q₈	C₂	semidirect
3. C₁₁×#125	C₂	semidirect
4. C₁₁×#125	C₂	semidirect
6. C₄×Q₈×C₁₁	C₂	semidirect
30. #541	C₁₁	direct (N × H)
40. C₄⋊Q₈	C₂×C₁₁	semidirect
42. #125	C₂×C₁₁	semidirect
43. #125	C₂×C₁₁	semidirect
45. C₄×Q₈	C₂×C₁₁	semidirect
63. C₁₁	#541	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×C₄⋊Q₈	2
C₁₁×#126	2
C₁₁×#125	2
C₁₁×C₂²⋊Q₈	2
C₄×Q₈×C₁₁	2
C₁₁×#117	2
#541	11

Subgroups — C11×#541 #10623402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#541 #10623402