Subgroups — C₁₁×#2176 #13065014

Order 1408.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×Q₁₆	C₂	1	2	yes	maximal
3	C₁₁×#367	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#358	C₂	1	2	yes	maximal
5	C₁₁×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
7	C₄×Q₈×C₁₁	—	2	2	no	—
8	C₁₁×Q₃₂	C₄	1	4	yes	complemented
9	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₁×#107	C₂²	1	2	yes	—
12	C₁₁×#103	—	2	2	no	—
13	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₁₁	—	2	2	no	—
15	C₁₁×Q₁₆	—	2	2	no	—
16	C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₁₁×C₄⋊C₄	—	2	2	no	—
20	C₁₁×C₄⋊C₄	—	4	2	no	—
21	C₄²×C₁₁	—	4	2	no	—
22	C₄²×C₁₁	D₄	1	1	yes	characteristic
23	C₁₁×C₁₆	—	2	1	no	—
24	C₁₁×C₁₆	C₂×C₄	1	2	yes	—
25	#2176	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	Q₈×C₁₁	—	2	4	no	—
27	Q₈×C₁₁	—	4	2	no	—
28	C₂×C₄×C₁₁	—	4	2	no	—
29	C₂×C₄×C₁₁	—	4	2	no	—
30	C₂×C₄×C₁₁	D₈	1	2	yes	—
31	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₈×C₁₁	—	2	1	no	—
33	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₁	#41	1	1	yes	characteristic
35	C₂×Q₃₂	C₂×C₁₁	1	1	yes	characteristic
36	C₄×Q₁₆	C₂×C₁₁	1	2	yes	—
37	#367	C₂×C₁₁	1	1	yes	characteristic
38	#358	C₂×C₁₁	1	2	yes	—
39	#346	C₂×C₁₁	1	1	yes	characteristic
40	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₁	—	2	2	no	—
42	C₄×C₁₁	—	4	4	no	—
43	C₄×C₁₁	—	8	2	no	—
44	C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
45	C₄×C₁₁	#135	1	1	yes	characteristic
46	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
47	C₄×Q₈	—	2	2	no	—
48	Q₃₂	C₄×C₁₁	1	4	yes	complemented
49	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
50	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
51	#107	C₂²×C₁₁	1	2	yes	—
52	#103	—	2	2	no	—
53	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
54	C₂×C₁₁	C₄×D₈	1	1	yes	characteristic
55	C₂×C₁₁	#510	1	2	yes	—
56	C₂×Q₈	—	2	2	no	—
57	Q₁₆	—	2	2	no	—
58	Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
59	C₂×C₈	D₄×C₁₁	1	1	yes	characteristic
60	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
61	C₄⋊C₄	—	2	2	no	—
62	C₄⋊C₄	—	4	2	no	—
63	C₄²	—	4	2	no	—
64	C₄²	D₄×C₁₁	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	C₂×C₄×C₁₁	1	2	yes	—
67	C₁₁	#2176	1	1	yes	characteristic, direct product factor, Sylow
68	Q₈	—	2	4	no	—
69	Q₈	—	4	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	C₁₁×D₈	1	2	yes	—
73	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
76	C₈	C₁₁×#41	1	1	yes	characteristic
77	C₂²	C₂×C₁₁×D₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	4	4	no	—
80	C₄	—	8	2	no	—
81	C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
82	C₄	C₁₁×#135	1	1	yes	characteristic
83	C₂	C₄×C₁₁×D₈	1	1	yes	characteristic
84	C₂	C₁₁×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂³×C₁₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₁×Q₃₂	C₄	semidirect
25. #2176	C₁₁	direct (N × H)
48. Q₃₂	C₄×C₁₁	semidirect
67. C₁₁	#2176	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×Q₃₂	2
C₄×C₁₁×Q₁₆	2
C₁₁×#367	2
C₁₁×#358	2
C₁₁×#346	2
#2176	11

Subgroups — C11×#2176 #13065014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2176 #13065014