Subgroups — C₂×#10622157 #13070913

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622157	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×D₈	—	2	1	no	—
6	C₂×D₈₈	—	2	1	no	—
7	C₁₁×D₁₆	—	2	1	no	—
8	C₁₁×D₁₆	C₂²	1	2	yes	complemented
9	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	D₁₇₆	—	2	1	no	—
11	D₁₇₆	C₂²	1	2	yes	complemented
12	C₁₁⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂×D₄×C₁₁	—	4	1	no	—
14	C₂×D₄₄	—	4	1	no	—
15	C₁₁×D₈	—	2	2	no	—
16	C₁₁×D₈	—	4	1	no	—
17	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
18	D₈₈	—	2	2	no	—
19	D₈₈	—	4	1	no	—
20	C₁₁×C₁₆	D₄	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×D₃₂	—	11	1	no	maximal, Sylow
23	C₂³×C₁₁	—	8	1	no	—
24	C₂²×D₁₁	—	8	1	no	—
25	D₄×C₁₁	—	4	2	no	—
26	D₄×C₁₁	—	8	1	no	—
27	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
28	D₄₄	—	4	2	no	—
29	D₄₄	—	8	1	no	—
30	C₈×C₁₁	D₈	1	1	yes	characteristic
31	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₆	—	11	1	no	—
33	C₂×D₁₆	D₁₁	1	1	yes	characteristic, complemented
34	D₃₂	—	11	4	no	—
35	C₂×C₃₂	—	11	1	no	—
36	C₂²×C₁₁	—	8	2	no	—
37	C₂²×C₁₁	—	16	2	no	—
38	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
39	C₂×D₁₁	—	8	2	no	—
40	C₂×D₁₁	—	16	2	no	—
41	C₄×C₁₁	D₁₆	1	1	yes	characteristic
42	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
43	C₂×D₈	—	2	1	no	—
44	C₂×D₈	—	22	1	no	—
45	D₁₆	—	2	1	no	—
46	D₁₆	—	11	2	no	—
47	D₁₆	—	22	1	no	—
48	D₁₆	C₂×D₁₁	1	2	yes	complemented
49	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
50	C₃₂	—	11	2	no	—
51	C₂×C₁₁	—	16	2	no	—
52	C₂×C₁₁	D₃₂	1	2	yes	complemented
53	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
54	D₁₁	—	16	2	no	—
55	C₂×D₄	—	4	1	no	—
56	C₂×D₄	—	44	1	no	—
57	D₈	—	2	2	no	—
58	D₈	—	4	1	no	—
59	D₈	—	22	2	no	—
60	D₈	—	44	1	no	—
61	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
62	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
63	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
64	C₁₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	8	1	no	—
66	C₂³	—	88	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	44	2	no	—
70	D₄	—	88	1	no	—
71	C₂×C₄	#4323	1	1	yes	characteristic
72	C₈	#4323	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	88	2	no	—
77	C₂²	—	176	2	no	—
78	C₂²	#66890	1	1	yes	characteristic
79	C₄	#66890	1	1	yes	characteristic
80	C₄	C₂×#4323	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	176	2	no	—
83	C₂	#10622157	1	2	yes	direct product factor
84	C₂	C₂×#66890	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66890
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×D₁₆	C₂
socle	C₂²×C₁₁	D₁₆
hypercenter	C₂×D₁₆	D₁₁
hypocenter	C₁₁	C₂×D₃₂
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×D₁₆	C₂	semidirect
2. C₂×D₁₇₆	C₂	semidirect
3. #10622157	C₂	direct (N × H)
4. C₂×C₁₁⋊C₃₂	C₂	semidirect
8. C₁₁×D₁₆	C₂²	semidirect
11. D₁₇₆	C₂²	semidirect
12. C₁₁⋊C₃₂	C₂²	semidirect
33. C₂×D₁₆	D₁₁	semidirect
48. D₁₆	C₂×D₁₁	semidirect
52. C₂×C₁₁	D₃₂	semidirect
64. C₁₁	C₂×D₃₂	semidirect
83. C₂	#10622157	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×D₁₆	2
C₂×D₁₇₆	2
#10622157	2
C₂×C₁₁⋊C₃₂	2
C₂×D₃₂	11

Subgroups — C2×#10622157 #13070913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10622157 #13070913