Subgroups — C₂×#20292462 #28338758

Order 13696.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#20292462	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈₅₆	—	2	1	no	—
6	D₁₇₁₂	—	2	1	no	—
7	D₁₇₁₂	C₂²	1	2	yes	complemented
8	C₁₀₇⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₁₀₇	—	2	1	no	—
10	D₁₆×C₁₀₇	—	2	1	no	—
11	D₁₆×C₁₀₇	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂×D₄₂₈	—	4	1	no	—
14	D₈₅₆	—	2	2	no	—
15	D₈₅₆	—	4	1	no	—
16	C₂×D₄×C₁₀₇	—	4	1	no	—
17	D₈×C₁₀₇	—	2	2	no	—
18	D₈×C₁₀₇	—	4	1	no	—
19	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
20	C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
21	C₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
22	C₂³×C₁₀₇	—	8	1	no	—
23	C₂²×D₁₀₇	—	8	1	no	—
24	D₄×C₁₀₇	—	4	2	no	—
25	D₄×C₁₀₇	—	8	1	no	—
26	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
27	D₄₂₈	—	4	2	no	—
28	D₄₂₈	—	8	1	no	—
29	C₈×C₁₀₇	D₈	1	1	yes	characteristic
30	C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₀₇	—	8	2	no	—
32	C₂²×C₁₀₇	—	16	2	no	—
33	C₂²×C₁₀₇	D₁₆	1	1	yes	characteristic
34	C₂×D₁₀₇	—	8	2	no	—
35	C₂×D₁₀₇	—	16	2	no	—
36	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
37	C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
38	C₂×C₁₀₇	—	16	2	no	—
39	C₂×C₁₀₇	D₃₂	1	2	yes	complemented
40	C₂×C₁₀₇	C₂×D₁₆	1	1	yes	characteristic
41	D₁₀₇	—	16	2	no	—
42	C₂×D₃₂	—	107	1	no	maximal, Sylow
43	C₁₀₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₁₆	—	107	1	no	—
45	C₂×D₁₆	D₁₀₇	1	1	yes	characteristic, complemented
46	D₃₂	—	107	4	no	—
47	C₂×C₃₂	—	107	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	214	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	107	2	no	—
52	D₁₆	—	214	1	no	—
53	D₁₆	C₂×D₁₀₇	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
55	C₃₂	—	107	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	428	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	428	1	no	—
61	D₈	—	214	2	no	—
62	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₁₀₇	1	1	yes	characteristic
64	C₁₆	C₂²×D₁₀₇	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	856	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	856	1	no	—
70	D₄	—	428	2	no	—
71	C₂×C₄	#13133803	1	1	yes	characteristic
72	C₈	#13133803	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₁₀₇	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	856	2	no	—
77	C₂²	—	1712	2	no	—
78	C₂²	#16812050	1	1	yes	characteristic
79	C₄	#16812050	1	1	yes	characteristic
80	C₄	C₂×#13133803	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	1712	2	no	—
83	C₂	#20292462	1	2	yes	direct product factor
84	C₂	C₂×#16812050	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812050
commutator, cosocle	C₁₆×C₁₀₇	C₂³
Frattini	C₁₆	C₂²×D₁₀₇
Fitting	C₂×D₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	D₁₆
hypercenter	C₂×D₁₆	D₁₀₇
hypocenter	C₁₀₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
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×D₁₇₁₂	C₂	semidirect
2. #20292462	C₂	direct (N × H)
3. C₂×C₁₀₇⋊C₃₂	C₂	semidirect
4. C₂×D₁₆×C₁₀₇	C₂	semidirect
7. D₁₇₁₂	C₂²	semidirect
8. C₁₀₇⋊C₃₂	C₂²	semidirect
11. D₁₆×C₁₀₇	C₂²	semidirect
39. C₂×C₁₀₇	D₃₂	semidirect
43. C₁₀₇	C₂×D₃₂	semidirect
45. C₂×D₁₆	D₁₀₇	semidirect
53. D₁₆	C₂×D₁₀₇	semidirect
83. C₂	#20292462	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×D₁₇₁₂	2
#20292462	2
C₂×C₁₀₇⋊C₃₂	2
C₂×D₁₆×C₁₀₇	2
C₂×D₃₂	107

Subgroups — C2×#20292462 #28338758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20292462 #28338758