Subgroups — C₂×#20292464 #28338761

Order 13696.

112 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
2	#20292464	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₃₂×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	—
8	C₁₀₇⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
10	Q₃₂×C₁₀₇	—	2	1	no	—
11	Q₃₂×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×Q₈×C₁₀₇	—	4	1	no	—
17	Q₁₆×C₁₀₇	—	2	2	no	—
18	Q₁₆×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	C₂²×D₁₀₇	—	8	1	no	—
23	Q₈×C₁₀₇	—	4	2	no	—
24	Q₈×C₁₀₇	—	8	1	no	—
25	C₂×C₄×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	D₁₆	1	1	yes	characteristic
32	C₂×D₁₀₇	—	8	2	no	—
33	C₂×D₁₀₇	—	16	2	no	—
34	C₄×C₁₀₇	—	8	2	no	—
35	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
36	C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
37	C₂×C₁₀₇	SD₆₄	1	2	yes	complemented
38	C₂×C₁₀₇	C₂×D₁₆	1	1	yes	characteristic
39	D₁₀₇	—	16	2	no	—
40	C₂×SD₆₄	—	107	1	no	maximal, Sylow
41	C₁₀₇	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₃₂	D₁₀₇	1	1	yes	characteristic, complemented
43	C₂×D₁₆	—	107	1	no	—
44	SD₆₄	—	107	4	no	—
45	C₂×C₃₂	—	107	1	no	—
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×D₈	—	214	1	no	—
48	Q₃₂	—	2	1	no	—
49	Q₃₂	C₂×D₁₀₇	1	2	yes	complemented
50	D₁₆	—	107	2	no	—
51	D₁₆	—	214	1	no	—
52	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
53	C₃₂	—	107	2	no	—
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	428	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	428	1	no	—
59	D₈	—	214	2	no	—
60	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₁₀₇	1	1	yes	characteristic
62	C₁₆	C₂²×D₁₀₇	1	1	yes	characteristic
63	C₂³	—	856	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	856	1	no	—
67	D₄	—	428	2	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	#13133803	1	1	yes	characteristic
70	C₈	#13133803	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₁₀₇	1	1	yes	characteristic
72	C₂²	—	856	2	no	—
73	C₂²	—	1712	2	no	—
74	C₂²	#16812050	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#16812050	1	1	yes	characteristic
77	C₄	C₂×#13133803	1	1	yes	characteristic
78	C₂	—	1712	2	no	—
79	C₂	#20292464	1	2	yes	direct product factor
80	C₂	C₂×#16812050	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812050
commutator, cosocle	C₁₆×C₁₀₇	C₂³
Frattini	C₁₆	C₂²×D₁₀₇
Fitting	C₂×Q₃₂×C₁₀₇	C₂
socle	C₂²×C₁₀₇	D₁₆
prime radical	C₂×D₁₇₁₂	C₂
hypercenter	C₂×Q₃₂	D₁₀₇
hypocenter	C₁₀₇	C₂×SD₆₄
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #20292464	C₂	direct (N × H)
3. C₂×C₁₀₇⋊C₃₂	C₂	semidirect
4. C₂×Q₃₂×C₁₀₇	C₂	semidirect
8. C₁₀₇⋊C₃₂	C₂²	semidirect
11. Q₃₂×C₁₀₇	C₂²	semidirect
37. C₂×C₁₀₇	SD₆₄	semidirect
41. C₁₀₇	C₂×SD₆₄	semidirect
42. C₂×Q₃₂	D₁₀₇	semidirect
49. Q₃₂	C₂×D₁₀₇	semidirect
79. C₂	#20292464	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
#20292464	2
C₂×C₁₀₇⋊C₃₂	2
C₂×Q₃₂×C₁₀₇	2
C₂×SD₆₄	107

Subgroups — C2×#20292464 #28338761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20292464 #28338761