Subgroups — #28334499

Order 13696.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293007	C₂	1	1	yes	maximal, characteristic
2	#20292448	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₂₈	—	2	1	no	—
5	C₂×Dic₄₂₈	—	2	1	no	—
6	#16812109	C₄	1	2	yes	—
7	#16812049	—	2	1	no	—
8	M₃₂×C₁₀₇	—	2	1	no	—
9	C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₂₁₄	—	2	2	no	—
11	Dic₄₂₈	—	4	1	no	—
12	Dic₄₂₈	—	4	1	no	—
13	Dic₄₂₈	—	4	1	no	—
14	Dic₄₂₈	—	4	1	no	—
15	C₄⋊Dic₁₀₇	—	4	2	no	—
16	C₁₀₇⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
19	C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₀₇	—	4	1	no	—
21	C₂×C₄×C₁₀₇	—	2	1	no	—
22	C₂×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₀₇	—	4	2	no	—
24	Dic₂₁₄	—	4	2	no	—
25	Dic₂₁₄	—	4	2	no	—
26	C₈×C₁₀₇	D₈	1	1	yes	characteristic
27	C₈×C₁₀₇	D₈	1	1	yes	characteristic
28	C₈×C₁₀₇	SD₁₆	1	1	yes	characteristic
29	C₈×C₁₀₇	SD₁₆	1	1	yes	characteristic
30	C₂²×C₁₀₇	#100	1	1	yes	characteristic
31	C₄×C₁₀₇	—	2	2	no	—
32	C₄×C₁₀₇	#102	1	1	yes	characteristic
33	C₄×C₁₀₇	#102	1	1	yes	characteristic
34	Dic₁₀₇	—	8	2	no	—
35	C₂×C₁₀₇	—	2	1	no	—
36	C₂×C₁₀₇	#331	1	1	yes	characteristic
37	#1358	—	107	1	no	maximal, Sylow
38	C₁₀₇	#1358	1	1	yes	characteristic, complemented, Sylow
39	#494	—	107	1	no	—
40	#364	—	107	1	no	—
41	#364	D₁₀₇	1	1	yes	characteristic
42	C₂×Q₁₆	—	214	1	no	—
43	C₂×Q₁₆	—	214	1	no	—
44	C₄⋊Q₈	—	107	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	214	1	no	—
47	C₄×C₈	C₂×D₁₀₇	1	1	yes	characteristic
48	C₂×Q₈	—	214	2	no	—
49	Q₁₆	—	428	1	no	—
50	Q₁₆	—	428	1	no	—
51	Q₁₆	—	428	1	no	—
52	Q₁₆	—	428	1	no	—
53	C₂×C₈	D₄₂₈	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
55	C₄⋊C₄	—	428	2	no	—
56	C₄²	C₄×D₁₀₇	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	428	1	no	—
59	Q₈	—	428	2	no	—
60	Q₈	—	428	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	428	2	no	—
63	C₂×C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
64	C₈	#13133803	1	1	yes	characteristic
65	C₈	D₈₅₆	1	1	yes	characteristic
66	C₈	#13133805	1	1	yes	characteristic
67	C₈	#13133807	1	1	yes	characteristic
68	C₂²	#16812025	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	856	2	no	—
71	C₄	#16812029	1	1	yes	characteristic
72	C₄	#16812031	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#20292370	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20292370
commutator	C₄²×C₁₀₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₀₇
Fitting	#364×C₁₀₇	C₂
socle	C₂×C₁₀₇	#331
prime radical	C₂²×C₁₀₇	#100
cosocle	C₄×C₈×C₁₀₇	C₂²
hypercenter	#364	D₁₀₇
hypocenter	C₁₀₇	#1358
LCS	G ▷ C₄²×C₁₀₇ ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
38. C₁₀₇	#1358	semidirect

Maximal subgroups

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

subgroup	index
#20293007	2
#20292448	2
#364×C₁₀₇	2
#1358	107