Subgroups — #28334442

Order 13696.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20292757	C₂	1	1	yes	maximal, characteristic
2	#20292403	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₂₁₄	C₄	1	1	yes	characteristic
5	C₂×C₁₀₇⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₁₀₇⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₁₀₇⋊C₈	—	2	1	no	—
8	#16812019	—	2	1	no	—
9	C₂×C₁₆×C₁₀₇	—	2	1	no	—
10	C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₁₄	C₈	1	1	yes	characteristic
12	C₂×C₁₀₇⋊C₈	—	2	1	no	—
13	C₄⋊Dic₁₀₇	C₈	1	1	yes	characteristic
14	Dic₁₀₇⋊C₄	—	2	1	no	—
15	C₄×Dic₁₀₇	—	2	1	no	—
16	C₁₀₇⋊C₁₆	—	2	2	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	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₀₇	M₁₆	1	1	yes	characteristic
24	C₂×Dic₁₀₇	—	2	1	no	—
25	C₂×Dic₁₀₇	—	2	1	no	—
26	Dic₂₁₄	—	4	1	no	—
27	C₈×C₁₀₇	—	2	1	no	—
28	C₈×C₁₀₇	SD₁₆	1	1	yes	characteristic
29	C₈×C₁₀₇	Q₁₆	1	1	yes	characteristic
30	C₁₀₇⋊C₈	—	4	1	no	—
31	C₂²×C₁₀₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₀₇	—	2	1	no	—
33	C₄×C₁₀₇	—	2	1	no	—
34	C₄×C₁₀₇	#103	1	1	yes	characteristic
35	C₄×C₁₀₇	#104	1	1	yes	characteristic
36	Dic₁₀₇	—	4	1	no	—
37	Dic₁₀₇	—	4	1	no	—
38	C₂×C₁₀₇	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₁₀₇	#349	1	1	yes	characteristic
40	C₂×C₁₀₇	#350	1	1	yes	characteristic
41	#1338	—	107	1	no	maximal, Sylow
42	C₁₀₇	#1338	1	1	yes	characteristic, complemented, Sylow
43	#446	—	107	1	no	—
44	C₄⋊C₁₆	D₁₀₇	1	1	yes	characteristic
45	#346	—	107	1	no	—
46	C₄×Q₈	—	107	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	214	1	no	—
49	C₄⋊C₈	—	107	1	no	—
50	C₄⋊C₈	—	214	1	no	—
51	#97	—	214	1	no	—
52	C₄×C₈	C₂×D₁₀₇	1	1	yes	characteristic
53	C₂×Q₈	—	107	1	no	—
54	C₂×C₈	—	214	1	no	—
55	C₂×C₈	D₄₂₈	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₁₀₇	1	1	yes	characteristic
57	C₄⋊C₄	—	107	1	no	—
58	C₄⋊C₄	—	214	1	no	—
59	C₄²	—	214	1	no	—
60	C₄²	C₄×D₁₀₇	1	1	yes	characteristic
61	C₁₆	—	4	1	no	—
62	C₁₆	—	214	2	no	—
63	Q₈	—	428	1	no	—
64	C₂×C₄	—	214	1	no	—
65	C₂×C₄	—	214	1	no	—
66	C₂×C₄	(C₂×D₁₀₇)⋊C₄	1	1	yes	characteristic
67	C₂×C₄	C₈×D₁₀₇	1	1	yes	characteristic
68	C₂×C₄	#13133801	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	428	1	no	—
71	C₈	#13133806	1	1	yes	characteristic
72	C₈	#13133808	1	1	yes	characteristic
73	C₂²	(C₂×D₁₀₇)⋊C₈	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	428	1	no	—
77	C₄	—	428	1	no	—
78	C₄	#16812032	1	1	yes	characteristic
79	C₄	#16812035	1	1	yes	characteristic
80	C₂	#20292357	1	1	yes	characteristic
81	C₂	#20292408	1	1	yes	characteristic
82	C₂	#20292410	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₀₇)⋊C₄
commutator	C₂×C₄×C₁₀₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₇
Fitting	C₄⋊C₁₆×C₁₀₇	C₂
socle, prime radical	C₂²×C₁₀₇	C₂²⋊C₈
cosocle	C₄×C₈×C₁₀₇	C₂²
hypercenter	C₄⋊C₁₆	D₁₀₇
hypocenter	C₁₀₇	#1338
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
42. C₁₀₇	#1338	semidirect

Maximal subgroups

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

subgroup	index
#20292757	2
#20292403	2
C₄⋊C₁₆×C₁₀₇	2
#1338	107