Subgroups — C₂×#20292457 #28338253

Order 13696.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812045	C₂	1	2	yes	maximal
2	#20292457	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#13133802	—	2	2	no	—
5	#16812045	—	2	2	no	—
6	#16812045	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₀₇	C₄	1	2	yes	—
9	C₂×C₁₆×C₁₀₇	C₄	1	2	yes	—
10	C₂×C₁₆×C₁₀₇	C₂²	1	2	yes	—
11	#13133802	—	2	4	no	—
12	#13133802	—	4	2	no	—
13	C₂×C₁₀₇⋊C₈	—	4	2	no	—
14	C₂²×C₄×C₁₀₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₀₇	Q₈	1	1	yes	characteristic
19	C₂×C₈×C₁₀₇	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
21	C₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
22	C₂³×C₁₀₇	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
26	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₀₇	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
29	C₈×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
33	C₁₀₇⋊C₈	—	4	4	no	—
34	C₂²×C₁₀₇	—	2	2	no	—
35	C₂²×C₁₀₇	#107	1	1	yes	characteristic
36	C₂²×C₁₀₇	#107	1	1	yes	characteristic
37	C₂²×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
38	C₄×C₁₀₇	#107	1	1	yes	characteristic
39	C₄×C₁₀₇	#107	1	1	yes	characteristic
40	C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
42	C₂×C₁₀₇	—	2	1	no	—
43	C₂×C₁₀₇	—	2	1	no	—
44	C₂×C₁₀₇	#368	1	2	yes	complemented
45	C₂×C₁₀₇	C₂×#107	1	1	yes	characteristic
46	C₂×#368	—	107	1	no	maximal, Sylow
47	C₁₀₇	C₂×#368	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₁₆	D₁₀₇	1	1	yes	characteristic
49	C₂×#108	—	107	2	no	—
50	#368	—	107	4	no	—
51	C₂×M₁₆	—	214	2	no	—
52	C₂²×C₈	C₂×D₁₀₇	1	1	yes	characteristic
53	C₂×C₁₆	Dic₁₀₇	1	2	yes	—
54	C₂×C₁₆	Dic₁₀₇	1	2	yes	—
55	C₂×C₁₆	C₂×D₁₀₇	1	2	yes	—
56	#108	—	107	4	no	—
57	#108	—	214	2	no	—
58	C₂²×C₄	D₄₂₈	1	1	yes	characteristic
59	M₁₆	—	428	2	no	—
60	M₁₆	—	214	4	no	—
61	C₂×C₈	—	428	2	no	—
62	C₂×C₈	Dic₂₁₄	1	1	yes	characteristic
63	C₂×C₈	Dic₂₁₄	1	1	yes	characteristic
64	C₂×C₈	D₄₂₈	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₁₀₇	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₁₀₇	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₁₀₇	1	1	yes	characteristic
68	C₁₆	C₂×Dic₁₀₇	1	4	yes	—
69	C₂³	Dic₄₂₈	1	1	yes	characteristic
70	C₂×C₄	C₄⋊Dic₁₀₇	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₁₀₇	1	1	yes	characteristic
72	C₂×C₄	D₈₅₆	1	1	yes	characteristic
73	C₂×C₄	D₈₅₆	1	1	yes	characteristic
74	C₂×C₄	Dic₄₂₈	1	1	yes	characteristic
75	C₂×C₄	C₂×D₄₂₈	1	1	yes	characteristic
76	C₈	—	428	4	no	—
77	C₈	C₄⋊Dic₁₀₇	1	1	yes	characteristic
78	C₈	C₄⋊Dic₁₀₇	1	1	yes	characteristic
79	C₈	C₂²×Dic₁₀₇	1	1	yes	characteristic
80	C₈	C₂×Dic₂₁₄	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#16812043	1	1	yes	characteristic
83	C₂²	#16812043	1	1	yes	characteristic
84	C₂²	C₂×Dic₄₂₈	1	1	yes	characteristic
85	C₄	#16812043	1	1	yes	characteristic
86	C₄	#16812043	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₁₀₇	1	1	yes	characteristic
88	C₄	C₂×D₈₅₆	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#20292457	1	2	yes	direct product factor
92	C₂	C₂×#16812043	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈₅₆
commutator	C₈×C₁₀₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₀₇
Fitting	C₂²×C₁₆×C₁₀₇	C₂
socle	C₂²×C₁₀₇	#107
prime radical	C₂³×C₁₀₇	Q₁₆
cosocle	C₂×C₈×C₁₀₇	C₂³
hypercenter	C₂²×C₁₆	D₁₀₇
hypocenter	C₁₀₇	C₂×#368
LCS	G ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #20292457	C₂	direct (N × H)
44. C₂×C₁₀₇	#368	semidirect
47. C₁₀₇	C₂×#368	semidirect
91. C₂	#20292457	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×#16812045	2
#20292457	2
C₂²×C₁₆×C₁₀₇	2
C₂×#368	107

Subgroups — C2×#20292457 #28338253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20292457 #28338253