Subgroups — C₂×#16812040 #20292657

Order 6848.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₀₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₀₇	C₂	1	1	yes	maximal, characteristic
3	#16812040	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₇	—	2	1	no	—
6	C₂×C₁₀₇⋊C₈	C₄	1	4	yes	complemented
7	C₂×C₁₀₇⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₇	—	2	1	no	—
9	C₄⋊Dic₁₀₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₀₇	—	2	1	no	—
11	C₂²×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₀₇	—	2	1	no	—
13	C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
14	C₂³×C₁₀₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₇	—	2	2	no	—
16	C₂×C₄×C₁₀₇	—	4	2	no	—
17	C₂×C₄×C₁₀₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₇	Q₈	1	2	yes	—
20	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₇	—	2	2	no	—
22	C₂×Dic₁₀₇	—	4	2	no	—
23	C₁₀₇⋊C₈	C₂×C₄	1	4	yes	complemented
24	C₂²×C₁₀₇	C₄⋊C₄	1	2	yes	—
25	C₂²×C₁₀₇	SD₁₆	1	2	yes	—
26	C₂²×C₁₀₇	SD₁₆	1	2	yes	—
27	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₇	—	4	2	no	—
29	C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₇	—	4	2	no	—
33	C₂×C₁₀₇	#106	1	4	yes	complemented
34	C₂×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
37	C₁₀₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
38	C₂×#106	—	107	1	no	maximal, Sylow
39	C₂²×C₈	—	107	1	no	—
40	C₂×C₄⋊C₄	—	107	1	no	—
41	C₂×C₄⋊C₄	D₁₀₇	1	1	yes	characteristic
42	#106	—	107	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	214	1	no	—
45	C₂²×C₄	C₂×D₁₀₇	1	1	yes	characteristic
46	C₂×C₈	—	107	4	no	—
47	C₂×C₈	—	107	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	107	2	no	—
50	C₄⋊C₄	—	214	1	no	—
51	C₄⋊C₄	C₂×D₁₀₇	1	2	yes	—
52	C₂³	C₂²⋊D₁₀₇	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	428	2	no	—
56	C₂×C₄	—	214	2	no	—
57	C₂×C₄	Dic₂₁₄	1	2	yes	—
58	C₂×C₄	C₄×D₁₀₇	1	2	yes	—
59	C₂×C₄	C₂²⋊D₁₀₇	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
61	C₈	—	107	4	no	—
62	C₂²	Dic₁₀₇⋊C₄	1	2	yes	—
63	C₂²	#13133805	1	2	yes	—
64	C₂²	#13133806	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₁₀₇	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	428	2	no	—
68	C₄	Dic₁₀₇⋊C₄	1	2	yes	—
69	C₄	C₂×C₄×D₁₀₇	1	1	yes	characteristic
70	C₄	C₂×Dic₂₁₄	1	1	yes	characteristic
71	C₂	#16812040	1	4	yes	direct product factor
72	C₂	C₂×Dic₁₀₇⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#13133805	1	1	yes	characteristic
74	C₂	C₂×#13133806	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₇
commutator	C₄×C₁₀₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	C₂×C₄⋊C₄×C₁₀₇	C₂
socle	C₂³×C₁₀₇	D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₇
hypocenter	C₁₀₇	C₂×#106
LCS	G ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #16812040	C₂	direct (N × H)
6. C₂×C₁₀₇⋊C₈	C₄	semidirect
23. C₁₀₇⋊C₈	C₂×C₄	semidirect
33. C₂×C₁₀₇	#106	semidirect
37. C₁₀₇	C₂×#106	semidirect
71. C₂	#16812040	direct (N × H)

Subgroups — C2×#16812040 #20292657

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812040 #20292657