Subgroups — C₂×#19128768 #24923315

Order 10688.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581934	C₂	1	2	yes	maximal
2	#19128768	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic
4	#14581934	—	2	2	no	—
5	#14581934	C₂²	1	4	yes	—
6	C₂×C₁₆₇⋊C₈	—	2	2	no	—
7	C₂²×C₄×C₁₆₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₆₇	C₄	1	2	yes	—
9	C₂×C₈×C₁₆₇	C₄	1	2	yes	—
10	C₂×C₈×C₁₆₇	C₂²	1	2	yes	—
11	C₁₆₇⋊C₈	—	2	4	no	—
12	C₂³×C₁₆₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₆₇	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
19	C₈×C₁₆₇	C₂×C₄	1	4	yes	—
20	C₂²×C₁₆₇	—	2	2	no	—
21	C₂²×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₁₆₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
26	C₄×C₁₆₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₆₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₁₆₇	—	2	1	no	—
29	C₂×C₁₆₇	—	2	1	no	—
30	C₂×C₁₆₇	#108	1	2	yes	complemented
31	C₂×C₁₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₁₆₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
33	C₂×#108	—	167	1	no	maximal, Sylow
34	C₂×M₁₆	—	167	2	no	—
35	C₂²×C₈	D₁₆₇	1	1	yes	characteristic
36	#108	—	167	4	no	—
37	C₂²×C₄	C₂×D₁₆₇	1	1	yes	characteristic
38	M₁₆	—	334	2	no	—
39	M₁₆	—	167	4	no	—
40	C₂×C₈	—	334	2	no	—
41	C₂×C₈	Dic₁₆₇	1	2	yes	—
42	C₂×C₈	Dic₁₆₇	1	2	yes	—
43	C₂×C₈	C₂×D₁₆₇	1	2	yes	—
44	C₂³	Dic₃₃₄	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₁₆₇	1	1	yes	characteristic
46	C₂×C₄	C₂×Dic₁₆₇	1	1	yes	characteristic
47	C₂×C₄	D₆₆₈	1	1	yes	characteristic
48	C₂×C₄	D₆₆₈	1	1	yes	characteristic
49	C₂×C₄	Dic₃₃₄	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
51	C₈	—	334	4	no	—
52	C₈	C₂×Dic₁₆₇	1	4	yes	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₁₆₇	1	1	yes	characteristic
55	C₂²	C₄⋊Dic₁₆₇	1	1	yes	characteristic
56	C₂²	C₂×Dic₃₃₄	1	1	yes	characteristic
57	C₄	C₄⋊Dic₁₆₇	1	1	yes	characteristic
58	C₄	C₄⋊Dic₁₆₇	1	1	yes	characteristic
59	C₄	C₂²×Dic₁₆₇	1	1	yes	characteristic
60	C₄	C₂×D₆₆₈	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	#19128768	1	2	yes	direct product factor
64	C₂	C₂×C₄⋊Dic₁₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₆₆₈
commutator	C₄×C₁₆₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₆₇
Fitting	C₂²×C₈×C₁₆₇	C₂
socle	C₂²×C₁₆₇	C₄⋊C₄
prime radical	C₂³×C₁₆₇	Q₈
cosocle	C₂×C₄×C₁₆₇	C₂³
hypercenter	C₂²×C₈	D₁₆₇
hypocenter	C₁₆₇	C₂×#108
LCS	G ▷ C₄×C₁₆₇ ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #19128768	C₂	direct (N × H)
30. C₂×C₁₆₇	#108	semidirect
32. C₁₆₇	C₂×#108	semidirect
63. C₂	#19128768	direct (N × H)

Subgroups — C2×#19128768 #24923315

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19128768 #24923315