Subgroups — #495×C₁₆₇ #24922896

Order 10688.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×C₁₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×D₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic
4	#124×C₁₆₇	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₁₆₇	C₂²	1	2	yes	—
7	C₂×D₄×C₁₆₇	C₂²	1	2	yes	—
8	Q₁₆×C₁₆₇	—	2	2	no	—
9	SD₁₆×C₁₆₇	—	2	4	no	—
10	D₈×C₁₆₇	—	2	2	no	—
11	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₁₆₇	—	2	4	no	—
14	C₄²×C₁₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₁₆₇	—	2	2	no	—
16	Q₈×C₁₆₇	—	2	2	no	—
17	Q₈×C₁₆₇	—	2	2	no	—
18	D₄×C₁₆₇	—	2	2	no	—
19	D₄×C₁₆₇	—	2	2	no	—
20	C₂×C₄×C₁₆₇	—	2	2	no	—
21	C₂×C₄×C₁₆₇	D₄	1	2	yes	—
22	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
23	C₈×C₁₆₇	D₄	1	2	yes	—
24	C₈×C₁₆₇	D₄	1	2	yes	—
25	C₂²×C₁₆₇	—	4	2	no	—
26	C₂²×C₁₆₇	—	4	4	no	—
27	C₂²×C₁₆₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₆₇	—	2	2	no	—
29	C₄×C₁₆₇	—	4	2	no	—
30	C₄×C₁₆₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₆₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₁₆₇	—	8	2	no	—
33	C₂×C₁₆₇	#127	1	1	yes	characteristic
34	C₂×C₁₆₇	#135	1	2	yes	—
35	C₁₆₇	#495	1	1	yes	characteristic, direct product factor, Sylow
36	#495	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×Q₁₆	C₂×C₁₆₇	1	1	yes	characteristic, complemented
38	C₂×SD₁₆	C₂×C₁₆₇	1	2	yes	complemented
39	C₂×D₈	C₂×C₁₆₇	1	1	yes	characteristic
40	#124	C₂×C₁₆₇	1	2	yes	complemented
41	C₄×C₈	C₂×C₁₆₇	1	1	yes	characteristic, complemented
42	C₂×Q₈	C₂²×C₁₆₇	1	2	yes	—
43	C₂×D₄	C₂²×C₁₆₇	1	2	yes	—
44	Q₁₆	—	2	2	no	—
45	SD₁₆	—	2	4	no	—
46	D₈	—	2	2	no	—
47	C₂×C₈	C₂²×C₁₆₇	1	1	yes	characteristic
48	C₂×C₈	C₂²×C₁₆₇	1	1	yes	characteristic
49	C₂²⋊C₄	—	2	4	no	—
50	C₄²	C₂²×C₁₆₇	1	1	yes	characteristic
51	C₂³	—	2	2	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	D₄	—	2	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	D₄×C₁₆₇	1	2	yes	—
58	C₂×C₄	C₂³×C₁₆₇	1	1	yes	characteristic
59	C₈	D₄×C₁₆₇	1	2	yes	—
60	C₈	D₄×C₁₆₇	1	2	yes	—
61	C₂²	—	4	2	no	—
62	C₂²	—	4	4	no	—
63	C₂²	C₂×D₄×C₁₆₇	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	2	no	—
66	C₄	C₂×D₄×C₁₆₇	1	1	yes	characteristic
67	C₄	C₂×D₄×C₁₆₇	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	#127×C₁₆₇	1	1	yes	characteristic
70	C₂	#135×C₁₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₆₇
prime radical	C₂×D₈×C₁₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆₇ ◁ C₄²×C₁₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×C₁₆₇	C₂	semidirect
2. C₂×SD₁₆×C₁₆₇	C₂	semidirect
4. #124×C₁₆₇	C₂	semidirect
5. C₄×C₈×C₁₆₇	C₂	semidirect
35. C₁₆₇	#495	direct (N × H)
36. #495	C₁₆₇	direct (N × H)
37. C₂×Q₁₆	C₂×C₁₆₇	semidirect
38. C₂×SD₁₆	C₂×C₁₆₇	semidirect
40. #124	C₂×C₁₆₇	semidirect
41. C₄×C₈	C₂×C₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₁₆₇	2
C₂×SD₁₆×C₁₆₇	2
C₂×D₈×C₁₆₇	2
#124×C₁₆₇	2
C₄×C₈×C₁₆₇	2
#495	167

Subgroups — #495×C167 #24922896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #495×C₁₆₇ #24922896