Subgroups — C₂×#19128854 #24924051

Order 10688.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581950	C₂	1	2	yes	maximal, complemented
2	#19128854	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₆₆₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14581939	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₃₃₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#14581950	—	2	4	no	—
8	#14581950	C₂²	1	8	yes	complemented
9	C₂×Dic₃₃₄	C₂²	1	2	yes	—
10	C₂×D₆₆₈	C₂²	1	2	yes	—
11	C₂×C₂²⋊D₁₆₇	—	2	2	no	—
12	C₂×C₄×D₁₆₇	—	2	2	no	—
13	Dic₆₆₈	C₂²	1	4	yes	complemented
14	#14581939	C₂²	1	8	yes	complemented
15	D₁₃₃₆	C₂²	1	4	yes	complemented
16	C₂²×C₄×C₁₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₁₆₇	C₂²	1	4	yes	complemented
20	C₂²×D₁₆₇	—	2	2	no	—
21	Dic₃₃₄	—	2	2	no	—
22	Dic₃₃₄	C₂³	1	4	yes	—
23	D₆₆₈	—	2	2	no	—
24	D₆₆₈	C₂³	1	4	yes	—
25	C₂²⋊D₁₆₇	—	2	8	no	—
26	C₂×Dic₁₆₇	—	2	2	no	—
27	C₄×D₁₆₇	—	2	8	no	—
28	C₂³×C₁₆₇	D₄	1	1	yes	characteristic
29	C₂×C₄×C₁₆₇	D₄	1	2	yes	—
30	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₆₇	C₂³	1	1	yes	characteristic
32	C₂×C₄×C₁₆₇	C₂³	1	2	yes	—
33	C₈×C₁₆₇	C₂³	1	2	yes	—
34	C₈×C₁₆₇	C₂³	1	2	yes	—
35	C₂²×C₁₆₇	—	2	2	no	—
36	C₂²×C₁₆₇	C₂×D₄	1	2	yes	—
37	C₂²×C₁₆₇	C₂×D₄	1	1	yes	characteristic
38	C₂×D₁₆₇	—	2	4	no	—
39	C₂×D₁₆₇	—	4	4	no	—
40	C₄×C₁₆₇	C₂×D₄	1	2	yes	—
41	C₄×C₁₆₇	C₂×D₄	1	1	yes	characteristic
42	C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
43	Dic₁₆₇	—	2	4	no	—
44	C₂×C₁₆₇	—	2	2	no	—
45	C₂×C₁₆₇	#135	1	2	yes	complemented
46	C₂×C₁₆₇	C₂²×D₄	1	1	yes	characteristic
47	D₁₆₇	—	4	4	no	—
48	C₁₆₇	C₂×#135	1	1	yes	characteristic, complemented, Sylow
49	C₂×#135	—	167	1	no	maximal, Sylow
50	C₂×#41	—	167	2	no	—
51	#135	—	167	8	no	—
52	C₂×Q₁₆	—	167	1	no	—
53	C₂×SD₁₆	—	167	2	no	—
54	C₂×D₈	—	167	1	no	—
55	C₂²×C₈	D₁₆₇	1	1	yes	characteristic, complemented
56	#41	—	334	4	no	—
57	#41	—	167	8	no	—
58	C₂×Q₈	—	167	2	no	—
59	C₂×D₄	—	334	2	no	—
60	C₂×D₄	—	167	2	no	—
61	C₂²×C₄	—	334	2	no	—
62	C₂²×C₄	C₂×D₁₆₇	1	1	yes	characteristic
63	Q₁₆	—	167	4	no	—
64	SD₁₆	—	167	8	no	—
65	D₈	—	167	4	no	—
66	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
67	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
68	C₂×C₈	C₂×D₁₆₇	1	4	yes	complemented
69	C₂³	—	334	2	no	—
70	C₂³	D₆₆₈	1	1	yes	characteristic
71	Q₈	—	334	2	no	—
72	Q₈	—	167	4	no	—
73	D₄	—	334	8	no	—
74	D₄	—	334	2	no	—
75	D₄	—	167	4	no	—
76	C₂×C₄	—	334	2	no	—
77	C₂×C₄	—	334	8	no	—
78	C₂×C₄	D₆₆₈	1	2	yes	—
79	C₂×C₄	D₆₆₈	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₁₆₇	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₁₆₇	1	2	yes	—
82	C₈	C₂²×D₁₆₇	1	2	yes	—
83	C₈	C₂²×D₁₆₇	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	334	4	no	—
86	C₂²	—	668	4	no	—
87	C₂²	C₂×D₆₆₈	1	2	yes	—
88	C₂²	C₂×D₆₆₈	1	1	yes	characteristic
89	C₄	—	334	4	no	—
90	C₄	C₂×D₆₆₈	1	2	yes	—
91	C₄	C₂×D₆₆₈	1	1	yes	characteristic
92	C₄	C₂³×D₁₆₇	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	668	4	no	—
95	C₂	#19128854	1	2	yes	direct product factor
96	C₂	C₂²×D₆₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₆₆₈
commutator, cosocle	C₄×C₁₆₇	C₂⁴
Frattini	C₄	C₂³×D₁₆₇
Fitting	C₂²×C₈×C₁₆₇	C₂
socle	C₂²×C₁₆₇	C₂×D₄
hypercenter	C₂²×C₈	D₁₆₇
hypocenter	C₁₆₇	C₂×#135
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
1. C₂×#14581950	C₂	semidirect
2. #19128854	C₂	direct (N × H)
3. C₂×Dic₆₆₈	C₂	semidirect
4. C₂×#14581939	C₂	semidirect
5. C₂×D₁₃₃₆	C₂	semidirect
6. C₂²×C₈×C₁₆₇	C₂	semidirect
8. #14581950	C₂²	semidirect
13. Dic₆₆₈	C₂²	semidirect
14. #14581939	C₂²	semidirect
15. D₁₃₃₆	C₂²	semidirect
19. C₂×C₈×C₁₆₇	C₂²	semidirect
45. C₂×C₁₆₇	#135	semidirect
48. C₁₆₇	C₂×#135	semidirect
55. C₂²×C₈	D₁₆₇	semidirect
68. C₂×C₈	C₂×D₁₆₇	semidirect
95. C₂	#19128854	direct (N × H)

Subgroups — C2×#19128854 #24924051

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19128854 #24924051