Subgroups — C₂×#912 #5756

Order 192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#237	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#214	C₂	1	2	yes	maximal, complemented
4	#912	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#135	—	3	1	no	maximal, Sylow
8	C₂×C₃×D₄	C₂²	1	2	yes	—
9	C₂×#67	—	2	2	no	—
10	C₂²×Dic₃	—	2	2	no	—
11	#237	—	2	4	no	—
12	#237	C₂²	1	8	yes	complemented
13	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₆	C₂²	1	2	yes	—
15	C₃×D₈	C₂²	1	4	yes	complemented
16	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
17	#214	C₂²	1	8	yes	complemented
18	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	Dic₁₂	C₂²	1	4	yes	complemented
20	D₃×C₈	C₂²	1	4	yes	complemented
21	C₂×#41	—	3	2	no	—
22	#135	—	3	8	no	—
23	C₂×Q₁₆	—	3	1	no	—
24	C₂×SD₁₆	—	3	2	no	—
25	C₂×D₈	D₃	1	1	yes	characteristic, complemented
26	C₂²×C₈	—	3	1	no	—
27	C₂³×C₃	—	2	2	no	—
28	C₂²×D₃	D₄	1	1	yes	characteristic
29	C₃×D₄	—	2	2	no	—
30	C₃×D₄	C₂³	1	4	yes	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	#67	—	2	8	no	—
33	C₂×Dic₃	—	2	2	no	—
34	C₂×Dic₃	—	2	8	no	—
35	C₂×Dic₃	D₄	1	1	yes	characteristic
36	C₄×D₃	D₄	1	2	yes	—
37	C₄×D₃	C₂³	1	2	yes	—
38	Dic₆	—	2	2	no	—
39	Dic₆	C₂³	1	4	yes	—
40	C₃×C₈	C₂³	1	2	yes	—
41	C₃⋊C₈	C₂³	1	2	yes	—
42	#41	—	3	8	no	—
43	#41	—	6	4	no	—
44	C₂×Q₈	—	3	2	no	—
45	C₂×D₄	—	6	2	no	—
46	C₂×D₄	C₂×D₃	1	2	yes	—
47	C₂²×C₄	—	3	1	no	—
48	C₂²×C₄	—	6	2	no	—
49	Q₁₆	—	3	4	no	—
50	SD₁₆	—	3	8	no	—
51	D₈	C₂×D₃	1	4	yes	complemented
52	C₂×C₈	—	3	1	no	—
53	C₂×C₈	—	3	4	no	—
54	C₂×C₈	C₂×D₃	1	1	yes	characteristic
55	C₂²×C₃	—	2	4	no	—
56	C₂²×C₃	—	4	4	no	—
57	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
58	C₂×D₃	—	2	2	no	—
59	C₂×D₃	C₂×D₄	1	2	yes	—
60	C₃×C₄	C₂×D₄	1	1	yes	characteristic
61	C₃×C₄	C₂⁴	1	1	yes	characteristic
62	Dic₃	—	2	4	no	—
63	Dic₃	C₂×D₄	1	2	yes	—
64	C₂³	—	2	2	no	—
65	C₂³	—	3	1	no	—
66	Q₈	—	3	4	no	—
67	Q₈	—	6	2	no	—
68	D₄	—	2	2	no	—
69	D₄	—	6	8	no	—
70	D₄	C₂²×D₃	1	4	yes	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	3	2	no	—
74	C₂×C₄	—	6	8	no	—
75	C₂×C₄	—	6	2	no	—
76	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
77	C₈	—	3	2	no	—
78	C₈	C₂²×D₃	1	2	yes	—
79	C₂×C₃	—	4	4	no	—
80	C₂×C₃	#135	1	2	yes	complemented
81	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
82	D₃	—	2	2	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	3	2	no	—
85	C₂²	—	4	4	no	—
86	C₂²	—	6	2	no	—
87	C₂²	D₃×D₄	1	1	yes	characteristic
88	C₄	—	3	2	no	—
89	C₄	—	6	4	no	—
90	C₄	D₃×D₄	1	1	yes	characteristic
91	C₄	C₂³×D₃	1	1	yes	characteristic
92	C₃	C₂×#135	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	4	4	no	—
94	C₂	—	6	2	no	—
95	C₂	#912	1	2	yes	direct product factor
96	C₂	C₂×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴
Frattini	C₄	C₂³×D₃
Fitting	C₂×C₃×D₈	C₂
socle	C₂²×C₃	C₂×D₄
hypercenter	C₂×D₈	D₃
hypocenter	C₃	C₂×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#237	C₂	semidirect
2. C₂×C₃×D₈	C₂	semidirect
3. C₂×#214	C₂	semidirect
4. #912	C₂	direct (N × H)
5. C₂×Dic₁₂	C₂	semidirect
6. C₂×D₃×C₈	C₂	semidirect
12. #237	C₂²	semidirect
15. C₃×D₈	C₂²	semidirect
17. #214	C₂²	semidirect
19. Dic₁₂	C₂²	semidirect
20. D₃×C₈	C₂²	semidirect
25. C₂×D₈	D₃	semidirect
51. D₈	C₂×D₃	semidirect
80. C₂×C₃	#135	semidirect
92. C₃	C₂×#135	semidirect
95. C₂	#912	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×#237	2
C₂×C₃×D₈	2
C₂×#214	2
#912	2
C₂×Dic₁₂	2
C₂×D₃×C₈	2
C₂×#135	3

Subgroups — C2×#912 #5756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#912 #5756