Subgroups — C₂×#904 #5741

Order 192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#235	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#904	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#204	C₂	1	2	yes	maximal, complemented
7	C₂×#135	—	3	1	no	maximal, Sylow
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×#67	—	2	2	no	—
10	#235	—	2	4	no	—
11	#235	C₂²	1	8	yes	complemented
12	C₂×D₁₂	C₂²	1	2	yes	—
13	C₂×C₄×D₃	—	2	2	no	—
14	C₂×Dic₆	C₂²	1	2	yes	—
15	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈	C₂²	1	4	yes	complemented
18	Dic₁₂	C₂²	1	4	yes	complemented
19	D₂₄	C₂²	1	4	yes	complemented
20	#204	C₂²	1	8	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	—	3	1	no	—
26	C₂²×C₈	D₃	1	1	yes	characteristic, complemented
27	C₂³×C₃	D₄	1	1	yes	characteristic
28	C₂²×D₃	—	2	2	no	—
29	C₂×C₃×C₄	D₄	1	2	yes	—
30	C₂×C₃×C₄	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₂×C₃×C₄	C₂³	1	2	yes	—
33	#67	—	2	8	no	—
34	C₂×Dic₃	—	2	2	no	—
35	D₁₂	—	2	2	no	—
36	D₁₂	C₂³	1	4	yes	—
37	C₄×D₃	—	2	8	no	—
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	—	3	2	no	—
46	C₂×D₄	—	6	2	no	—
47	C₂²×C₄	—	6	2	no	—
48	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
49	Q₁₆	—	3	4	no	—
50	SD₁₆	—	3	8	no	—
51	D₈	—	3	4	no	—
52	C₂×C₈	C₂×D₃	1	1	yes	characteristic
53	C₂×C₈	C₂×D₃	1	1	yes	characteristic
54	C₂×C₈	C₂×D₃	1	4	yes	complemented
55	C₂²×C₃	—	2	2	no	—
56	C₂²×C₃	C₂×D₄	1	2	yes	—
57	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
58	C₂×D₃	—	2	4	no	—
59	C₂×D₃	—	4	4	no	—
60	C₃×C₄	C₂×D₄	1	1	yes	characteristic
61	C₃×C₄	C₂×D₄	1	2	yes	—
62	C₃×C₄	C₂⁴	1	1	yes	characteristic
63	Dic₃	—	2	4	no	—
64	C₂³	—	6	2	no	—
65	C₂³	D₁₂	1	1	yes	characteristic
66	Q₈	—	3	4	no	—
67	Q₈	—	6	2	no	—
68	D₄	—	3	4	no	—
69	D₄	—	6	8	no	—
70	D₄	—	6	2	no	—
71	C₂×C₄	—	6	2	no	—
72	C₂×C₄	—	6	8	no	—
73	C₂×C₄	D₁₂	1	2	yes	—
74	C₂×C₄	D₁₂	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₃	1	2	yes	—
77	C₈	C₂²×D₃	1	2	yes	—
78	C₈	C₂²×D₃	1	2	yes	—
79	C₂×C₃	—	2	2	no	—
80	C₂×C₃	#135	1	2	yes	complemented
81	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
82	D₃	—	4	4	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	6	4	no	—
85	C₂²	—	12	4	no	—
86	C₂²	C₂×D₁₂	1	2	yes	—
87	C₂²	C₂×D₁₂	1	1	yes	characteristic
88	C₄	—	6	4	no	—
89	C₄	C₂×D₁₂	1	2	yes	—
90	C₄	C₂×D₁₂	1	1	yes	characteristic
91	C₄	C₂³×D₃	1	1	yes	characteristic
92	C₃	C₂×#135	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	2	2	no	—
94	C₂	—	12	4	no	—
95	C₂	#904	1	2	yes	direct product factor
96	C₂	C₂²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₂
commutator, cosocle	C₃×C₄	C₂⁴
Frattini	C₄	C₂³×D₃
Fitting	C₂²×C₃×C₈	C₂
socle	C₂²×C₃	C₂×D₄
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
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×#235	C₂	semidirect
2. C₂²×C₃×C₈	C₂	semidirect
3. C₂×Dic₁₂	C₂	semidirect
4. #904	C₂	direct (N × H)
5. C₂×D₂₄	C₂	semidirect
6. C₂×#204	C₂	semidirect
11. #235	C₂²	semidirect
17. C₂×C₃×C₈	C₂²	semidirect
18. Dic₁₂	C₂²	semidirect
19. D₂₄	C₂²	semidirect
20. #204	C₂²	semidirect
26. C₂²×C₈	D₃	semidirect
54. C₂×C₈	C₂×D₃	semidirect
80. C₂×C₃	#135	semidirect
92. C₃	C₂×#135	semidirect
95. C₂	#904	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×#235	2
C₂²×C₃×C₈	2
C₂×Dic₁₂	2
#904	2
C₂×D₂₄	2
C₂×#204	2
C₂×#135	3

Subgroups — C2×#904 #5741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#904 #5741