Subgroups — C₂×#940 #5803

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#67	C₂	1	4	yes	maximal, complemented
3	C₂²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#940	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#127	—	3	1	no	maximal, Sylow
7	C₂⁴×C₃	C₂²	1	2	yes	—
8	C₂³×D₃	C₂²	1	2	yes	—
9	C₂×C₃×D₄	—	2	4	no	—
10	C₂×C₃×D₄	C₂²	1	4	yes	complemented
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂×#67	—	2	16	no	—
13	C₂×#67	C₂²	1	16	yes	complemented
14	C₂²×Dic₃	C₂²	1	2	yes	—
15	C₂×D₁₂	—	2	4	no	—
16	C₂×D₁₂	C₂²	1	4	yes	complemented
17	C₄×Dic₃	C₂²	1	4	yes	complemented
18	C₂²×D₄	—	3	4	no	—
19	C₂²×D₄	—	3	1	no	—
20	C₂²×D₄	D₃	1	1	yes	characteristic, complemented
21	#127	—	3	8	no	—
22	C₂×C₄²	—	3	1	no	—
23	C₂³×C₃	—	2	8	no	—
24	C₂³×C₃	—	2	4	no	—
25	C₂³×C₃	C₂³	1	4	yes	—
26	C₂³×C₃	C₂³	1	1	yes	characteristic
27	C₂²×D₃	—	2	4	no	—
28	C₂²×D₃	—	2	8	no	—
29	C₂²×D₃	C₂³	1	4	yes	—
30	C₃×D₄	—	2	8	no	—
31	C₂×C₃×C₄	D₄	1	4	yes	complemented
32	C₂×C₃×C₄	C₂³	1	2	yes	—
33	#67	—	2	32	no	—
34	C₂×Dic₃	D₄	1	8	yes	complemented
35	C₂×Dic₃	C₂³	1	4	yes	—
36	D₁₂	—	2	8	no	—
37	C₂⁴	—	3	2	no	—
38	C₂⁴	C₂×D₃	1	2	yes	—
39	C₂×D₄	—	2	4	no	—
40	C₂×D₄	—	3	16	no	—
41	C₂×D₄	—	3	4	no	—
42	C₂×D₄	—	6	16	no	—
43	C₂×D₄	—	6	4	no	—
44	C₂×D₄	C₂×D₃	1	4	yes	complemented
45	C₂²×C₄	—	3	2	no	—
46	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
47	C₄²	—	3	4	no	—
48	C₂²×C₃	—	2	8	no	—
49	C₂²×C₃	—	2	4	no	—
50	C₂²×C₃	—	4	8	no	—
51	C₂²×C₃	C₂×D₄	1	4	yes	—
52	C₂²×C₃	C₂×D₄	1	2	yes	—
53	C₂²×C₃	C₂⁴	1	1	yes	characteristic
54	C₂×D₃	—	2	4	no	—
55	C₂×D₃	—	2	8	no	—
56	C₂×D₃	—	4	8	no	—
57	C₃×C₄	C₂×D₄	1	4	yes	complemented
58	Dic₃	C₂×D₄	1	8	yes	complemented
59	C₂³	—	2	8	no	—
60	C₂³	—	2	4	no	—
61	C₂³	—	3	4	no	—
62	C₂³	—	6	8	no	—
63	C₂³	—	6	4	no	—
64	C₂³	C₂²×D₃	1	4	yes	—
65	C₂³	C₂²×D₃	1	1	yes	characteristic
66	D₄	—	2	8	no	—
67	D₄	—	6	32	no	—
68	D₄	—	6	8	no	—
69	C₂×C₄	—	3	8	no	—
70	C₂×C₄	—	3	4	no	—
71	C₂×C₄	#67	1	4	yes	complemented
72	C₂×C₄	C₂²×D₃	1	2	yes	—
73	C₂×C₃	—	4	4	no	—
74	C₂×C₃	#127	1	4	yes	complemented
75	C₂×C₃	C₂²×D₄	1	2	yes	—
76	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
77	D₃	—	4	4	no	—
78	C₂²	—	2	8	no	—
79	C₂²	—	2	4	no	—
80	C₂²	—	4	8	no	—
81	C₂²	—	6	8	no	—
82	C₂²	—	6	4	no	—
83	C₂²	—	12	8	no	—
84	C₂²	D₃×D₄	1	4	yes	—
85	C₂²	C₂×#67	1	2	yes	—
86	C₂²	C₂³×D₃	1	1	yes	characteristic
87	C₄	—	3	8	no	—
88	C₄	C₂×#67	1	4	yes	complemented
89	C₃	C₂×#127	1	1	yes	characteristic, complemented, Sylow
90	C₂	—	4	4	no	—
91	C₂	—	12	4	no	—
92	C₂	#940	1	4	yes	direct product factor
93	C₂	C₂×D₃×D₄	1	2	yes	—
94	C₂	C₂²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂²×C₃×D₄	C₂
socle	C₂³×C₃	C₂³
hypercenter	C₂²×D₄	D₃
hypocenter	C₃	C₂×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄	C₂	semidirect
2. C₂²×#67	C₂	semidirect
3. C₂²×D₁₂	C₂	semidirect
4. #940	C₂	direct (N × H)
5. C₂×C₄×Dic₃	C₂	semidirect
10. C₂×C₃×D₄	C₂²	semidirect
13. C₂×#67	C₂²	semidirect
16. C₂×D₁₂	C₂²	semidirect
17. C₄×Dic₃	C₂²	semidirect
20. C₂²×D₄	D₃	semidirect
31. C₂×C₃×C₄	D₄	semidirect
34. C₂×Dic₃	D₄	semidirect
44. C₂×D₄	C₂×D₃	semidirect
57. C₃×C₄	C₂×D₄	semidirect
58. Dic₃	C₂×D₄	semidirect
71. C₂×C₄	#67	semidirect
74. C₂×C₃	#127	semidirect
88. C₄	C₂×#67	semidirect
89. C₃	C₂×#127	semidirect
92. C₂	#940	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄	2
C₂²×#67	2
C₂²×D₁₂	2
#940	2
C₂×C₄×Dic₃	2
C₂×#127	3

Subgroups — C2×#940 #5803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#940 #5803