Subgroups — C₂×#947 #5814

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₂	C₂	1	1	yes	maximal, characteristic
3	#947	C₂	1	8	yes	maximal, direct product factor
4	C₂×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#124	—	3	1	no	maximal, Sylow
7	C₂³×D₃	C₂²	1	2	yes	—
8	C₂×C₃×Q₈	—	2	4	no	—
9	C₂×C₃×Q₈	C₂²	1	4	yes	complemented
10	C₂²×C₃×C₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃	C₂²	1	2	yes	—
13	C₂×D₁₂	—	2	4	no	—
14	C₂×D₁₂	C₂²	1	4	yes	—
15	(C₂×D₃)⋊C₄	C₂²	1	16	yes	complemented
16	C₄×Dic₃	C₂²	1	4	yes	complemented
17	C₂²×Q₈	D₃	1	1	yes	characteristic, complemented
18	C₂²×D₄	—	3	1	no	—
19	#124	—	3	8	no	—
20	C₂×C₂²⋊C₄	—	3	4	no	—
21	C₂×C₄²	—	3	1	no	—
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₂²×D₃	—	2	4	no	—
24	C₂²×D₃	—	2	8	no	—
25	C₂²×D₃	C₂³	1	4	yes	—
26	C₃×Q₈	—	2	8	no	—
27	C₂×C₃×C₄	—	2	4	no	—
28	C₂×C₃×C₄	D₄	1	4	yes	—
29	C₂×C₃×C₄	C₂³	1	4	yes	—
30	C₂×C₃×C₄	C₂³	1	2	yes	—
31	C₂×Dic₃	—	2	4	no	—
32	C₂×Dic₃	C₂³	1	4	yes	—
33	D₁₂	—	2	8	no	—
34	C₂⁴	—	3	2	no	—
35	C₂×Q₈	—	2	4	no	—
36	C₂×Q₈	C₂×D₃	1	4	yes	complemented
37	C₂×D₄	—	3	4	no	—
38	C₂×D₄	—	6	4	no	—
39	C₂²×C₄	—	3	2	no	—
40	C₂²×C₄	C₂×D₃	1	2	yes	—
41	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂²⋊C₄	—	3	16	no	—
43	C₄²	—	3	4	no	—
44	C₂²×C₃	C₂×D₄	1	2	yes	—
45	C₂²×C₃	#41	1	4	yes	—
46	C₂²×C₃	C₂⁴	1	1	yes	characteristic
47	C₂×D₃	—	2	4	no	—
48	C₂×D₃	—	2	8	no	—
49	C₂×D₃	—	4	8	no	—
50	C₃×C₄	—	2	4	no	—
51	C₃×C₄	C₂×D₄	1	4	yes	—
52	Dic₃	—	2	4	no	—
53	C₂³	—	3	4	no	—
54	C₂³	—	6	8	no	—
55	C₂³	—	6	4	no	—
56	C₂³	C₂²×D₃	1	1	yes	characteristic
57	Q₈	—	2	8	no	—
58	D₄	—	6	8	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	3	4	no	—
61	C₂×C₄	—	6	4	no	—
62	C₂×C₄	#67	1	4	yes	—
63	C₂×C₄	C₂²×D₃	1	4	yes	—
64	C₂×C₄	C₂²×D₃	1	2	yes	—
65	C₂×C₃	#124	1	4	yes	complemented
66	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
67	C₂×C₃	C₂×#41	1	2	yes	—
68	D₃	—	4	4	no	—
69	C₂²	—	6	8	no	—
70	C₂²	—	6	4	no	—
71	C₂²	—	12	8	no	—
72	C₂²	#239	1	4	yes	—
73	C₂²	C₂×#67	1	2	yes	—
74	C₂²	C₂³×D₃	1	1	yes	characteristic
75	C₄	—	2	4	no	—
76	C₄	—	6	4	no	—
77	C₄	C₂×#67	1	4	yes	—
78	C₃	C₂×#124	1	1	yes	characteristic, complemented, Sylow
79	C₂	—	12	4	no	—
80	C₂	#947	1	4	yes	direct product factor
81	C₂	C₂×#239	1	2	yes	—
82	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×Q₈	C₂
socle	C₂³×C₃	C₂³
prime radical	C₂²×D₁₂	C₂
hypercenter	C₂²×Q₈	D₃
hypocenter	C₃	C₂×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈	C₂	semidirect
3. #947	C₂	direct (N × H)
4. C₂×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₄×Dic₃	C₂	semidirect
9. C₂×C₃×Q₈	C₂²	semidirect
15. (C₂×D₃)⋊C₄	C₂²	semidirect
16. C₄×Dic₃	C₂²	semidirect
17. C₂²×Q₈	D₃	semidirect
36. C₂×Q₈	C₂×D₃	semidirect
65. C₂×C₃	#124	semidirect
78. C₃	C₂×#124	semidirect
80. C₂	#947	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×Q₈	2
C₂²×D₁₂	2
#947	2
C₂×(C₂×D₃)⋊C₄	2
C₂×C₄×Dic₃	2
C₂×#124	3

Subgroups — C2×#947 #5814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#947 #5814