Subgroups — #5073

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#213	C₂	1	4	yes	maximal, complemented
3	#874	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#493	—	3	1	no	maximal, Sylow
6	C₂×C₃×D₄	—	2	2	no	—
7	C₂×C₃×D₄	C₂²	1	2	yes	—
8	C₂×D₁₂	—	2	2	no	—
9	C₂×D₁₂	C₂²	1	2	yes	—
10	C₃×C₄²	C₂²	1	1	yes	characteristic
11	#213	—	2	8	no	—
12	C₂×C₃⋊C₈	C₂²	1	2	yes	—
13	C₂×D₈	—	3	4	no	—
14	#127	—	3	1	no	—
15	#127	D₃	1	1	yes	characteristic, complemented
16	C₄×C₈	—	3	1	no	—
17	C₂³×C₃	—	2	2	no	—
18	C₂²×D₃	—	2	2	no	—
19	C₃×D₄	—	2	4	no	—
20	C₃×D₄	—	4	4	no	—
21	C₂×C₃×C₄	D₄	1	2	yes	—
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	D₁₂	—	2	4	no	—
24	D₁₂	—	4	4	no	—
25	C₃⋊C₈	D₄	1	4	yes	complemented
26	C₂×D₄	—	2	2	no	—
27	C₂×D₄	—	3	2	no	—
28	C₂×D₄	—	6	2	no	—
29	C₂×D₄	C₂×D₃	1	2	yes	—
30	D₈	—	6	8	no	—
31	C₂×C₈	—	3	2	no	—
32	C₄²	C₂×D₃	1	1	yes	characteristic
33	C₂²×C₃	—	4	2	no	—
34	C₂²×C₃	—	4	4	no	—
35	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
36	C₂×D₃	—	4	2	no	—
37	C₂×D₃	—	4	4	no	—
38	C₃×C₄	D₈	1	4	yes	complemented
39	C₃×C₄	C₂×D₄	1	2	yes	—
40	C₂³	—	2	2	no	—
41	C₂³	—	6	2	no	—
42	D₄	—	2	4	no	—
43	D₄	—	4	4	no	—
44	D₄	—	6	4	no	—
45	D₄	—	12	4	no	—
46	C₂×C₄	#67	1	2	yes	—
47	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
48	C₈	—	3	4	no	—
49	C₂×C₃	—	8	2	no	—
50	C₂×C₃	#127	1	1	yes	characteristic
51	C₂×C₃	C₂×D₈	1	2	yes	—
52	D₃	—	8	2	no	—
53	C₂²	—	4	4	no	—
54	C₂²	—	4	2	no	—
55	C₂²	—	12	4	no	—
56	C₂²	—	12	2	no	—
57	C₂²	C₂×#67	1	1	yes	characteristic
58	C₄	#213	1	4	yes	complemented
59	C₄	D₃×D₄	1	2	yes	—
60	C₃	#493	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	8	2	no	—
62	C₂	—	24	2	no	—
63	C₂	C₂×#213	1	2	yes	—
64	C₂	#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#127	C₂
socle	C₂²×C₃	C₂×D₄
hypercenter	#127	D₃
hypocenter	C₃	#493
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₃×#127	C₂	semidirect
2. C₂×#213	C₂	semidirect
3. #874	C₂	semidirect
4. C₄×C₃⋊C₈	C₂	semidirect
15. #127	D₃	semidirect
25. C₃⋊C₈	D₄	semidirect
38. C₃×C₄	D₈	semidirect
58. C₄	#213	semidirect
60. C₃	#493	semidirect

Maximal subgroups

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

subgroup	index
C₃×#127	2
C₂×#213	2
#874	2
C₄×C₃⋊C₈	2
#493	3