Subgroups — #4677

Order 192.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
2	C₂×C₄⋊Dic₃	C₂	1	3	yes	maximal, complemented
3	C₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	#399	—	3	1	no	maximal, Sylow
5	C₂³×D₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₂²	1	3	yes	—
7	C₂²×Dic₃	C₂²	1	3	yes	—
8	(C₂×D₃)⋊C₄	—	2	6	no	—
9	C₄⋊Dic₃	—	2	6	no	—
10	C₂×C₄⋊C₄	—	3	3	no	—
11	C₂×C₂²⋊C₄	—	3	3	no	—
12	#95	D₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₂²×D₃	—	2	3	no	—
15	C₂²×D₃	—	2	3	no	—
16	C₂²×D₃	Q₈	1	2	yes	—
17	C₂×C₃×C₄	—	2	6	no	—
18	C₂×C₃×C₄	D₄	1	6	yes	—
19	C₂×Dic₃	—	2	6	no	—
20	C₂×Dic₃	—	2	3	no	—
21	C₂⁴	—	3	1	no	—
22	C₂²×C₄	—	3	3	no	—
23	C₂²×C₄	C₂×D₃	1	3	yes	—
24	C₄⋊C₄	—	6	6	no	—
25	C₂²⋊C₄	—	6	6	no	—
26	C₂²×C₃	C₂×D₄	1	3	yes	—
27	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₃	#41	1	3	yes	—
29	C₂×D₃	—	2	6	no	—
30	C₂×D₃	—	4	3	no	—
31	C₂×D₃	—	4	1	no	—
32	C₃×C₄	—	2	6	no	—
33	Dic₃	—	4	3	no	—
34	C₂³	—	3	2	no	—
35	C₂³	—	6	3	no	—
36	C₂³	—	6	3	no	—
37	C₂³	C₂²×D₃	1	1	yes	characteristic
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	6	3	no	—
40	C₂×C₄	—	6	6	no	—
41	C₂×C₄	D₁₂	1	6	yes	—
42	C₂×C₃	C₂²⋊Q₈	1	3	yes	—
43	C₂×C₃	#123	1	3	yes	—
44	C₂×C₃	#127	1	1	yes	characteristic
45	D₃	—	4	2	no	—
46	C₂²	—	6	6	no	—
47	C₂²	—	12	1	no	—
48	C₂²	—	12	3	no	—
49	C₂²	C₂×D₁₂	1	3	yes	—
50	C₂²	#237	1	3	yes	—
51	C₂²	D₃×Q₈	1	1	yes	characteristic
52	C₄	—	2	6	no	—
53	C₄	—	12	3	no	—
54	C₃	#399	1	1	yes	characteristic, complemented, Sylow
55	C₂	—	12	2	no	—
56	C₂	#874	1	1	yes	characteristic
57	C₂	#886	1	3	yes	—
58	C₂	#897	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator, socle, cosocle	C₂³×C₃	C₂³
Fitting	C₃×#95	C₂
prime radical	C₂³×D₃	C₂²
hypercenter	#95	D₃
hypocenter	C₃	#399
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₃	C₂	semidirect
3. C₃×#95	C₂	semidirect
12. #95	D₃	semidirect
54. C₃	#399	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂×D₃)⋊C₄	2
C₂×C₄⋊Dic₃	2
C₃×#95	2
#399	3