Subgroups — #4932

Order 192.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃	C₂	1	2	yes	maximal
3	C₃⋊#95	C₂	1	4	yes	maximal
4	#376	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₄	C₂²	1	2	yes	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃	C₂²	1	4	yes	—
8	C₃×C₄²	C₄	1	4	yes	complemented
9	C₄×Dic₃	C₄	1	8	yes	complemented
10	C₂×C₄²	—	3	2	no	—
11	C₂×C₄²	D₃	1	1	yes	characteristic
12	#95	—	3	4	no	—
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₄	—	2	4	no	—
15	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
16	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
17	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
18	C₂×Dic₃	—	2	8	no	—
19	C₂×Dic₃	C₂×C₄	1	8	yes	—
20	C₂²×C₄	—	3	4	no	—
21	C₂²×C₄	C₂×D₃	1	2	yes	—
22	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
23	C₄²	—	3	8	no	—
24	C₄²	Dic₃	1	4	yes	complemented
25	C₂²×C₃	C₂²×C₄	1	2	yes	—
26	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₃	#41	1	4	yes	—
28	C₃×C₄	—	2	4	no	—
29	C₃×C₄	C₄²	1	4	yes	—
30	Dic₃	—	2	8	no	—
31	C₂³	C₂²×D₃	1	1	yes	characteristic
32	C₂×C₄	—	2	4	no	—
33	C₂×C₄	—	3	8	no	—
34	C₂×C₄	—	6	8	no	—
35	C₂×C₄	C₄×D₃	1	4	yes	—
36	C₂×C₄	C₂×Dic₃	1	4	yes	—
37	C₂×C₄	C₂×Dic₃	1	2	yes	—
38	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₃	#117	1	4	yes	—
40	C₂×C₃	#117	1	2	yes	—
41	C₂²	C₂×C₄×D₃	1	2	yes	—
42	C₂²	#235	1	4	yes	—
43	C₂²	C₂²×Dic₃	1	1	yes	characteristic
44	C₄	—	2	4	no	—
45	C₄	—	6	8	no	—
46	C₄	C₄×Dic₃	1	4	yes	—
47	C₃	#376	1	1	yes	characteristic, complemented, Sylow
48	C₂	#872	1	4	yes	—
49	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic
50	C₂	#926	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂³	C₂²×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	#376
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
8. C₃×C₄²	C₄	semidirect
9. C₄×Dic₃	C₄	semidirect
24. C₄²	Dic₃	semidirect
47. C₃	#376	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²	2
C₂×C₄×Dic₃	2
C₃⋊#95	2
#376	3