Subgroups — #5230

Order 192.

182 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
2	C₂×Dic₃⋊C₄	C₂	1	3	yes	maximal
3	C₃⋊#95	C₂	1	3	yes	maximal
4	#395	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	—	2	6	no	—
6	C₂²×C₃×C₄	C₂²	1	3	yes	—
7	C₂²×Dic₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃	C₂²	1	3	yes	—
9	Dic₃⋊C₄	—	2	6	no	—
10	C₂²×Q₈	D₃	1	1	yes	characteristic
11	C₂×C₄⋊C₄	—	3	3	no	—
12	#95	—	3	3	no	—
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₃×Q₈	—	2	8	no	—
15	C₂×C₃×C₄	—	2	6	no	—
16	C₂×C₃×C₄	D₄	1	6	yes	—
17	C₂×Dic₃	—	2	3	no	—
18	C₂×Dic₃	—	2	3	no	—
19	C₂×Dic₃	—	2	3	no	—
20	C₂×Dic₃	Q₈	1	6	yes	complemented
21	C₂×Q₈	—	2	6	no	—
22	C₂²×C₄	—	3	3	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₂²×C₄	C₂×D₃	1	3	yes	—
25	C₄⋊C₄	—	6	6	no	—
26	C₂²×C₃	C₂×D₄	1	3	yes	—
27	C₂²×C₃	C₂×Q₈	1	3	yes	—
28	C₂²×C₃	#41	1	1	yes	characteristic
29	C₃×C₄	—	2	6	no	—
30	Dic₃	—	2	6	no	—
31	Dic₃	—	4	1	no	—
32	C₂³	C₂²×D₃	1	1	yes	characteristic
33	Q₈	—	2	8	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	3	6	no	—
36	C₂×C₄	—	6	3	no	—
37	C₂×C₄	—	6	3	no	—
38	C₂×C₄	—	6	3	no	—
39	C₂×C₄	#67	1	6	yes	—
40	C₂×C₃	#120	1	1	yes	characteristic
41	C₂×C₃	C₂²⋊Q₈	1	3	yes	—
42	C₂×C₃	C₄⋊Q₈	1	3	yes	—
43	C₂²	D₃×Q₈	1	3	yes	—
44	C₂²	#239	1	1	yes	characteristic
45	C₂²	C₂×#67	1	3	yes	—
46	C₄	—	2	6	no	—
47	C₄	—	6	6	no	—
48	C₄	—	12	1	no	—
49	C₃	#395	1	1	yes	characteristic, complemented, Sylow
50	C₂	#944	1	3	yes	—
51	C₂	#946	1	3	yes	—
52	C₂	#953	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator, socle, prime radical, cosocle	C₂³×C₃	C₂³
Fitting	C₂²×C₃×Q₈	C₂
hypercenter	C₂²×Q₈	D₃
hypocenter	C₃	#395
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

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

N	H ≅ G/N	type
20. C₂×Dic₃	Q₈	semidirect
49. C₃	#395	semidirect

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