Subgroups — #4936

Order 192.

154 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	#382	—	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	—	2	4	no	—
10	C₂×C₄⋊C₄	—	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	2	yes	—
17	C₂×C₃×C₄	D₄	1	2	yes	—
18	C₂×C₃×C₄	Q₈	1	2	yes	—
19	C₂×Dic₃	—	2	4	no	—
20	C₂×Dic₃	—	2	8	no	—
21	C₂²×C₄	—	3	4	no	—
22	C₂²×C₄	C₂×D₃	1	2	yes	—
23	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
24	C₄⋊C₄	—	6	4	no	—
25	C₄²	Dic₃	1	4	yes	complemented
26	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
28	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₃	#41	1	4	yes	—
30	C₃×C₄	—	2	4	no	—
31	C₃×C₄	C₄⋊C₄	1	4	yes	—
32	Dic₃	—	4	4	no	—
33	C₂³	C₂²×D₃	1	1	yes	characteristic
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	—	6	4	no	—
36	C₂×C₄	—	6	8	no	—
37	C₂×C₄	Dic₆	1	2	yes	—
38	C₂×C₄	D₁₂	1	2	yes	—
39	C₂×C₄	C₂×Dic₃	1	4	yes	—
40	C₂×C₄	C₂×Dic₃	1	2	yes	—
41	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₃	#117	1	2	yes	—
43	C₂×C₃	#124	1	2	yes	—
44	C₂×C₃	#125	1	2	yes	—
45	C₂²	C₂×Dic₆	1	1	yes	characteristic
46	C₂²	C₂×D₁₂	1	1	yes	characteristic
47	C₂²	#235	1	4	yes	—
48	C₂²	C₂²×Dic₃	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	12	4	no	—
51	C₄	C₄⋊Dic₃	1	4	yes	—
52	C₃	#382	1	1	yes	characteristic, complemented, Sylow
53	C₂	#870	1	2	yes	—
54	C₂	#875	1	2	yes	—
55	C₂	C₂×C₄⋊Dic₃	1	1	yes	characteristic
56	C₂	#926	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	#382
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
8. C₃×C₄²	C₄	semidirect
25. C₄²	Dic₃	semidirect
52. C₃	#382	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
#382	3