Subgroups — #4650

Order 192.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃⋊C₄	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×#95	C₂	1	1	yes	maximal, characteristic
4	C₃⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₃⋊#95	C₂	1	2	yes	maximal
6	#382	—	3	1	no	maximal, Sylow
7	C₂²×C₃×C₄	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃	C₂²	1	2	yes	—
10	C₂²×Dic₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	1	yes	characteristic
12	Dic₃⋊C₄	—	2	4	no	—
13	C₄×Dic₃	C₄	1	4	yes	complemented
14	C₂×C₄⋊C₄	—	3	2	no	—
15	C₂×C₄²	—	3	1	no	—
16	#95	—	3	2	no	—
17	#95	—	3	1	no	—
18	#95	D₃	1	1	yes	characteristic
19	C₂³×C₃	C₂³	1	1	yes	characteristic
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
25	C₂×Dic₃	—	2	2	no	—
26	C₂×Dic₃	—	2	2	no	—
27	C₂×Dic₃	—	2	2	no	—
28	C₂×Dic₃	—	2	2	no	—
29	C₂×Dic₃	C₂×C₄	1	2	yes	—
30	C₂×Dic₃	C₂×C₄	1	2	yes	—
31	C₂×Dic₃	D₄	1	2	yes	—
32	C₂×Dic₃	Q₈	1	2	yes	—
33	C₂²×C₄	—	3	1	no	—
34	C₂²×C₄	—	3	1	no	—
35	C₂²×C₄	—	3	2	no	—
36	C₂²×C₄	C₂×D₃	1	2	yes	—
37	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
38	C₄⋊C₄	—	6	4	no	—
39	C₄²	—	3	4	no	—
40	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₃	#41	1	2	yes	—
44	C₂²×C₃	#41	1	2	yes	—
45	C₃×C₄	—	2	2	no	—
46	C₃×C₄	—	4	2	no	—
47	Dic₃	—	2	2	no	—
48	Dic₃	—	4	2	no	—
49	Dic₃	C₄⋊C₄	1	4	yes	—
50	C₂³	C₂²×D₃	1	1	yes	characteristic
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	3	2	no	—
56	C₂×C₄	—	3	2	no	—
57	C₂×C₄	—	3	2	no	—
58	C₂×C₄	—	3	2	no	—
59	C₂×C₄	—	6	2	no	—
60	C₂×C₄	—	6	2	no	—
61	C₂×C₄	—	6	2	no	—
62	C₂×C₄	—	6	2	no	—
63	C₂×C₄	C₄×D₃	1	2	yes	—
64	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₃	#117	1	1	yes	characteristic
66	C₂×C₃	#117	1	1	yes	characteristic
67	C₂×C₃	#124	1	2	yes	—
68	C₂×C₃	#125	1	2	yes	—
69	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
70	C₂²	#235	1	2	yes	—
71	C₂²	D₃×D₄	1	1	yes	characteristic
72	C₂²	#237	1	2	yes	—
73	C₂²	D₃×Q₈	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	3	4	no	—
76	C₄	—	4	2	no	—
77	C₄	—	6	2	no	—
78	C₄	—	12	2	no	—
79	C₃	#382	1	1	yes	characteristic, complemented, Sylow
80	C₂	#872	1	1	yes	characteristic
81	C₂	#877	1	1	yes	characteristic
82	C₂	#885	1	2	yes	—
83	C₂	#889	1	2	yes	—
84	C₂	D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄
Fitting	C₃×#95	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	#95	D₃
hypocenter	C₃	#382
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
13. C₄×Dic₃	C₄	semidirect
79. 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×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
C₃×#95	2
C₃⋊#95	2
#382	3