Subgroups — #4795

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#944	C₂	1	1	yes	maximal, characteristic
2	C₂×#216	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic
4	#887	C₂	1	1	yes	maximal, characteristic
5	C₃×#103	C₂	1	1	yes	maximal, characteristic
6	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#810	C₂	1	1	yes	maximal, characteristic
8	#462	—	3	1	no	maximal, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×Dic₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	#216	—	2	2	no	—
15	Dic₃⋊C₄	—	2	1	no	—
16	Dic₃⋊C₄	—	2	1	no	—
17	Dic₃⋊C₄	—	2	1	no	—
18	C₄×Dic₃	—	2	1	no	—
19	C₄×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	Dic₁₂	—	2	2	no	—
22	C₂×Q₁₆	—	3	1	no	—
23	C₂×Q₁₆	—	3	1	no	—
24	C₄⋊Q₈	—	3	1	no	—
25	C₄×Q₈	—	3	1	no	—
26	C₄⋊C₈	—	3	1	no	—
27	#103	—	3	1	no	—
28	#103	D₃	1	1	yes	characteristic
29	C₃×Q₈	—	2	1	no	—
30	C₃×Q₈	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₂×Dic₃	—	2	1	no	—
35	C₂×Dic₃	—	2	1	no	—
36	C₂×Dic₃	D₄	1	1	yes	characteristic
37	C₂×Dic₃	D₄	1	1	yes	characteristic
38	Dic₆	—	2	1	no	—
39	Dic₆	—	2	1	no	—
40	Dic₆	—	2	1	no	—
41	Dic₆	D₄	1	2	yes	—
42	C₃×C₈	—	2	1	no	—
43	C₃⋊C₈	—	2	1	no	—
44	C₂×Q₈	—	3	1	no	—
45	C₂×Q₈	—	3	1	no	—
46	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
47	Q₁₆	—	6	2	no	—
48	Q₁₆	—	6	2	no	—
49	C₂×C₈	—	3	1	no	—
50	C₂×C₈	C₂×D₃	1	1	yes	characteristic
51	C₄⋊C₄	—	6	1	no	—
52	C₄⋊C₄	—	6	1	no	—
53	C₄⋊C₄	—	6	1	no	—
54	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
55	C₄²	—	3	1	no	—
56	C₄²	—	6	1	no	—
57	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
58	C₃×C₄	—	4	1	no	—
59	C₃×C₄	—	4	1	no	—
60	C₃×C₄	C₂×D₄	1	1	yes	characteristic
61	C₃×C₄	#41	1	1	yes	characteristic
62	Dic₃	—	2	2	no	—
63	Dic₃	—	2	1	no	—
64	Dic₃	—	4	1	no	—
65	Dic₃	Q₁₆	1	2	yes	complemented
66	Q₈	—	2	1	no	—
67	Q₈	—	2	1	no	—
68	Q₈	—	3	2	no	—
69	Q₈	—	6	1	no	—
70	Q₈	—	6	1	no	—
71	Q₈	—	6	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	3	1	no	—
75	C₂×C₄	—	3	1	no	—
76	C₂×C₄	—	6	1	no	—
77	C₂×C₄	—	6	1	no	—
78	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	—	6	1	no	—
81	C₂×C₃	#121	1	1	yes	characteristic
82	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×C₃	#137	1	1	yes	characteristic
84	C₂²	D₃×D₄	1	1	yes	characteristic
85	C₄	—	3	2	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	6	2	no	—
89	C₄	—	6	1	no	—
90	C₄	—	12	1	no	—
91	C₄	#235	1	1	yes	characteristic
92	C₄	D₃×D₄	1	1	yes	characteristic
93	C₃	#462	1	1	yes	characteristic, complemented, Sylow
94	C₂	#884	1	1	yes	characteristic
95	C₂	#915	1	1	yes	characteristic
96	C₂	D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#103	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#103	D₃
hypocenter	C₃	#462
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
65. Dic₃	Q₁₆	semidirect
93. C₃	#462	semidirect

Maximal subgroups

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

subgroup	index
#944	2
C₂×#216	2
C₂×Dic₁₂	2
#887	2
C₃×#103	2
Dic₃⋊C₈	2
#810	2
#462	3