Subgroups — #4701

Order 192.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#97	C₂	1	1	yes	maximal, characteristic
3	#815	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
7	C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	#446	—	3	1	no	maximal, Sylow
9	C₂×Dic₆	C₄	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄²	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₃	C₄	1	1	yes	characteristic
14	Dic₃⋊C₄	C₄	1	1	yes	characteristic
15	Dic₃⋊C₄	C₄	1	1	yes	characteristic
16	C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₄×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×Q₈	—	3	1	no	—
21	C₄⋊C₈	—	3	1	no	—
22	C₄⋊C₈	—	3	1	no	—
23	C₄⋊C₈	—	3	1	no	—
24	#97	—	3	1	no	—
25	#97	D₃	1	1	yes	characteristic
26	C₄×C₈	—	3	1	no	—
27	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
30	C₂×Dic₃	C₂×C₄	1	1	yes	characteristic
31	C₂×Dic₃	C₂×C₄	1	1	yes	characteristic
32	C₂×Dic₃	C₂×C₄	1	1	yes	characteristic
33	C₂×Dic₃	C₂×C₄	1	1	yes	characteristic
34	Dic₆	—	2	2	no	—
35	C₃×C₈	—	2	1	no	—
36	C₃×C₈	Q₈	1	2	yes	complemented
37	C₃⋊C₈	—	2	1	no	—
38	C₃⋊C₈	—	2	1	no	—
39	C₂×Q₈	—	3	1	no	—
40	C₂×C₈	—	3	1	no	—
41	C₂×C₈	—	3	1	no	—
42	C₂×C₈	C₂×D₃	1	1	yes	characteristic
43	C₂×C₈	C₂×D₃	1	1	yes	characteristic
44	C₄⋊C₄	—	3	1	no	—
45	C₄⋊C₄	—	3	1	no	—
46	C₄⋊C₄	—	3	1	no	—
47	C₄²	—	3	1	no	—
48	C₄²	—	3	1	no	—
49	C₄²	C₂×D₃	1	1	yes	characteristic
50	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
51	C₃×C₄	—	2	1	no	—
52	C₃×C₄	—	2	1	no	—
53	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
54	C₃×C₄	#41	1	1	yes	characteristic
55	Dic₃	—	2	1	no	—
56	Dic₃	—	2	1	no	—
57	Dic₃	—	2	1	no	—
58	Dic₃	M₁₆	1	2	yes	—
59	Q₈	—	6	2	no	—
60	C₂×C₄	—	3	1	no	—
61	C₂×C₄	—	3	1	no	—
62	C₂×C₄	—	3	1	no	—
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	C₄×D₃	1	1	yes	characteristic
65	C₂×C₄	C₄×D₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	6	1	no	—
69	C₈	—	6	1	no	—
70	C₈	Dic₆	1	2	yes	complemented
71	C₂×C₃	C₄×Q₈	1	1	yes	characteristic
72	C₂×C₃	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₃	#131	1	1	yes	characteristic
74	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	2	1	no	—
77	C₄	—	3	2	no	—
78	C₄	—	6	1	no	—
79	C₄	—	6	1	no	—
80	C₄	—	6	1	no	—
81	C₄	C₂×Dic₆	1	1	yes	characteristic
82	C₄	#235	1	1	yes	characteristic
83	C₃	#446	1	1	yes	characteristic, complemented, Sylow
84	C₂	C₄×Dic₆	1	1	yes	characteristic
85	C₂	D₃×M₁₆	1	1	yes	characteristic
86	C₂	#907	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃
commutator, socle, prime radical	C₂²×C₃	C₂²×C₄
Fitting	C₃×#97	C₂
cosocle	C₂×C₃×C₄	C₂³
hypercenter	#97	D₃
hypocenter	C₃	#446
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
36. C₃×C₈	Q₈	semidirect
70. C₈	Dic₆	semidirect
83. C₃	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₆	2
C₃×#97	2
#815	2
Dic₃⋊C₈	2
C₈×Dic₃	2
C₄⋊(C₃⋊C₈)	2
#446	3