Subgroups — #4791

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic
2	#888	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	1	yes	maximal, characteristic
4	#835	C₂	1	1	yes	maximal, characteristic
5	#817	C₂	1	1	yes	maximal, characteristic
6	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#808	C₂	1	1	yes	maximal, characteristic
8	#475	—	3	1	no	maximal, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×Dic₆	—	2	1	no	—
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₃	—	2	1	no	—
14	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	Dic₃⋊C₄	—	2	1	no	—
17	C₄×Dic₃	—	2	1	no	—
18	C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈	—	3	1	no	—
21	C₄×Q₈	—	3	1	no	—
22	#106	—	3	1	no	—
23	#106	—	3	1	no	—
24	C₄⋊C₈	—	3	1	no	—
25	#103	—	3	1	no	—
26	#103	D₃	1	1	yes	characteristic
27	C₃×Q₈	—	2	1	no	—
28	C₃×Q₈	Q₈	1	2	yes	complemented
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₂×Dic₃	—	2	1	no	—
33	C₂×Dic₃	—	2	1	no	—
34	C₂×Dic₃	D₄	1	1	yes	characteristic
35	C₂×Dic₃	D₄	1	1	yes	characteristic
36	Dic₆	—	4	2	no	—
37	C₃×C₈	—	2	1	no	—
38	C₃⋊C₈	—	2	1	no	—
39	C₂×Q₈	—	6	1	no	—
40	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
41	C₂×C₈	—	3	1	no	—
42	C₂×C₈	C₂×D₃	1	1	yes	characteristic
43	C₄⋊C₄	—	3	1	no	—
44	C₄⋊C₄	—	3	1	no	—
45	C₄⋊C₄	—	6	1	no	—
46	C₄⋊C₄	—	6	1	no	—
47	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
48	C₄²	—	3	1	no	—
49	C₄²	—	6	1	no	—
50	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
51	C₃×C₄	—	2	2	no	—
52	C₃×C₄	—	4	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	—	4	1	no	—
57	Dic₃	—	4	1	no	—
58	Dic₃	SD₁₆	1	2	yes	—
59	Q₈	—	2	1	no	—
60	Q₈	—	12	2	no	—
61	Q₈	Dic₆	1	2	yes	complemented
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	6	1	no	—
67	C₂×C₄	—	6	1	no	—
68	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	6	1	no	—
71	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
72	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
73	C₂×C₃	#137	1	1	yes	characteristic
74	C₂²	D₃×D₄	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	3	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	6	1	no	—
79	C₄	—	12	1	no	—
80	C₄	—	12	1	no	—
81	C₄	C₂×Dic₆	1	1	yes	characteristic
82	C₄	#237	1	1	yes	characteristic
83	C₃	#475	1	1	yes	characteristic, complemented, Sylow
84	C₂	#878	1	1	yes	characteristic
85	C₂	D₃×SD₁₆	1	1	yes	characteristic
86	C₂	#918	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	#475
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
28. C₃×Q₈	Q₈	semidirect
61. Q₈	Dic₆	semidirect
83. C₃	#475	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₃	2
#888	2
C₃×#103	2
#835	2
#817	2
Dic₃⋊C₈	2
#808	2
#475	3