Subgroups — #4875

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#888	C₂	1	1	yes	maximal, characteristic
2	#887	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	1	yes	maximal, characteristic
4	#816	C₂	1	1	yes	maximal, characteristic
5	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#810	C₂	1	1	yes	maximal, characteristic
7	#807	C₂	1	1	yes	maximal, characteristic
8	#477	—	3	1	no	maximal, Sylow
9	C₂×Dic₆	—	2	1	no	—
10	C₂×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	Dic₃⋊C₄	—	2	1	no	—
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	#107	—	3	1	no	—
23	#107	D₃	1	1	yes	characteristic
24	C₄⋊C₈	—	3	1	no	—
25	#103	—	3	1	no	—
26	#103	—	3	1	no	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
30	C₂×Dic₃	—	2	1	no	—
31	C₂×Dic₃	—	2	1	no	—
32	C₂×Dic₃	D₄	1	1	yes	characteristic
33	C₂×Dic₃	D₄	1	1	yes	characteristic
34	Dic₆	—	2	1	no	—
35	Dic₆	—	4	2	no	—
36	Dic₆	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×Q₈	—	6	1	no	—
41	C₂×C₈	—	3	1	no	—
42	C₂×C₈	C₂×D₃	1	1	yes	characteristic
43	C₄⋊C₄	—	3	1	no	—
44	C₄⋊C₄	—	6	1	no	—
45	C₄⋊C₄	—	6	1	no	—
46	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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	—	4	1	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	2	no	—
56	Dic₃	—	2	1	no	—
57	Dic₃	—	4	1	no	—
58	Dic₃	Q₁₆	1	2	yes	—
59	Q₈	—	3	2	no	—
60	Q₈	—	6	1	no	—
61	Q₈	—	12	2	no	—
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×Q₁₆	1	1	yes	characteristic
73	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
74	C₂²	D₃×D₄	1	1	yes	characteristic
75	C₄	—	3	2	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	6	2	no	—
79	C₄	—	6	1	no	—
80	C₄	—	12	1	no	—
81	C₄	#235	1	1	yes	characteristic
82	C₄	D₃×Q₈	1	1	yes	characteristic
83	C₃	#477	1	1	yes	characteristic, complemented, Sylow
84	C₂	#896	1	1	yes	characteristic
85	C₂	#911	1	1	yes	characteristic
86	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×#107	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#107	D₃
hypocenter	C₃	#477
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
36. Dic₆	Q₈	semidirect
83. C₃	#477	semidirect

Maximal subgroups

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

subgroup	index
#888	2
#887	2
C₃×#107	2
#816	2
Dic₃⋊C₈	2
#810	2
#807	2
#477	3