Subgroups — #4761

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
2	#888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#102	C₂	1	1	yes	maximal, characteristic
4	#832	C₂	1	1	yes	maximal, characteristic
5	#817	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#808	C₂	1	1	yes	maximal, characteristic, complemented
8	#476	—	3	1	no	maximal, Sylow
9	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃	—	2	1	no	—
11	C₂×Dic₆	—	2	1	no	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	#217	—	2	1	no	—
15	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	Dic₃⋊C₄	—	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×D₄	—	3	1	no	—
22	#106	—	3	1	no	—
23	#106	—	3	1	no	—
24	C₄⋊C₈	—	3	1	no	—
25	#102	—	3	1	no	—
26	#102	D₃	1	1	yes	characteristic
27	C₂³×C₃	—	2	1	no	—
28	C₃×D₄	—	2	1	no	—
29	C₃×D₄	Q₈	1	2	yes	complemented
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	—	4	2	no	—
35	C₂×Dic₃	D₄	1	1	yes	characteristic
36	C₂×Dic₃	D₄	1	1	yes	characteristic
37	Dic₆	—	4	2	no	—
38	C₃×C₈	—	2	1	no	—
39	C₃⋊C₈	—	2	1	no	—
40	C₂×Q₈	—	6	1	no	—
41	C₂×D₄	C₂×D₃	1	1	yes	characteristic
42	C₂²×C₄	—	6	1	no	—
43	C₂×C₈	—	3	1	no	—
44	C₂×C₈	C₂×D₃	1	1	yes	characteristic
45	C₄⋊C₄	—	3	1	no	—
46	C₄⋊C₄	—	3	1	no	—
47	C₄⋊C₄	—	6	1	no	—
48	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
49	C₂²⋊C₄	—	6	1	no	—
50	C₄²	—	3	1	no	—
51	C₂²×C₃	—	2	2	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	—	4	1	no	—
54	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
57	C₃×C₄	#41	1	1	yes	characteristic
58	Dic₃	—	2	1	no	—
59	Dic₃	—	4	1	no	—
60	Dic₃	—	4	1	no	—
61	Dic₃	SD₁₆	1	2	yes	—
62	C₂³	—	2	1	no	—
63	Q₈	—	12	2	no	—
64	D₄	—	2	1	no	—
65	D₄	Dic₆	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	6	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	—	12	2	no	—
72	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	6	1	no	—
75	C₂×C₃	—	4	2	no	—
76	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
78	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
79	C₂²	—	2	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	D₃×D₄	1	1	yes	characteristic
83	C₄	—	3	2	no	—
84	C₄	—	4	1	no	—
85	C₄	—	6	1	no	—
86	C₄	—	12	1	no	—
87	C₄	—	12	1	no	—
88	C₄	C₂×Dic₆	1	1	yes	characteristic
89	C₄	#237	1	1	yes	characteristic
90	C₃	#476	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	4	2	no	—
92	C₂	#878	1	1	yes	characteristic
93	C₂	#911	1	1	yes	characteristic
94	C₂	D₃×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#102	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×C₃×D₄	C₂²
hypercenter	#102	D₃
hypocenter	C₃	#476
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #888	C₂	semidirect
5. #817	C₂	semidirect
6. Dic₃⋊C₈	C₂	semidirect
7. #808	C₂	semidirect
29. C₃×D₄	Q₈	semidirect
65. D₄	Dic₆	semidirect
90. C₃	#476	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₃	2
#888	2
C₃×#102	2
#832	2
#817	2
Dic₃⋊C₈	2
#808	2
#476	3