Subgroups — #4765

Order 192.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#936	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	#816	C₂	1	1	yes	maximal, characteristic, complemented
6	#815	C₂	1	1	yes	maximal, characteristic, complemented
7	#810	C₂	1	1	yes	maximal, characteristic, complemented
8	#489	—	3	1	no	maximal, Sylow
9	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₆	—	2	1	no	—
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	#217	—	2	1	no	—
15	#217	—	2	1	no	—
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	#124	—	3	1	no	—
22	#103	—	3	1	no	—
23	#103	—	3	1	no	—
24	#102	—	3	1	no	—
25	#102	D₃	1	1	yes	characteristic
26	#97	—	3	1	no	—
27	C₂³×C₃	—	2	1	no	—
28	C₃×D₄	—	2	1	no	—
29	C₃×D₄	—	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	—	2	1	no	—
37	Dic₆	—	2	1	no	—
38	Dic₆	—	4	2	no	—
39	C₃×C₈	—	2	1	no	—
40	C₃⋊C₈	—	2	1	no	—
41	C₂×Q₈	—	3	1	no	—
42	C₂×Q₈	—	6	1	no	—
43	C₂×D₄	C₂×D₃	1	1	yes	characteristic
44	C₂×C₈	—	3	1	no	—
45	C₂×C₈	C₂×D₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	6	1	no	—
51	C₄²	—	3	1	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	—	4	1	no	—
54	C₂²×C₃	—	4	1	no	—
55	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	#41	1	1	yes	characteristic
58	C₃×C₄	#41	1	1	yes	characteristic
59	Dic₃	—	2	1	no	—
60	Dic₃	—	2	1	no	—
61	Dic₃	—	4	1	no	—
62	Dic₃	—	4	1	no	—
63	C₂³	—	2	1	no	—
64	Q₈	—	6	1	no	—
65	Q₈	—	6	1	no	—
66	Q₈	—	12	2	no	—
67	D₄	—	2	1	no	—
68	D₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	6	1	no	—
73	C₂×C₄	—	6	1	no	—
74	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	6	1	no	—
77	C₂×C₃	—	8	1	no	—
78	C₂×C₃	#124	1	1	yes	characteristic
79	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
80	C₂×C₃	#137	1	1	yes	characteristic
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	D₃×D₄	1	1	yes	characteristic
85	C₄	—	4	1	no	—
86	C₄	—	6	1	no	—
87	C₄	—	6	1	no	—
88	C₄	—	12	1	no	—
89	C₄	—	12	1	no	—
90	C₄	#235	1	1	yes	characteristic
91	C₄	#237	1	1	yes	characteristic
92	C₃	#489	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	8	1	no	—
94	C₂	#885	1	1	yes	characteristic
95	C₂	#911	1	1	yes	characteristic
96	C₂	#915	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	#489
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. #816	C₂	semidirect
6. #815	C₂	semidirect
7. #810	C₂	semidirect
92. C₃	#489	semidirect

Maximal subgroups

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

subgroup	index
#936	2
#888	2
C₃×#102	2
#832	2
#816	2
#815	2
#810	2
#489	3