Subgroups — #4996

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#117	C₂	1	1	yes	maximal, characteristic
2	#924	C₂	1	1	yes	maximal, characteristic
3	#830	C₂	1	1	yes	maximal, characteristic
4	#810	C₂	1	1	yes	maximal, characteristic, complemented
5	#810	C₂	1	1	yes	maximal, characteristic, complemented
6	#808	C₂	1	1	yes	maximal, characteristic, complemented
7	#807	C₂	1	1	yes	maximal, characteristic, complemented
8	#485	—	3	1	no	maximal, Sylow
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₆	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₃×C₂²⋊C₄	—	2	1	no	—
14	C₃×C₄²	—	2	1	no	—
15	#217	—	2	1	no	—
16	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	Dic₃⋊C₄	—	2	1	no	—
18	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²⋊Q₈	—	3	1	no	—
21	#117	D₃	1	1	yes	characteristic
22	#107	—	3	1	no	—
23	#106	—	3	1	no	—
24	#103	—	3	1	no	—
25	#103	—	3	1	no	—
26	C₂²⋊C₈	—	3	1	no	—
27	C₂³×C₃	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	D₄	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₂×Dic₃	—	2	1	no	—
35	C₂×Dic₃	—	2	1	no	—
36	Dic₆	—	2	1	no	—
37	Dic₆	—	2	1	no	—
38	C₃⋊C₈	—	2	1	no	—
39	C₃⋊C₈	—	2	1	no	—
40	C₂×Q₈	—	3	1	no	—
41	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₈	—	3	1	no	—
43	C₂×C₈	—	3	1	no	—
44	C₄⋊C₄	—	3	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	C₂²⋊C₄	—	2	1	no	—
49	C₂²⋊C₄	—	6	1	no	—
50	C₄²	—	2	1	no	—
51	C₂²×C₃	—	2	1	no	—
52	C₂²×C₃	—	2	1	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
55	C₃×C₄	—	2	1	no	—
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	#41	1	1	yes	characteristic
59	C₃×C₄	#41	1	1	yes	characteristic
60	Dic₃	—	4	1	no	—
61	Dic₃	—	4	1	no	—
62	C₂³	#67	1	1	yes	characteristic
63	Q₈	—	6	1	no	—
64	Q₈	—	6	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	6	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	#67	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₈	—	6	1	no	—
74	C₈	—	6	1	no	—
75	C₂×C₃	—	4	1	no	—
76	C₂×C₃	#123	1	1	yes	characteristic
77	C₂×C₃	#135	1	1	yes	characteristic
78	C₂×C₃	#137	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	C₂×#67	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	12	1	no	—
87	C₄	—	12	1	no	—
88	C₄	#235	1	1	yes	characteristic
89	C₄	#235	1	1	yes	characteristic
90	C₃	#485	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	4	1	no	—
92	C₂	#929	1	1	yes	characteristic
93	C₂	#950	1	1	yes	characteristic
94	C₂	#951	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#117	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂³×C₃	D₄
hypercenter	#117	D₃
hypocenter	C₃	#485
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. #810	C₂	semidirect
5. #810	C₂	semidirect
6. #808	C₂	semidirect
7. #807	C₂	semidirect
90. C₃	#485	semidirect

Maximal subgroups

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

subgroup	index
C₃×#117	2
#924	2
#830	2
#810	2
#808	2
#807	2
#485	3