Subgroups — #5143

Order 192.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#131	C₂	1	1	yes	maximal, characteristic
2	#951	C₂	1	2	yes	maximal
3	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#824	C₂	1	2	yes	maximal, complemented
5	#819	C₂	1	1	yes	maximal, characteristic, complemented
6	#473	—	3	1	no	maximal, Sylow
7	C₃×#41	C₂²	1	1	yes	characteristic
8	C₂×Dic₆	C₂²	1	2	yes	—
9	C₃×M₁₆	—	2	1	no	—
10	C₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	—	2	1	no	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	#216	—	2	2	no	—
14	#214	—	2	2	no	—
15	#208	C₂²	1	2	yes	—
16	Dic₁₂	—	2	1	no	—
17	Dic₁₂	—	2	1	no	—
18	#137	—	3	2	no	—
19	C₂×Q₁₆	—	3	1	no	—
20	#131	D₃	1	1	yes	characteristic
21	#108	—	3	1	no	—
22	#101	—	3	2	no	—
23	C₃×Q₈	D₄	1	1	yes	characteristic
24	C₃×D₄	—	2	1	no	—
25	C₃×D₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₂×Dic₃	—	2	2	no	—
29	Dic₆	—	2	2	no	—
30	Dic₆	—	2	2	no	—
31	C₃×C₈	—	2	1	no	—
32	C₃×C₈	D₄	1	1	yes	characteristic
33	C₃×C₈	D₄	1	1	yes	characteristic
34	C₃⋊C₈	—	2	2	no	—
35	#41	C₂×D₃	1	1	yes	characteristic
36	C₂×Q₈	—	3	2	no	—
37	Q₁₆	—	6	2	no	—
38	Q₁₆	—	6	1	no	—
39	Q₁₆	—	6	1	no	—
40	SD₁₆	—	6	2	no	—
41	M₁₆	—	2	1	no	—
42	M₁₆	—	3	2	no	—
43	M₁₆	C₂×D₃	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	C₂×D₃	1	1	yes	characteristic
46	C₂²×C₃	—	2	1	no	—
47	C₂²×C₃	#41	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	C₂×D₄	1	1	yes	characteristic
50	C₃×C₄	C₂×D₄	1	1	yes	characteristic
51	Dic₃	—	4	2	no	—
52	Q₈	—	6	2	no	—
53	Q₈	—	6	2	no	—
54	Q₈	D₁₂	1	1	yes	characteristic
55	D₄	—	2	1	no	—
56	D₄	D₁₂	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	6	2	no	—
59	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	—	6	2	no	—
62	C₈	#67	1	1	yes	characteristic
63	C₈	#67	1	1	yes	characteristic
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	—	4	1	no	—
66	C₂×C₃	#121	1	1	yes	characteristic
67	C₂²	—	2	1	no	—
68	C₂²	#235	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	12	2	no	—
71	C₄	C₂×D₁₂	1	1	yes	characteristic
72	C₄	C₂×#67	1	1	yes	characteristic
73	C₃	#473	1	1	yes	characteristic, complemented, Sylow
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#930
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#131	C₂
socle	C₂×C₃	#121
prime radical	C₃×#41	C₂²
hypercenter	#131	D₃
hypocenter	C₃	#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₂	C₂	semidirect
4. #824	C₂	semidirect
5. #819	C₂	semidirect
73. C₃	#473	semidirect

Maximal subgroups

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

subgroup	index
C₃×#131	2
#951	2
C₂×Dic₁₂	2
#824	2
#819	2
#473	3