Subgroups — #4896

Order 192.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#909	C₂	1	2	yes	maximal
2	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#901	C₂	1	1	yes	maximal, characteristic
4	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	#824	C₂	1	2	yes	maximal, complemented
6	#473	—	3	1	no	maximal, Sylow
7	#235	C₂²	1	1	yes	characteristic
8	C₂×Dic₆	C₂²	1	2	yes	—
9	C₃×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	#208	C₂²	1	1	yes	characteristic
12	Dic₁₂	—	2	2	no	—
13	Dic₁₂	—	2	1	no	—
14	Dic₁₂	—	2	1	no	—
15	#204	—	2	2	no	—
16	ΓL(1,𝔽₂₅)	—	2	1	no	—
17	D₃×C₈	—	2	1	no	—
18	#137	—	3	2	no	—
19	C₂×Q₁₆	—	3	1	no	—
20	#131	—	3	1	no	—
21	#108	D₃	1	1	yes	characteristic, complemented
22	#101	—	3	2	no	—
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	#67	—	2	1	no	—
25	C₂×Dic₃	—	2	2	no	—
26	D₁₂	D₄	1	1	yes	characteristic
27	C₄×D₃	—	2	1	no	—
28	Dic₆	—	2	2	no	—
29	Dic₆	—	2	2	no	—
30	Dic₆	D₄	1	1	yes	characteristic
31	C₃×C₈	—	2	2	no	—
32	C₃×C₈	D₄	1	1	yes	characteristic
33	C₃×C₈	D₄	1	1	yes	characteristic
34	C₃⋊C₈	—	2	1	no	—
35	#41	—	3	1	no	—
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	—	3	1	no	—
42	M₁₆	—	6	1	no	—
43	M₁₆	C₂×D₃	1	2	yes	—
44	C₂×C₈	—	6	1	no	—
45	C₂×C₈	C₂×D₃	1	1	yes	characteristic
46	C₂²×C₃	#41	1	1	yes	characteristic
47	C₂×D₃	—	2	1	no	—
48	C₃×C₄	C₂×D₄	1	1	yes	characteristic
49	C₃×C₄	C₂×D₄	1	1	yes	characteristic
50	Dic₃	—	2	1	no	—
51	Dic₃	—	4	2	no	—
52	Q₈	—	3	1	no	—
53	Q₈	—	6	2	no	—
54	Q₈	—	6	2	no	—
55	D₄	—	3	1	no	—
56	D₄	—	6	1	no	—
57	C₂×C₄	—	6	1	no	—
58	C₂×C₄	—	6	2	no	—
59	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	6	1	no	—
62	C₈	D₁₂	1	1	yes	characteristic
63	C₈	D₁₂	1	1	yes	characteristic
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	#121	1	1	yes	characteristic
66	D₃	—	4	1	no	—
67	C₂²	—	6	1	no	—
68	C₂²	#239	1	1	yes	characteristic
69	C₄	—	6	1	no	—
70	C₄	—	12	2	no	—
71	C₄	C₂×D₁₂	1	1	yes	characteristic
72	C₄	D₃×D₄	1	1	yes	characteristic
73	C₃	#473	1	1	yes	characteristic, complemented, Sylow
74	C₂	—	2	1	no	—
75	C₂	—	12	1	no	—
76	C₂	#895	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#895
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#108	C₂
socle	C₂×C₃	#121
prime radical	#235	C₂²
hypercenter	#108	D₃
hypocenter	C₃	#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₂	C₂	semidirect
4. C₃×#108	C₂	semidirect
5. #824	C₂	semidirect
21. #108	D₃	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
#909	2
C₂×Dic₁₂	2
#901	2
C₃×#108	2
#824	2
#473	3