Subgroups — #4702

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#870	C₂	1	1	yes	maximal, characteristic
2	#869	C₂	1	1	yes	maximal, characteristic
3	C₃×#97	C₂	1	1	yes	maximal, characteristic
4	#818	C₂	1	2	yes	maximal
5	#817	C₂	1	2	yes	maximal
6	#501	—	3	1	no	maximal, Sylow
7	C₂×Dic₆	—	2	1	no	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃	—	2	1	no	—
11	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
14	Dic₃⋊C₄	—	2	1	no	—
15	Dic₃⋊C₄	—	2	1	no	—
16	C₄⋊Q₈	—	3	1	no	—
17	#125	—	3	1	no	—
18	#107	—	3	2	no	—
19	#106	—	3	2	no	—
20	#97	D₃	1	1	yes	characteristic
21	C₂×C₃×C₄	D₄	1	1	yes	characteristic
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₂×Dic₃	—	2	1	no	—
25	C₂×Dic₃	—	2	1	no	—
26	C₂×Dic₃	—	2	2	no	—
27	Dic₆	—	4	2	no	—
28	C₃×C₈	Q₈	1	4	yes	complemented
29	C₂×Q₈	—	6	1	no	—
30	C₂×C₈	C₂×D₃	1	2	yes	—
31	C₄⋊C₄	—	3	1	no	—
32	C₄⋊C₄	—	3	2	no	—
33	C₄⋊C₄	—	3	1	no	—
34	C₄⋊C₄	—	6	1	no	—
35	C₄⋊C₄	—	6	1	no	—
36	C₄⋊C₄	—	6	1	no	—
37	C₄²	C₂×D₃	1	1	yes	characteristic
38	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	C₂×Q₈	1	2	yes	—
42	Dic₃	—	4	2	no	—
43	Dic₃	—	4	1	no	—
44	Dic₃	—	4	1	no	—
45	Q₈	—	12	2	no	—
46	C₂×C₄	—	6	1	no	—
47	C₂×C₄	—	6	1	no	—
48	C₂×C₄	—	6	2	no	—
49	C₂×C₄	D₁₂	1	1	yes	characteristic
50	C₂×C₄	D₁₂	1	1	yes	characteristic
51	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
52	C₈	Dic₆	1	4	yes	complemented
53	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₂×C₃	#137	1	1	yes	characteristic
56	C₂²	C₂×D₁₂	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	12	2	no	—
60	C₄	—	12	1	no	—
61	C₄	—	12	1	no	—
62	C₄	C₂×Dic₆	1	2	yes	—
63	C₃	#501	1	1	yes	characteristic, complemented, Sylow
64	C₂	#869	1	1	yes	characteristic
65	C₂	#908	1	1	yes	characteristic
66	C₂	#909	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#97	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#97	D₃
hypocenter	C₃	#501
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
28. C₃×C₈	Q₈	semidirect
52. C₈	Dic₆	semidirect
63. C₃	#501	semidirect

Maximal subgroups

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

subgroup	index
#870	2
#869	2
C₃×#97	2
#818	2
#817	2
#501	3