Subgroups — #4694

Order 192.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#874	C₂	1	1	yes	maximal, characteristic
2	#869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#821	C₂	1	4	yes	maximal, complemented
5	#486	—	3	1	no	maximal, Sylow
6	C₂×D₁₂	—	2	1	no	—
7	C₂×D₁₂	—	2	1	no	—
8	C₂×D₁₂	C₂²	1	2	yes	—
9	C₂×Dic₆	—	2	1	no	—
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄²	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃	—	2	1	no	—
13	C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₄⋊Q₈	—	3	1	no	—
15	#127	—	3	1	no	—
16	#102	—	3	4	no	—
17	C₄×C₈	D₃	1	1	yes	characteristic, complemented
18	C₂²×D₃	—	2	2	no	—
19	C₂×C₃×C₄	D₄	1	1	yes	characteristic
20	C₂×C₃×C₄	D₄	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
22	C₂×Dic₃	—	2	2	no	—
23	D₁₂	—	2	4	no	—
24	D₁₂	—	4	2	no	—
25	D₁₂	—	4	2	no	—
26	Dic₆	—	4	2	no	—
27	C₃×C₈	—	2	2	no	—
28	C₂×Q₈	—	6	1	no	—
29	C₂×D₄	—	3	2	no	—
30	C₂×D₄	—	6	1	no	—
31	C₂×D₄	—	6	1	no	—
32	C₂×C₈	C₂×D₃	1	2	yes	—
33	C₄⋊C₄	—	3	2	no	—
34	C₄⋊C₄	—	6	1	no	—
35	C₄²	C₂×D₃	1	1	yes	characteristic
36	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
37	C₂×D₃	—	4	2	no	—
38	C₂×D₃	—	4	2	no	—
39	C₂×D₃	—	4	2	no	—
40	C₃×C₄	D₈	1	2	yes	—
41	C₃×C₄	SD₁₆	1	2	yes	—
42	C₃×C₄	#41	1	2	yes	—
43	Dic₃	—	4	2	no	—
44	C₂³	—	6	2	no	—
45	Q₈	—	12	2	no	—
46	D₄	—	6	4	no	—
47	D₄	—	12	2	no	—
48	D₄	—	12	2	no	—
49	C₂×C₄	—	6	2	no	—
50	C₂×C₄	D₁₂	1	1	yes	characteristic
51	C₂×C₄	D₁₂	1	1	yes	characteristic
52	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₂×C₃	#124	1	1	yes	characteristic
55	C₂×C₃	C₂×D₈	1	1	yes	characteristic
56	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
57	D₃	—	8	2	no	—
58	C₂²	—	12	2	no	—
59	C₂²	—	12	2	no	—
60	C₂²	—	12	2	no	—
61	C₂²	C₂×D₁₂	1	1	yes	characteristic
62	C₄	—	12	2	no	—
63	C₄	#204	1	2	yes	—
64	C₄	D₂₄	1	2	yes	—
65	C₄	#235	1	2	yes	—
66	C₃	#486	1	1	yes	characteristic, complemented, Sylow
67	C₂	—	24	2	no	—
68	C₂	#875	1	1	yes	characteristic
69	C₂	C₂×#204	1	1	yes	characteristic
70	C₂	C₂×D₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×C₄×C₈	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	#874	C₂
hypercenter	C₄×C₈	D₃
hypocenter	C₃	#486
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #869	C₂	semidirect
3. C₃×C₄×C₈	C₂	semidirect
4. #821	C₂	semidirect
17. C₄×C₈	D₃	semidirect
66. C₃	#486	semidirect

Maximal subgroups

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

subgroup	index
#874	2
#869	2
C₃×C₄×C₈	2
#821	2
#486	3