Subgroups — #5425

Order 192.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#226	C₂	1	1	yes	maximal, characteristic, complemented
3	#859	C₂	1	1	yes	maximal, characteristic, complemented
4	#452	—	3	1	no	maximal, Sylow
5	#41⋊C₃	—	2	1	no	—
6	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	#226	—	2	1	no	—
8	Dic₃⋊C₄	—	4	1	no	maximal
9	C₂×#41	D₃	1	1	yes	characteristic
10	C₂×Q₁₆	—	3	1	no	—
11	C₂×SD₁₆	—	3	1	no	—
12	C₂²⋊Q₈	—	3	1	no	—
13	#103	—	3	1	no	—
14	#102	—	3	1	no	—
15	C₂²⋊C₈	—	3	1	no	—
16	C₂×C₃×C₄	—	4	1	no	—
17	C₂×Dic₃	—	4	1	no	—
18	C₂×Dic₃	—	4	1	no	—
19	SL(2,𝔽₃)	D₄	1	1	yes	characteristic
20	#41	—	2	1	no	—
21	#41	—	6	1	no	—
22	C₂×Q₈	—	3	1	no	—
23	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
24	C₂×D₄	—	3	1	no	—
25	C₂²×C₄	—	3	1	no	—
26	Q₁₆	—	6	1	no	—
27	Q₁₆	—	6	1	no	—
28	SD₁₆	—	6	2	no	—
29	C₂×C₈	—	3	1	no	—
30	C₂×C₈	—	3	1	no	—
31	C₄⋊C₄	—	3	1	no	—
32	C₄⋊C₄	—	6	1	no	—
33	C₂²⋊C₄	—	6	1	no	—
34	C₂²×C₃	—	4	1	no	—
35	C₃×C₄	—	8	1	no	—
36	Dic₃	—	4	2	no	—
37	Dic₃	—	8	1	no	—
38	C₂³	—	3	1	no	—
39	Q₈	—	3	1	no	—
40	Q₈	—	6	1	no	—
41	Q₈	—	6	1	no	—
42	Q₈	#67	1	1	yes	characteristic
43	D₄	—	3	2	no	—
44	D₄	—	6	1	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	6	1	no	—
47	C₂×C₄	—	6	1	no	—
48	C₂×C₄	—	6	1	no	—
49	C₂×C₄	—	6	1	no	—
50	C₂×C₄	S₄	1	1	yes	characteristic
51	C₈	—	6	1	no	—
52	C₈	—	6	1	no	—
53	C₂×C₃	—	4	1	no	—
54	C₂×C₃	—	4	1	no	—
55	C₂×C₃	—	4	1	no	—
56	C₂²	—	6	1	no	—
57	C₂²	—	6	1	no	—
58	C₂²	—	6	1	no	—
59	C₂²	C₂×S₄	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	3	1	no	—
62	C₄	—	3	1	no	—
63	C₄	—	12	1	no	—
64	C₄	—	12	1	no	—
65	C₃	—	4	1	no	Sylow
66	C₂	—	12	1	no	—
67	C₂	#984	1	1	yes	characteristic
68	C₂	#985	1	1	yes	characteristic
69	C₂	GL(2,ℤ/4)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂²	C₂×S₄
commutator, cosocle	C₂×SL(2,𝔽₃)	C₂²
Fitting	C₂×#41	D₃
prime radical	C₂×#41⋊C₃	C₂
hypercenter	C₂×C₄	S₄
hypocenter	SL(2,𝔽₃)	D₄
LCS	G ▷ C₂×SL(2,𝔽₃) ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#226	C₂	semidirect
3. #859	C₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41⋊C₃	2
C₂×#226	2
#859	2
#452	3
Dic₃⋊C₄	4