Subgroups — C₄×#226 #5387

Order 192.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#226	C₂	1	1	yes	maximal, characteristic
2	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
3	#859	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₁₆	—	3	1	no	maximal, Sylow
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	#226	C₄	1	2	yes	direct product factor
7	C₄×Dic₃	—	4	1	no	maximal
8	C₂×Q₁₆	—	3	1	no	—
9	C₄×Q₈	—	3	1	no	—
10	C₄×Q₈	D₃	1	1	yes	characteristic
11	#107	—	3	1	no	—
12	#103	—	3	1	no	—
13	#103	—	3	1	no	—
14	C₄×C₈	—	3	1	no	—
15	C₂×C₃×C₄	—	4	1	no	—
16	C₂×Dic₃	—	4	1	no	—
17	C₂×Dic₃	—	4	1	no	—
18	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
19	C₂×Q₈	—	3	1	no	—
20	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
21	Q₁₆	—	3	2	no	—
22	Q₁₆	—	3	2	no	—
23	C₂×C₈	—	3	1	no	—
24	C₂×C₈	—	3	1	no	—
25	C₄⋊C₄	—	3	1	no	—
26	C₄⋊C₄	—	3	1	no	—
27	C₄⋊C₄	—	6	1	no	—
28	C₄²	—	3	1	no	—
29	C₄²	—	6	1	no	—
30	C₂²×C₃	—	4	1	no	—
31	C₃×C₄	—	4	2	no	—
32	Dic₃	—	4	2	no	—
33	Dic₃	—	4	2	no	—
34	Q₈	—	3	1	no	—
35	Q₈	—	3	2	no	—
36	Q₈	—	6	1	no	—
37	Q₈	C₄×D₃	1	1	yes	characteristic
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	6	1	no	—
41	C₂×C₄	—	6	1	no	—
42	C₂×C₄	S₄	1	1	yes	characteristic
43	C₈	—	3	2	no	—
44	C₈	—	6	1	no	—
45	C₂×C₃	—	4	1	no	—
46	C₂×C₃	—	4	1	no	—
47	C₂×C₃	—	4	1	no	—
48	C₂²	C₂×S₄	1	1	yes	characteristic
49	C₄	—	3	1	no	—
50	C₄	—	3	1	no	—
51	C₄	—	6	2	no	—
52	C₄	—	6	1	no	—
53	C₄	—	12	1	no	—
54	C₄	#226	1	2	yes	direct product factor
55	C₃	—	4	1	no	Sylow
56	C₂	C₄×S₄	1	1	yes	characteristic
57	C₂	C₂×#226	1	1	yes	characteristic
58	C₂	#985	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	S₄
commutator, hypocenter	SL(2,𝔽₃)	C₂×C₄
Frattini, socle	C₂²	C₂×S₄
Fitting	C₄×Q₈	D₃
prime radical, cosocle	C₂×SL(2,𝔽₃)	C₂²
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
6. #226	C₄	direct (N × H)
54. C₄	#226	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#226	2
C₄×SL(2,𝔽₃)	2
#859	2
C₄×Q₁₆	3
C₄×Dic₃	4

Subgroups — C4×#226 #5387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#226 #5387