Subgroups — C₂²×#226 #5915

Order 192.

153 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×#226	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Q₁₆	—	3	1	no	maximal, Sylow
4	C₂²×Dic₃	—	4	1	no	maximal
5	C₂×SL(2,𝔽₃)	C₂²	1	3	yes	—
6	#226	C₂²	1	4	yes	direct product factor
7	C₂²×Q₈	—	3	1	no	—
8	C₂²×Q₈	D₃	1	1	yes	characteristic
9	C₂×Q₁₆	—	3	6	no	—
10	C₂×Q₁₆	—	3	6	no	—
11	C₂²×C₈	—	3	1	no	—
12	C₂³×C₃	—	4	1	no	—
13	C₂×Dic₃	—	4	6	no	—
14	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic
15	C₂×Q₈	—	3	3	no	—
16	C₂×Q₈	—	3	6	no	—
17	C₂×Q₈	—	6	3	no	—
18	C₂×Q₈	C₂×D₃	1	3	yes	—
19	C₂²×C₄	—	3	1	no	—
20	C₂²×C₄	—	6	1	no	—
21	Q₁₆	—	3	12	no	—
22	Q₁₆	—	3	4	no	—
23	C₂×C₈	—	3	6	no	—
24	C₂²×C₃	—	4	4	no	—
25	C₂²×C₃	—	4	3	no	—
26	Dic₃	—	4	4	no	—
27	C₂³	S₄	1	1	yes	characteristic
28	Q₈	—	3	3	no	—
29	Q₈	—	3	4	no	—
30	Q₈	—	6	1	no	—
31	Q₈	—	6	6	no	—
32	Q₈	C₂²×D₃	1	1	yes	characteristic
33	C₂×C₄	—	3	3	no	—
34	C₂×C₄	—	3	3	no	—
35	C₂×C₄	—	6	6	no	—
36	C₈	—	3	4	no	—
37	C₂×C₃	—	4	6	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂²	#226	1	4	yes	direct product factor
40	C₂²	C₂×S₄	1	3	yes	—
41	C₄	—	3	1	no	—
42	C₄	—	3	3	no	—
43	C₄	—	6	4	no	—
44	C₃	—	4	1	no	Sylow
45	C₂	C₂×#226	1	6	yes	direct product factor
46	C₂	C₂²×S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, hypercenter	C₂³	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂³
Frattini	C₂	C₂²×S₄
Fitting	C₂²×Q₈	D₃
prime radical	C₂²×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

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

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