Subgroups — #5403

Order 192.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#984	C₂	1	2	yes	maximal
2	#131⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#473	—	3	1	no	maximal, Sylow
4	#41⋊C₃	C₂²	1	1	yes	characteristic
5	#226	—	2	2	no	—
6	Dic₁₂	—	4	1	no	maximal
7	#137	—	3	2	no	—
8	C₂×Q₁₆	—	3	1	no	—
9	#131	D₃	1	1	yes	characteristic
10	#108	—	3	1	no	—
11	#101	—	3	2	no	—
12	Dic₆	—	4	2	no	—
13	SL(2,𝔽₃)	D₄	1	1	yes	characteristic
14	C₃×C₈	—	4	1	no	—
15	#41	C₂×D₃	1	1	yes	characteristic
16	C₂×Q₈	—	3	2	no	—
17	Q₁₆	—	6	1	no	—
18	Q₁₆	—	6	2	no	—
19	Q₁₆	—	6	1	no	—
20	SD₁₆	—	6	2	no	—
21	M₁₆	—	3	1	no	—
22	M₁₆	—	3	2	no	—
23	C₂×C₈	—	3	1	no	—
24	C₃×C₄	—	4	1	no	—
25	Dic₃	—	8	2	no	—
26	Q₈	—	6	2	no	—
27	Q₈	—	6	2	no	—
28	Q₈	D₁₂	1	1	yes	characteristic
29	D₄	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₂×C₄	—	6	2	no	—
32	C₈	—	3	1	no	—
33	C₈	—	6	2	no	—
34	C₈	S₄	1	1	yes	characteristic
35	C₂×C₃	—	4	1	no	—
36	C₂²	—	3	1	no	—
37	C₄	—	3	1	no	—
38	C₄	—	12	2	no	—
39	C₄	C₂×S₄	1	1	yes	characteristic
40	C₃	—	4	1	no	Sylow
41	C₂	—	6	1	no	—
42	C₂	C₄⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₄⋊S₄
commutator, prime radical, cosocle	#41⋊C₃	C₂²
Frattini	C₄	C₂×S₄
Fitting	#131	D₃
hypercenter	C₈	S₄
hypocenter	SL(2,𝔽₃)	D₄
LCS	G ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

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