Subgroups — #4458

Order 192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal
3	#335	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₄	1	1	yes	characteristic
6	C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₈	—	2	2	no	—
8	C₄⋊C₈	—	3	2	no	—
9	C₄×C₈	D₃	1	1	yes	characteristic
10	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₄	D₄	1	1	yes	characteristic
12	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
13	C₃×C₈	—	2	1	no	—
14	C₃×C₈	C₈	1	2	yes	complemented
15	C₃⋊C₈	—	4	2	no	—
16	C₂×C₈	—	6	2	no	—
17	C₂×C₈	Dic₃	1	1	yes	characteristic
18	C₂×C₈	Dic₃	1	1	yes	characteristic
19	C₄²	C₂×D₃	1	1	yes	characteristic
20	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₂×C₈	1	1	yes	characteristic
23	C₃×C₄	M₁₆	1	1	yes	characteristic
24	C₃×C₄	D₈	1	1	yes	characteristic
25	C₃×C₄	Q₁₆	1	1	yes	characteristic
26	C₂×C₄	Dic₆	1	1	yes	characteristic
27	C₂×C₄	D₁₂	1	1	yes	characteristic
28	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
29	C₈	—	2	1	no	—
30	C₈	—	12	2	no	—
31	C₈	C₃⋊C₈	1	2	yes	complemented
32	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
33	C₂×C₃	#107	1	1	yes	characteristic
34	C₂×C₃	#108	1	1	yes	characteristic
35	C₂²	C₄⋊Dic₃	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	D₂₄	1	1	yes	characteristic
38	C₄	Dic₁₂	1	1	yes	characteristic
39	C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
40	C₄	#208	1	1	yes	characteristic
41	C₃	#335	1	1	yes	characteristic, complemented, Sylow
42	C₂	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
43	C₂	#818	1	1	yes	characteristic
44	C₂	#819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₂
commutator	C₃×C₄	C₂×C₈
Frattini	C₄²	C₂×D₃
Fitting	C₃×C₄×C₈	C₂
socle, prime radical	C₂²×C₃	C₄⋊C₄
cosocle	C₃×C₄²	C₂²
hypercenter	C₄×C₈	D₃
hypocenter	C₃	#335
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
14. C₃×C₈	C₈	semidirect
31. C₈	C₃⋊C₈	semidirect
41. C₃	#335	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₈	2
C₄⋊(C₃⋊C₈)	2
#335	3