Subgroups — #401⋊C₃ #4640

Order 192.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#95⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#401	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₄×A₄	—	4	1	no	maximal
4	#95	—	3	1	no	—
5	#95	—	3	1	no	—
6	#95	C₂×C₃	1	1	yes	characteristic
7	C₂×A₄	—	4	1	no	—
8	C₂²×C₄	—	3	1	no	—
9	C₂²×C₄	—	3	1	no	—
10	C₂²×C₄	A₄	1	1	yes	characteristic
11	A₄	—	4	1	no	—
12	C₃×C₄	—	16	1	no	—
13	C₂³	C₂×A₄	1	1	yes	characteristic
14	C₂×C₄	—	6	1	no	—
15	C₂×C₄	—	6	1	no	—
16	C₂×C₄	—	6	2	no	—
17	C₂×C₄	—	6	1	no	—
18	C₂×C₄	—	6	1	no	—
19	C₂×C₄	—	6	1	no	—
20	C₂×C₃	—	16	1	no	—
21	C₂²	—	3	1	no	—
22	C₂²	—	3	1	no	—
23	C₂²	#41⋊C₃	1	1	yes	characteristic
24	C₄	—	4	1	no	—
25	C₄	—	12	1	no	—
26	C₄	—	12	1	no	—
27	C₃	—	16	1	no	Sylow
28	C₂	—	3	1	no	—
29	C₂	—	3	1	no	—
30	C₂	#126⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#126⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃
Frattini, socle	C₂³	C₂×A₄
Fitting	#401	C₃
prime radical	#95⋊C₃	C₂
LCS	G ▷ #95
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. #401	C₃	semidirect

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