Subgroups — #73290

Order 384.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2811	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂²⋊SL(2,𝔽₃)	—	4	2	no	maximal
3	C₂×C₄²⋊C₃	—	4	3	no	maximal
4	#395	—	3	2	no	—
5	#391	—	3	3	no	—
6	C₄²⋊C₃	—	4	3	no	—
7	C₂²×Q₈	—	3	1	no	—
8	C₂²×Q₈	A₄	1	2	yes	—
9	C₂×C₄⋊C₄	—	3	3	no	—
10	C₂×C₄²	A₄	1	3	yes	—
11	#95	—	3	6	no	—
12	C₂×A₄	—	16	1	no	—
13	SL(2,𝔽₃)	—	16	8	no	—
14	C₂×Q₈	—	3	4	no	—
15	C₂×Q₈	—	12	2	no	—
16	C₂×Q₈	—	12	1	no	—
17	C₂×Q₈	—	12	1	no	—
18	C₂²×C₄	—	3	3	no	—
19	C₂²×C₄	—	3	2	no	—
20	C₄⋊C₄	—	12	3	no	—
21	C₄²	—	4	3	no	—
22	A₄	—	16	1	no	—
23	C₂³	C₂²⋊A₄	1	1	yes	characteristic
24	Q₈	—	4	8	no	—
25	Q₈	—	12	4	no	—
26	C₂×C₄	—	3	6	no	—
27	C₂×C₄	—	6	3	no	—
28	C₂×C₄	—	6	3	no	—
29	C₂×C₄	—	6	6	no	—
30	C₂×C₃	—	64	1	no	—
31	C₂²	—	3	1	no	—
32	C₂²	—	3	1	no	—
33	C₂²	#997	1	1	yes	characteristic
34	C₄	—	6	6	no	—
35	C₄	—	12	2	no	—
36	C₃	—	64	1	no	Sylow
37	C₂	—	3	1	no	—
38	C₂	—	3	1	no	—
39	C₂	#5464	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#5464
commutator, Fitting, cosocle, hypocenter	#2811	C₃
Frattini, socle	C₂³	C₂²⋊A₄
LCS	G ▷ #2811
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
1. #2811	C₃	semidirect

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