Subgroups — #10590178

Order 576.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#63773	C₂	1	2	yes	maximal
2	C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₈	C₄	1	1	yes	characteristic
4	C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	#3708	—	2	2	no	—
7	C₈×Dic₃	—	6	2	no	—
8	C₂×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
9	C₂×C₃⋊Dic₃	—	2	1	no	—
10	C₃²×C₈	C₈	1	2	yes	—
11	C₃⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
12	C₃⋊(C₃⋊C₈)	Q₈	1	1	yes	characteristic
13	#364	—	9	1	no	maximal, Sylow
14	C₂×C₃×C₈	—	2	2	no	—
15	C₄×Dic₃	—	6	2	no	—
16	C₂×C₃⋊C₈	—	6	2	no	—
17	C₂²×C₃²	M₁₆	1	1	yes	characteristic
18	C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
19	C₃²×C₄	C₂×C₈	1	1	yes	characteristic
20	C₃⋊Dic₃	—	2	2	no	—
21	M₃₂	—	9	2	no	—
22	C₄×C₈	—	9	1	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×Dic₃	—	6	4	no	—
25	C₃×C₈	—	2	4	no	—
26	C₃⋊C₈	—	6	2	no	—
27	C₃⋊C₈	—	6	2	no	—
28	C₂×C₃²	—	2	1	no	—
29	C₂×C₃²	C₄⋊C₈	1	1	yes	characteristic
30	C₂×C₈	—	9	1	no	—
31	C₂×C₈	#157	1	1	yes	characteristic
32	C₄²	—	9	1	no	—
33	C₁₆	—	18	2	no	—
34	C₂²×C₃	—	2	2	no	—
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	—	2	2	no	—
37	Dic₃	—	6	8	no	—
38	C₃²	#364	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄	—	18	1	no	—
40	C₂×C₄	C₂×#157	1	1	yes	characteristic
41	C₈	—	9	1	no	—
42	C₈	—	9	1	no	—
43	C₈	#622	1	2	yes	—
44	C₂×C₃	—	2	4	no	—
45	C₂×C₃	—	2	2	no	—
46	C₂²	#3788	1	1	yes	characteristic
47	C₄	—	18	2	no	—
48	C₄	C₄⋊#157	1	1	yes	characteristic
49	C₄	C₂×#622	1	1	yes	characteristic
50	C₃	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₄⋊#622	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#157
commutator	C₃²×C₄	C₂×C₈
Frattini	C₂×C₄	C₂×#157
Fitting	C₂×C₃²×C₈	C₄
socle	C₂×C₃²	C₄⋊C₈
prime radical	C₂²×C₃²	M₁₆
cosocle	C₂×C₃⋊(C₃⋊C₈)	C₂²
hypercenter	C₂×C₈	#157
hypocenter	C₃²	#364
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
38. C₃²	#364	semidirect

Maximal subgroups

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

subgroup	index
#63773	2
C₈×C₃⋊Dic₃	2
#364	9