Subgroups — #10593838

Order 576.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64157	C₂	1	1	yes	maximal, characteristic
2	#63773	C₂	1	3	yes	maximal, complemented
3	C₂×#3708	C₂	1	3	yes	maximal, complemented
4	C₃²×#41	C₄	1	1	yes	characteristic
5	#3748	C₄	1	3	yes	—
6	C₂×C₃⋊(C₃⋊C₈)	C₂²	1	3	yes	—
7	#3708	C₂²	1	1	yes	characteristic
8	#3708	C₂²	1	3	yes	—
9	#948	—	6	2	no	—
10	C₃²×Q₈	C₈	1	1	yes	characteristic
11	C₃²×D₄	C₈	1	3	yes	—
12	C₂×C₃²×C₄	C₂×C₄	1	3	yes	—
13	C₃⋊(C₃⋊C₈)	C₂×C₄	1	3	yes	—
14	C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
15	#504	—	9	1	no	maximal, Sylow
16	C₃×#41	—	2	2	no	—
17	#208	—	6	6	no	—
18	C₂×C₃⋊C₈	—	6	6	no	—
19	C₂²×C₃²	C₂×C₈	1	3	yes	—
20	C₃²×C₄	C₂×C₈	1	3	yes	—
21	C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
22	#131	—	9	1	no	—
23	M₃₂	—	9	3	no	—
24	C₂×C₁₆	—	9	3	no	—
25	C₃×Q₈	—	2	2	no	—
26	C₃×D₄	—	2	6	no	—
27	C₂×C₃×C₄	—	2	6	no	—
28	C₃⋊C₈	—	6	6	no	—
29	C₃⋊C₈	—	6	2	no	—
30	C₂×C₃²	—	2	3	no	—
31	C₂×C₃²	C₂²×C₈	1	1	yes	characteristic
32	#41	#157	1	1	yes	characteristic
33	M₁₆	—	9	3	no	—
34	C₂×C₈	—	9	3	no	—
35	C₁₆	—	9	1	no	—
36	C₁₆	—	9	3	no	—
37	C₂²×C₃	—	2	6	no	—
38	C₃×C₄	—	2	2	no	—
39	C₃×C₄	—	2	6	no	—
40	C₃²	#504	1	1	yes	characteristic, complemented, Sylow
41	Q₈	#622	1	1	yes	characteristic
42	D₄	#622	1	3	yes	—
43	C₂×C₄	C₂×#157	1	3	yes	—
44	C₈	—	9	1	no	—
45	C₈	—	9	3	no	—
46	C₂×C₃	—	2	2	no	—
47	C₂×C₃	—	4	6	no	—
48	C₂²	C₂×#622	1	3	yes	—
49	C₄	C₂×#622	1	3	yes	—
50	C₄	C₂²×#157	1	1	yes	characteristic
51	C₃	—	2	2	no	—
52	C₂	—	2	3	no	—
53	C₂	C₂²×#622	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#157
commutator, socle	C₂×C₃²	C₂²×C₈
Fitting, prime radical	C₃²×#41	C₄
cosocle	C₃⋊(C₃⋊C₈)	C₂³
hypercenter	#41	#157
hypocenter	C₃²	#504
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. #63773	C₂	semidirect
3. C₂×#3708	C₂	semidirect
40. C₃²	#504	semidirect

Maximal subgroups

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

subgroup	index
#64157	2
#63773	2
C₂×#3708	2
#504	9