Subgroups — C₂³×#622 #10596651

Order 576.

574 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#622	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₃²	C₄	1	1	yes	characteristic
4	C₂²×C₃⋊Dic₃	C₄	1	7	yes	—
5	C₂²×C₃⋊Dic₃	C₂²	1	7	yes	—
6	C₂×#622	C₂²	1	28	yes	direct product factor
7	C₂³×Dic₃	—	6	2	no	—
8	C₂³×C₃²	C₈	1	8	yes	complemented
9	C₂³×C₃²	C₂×C₄	1	7	yes	—
10	C₂×C₃⋊Dic₃	C₂×C₄	1	21	yes	—
11	C₂×C₃⋊Dic₃	C₂³	1	7	yes	—
12	#622	C₂³	1	8	yes	direct product factor
13	C₂³×C₈	—	9	1	no	maximal, Sylow
14	C₂⁴×C₃	—	2	2	no	—
15	C₂²×Dic₃	—	6	14	no	—
16	C₂²×Dic₃	—	6	14	no	—
17	C₂²×C₃²	C₂×C₈	1	28	yes	complemented
18	C₂²×C₃²	C₂²×C₄	1	7	yes	—
19	C₃⋊Dic₃	C₂²×C₄	1	7	yes	—
20	C₃⋊Dic₃	C₂⁴	1	1	yes	characteristic
21	C₂³×C₄	—	9	1	no	—
22	C₂²×C₈	—	9	14	no	—
23	C₂³×C₃	—	2	16	no	—
24	C₂³×C₃	—	2	14	no	—
25	C₂×Dic₃	—	6	42	no	—
26	C₂×Dic₃	—	6	14	no	—
27	C₂×C₃²	C₂²×C₈	1	14	yes	complemented
28	C₂×C₃²	C₂³×C₄	1	1	yes	characteristic
29	C₂⁴	#157	1	1	yes	characteristic
30	C₂²×C₄	—	9	7	no	—
31	C₂²×C₄	—	9	7	no	—
32	C₂×C₈	—	9	28	no	—
33	C₂²×C₃	—	2	14	no	—
34	C₂²×C₃	—	2	56	no	—
35	Dic₃	—	6	14	no	—
36	Dic₃	—	6	2	no	—
37	C₃²	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
38	C₂³	#622	1	8	yes	direct product factor
39	C₂³	C₂×#157	1	7	yes	—
40	C₂×C₄	—	9	7	no	—
41	C₂×C₄	—	9	21	no	—
42	C₈	—	9	8	no	—
43	C₂×C₃	—	2	28	no	—
44	C₂×C₃	—	2	2	no	—
45	C₂²	C₂×#622	1	28	yes	direct product factor
46	C₂²	C₂²×#157	1	7	yes	—
47	C₄	—	9	1	no	—
48	C₄	—	9	7	no	—
49	C₃	—	2	2	no	—
50	C₂	C₂²×#622	1	14	yes	direct product factor
51	C₂	C₂³×#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	#157
commutator, hypocenter	C₃²	C₂³×C₈
Frattini	C₂	C₂³×#157
Fitting, socle, prime radical	C₂⁴×C₃²	C₄
cosocle	C₃⋊Dic₃	C₂⁴
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×#622	C₂	direct (N × H)
6. C₂×#622	C₂²	direct (N × H)
8. C₂³×C₃²	C₈	semidirect
12. #622	C₂³	direct (N × H)
17. C₂²×C₃²	C₂×C₈	semidirect
27. C₂×C₃²	C₂²×C₈	semidirect
37. C₃²	C₂³×C₈	semidirect
38. C₂³	#622	direct (N × H)
45. C₂²	C₂×#622	direct (N × H)
50. C₂	C₂²×#622	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃⋊Dic₃	2
C₂²×#622	2
C₂³×C₈	9

Subgroups — C23×#622 #10596651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#622 #10596651