Subgroups — #10590875

Order 576.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#63872	C₂	1	2	yes	maximal
2	C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×#818	C₂	1	2	yes	maximal
4	#63574	C₂	1	2	yes	maximal
5	#4878	—	3	2	no	maximal
6	C₂×C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊Dic₃	C₂²	1	4	yes	—
10	Dic₃⋊Dic₃	—	2	4	no	—
11	#890	—	3	4	no	—
12	C₃×#107	—	3	2	no	—
13	#818	D₃	1	2	yes	—
14	C₈×Dic₃	—	3	2	no	—
15	C₈×Dic₃	—	6	1	no	—
16	#808	—	3	4	no	—
17	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
18	C₂×C₃⋊Dic₃	D₄	1	2	yes	—
19	C₂×C₃×Dic₃	—	2	4	no	—
20	C₃²×C₈	Q₈	1	2	yes	—
21	C₃⋊(C₃⋊C₈)	Q₈	1	2	yes	—
22	#499	—	9	1	no	Sylow
23	C₂×C₃×C₈	—	2	1	no	—
24	C₂×C₃×C₈	C₂×D₃	1	2	yes	—
25	C₃×C₄⋊C₄	—	3	4	no	—
26	C₄⋊Dic₃	—	6	4	no	—
27	C₄⋊Dic₃	C₂×D₃	1	4	yes	—
28	Dic₃⋊C₄	—	6	4	no	—
29	C₄×Dic₃	—	3	2	no	—
30	C₄×Dic₃	—	6	1	no	—
31	C₂×C₃⋊C₈	—	3	2	no	—
32	C₂×C₃⋊C₈	—	6	1	no	—
33	C₂²×C₃²	C₂×D₄	1	1	yes	characteristic
34	C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
35	C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
36	C₃⋊Dic₃	—	2	2	no	—
37	C₃×Dic₃	—	4	4	no	—
38	#125	—	9	2	no	—
39	#107	—	3	2	no	—
40	#106	—	9	2	no	—
41	C₄×C₈	—	9	1	no	—
42	C₂×C₃×C₄	—	2	1	no	—
43	C₂×C₃×C₄	—	6	4	no	—
44	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
45	C₂×Dic₃	—	2	4	no	—
46	C₂×Dic₃	—	3	2	no	—
47	C₂×Dic₃	—	3	2	no	—
48	C₂×Dic₃	—	6	2	no	—
49	C₃×C₈	—	2	2	no	—
50	C₃×C₈	Dic₆	1	4	yes	—
51	C₃⋊C₈	—	3	4	no	—
52	C₃⋊C₈	—	6	2	no	—
53	C₂×C₃²	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₃²	#135	1	2	yes	—
55	C₂×C₈	—	9	1	no	—
56	C₂×C₈	D₃²	1	1	yes	characteristic
57	C₄⋊C₄	—	3	4	no	—
58	C₄⋊C₄	—	18	4	no	—
59	C₄²	—	9	1	no	—
60	C₂²×C₃	—	2	1	no	—
61	C₂²×C₃	D₃×D₄	1	2	yes	—
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	12	4	no	—
65	C₃×C₄	C₂×Dic₆	1	2	yes	—
66	C₃×C₄	D₃×Q₈	1	2	yes	—
67	Dic₃	—	4	4	no	—
68	Dic₃	—	6	4	no	—
69	Dic₃	—	6	2	no	—
70	Dic₃	—	6	2	no	—
71	C₃²	#499	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₄	—	6	4	no	—
73	C₂×C₄	—	9	2	no	—
74	C₂×C₄	C₂×D₃²	1	1	yes	characteristic
75	C₈	—	9	2	no	—
76	C₈	#627	1	2	yes	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	#888	1	2	yes	—
80	C₂×C₃	#912	1	2	yes	—
81	C₂×C₃	#919	1	2	yes	—
82	C₂²	#3802	1	1	yes	characteristic
83	C₄	—	12	4	no	—
84	C₄	—	18	2	no	—
85	C₄	#3797	1	1	yes	characteristic
86	C₄	C₂×#627	1	1	yes	characteristic
87	C₃	—	2	1	no	—
88	C₃	#4878	1	2	yes	complemented
89	C₂	#63810	1	2	yes	—
90	C₂	#63919	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#3802
commutator, cosocle	C₂×C₃²×C₄	C₂³
Frattini	C₂×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₈	C₂²
socle, prime radical	C₂²×C₃²	C₂×D₄
hypercenter	C₂×C₈	D₃²
hypocenter	C₃²	#499
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
71. C₃²	#499	semidirect
88. C₃	#4878	semidirect

Maximal subgroups

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

subgroup	index
#63872	2
C₈×C₃⋊Dic₃	2
C₃×#818	2
#63574	2
#4878	3