Subgroups — #10593779

Order 576.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64287	C₂	1	2	yes	maximal, complemented
2	#64121	C₂	1	1	yes	maximal, characteristic
3	#63783	C₂	1	2	yes	maximal, complemented
4	#63771	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#157	C₂	1	1	yes	maximal, characteristic, complemented
6	#3830	C₂²	1	2	yes	—
7	#3792	—	2	2	no	—
8	C₂×#622	—	2	2	no	—
9	C₄×#157	C₂²	1	1	yes	characteristic
10	#3788	C₂²	1	2	yes	—
11	#3787	C₂²	1	1	yes	characteristic
12	C₃²×D₈	C₄	1	1	yes	characteristic, complemented
13	#3754	C₄	1	2	yes	complemented
14	#3746	C₄	1	1	yes	characteristic, complemented
15	C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	#912	—	6	2	no	—
17	C₂×#157	—	2	1	no	—
18	C₃²×D₄	C₂×C₄	1	2	yes	—
19	#638	—	2	2	no	—
20	C₂×C₃⋊Dic₃	—	2	2	no	—
21	C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
22	#634	C₂×C₄	1	2	yes	—
23	#622	—	2	2	no	—
24	#622	D₄	1	1	yes	characteristic
25	#622	D₄	1	1	yes	characteristic
26	C₃²×C₈	C₂×C₄	1	1	yes	characteristic
27	C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
28	#443	—	9	1	no	maximal, Sylow
29	#237	—	6	4	no	—
30	C₃×D₈	—	2	2	no	—
31	#214	—	6	4	no	—
32	Dic₁₂	—	6	2	no	—
33	D₃×C₈	—	6	2	no	—
34	C₂²×C₃²	—	2	2	no	—
35	C₂×C₃⋊D₃	#41	1	1	yes	characteristic
36	#157	—	2	2	no	—
37	C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
38	C₃⋊Dic₃	—	2	2	no	—
39	C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
40	#135	—	9	1	no	—
41	#131	—	9	2	no	—
42	#108	—	9	1	no	—
43	#104	—	9	2	no	—
44	C₄×C₈	—	9	1	no	—
45	C₃×D₄	—	2	4	no	—
46	#67	—	12	4	no	—
47	C₂×Dic₃	—	12	4	no	—
48	C₄×D₃	—	6	2	no	—
49	Dic₆	—	6	4	no	—
50	C₃×C₈	—	2	2	no	—
51	C₃⋊C₈	—	6	2	no	—
52	C₂×C₃²	—	4	2	no	—
53	C₂×C₃²	C₄×D₄	1	1	yes	characteristic
54	C₃⋊D₃	—	2	1	no	—
55	#41	—	9	2	no	—
56	Q₁₆	—	9	1	no	—
57	SD₁₆	—	9	2	no	—
58	D₈	#157	1	1	yes	characteristic, complemented
59	M₁₆	—	9	2	no	—
60	M₁₆	—	18	2	no	—
61	C₂×C₈	—	9	1	no	—
62	C₂×C₈	—	9	1	no	—
63	C₂×C₈	—	18	2	no	—
64	C₄²	—	9	1	no	—
65	C₂²×C₃	—	4	4	no	—
66	C₂×D₃	—	6	2	no	—
67	C₃×C₄	—	2	2	no	—
68	Dic₃	—	6	2	no	—
69	Dic₃	—	12	4	no	—
70	C₃²	#443	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	9	2	no	—
72	D₄	—	18	2	no	—
73	D₄	C₂×#157	1	2	yes	—
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	—	18	2	no	—
76	C₂×C₄	—	18	1	no	—
77	C₈	—	9	1	no	—
78	C₈	—	9	1	no	—
79	C₈	—	9	1	no	—
80	C₈	—	18	2	no	—
81	C₈	C₂×#157	1	1	yes	characteristic
82	C₂×C₃	—	2	2	no	—
83	C₂×C₃	—	8	4	no	—
84	D₃	—	12	2	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	9	1	no	—
87	C₄	—	9	1	no	—
88	C₄	—	18	2	no	—
89	C₄	—	18	2	no	—
90	C₄	C₂²×#157	1	1	yes	characteristic
91	C₃	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	—	18	1	no	—
94	C₂	D₄×#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#157
commutator	C₃²×C₄	C₂²×C₄
Frattini	C₄	C₂²×#157
Fitting	C₃²×D₈	C₄
socle	C₂×C₃²	C₄×D₄
prime radical	#64121	C₂
cosocle	C₄×C₃⋊D₃	C₂³
hypercenter	D₈	#157
hypocenter	C₃²	#443
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #64287	C₂	semidirect
3. #63783	C₂	semidirect
4. #63771	C₂	semidirect
5. C₈×#157	C₂	semidirect
12. C₃²×D₈	C₄	semidirect
13. #3754	C₄	semidirect
14. #3746	C₄	semidirect
58. D₈	#157	semidirect
70. C₃²	#443	semidirect

Maximal subgroups

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

subgroup	index
#64287	2
#64121	2
#63783	2
#63771	2
C₈×#157	2
#443	9