Subgroups — #10593736

Order 576.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#157	C₂	1	2	yes	maximal
2	C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	#63781	C₂	1	4	yes	maximal
4	C₂²×#157	C₂²	1	4	yes	—
5	C₂×C₄×C₃⋊D₃	C₂²	1	2	yes	—
6	C₂×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₄⋊#157	—	2	4	no	—
8	C₃²×C₄²	C₄	1	1	yes	characteristic, complemented
9	C₄×C₃⋊Dic₃	C₄	1	1	yes	characteristic, complemented
10	C₄×C₃⋊Dic₃	C₄	1	2	yes	complemented
11	C₄²×D₃	—	6	2	no	—
12	C₂²×C₃⋊D₃	C₂³	1	1	yes	characteristic
13	C₂×#157	—	2	4	no	—
14	C₂×#157	—	2	8	no	—
15	C₂×C₃²×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
18	C₂×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₃⋊D₃	—	2	4	no	—
20	C₄×C₃⋊D₃	D₄	1	2	yes	—
21	C₄×C₃⋊D₃	Q₈	1	2	yes	—
22	#382	—	9	1	no	maximal, Sylow
23	C₂×C₄×D₃	—	6	2	no	—
24	C₂×C₄×D₃	—	6	4	no	—
25	C₃×C₄²	—	2	2	no	—
26	C₄×Dic₃	—	6	4	no	—
27	C₄×Dic₃	—	6	2	no	—
28	C₂²×C₃²	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃⋊D₃	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₃⋊D₃	#41	1	4	yes	—
32	#157	—	4	4	no	—
33	C₃²×C₄	—	2	2	no	—
34	C₃²×C₄	C₄⋊C₄	1	2	yes	—
35	C₃⋊Dic₃	—	2	2	no	—
36	C₃⋊Dic₃	C₄⋊C₄	1	2	yes	—
37	C₂×C₄⋊C₄	—	9	2	no	—
38	C₂×C₄²	—	9	1	no	—
39	#95	—	9	4	no	—
40	C₂²×D₃	—	6	2	no	—
41	C₂×C₃×C₄	—	2	4	no	—
42	C₂×C₃×C₄	—	2	2	no	—
43	C₂×Dic₃	—	6	2	no	—
44	C₂×Dic₃	—	6	4	no	—
45	C₄×D₃	—	6	4	no	—
46	C₄×D₃	—	6	4	no	—
47	C₄×D₃	—	6	16	no	—
48	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₃²	#117	1	2	yes	—
50	C₃⋊D₃	#124	1	2	yes	—
51	C₃⋊D₃	#125	1	2	yes	—
52	C₂²×C₄	—	9	1	no	—
53	C₂²×C₄	—	9	2	no	—
54	C₂²×C₄	—	9	4	no	—
55	C₄⋊C₄	—	18	4	no	—
56	C₄²	—	9	2	no	—
57	C₄²	—	9	1	no	—
58	C₄²	#157	1	1	yes	characteristic, complemented
59	C₂²×C₃	—	2	2	no	—
60	C₂×D₃	—	6	2	no	—
61	C₂×D₃	—	6	2	no	—
62	C₂×D₃	—	6	8	no	—
63	C₃×C₄	—	2	8	no	—
64	C₃×C₄	—	2	4	no	—
65	Dic₃	—	6	4	no	—
66	Dic₃	—	6	8	no	—
67	C₃²	#382	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	9	1	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	2	no	—
71	C₂×C₄	—	9	2	no	—
72	C₂×C₄	—	9	2	no	—
73	C₂×C₄	—	18	4	no	—
74	C₂×C₄	—	18	4	no	—
75	C₂×C₄	—	18	8	no	—
76	C₂×C₄	C₂×#157	1	2	yes	—
77	C₂×C₄	C₂×#157	1	1	yes	characteristic
78	C₂×C₃	—	2	2	no	—
79	C₂×C₃	—	2	4	no	—
80	D₃	—	6	4	no	—
81	D₃	—	6	4	no	—
82	C₂²	—	9	1	no	—
83	C₂²	—	9	1	no	—
84	C₂²	—	9	4	no	—
85	C₂²	C₂²×#157	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	9	2	no	—
88	C₄	—	18	2	no	—
89	C₄	—	36	4	no	—
90	C₄	C₄⋊#157	1	2	yes	—
91	C₃	—	2	2	no	—
92	C₂	—	9	2	no	—
93	C₂	—	9	2	no	—
94	C₂	C₂×C₄⋊#157	1	1	yes	characteristic
95	C₂	#64286	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#157
commutator, socle	C₂²×C₃²	C₂²×C₄
Fitting	C₃²×C₄²	C₄
prime radical, cosocle	C₂²×C₃⋊D₃	C₂³
hypercenter	C₄²	#157
hypocenter	C₃²	#382
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
8. C₃²×C₄²	C₄	semidirect
9. C₄×C₃⋊Dic₃	C₄	semidirect
10. C₄×C₃⋊Dic₃	C₄	semidirect
58. C₄²	#157	semidirect
67. C₃²	#382	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#157	2
C₄²×C₃⋊D₃	2
#63781	2
#382	9