Group #30603694 — subgroups

Subgroups — #30603694

Order 15616.

322 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14519852	C₂	1	2	yes	maximal
2	#21460732	C₂	1	4	yes	maximal, complemented
3	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14519852	C₄	1	4	yes	—
5	#16840651	C₄	1	4	yes	—
6	C₄×#11758187	C₂²	1	4	yes	—
7	C₄×C₈×D₆₁	C₄	1	2	yes	—
8	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
9	C₈×#92418	C₄	1	1	yes	characteristic
10	C₈×#92418	C₂²	1	2	yes	—
11	C₈²×C₆₁	C₄	1	1	yes	characteristic
12	#14519852	—	2	8	no	—
13	C₂×#11758187	C₂×C₄	1	8	yes	—
14	C₂×C₈×D₆₁	C₈	1	4	yes	—
15	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
16	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×#92418	C₂×C₄	1	2	yes	—
18	C₄×#92418	C₂³	1	1	yes	characteristic
19	C₈×Dic₆₁	C₈	1	4	yes	—
20	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
23	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
25	C₂×C₈×C₆₁	C₄²	1	2	yes	—
26	C₂×C₈×C₆₁	C₂×C₈	1	4	yes	—
27	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
30	C₂×#92418	C₂×C₈	1	4	yes	—
31	C₂×#92418	C₂²×C₄	1	2	yes	—
32	C₈×D₆₁	—	2	8	no	—
33	C₈×D₆₁	M₁₆	1	8	yes	—
34	#11758187	—	2	8	no	—
35	C₂²×D₆₁	C₄×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
38	C₂×Dic₆₁	C₄×C₈	1	2	yes	—
39	C₂×Dic₆₁	C₄×C₈	1	1	yes	characteristic
40	C₄×D₆₁	—	2	4	no	—
41	C₄×D₆₁	#97	1	4	yes	—
42	C₈×C₆₁	#97	1	4	yes	—
43	C₈×C₆₁	M₃₂	1	8	yes	complemented
44	#92418	—	2	4	no	—
45	#92418	C₂×M₁₆	1	4	yes	—
46	#11402	—	61	1	no	maximal, Sylow
47	C₂²×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂×D₆₁	—	2	2	no	—
49	C₂×D₆₁	#322	1	2	yes	—
50	C₄×C₆₁	C₂×#97	1	2	yes	—
51	C₄×C₆₁	C₂×M₃₂	1	4	yes	—
52	Dic₆₁	—	2	2	no	—
53	Dic₆₁	#322	1	2	yes	—
54	C₄×M₃₂	—	61	2	no	—
55	C₂×C₈²	—	61	1	no	—
56	#1312	—	61	4	no	—
57	C₂×C₆₁	C₂×#322	1	1	yes	characteristic
58	C₂×C₆₁	C₄×M₃₂	1	2	yes	—
59	D₆₁	—	2	2	no	—
60	C₂×M₃₂	—	61	4	no	—
61	C₂×C₄×C₈	—	61	2	no	—
62	C₂×C₄×C₈	—	61	1	no	—
63	#346	—	61	4	no	—
64	C₄×C₁₆	—	61	4	no	—
65	C₈²	—	61	2	no	—
66	C₈²	—	61	1	no	—
67	C₈²	#6923	1	1	yes	characteristic
68	C₆₁	#11402	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	61	2	no	—
70	C₂²×C₈	—	61	4	no	—
71	C₂×C₄²	—	61	1	no	—
72	M₃₂	—	122	8	no	—
73	C₂×C₁₆	—	61	8	no	—
74	C₄×C₈	—	61	4	no	—
75	C₄×C₈	—	61	2	no	—
76	C₄×C₈	—	61	1	no	—
77	C₄×C₈	—	61	2	no	—
78	C₄×C₈	C₂×#6923	1	2	yes	—
79	C₄×C₈	C₂×#6923	1	1	yes	characteristic
80	C₂²×C₄	—	61	1	no	—
81	C₂²×C₄	—	61	2	no	—
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	61	8	no	—
84	C₂×C₈	—	61	4	no	—
85	C₂×C₈	—	122	8	no	—
86	C₂×C₈	D₆₁⋊C₈	1	4	yes	—
87	C₂×C₈	C₄×#6923	1	2	yes	—
88	C₄²	—	61	1	no	—
89	C₄²	—	61	2	no	—
90	C₄²	C₂²×#6923	1	1	yes	characteristic
91	C₁₆	—	122	8	no	—
92	C₂³	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	4	no	—
95	C₂×C₄	—	61	2	no	—
96	C₂×C₄	—	122	4	no	—
97	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
98	C₂×C₄	C₂×D₆₁⋊C₈	1	2	yes	—
99	C₈	—	61	4	no	—
100	C₈	—	122	4	no	—
101	C₈	#14519831	1	4	yes	—
102	C₈	#14519852	1	8	yes	complemented
103	C₂²	—	61	2	no	—
104	C₂²	—	122	2	no	—
105	C₂²	C₄×D₆₁⋊C₈	1	1	yes	characteristic
106	C₄	—	61	2	no	—
107	C₄	—	122	2	no	—
108	C₄	C₂×#14519831	1	2	yes	—
109	C₄	C₂×#14519852	1	4	yes	—
110	C₂	—	122	2	no	—
111	C₂	#21461013	1	1	yes	characteristic
112	C₂	C₄×#14519852	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14519852

C₂

yes

maximal

#21460732

C₂

yes

maximal, complemented

C₈²×D₆₁

C₂

yes

maximal, characteristic

C₂×#14519852

C₄

yes

—

#16840651

C₄

yes

—

C₄×#11758187

C₂²

yes

—

C₄×C₈×D₆₁

C₄

yes

—

C₄×C₈×D₆₁

C₂²

yes

characteristic

C₈×#92418

C₄

yes

characteristic

C₈×#92418

C₂²

yes

—

C₈²×C₆₁

C₄

yes

characteristic

#14519852

—

C₂×#11758187

C₂×C₄

yes

—

C₂×C₈×D₆₁

C₈

yes

—

C₂×C₈×D₆₁

C₂×C₄

yes

—

C₄²×D₆₁

C₂×C₄

yes

characteristic

C₄×#92418

C₂×C₄

yes

—

C₄×#92418

C₂³

yes

characteristic

C₈×Dic₆₁

C₈

yes

—

C₈×Dic₆₁

C₂×C₄

yes

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₄²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₈

yes

—

C₂×C₈×C₆₁

C₄²

yes

—

C₂×C₈×C₆₁

C₂×C₈

yes

—

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄×Dic₆₁

C₄²

yes

characteristic

C₄×Dic₆₁

C₂×C₈

yes

—

C₂×#92418

C₂×C₈

yes

—

C₂×#92418

C₂²×C₄

yes

—

C₈×D₆₁

—

C₈×D₆₁

M₁₆

yes

—

#11758187

—

C₂²×D₆₁

C₄×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₈

yes

—

C₂×Dic₆₁

C₄×C₈

yes

—

C₂×Dic₆₁

C₄×C₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

#97

yes

—

C₈×C₆₁

#97

yes

—

C₈×C₆₁

M₃₂

yes

complemented

#92418

—

#92418

C₂×M₁₆

yes

—

#11402

—

maximal, Sylow

C₂²×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#322

yes

—

C₄×C₆₁

C₂×#97

yes

—

C₄×C₆₁

C₂×M₃₂

yes

—

Dic₆₁

—

Dic₆₁

#322

yes

—

C₄×M₃₂

—

C₂×C₈²

—

#1312

—

C₂×C₆₁

C₂×#322

yes

characteristic

C₂×C₆₁

C₄×M₃₂

yes

—

D₆₁

—

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₈²

—

C₈²

—

C₈²

#6923

yes

characteristic

C₆₁

#11402

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

122

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#6923

yes

—

C₄×C₈

C₂×#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

D₆₁⋊C₈

yes

—

C₂×C₈

C₄×#6923

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#6923

yes

characteristic

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×#6923

yes

characteristic

C₂×C₄

C₂×D₆₁⋊C₈

yes

—

C₈

—

100

C₈

—

122

—

101

C₈

#14519831

yes

—

102

C₈

#14519852

yes

complemented

103

C₂²

—

104

C₂²

—

122

—

105

C₂²

C₄×D₆₁⋊C₈

yes

characteristic

106

C₄

—

107

C₄

—

122

—

108

C₄

C₂×#14519831

yes

—

109

C₄

C₂×#14519852

yes

—

110

C₂

—

122

—

111

C₂

#21461013

yes

characteristic

112

C₂

C₄×#14519852

yes

—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄×C₈
Fitting	C₈²×C₆₁	C₄
prime radical	C₂²×D₆₁	C₄×C₈
cosocle	C₄×#92418	C₂³
hypercenter	C₈²	#6923
hypocenter	C₆₁	#11402
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₈²

subgroup

G/H

center, Frattini

C₄²

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂×C₄×C₈

Fitting

C₈²×C₆₁

C₄

prime radical

C₂²×D₆₁

C₄×C₈

C₂³

C₈²

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₄² ◁ C₈²

N	H ≅ G/N	type
2. #21460732	C₂	semidirect
43. C₈×C₆₁	M₃₂	semidirect
68. C₆₁	#11402	semidirect
102. C₈	#14519852	semidirect

H ≅ G/N

type

2. #21460732

C₂

semidirect

43. C₈×C₆₁

M₃₂

semidirect

68. C₆₁

#11402

semidirect

102. C₈

#14519852

semidirect

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

subgroup	index
C₄×#14519852	2
#21460732	2
C₈²×D₆₁	2
#11402	61

subgroup

index

C₄×#14519852

#21460732

C₈²×D₆₁

#11402

Subgroups — #30603694

Conjugacy classes of subgroups

Complements

Maximal subgroups