Group #30599465 — subgroups

Subgroups — #30599465

Order 15616.

262 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 80 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	#21461744	C₂	1	1	yes	maximal, characteristic
2	#21461741	C₂	1	1	yes	maximal, characteristic
3	#21460673	C₂	1	4	yes	maximal
4	#21444104	C₂	1	1	yes	maximal, characteristic
5	#16840767	C₂²	1	2	yes	—
6	#16840706	C₂²	1	2	yes	—
7	#16840638	—	2	2	no	—
8	#16840636	—	2	2	no	—
9	#16839813	C₂²	1	2	yes	—
10	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	#16839483	C₄	1	1	yes	characteristic, complemented
12	C₈×#92418	C₄	1	2	yes	complemented
13	C₆₁×#322	C₄	1	1	yes	characteristic, complemented
14	C₂×#11758213	—	2	2	no	—
15	C₂×C₄⋊#6923	—	2	2	no	—
16	#14519844	—	2	4	no	—
17	(C₂×#6923)⋊C₄	—	2	4	no	—
18	C₂×C₈×D₆₁	D₄	1	2	yes	—
19	C₄²×D₆₁	C₂³	1	1	yes	characteristic
20	#14519706	—	2	2	no	—
21	#14519689	—	2	2	no	—
22	C₄×#92418	C₂×C₄	1	2	yes	—
23	C₄×#92418	C₂×C₄	1	1	yes	characteristic
24	C₈×Dic₆₁	Q₈	1	2	yes	—
25	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×#6923	—	4	2	no	—
28	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×D₆₁	#41	1	2	yes	—
30	C₂×#92420	—	4	2	no	—
31	C₄⋊#6923	—	4	4	no	—
32	#11758213	—	4	4	no	—
33	C₂×C₈×C₆₁	—	2	2	no	—
34	C₂×C₈×C₆₁	C₄⋊C₄	1	2	yes	—
35	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
37	C₄×Dic₆₁	#41	1	2	yes	—
38	C₂×#92418	—	2	2	no	—
39	C₂×#92418	C₄⋊C₄	1	2	yes	—
40	C₈×D₆₁	—	2	4	no	—
41	C₂²×D₆₁	#124	1	1	yes	characteristic
42	C₂×#6923	—	8	4	no	—
43	C₂×#6923	—	8	2	no	—
44	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₆₁	#117	1	2	yes	—
46	C₂×Dic₆₁	#124	1	1	yes	characteristic
47	C₂×Dic₆₁	#125	1	2	yes	—
48	C₄×D₆₁	—	4	2	no	—
49	C₄×D₆₁	#135	1	4	yes	—
50	#92420	—	8	2	no	—
51	C₈×C₆₁	—	2	2	no	—
52	C₈×C₆₁	—	4	2	no	—
53	#92418	—	2	2	no	—
54	#92418	—	4	2	no	—
55	#8791	—	61	1	no	maximal, Sylow
56	C₂²×C₆₁	#382	1	1	yes	characteristic
57	C₂×D₆₁	—	2	2	no	—
58	C₂×D₆₁	#488	1	2	yes	—
59	#6923	—	16	2	no	—
60	C₄×C₆₁	—	2	2	no	—
61	C₄×C₆₁	#427	1	2	yes	—
62	Dic₆₁	—	2	2	no	—
63	Dic₆₁	#488	1	2	yes	—
64	#1837	—	61	1	no	—
65	#1835	—	61	1	no	—
66	#1450	—	61	1	no	—
67	#1286	—	61	4	no	—
68	C₂×C₆₁	#1833	1	2	yes	—
69	C₂×C₆₁	#1835	1	1	yes	characteristic
70	D₆₁	—	2	2	no	—
71	#431	—	61	2	no	—
72	#423	—	61	2	no	—
73	C₂×C₄×C₈	—	61	1	no	—
74	#382	—	61	2	no	—
75	#341	—	122	2	no	—
76	#340	—	122	2	no	—
77	#322	—	61	1	no	—
78	#322	#6923	1	1	yes	characteristic, complemented
79	C₈²	—	61	2	no	—
80	C₆₁	#8791	1	1	yes	characteristic, complemented, Sylow
81	C₂×M₁₆	—	122	2	no	—
82	C₂²×C₈	—	61	2	no	—
83	C₂×C₄⋊C₄	—	122	2	no	—
84	C₂×C₄²	—	61	1	no	—
85	C₄⋊C₈	—	122	2	no	—
86	C₄⋊C₈	—	122	4	no	—
87	C₂²⋊C₈	—	122	2	no	—
88	C₄×C₈	—	61	2	no	—
89	C₄×C₈	—	61	1	no	—
90	C₄×C₈	—	61	2	no	—
91	C₄×C₈	C₂×#6923	1	2	yes	—
92	C₄×C₈	C₂×#6923	1	1	yes	characteristic
93	#95	—	122	4	no	—
94	C₂²×C₄	—	61	1	no	—
95	C₂²×C₄	—	61	2	no	—
96	C₂²×C₄	—	244	2	no	—
97	M₁₆	—	244	4	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	61	2	no	—
100	C₂×C₈	—	122	4	no	—
101	C₂×C₈	—	122	2	no	—
102	C₂×C₈	—	244	2	no	—
103	C₂×C₈	C₄⋊#6923	1	2	yes	—
104	C₄⋊C₄	—	244	4	no	—
105	C₄²	—	61	1	no	—
106	C₄²	—	61	2	no	—
107	C₄²	C₂²×#6923	1	1	yes	characteristic
108	C₂³	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	61	4	no	—
111	C₂×C₄	—	61	2	no	—
112	C₂×C₄	—	488	2	no	—
113	C₂×C₄	—	488	4	no	—
114	C₂×C₄	—	244	2	no	—
115	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
116	C₂×C₄	#14519856	1	2	yes	—
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	122	2	no	—
120	C₈	—	488	2	no	—
121	C₈	—	244	2	no	—
122	C₂²	—	61	2	no	—
123	C₂²	—	122	2	no	—
124	C₂²	#16840706	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	61	2	no	—
127	C₄	—	122	2	no	—
128	C₄	—	976	2	no	—
129	C₄	#16840772	1	2	yes	—
130	C₂	—	122	2	no	—
131	C₂	#21461739	1	2	yes	—
132	C₂	#21461741	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21461744

C₂

yes

maximal, characteristic

#21461741

C₂

yes

maximal, characteristic

#21460673

C₂

yes

maximal

#21444104

C₂

yes

maximal, characteristic

#16840767

C₂²

yes

—

#16840706

C₂²

yes

—

#16840638

—

#16840636

—

#16839813

C₂²

yes

—

C₄×C₈×D₆₁

C₂²

yes

characteristic

#16839483

C₄

yes

characteristic, complemented

C₈×#92418

C₄

yes

complemented

C₆₁×#322

C₄

yes

characteristic, complemented

C₂×#11758213

—

C₂×C₄⋊#6923

—

#14519844

—

(C₂×#6923)⋊C₄

—

C₂×C₈×D₆₁

D₄

yes

—

C₄²×D₆₁

C₂³

yes

—

—

C₂×C₄

yes

—

C₄×#92418

C₂×C₄

yes

characteristic

C₈×Dic₆₁

Q₈

yes

—

C₄×C₈×C₆₁

C₂×C₄

yes

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂²×#6923

—

C₂×C₄×D₆₁

C₂×D₄

yes

characteristic

C₂×C₄×D₆₁

#41

yes

—

C₂×#92420

—

C₄⋊#6923

—

#11758213

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₄⋊C₄

yes

—

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄×Dic₆₁

C₂×Q₈

yes

characteristic

C₄×Dic₆₁

#41

yes

—

C₂×#92418

—

C₂×#92418

C₄⋊C₄

yes

—

C₈×D₆₁

—

C₂²×D₆₁

yes

—

—

C₂×C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

#117

yes

—

C₂×Dic₆₁

#124

yes

characteristic

C₂×Dic₆₁

#125

yes

—

C₄×D₆₁

—

C₄×D₆₁

#135

yes

—

#92420

—

C₈×C₆₁

—

C₈×C₆₁

—

—

—

—

C₂²×C₆₁

yes

C₂×D₆₁

—

C₂×D₆₁

#488

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

#427

yes

—

Dic₆₁

—

Dic₆₁

#488

yes

—

—

—

—

—

C₂×C₆₁

#1833

yes

—

C₂×C₆₁

#1835

yes

characteristic

D₆₁

—

#431

—

#423

—

C₂×C₄×C₈

—

#382

—

#341

—

122

—

#340

—

122

—

#322

—

#322

#6923

yes

characteristic, complemented

C₈²

—

C₆₁

#8791

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#6923

yes

—

C₄×C₈

C₂×#6923

yes

characteristic

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

244

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

122

—

101

C₂×C₈

—

122

—

102

C₂×C₈

—

244

—

103

C₂×C₈

C₄⋊#6923

yes

—

104

C₄⋊C₄

—

244

—

105

C₄²

—

106

C₄²

—

107

C₄²

C₂²×#6923

yes

characteristic

108

C₂³

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

488

—

113

C₂×C₄

—

488

—

114

C₂×C₄

—

244

—

115

C₂×C₄

C₂×C₄⋊#6923

yes

characteristic

116

C₂×C₄

#14519856

yes

—

117

C₈

—

118

C₈

—

119

C₈

—

122

—

120

C₈

—

488

—

121

C₈

—

244

—

122

C₂²

—

123

C₂²

—

122

—

124

C₂²

#16840706

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

122

—

128

C₄

—

976

—

129

C₄

#16840772

yes

—

130

C₂

—

122

—

131

C₂

#21461739

yes

—

132

C₂

#21461741

yes

characteristic

	subgroup	G/H
center	C₂²	#16840706
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×#6923
Fitting	C₆₁×#322	C₄
socle	C₂²×C₆₁	#382
prime radical	C₂²×D₆₁	#124
cosocle	C₄²×D₆₁	C₂³
hypercenter	#322	#6923
hypocenter	C₆₁	#8791
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#16840706

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×#6923

Fitting

C₆₁×#322

C₄

C₂²×C₆₁

C₂²×D₆₁

C₄²×D₆₁

C₂³

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
11. #16839483	C₄	semidirect
12. C₈×#92418	C₄	semidirect
13. C₆₁×#322	C₄	semidirect
78. #322	#6923	semidirect
80. C₆₁	#8791	semidirect

H ≅ G/N

type

11. #16839483

C₄

semidirect

12. C₈×#92418

C₄

semidirect

13. C₆₁×#322

C₄

semidirect

78. #322

#6923

semidirect

80. C₆₁

#8791

semidirect

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

subgroup	index
#21461744	2
#21461741	2
#21460673	2
#21444104	2
#8791	61

subgroup

index

Subgroups — #30599465

Conjugacy classes of subgroups

Complements

Maximal subgroups