Group #44507494 — subgroups

Subgroups — #44507494

Order 30848.

252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₂×#21440650	C₂	1	1	yes	maximal, characteristic
2	C₂×#21440577	C₂	1	2	yes	maximal, complemented
3	#29507699	C₂	1	2	yes	maximal
4	#29507475	C₂	1	1	yes	maximal, characteristic, complemented
5	#338×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16838770	C₂²	1	1	yes	characteristic
7	#21440650	—	2	4	no	—
8	C₂×#16838754	C₂²	1	2	yes	—
9	C₂×#16838753	C₄	1	2	yes	—
10	C₂²×#14515349	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₂₄₁	C₄	1	2	yes	—
12	#21440577	—	2	4	no	—
13	#21440560	—	2	2	no	—
14	#21440558	—	2	2	no	—
15	C₂×M₁₆×C₂₄₁	C₂²	1	2	yes	—
16	C₂×M₁₆×C₂₄₁	C₂²	1	1	yes	characteristic
17	#16838770	—	2	2	no	—
18	#16838770	—	2	2	no	—
19	C₂×Dic₄₈₂	D₄	1	1	yes	characteristic
20	C₂×D₉₆₄	D₄	1	1	yes	characteristic
21	C₂×C₂²⋊D₂₄₁	Q₈	1	2	yes	—
22	C₂×C₄×D₂₄₁	C₂×C₄	1	2	yes	—
23	#16838754	—	2	2	no	—
24	#16838754	—	2	2	no	—
25	#16838753	—	2	4	no	—
26	C₂×#14515349	—	2	2	no	—
27	C₂×#14515349	C₂×C₄	1	1	yes	characteristic
28	C₂×#14515349	C₂×C₄	1	1	yes	characteristic
29	C₂×#14515349	D₄	1	4	yes	—
30	C₈×D₂₄₁	—	2	4	no	—
31	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
32	M₁₆×C₂₄₁	—	2	2	no	—
33	M₁₆×C₂₄₁	—	2	2	no	—
34	M₁₆×C₂₄₁	—	2	2	no	—
35	C₂×C₈×C₂₄₁	—	2	2	no	—
36	C₂×C₈×C₂₄₁	C₂×C₄	1	2	yes	—
37	C₂²×D₂₄₁	C₄⋊C₄	1	2	yes	—
38	Dic₄₈₂	—	2	2	no	—
39	D₉₆₄	—	2	2	no	—
40	C₂²⋊D₂₄₁	—	2	4	no	—
41	C₂×Dic₂₄₁	C₄⋊C₄	1	2	yes	—
42	C₄×D₂₄₁	—	2	2	no	—
43	C₄×D₂₄₁	—	2	2	no	—
44	#14515349	—	4	2	no	—
45	#14515349	C₂²⋊C₄	1	2	yes	—
46	#14515349	C₂²⋊C₄	1	2	yes	—
47	C₂³×C₂₄₁	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₂₄₁	#41	1	2	yes	—
52	C₈×C₂₄₁	—	2	2	no	—
53	C₈×C₂₄₁	—	4	2	no	—
54	C₂²×C₂₄₁	—	4	1	no	—
55	C₂²×C₂₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₂₄₁	C₂²⋊Q₈	1	2	yes	—
57	C₂×D₂₄₁	—	2	2	no	—
58	C₂×D₂₄₁	—	4	2	no	—
59	C₄×C₂₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₄×C₂₄₁	#117	1	1	yes	characteristic
61	C₄×C₂₄₁	#121	1	2	yes	—
62	Dic₂₄₁	—	2	2	no	—
63	C₂×C₂₄₁	—	2	1	no	—
64	C₂×C₂₄₁	—	2	2	no	—
65	C₂×C₂₄₁	#380	1	1	yes	characteristic
66	D₂₄₁	—	4	2	no	—
67	C₂₄₁	#1813	1	1	yes	characteristic, complemented, Sylow
68	#1813	—	241	1	no	maximal, Sylow
69	C₂×#131	—	241	1	no	—
70	C₂×#108	—	241	2	no	—
71	#413	—	241	2	no	—
72	#338	—	241	1	no	—
73	#338	D₂₄₁	1	1	yes	characteristic, complemented
74	C₂×#41	—	241	1	no	—
75	#131	—	482	4	no	—
76	C₂×M₁₆	—	241	2	no	—
77	C₂×M₁₆	—	241	2	no	—
78	C₂×M₁₆	C₂×D₂₄₁	1	2	yes	—
79	C₂×M₁₆	C₂×D₂₄₁	1	1	yes	characteristic
80	C₂²×C₈	—	241	2	no	—
81	C₂²×C₈	—	241	1	no	—
82	#108	—	482	4	no	—
83	#101	—	482	2	no	—
84	#100	—	482	2	no	—
85	#41	—	482	2	no	—
86	#41	—	482	2	no	—
87	C₂×Q₈	—	241	1	no	—
88	C₂×D₄	—	241	2	no	—
89	C₂×D₄	—	241	1	no	—
90	C₂²×C₄	—	241	2	no	—
91	C₂²×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
92	M₁₆	—	2	2	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	482	4	no	—
96	M₁₆	—	482	2	no	—
97	M₁₆	—	482	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	482	4	no	—
100	C₂×C₈	—	482	2	no	—
101	C₂×C₈	—	241	1	no	—
102	C₂×C₈	—	241	1	no	—
103	C₂×C₈	—	241	4	no	—
104	C₂×C₈	C₄×D₂₄₁	1	2	yes	—
105	C₂³	—	241	2	no	—
106	C₂³	Q₈×D₂₄₁	1	1	yes	characteristic
107	Q₈	—	482	2	no	—
108	D₄	—	482	4	no	—
109	D₄	—	482	2	no	—
110	C₂×C₄	—	482	2	no	—
111	C₂×C₄	—	482	2	no	—
112	C₂×C₄	—	241	2	no	—
113	C₂×C₄	C₂×C₄×D₂₄₁	1	1	yes	characteristic
114	C₂×C₄	D₄×D₂₄₁	1	2	yes	—
115	C₂×C₄	D₄×D₂₄₁	1	1	yes	characteristic
116	C₂×C₄	#16838770	1	2	yes	—
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	964	2	no	—
120	C₈	—	241	2	no	—
121	C₈	—	241	2	no	—
122	C₂²	—	4	1	no	—
123	C₂²	—	964	2	no	—
124	C₂²	—	482	2	no	—
125	C₂²	C₄⋊C₄×D₂₄₁	1	1	yes	characteristic
126	C₂²	#21440620	1	2	yes	—
127	C₄	—	482	2	no	—
128	C₄	C₂²⋊C₄×D₂₄₁	1	1	yes	characteristic
129	C₄	#21440599	1	1	yes	characteristic
130	C₄	#21440615	1	2	yes	—
131	C₂	—	2	1	no	—
132	C₂	—	2	2	no	—
133	C₂	—	964	2	no	—
134	C₂	#29507576	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#21440650

C₂

yes

maximal, characteristic

C₂×#21440577

C₂

yes

maximal, complemented

#29507699

C₂

yes

maximal

#29507475

C₂

yes

maximal, characteristic, complemented

#338×C₂₄₁

C₂

yes

maximal, characteristic, complemented

C₂×#16838770

C₂²

yes

characteristic

#21440650

—

C₂×#16838754

C₂²

yes

—

C₂×#16838753

C₄

yes

—

C₂²×#14515349

C₂²

yes

characteristic

C₂×C₈×D₂₄₁

C₄

yes

—

#21440577

—

#21440560

—

#21440558

—

C₂×M₁₆×C₂₄₁

C₂²

yes

—

C₂×M₁₆×C₂₄₁

C₂²

yes

characteristic

#16838770

—

#16838770

—

C₂×Dic₄₈₂

D₄

yes

characteristic

C₂×D₉₆₄

D₄

yes

characteristic

C₂×C₂²⋊D₂₄₁

Q₈

yes

—

C₂×C₄×D₂₄₁

C₂×C₄

yes

—

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#14515349

C₂×C₄

yes

characteristic

C₂×#14515349

D₄

yes

—

C₈×D₂₄₁

—

C₂²×C₄×C₂₄₁

C₂³

yes

characteristic

M₁₆×C₂₄₁

—

M₁₆×C₂₄₁

—

M₁₆×C₂₄₁

—

C₂×C₈×C₂₄₁

—

C₂×C₈×C₂₄₁

C₂×C₄

yes

—

C₂²×D₂₄₁

C₄⋊C₄

yes

—

Dic₄₈₂

—

D₉₆₄

—

C₂²⋊D₂₄₁

—

C₂×Dic₂₄₁

C₄⋊C₄

yes

—

C₄×D₂₄₁

—

C₄×D₂₄₁

—

#14515349

—

#14515349

C₂²⋊C₄

yes

—

#14515349

C₂²⋊C₄

yes

—

C₂³×C₂₄₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₄₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₄₁

C₂×D₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₄₁

#41

yes

—

C₈×C₂₄₁

—

C₈×C₂₄₁

—

C₂²×C₂₄₁

—

C₂²×C₂₄₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₄₁

C₂²⋊Q₈

yes

—

C₂×D₂₄₁

—

C₂×D₂₄₁

—

C₄×C₂₄₁

C₂×C₂²⋊C₄

yes

C₄×C₂₄₁

yes

C₄×C₂₄₁

yes

—

Dic₂₄₁

—

C₂×C₂₄₁

—

C₂×C₂₄₁

—

C₂×C₂₄₁

#380

yes

characteristic

D₂₄₁

—

C₂₄₁

#1813

yes

characteristic, complemented, Sylow

#1813

—

241

maximal, Sylow

C₂×#131

—

241

—

C₂×#108

—

241

—

#413

—

241

—

#338

—

241

—

#338

D₂₄₁

yes

characteristic, complemented

C₂×#41

—

241

—

#131

—

482

—

C₂×M₁₆

—

241

—

C₂×M₁₆

—

241

—

C₂×M₁₆

C₂×D₂₄₁

yes

—

C₂×M₁₆

C₂×D₂₄₁

yes

characteristic

C₂²×C₈

—

241

—

C₂²×C₈

—

241

—

#108

—

482

—

#101

—

482

—

#100

—

482

—

#41

—

482

—

#41

—

482

—

C₂×Q₈

—

241

—

C₂×D₄

—

241

—

C₂×D₄

—

241

—

C₂²×C₄

—

241

—

C₂²×C₄

C₂²×D₂₄₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

482

—

M₁₆

—

482

—

M₁₆

—

482

—

C₂×C₈

—

C₂×C₈

—

482

—

100

C₂×C₈

—

482

—

101

C₂×C₈

—

241

—

102

C₂×C₈

—

241

—

103

C₂×C₈

—

241

—

104

C₂×C₈

C₄×D₂₄₁

yes

—

105

C₂³

—

241

—

106

C₂³

Q₈×D₂₄₁

yes

characteristic

107

Q₈

—

482

—

108

D₄

—

482

—

109

D₄

—

482

—

110

C₂×C₄

—

482

—

111

C₂×C₄

—

482

—

112

C₂×C₄

—

241

—

113

C₂×C₄

C₂×C₄×D₂₄₁

yes

characteristic

114

C₂×C₄

D₄×D₂₄₁

yes

—

115

C₂×C₄

D₄×D₂₄₁

yes

characteristic

116

C₂×C₄

#16838770

yes

—

117

C₈

—

118

C₈

—

119

C₈

—

964

—

120

C₈

—

241

—

121

C₈

—

241

—

122

C₂²

—

123

C₂²

—

964

—

124

C₂²

—

482

—

125

C₂²

C₄⋊C₄×D₂₄₁

yes

characteristic

126

C₂²

#21440620

yes

—

127

C₄

—

482

—

128

C₄

C₂²⋊C₄×D₂₄₁

yes

characteristic

129

C₄

#21440599

yes

characteristic

130

C₄

#21440615

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

964

—

134

C₂

#29507576

yes

characteristic

	subgroup	G/H
center	C₄	#21440599
commutator	C₂×C₄×C₂₄₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₄₁
Fitting	#338×C₂₄₁	C₂
socle	C₂×C₂₄₁	#380
prime radical	C₂×#16838770	C₂²
cosocle	C₂²×C₄×C₂₄₁	C₂³
hypercenter	#338	D₂₄₁
hypocenter	C₂₄₁	#1813
LCS	G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#21440599

commutator

C₂×C₄×C₂₄₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₄₁

Fitting

#338×C₂₄₁

C₂

C₂×C₂₄₁

C₂²

C₂²×C₄×C₂₄₁

C₂³

D₂₄₁

C₂₄₁

G ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
2. C₂×#21440577	C₂	semidirect
4. #29507475	C₂	semidirect
5. #338×C₂₄₁	C₂	semidirect
67. C₂₄₁	#1813	semidirect
73. #338	D₂₄₁	semidirect

H ≅ G/N

type

2. C₂×#21440577

C₂

semidirect

4. #29507475

C₂

semidirect

5. #338×C₂₄₁

C₂

semidirect

67. C₂₄₁

#1813

semidirect

73. #338

D₂₄₁

semidirect

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

subgroup	index
C₂×#21440650	2
C₂×#21440577	2
#29507699	2
#29507475	2
#338×C₂₄₁	2
#1813	241

subgroup

index

#338×C₂₄₁

241

Subgroups — #44507494

Conjugacy classes of subgroups

Complements

Maximal subgroups