Group #25001093 — subgroups

Subgroups — #25001093

Order 11008.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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	#19134764	C₂	1	3	yes	maximal
2	#19132476	C₂	1	3	yes	maximal
3	C₄₃×#2844	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063258	—	2	3	no	—
5	C₂×#13063256	—	2	3	no	—
6	C₂×#13063236	C₂²	1	3	yes	—
7	#14582769	C₂²	1	1	yes	characteristic
8	C₄₃×#400	—	2	3	no	—
9	C₄₃×#395	—	2	3	no	—
10	C₄₃×#382	C₂²	1	3	yes	—
11	C₂²×C₄₃⋊C₈	—	2	3	no	—
12	C₂×C₄⋊Dic₄₃	—	2	3	no	—
13	#13063258	—	4	6	no	—
14	#13063256	—	4	6	no	—
15	#13063236	—	2	3	no	—
16	#13063236	Q₈	1	6	yes	complemented
17	C₂²×Q₈×C₄₃	—	2	1	no	—
18	C₂×C₄⋊C₄×C₄₃	—	2	3	no	—
19	C₂×C₄⋊C₄×C₄₃	D₄	1	3	yes	—
20	C₂×C₄⋊C₄×C₄₃	D₄	1	3	yes	—
21	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	#95×C₄₃	—	2	3	no	—
23	#95×C₄₃	—	2	1	no	—
24	#95×C₄₃	—	2	6	no	—
25	C₂×Q₈×C₄₃	—	8	3	no	—
26	C₂²×C₄×C₄₃	—	2	3	no	—
27	C₂²×C₄×C₄₃	—	2	3	no	—
28	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
29	C₂²×Dic₄₃	—	4	1	no	—
30	C₄⋊C₄×C₄₃	—	4	3	no	—
31	C₄⋊C₄×C₄₃	—	4	3	no	—
32	C₄⋊C₄×C₄₃	—	8	3	no	—
33	C₄²×C₄₃	C₂×Q₈	1	3	yes	—
34	C₄²×C₄₃	#41	1	1	yes	characteristic
35	C₄⋊Dic₄₃	—	4	3	no	—
36	C₄⋊Dic₄₃	—	4	3	no	—
37	C₂×C₄₃⋊C₈	—	2	6	no	—
38	C₂×C₄₃⋊C₈	—	2	6	no	—
39	C₂×C₄₃⋊C₈	—	2	6	no	—
40	C₂³×C₄₃	#120	1	1	yes	characteristic
41	Q₈×C₄₃	—	8	4	no	—
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	—	4	3	no	—
45	C₂×C₄×C₄₃	—	4	3	no	—
46	C₂×C₄×C₄₃	—	4	6	no	—
47	C₂×C₄×C₄₃	—	4	6	no	—
48	C₂×C₄×C₄₃	C₂²⋊Q₈	1	3	yes	—
49	C₂×C₄×C₄₃	C₄⋊Q₈	1	3	yes	—
50	C₂×Dic₄₃	—	8	3	no	—
51	C₄₃⋊C₈	—	2	12	no	—
52	#10583	—	43	1	no	maximal, Sylow
53	C₂²×C₄₃	#395	1	1	yes	characteristic
54	C₂²×C₄₃	#453	1	3	yes	—
55	C₂²×C₄₃	#456	1	3	yes	—
56	C₄×C₄₃	—	2	3	no	—
57	C₄×C₄₃	—	2	3	no	—
58	C₄×C₄₃	—	8	3	no	—
59	C₄×C₄₃	—	8	3	no	—
60	Dic₄₃	—	16	1	no	—
61	#2844	D₄₃	1	1	yes	characteristic
62	#1847	—	43	3	no	—
63	#1295	—	43	3	no	—
64	C₂×C₄₃	#1655	1	1	yes	characteristic
65	C₂×C₄₃	#1660	1	3	yes	—
66	C₂×C₄₃	#2060	1	3	yes	—
67	C₂×#107	—	86	3	no	—
68	C₂×#106	—	86	3	no	—
69	C₂×#97	—	43	3	no	—
70	#400	—	2	3	no	—
71	#395	—	2	3	no	—
72	#384	—	43	1	no	—
73	#382	C₂×D₄₃	1	3	yes	—
74	C₄₃	#10583	1	1	yes	characteristic, complemented, Sylow
75	C₂²×Q₈	—	2	1	no	—
76	C₂²×C₈	—	86	3	no	—
77	C₂×C₄⋊C₄	—	2	3	no	—
78	C₂×C₄⋊C₄	—	86	3	no	—
79	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	3	yes	—
80	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	3	yes	—
81	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
82	#107	—	172	6	no	—
83	#106	—	172	6	no	—
84	#97	—	43	6	no	—
85	#97	—	86	3	no	—
86	#95	—	2	3	no	—
87	#95	—	2	1	no	—
88	#95	—	2	6	no	—
89	C₂×Q₈	—	8	3	no	—
90	C₂²×C₄	—	2	3	no	—
91	C₂²×C₄	—	2	3	no	—
92	C₂²×C₄	—	172	1	no	—
93	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
94	C₂×C₈	—	86	6	no	—
95	C₂×C₈	—	86	6	no	—
96	C₂×C₈	—	86	6	no	—
97	C₄⋊C₄	—	4	3	no	—
98	C₄⋊C₄	—	4	3	no	—
99	C₄⋊C₄	—	8	3	no	—
100	C₄⋊C₄	—	172	3	no	—
101	C₄⋊C₄	—	172	3	no	—
102	C₄²	Q₈×D₄₃	1	3	yes	—
103	C₄²	#10621902	1	1	yes	characteristic
104	C₂³	#13063294	1	1	yes	characteristic
105	Q₈	—	8	4	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	4	3	no	—
109	C₂×C₄	—	4	3	no	—
110	C₂×C₄	—	4	6	no	—
111	C₂×C₄	—	4	6	no	—
112	C₂×C₄	—	344	3	no	—
113	C₂×C₄	#13063301	1	3	yes	—
114	C₂×C₄	#13063323	1	3	yes	—
115	C₈	—	86	12	no	—
116	C₂²	#14582818	1	1	yes	characteristic
117	C₂²	#14583067	1	3	yes	—
118	C₂²	#14583082	1	3	yes	—
119	C₄	—	2	3	no	—
120	C₄	—	2	3	no	—
121	C₄	—	8	3	no	—
122	C₄	—	8	3	no	—
123	C₄	—	688	1	no	—
124	C₂	#19133884	1	1	yes	characteristic
125	C₂	#19133906	1	3	yes	—
126	C₂	#19135937	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134764

C₂

yes

maximal

#19132476

C₂

yes

maximal

C₄₃×#2844

C₂

yes

maximal, characteristic

C₂×#13063258

—

C₂×#13063256

—

C₂×#13063236

C₂²

yes

—

#14582769

C₂²

yes

characteristic

C₄₃×#400

—

C₄₃×#395

—

C₄₃×#382

C₂²

yes

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

—

—

—

Q₈

yes

complemented

C₂²×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#456

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#2844

D₄₃

yes

characteristic

#1847

—

#1295

—

C₂×C₄₃

#1655

yes

characteristic

C₂×C₄₃

#1660

yes

—

C₂×C₄₃

#2060

yes

—

C₂×#107

—

C₂×#106

—

C₂×#97

—

—

—

—

C₂×D₄₃

yes

—

C₄₃

#10583

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#107

—

172

—

#106

—

172

—

—

—

—

—

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

172

—

101

C₄⋊C₄

—

172

—

102

C₄²

Q₈×D₄₃

yes

—

103

C₄²

#10621902

yes

characteristic

104

C₂³

#13063294

yes

characteristic

105

Q₈

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

344

—

113

C₂×C₄

#13063301

yes

—

114

C₂×C₄

#13063323

yes

—

115

C₈

—

116

C₂²

#14582818

yes

characteristic

117

C₂²

#14583067

yes

—

118

C₂²

#14583082

yes

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

688

—

124

C₂

#19133884

yes

characteristic

125

C₂

#19133906

yes

—

126

C₂

#19135937

yes

—

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2844	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#2844	D₄₃
hypocenter	C₄₃	#10583
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2844

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2844

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2844

N	H ≅ G/N	type
16. #13063236	Q₈	semidirect
74. C₄₃	#10583	semidirect

H ≅ G/N

type

16. #13063236

Q₈

semidirect

74. C₄₃

#10583

semidirect

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

subgroup	index
#19134764	2
#19132476	2
C₄₃×#2844	2
#10583	43

subgroup

index

#19134764

#19132476

C₄₃×#2844

#10583

Subgroups — #25001093

Conjugacy classes of subgroups

Complements

Maximal subgroups