Group #25249188 — subgroups

Subgroups — #25249188

Order 11008.

806 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 331 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×#14583301	C₂	1	4	yes	maximal
2	#19142958	C₂	1	2	yes	maximal
3	#19134763	C₂	1	8	yes	maximal
4	C₄×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063317	C₂²	1	4	yes	—
6	#14583301	—	2	16	no	—
7	C₂×#13063259	C₂²	1	8	yes	—
8	C₂×#13063257	C₂²	1	8	yes	—
9	#14582797	—	2	8	no	—
10	#14582769	C₂²	1	4	yes	—
11	#14582765	C₂²	1	4	yes	—
12	C₂×#97×C₄₃	C₂²	1	4	yes	—
13	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
14	C₄³×C₄₃	C₂²	1	1	yes	characteristic
15	#13063317	—	2	16	no	—
16	C₂×C₄⋊Dic₄₃	—	2	8	no	—
17	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
18	C₂×Dic₄₃⋊C₄	—	2	8	no	—
19	#13063259	—	2	16	no	—
20	#13063257	—	2	16	no	—
21	C₄₃⋊#95	—	2	8	no	—
22	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
23	C₂×C₄²×C₄₃	D₄	1	4	yes	—
24	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
26	#97×C₄₃	Q₈	1	16	yes	—
27	C₄×C₈×C₄₃	D₄	1	8	yes	—
28	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
30	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂²×Dic₄₃	—	2	8	no	—
32	C₂×C₈×C₄₃	C₂×D₄	1	8	yes	—
33	C₂×C₈×C₄₃	C₂×Q₈	1	16	yes	—
34	C₄²×C₄₃	—	4	4	no	—
35	C₄²×C₄₃	C₂×D₄	1	4	yes	—
36	C₄²×C₄₃	C₂×Q₈	1	8	yes	—
37	C₄⋊Dic₄₃	—	2	16	no	—
38	C₄⋊Dic₄₃	—	4	16	no	—
39	Dic₄₃⋊C₄	—	4	16	no	—
40	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	8	no	—
42	C₂×C₄×C₄₃	—	2	4	no	—
43	C₂×C₄×C₄₃	#127	1	4	yes	—
44	C₂×C₄×C₄₃	C₄⋊Q₈	1	8	yes	—
45	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
47	C₂×Dic₄₃	—	4	8	no	—
48	C₂×Dic₄₃	—	4	16	no	—
49	C₈×C₄₃	C₄⋊Q₈	1	16	yes	—
50	#33315	—	43	1	no	maximal, Sylow
51	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
52	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
53	C₂²×C₄₃	#575	1	4	yes	—
54	C₄×C₄₃	—	2	4	no	—
55	C₄×C₄₃	—	2	8	no	—
56	C₄×C₄₃	C₂×C₄⋊Q₈	1	4	yes	—
57	Dic₄₃	—	8	8	no	—
58	C₂×#499	—	43	4	no	—
59	#2859	—	43	2	no	—
60	#1847	—	43	8	no	—
61	C₄×#97	D₄₃	1	1	yes	characteristic
62	C₂×C₄₃	#2868	1	1	yes	characteristic
63	C₂×C₄₃	#3150	1	2	yes	—
64	C₂×C₄₃	#3166	1	4	yes	—
65	C₂×#125	—	43	4	no	—
66	#499	—	86	16	no	—
67	C₂×#107	—	43	8	no	—
68	C₂×#106	—	43	8	no	—
69	C₂×#97	C₂×D₄₃	1	4	yes	—
70	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
71	#389	—	86	8	no	—
72	#384	—	43	4	no	—
73	#382	—	43	4	no	—
74	C₄³	C₂×D₄₃	1	1	yes	characteristic
75	C₄₃	#33315	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
77	#125	—	86	16	no	—
78	C₂×C₄⋊C₄	—	43	8	no	—
79	C₂×C₄⋊C₄	—	86	8	no	—
80	C₂×C₄⋊C₄	—	86	8	no	—
81	C₂×C₄²	D₁₇₂	1	4	yes	—
82	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
83	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
84	#107	—	86	16	no	—
85	#106	—	86	16	no	—
86	#97	Dic₈₆	1	16	yes	—
87	C₄×C₈	D₁₇₂	1	8	yes	—
88	#95	—	86	8	no	—
89	C₂²×C₄	—	86	8	no	—
90	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
91	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
92	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
93	C₂×C₈	C₂×Dic₈₆	1	16	yes	—
94	C₂×C₈	C₂×D₁₇₂	1	8	yes	—
95	C₄⋊C₄	—	86	16	no	—
96	C₄⋊C₄	—	172	16	no	—
97	C₄⋊C₄	—	172	16	no	—
98	C₄²	—	4	4	no	—
99	C₄²	C₂×Dic₈₆	1	8	yes	—
100	C₄²	C₂×D₁₇₂	1	4	yes	—
101	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	172	8	no	—
105	C₂×C₄	—	172	16	no	—
106	C₂×C₄	#13063322	1	4	yes	—
107	C₂×C₄	#13063325	1	8	yes	—
108	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
109	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
110	C₈	#13063325	1	16	yes	—
111	C₂²	C₂×#13063322	1	1	yes	characteristic
112	C₂²	C₂×#13063325	1	2	yes	—
113	C₂²	#14583699	1	4	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	2	8	no	—
116	C₄	—	344	8	no	—
117	C₄	C₂×#13063325	1	4	yes	—
118	C₂	#19142993	1	1	yes	characteristic
119	C₂	#19145041	1	2	yes	—
120	C₂	#19145147	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583301

C₂

yes

maximal

#19142958

C₂

yes

maximal

#19134763

C₂

yes

maximal

C₄×#97×C₄₃

C₂

yes

maximal, characteristic

C₂×#13063317

C₂²

yes

—

#14583301

—

C₂×#13063259

C₂²

yes

—

C₂×#13063257

C₂²

yes

—

#14582797

—

#14582769

C₂²

yes

—

#14582765

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

#13063317

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×Dic₄₃⋊C₄

—

#13063259

—

#13063257

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

—

#97×C₄₃

Q₈

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#127

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×D₄

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

C₄⋊Q₈

yes

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

—

C₂²×C₄₃

#575

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊Q₈

yes

—

Dic₄₃

—

C₂×#499

—

#2859

—

#1847

—

C₄×#97

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#3166

yes

—

—

—

—

—

C₂×#97

C₂×D₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

#389

—

#384

—

#382

—

C₄³

C₂×D₄₃

yes

characteristic

C₄₃

#33315

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂²×D₄₃

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

D₁₇₂

yes

—

C₂×C₄²

C₂²×D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

—

—

Dic₈₆

yes

—

C₄×C₈

D₁₇₂

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂²×C₄

C₂³×D₄₃

yes

characteristic

C₂×C₈

C₂×Dic₈₆

yes

—

C₂×C₈

C₂×D₁₇₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

C₂×Dic₈₆

yes

—

100

C₄²

C₂×D₁₇₂

yes

—

101

C₂³

C₂²×D₁₇₂

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

172

—

105

C₂×C₄

—

172

—

106

C₂×C₄

#13063322

yes

—

107

C₂×C₄

#13063325

yes

—

108

C₂×C₄

C₂²×D₁₇₂

yes

—

109

C₂×C₄

C₂²×Dic₈₆

yes

—

110

C₈

#13063325

yes

—

111

C₂²

C₂×#13063322

yes

characteristic

112

C₂²

C₂×#13063325

yes

—

113

C₂²

#14583699

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

344

—

117

C₄

C₂×#13063325

yes

—

118

C₂

#19142993

yes

characteristic

119

C₂

#19145041

yes

—

120

C₂

#19145147

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#97×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	C₄×#97	D₄₃
hypocenter	C₄₃	#33315
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

subgroup

G/H

center

C₂³

C₂²×D₁₇₂

commutator, cosocle

C₂²×C₄×C₄₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄×#97×C₄₃

C₂

socle, prime radical

C₂³×C₄₃

C₂²×D₄

hypercenter

C₄×#97

D₄₃

hypocenter

C₄₃

#33315

LCS

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
75. C₄₃	#33315	semidirect

H ≅ G/N

type

75. C₄₃

#33315

semidirect

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

subgroup	index
C₂×#14583301	2
#19142958	2
#19134763	2
C₄×#97×C₄₃	2
#33315	43

subgroup

index

C₄×#97×C₄₃

Subgroups — #25249188

Conjugacy classes of subgroups

Complements

Maximal subgroups