Group #25012980 — subgroups

Subgroups — #25012980

Order 11008.

310 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 163 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	#19134759	C₂	1	2	yes	maximal
2	#19132687	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063259	C₂²	1	4	yes	—
5	C₂×#13063257	—	2	2	no	—
6	#14582765	—	2	2	no	—
7	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₆×C₄₃	C₄	1	4	yes	complemented
10	C₂×C₄⋊Dic₄₃	—	2	4	no	—
11	#13063259	—	2	8	no	—
12	#13063257	—	4	4	no	—
13	C₄₃⋊#95	—	4	4	no	—
14	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	—	2	4	no	—
18	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₄₃	Q₈	1	2	yes	—
21	C₂²×C₄×C₄₃	D₈	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
23	C₂²×Dic₄₃	—	4	4	no	—
24	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
26	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₈×C₄₃	#41	1	4	yes	—
29	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
30	C₄²×C₄₃	Q₁₆	1	2	yes	—
31	C₄⋊Dic₄₃	—	4	4	no	—
32	C₄⋊Dic₄₃	—	4	4	no	—
33	C₁₆×C₄₃	—	2	4	no	—
34	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	#107	1	4	yes	—
37	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#124	1	2	yes	—
39	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
40	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
41	C₂×Dic₄₃	—	8	4	no	—
42	C₂×Dic₄₃	—	8	8	no	—
43	C₈×C₄₃	#106	1	4	yes	—
44	C₈×C₄₃	#117	1	2	yes	—
45	C₈×C₄₃	#125	1	2	yes	—
46	#12889	—	43	1	no	maximal, Sylow
47	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
48	C₂²×C₄₃	#486	1	2	yes	—
49	C₂²×C₄₃	#508	1	4	yes	—
50	C₄×C₄₃	—	2	4	no	—
51	C₄×C₄₃	#382	1	1	yes	characteristic
52	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
53	C₄×C₄₃	#487	1	2	yes	—
54	Dic₄₃	—	16	4	no	—
55	C₂×C₄×C₁₆	D₄₃	1	1	yes	characteristic
56	#1846	—	43	2	no	—
57	#1380	—	43	4	no	—
58	C₂×C₄₃	#1834	1	1	yes	characteristic
59	C₂×C₄₃	#2158	1	2	yes	—
60	C₂×C₄₃	#2242	1	4	yes	—
61	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
62	C₂×#107	—	43	4	no	—
63	C₂×#106	—	86	2	no	—
64	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	#382	—	86	2	no	—
66	C₄×C₁₆	Dic₄₃	1	4	yes	complemented
67	C₄₃	#12889	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
69	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
70	C₂×C₄⋊C₄	—	86	4	no	—
71	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
72	C₂×C₁₆	—	2	4	no	—
73	C₂×C₁₆	C₂×Dic₄₃	1	4	yes	—
74	#107	—	86	8	no	—
75	#106	—	172	4	no	—
76	C₄×C₈	Dic₈₆	1	2	yes	—
77	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
78	#95	—	172	4	no	—
79	C₂²×C₄	—	172	4	no	—
80	C₂²×C₄	D₃₄₄	1	2	yes	—
81	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
82	C₂×C₈	#10621873	1	4	yes	—
83	C₂×C₈	C₄⋊Dic₄₃	1	2	yes	—
84	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
85	C₂×C₈	#10621898	1	4	yes	—
86	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
87	C₄⋊C₄	—	172	4	no	—
88	C₄⋊C₄	—	172	4	no	—
89	C₄²	Dic₁₇₂	1	2	yes	—
90	C₄²	C₄⋊Dic₄₃	1	2	yes	—
91	C₁₆	—	2	4	no	—
92	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	344	8	no	—
95	C₂×C₄	—	344	4	no	—
96	C₂×C₄	#13063259	1	4	yes	—
97	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
98	C₂×C₄	#13063313	1	2	yes	—
99	C₂×C₄	C₂×#10621873	1	2	yes	—
100	C₂×C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
101	C₈	#13063257	1	4	yes	—
102	C₈	#13063284	1	2	yes	—
103	C₈	#13063317	1	2	yes	—
104	C₂²	C₂×#13063259	1	1	yes	characteristic
105	C₂²	#14583246	1	2	yes	—
106	C₂²	#14583331	1	4	yes	—
107	C₄	—	2	4	no	—
108	C₄	—	688	4	no	—
109	C₄	#14582765	1	1	yes	characteristic
110	C₄	C₂×#13063257	1	1	yes	characteristic
111	C₄	#14583250	1	2	yes	—
112	C₂	#19134723	1	1	yes	characteristic
113	C₂	#19136379	1	2	yes	—
114	C₂	#19136827	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134759

C₂

yes

maximal

#19132687

C₂

yes

maximal

C₂×C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂×#13063259

C₂²

yes

—

C₂×#13063257

—

#14582765

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₁₆×C₄₃

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

—

#13063259

—

#13063257

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

D₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₃

#41

yes

—

C₄²×C₄₃

C₄⋊C₄

yes

—

C₄²×C₄₃

Q₁₆

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#107

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

#106

yes

—

C₈×C₄₃

#117

yes

—

C₈×C₄₃

#125

yes

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#508

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

C₂×C₄×C₁₆

D₄₃

yes

characteristic

#1846

—

#1380

—

C₂×C₄₃

#1834

yes

characteristic

C₂×C₄₃

#2158

yes

—

C₂×C₄₃

#2242

yes

—

C₂²×C₁₆

C₂×D₄₃

yes

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#382

—

C₄×C₁₆

Dic₄₃

yes

complemented

C₄₃

#12889

yes

characteristic, complemented, Sylow

C₂²×C₈

D₁₇₂

yes

characteristic

C₂²×C₈

C₂²×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₄₃

yes

—

#107

—

#106

—

172

—

C₄×C₈

Dic₈₆

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

#95

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

D₃₄₄

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₈

#10621873

yes

—

C₂×C₈

C₄⋊Dic₄₃

yes

—

C₂×C₈

C₂×Dic₈₆

yes

characteristic

C₂×C₈

#10621898

yes

—

C₂×C₈

C₂²×Dic₄₃

yes

characteristic

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

Dic₁₇₂

yes

—

C₄²

C₄⋊Dic₄₃

yes

—

C₁₆

—

C₂³

C₂×D₃₄₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

344

—

C₂×C₄

#13063259

yes

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

#13063313

yes

—

C₂×C₄

C₂×#10621873

yes

—

100

C₂×C₄

C₂×Dic₁₇₂

yes

characteristic

101

C₈

#13063257

yes

—

102

C₈

#13063284

yes

—

103

C₈

#13063317

yes

—

104

C₂²

C₂×#13063259

yes

characteristic

105

C₂²

#14583246

yes

—

106

C₂²

#14583331

yes

—

107

C₄

—

108

C₄

—

688

—

109

C₄

#14582765

yes

characteristic

110

C₄

C₂×#13063257

yes

characteristic

111

C₄

#14583250

yes

—

112

C₂

#19134723

yes

characteristic

113

C₂

#19136379

yes

—

114

C₂

#19136827

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄×C₁₆×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₄₃
hypocenter	C₄₃	#12889
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄×C₁₆×C₄₃

C₂

socle, prime radical

C₂³×C₄₃

C₂×D₈

cosocle

C₂²×C₈×C₄₃

C₂³

hypercenter

C₂×C₄×C₁₆

D₄₃

hypocenter

C₄₃

#12889

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
9. C₄×C₁₆×C₄₃	C₄	semidirect
66. C₄×C₁₆	Dic₄₃	semidirect
67. C₄₃	#12889	semidirect

H ≅ G/N

type

9. C₄×C₁₆×C₄₃

C₄

semidirect

66. C₄×C₁₆

Dic₄₃

semidirect

67. C₄₃

#12889

semidirect

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

subgroup	index
#19134759	2
#19132687	2
C₂×C₄×C₁₆×C₄₃	2
#12889	43

subgroup

index

#19134759

#19132687

C₂×C₄×C₁₆×C₄₃

#12889

Subgroups — #25012980

Conjugacy classes of subgroups

Complements

Maximal subgroups