Group #25017588 — subgroups

Subgroups — #25017588

Order 11008.

174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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	#19136874	C₂	1	1	yes	maximal, characteristic
2	#19136848	C₂	1	1	yes	maximal, characteristic
3	#19132777	C₂	1	4	yes	maximal
4	C₄₃×#1397	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₃₄₄	—	2	1	no	—
6	C₂×Dic₃₄₄	C₂²	1	2	yes	—
7	#14583301	—	2	1	no	—
8	#14583279	—	2	1	no	—
9	#14582727	—	2	1	no	—
10	#14582725	C₂²	1	2	yes	—
11	C₂×C₃₂×C₄₃	C₂²	1	2	yes	—
12	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₇₂	—	2	2	no	—
14	C₂×Dic₁₇₂	—	4	1	no	—
15	#13063325	—	4	1	no	—
16	#13063317	—	4	1	no	—
17	Dic₃₄₄	—	2	4	no	—
18	Dic₃₄₄	—	4	2	no	—
19	#13063259	—	2	2	no	—
20	#13063257	—	4	1	no	—
21	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
23	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₃₂×C₄₃	—	2	2	no	—
25	C₂×Dic₈₆	—	4	2	no	—
26	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
27	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₄²×C₄₃	D₈	1	1	yes	characteristic
29	C₄⋊Dic₄₃	—	4	2	no	—
30	C₄⋊Dic₄₃	—	8	2	no	—
31	Dic₄₃⋊C₄	—	8	2	no	—
32	Dic₁₇₂	—	4	2	no	—
33	Dic₁₇₂	—	4	2	no	—
34	Dic₁₇₂	—	8	2	no	—
35	C₁₆×C₄₃	SD₁₆	1	2	yes	—
36	C₁₆×C₄₃	#41	1	2	yes	—
37	C₂×C₄×C₄₃	D₁₆	1	2	yes	—
38	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
39	C₂×Dic₄₃	—	8	2	no	—
40	C₂×Dic₄₃	—	8	2	no	—
41	Dic₈₆	—	8	2	no	—
42	Dic₈₆	—	8	2	no	—
43	C₈×C₄₃	SD₃₂	1	2	yes	—
44	C₈×C₄₃	#124	1	1	yes	characteristic
45	C₈×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
46	#13724	—	43	1	no	maximal, Sylow
47	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
48	C₄×C₄₃	—	2	2	no	—
49	C₄×C₄₃	#486	1	1	yes	characteristic
50	C₄×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
51	Dic₄₃	—	16	2	no	—
52	Dic₄₃	—	16	2	no	—
53	#2253	—	43	1	no	—
54	#2247	—	43	1	no	—
55	#1416	—	43	4	no	—
56	#1397	D₄₃	1	1	yes	characteristic
57	C₂×C₄₃	#2240	1	1	yes	characteristic
58	C₂×C₄₃	#2264	1	2	yes	—
59	C₂×Q₃₂	—	43	2	no	—
60	C₂×Q₃₂	—	86	1	no	—
61	#499	—	86	1	no	—
62	#494	—	86	1	no	—
63	C₂×C₃₂	C₂×D₄₃	1	2	yes	—
64	#367	—	86	1	no	—
65	#366	—	43	2	no	—
66	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
67	C₄₃	#13724	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	—	86	2	no	—
69	C₂×Q₁₆	—	172	1	no	—
70	C₄⋊Q₈	—	172	1	no	—
71	#125	—	172	1	no	—
72	Q₃₂	—	86	4	no	—
73	Q₃₂	—	172	2	no	—
74	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
75	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
76	#107	—	86	2	no	—
77	#106	—	172	1	no	—
78	C₄×C₈	D₁₇₂	1	1	yes	characteristic
79	C₃₂	—	2	2	no	—
80	C₂×Q₈	—	172	2	no	—
81	Q₁₆	—	344	2	no	—
82	Q₁₆	—	172	2	no	—
83	Q₁₆	—	172	2	no	—
84	C₂×C₈	D₃₄₄	1	1	yes	characteristic
85	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
86	C₄⋊C₄	—	344	2	no	—
87	C₄⋊C₄	—	344	2	no	—
88	C₄⋊C₄	—	172	2	no	—
89	C₄²	D₃₄₄	1	1	yes	characteristic
90	C₁₆	#10621873	1	2	yes	—
91	C₁₆	#10621898	1	2	yes	—
92	Q₈	—	344	2	no	—
93	Q₈	—	344	2	no	—
94	C₂×C₄	—	344	2	no	—
95	C₂×C₄	—	344	2	no	—
96	C₂×C₄	D₆₈₈	1	2	yes	—
97	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
98	C₈	#13063270	1	2	yes	—
99	C₈	#13063313	1	1	yes	characteristic
100	C₈	C₂×#10621873	1	1	yes	characteristic
101	C₂²	C₂×D₆₈₈	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	688	2	no	—
104	C₄	—	688	2	no	—
105	C₄	#14583246	1	1	yes	characteristic
106	C₄	C₂×#13063270	1	1	yes	characteristic
107	C₂	#19136819	1	1	yes	characteristic
108	C₂	#19136915	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19136874

C₂

yes

maximal, characteristic

#19136848

C₂

yes

maximal, characteristic

#19132777

C₂

yes

maximal

C₄₃×#1397

C₂

yes

maximal, characteristic

C₂×Dic₃₄₄

—

C₂×Dic₃₄₄

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×C₃₂×C₄₃

C₂²

yes

—

C₄×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

#13063325

—

#13063317

—

Dic₃₄₄

—

Dic₃₄₄

—

#13063259

—

#13063257

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₃₂×C₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

SD₁₆

yes

—

C₁₆×C₄₃

#41

yes

—

C₂×C₄×C₄₃

D₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

SD₃₂

yes

—

C₈×C₄₃

#124

yes

characteristic

C₈×C₄₃

C₂×SD₁₆

yes

characteristic

#13724

—

maximal, Sylow

C₂²×C₄₃

C₂×D₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#486

yes

characteristic

C₄×C₄₃

C₂×SD₃₂

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

—

—

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#499

—

#494

—

C₂×C₃₂

C₂×D₄₃

yes

—

#367

—

#366

—

C₄×C₁₆

C₂×D₄₃

yes

characteristic

C₄₃

#13724

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

172

—

C₄⋊Q₈

—

172

—

#125

—

172

—

Q₃₂

—

Q₃₂

—

172

—

C₂×C₁₆

D₁₇₂

yes

characteristic

C₂×C₁₆

C₂²×D₄₃

yes

characteristic

#107

—

#106

—

172

—

C₄×C₈

D₁₇₂

yes

characteristic

C₃₂

—

C₂×Q₈

—

172

—

Q₁₆

—

344

—

Q₁₆

—

172

—

Q₁₆

—

172

—

C₂×C₈

D₃₄₄

yes

characteristic

C₂×C₈

C₂×D₁₇₂

yes

characteristic

C₄⋊C₄

—

344

—

C₄⋊C₄

—

344

—

C₄⋊C₄

—

172

—

C₄²

D₃₄₄

yes

characteristic

C₁₆

#10621873

yes

—

C₁₆

#10621898

yes

—

Q₈

—

344

—

Q₈

—

344

—

C₂×C₄

—

344

—

C₂×C₄

—

344

—

C₂×C₄

D₆₈₈

yes

—

C₂×C₄

C₂×D₃₄₄

yes

characteristic

C₈

#13063270

yes

—

C₈

#13063313

yes

characteristic

100

C₈

C₂×#10621873

yes

characteristic

101

C₂²

C₂×D₆₈₈

yes

characteristic

102

C₄

—

103

C₄

—

688

—

104

C₄

—

688

—

105

C₄

#14583246

yes

characteristic

106

C₄

C₂×#13063270

yes

characteristic

107

C₂

#19136819

yes

characteristic

108

C₂

#19136915

yes

—

	subgroup	G/H
center	C₂²	C₂×D₆₈₈
commutator, cosocle	C₂×C₁₆×C₄₃	C₂³
Frattini	C₂×C₁₆	C₂²×D₄₃
Fitting	C₄₃×#1397	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₁₆
hypercenter	#1397	D₄₃
hypocenter	C₄₃	#13724
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂²

C₂×D₆₈₈

commutator, cosocle

C₂×C₁₆×C₄₃

C₂³

Frattini

C₂×C₁₆

C₂²×D₄₃

Fitting

C₄₃×#1397

C₂

socle, prime radical

C₂²×C₄₃

C₂×D₁₆

D₄₃

C₄₃

G ▷ C₂×C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
67. C₄₃	#13724	semidirect

H ≅ G/N

type

67. C₄₃

#13724

semidirect

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

subgroup	index
#19136874	2
#19136848	2
#19132777	2
C₄₃×#1397	2
#13724	43

subgroup

index

C₄₃×#1397

Subgroups — #25017588

Conjugacy classes of subgroups

Complements

Maximal subgroups