Group #25012990 — subgroups

Subgroups — #25012990

Order 11008.

274 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 147 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	#19134767	C₂	1	2	yes	maximal
2	#19132689	C₂	1	4	yes	maximal
3	C₂×C₄₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063261	—	2	2	no	—
5	C₂×#13063261	C₂²	1	4	yes	—
6	#14582923	—	2	2	no	—
7	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#346	C₄	1	4	yes	—
10	C₂×#10621877	—	2	4	no	—
11	#13063261	—	2	8	no	—
12	#13063261	—	4	4	no	—
13	C₄⋊(C₄₃⋊C₈)	—	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	Q₁₆	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
25	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₈×C₄₃	#41	1	4	yes	—
28	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
29	C₄²×C₄₃	D₈	1	2	yes	—
30	#10621877	—	4	4	no	—
31	#10621877	—	4	4	no	—
32	C₂×C₄₃⋊C₈	—	4	4	no	—
33	C₁₆×C₄₃	—	2	4	no	—
34	C₂³×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	4	2	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×D₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
41	C₈×C₄₃	#106	1	4	yes	—
42	C₈×C₄₃	#117	1	2	yes	—
43	C₈×C₄₃	#125	1	2	yes	—
44	C₄₃⋊C₈	—	8	4	no	—
45	#12892	—	43	1	no	maximal, Sylow
46	C₂²×C₄₃	—	2	2	no	—
47	C₂²×C₄₃	C₂×#107	1	1	yes	characteristic
48	C₂²×C₄₃	#487	1	2	yes	—
49	C₄×C₄₃	—	2	4	no	—
50	C₄×C₄₃	#382	1	1	yes	characteristic
51	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
52	C₄×C₄₃	#486	1	2	yes	—
53	C₂×#346	D₄₃	1	1	yes	characteristic
54	#1848	—	43	2	no	—
55	#1381	—	43	4	no	—
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	#1834	1	1	yes	characteristic
58	C₂×C₄₃	#2161	1	2	yes	—
59	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
60	C₂×#108	—	43	4	no	—
61	C₂×#108	—	86	2	no	—
62	#423	—	86	2	no	—
63	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
64	#346	Dic₄₃	1	4	yes	—
65	C₄₃	#12892	1	1	yes	characteristic, complemented, Sylow
66	C₂×M₁₆	—	86	4	no	—
67	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
68	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
69	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
70	C₂×C₁₆	—	2	4	no	—
71	C₂×C₁₆	C₂×Dic₄₃	1	4	yes	—
72	#108	—	86	8	no	—
73	#108	—	172	4	no	—
74	C₄⋊C₈	—	172	4	no	—
75	C₄×C₈	Dic₈₆	1	2	yes	—
76	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
77	C₂²×C₄	Dic₁₇₂	1	2	yes	—
78	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
79	M₁₆	—	172	4	no	—
80	M₁₆	—	172	4	no	—
81	C₂×C₈	—	172	4	no	—
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	C₄²	D₃₄₄	1	2	yes	—
88	C₄²	C₄⋊Dic₄₃	1	2	yes	—
89	C₁₆	—	2	4	no	—
90	C₂³	C₂×Dic₁₇₂	1	1	yes	characteristic
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#13063259	1	4	yes	—
93	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
94	C₂×C₄	#13063313	1	2	yes	—
95	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
96	C₂×C₄	C₂×#10621873	1	2	yes	—
97	C₈	—	344	4	no	—
98	C₈	#13063257	1	4	yes	—
99	C₈	#13063284	1	2	yes	—
100	C₈	#13063317	1	2	yes	—
101	C₂²	—	2	2	no	—
102	C₂²	C₂×#13063259	1	1	yes	characteristic
103	C₂²	#14583250	1	2	yes	—
104	C₄	—	2	4	no	—
105	C₄	#14582765	1	1	yes	characteristic
106	C₄	C₂×#13063257	1	1	yes	characteristic
107	C₄	#14583246	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	#19134723	1	1	yes	characteristic
110	C₂	#19136390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134767

C₂

yes

maximal

#19132689

C₂

yes

maximal

C₂×C₄₃×#346

C₂

yes

maximal, characteristic

C₂×#13063261

—

C₂×#13063261

C₂²

yes

—

#14582923

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#346

C₄

yes

—

C₂×#10621877

—

#13063261

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

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

Q₁₆

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

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

D₈

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×Q₁₆

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×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₈×C₄₃

#106

yes

—

C₈×C₄₃

#117

yes

—

C₈×C₄₃

#125

yes

—

C₄₃⋊C₈

—

#12892

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#107

yes

characteristic

C₂²×C₄₃

#487

yes

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×#346

D₄₃

yes

characteristic

#1848

—

#1381

—

C₂×C₄₃

—

C₂×C₄₃

#1834

yes

characteristic

C₂×C₄₃

#2161

yes

—

C₂²×C₁₆

C₂×D₄₃

yes

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#346

Dic₄₃

yes

—

C₄₃

#12892

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

D₁₇₂

yes

characteristic

C₂²×C₈

C₂²×D₄₃

yes

characteristic

C₂×C₄²

D₁₇₂

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₄₃

yes

—

#108

—

#108

—

172

—

C₄⋊C₈

—

172

—

C₄×C₈

Dic₈₆

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₂²×C₄

Dic₁₇₂

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

M₁₆

—

172

—

M₁₆

—

172

—

C₂×C₈

—

172

—

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

C₄²

D₃₄₄

yes

—

C₄²

C₄⋊Dic₄₃

yes

—

C₁₆

—

C₂³

C₂×Dic₁₇₂

yes

characteristic

C₂×C₄

—

C₂×C₄

#13063259

yes

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

#13063313

yes

—

C₂×C₄

C₂×D₃₄₄

yes

characteristic

C₂×C₄

C₂×#10621873

yes

—

C₈

—

344

—

C₈

#13063257

yes

—

C₈

#13063284

yes

—

100

C₈

#13063317

yes

—

101

C₂²

—

102

C₂²

C₂×#13063259

yes

characteristic

103

C₂²

#14583250

yes

—

104

C₄

—

105

C₄

#14582765

yes

characteristic

106

C₄

C₂×#13063257

yes

characteristic

107

C₄

#14583246

yes

—

108

C₂

—

109

C₂

#19134723

yes

characteristic

110

C₂

#19136390

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂×#107
prime radical	C₂³×C₄₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#346	D₄₃
hypocenter	C₄₃	#12892
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#346

C₂

socle

C₂²×C₄₃

C₂×#107

prime radical

C₂³×C₄₃

C₂×Q₁₆

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
65. C₄₃	#12892	semidirect

H ≅ G/N

type

65. C₄₃

#12892

semidirect

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

subgroup	index
#19134767	2
#19132689	2
C₂×C₄₃×#346	2
#12892	43

subgroup

index

#19134767

#19132689

C₂×C₄₃×#346

#12892

Subgroups — #25012990

Conjugacy classes of subgroups

Complements

Maximal subgroups