Group #24999436 — subgroups

Subgroups — #24999436

Order 11008.

586 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14583297	C₂	1	3	yes	maximal
2	#19135397	C₂	1	3	yes	maximal
3	C₄₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063325	C₂²	1	3	yes	—
5	#14583297	—	2	12	no	—
6	C₂×#13063257	—	2	6	no	—
7	C₂×#13063250	—	2	6	no	—
8	#14582769	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
10	C₂²×Dic₈₆	—	2	3	no	—
11	#13063325	—	2	6	no	—
12	#13063325	—	2	3	no	—
13	#13063325	D₄	1	6	yes	—
14	C₂×C₄⋊Dic₄₃	—	2	6	no	—
15	C₂×C₄⋊Dic₄₃	—	2	3	no	—
16	#13063257	—	2	24	no	—
17	#13063250	—	4	12	no	—
18	C₂²×C₈×C₄₃	D₄	1	6	yes	—
19	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₄₃	—	2	6	no	—
21	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
22	C₂²×Dic₄₃	—	4	3	no	—
23	C₂²×Dic₄₃	—	4	1	no	—
24	C₂×Dic₈₆	—	2	6	no	—
25	C₂×Dic₈₆	—	4	6	no	—
26	C₂×Dic₈₆	—	4	6	no	—
27	C₂×Dic₈₆	—	4	3	no	—
28	C₂×C₈×C₄₃	—	2	6	no	—
29	C₂×C₈×C₄₃	—	2	6	no	—
30	C₂×C₈×C₄₃	SD₁₆	1	12	yes	—
31	C₄²×C₄₃	C₂×D₄	1	3	yes	—
32	C₄²×C₄₃	#41	1	1	yes	characteristic
33	C₄⋊Dic₄₃	—	2	12	no	—
34	C₄⋊Dic₄₃	—	4	6	no	—
35	C₄⋊Dic₄₃	—	4	6	no	—
36	C₂³×C₄₃	#127	1	1	yes	characteristic
37	C₂×C₄×C₄₃	#120	1	3	yes	—
38	C₂×C₄×C₄₃	#121	1	3	yes	—
39	C₂×C₄×C₄₃	C₂×SD₁₆	1	6	yes	—
40	C₂×C₄×C₄₃	#137	1	6	yes	—
41	C₂×Dic₄₃	—	4	6	no	—
42	C₂×Dic₄₃	—	8	3	no	—
43	C₂×Dic₄₃	—	8	3	no	—
44	C₂×Dic₄₃	—	8	3	no	—
45	Dic₈₆	—	4	12	no	—
46	Dic₈₆	—	8	6	no	—
47	C₈×C₄₃	—	2	12	no	—
48	#10316	—	43	1	no	maximal, Sylow
49	C₂²×C₄₃	#392	1	1	yes	characteristic
50	C₂²×C₄₃	#492	1	3	yes	—
51	C₂²×C₄₃	#497	1	3	yes	—
52	C₄×C₄₃	#448	1	6	yes	—
53	C₄×C₄₃	#461	1	6	yes	—
54	Dic₄₃	—	8	6	no	—
55	Dic₄₃	—	16	1	no	—
56	C₂×#498	—	43	3	no	—
57	#1956	—	43	3	no	—
58	#1273	D₄₃	1	1	yes	characteristic
59	C₂×C₄₃	#1705	1	1	yes	characteristic
60	C₂×C₄₃	#1716	1	3	yes	—
61	C₂×C₄₃	#2013	1	3	yes	—
62	C₂×C₄⋊Q₈	—	43	3	no	—
63	#498	—	86	12	no	—
64	C₂×#106	—	86	6	no	—
65	C₂×#103	—	86	6	no	—
66	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
67	#384	—	43	1	no	—
68	C₄₃	#10316	1	1	yes	characteristic, complemented, Sylow
69	C₂²×Q₈	—	86	3	no	—
70	C₂²×C₈	D₁₇₂	1	6	yes	—
71	C₄⋊Q₈	—	43	6	no	—
72	C₄⋊Q₈	—	86	6	no	—
73	C₄⋊Q₈	—	86	3	no	—
74	C₂×C₄⋊C₄	—	86	6	no	—
75	C₂×C₄⋊C₄	—	86	3	no	—
76	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
77	#106	—	86	24	no	—
78	#103	—	172	12	no	—
79	C₄×C₈	—	2	6	no	—
80	C₂×Q₈	—	86	6	no	—
81	C₂×Q₈	—	172	6	no	—
82	C₂×Q₈	—	172	6	no	—
83	C₂×Q₈	—	172	3	no	—
84	C₂²×C₄	—	172	1	no	—
85	C₂²×C₄	—	172	3	no	—
86	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
87	C₂×C₈	—	2	6	no	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	#10621873	1	12	yes	—
90	C₄⋊C₄	—	86	12	no	—
91	C₄⋊C₄	—	172	6	no	—
92	C₄⋊C₄	—	172	6	no	—
93	C₄²	D₄×D₄₃	1	3	yes	—
94	C₄²	#10621902	1	1	yes	characteristic
95	C₂³	#13063322	1	1	yes	characteristic
96	Q₈	—	344	6	no	—
97	Q₈	—	172	12	no	—
98	C₂×C₄	—	344	3	no	—
99	C₂×C₄	—	344	3	no	—
100	C₂×C₄	—	344	3	no	—
101	C₂×C₄	—	172	6	no	—
102	C₂×C₄	#13063295	1	3	yes	—
103	C₂×C₄	#13063300	1	3	yes	—
104	C₂×C₄	C₂×#10621873	1	6	yes	—
105	C₂×C₄	#13063358	1	6	yes	—
106	C₈	—	2	12	no	—
107	C₂²	#14582809	1	1	yes	characteristic
108	C₂²	#14583272	1	3	yes	—
109	C₂²	#14583293	1	3	yes	—
110	C₄	—	344	6	no	—
111	C₄	—	688	1	no	—
112	C₄	#14583040	1	6	yes	—
113	C₄	#14583105	1	6	yes	—
114	C₂	#19134182	1	1	yes	characteristic
115	C₂	#19134228	1	3	yes	—
116	C₂	#19135680	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583297

C₂

yes

maximal

#19135397

C₂

yes

maximal

C₄₃×#1273

C₂

yes

maximal, characteristic

C₂×#13063325

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₂²×Dic₈₆

—

#13063325

—

#13063325

—

#13063325

D₄

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

#13063257

—

#13063250

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#497

yes

—

C₄×C₄₃

#448

yes

—

C₄×C₄₃

#461

yes

—

Dic₄₃

—

Dic₄₃

—

C₂×#498

—

#1956

—

#1273

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#2013

yes

—

C₂×C₄⋊Q₈

—

#498

—

C₂×#106

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

#384

—

C₄₃

#10316

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

D₁₇₂

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#106

—

#103

—

172

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10621873

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

D₄×D₄₃

yes

—

C₄²

yes

C₂³

yes

Q₈

—

344

—

Q₈

—

172

—

C₂×C₄

—

344

—

C₂×C₄

—

344

—

100

C₂×C₄

—

344

—

101

C₂×C₄

—

172

—

102

C₂×C₄

#13063295

yes

—

103

C₂×C₄

#13063300

yes

—

104

C₂×C₄

C₂×#10621873

yes

—

105

C₂×C₄

#13063358

yes

—

106

C₈

—

107

C₂²

#14582809

yes

characteristic

108

C₂²

#14583272

yes

—

109

C₂²

#14583293

yes

—

110

C₄

—

344

—

111

C₄

—

688

—

112

C₄

#14583040

yes

—

113

C₄

#14583105

yes

—

114

C₂

#19134182

yes

characteristic

115

C₂

#19134228

yes

—

116

C₂

#19135680

yes

—

	subgroup	G/H
center	C₂³	#13063322
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1273	C₂
socle, prime radical	C₂³×C₄₃	#127
hypercenter	#1273	D₄₃
hypocenter	C₄₃	#10316
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#13063322

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1273

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
68. C₄₃	#10316	semidirect

H ≅ G/N

type

68. C₄₃

#10316

semidirect

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

subgroup	index
C₂×#14583297	2
#19135397	2
C₄₃×#1273	2
#10316	43

subgroup

index

C₂×#14583297

#19135397

C₄₃×#1273

#10316

Subgroups — #24999436

Conjugacy classes of subgroups

Complements

Maximal subgroups