Group #25249109 — subgroups

Subgroups — #25249109

Order 11008.

662 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 235 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	#19142958	C₂	1	2	yes	maximal
2	#19135564	C₂	1	8	yes	maximal
3	#19134726	C₂	1	4	yes	maximal
4	C₄×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063317	C₂²	1	4	yes	—
6	#14582797	—	2	8	no	—
7	#14582769	C₂²	1	4	yes	—
8	#14582765	C₂²	1	4	yes	—
9	#14582662	C₂²	1	16	yes	—
10	C₂×#97×C₄₃	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
12	C₄³×C₄₃	C₂²	1	1	yes	characteristic
13	#13063317	—	2	16	no	—
14	C₂×C₄⋊Dic₄₃	—	2	8	no	—
15	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
16	C₂×Dic₄₃⋊C₄	—	2	8	no	—
17	C₄₃⋊#95	—	2	8	no	—
18	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
19	C₂×C₄²×C₄₃	D₄	1	4	yes	—
20	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
22	#97×C₄₃	—	2	8	no	—
23	C₄×C₈×C₄₃	Q₈	1	8	yes	—
24	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
25	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
27	C₂²×Dic₄₃	—	2	8	no	—
28	C₂×C₈×C₄₃	—	2	8	no	—
29	C₂×C₈×C₄₃	C₂×Q₈	1	8	yes	—
30	C₄²×C₄₃	—	4	4	no	—
31	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
32	C₄²×C₄₃	#41	1	8	yes	—
33	C₄⋊Dic₄₃	—	2	16	no	—
34	C₄⋊Dic₄₃	—	4	16	no	—
35	Dic₄₃⋊C₄	—	4	16	no	—
36	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	8	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	#124	1	8	yes	—
40	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
41	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
43	C₂×Dic₄₃	—	4	8	no	—
44	C₂×Dic₄₃	—	4	16	no	—
45	C₈×C₄₃	—	2	8	no	—
46	#33299	—	43	1	no	maximal, Sylow
47	C₂²×C₄₃	C₂×#124	1	2	yes	—
48	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₄₃	#575	1	4	yes	—
50	C₄×C₄₃	—	2	8	no	—
51	C₄×C₄₃	—	2	4	no	—
52	C₄×C₄₃	#533	1	4	yes	—
53	Dic₄₃	—	8	8	no	—
54	#2859	—	43	2	no	—
55	#1992	—	43	8	no	—
56	#1835	—	43	4	no	—
57	C₄×#97	D₄₃	1	1	yes	characteristic
58	C₂×C₄₃	#2862	1	1	yes	characteristic
59	C₂×C₄₃	#3142	1	4	yes	—
60	C₂×C₄₃	#3162	1	2	yes	—
61	C₂×#125	—	43	4	no	—
62	C₂×#97	C₂×D₄₃	1	4	yes	—
63	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
64	#389	—	86	8	no	—
65	#384	—	43	4	no	—
66	#382	—	43	4	no	—
67	C₄³	C₂×D₄₃	1	1	yes	characteristic
68	#340	—	43	16	no	—
69	C₄₃	#33299	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
71	#125	—	86	16	no	—
72	C₂×C₄⋊C₄	—	43	8	no	—
73	C₂×C₄⋊C₄	—	86	8	no	—
74	C₂×C₄⋊C₄	—	86	8	no	—
75	C₂×C₄²	D₁₇₂	1	4	yes	—
76	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
77	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
78	#97	—	2	8	no	—
79	C₄×C₈	Dic₈₆	1	8	yes	—
80	#95	—	86	8	no	—
81	C₂²×C₄	—	86	8	no	—
82	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
83	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
84	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
85	C₂×C₈	—	2	8	no	—
86	C₂×C₈	C₂×Dic₈₆	1	8	yes	—
87	C₄⋊C₄	—	86	16	no	—
88	C₄⋊C₄	—	172	16	no	—
89	C₄⋊C₄	—	172	16	no	—
90	C₄²	—	4	4	no	—
91	C₄²	C₂×Dic₈₆	1	4	yes	—
92	C₄²	#10621898	1	8	yes	—
93	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	172	8	no	—
97	C₂×C₄	—	172	16	no	—
98	C₂×C₄	#13063313	1	8	yes	—
99	C₂×C₄	#13063325	1	4	yes	—
100	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
101	C₂×C₄	C₂×#10621898	1	4	yes	—
102	C₈	—	2	8	no	—
103	C₂²	C₂×#13063313	1	2	yes	—
104	C₂²	C₂×#13063325	1	1	yes	characteristic
105	C₂²	#14583699	1	4	yes	—
106	C₄	—	2	8	no	—
107	C₄	—	2	4	no	—
108	C₄	—	344	8	no	—
109	C₄	#14583456	1	4	yes	—
110	C₂	#19142973	1	1	yes	characteristic
111	C₂	#19144996	1	4	yes	—
112	C₂	#19145119	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19142958

C₂

yes

maximal

#19135564

C₂

yes

maximal

#19134726

C₂

yes

maximal

C₄×#97×C₄₃

C₂

yes

maximal, characteristic

C₂×#13063317

C₂²

yes

—

#14582797

—

#14582769

C₂²

yes

—

#14582765

C₂²

yes

—

#14582662

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

—

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

—

C₄×C₈×C₄₃

Q₈

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×C₈×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

#33299

—

maximal, Sylow

C₂²×C₄₃

C₂×#124

yes

—

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

#575

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#533

yes

—

Dic₄₃

—

#2859

—

#1992

—

#1835

—

C₄×#97

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#3162

yes

—

C₂×#125

—

C₂×#97

C₂×D₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

#389

—

#384

—

#382

—

C₄³

C₂×D₄₃

yes

characteristic

#340

—

C₄₃

#33299

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

characteristic

C₂×C₄²

C₂²×D₄₃

yes

—

#97

—

C₄×C₈

Dic₈₆

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

—

C₂²×C₄

C₂³×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₈₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

C₂×Dic₈₆

yes

—

C₄²

#10621898

yes

—

C₂³

C₂²×D₁₇₂

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#13063313

yes

—

C₂×C₄

#13063325

yes

—

100

C₂×C₄

C₂²×Dic₈₆

yes

—

101

C₂×C₄

C₂×#10621898

yes

—

102

C₈

—

103

C₂²

C₂×#13063313

yes

—

104

C₂²

C₂×#13063325

yes

characteristic

105

C₂²

#14583699

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

344

—

109

C₄

#14583456

yes

—

110

C₂

#19142973

yes

characteristic

111

C₂

#19144996

yes

—

112

C₂

#19145119

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	#33299
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

#33299

LCS

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

N	H ≅ G/N	type
69. C₄₃	#33299	semidirect

H ≅ G/N

type

69. C₄₃

#33299

semidirect

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

subgroup	index
#19142958	2
#19135564	2
#19134726	2
C₄×#97×C₄₃	2
#33299	43

subgroup

index

C₄×#97×C₄₃

Subgroups — #25249109

Conjugacy classes of subgroups

Complements

Maximal subgroups