Group #25005576 — subgroups

Subgroups — C₈×#13063265 #25005576

Order 11008.

354 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 251 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	C₄×#13063265	C₂	1	2	yes	maximal
2	#19132512	C₂	1	2	yes	maximal, complemented
3	C₈×C₄₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063265	C₄	1	4	yes	—
6	#14582675	C₄	1	4	yes	—
7	C₄×C₄₃⋊C₁₆	C₂²	1	4	yes	—
8	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
9	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₈²×C₄₃	C₄	1	2	yes	—
11	C₈²×C₄₃	C₂²	1	1	yes	characteristic
12	C₈²×C₄₃	C₂²	1	1	yes	characteristic
13	#13063265	C₈	1	16	yes	direct product factor
14	C₂×C₄₃⋊C₁₆	C₂×C₄	1	8	yes	—
15	C₂²×C₈×C₄₃	C₈	1	4	yes	—
16	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₄₃	C₈	1	4	yes	—
19	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
26	C₂×C₈×C₄₃	—	2	8	no	—
27	C₂×C₈×C₄₃	C₄²	1	2	yes	—
28	C₂×C₈×C₄₃	C₂×C₈	1	8	yes	—
29	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
30	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
32	C₄²×C₄₃	C₄²	1	1	yes	characteristic
33	C₄²×C₄₃	C₂×C₈	1	2	yes	—
34	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₄₃⋊C₁₆	C₂×C₈	1	16	yes	complemented
36	C₂³×C₄₃	C₄×C₈	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	C₄×C₈	1	4	yes	—
39	C₂×C₄×C₄₃	C₄×C₈	1	2	yes	—
40	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
43	C₈×C₄₃	—	2	4	no	—
44	C₈×C₄₃	C₄×C₈	1	4	yes	—
45	C₈×C₄₃	M₃₂	1	8	yes	complemented
46	C₈×C₄₃	C₂²×C₈	1	4	yes	—
47	C₈×M₃₂	—	43	1	no	maximal, Sylow
48	C₂²×C₄₃	—	2	2	no	—
49	C₂²×C₄₃	C₈²	1	2	yes	—
50	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₄×C₄₃	—	2	2	no	—
52	C₄×C₄₃	C₈²	1	2	yes	—
53	C₄×C₄₃	C₂×C₄×C₈	1	2	yes	—
54	C₄×C₄₃	C₂×M₃₂	1	4	yes	—
55	C₄×M₃₂	—	43	2	no	—
56	C₂×C₈²	D₄₃	1	1	yes	characteristic
57	#1311	—	43	2	no	—
58	C₈×C₁₆	—	43	2	no	—
59	C₂×C₄₃	—	2	2	no	—
60	C₂×C₄₃	C₂×C₈²	1	1	yes	characteristic
61	C₂×C₄₃	C₄×M₃₂	1	2	yes	—
62	C₂×M₃₂	—	43	4	no	—
63	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
64	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	#346	—	43	4	no	—
66	C₄×C₁₆	—	43	4	no	—
67	C₈²	Dic₄₃	1	2	yes	—
68	C₈²	C₂×D₄₃	1	1	yes	characteristic
69	C₈²	C₂×D₄₃	1	1	yes	characteristic
70	C₄₃	C₈×M₃₂	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	C₄₃⋊C₈	1	4	yes	—
72	C₂²×C₈	C₄×D₄₃	1	2	yes	—
73	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
74	M₃₂	—	43	16	no	—
75	C₂×C₁₆	—	43	8	no	—
76	C₄×C₈	C₄₃⋊C₈	1	4	yes	—
77	C₄×C₈	C₄×D₄₃	1	2	yes	—
78	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
79	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
80	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
81	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
83	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
84	C₂×C₈	—	2	8	no	—
85	C₂×C₈	C₈×D₄₃	1	8	yes	—
86	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
87	C₂×C₈	C₂×C₄₃⋊C₈	1	4	yes	—
88	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
89	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
90	C₄²	C₂×C₄₃⋊C₈	1	2	yes	—
91	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
92	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
93	C₁₆	—	43	16	no	—
94	C₂³	C₄×C₄₃⋊C₈	1	1	yes	characteristic
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	C₈×Dic₄₃	1	4	yes	—
97	C₂×C₄	C₄×C₄₃⋊C₈	1	2	yes	—
98	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
99	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
100	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	C₈×Dic₄₃	1	4	yes	—
103	C₈	#13063265	1	8	yes	direct product factor
104	C₈	C₂×C₈×D₄₃	1	4	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	C₈×C₄₃⋊C₈	1	2	yes	—
107	C₂²	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	C₈×C₄₃⋊C₈	1	2	yes	—
110	C₄	C₂×C₈×Dic₄₃	1	2	yes	—
111	C₄	C₂×#13063265	1	4	yes	—
112	C₂	—	2	2	no	—
113	C₂	C₂×C₈×C₄₃⋊C₈	1	1	yes	characteristic
114	C₂	C₄×#13063265	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063265

C₂

yes

maximal

#19132512

C₂

yes

maximal, complemented

C₈×C₄₃⋊C₁₆

C₂

yes

maximal, complemented

C₂×C₈²×C₄₃

C₂

yes

maximal, characteristic

C₂×#13063265

C₄

yes

—

#14582675

C₄

yes

—

C₄×C₄₃⋊C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₈²×C₄₃

C₄

yes

—

C₈²×C₄₃

C₂²

yes

characteristic

C₈²×C₄₃

C₂²

yes

characteristic

#13063265

C₈

yes

direct product factor

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₈

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₈

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₄²

yes

characteristic

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄₃⋊C₁₆

C₂×C₈

yes

complemented

C₂³×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₄×C₈

yes

—

C₈×C₄₃

M₃₂

yes

complemented

C₈×C₄₃

C₂²×C₈

yes

—

C₈×M₃₂

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₈²

yes

—

C₂²×C₄₃

C₂×C₄×C₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₈²

yes

—

C₄×C₄₃

C₂×C₄×C₈

yes

—

C₄×C₄₃

C₂×M₃₂

yes

—

C₄×M₃₂

—

C₂×C₈²

D₄₃

yes

characteristic

#1311

—

C₈×C₁₆

—

C₂×C₄₃

—

C₂×C₄₃

C₂×C₈²

yes

characteristic

C₂×C₄₃

C₄×M₃₂

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

Dic₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#346

—

C₄×C₁₆

—

C₈²

Dic₄₃

yes

—

C₈²

C₂×D₄₃

yes

characteristic

C₈²

C₂×D₄₃

yes

characteristic

C₄₃

C₈×M₃₂

yes

characteristic, complemented, Sylow

C₂²×C₈

C₄₃⋊C₈

yes

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄×C₈

C₄₃⋊C₈

yes

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

characteristic

C₄×C₈

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂×C₄₃⋊C₈

yes

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₈×D₄₃

yes

—

C₂×C₈

C₂×C₄₃⋊C₈

yes

—

C₂×C₈

C₂×C₄₃⋊C₈

yes

—

C₂×C₈

C₄×Dic₄₃

yes

—

C₂×C₈

C₂×C₄×D₄₃

yes

—

C₄²

C₂×C₄₃⋊C₈

yes

—

C₄²

C₄×Dic₄₃

yes

characteristic

C₄²

C₂²×Dic₄₃

yes

characteristic

C₁₆

—

C₂³

C₄×C₄₃⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

C₈×Dic₄₃

yes

—

C₂×C₄

C₄×C₄₃⋊C₈

yes

—

C₂×C₄

C₄×C₄₃⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

100

C₂×C₄

C₂²×C₄₃⋊C₈

yes

—

101

C₈

—

102

C₈

C₈×Dic₄₃

yes

—

103

C₈

#13063265

yes

direct product factor

104

C₈

C₂×C₈×D₄₃

yes

—

105

C₂²

—

106

C₂²

C₈×C₄₃⋊C₈

yes

—

107

C₂²

C₂×C₄×C₄₃⋊C₈

yes

characteristic

108

C₄

—

109

C₄

C₈×C₄₃⋊C₈

yes

—

110

C₄

C₂×C₈×Dic₄₃

yes

—

111

C₄

C₂×#13063265

yes

—

112

C₂

—

113

C₂

C₂×C₈×C₄₃⋊C₈

yes

characteristic

114

C₂

C₄×#13063265

yes

—

	subgroup	G/H
center	C₈²	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₈²
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₂×C₈²×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×C₈
prime radical	C₂³×C₄₃	C₄×C₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	C₂×C₈²	D₄₃
hypocenter	C₄₃	C₈×M₃₂
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈² ◁ C₂×C₈²

subgroup

G/H

center

C₈²

C₂×D₄₃

commutator

C₂×C₄₃

C₂×C₈²

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₂×C₈²×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₄×C₈

prime radical

C₂³×C₄₃

C₄×C₈

cosocle

C₄×C₈×C₄₃

C₂³

hypercenter

C₂×C₈²

D₄₃

hypocenter

C₄₃

C₈×M₃₂

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈² ◁ C₂×C₈²

N	H ≅ G/N	type
2. #19132512	C₂	semidirect
3. C₈×C₄₃⋊C₁₆	C₂	semidirect
13. #13063265	C₈	direct (N × H)
35. C₄₃⋊C₁₆	C₂×C₈	semidirect
45. C₈×C₄₃	M₃₂	semidirect
70. C₄₃	C₈×M₃₂	semidirect
103. C₈	#13063265	direct (N × H)

H ≅ G/N

type

2. #19132512

C₂

semidirect

3. C₈×C₄₃⋊C₁₆

C₂

semidirect

13. #13063265

C₈

direct (N × H)

35. C₄₃⋊C₁₆

C₂×C₈

semidirect

45. C₈×C₄₃

M₃₂

semidirect

70. C₄₃

C₈×M₃₂

semidirect

103. C₈

#13063265

direct (N × H)

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

subgroup	index
C₄×#13063265	2
#19132512	2
C₈×C₄₃⋊C₁₆	2
C₂×C₈²×C₄₃	2
C₈×M₃₂	43

subgroup

index

C₄×#13063265

#19132512

C₈×C₄₃⋊C₁₆

C₂×C₈²×C₄₃

C₈×M₃₂

Subgroups — C₈×#13063265 #25005576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C8×#13063265 #25005576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13063265 #25005576