Group #25005652 — subgroups

Subgroups — #25005652

Order 11008.

228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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	#19136398	C₂	1	2	yes	maximal
2	#19132516	C₂	1	4	yes	maximal, complemented
3	C₄₃×#1450	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₁₆)	C₄	1	4	yes	—
5	C₂²⋊(C₄₃⋊C₁₆)	C₄	1	4	yes	—
6	#14582675	C₂²	1	4	yes	—
7	C₄₃×#431	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#322	C₂²	1	2	yes	—
10	C₈²×C₄₃	C₄	1	2	yes	—
11	C₂×C₄₃⋊C₁₆	C₂×C₄	1	8	yes	—
12	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	—	2	2	no	—
15	C₂²⋊C₈×C₄₃	—	2	2	no	—
16	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
22	C₂×C₈×C₄₃	—	2	4	no	—
23	C₂×C₈×C₄₃	—	2	4	no	—
24	C₂×C₈×C₄₃	C₄²	1	2	yes	—
25	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
26	C₄²×C₄₃	C₄²	1	1	yes	characteristic
27	C₄²×C₄₃	M₁₆	1	2	yes	—
28	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₄₃⋊C₁₆	—	2	8	no	—
30	C₂³×C₄₃	#97	1	1	yes	characteristic
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	#97	1	2	yes	—
34	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
37	C₈×C₄₃	—	2	2	no	—
38	C₈×C₄₃	—	4	4	no	—
39	C₈×C₄₃	#131	1	4	yes	—
40	#11416	—	43	1	no	maximal, Sylow
41	C₂²×C₄₃	—	2	2	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	—	2	2	no	—
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	#405	1	2	yes	—
48	#2163	—	43	2	no	—
49	#1450	D₄₃	1	1	yes	characteristic
50	#1313	—	43	4	no	—
51	C₂×C₄₃	—	4	1	no	—
52	C₂×C₄₃	#1452	1	1	yes	characteristic
53	C₂×C₄₃	#2110	1	2	yes	—
54	#431	Dic₄₃	1	2	yes	—
55	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
56	C₄⋊C₁₆	—	43	4	no	—
57	C₂²⋊C₁₆	—	43	4	no	—
58	#346	—	43	4	no	—
59	#322	C₂×D₄₃	1	2	yes	—
60	C₈²	Dic₄₃	1	2	yes	—
61	C₄₃	#11416	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	C₄×D₄₃	1	2	yes	—
63	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
64	C₂×C₁₆	—	43	8	no	—
65	C₄⋊C₈	—	2	2	no	—
66	C₂²⋊C₈	—	2	2	no	—
67	C₄×C₈	C₄×D₄₃	1	2	yes	—
68	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
69	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
70	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
71	C₂²×C₄	#10621877	1	2	yes	—
72	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
76	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
77	C₄²	#10621877	1	2	yes	—
78	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
79	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
80	C₁₆	—	86	8	no	—
81	C₂³	#13063236	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	#13063236	1	1	yes	characteristic
85	C₂×C₄	#13063236	1	2	yes	—
86	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
87	C₂×C₄	C₂×#10621877	1	2	yes	—
88	C₈	—	2	2	no	—
89	C₈	—	4	4	no	—
90	C₈	#13063331	1	4	yes	—
91	C₂²	—	2	2	no	—
92	C₂²	—	2	1	no	—
93	C₂²	C₂×#13063236	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	—	2	1	no	—
97	C₄	#14582854	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	#19132887	1	1	yes	characteristic
100	C₂	#19136200	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19136398

C₂

yes

maximal

#19132516

C₂

yes

maximal, complemented

C₄₃×#1450

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₁₆)

C₄

yes

—

C₂²⋊(C₄₃⋊C₁₆)

C₄

yes

—

#14582675

C₂²

yes

—

C₄₃×#431

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

C₂²

yes

—

C₈²×C₄₃

C₄

yes

—

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

M₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₄²

yes

characteristic

C₄²×C₄₃

M₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄₃⋊C₁₆

—

C₂³×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#97

yes

—

C₂×C₄×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#131

yes

—

#11416

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×#97

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#405

yes

—

#2163

—

#1450

D₄₃

yes

characteristic

#1313

—

C₂×C₄₃

—

C₂×C₄₃

#1452

yes

characteristic

C₂×C₄₃

#2110

yes

—

#431

Dic₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

C₂×D₄₃

yes

—

C₈²

Dic₄₃

yes

—

C₄₃

#11416

yes

characteristic, complemented, Sylow

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

characteristic

C₄×C₈

C₂²×D₄₃

yes

characteristic

C₂²×C₄

#10621877

yes

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₄₃

yes

—

C₂×C₈

C₂×C₄×D₄₃

yes

—

C₄²

#10621877

yes

—

C₄²

C₄×Dic₄₃

yes

characteristic

C₄²

C₂²×Dic₄₃

yes

characteristic

C₁₆

—

C₂³

#13063236

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#13063236

yes

characteristic

C₂×C₄

#13063236

yes

—

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

C₂×C₄

C₂×#10621877

yes

—

C₈

—

C₈

—

C₈

#13063331

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#13063236

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#14582854

yes

—

C₂

—

C₂

#19132887

yes

characteristic

100

C₂

#19136200

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1450	C₂
socle	C₂²×C₄₃	C₂×#97
prime radical	C₂³×C₄₃	#97
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1450	D₄₃
hypocenter	C₄₃	#11416
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #1450

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₄₃

commutator

C₂×C₄×C₄₃

C₂×C₄²

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#1450

C₂

socle

C₂²×C₄₃

C₂×#97

prime radical

C₂³×C₄₃

#97

cosocle

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #1450

N	H ≅ G/N	type
2. #19132516	C₂	semidirect
61. C₄₃	#11416	semidirect

H ≅ G/N

type

2. #19132516

C₂

semidirect

61. C₄₃

#11416

semidirect

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

subgroup	index
#19136398	2
#19132516	2
C₄₃×#1450	2
#11416	43

subgroup

index

#19136398

#19132516

C₄₃×#1450

#11416

Subgroups — #25005652

Conjugacy classes of subgroups

Complements

Maximal subgroups