Group #24984078 — subgroups

Subgroups — #24984078

Order 11008.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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	#19136503	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1397	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₈₆	C₄	1	1	yes	characteristic
5	C₂×C₄₃⋊C₃₂	—	2	1	no	—
6	C₄⋊(C₄₃⋊C₁₆)	C₄	1	1	yes	characteristic
7	Dic₄₃⋊C₁₆	—	2	1	no	—
8	#14582674	—	2	1	no	—
9	C₂×C₃₂×C₄₃	—	2	1	no	—
10	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₈₆	C₈	1	1	yes	characteristic
12	C₂×C₄₃⋊C₁₆	—	2	1	no	—
13	C₄⋊(C₄₃⋊C₈)	C₈	1	1	yes	characteristic
14	Dic₄₃⋊C₈	—	2	1	no	—
15	C₈×Dic₄₃	—	2	1	no	—
16	C₄₃⋊C₃₂	—	4	1	no	—
17	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
19	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₃₂×C₄₃	—	2	2	no	—
21	C₂×Dic₈₆	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
24	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
25	C₄⋊Dic₄₃	C₁₆	1	1	yes	characteristic
26	Dic₄₃⋊C₄	—	2	1	no	—
27	C₄×Dic₄₃	—	2	1	no	—
28	C₂×C₄₃⋊C₈	—	2	1	no	—
29	C₁₆×C₄₃	—	2	1	no	—
30	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
31	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
32	C₄₃⋊C₁₆	—	4	1	no	—
33	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
35	C₂×C₄×C₄₃	M₃₂	1	1	yes	characteristic
36	C₂×Dic₄₃	—	2	1	no	—
37	C₂×Dic₄₃	—	2	1	no	—
38	Dic₈₆	—	4	1	no	—
39	C₈×C₄₃	—	2	1	no	—
40	C₈×C₄₃	#103	1	1	yes	characteristic
41	C₈×C₄₃	#104	1	1	yes	characteristic
42	C₄₃⋊C₈	—	4	1	no	—
43	#7393	—	43	1	no	maximal, Sylow
44	C₂²×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	Q₈⋊C₈	1	1	yes	characteristic
48	C₄×C₄₃	#350	1	1	yes	characteristic
49	Dic₄₃	—	4	1	no	—
50	Dic₄₃	—	4	1	no	—
51	#2183	—	43	1	no	—
52	C₄⋊C₃₂	—	43	1	no	—
53	#1397	D₄₃	1	1	yes	characteristic
54	C₂×C₄₃	Q₈⋊C₁₆	1	1	yes	characteristic
55	C₂×C₄₃	#1400	1	1	yes	characteristic
56	C₂×C₄₃	#1401	1	1	yes	characteristic
57	C₈×Q₈	—	43	1	no	—
58	C₂×C₃₂	—	2	1	no	—
59	C₂×C₃₂	—	86	1	no	—
60	C₄⋊C₁₆	—	43	1	no	—
61	C₄⋊C₁₆	—	86	1	no	—
62	#346	—	86	1	no	—
63	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
64	C₄₃	#7393	1	1	yes	characteristic, complemented, Sylow
65	C₄×Q₈	—	43	1	no	—
66	C₂×C₁₆	—	86	1	no	—
67	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
69	C₄⋊C₈	—	43	1	no	—
70	C₄⋊C₈	—	86	1	no	—
71	C₄×C₈	—	86	1	no	—
72	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
73	C₃₂	—	2	2	no	—
74	C₃₂	—	172	1	no	—
75	C₂×Q₈	—	43	1	no	—
76	C₂×C₈	—	86	1	no	—
77	C₂×C₈	#10621872	1	1	yes	characteristic
78	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
79	C₄⋊C₄	—	43	1	no	—
80	C₄⋊C₄	—	86	1	no	—
81	C₄²	—	86	1	no	—
82	C₄²	C₈×D₄₃	1	1	yes	characteristic
83	C₁₆	—	2	1	no	—
84	C₁₆	—	172	1	no	—
85	C₁₆	#10621873	1	1	yes	characteristic
86	C₁₆	Dic₁₇₂	1	1	yes	characteristic
87	Q₈	—	172	1	no	—
88	C₂×C₄	—	86	1	no	—
89	C₂×C₄	—	86	1	no	—
90	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
91	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
92	C₂×C₄	#13063264	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	172	1	no	—
95	C₈	#13063250	1	1	yes	characteristic
96	C₈	#13063253	1	1	yes	characteristic
97	C₂²	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	172	1	no	—
101	C₄	—	172	1	no	—
102	C₄	#14582631	1	1	yes	characteristic
103	C₄	#14582682	1	1	yes	characteristic
104	C₂	#19132575	1	1	yes	characteristic
105	C₂	#19132734	1	1	yes	characteristic
106	C₂	#19132738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136503

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₃₂)

C₂

yes

maximal, characteristic

C₄₃×#1397

C₂

yes

maximal, characteristic

C₈×Dic₈₆

C₄

yes

characteristic

C₂×C₄₃⋊C₃₂

—

C₄⋊(C₄₃⋊C₁₆)

C₄

yes

characteristic

Dic₄₃⋊C₁₆

—

#14582674

—

C₂×C₃₂×C₄₃

—

C₄×C₁₆×C₄₃

C₂²

yes

characteristic

C₄×Dic₈₆

C₈

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₄⋊(C₄₃⋊C₈)

C₈

yes

characteristic

Dic₄₃⋊C₈

—

C₈×Dic₄₃

—

C₄₃⋊C₃₂

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₃₂×C₄₃

—

C₂×Dic₈₆

C₁₆

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

M₁₆

yes

characteristic

C₄²×C₄₃

C₂×C₈

yes

characteristic

C₄⋊Dic₄₃

C₁₆

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₁₆×C₄₃

SD₁₆

yes

characteristic

C₁₆×C₄₃

Q₁₆

yes

characteristic

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₄₃

M₃₂

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7393

—

maximal, Sylow

C₂²×C₄₃

C₂²⋊C₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

Q₈⋊C₈

yes

characteristic

C₄×C₄₃

#350

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2183

—

C₄⋊C₃₂

—

#1397

D₄₃

yes

characteristic

C₂×C₄₃

Q₈⋊C₁₆

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

C₄×C₁₆

C₂×D₄₃

yes

characteristic

C₄₃

#7393

yes

characteristic, complemented, Sylow

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

D₁₇₂

yes

characteristic

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₃₂

—

C₃₂

—

172

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

#10621872

yes

characteristic

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₈×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

172

—

C₁₆

#10621873

yes

characteristic

C₁₆

Dic₁₇₂

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

C₂×C₄

C₁₆×D₄₃

yes

characteristic

C₂×C₄

#13063264

yes

characteristic

C₈

—

C₈

—

172

—

C₈

yes

C₈

yes

C₂²

(C₂×D₄₃)⋊C₁₆

yes

characteristic

C₄

—

C₄

—

100

C₄

—

172

—

101

C₄

—

172

—

102

C₄

#14582631

yes

characteristic

103

C₄

#14582682

yes

characteristic

104

C₂

#19132575

yes

characteristic

105

C₂

#19132734

yes

characteristic

106

C₂

#19132738

yes

characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1397	C₂
socle, prime radical	C₂²×C₄₃	C₂²⋊C₁₆
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1397	D₄₃
hypocenter	C₄₃	#7393
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂×C₈

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₄₃

Fitting

C₄₃×#1397

C₂

socle, prime radical

C₂²×C₄₃

C₂²⋊C₁₆

cosocle

C₄×C₁₆×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
64. C₄₃	#7393	semidirect

H ≅ G/N

type

64. C₄₃

#7393

semidirect

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

subgroup	index
#19136503	2
C₄⋊(C₄₃⋊C₃₂)	2
C₄₃×#1397	2
#7393	43

subgroup

index

#19136503

C₄⋊(C₄₃⋊C₃₂)

C₄₃×#1397

#7393

Subgroups — #24984078

Conjugacy classes of subgroups

Complements

Maximal subgroups