Group #24983694 — subgroups

Subgroups — #24983694

Order 11008.

148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19136411	C₂	1	2	yes	maximal
2	C₄₃×#2151	C₂	1	1	yes	maximal, characteristic
3	#14582720	—	2	2	no	—
4	#14582681	—	2	2	no	—
5	#14582677	C₄	1	4	yes	—
6	C₂×M₃₂×C₄₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₄₃	C₄	1	1	yes	characteristic
8	C₄₃×#405	C₂²	1	1	yes	characteristic
9	C₄₃×C₄⋊C₁₆	—	2	2	no	—
10	#13063265	—	2	4	no	—
11	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	#117×C₄₃	Q₈	1	1	yes	characteristic
14	M₃₂×C₄₃	—	4	1	no	—
15	C₂×C₁₆×C₄₃	—	2	1	no	—
16	C₂×C₁₆×C₄₃	—	2	1	no	—
17	C₂×C₁₆×C₄₃	—	4	1	no	—
18	#97×C₄₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
21	M₁₆×C₄₃	—	4	1	no	—
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	—	2	1	no	—
24	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₄₃	—	2	1	no	—
28	C₂²⋊C₄×C₄₃	—	2	1	no	—
29	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
30	C₁₆×C₄₃	—	4	1	no	—
31	C₁₆×C₄₃	—	4	1	no	—
32	C₄₃⋊C₁₆	—	4	4	no	—
33	C₂³×C₄₃	#108	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#108	1	1	yes	characteristic
39	C₈×C₄₃	—	2	2	no	—
40	C₈×C₄₃	—	2	1	no	—
41	C₈×C₄₃	#100	1	1	yes	characteristic
42	C₈×C₄₃	#101	1	1	yes	characteristic
43	#7240	—	43	1	no	maximal, Sylow
44	C₂²×C₄₃	—	2	1	no	—
45	C₂²×C₄₃	—	4	1	no	—
46	C₂²×C₄₃	#341	1	1	yes	characteristic
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	4	2	no	—
49	C₄×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
50	C₄×C₄₃	#343	1	1	yes	characteristic
51	#2166	—	43	2	no	—
52	#2151	D₄₃	1	1	yes	characteristic
53	C₂×C₄₃	—	2	1	no	—
54	C₂×C₄₃	—	4	1	no	—
55	C₂×C₄₃	#1290	1	1	yes	characteristic
56	C₂×M₃₂	Dic₄₃	1	1	yes	characteristic
57	C₂²×C₁₆	Dic₄₃	1	1	yes	characteristic
58	#405	C₂×D₄₃	1	1	yes	characteristic
59	#364	—	86	2	no	—
60	C₄⋊C₁₆	—	2	2	no	—
61	#349	—	86	2	no	—
62	#347	—	43	4	no	—
63	C₄₃	#7240	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
65	C₂²×C₈	C₂×Dic₄₃	1	1	yes	characteristic
66	#117	Dic₈₆	1	1	yes	characteristic
67	M₃₂	—	4	1	no	—
68	M₃₂	—	86	4	no	—
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	2	1	no	—
71	C₂×C₁₆	—	4	1	no	—
72	#97	C₄×D₄₃	1	2	yes	—
73	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
74	C₂²×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
79	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
80	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₄²	Dic₄₃⋊C₄	1	2	yes	—
84	C₁₆	—	4	1	no	—
85	C₁₆	—	4	1	no	—
86	C₁₆	—	172	4	no	—
87	C₂³	#13063261	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
92	C₂×C₄	#13063261	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	2	1	no	—
95	C₈	#13063242	1	1	yes	characteristic
96	C₈	#13063244	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#14582664	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	#14582656	1	1	yes	characteristic
103	C₄	#14582668	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	#19132465	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136411

C₂

yes

maximal

C₄₃×#2151

C₂

yes

maximal, characteristic

#14582720

—

#14582681

—

#14582677

C₄

yes

—

C₂×M₃₂×C₄₃

C₄

yes

characteristic

C₂²×C₁₆×C₄₃

C₄

yes

characteristic

C₄₃×#405

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

#13063265

—

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

#117×C₄₃

Q₈

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

#97×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₄⋊C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄²

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₄⋊C₄

yes

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#108

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#341

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1290

yes

characteristic

C₂×M₃₂

Dic₄₃

yes

characteristic

C₂²×C₁₆

Dic₄₃

yes

characteristic

#405

C₂×D₄₃

yes

characteristic

#364

—

C₄⋊C₁₆

—

#349

—

#347

—

C₄₃

#7240

yes

characteristic, complemented, Sylow

C₂×M₁₆

D₁₇₂

yes

characteristic

C₂²×C₈

C₂×Dic₄₃

yes

characteristic

#117

Dic₈₆

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

C₄×D₄₃

yes

—

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₄⋊Dic₄₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₄₃

yes

characteristic

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

Dic₄₃⋊C₄

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

172

—

C₂³

#13063261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄₃⋊#95

yes

characteristic

C₂×C₄

#13063261

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

#14582664

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#14582656

yes

characteristic

103

C₄

#14582668

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#19132465

yes

characteristic

	subgroup	G/H
center	C₄	#14582656
commutator	C₂×C₈×C₄₃	C₄²
Frattini	#405	C₂×D₄₃
Fitting	C₄₃×#2151	C₂
socle	C₂×C₄₃	#1290
prime radical	C₂³×C₄₃	#108
cosocle	C₄₃×#405	C₂²
hypercenter	#2151	D₄₃
hypocenter	C₄₃	#7240
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

subgroup

G/H

center

C₄

#14582656

commutator

C₂×C₈×C₄₃

C₄²

Frattini

#405

C₂×D₄₃

Fitting

C₄₃×#2151

C₂

C₂×C₄₃

C₂³×C₄₃

C₄₃×#405

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

N	H ≅ G/N	type
63. C₄₃	#7240	semidirect

H ≅ G/N

type

63. C₄₃

#7240

semidirect

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

subgroup	index
#19136411	2
C₄₃×#2151	2
#7240	43

subgroup

index

#19136411

C₄₃×#2151

#7240

Subgroups — #24983694

Conjugacy classes of subgroups

Complements

Maximal subgroups