Group #24983429 — subgroups

Subgroups — #24983429

Order 11008.

278 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 151 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	C₂×C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063265	C₄	1	4	yes	—
4	#14582675	—	2	2	no	—
5	C₄×C₄₃⋊C₁₆	—	2	2	no	—
6	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₈²×C₄₃	—	2	2	no	—
9	#13063265	—	2	4	no	—
10	#13063265	C₈	1	8	yes	complemented
11	C₂×C₄₃⋊C₁₆	—	2	4	no	—
12	C₂²×C₈×C₄₃	—	2	2	no	—
13	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₄₃	—	2	2	no	—
16	C₄×C₈×C₄₃	C₈	1	4	yes	—
17	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₄×C₈×C₄₃	D₄	1	2	yes	—
19	C₄×C₈×C₄₃	Q₈	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	8	no	—
23	C₂×C₈×C₄₃	—	2	4	no	—
24	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
25	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₄₃	C₂×C₈	1	4	yes	—
27	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
28	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄²×C₄₃	C₂×C₈	1	2	yes	—
31	C₄₃⋊C₁₆	—	2	8	no	—
32	C₂³×C₄₃	#97	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	4	no	—
34	C₂×C₄×C₄₃	#95	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₄×C₈	1	2	yes	—
36	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
37	C₂×C₄×C₄₃	#97	1	2	yes	—
38	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
39	C₂×C₄×C₄₃	C₄⋊C₈	1	2	yes	—
40	C₈×C₄₃	—	2	8	no	—
41	C₈×C₄₃	C₂²⋊C₈	1	4	yes	—
42	C₈×C₄₃	C₄⋊C₈	1	4	yes	—
43	#7138	—	43	1	no	maximal, Sylow
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	#322	1	2	yes	—
46	C₂²×C₄₃	#336	1	1	yes	characteristic
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	C₈²	1	1	yes	characteristic
49	C₄×C₄₃	#322	1	1	yes	characteristic
50	C₄×C₄₃	#336	1	2	yes	—
51	C₄×C₄₃	#364	1	4	yes	—
52	C₄×M₃₂	—	43	2	no	—
53	C₂×C₈²	D₄₃	1	1	yes	characteristic
54	C₂×C₄₃	—	2	2	no	—
55	C₂×C₄₃	#1273	1	1	yes	characteristic
56	C₂×C₄₃	#1376	1	2	yes	—
57	C₂×M₃₂	—	43	4	no	—
58	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
59	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
60	#346	—	86	2	no	—
61	C₄×C₁₆	—	86	2	no	—
62	C₈²	—	2	2	no	—
63	C₄₃	#7138	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	2	2	no	—
65	C₂²×C₈	C₄×D₄₃	1	2	yes	—
66	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
67	M₃₂	—	43	8	no	—
68	M₃₂	—	86	4	no	—
69	C₂×C₁₆	—	86	4	no	—
70	C₄×C₈	—	2	2	no	—
71	C₄×C₈	C₄₃⋊C₈	1	4	yes	—
72	C₄×C₈	Dic₈₆	1	1	yes	characteristic
73	C₄×C₈	D₁₇₂	1	1	yes	characteristic
74	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
75	C₂²×C₄	#10621877	1	2	yes	—
76	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
77	C₂×C₈	—	2	8	no	—
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	C₈×D₄₃	1	4	yes	—
80	C₂×C₈	#10621872	1	4	yes	—
81	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
82	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
83	C₄²	C₂×C₄₃⋊C₈	1	2	yes	—
84	C₄²	C₄⋊Dic₄₃	1	1	yes	characteristic
85	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
86	C₁₆	—	86	8	no	—
87	C₂³	#13063236	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	C₄₃⋊#95	1	1	yes	characteristic
90	C₂×C₄	C₈×Dic₄₃	1	2	yes	—
91	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
92	C₂×C₄	#13063235	1	2	yes	—
93	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	2	yes	—
94	C₂×C₄	C₄⋊(C₄₃⋊C₈)	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	(C₂×D₄₃)⋊C₈	1	4	yes	—
97	C₈	Dic₄₃⋊C₈	1	4	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	#14582621	1	2	yes	—
100	C₂²	#14582654	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	C₈×C₄₃⋊C₈	1	1	yes	characteristic
103	C₄	#14582620	1	1	yes	characteristic
104	C₄	#14582653	1	2	yes	—
105	C₄	#14582720	1	4	yes	—
106	C₂	—	2	2	no	—
107	C₂	C₄₃⋊#1273	1	1	yes	characteristic
108	C₂	#19132677	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063265

C₂

yes

maximal

C₂×C₈²×C₄₃

C₂

yes

maximal, characteristic

C₂×#13063265

C₄

yes

—

#14582675

—

C₄×C₄₃⋊C₁₆

—

C₂×C₄×C₈×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₈²×C₄₃

—

#13063265

—

#13063265

C₈

yes

complemented

C₂×C₄₃⋊C₁₆

—

C₂²×C₈×C₄₃

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₈

yes

—

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

M₁₆

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

M₁₆

yes

—

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₄⋊C₄

yes

characteristic

C₄²×C₄₃

C₂×C₈

yes

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#97

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#95

yes

characteristic

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

#97

yes

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

C₄⋊C₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₂²⋊C₈

yes

—

C₈×C₄₃

C₄⋊C₈

yes

—

#7138

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#322

yes

—

C₂²×C₄₃

#336

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₈²

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₄×C₄₃

#364

yes

—

C₄×M₃₂

—

C₂×C₈²

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1273

yes

characteristic

C₂×C₄₃

#1376

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

Dic₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#346

—

C₄×C₁₆

—

C₈²

—

C₄₃

#7138

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

C₄₃⋊C₈

yes

—

C₄×C₈

Dic₈₆

yes

characteristic

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

C₂²⋊D₄₃

yes

—

C₂²×C₄

#10621877

yes

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₄₃

yes

—

C₂×C₈

#10621872

yes

—

C₂×C₈

Dic₄₃⋊C₄

yes

—

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

C₄²

C₂×C₄₃⋊C₈

yes

—

C₄²

C₄⋊Dic₄₃

yes

characteristic

C₄²

C₂²⋊Dic₄₃

yes

characteristic

C₁₆

—

C₂³

#13063236

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄₃⋊#95

yes

characteristic

C₂×C₄

C₈×Dic₄₃

yes

—

C₂×C₄

C₄×C₄₃⋊C₈

yes

characteristic

C₂×C₄

#13063235

yes

—

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

—

C₂×C₄

C₄⋊(C₄₃⋊C₈)

yes

—

C₈

—

C₈

(C₂×D₄₃)⋊C₈

yes

—

C₈

Dic₄₃⋊C₈

yes

—

C₂²

—

C₂²

#14582621

yes

—

100

C₂²

#14582654

yes

characteristic

101

C₄

—

102

C₄

C₈×C₄₃⋊C₈

yes

characteristic

103

C₄

#14582620

yes

characteristic

104

C₄

#14582653

yes

—

105

C₄

#14582720

yes

—

106

C₂

—

107

C₂

C₄₃⋊#1273

yes

characteristic

108

C₂

#19132677

yes

—

	subgroup	G/H
center	C₄×C₈	D₁₇₂
commutator	C₄×C₄₃	C₈²
Frattini	C₂×C₄×C₈	C₂×D₄₃
Fitting	C₂×C₈²×C₄₃	C₂
socle	C₂²×C₄₃	#336
prime radical	C₂³×C₄₃	#97
cosocle	C₂×C₄×C₈×C₄₃	C₂²
hypercenter	C₂×C₈²	D₄₃
hypocenter	C₄₃	#7138
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

subgroup

G/H

center

C₄×C₈

D₁₇₂

commutator

C₄×C₄₃

C₈²

Frattini

C₂×C₄×C₈

C₂×D₄₃

Fitting

C₂×C₈²×C₄₃

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄×C₈×C₄₃

C₂²

hypercenter

C₂×C₈²

D₄₃

hypocenter

C₄₃

#7138

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

N	H ≅ G/N	type
10. #13063265	C₈	semidirect
63. C₄₃	#7138	semidirect

H ≅ G/N

type

10. #13063265

C₈

semidirect

63. C₄₃

#7138

semidirect

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

subgroup	index
C₄×#13063265	2
C₂×C₈²×C₄₃	2
#7138	43

subgroup

index

C₄×#13063265

C₂×C₈²×C₄₃

#7138

Subgroups — #24983429

Conjugacy classes of subgroups

Complements

Maximal subgroups