Group #24984465 — subgroups

Subgroups — #24984465

Order 11008.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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	#19134226	C₂	1	1	yes	maximal, characteristic
2	#19132764	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1411	C₂	1	1	yes	maximal, characteristic
4	#14583297	C₄	1	1	yes	characteristic
5	#14583295	—	2	1	no	—
6	#14583251	—	2	1	no	—
7	#14582698	—	2	1	no	—
8	#14582620	C₄	1	1	yes	characteristic
9	C₄₃×#494	C₂²	1	1	yes	characteristic
10	C₄₃×#356	—	2	1	no	—
11	#13063325	—	2	1	no	—
12	#13063257	—	4	1	no	—
13	#13063256	—	4	2	no	—
14	#13063248	—	4	2	no	—
15	#13063244	—	4	1	no	—
16	C₄×C₄₃⋊C₈	—	2	1	no	—
17	C₂×Q₁₆×C₄₃	—	4	1	no	—
18	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
19	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
20	#101×C₄₃	—	4	1	no	—
21	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×Q₈×C₄₃	—	2	1	no	—
24	C₂×Dic₈₆	—	4	1	no	—
25	Q₁₆×C₄₃	—	8	2	no	—
26	M₁₆×C₄₃	—	8	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₄⋊C₄×C₄₃	—	4	1	no	—
29	C₄⋊C₄×C₄₃	—	4	1	no	—
30	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄⋊Dic₄₃	—	4	1	no	—
32	C₄⋊Dic₄₃	—	4	1	no	—
33	#10621877	—	8	1	no	—
34	C₂×C₄₃⋊C₈	—	2	2	no	—
35	Q₈×C₄₃	—	8	1	no	—
36	Q₈×C₄₃	—	8	1	no	—
37	C₂×C₄×C₄₃	—	2	1	no	—
38	C₂×C₄×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
41	C₂×Dic₄₃	—	8	1	no	—
42	Dic₈₆	—	8	2	no	—
43	C₈×C₄₃	—	2	2	no	—
44	C₈×C₄₃	—	16	1	no	—
45	C₄₃⋊C₈	—	4	2	no	—
46	C₄₃⋊C₈	—	16	1	no	—
47	#7534	—	43	1	no	maximal, Sylow
48	C₂²×C₄₃	#353	1	1	yes	characteristic
49	C₄×C₄₃	—	2	2	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	—	8	1	no	—
52	C₄×C₄₃	—	8	1	no	—
53	Dic₄₃	—	16	1	no	—
54	#1716	—	43	1	no	—
55	#1411	—	43	1	no	—
56	#1411	D₄₃	1	1	yes	characteristic
57	C₂×C₄₃	—	2	1	no	—
58	C₂×C₄₃	#1409	1	1	yes	characteristic
59	#498	—	43	1	no	—
60	#498	—	86	1	no	—
61	#494	C₂×D₄₃	1	1	yes	characteristic
62	#487	—	86	1	no	—
63	#356	—	2	1	no	—
64	#356	—	86	1	no	—
65	#322	—	43	1	no	—
66	C₄₃	#7534	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₁₆	—	4	1	no	—
68	C₄⋊Q₈	—	86	1	no	—
69	C₄⋊Q₈	D₁₇₂	1	1	yes	characteristic
70	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
71	#106	—	172	2	no	—
72	#106	—	172	1	no	—
73	#103	—	172	2	no	—
74	#101	—	4	1	no	—
75	#101	—	172	1	no	—
76	C₄×C₈	—	86	1	no	—
77	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
78	C₂×Q₈	—	2	1	no	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	172	1	no	—
81	Q₁₆	—	8	2	no	—
82	M₁₆	—	8	1	no	—
83	M₁₆	—	344	1	no	—
84	C₂×C₈	—	2	1	no	—
85	C₂×C₈	—	86	2	no	—
86	C₄⋊C₄	—	4	1	no	—
87	C₄⋊C₄	—	4	1	no	—
88	C₄⋊C₄	—	172	1	no	—
89	C₄⋊C₄	—	172	1	no	—
90	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
91	Q₈	—	8	1	no	—
92	Q₈	—	8	1	no	—
93	Q₈	—	344	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	344	1	no	—
98	C₂×C₄	#13063239	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	16	1	no	—
101	C₈	—	172	2	no	—
102	C₈	—	688	1	no	—
103	C₂²	#14582691	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	1	no	—
107	C₄	—	8	1	no	—
108	C₄	—	688	1	no	—
109	C₂	—	2	1	no	—
110	C₂	#19132759	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134226

C₂

yes

maximal, characteristic

#19132764

C₂

yes

maximal, characteristic

C₄₃×#1411

C₂

yes

maximal, characteristic

#14583297

C₄

yes

—

—

—

C₄

yes

characteristic

C₄₃×#494

C₂²

yes

characteristic

C₄₃×#356

—

—

—

—

—

—

C₄×C₄₃⋊C₈

—

C₂×Q₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

D₄

yes

characteristic

C₄⋊Q₈×C₄₃

D₄

yes

characteristic

#101×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#99

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1716

—

#1411

—

#1411

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

C₂×D₄₃

yes

—

—

—

—

C₄₃

#7534

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

D₁₇₂

yes

characteristic

C₄⋊Q₈

C₂²⋊D₄₃

yes

characteristic

#106

—

172

—

#106

—

172

—

#103

—

172

—

#101

—

#101

—

172

—

C₄×C₈

—

C₄×C₈

C₄×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

Q₁₆

—

M₁₆

—

M₁₆

—

344

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

344

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

#13063239

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

172

—

102

C₈

—

688

—

103

C₂²

#14582691

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

688

—

109

C₂

—

110

C₂

#19132759

yes

characteristic

	subgroup	G/H
center	C₂	#19132759
commutator	C₄×C₈×C₄₃	C₂×C₄
Frattini	#494	C₂×D₄₃
Fitting	C₄₃×#1411	C₂
socle	C₂×C₄₃	#1409
prime radical	C₂²×C₄₃	#353
cosocle	C₄₃×#494	C₂²
hypercenter	#1411	D₄₃
hypocenter	C₄₃	#7534
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1411

subgroup

G/H

center

C₂

#19132759

commutator

C₄×C₈×C₄₃

C₂×C₄

Frattini

#494

C₂×D₄₃

Fitting

C₄₃×#1411

C₂

C₂×C₄₃

C₂²×C₄₃

C₄₃×#494

C₂²

D₄₃

C₄₃

G ▷ C₄×C₈×C₄₃ ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #494 ◁ #1411

N	H ≅ G/N	type
66. C₄₃	#7534	semidirect

H ≅ G/N

type

66. C₄₃

#7534

semidirect

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

subgroup	index
#19134226	2
#19132764	2
C₄₃×#1411	2
#7534	43

subgroup

index

#19134226

#19132764

C₄₃×#1411

#7534

Subgroups — #24984465

Conjugacy classes of subgroups

Complements

Maximal subgroups