Group #24990411 — subgroups

Subgroups — #24990411

Order 11008.

338 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 187 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	#19134767	C₂	1	2	yes	maximal
2	#19133354	C₂	1	4	yes	maximal
3	C₂×C₄₃×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063261	—	2	4	no	—
5	#14582923	C₂²	1	4	yes	—
6	#14582652	—	2	8	no	—
7	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#322	C₄	1	4	yes	—
10	C₂×#10621877	—	2	4	no	—
11	#13063261	—	4	8	no	—
12	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
13	C₂²×C₈×C₄₃	D₄	1	2	yes	—
14	C₂²×C₈×C₄₃	Q₈	1	4	yes	—
15	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₄₃	D₄	1	4	yes	—
19	C₄×C₈×C₄₃	Q₈	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
22	C₂×C₈×C₄₃	—	4	4	no	—
23	C₂×C₈×C₄₃	C₄⋊C₄	1	8	yes	—
24	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
25	C₂×C₈×C₄₃	D₈	1	4	yes	—
26	C₂×C₈×C₄₃	Q₁₆	1	4	yes	—
27	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₄₃	C₂×D₄	1	2	yes	—
29	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
30	#10621877	—	4	8	no	—
31	C₂×C₄₃⋊C₈	—	4	4	no	—
32	C₂³×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	4	no	—
34	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
38	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
39	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
40	C₈×C₄₃	—	2	8	no	—
41	C₈×C₄₃	#107	1	8	yes	—
42	C₄₃⋊C₈	—	8	4	no	—
43	#8826	—	43	1	no	maximal, Sylow
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	#384	1	1	yes	characteristic
46	C₂²×C₄₃	#500	1	2	yes	—
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	C₂×#107	1	2	yes	—
49	C₄×C₄₃	#430	1	4	yes	—
50	C₄×C₄₃	#493	1	1	yes	characteristic
51	C₄×C₄₃	#494	1	1	yes	characteristic
52	#1848	—	43	2	no	—
53	#1567	—	43	4	no	—
54	C₂×#322	D₄₃	1	1	yes	characteristic
55	C₂×C₄₃	—	2	2	no	—
56	C₂×C₄₃	#1845	1	1	yes	characteristic
57	C₂×C₄₃	#1849	1	2	yes	—
58	C₂×#108	—	86	4	no	—
59	#423	—	43	4	no	—
60	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
62	#335	—	86	8	no	—
63	#322	Dic₄₃	1	4	yes	—
64	C₄₃	#8826	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	86	4	no	—
66	C₂²×C₈	Dic₈₆	1	4	yes	—
67	C₂²×C₈	D₁₇₂	1	2	yes	—
68	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
69	#108	—	172	8	no	—
70	C₄⋊C₈	—	86	8	no	—
71	C₄×C₈	Dic₈₆	1	2	yes	—
72	C₄×C₈	D₁₇₂	1	4	yes	—
73	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
74	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
75	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
76	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
77	M₁₆	—	172	8	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	—	172	4	no	—
80	C₂×C₈	D₃₄₄	1	4	yes	—
81	C₂×C₈	Dic₁₇₂	1	4	yes	—
82	C₂×C₈	C₄⋊Dic₄₃	1	8	yes	—
83	C₂×C₈	C₄⋊Dic₄₃	1	4	yes	—
84	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
85	C₄²	C₂×D₁₇₂	1	2	yes	—
86	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
87	C₂³	#13063325	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
91	C₂×C₄	#13063322	1	1	yes	characteristic
92	C₂×C₄	#13063325	1	2	yes	—
93	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
94	C₂×C₄	C₂×Dic₁₇₂	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	—	344	4	no	—
97	C₈	#13063259	1	8	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	#14582769	1	1	yes	characteristic
100	C₂²	#14583304	1	2	yes	—
101	C₄	—	2	2	no	—
102	C₄	C₂×#13063259	1	2	yes	—
103	C₄	#14582948	1	4	yes	—
104	C₄	#14583276	1	1	yes	characteristic
105	C₄	#14583279	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	#19134755	1	1	yes	characteristic
108	C₂	#19134770	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134767

C₂

yes

maximal

#19133354

C₂

yes

maximal

C₂×C₄₃×#322

C₂

yes

maximal, characteristic

C₂×#13063261

—

#14582923

C₂²

yes

—

#14582652

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

C₄

yes

—

C₂×#10621877

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

Q₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×D₈

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

#107

yes

—

C₄₃⋊C₈

—

#8826

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#384

yes

characteristic

C₂²×C₄₃

#500

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#107

yes

—

C₄×C₄₃

#430

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

—

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1845

yes

characteristic

C₂×C₄₃

#1849

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄×C₈

C₂×D₄₃

yes

—

#335

—

#322

Dic₄₃

yes

—

C₄₃

#8826

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

Dic₈₆

yes

—

C₂²×C₈

D₁₇₂

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#108

—

172

—

C₄⋊C₈

—

C₄×C₈

Dic₈₆

yes

—

C₄×C₈

D₁₇₂

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₈₆

yes

—

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

D₃₄₄

yes

—

C₂×C₈

Dic₁₇₂

yes

—

C₂×C₈

C₄⋊Dic₄₃

yes

—

C₂×C₈

C₄⋊Dic₄₃

yes

—

C₄²

C₂×Dic₈₆

yes

characteristic

C₄²

C₂×D₁₇₂

yes

—

C₄²

C₂²×Dic₄₃

yes

characteristic

C₂³

#13063325

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

—

C₂×C₄

#13063322

yes

characteristic

C₂×C₄

#13063325

yes

—

C₂×C₄

C₂×D₃₄₄

yes

—

C₂×C₄

C₂×Dic₁₇₂

yes

—

C₈

—

C₈

—

344

—

C₈

#13063259

yes

—

C₂²

—

C₂²

#14582769

yes

characteristic

100

C₂²

#14583304

yes

—

101

C₄

—

102

C₄

C₂×#13063259

yes

—

103

C₄

#14582948

yes

—

104

C₄

#14583276

yes

characteristic

105

C₄

#14583279

yes

characteristic

106

C₂

—

107

C₂

#19134755

yes

characteristic

108

C₂

#19134770

yes

—

	subgroup	G/H
center	C₂×C₄	#13063322
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#322	C₂
socle	C₂²×C₄₃	#384
prime radical	C₂³×C₄₃	C₄⋊Q₈
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#322	D₄₃
hypocenter	C₄₃	#8826
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#13063322

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₂×C₄₃×#322

C₂

socle

C₂²×C₄₃

#384

prime radical

C₂³×C₄₃

C₄⋊Q₈

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
64. C₄₃	#8826	semidirect

H ≅ G/N

type

64. C₄₃

#8826

semidirect

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

subgroup	index
#19134767	2
#19133354	2
C₂×C₄₃×#322	2
#8826	43

subgroup

index

#19134767

#19133354

C₂×C₄₃×#322

#8826

Subgroups — #24990411

Conjugacy classes of subgroups

Complements

Maximal subgroups