Group #24990408 — subgroups

Subgroups — #24990408

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	#19133351	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	#14582650	—	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	SD₁₆	1	8	yes	—
26	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₄²×C₄₃	C₂×D₄	1	2	yes	—
28	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
29	#10621877	—	4	8	no	—
30	C₂×C₄₃⋊C₈	—	4	4	no	—
31	C₂³×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	4	no	—
33	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
38	C₈×C₄₃	—	2	8	no	—
39	C₈×C₄₃	#106	1	8	yes	—
40	C₄₃⋊C₈	—	8	4	no	—
41	#8825	—	43	1	no	maximal, Sylow
42	C₂²×C₄₃	—	2	2	no	—
43	C₂²×C₄₃	#384	1	1	yes	characteristic
44	C₂²×C₄₃	#498	1	2	yes	—
45	C₄×C₄₃	—	2	2	no	—
46	C₄×C₄₃	C₂×#106	1	2	yes	—
47	C₄×C₄₃	#430	1	4	yes	—
48	C₄×C₄₃	#492	1	2	yes	—
49	#1848	—	43	2	no	—
50	#1566	—	43	4	no	—
51	C₂×#322	D₄₃	1	1	yes	characteristic
52	C₂×C₄₃	—	2	2	no	—
53	C₂×C₄₃	#1844	1	1	yes	characteristic
54	C₂×C₄₃	#1849	1	2	yes	—
55	C₂×#108	—	86	4	no	—
56	#423	—	43	4	no	—
57	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
58	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
59	#334	—	86	8	no	—
60	#322	Dic₄₃	1	4	yes	—
61	C₄₃	#8825	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₁₆	—	86	4	no	—
63	C₂²×C₈	Dic₈₆	1	4	yes	—
64	C₂²×C₈	D₁₇₂	1	2	yes	—
65	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
66	#108	—	172	8	no	—
67	C₄⋊C₈	—	86	8	no	—
68	C₄×C₈	Dic₈₆	1	2	yes	—
69	C₄×C₈	D₁₇₂	1	4	yes	—
70	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
71	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
72	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
73	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
74	M₁₆	—	172	8	no	—
75	C₂×C₈	—	4	4	no	—
76	C₂×C₈	—	172	4	no	—
77	C₂×C₈	#10621873	1	8	yes	—
78	C₂×C₈	C₄⋊Dic₄₃	1	8	yes	—
79	C₂×C₈	C₄⋊Dic₄₃	1	4	yes	—
80	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
81	C₄²	C₂×D₁₇₂	1	2	yes	—
82	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
83	C₂³	#13063325	1	1	yes	characteristic
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
86	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
87	C₂×C₄	#13063322	1	1	yes	characteristic
88	C₂×C₄	#13063325	1	2	yes	—
89	C₂×C₄	C₂×#10621873	1	4	yes	—
90	C₈	—	2	8	no	—
91	C₈	—	344	4	no	—
92	C₈	#13063257	1	8	yes	—
93	C₂²	—	2	2	no	—
94	C₂²	#14582769	1	1	yes	characteristic
95	C₂²	#14583297	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	C₂×#13063257	1	2	yes	—
98	C₄	#14582948	1	4	yes	—
99	C₄	#14583272	1	2	yes	—
100	C₂	—	2	2	no	—
101	C₂	#19134752	1	1	yes	characteristic
102	C₂	#19134770	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134767

C₂

yes

maximal

#19133351

C₂

yes

maximal

C₂×C₄₃×#322

C₂

yes

maximal, characteristic

C₂×#13063261

—

#14582923

C₂²

yes

—

#14582650

—

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

SD₁₆

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×SD₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

#106

yes

—

C₄₃⋊C₈

—

#8825

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#384

yes

characteristic

C₂²×C₄₃

#498

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#106

yes

—

C₄×C₄₃

#430

yes

—

C₄×C₄₃

#492

yes

—

#1848

—

#1566

—

C₂×#322

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1844

yes

characteristic

C₂×C₄₃

#1849

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄×C₈

C₂×D₄₃

yes

—

#334

—

#322

Dic₄₃

yes

—

C₄₃

#8825

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

#10621873

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×#10621873

yes

—

C₈

—

C₈

—

344

—

C₈

#13063257

yes

—

C₂²

—

C₂²

#14582769

yes

characteristic

C₂²

#14583297

yes

—

C₄

—

C₄

C₂×#13063257

yes

—

C₄

#14582948

yes

—

C₄

#14583272

yes

—

100

C₂

—

101

C₂

#19134752

yes

characteristic

102

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	#8825
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
61. C₄₃	#8825	semidirect

H ≅ G/N

type

61. C₄₃

#8825

semidirect

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

subgroup	index
#19134767	2
#19133351	2
C₂×C₄₃×#322	2
#8825	43

subgroup

index

#19134767

#19133351

C₂×C₄₃×#322

#8825

Subgroups — #24990408

Conjugacy classes of subgroups

Complements

Maximal subgroups