Group #19133923 — subgroups

Subgroups — #19133923

Order 5504.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14583309	C₂	1	2	yes	maximal
2	#14583269	C₂	1	1	yes	maximal, characteristic
3	#14582641	C₂	1	2	yes	maximal
4	#14582641	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#564	C₂	1	1	yes	maximal, characteristic
6	#13063325	C₂²	1	1	yes	characteristic
7	#13063258	—	2	2	no	—
8	#13063256	—	2	2	no	—
9	#13063248	—	2	2	no	—
10	#13063236	C₂²	1	2	yes	—
11	#13063236	C₂²	1	1	yes	characteristic
12	#125×C₄₃	—	2	2	no	—
13	#125×C₄₃	—	2	2	no	—
14	#125×C₄₃	—	2	2	no	—
15	#125×C₄₃	C₂²	1	2	yes	—
16	#125×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₈₆	—	2	1	no	—
18	C₄⋊C₄×C₄₃	—	2	2	no	—
19	C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
25	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
26	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₄₃	—	4	1	no	—
38	Dic₈₆	—	4	2	no	—
39	C₄₃⋊C₈	—	2	4	no	—
40	C₄₃⋊C₈	—	4	1	no	—
41	C₂²×C₄₃	#120	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	—	4	2	no	—
45	C₄×C₄₃	—	4	2	no	—
46	C₄×C₄₃	—	4	2	no	—
47	Dic₄₃	—	8	1	no	—
48	#1663	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	#454	1	1	yes	characteristic
50	C₂×C₄₃	#456	1	2	yes	—
51	#564	D₄₃	1	1	yes	characteristic
52	#501	—	43	2	no	—
53	#491	—	43	1	no	—
54	#330	—	43	2	no	—
55	#330	—	43	1	no	—
56	C₄₃	#1663	1	1	yes	characteristic, complemented, Sylow
57	C₄⋊Q₈	—	43	1	no	—
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂×D₄₃	1	1	yes	characteristic
62	#125	C₂×D₄₃	1	2	yes	—
63	#107	—	86	2	no	—
64	#106	—	86	2	no	—
65	#103	—	86	2	no	—
66	#97	—	43	1	no	—
67	#97	—	43	2	no	—
68	C₂×Q₈	—	86	1	no	—
69	C₂×C₈	—	86	2	no	—
70	C₂×C₈	—	86	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	86	2	no	—
78	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
79	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
80	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂²×D₄₃	1	1	yes	characteristic
83	Q₈	—	172	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	172	1	no	—
88	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
90	C₈	—	86	4	no	—
91	C₈	—	172	1	no	—
92	C₂²	#13063294	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	344	1	no	—
99	C₂	#14583072	1	1	yes	characteristic
100	C₂	#14583082	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583309

C₂

yes

maximal

#14583269

C₂

yes

maximal, characteristic

#14582641

C₂

yes

maximal

#14582641

C₂

yes

maximal, characteristic

C₄₃×#564

C₂

yes

maximal, characteristic

#13063325

C₂²

yes

—

—

—

C₂²

yes

—

#13063236

C₂²

yes

characteristic

#125×C₄₃

—

#125×C₄₃

—

#125×C₄₃

—

#125×C₄₃

C₂²

yes

—

#125×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

#564

D₄₃

yes

—

—

—

—

C₄₃

#1663

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

—

—

—

C₂×D₄₃

yes

characteristic

#125

C₂×D₄₃

yes

—

—

—

—

—

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₂²

#13063294

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

344

—

C₂

#14583072

yes

characteristic

100

C₂

#14583082

yes

—

	subgroup	G/H
center	C₂²	#13063294
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#564	C₂
socle	C₂²×C₄₃	#120
hypercenter	#564	D₄₃
hypocenter	C₄₃	#1663
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

subgroup

G/H

center

C₂²

#13063294

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#564

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #564

N	H ≅ G/N	type
56. C₄₃	#1663	semidirect

H ≅ G/N

type

56. C₄₃

#1663

semidirect

Subgroups — #19133923

Conjugacy classes of subgroups

Complements