Group #17993924 — subgroups

Subgroups — #17993924

Order 4736.

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	#14557943	C₂	1	2	yes	maximal
2	#14557903	C₂	1	1	yes	maximal, characteristic
3	#14557275	C₂	1	1	yes	maximal, characteristic
4	#14557275	C₂	1	2	yes	maximal
5	C₃₇×#564	C₂	1	1	yes	maximal, characteristic
6	#11924536	C₂²	1	1	yes	characteristic
7	#11924469	—	2	2	no	—
8	#11924467	—	2	2	no	—
9	#11924459	—	2	2	no	—
10	#11924447	C₂²	1	1	yes	characteristic
11	#11924447	C₂²	1	2	yes	—
12	#125×C₃₇	—	2	2	no	—
13	#125×C₃₇	—	2	2	no	—
14	#125×C₃₇	—	2	2	no	—
15	#125×C₃₇	C₂²	1	1	yes	characteristic
16	#125×C₃₇	C₂²	1	2	yes	—
17	C₂×Dic₇₄	—	2	1	no	—
18	C₄⋊C₄×C₃₇	—	2	2	no	—
19	C₄⋊C₄×C₃₇	—	2	2	no	—
20	C₄⋊C₄×C₃₇	—	2	2	no	—
21	C₄⋊C₄×C₃₇	—	2	2	no	—
22	C₄⋊C₄×C₃₇	—	2	2	no	—
23	C₄⋊C₄×C₃₇	—	2	2	no	—
24	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
25	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
26	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
27	C₄²×C₃₇	—	2	2	no	—
28	C₄²×C₃₇	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₃₇	—	2	2	no	—
30	C₂×#64436	—	2	2	no	—
31	C₂×#64436	—	2	1	no	—
32	C₂×C₄×C₃₇	—	2	2	no	—
33	C₂×C₄×C₃₇	—	2	2	no	—
34	C₂×C₄×C₃₇	—	2	2	no	—
35	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₃₇	—	4	1	no	—
38	Dic₇₄	—	4	2	no	—
39	#64436	—	2	4	no	—
40	#64436	—	4	1	no	—
41	C₂²×C₃₇	#120	1	1	yes	characteristic
42	C₄×C₃₇	—	2	1	no	—
43	C₄×C₃₇	—	2	2	no	—
44	C₄×C₃₇	—	4	2	no	—
45	C₄×C₃₇	—	4	2	no	—
46	C₄×C₃₇	—	4	2	no	—
47	Dic₃₇	—	8	1	no	—
48	#1663	—	37	1	no	maximal, Sylow
49	C₂×C₃₇	#454	1	1	yes	characteristic
50	C₂×C₃₇	#456	1	2	yes	—
51	#564	D₃₇	1	1	yes	characteristic
52	#501	—	37	2	no	—
53	#491	—	37	1	no	—
54	#330	—	37	2	no	—
55	#330	—	37	1	no	—
56	C₃₇	#1663	1	1	yes	characteristic, complemented, Sylow
57	C₄⋊Q₈	—	37	1	no	—
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂×D₃₇	1	1	yes	characteristic
62	#125	C₂×D₃₇	1	2	yes	—
63	#107	—	74	2	no	—
64	#106	—	74	2	no	—
65	#103	—	74	2	no	—
66	#97	—	37	1	no	—
67	#97	—	37	2	no	—
68	C₂×Q₈	—	74	1	no	—
69	C₂×C₈	—	74	2	no	—
70	C₂×C₈	—	74	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	—	74	2	no	—
78	C₄⋊C₄	C₂²⋊D₃₇	1	2	yes	—
79	C₄⋊C₄	C₂²⋊D₃₇	1	2	yes	—
80	C₄⋊C₄	C₂²⋊D₃₇	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂²×D₃₇	1	1	yes	characteristic
83	Q₈	—	148	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	148	1	no	—
88	C₂×C₄	C₂×C₂²⋊D₃₇	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
90	C₈	—	74	4	no	—
91	C₈	—	148	1	no	—
92	C₂²	#11924505	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	—	296	1	no	—
99	C₂	#14557706	1	1	yes	characteristic
100	C₂	#14557716	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14557943

C₂

yes

maximal

#14557903

C₂

yes

maximal, characteristic

#14557275

C₂

yes

maximal, characteristic

#14557275

C₂

yes

maximal

C₃₇×#564

C₂

yes

maximal, characteristic

#11924536

C₂²

yes

—

—

—

C₂²

yes

characteristic

#11924447

C₂²

yes

—

#125×C₃₇

—

#125×C₃₇

—

#125×C₃₇

—

#125×C₃₇

C₂²

yes

characteristic

#125×C₃₇

C₂²

yes

—

C₂×Dic₇₄

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄²×C₃₇

—

C₄²×C₃₇

C₂³

yes

characteristic

C₄⋊Dic₃₇

—

C₂×#64436

—

C₂×#64436

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂×D₄

yes

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×Dic₃₇

—

Dic₇₄

—

#64436

—

#64436

—

C₂²×C₃₇

#120

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

#564

D₃₇

yes

—

—

—

—

C₃₇

#1663

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

—

—

—

C₂×D₃₇

yes

characteristic

#125

C₂×D₃₇

yes

—

—

—

—

—

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₃₇

yes

—

C₄⋊C₄

C₂²⋊D₃₇

yes

—

C₄⋊C₄

C₂²⋊D₃₇

yes

—

C₄²

—

C₄²

C₂²×D₃₇

yes

characteristic

Q₈

—

148

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

C₂×C₂²⋊D₃₇

yes

—

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

C₈

—

C₈

—

148

—

C₂²

#11924505

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

296

—

C₂

#14557706

yes

characteristic

100

C₂

#14557716

yes

—

	subgroup	G/H
center	C₂²	#11924505
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#564	C₂
socle, prime radical	C₂²×C₃₇	#120
hypercenter	#564	D₃₇
hypocenter	C₃₇	#1663
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

subgroup

G/H

center

C₂²

#11924505

commutator, cosocle

C₄²×C₃₇

C₂³

Frattini

C₄²

C₂²×D₃₇

Fitting

C₃₇×#564

C₂

C₂²×C₃₇

D₃₇

C₃₇

G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #564

N	H ≅ G/N	type
56. C₃₇	#1663	semidirect

H ≅ G/N

type

56. C₃₇

#1663

semidirect

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

subgroup	index
#14557943	2
#14557903	2
#14557275	2
C₃₇×#564	2
#1663	37

subgroup

index

C₃₇×#564

Subgroups — #17993924

Conjugacy classes of subgroups

Complements

Maximal subgroups