Group #18009570 — subgroups

Subgroups — #18009570

Order 4736.

110 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 26 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	#14558430	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558402	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557783	C₂	1	1	yes	maximal, characteristic
4	D₃₇⋊M₁₆	—	2	1	no	—
5	#11924610	—	2	1	no	—
6	C₂×#10596929	C₂²	1	1	yes	characteristic
7	#11924507	—	2	1	no	—
8	#11924468	C₄	1	1	yes	characteristic
9	#11924457	—	2	1	no	—
10	C₂×D₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×D₄×C₃₇	—	2	1	no	—
12	C₂×C₂²⋊D₃₇	—	4	1	no	—
13	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
14	#10596957	—	4	1	no	—
15	#10596953	—	4	1	no	—
16	D₃₇⋊C₈	—	2	2	no	—
17	D₈×C₃₇	—	4	1	no	—
18	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₃₇	—	4	1	no	—
20	C₄⋊Dic₃₇	—	2	1	no	—
21	C₂×#64436	D₄	1	1	yes	characteristic
22	#10596929	—	4	1	no	—
23	#10596927	—	4	1	no	—
24	C₂³×C₃₇	—	4	1	no	—
25	C₂²×D₃₇	SD₁₆	1	1	yes	characteristic
26	D₄×C₃₇	—	4	1	no	—
27	D₄×C₃₇	—	4	1	no	—
28	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²⋊D₃₇	—	8	2	no	—
30	C₂×Dic₃₇	—	4	1	no	—
31	C₂×Dic₃₇	D₈	1	1	yes	characteristic
32	C₄×D₃₇	—	2	1	no	—
33	C₄×D₃₇	—	2	1	no	—
34	#64438	—	4	2	no	—
35	C₈×C₃₇	—	2	1	no	—
36	#64436	—	2	1	no	—
37	C₂²×C₃₇	—	8	1	no	—
38	C₂²×C₃₇	—	8	1	no	—
39	C₂²×C₃₇	—	8	1	no	—
40	C₂²×C₃₇	#102	1	1	yes	characteristic
41	C₂×D₃₇	—	2	1	no	—
42	C₂×D₃₇	—	4	1	no	—
43	C₄×C₃₇	#99	1	1	yes	characteristic
44	C₄×C₃₇	#104	1	1	yes	characteristic
45	Dic₃₇	—	2	1	no	—
46	Dic₃₇	—	8	1	no	—
47	#1341	—	37	1	no	maximal, Sylow
48	C₂×C₃₇	—	2	1	no	—
49	C₂×C₃₇	—	16	1	no	—
50	C₂×C₃₇	#327	1	1	yes	characteristic
51	D₃₇	—	4	1	no	—
52	#469	—	37	1	no	—
53	#349	—	37	1	no	—
54	#338	—	37	1	no	—
55	C₃₇	#1341	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	#3866	1	1	yes	characteristic
57	C₂×M₁₆	—	37	1	no	—
58	C₂×M₁₆	—	74	1	no	—
59	#121	—	74	1	no	—
60	M₃₂	—	74	1	no	—
61	#106	—	37	1	no	—
62	#102	—	74	1	no	—
63	C₂×D₄	—	2	1	no	—
64	C₂×D₄	—	148	1	no	—
65	C₂²×C₄	—	37	1	no	—
66	D₈	—	4	1	no	—
67	M₁₆	—	148	1	no	—
68	M₁₆	—	148	1	no	—
69	M₁₆	—	148	1	no	—
70	C₂×C₈	—	37	1	no	—
71	C₂×C₈	—	74	2	no	—
72	C₂×C₈	C₂×#3866	1	1	yes	characteristic
73	C₄⋊C₄	—	74	1	no	—
74	C₂²⋊C₄	—	148	1	no	—
75	C₁₆	—	148	1	no	—
76	C₂³	—	4	1	no	—
77	C₂³	—	37	1	no	—
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	296	2	no	—
81	C₂×C₄	—	37	1	no	—
82	C₂×C₄	—	74	1	no	—
83	C₂×C₄	—	74	1	no	—
84	C₂×C₄	—	148	1	no	—
85	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	74	1	no	—
88	C₈	—	148	2	no	—
89	C₂²	—	8	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	74	1	no	—
93	C₂²	—	148	1	no	—
94	C₂²	#11924598	1	1	yes	characteristic
95	C₄	—	296	1	no	—
96	C₄	—	74	1	no	—
97	C₄	#11924594	1	1	yes	characteristic
98	C₄	#11924600	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	16	1	no	—
101	C₂	—	148	1	no	—
102	C₂	#14558384	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558430

C₂

yes

maximal, characteristic, complemented

#14558402

C₂

yes

maximal, characteristic, complemented

#14557783

C₂

yes

maximal, characteristic

D₃₇⋊M₁₆

—

#11924610

—

C₂×#10596929

C₂²

yes

characteristic

#11924507

—

#11924468

C₄

yes

characteristic

#11924457

—

C₂×D₈×C₃₇

C₄

yes

characteristic

C₂×D₄×C₃₇

—

C₂×C₂²⋊D₃₇

—

C₂×C₄×D₃₇

D₄

yes

characteristic

#10596957

—

#10596953

—

D₃₇⋊C₈

—

D₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂²⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₂×#64436

D₄

yes

characteristic

#10596929

—

#10596927

—

C₂³×C₃₇

—

C₂²×D₃₇

SD₁₆

yes

characteristic

D₄×C₃₇

—

D₄×C₃₇

—

C₂×C₄×C₃₇

C₂²⋊C₄

yes

characteristic

C₂²⋊D₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

D₈

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

#64438

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

#102

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₄×C₃₇

yes

C₄×C₃₇

yes

Dic₃₇

—

Dic₃₇

—

#1341

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

#327

yes

characteristic

D₃₇

—

#469

—

#349

—

#338

—

C₃₇

#1341

yes

characteristic, complemented, Sylow

C₂×D₈

#3866

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

#121

—

M₃₂

—

#106

—

#102

—

C₂×D₄

—

C₂×D₄

—

148

—

C₂²×C₄

—

D₈

—

M₁₆

—

148

—

M₁₆

—

148

—

M₁₆

—

148

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#3866

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

148

—

C₁₆

—

148

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

296

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

C₂²⋊#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

148

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

148

—

C₂²

#11924598

yes

characteristic

C₄

—

296

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

148

—

102

C₂

#14558384

yes

characteristic

	subgroup	G/H
center	C₂	#14558384
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×D₈×C₃₇	C₄
socle	C₂×C₃₇	#327
prime radical	#14557783	C₂
cosocle	C₂×#10596929	C₂²
hypercenter	C₂×D₈	#3866
hypocenter	C₃₇	#1341
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂

#14558384

commutator

C₂×C₈×C₃₇

C₂×C₄

Frattini

C₂×C₈

C₂×#3866

Fitting

C₂×D₈×C₃₇

C₄

C₂×C₃₇

C₂

C₂²

C₂×D₈

C₃₇

G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #14558430	C₂	semidirect
2. #14558402	C₂	semidirect
55. C₃₇	#1341	semidirect

H ≅ G/N

type

1. #14558430

C₂

semidirect

2. #14558402

C₂

semidirect

55. C₃₇

#1341

semidirect

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

subgroup	index
#14558430	2
#14558402	2
#14557783	2
#1341	37

subgroup

index

Subgroups — #18009570

Conjugacy classes of subgroups

Complements

Maximal subgroups