Group #17994752 — subgroups

Subgroups — #17994752

Order 4736.

280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#11924467	C₂	1	4	yes	maximal
2	C₂×C₄×#64436	C₂	1	1	yes	maximal, characteristic
3	#14557403	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64436	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₃₇	—	2	2	no	—
7	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
8	#11924467	—	2	8	no	—
9	C₄×#64436	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
11	C₂×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₃₇	—	2	2	no	—
14	C₂²×C₄×C₃₇	D₄	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	—	2	2	no	—
17	C₄⋊C₄×C₃₇	—	2	4	no	—
18	C₄⋊C₄×C₃₇	—	4	4	no	—
19	C₄²×C₃₇	C₂×C₄	1	2	yes	—
20	C₄²×C₃₇	Q₈	1	2	yes	—
21	C₄⋊Dic₃₇	—	2	4	no	—
22	C₄⋊Dic₃₇	—	4	4	no	—
23	C₂×#64436	C₂×C₄	1	4	yes	—
24	C₂×#64436	D₄	1	4	yes	—
25	C₂×#64436	Q₈	1	4	yes	—
26	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	—	4	4	no	—
29	C₂×C₄×C₃₇	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₃₇	SD₁₆	1	4	yes	—
31	C₂×C₄×C₃₇	SD₁₆	1	4	yes	—
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
36	C₂×Dic₃₇	—	4	2	no	—
37	C₂×Dic₃₇	—	4	4	no	—
38	#64436	C₄⋊C₄	1	8	yes	complemented
39	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₇	#127	1	1	yes	characteristic
41	C₂²×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₃₇	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₃₇	C₂×SD₁₆	1	2	yes	—
44	C₄×C₃₇	—	8	2	no	—
45	C₄×C₃₇	#106	1	8	yes	complemented
46	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
47	C₄×C₃₇	C₄⋊Q₈	1	2	yes	—
48	Dic₃₇	—	8	2	no	—
49	#1844	—	37	1	no	maximal, Sylow
50	C₂×C₃₇	#384	1	1	yes	characteristic
51	C₂×C₃₇	C₂×#106	1	2	yes	—
52	C₂×C₃₇	#492	1	1	yes	characteristic
53	C₂×C₃₇	#492	1	1	yes	characteristic
54	C₂×C₃₇	#498	1	2	yes	—
55	C₂×#106	—	37	4	no	—
56	C₂×C₄×C₈	—	37	1	no	—
57	#384	—	37	1	no	—
58	#384	D₃₇	1	1	yes	characteristic
59	C₃₇	#1844	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	37	2	no	—
61	C₂×C₄⋊C₄	—	2	2	no	—
62	C₂×C₄⋊C₄	—	37	2	no	—
63	C₂×C₄⋊C₄	—	74	2	no	—
64	C₂×C₄⋊C₄	C₂×D₃₇	1	2	yes	—
65	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
66	#106	—	74	8	no	—
67	C₄×C₈	—	37	4	no	—
68	C₂²×C₄	—	2	2	no	—
69	C₂²×C₄	—	74	2	no	—
70	C₂²×C₄	C₂²⋊D₃₇	1	2	yes	—
71	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
72	C₂×C₈	—	37	4	no	—
73	C₂×C₈	—	37	4	no	—
74	C₂×C₈	—	37	4	no	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	74	4	no	—
78	C₄⋊C₄	—	148	4	no	—
79	C₄²	Dic₇₄	1	2	yes	—
80	C₄²	C₄×D₃₇	1	2	yes	—
81	C₂³	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	148	2	no	—
85	C₂×C₄	—	148	4	no	—
86	C₂×C₄	#10596936	1	4	yes	—
87	C₂×C₄	#10596940	1	4	yes	—
88	C₂×C₄	#10596941	1	4	yes	—
89	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
91	C₂×C₄	D₄×D₃₇	1	2	yes	—
92	C₂×C₄	Q₈×D₃₇	1	2	yes	—
93	C₈	—	37	8	no	—
94	C₂²	C₂×#10596936	1	1	yes	characteristic
95	C₂²	#11924532	1	1	yes	characteristic
96	C₂²	#11924534	1	1	yes	characteristic
97	C₂²	C₂×#10596941	1	2	yes	—
98	C₂²	C₂×#10596940	1	2	yes	—
99	C₄	—	8	2	no	—
100	C₄	—	296	2	no	—
101	C₄	#11924467	1	8	yes	complemented
102	C₄	C₄⋊C₄×D₃₇	1	2	yes	—
103	C₄	#11924535	1	2	yes	—
104	C₂	#14557402	1	1	yes	characteristic
105	C₂	C₂×#11924467	1	2	yes	—
106	C₂	#14557905	1	1	yes	characteristic
107	C₂	#14557907	1	1	yes	characteristic
108	C₂	#14557929	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924467

C₂

yes

maximal

C₂×C₄×#64436

C₂

yes

maximal, characteristic

#14557403

C₂

yes

maximal, characteristic

C₃₇×#384

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄⋊Dic₃₇

—

C₂×C₄⋊Dic₃₇

C₂²

yes

—

#11924467

—

C₄×#64436

C₄

yes

complemented

C₂×C₄⋊C₄×C₃₇

—

C₂×C₄⋊C₄×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₂²×C₄×C₃₇

—

C₂²×C₄×C₃₇

D₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄²×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

Q₈

yes

—

C₄⋊Dic₃₇

—

C₄⋊Dic₃₇

—

C₂×#64436

C₂×C₄

yes

—

C₂×#64436

D₄

yes

—

C₂×#64436

Q₈

yes

—

C₂³×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

SD₁₆

yes

—

C₂×C₄×C₃₇

SD₁₆

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

—

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

#64436

C₄⋊C₄

yes

complemented

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃₇

#127

yes

characteristic

C₂²×C₃₇

C₄⋊Q₈

yes

characteristic

C₂²×C₃₇

C₂×SD₁₆

yes

—

C₂²×C₃₇

C₂×SD₁₆

yes

—

C₄×C₃₇

—

C₄×C₃₇

#106

yes

complemented

C₄×C₃₇

C₂×C₄⋊C₄

yes

—

C₄×C₃₇

C₄⋊Q₈

yes

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×#106

—

C₂×C₄×C₈

—

#384

—

#384

D₃₇

yes

characteristic

C₃₇

#1844

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₃₇

yes

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

#106

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₃₇

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

148

—

C₄²

Dic₇₄

yes

—

C₄²

C₄×D₃₇

yes

—

C₂³

C₂×C₂²⋊D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

148

—

C₂×C₄

—

148

—

C₂×C₄

#10596936

yes

—

C₂×C₄

#10596940

yes

—

C₂×C₄

#10596941

yes

—

C₂×C₄

C₂×Dic₇₄

yes

characteristic

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

D₄×D₃₇

yes

—

C₂×C₄

Q₈×D₃₇

yes

—

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#10596940

yes

—

C₄

—

100

C₄

—

296

—

101

C₄

#11924467

yes

complemented

102

C₄

C₄⋊C₄×D₃₇

yes

—

103

C₄

#11924535

yes

—

104

C₂

#14557402

yes

characteristic

105

C₂

C₂×#11924467

yes

—

106

C₂

#14557905

yes

characteristic

107

C₂

#14557907

yes

characteristic

108

C₂

#14557929

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#384	C₂
socle, prime radical	C₂³×C₃₇	C₂×D₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#384	D₃₇
hypocenter	C₃₇	#1844
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₃₇

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₃₇×#384

C₂

socle, prime radical

C₂³×C₃₇

C₂×D₄

cosocle

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×#64436	C₄	semidirect
38. #64436	C₄⋊C₄	semidirect
45. C₄×C₃₇	#106	semidirect
59. C₃₇	#1844	semidirect
101. C₄	#11924467	semidirect

H ≅ G/N

type

9. C₄×#64436

C₄

semidirect

38. #64436

C₄⋊C₄

semidirect

45. C₄×C₃₇

#106

semidirect

59. C₃₇

#1844

semidirect

101. C₄

#11924467

semidirect

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

subgroup	index
C₂×#11924467	2
C₂×C₄×#64436	2
#14557403	2
C₃₇×#384	2
#1844	37

subgroup

index

C₂×#11924467

C₂×C₄×#64436

#14557403

C₃₇×#384

#1844

Subgroups — #17994752

Conjugacy classes of subgroups

Complements

Maximal subgroups