Group #17994282 — subgroups

Subgroups — #17994282

Order 4736.

328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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×#11924447	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924446	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₃₇	C₂	1	2	yes	maximal
4	#14557379	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64436	C₂²	1	2	yes	—
7	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
8	#11924447	C₄	1	4	yes	complemented
9	#11924446	C₄	1	8	yes	complemented
10	C₈×Dic₃₇	C₄	1	8	yes	complemented
11	#11924443	C₄	1	4	yes	—
12	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₃₇	C₄	1	4	yes	complemented
16	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₃₇	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
23	C₄²×C₃₇	C₂×C₄	1	2	yes	—
24	C₄²×C₃₇	C₂×C₄	1	2	yes	—
25	C₄×Dic₃₇	C₂×C₄	1	4	yes	—
26	C₄×Dic₃₇	C₂×C₄	1	4	yes	—
27	C₂×#64436	C₂×C₄	1	4	yes	—
28	C₂×#64436	C₂×C₄	1	4	yes	—
29	C₂×#64436	C₂×C₄	1	4	yes	—
30	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	—	2	4	no	—
32	C₂×C₄×C₃₇	C₄²	1	4	yes	—
33	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₃₇	—	2	8	no	—
38	C₂×Dic₃₇	C₄²	1	8	yes	—
39	C₈×C₃₇	C₄²	1	4	yes	—
40	C₈×C₃₇	C₄²	1	4	yes	—
41	#64436	C₄²	1	8	yes	—
42	C₂²×C₃₇	C₂×C₄²	1	2	yes	—
43	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₃₇	#131	1	4	yes	—
45	C₄×C₃₇	—	2	4	no	—
46	C₄×C₃₇	C₂×C₄²	1	2	yes	—
47	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
49	Dic₃₇	—	2	8	no	—
50	#1726	—	37	1	no	maximal, Sylow
51	C₂×C₃₇	C₄³	1	1	yes	characteristic
52	C₂×C₃₇	#405	1	4	yes	—
53	C₂×C₃₇	#405	1	2	yes	—
54	C₂×#97	—	37	2	no	—
55	C₂×#97	—	37	1	no	—
56	C₂×C₄×C₈	—	37	2	no	—
57	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
58	#376	—	37	1	no	—
59	C₃₇	#1726	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	37	2	no	—
61	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
63	C₂×C₄²	—	37	2	no	—
64	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
65	#97	—	37	8	no	—
66	#97	—	37	4	no	—
67	C₄×C₈	—	37	8	no	—
68	C₄×C₈	Dic₃₇	1	4	yes	complemented
69	#95	—	37	4	no	—
70	C₂²×C₄	—	37	4	no	—
71	C₂²×C₄	C₄×D₃₇	1	2	yes	—
72	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
73	C₂×C₈	—	37	4	no	—
74	C₂×C₈	—	37	4	no	—
75	C₂×C₈	—	37	4	no	—
76	C₂×C₈	C₄×D₃₇	1	4	yes	—
77	C₂×C₈	C₄×D₃₇	1	4	yes	—
78	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
79	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
80	C₄²	—	37	4	no	—
81	C₄²	—	37	4	no	—
82	C₄²	C₄×D₃₇	1	2	yes	—
83	C₄²	C₂×Dic₃₇	1	2	yes	—
84	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	37	8	no	—
87	C₂×C₄	—	74	8	no	—
88	C₂×C₄	C₄×Dic₃₇	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
92	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
93	C₈	—	37	8	no	—
94	C₈	C₄×Dic₃₇	1	4	yes	—
95	C₈	C₄×Dic₃₇	1	4	yes	—
96	C₂²	C₄²×D₃₇	1	2	yes	—
97	C₂²	C₂×C₄×Dic₃₇	1	1	yes	characteristic
98	C₂²	#11924542	1	4	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	74	8	no	—
101	C₄	C₄²×D₃₇	1	2	yes	—
102	C₄	C₂×C₄×Dic₃₇	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₃₇	1	1	yes	characteristic
104	C₂	C₄²×Dic₃₇	1	1	yes	characteristic
105	C₂	#14557487	1	4	yes	—
106	C₂	#14557488	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924447

C₂

yes

maximal, characteristic

C₂×#11924446

C₂

yes

maximal

C₂×C₈×Dic₃₇

C₂

yes

maximal

#14557379

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₃₇

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

—

#11924447

C₄

yes

complemented

#11924446

C₄

yes

complemented

C₈×Dic₃₇

C₄

yes

complemented

#11924443

C₄

yes

—

C₂²×C₈×C₃₇

C₂²

yes

characteristic

C₂²×C₈×C₃₇

C₂²

yes

characteristic

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

complemented

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₂×#64436

C₂×C₄

yes

—

C₂×#64436

C₂×C₄

yes

—

C₂×#64436

C₂×C₄

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄²

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄²

yes

—

C₈×C₃₇

C₄²

yes

—

C₈×C₃₇

C₄²

yes

—

#64436

C₄²

yes

—

C₂²×C₃₇

C₂×C₄²

yes

—

C₂²×C₃₇

C₂×C₄²

yes

characteristic

C₂²×C₃₇

#131

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄²

yes

—

C₄×C₃₇

C₂×C₄²

yes

characteristic

C₄×C₃₇

C₂×C₄²

yes

characteristic

Dic₃₇

—

#1726

—

maximal, Sylow

C₂×C₃₇

C₄³

yes

characteristic

C₂×C₃₇

#405

yes

—

C₂×C₃₇

#405

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₃₇

yes

characteristic

#376

—

C₃₇

#1726

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

characteristic

C₂²×C₈

C₂×D₃₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₃₇

yes

complemented

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₇

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₇

yes

—

C₂×C₈

C₄×D₃₇

yes

—

C₂×C₈

C₂×Dic₃₇

yes

—

C₂×C₈

C₂×Dic₃₇

yes

—

C₄²

—

C₄²

—

C₄²

C₄×D₃₇

yes

—

C₄²

C₂×Dic₃₇

yes

—

C₂³

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₃₇

yes

—

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

C₂×C₄×D₃₇

yes

—

C₂×C₄

C₂×C₄×D₃₇

yes

—

C₂×C₄

C₂²×Dic₃₇

yes

characteristic

C₈

—

C₈

C₄×Dic₃₇

yes

—

C₈

C₄×Dic₃₇

yes

—

C₂²

C₄²×D₃₇

yes

—

C₂²

C₂×C₄×Dic₃₇

yes

characteristic

C₂²

#11924542

yes

—

C₄

—

100

C₄

—

101

C₄

C₄²×D₃₇

yes

—

102

C₄

C₂×C₄×Dic₃₇

yes

characteristic

103

C₄

C₂×C₄×Dic₃₇

yes

characteristic

104

C₂

C₄²×Dic₃₇

yes

characteristic

105

C₂

#14557487

yes

—

106

C₂

#14557488

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₃₇
commutator	C₂×C₃₇	C₄³
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	#1726
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₃₇

commutator

C₂×C₃₇

C₄³

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₂×C₄×C₈×C₃₇

C₂

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂²×C₄×C₃₇

C₂³

hypercenter

C₂×C₄×C₈

D₃₇

C₃₇

G ▷ C₂×C₃₇ ▷ C₃₇

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
8. #11924447	C₄	semidirect
9. #11924446	C₄	semidirect
10. C₈×Dic₃₇	C₄	semidirect
15. C₄×C₈×C₃₇	C₄	semidirect
59. C₃₇	#1726	semidirect
68. C₄×C₈	Dic₃₇	semidirect

H ≅ G/N

type

8. #11924447

C₄

semidirect

9. #11924446

C₄

semidirect

10. C₈×Dic₃₇

C₄

semidirect

15. C₄×C₈×C₃₇

C₄

semidirect

59. C₃₇

#1726

semidirect

68. C₄×C₈

Dic₃₇

semidirect

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

subgroup	index
C₂×#11924447	2
C₂×#11924446	2
C₂×C₈×Dic₃₇	2
#14557379	2
C₂×C₄×C₈×C₃₇	2
#1726	37

subgroup

index

C₂×C₈×Dic₃₇

C₂×C₄×C₈×C₃₇

Subgroups — #17994282

Conjugacy classes of subgroups

Complements

Maximal subgroups