Group #17994715 — subgroups

Subgroups — #17994715

Order 4736.

216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 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×C₄⋊#64436	C₂	1	1	yes	maximal, characteristic
2	#14557379	C₂	1	1	yes	maximal, characteristic
3	#14557287	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64436	C₂²	1	2	yes	—
6	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
7	C₄⋊#64436	—	2	2	no	—
8	#11924443	C₄	1	2	yes	—
9	#11924443	C₄	1	2	yes	—
10	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
11	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₃₇	—	2	2	no	—
13	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₃₇	—	2	2	no	—
18	C₂×C₈×C₃₇	—	2	4	no	—
19	C₄²×C₃₇	D₄	1	2	yes	—
20	C₄²×C₃₇	Q₈	1	2	yes	—
21	C₄×Dic₃₇	—	2	2	no	—
22	C₄×Dic₃₇	—	2	2	no	—
23	C₂×#64436	—	2	2	no	—
24	C₂×#64436	—	2	4	no	—
25	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	2	2	no	—
27	C₂×C₄×C₃₇	—	2	2	no	—
28	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₃₇	#41	1	2	yes	—
33	C₂×C₄×C₃₇	#41	1	2	yes	—
34	C₂×Dic₃₇	—	2	4	no	—
35	C₂×Dic₃₇	—	2	4	no	—
36	C₂×Dic₃₇	—	2	4	no	—
37	C₈×C₃₇	—	4	2	no	—
38	#64436	—	4	2	no	—
39	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₇	#117	1	2	yes	—
41	C₂²×C₃₇	#131	1	2	yes	—
42	C₂²×C₃₇	#131	1	2	yes	—
43	C₄×C₃₇	—	2	2	no	—
44	C₄×C₃₇	—	2	2	no	—
45	C₄×C₃₇	#124	1	1	yes	characteristic
46	C₄×C₃₇	#124	1	1	yes	characteristic
47	C₄×C₃₇	#125	1	2	yes	—
48	Dic₃₇	—	4	4	no	—
49	#1832	—	37	1	no	maximal, Sylow
50	C₂×C₃₇	#382	1	1	yes	characteristic
51	C₂×C₃₇	#424	1	1	yes	characteristic
52	C₂×C₃₇	#424	1	1	yes	characteristic
53	C₂×C₃₇	#433	1	4	yes	—
54	C₂×C₄⋊C₈	—	37	1	no	—
55	C₂×C₄⋊C₈	D₃₇	1	1	yes	characteristic
56	#376	—	37	1	no	—
57	#336	—	37	4	no	—
58	C₃₇	#1832	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	37	2	no	—
60	C₂²×C₈	C₂×D₃₇	1	2	yes	—
61	C₂×C₄²	—	37	2	no	—
62	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
63	C₄⋊C₈	—	2	2	no	—
64	C₄⋊C₈	—	74	2	no	—
65	#95	—	37	2	no	—
66	#95	—	37	2	no	—
67	C₂²×C₄	—	37	4	no	—
68	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	74	4	no	—
74	C₂×C₈	—	74	2	no	—
75	C₄²	—	74	2	no	—
76	C₄²	—	74	2	no	—
77	C₄²	Dic₇₄	1	2	yes	—
78	C₄²	C₂²⋊D₃₇	1	2	yes	—
79	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	74	4	no	—
83	C₂×C₄	—	74	4	no	—
84	C₂×C₄	—	74	4	no	—
85	C₂×C₄	#10596936	1	2	yes	—
86	C₂×C₄	#10596936	1	2	yes	—
87	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
88	C₂×C₄	#10596964	1	2	yes	—
89	C₂×C₄	#10596966	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	148	2	no	—
93	C₂²	C₂×#10596936	1	1	yes	characteristic
94	C₂²	#11924494	1	2	yes	—
95	C₂²	#11924542	1	2	yes	—
96	C₂²	#11924544	1	2	yes	—
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	148	4	no	—
100	C₄	#11924523	1	1	yes	characteristic
101	C₄	#11924525	1	1	yes	characteristic
102	C₄	#11924527	1	2	yes	—
103	C₂	#14557398	1	1	yes	characteristic
104	C₂	#14557559	1	1	yes	characteristic
105	C₂	#14557561	1	1	yes	characteristic
106	C₂	#14557593	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#64436

C₂

yes

maximal, characteristic

#14557379

C₂

yes

maximal, characteristic

#14557287

C₂

yes

maximal

C₂×C₄⋊C₈×C₃₇

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

—

C₄⋊#64436

—

#11924443

C₄

yes

—

#11924443

C₄

yes

—

C₂²×C₈×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₄⋊C₈×C₃₇

—

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₄²×C₃₇

D₄

yes

—

C₄²×C₃₇

Q₈

yes

—

C₄×Dic₃₇

—

C₄×Dic₃₇

—

C₂×#64436

—

C₂×#64436

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

#41

yes

—

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃₇

#117

yes

—

C₂²×C₃₇

#131

yes

—

C₂²×C₃₇

#131

yes

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

yes

C₄×C₃₇

yes

C₄×C₃₇

yes

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₃₇

yes

characteristic

#376

—

#336

—

C₃₇

#1832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₇

yes

characteristic

C₂²×C₄

C₄×D₃₇

yes

characteristic

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

Dic₇₄

yes

—

C₄²

C₂²⋊D₃₇

yes

—

C₂³

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10596936

yes

—

C₂×C₄

#10596936

yes

—

C₂×C₄

C₂×Dic₇₄

yes

characteristic

C₂×C₄

#10596964

yes

—

C₂×C₄

#10596966

yes

—

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

C₈

—

C₈

—

148

—

C₂²

C₂×#10596936

yes

characteristic

C₂²

#11924494

yes

—

C₂²

#11924542

yes

—

C₂²

#11924544

yes

—

C₄

—

C₄

—

C₄

—

148

—

100

C₄

#11924523

yes

characteristic

101

C₄

#11924525

yes

characteristic

102

C₄

#11924527

yes

—

103

C₂

#14557398

yes

characteristic

104

C₂

#14557559

yes

characteristic

105

C₂

#14557561

yes

characteristic

106

C₂

#14557593

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator, socle, prime radical	C₂³×C₃₇	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₃₇	C₂
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×C₄⋊C₈	D₃₇
hypocenter	C₃₇	#1832
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₃₇

commutator, socle, prime radical

C₂³×C₃₇

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₃₇

C₂

cosocle

C₂²×C₄×C₃₇

C₂³

hypercenter

C₂×C₄⋊C₈

D₃₇

C₃₇

G ▷ C₂³×C₃₇ ▷ C₃₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
58. C₃₇	#1832	semidirect

H ≅ G/N

type

58. C₃₇

#1832

semidirect

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

subgroup	index
C₂×C₄⋊#64436	2
#14557379	2
#14557287	2
C₂×C₄⋊C₈×C₃₇	2
#1832	37

subgroup

index

C₂×C₄⋊#64436

#14557379

#14557287

C₂×C₄⋊C₈×C₃₇

#1832

Subgroups — #17994715

Conjugacy classes of subgroups

Complements

Maximal subgroups