Group #37549930 — subgroups

Subgroups — #37549930

Order 23168.

184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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×#19153890	C₂	1	1	yes	maximal, characteristic
2	C₂²×#15668452	C₂	1	1	yes	maximal, characteristic
3	#26042167	C₂	1	2	yes	maximal, complemented
4	C₄×#15668452	C₂	1	2	yes	maximal, complemented
5	#26041235	C₂	1	1	yes	maximal, characteristic
6	#19153890	C₄	1	4	yes	complemented
7	C₂×#15668452	C₄	1	4	yes	complemented
8	C₂×#15668452	C₂²	1	1	yes	characteristic
9	C₂×#15668452	C₂²	1	2	yes	—
10	C₂×#15668452	C₂²	1	1	yes	characteristic
11	C₂×#15668433	C₄	1	1	yes	characteristic
12	C₂²×#13089678	C₂²	1	1	yes	characteristic
13	#19153727	C₄	1	2	yes	—
14	C₄×#13089678	C₂²	1	2	yes	—
15	#117×C₁₈₁	C₄	1	1	yes	characteristic
16	#15668452	C₂×C₄	1	2	yes	—
17	#15668452	C₂×C₄	1	2	yes	—
18	#15668452	C₂×C₄	1	4	yes	—
19	#15668433	C₈	1	4	yes	—
20	C₂×#13089678	C₂×C₄	1	2	yes	—
21	C₂×#13089678	C₂×C₄	1	2	yes	—
22	C₂×#13089678	C₂×C₄	1	1	yes	characteristic
23	C₂×#13089678	C₂×C₄	1	2	yes	—
24	C₂×#13089678	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
26	C₄⋊C₄×C₁₈₁	C₈	1	2	yes	—
27	C₂²⋊C₄×C₁₈₁	C₈	1	2	yes	—
28	C₄²×C₁₈₁	C₂×C₄	1	2	yes	—
29	#13089678	C₄²	1	2	yes	—
30	#13089678	C₂×C₈	1	4	yes	—
31	#13089678	C₂²×C₄	1	1	yes	characteristic
32	#13089678	C₂²×C₄	1	1	yes	characteristic
33	C₂³×C₁₈₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₈₁	C₄²	1	2	yes	—
35	C₂×C₄×C₁₈₁	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×C₁₈₁	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₁₈₁	—	2	2	no	—
40	C₂²×C₁₈₁	C₄×C₈	1	2	yes	—
41	C₂²×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₁₈₁	—	2	4	no	—
43	C₄×C₁₈₁	C₄×C₈	1	2	yes	—
44	C₄×C₁₈₁	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₁₈₁	C₂²×C₈	1	1	yes	characteristic
46	C₂×C₁₈₁	—	2	2	no	—
47	C₂×C₁₈₁	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂×C₁₈₁	#504	1	2	yes	—
49	C₁₈₁	#2108	1	1	yes	characteristic, complemented, Sylow
50	#2108	—	181	1	no	maximal, Sylow
51	C₂×M₃₂	—	181	1	no	—
52	C₂²×C₁₆	—	181	1	no	—
53	#405	—	181	1	no	—
54	#346	—	181	2	no	—
55	C₄×C₁₆	—	181	2	no	—
56	C₂×M₁₆	—	181	1	no	—
57	C₂²×C₈	—	181	1	no	—
58	#117	#10624382	1	1	yes	characteristic
59	M₃₂	—	181	4	no	—
60	C₂×C₁₆	—	181	1	no	—
61	C₂×C₁₆	—	181	2	no	—
62	C₂×C₁₆	—	181	1	no	—
63	C₂×C₁₆	—	181	4	no	—
64	#97	—	181	2	no	—
65	C₄×C₈	—	181	2	no	—
66	C₂²×C₄	C₂×#10624382	1	1	yes	characteristic
67	M₁₆	—	181	4	no	—
68	C₂×C₈	—	181	2	no	—
69	C₂×C₈	—	181	2	no	—
70	C₂×C₈	—	181	1	no	—
71	C₂×C₈	—	181	2	no	—
72	C₂×C₈	—	181	1	no	—
73	C₄⋊C₄	#13089685	1	2	yes	—
74	C₂²⋊C₄	#13089685	1	2	yes	—
75	C₄²	C₂×#10624382	1	2	yes	—
76	C₁₆	—	181	2	no	—
77	C₁₆	—	181	2	no	—
78	C₁₆	—	181	4	no	—
79	C₂³	C₂×#13089685	1	1	yes	characteristic
80	C₂×C₄	C₄×#10624382	1	2	yes	—
81	C₂×C₄	C₂×#13089685	1	4	yes	—
82	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
83	C₂×C₄	D₁₈₁⋊C₈	1	2	yes	—
84	C₂×C₄	C₂²×#10624382	1	1	yes	characteristic
85	C₈	—	181	1	no	—
86	C₈	—	181	1	no	—
87	C₈	—	181	2	no	—
88	C₈	—	181	4	no	—
89	C₂²	—	2	2	no	—
90	C₂²	C₄×#13089685	1	2	yes	—
91	C₂²	C₂²×#13089685	1	1	yes	characteristic
92	C₄	—	2	4	no	—
93	C₄	C₄×#13089685	1	2	yes	—
94	C₄	C₂×C₄×#10624382	1	1	yes	characteristic
95	C₄	C₂×D₁₈₁⋊C₈	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×#13089685	1	1	yes	characteristic
98	C₂	#26042337	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153890

C₂

yes

maximal, characteristic

C₂²×#15668452

C₂

yes

maximal, characteristic

#26042167

C₂

yes

maximal, complemented

C₄×#15668452

C₂

yes

maximal, complemented

#26041235

C₂

yes

maximal, characteristic

#19153890

C₄

yes

complemented

C₂×#15668452

C₄

yes

complemented

C₂×#15668452

C₂²

yes

characteristic

C₂×#15668452

C₂²

yes

—

C₂×#15668452

C₂²

yes

characteristic

C₂×#15668433

C₄

yes

characteristic

C₂²×#13089678

C₂²

yes

characteristic

#19153727

C₄

yes

—

C₄×#13089678

C₂²

yes

—

#117×C₁₈₁

C₄

yes

characteristic

#15668452

C₂×C₄

yes

—

#15668452

C₂×C₄

yes

—

#15668452

C₂×C₄

yes

—

#15668433

C₈

yes

—

C₂×#13089678

C₂×C₄

yes

—

C₂×#13089678

C₂×C₄

yes

—

C₂×#13089678

C₂×C₄

yes

characteristic

C₂×#13089678

C₂×C₄

yes

—

C₂×#13089678

C₂³

yes

characteristic

C₂²×C₄×C₁₈₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₁₈₁

C₈

yes

—

C₂²⋊C₄×C₁₈₁

C₈

yes

—

C₄²×C₁₈₁

C₂×C₄

yes

—

#13089678

C₄²

yes

—

#13089678

C₂×C₈

yes

—

#13089678

C₂²×C₄

yes

characteristic

#13089678

C₂²×C₄

yes

characteristic

C₂³×C₁₈₁

C₂×C₈

yes

characteristic

C₂×C₄×C₁₈₁

C₄²

yes

—

C₂×C₄×C₁₈₁

C₂×C₈

yes

—

C₂×C₄×C₁₈₁

C₂×C₈

yes

characteristic

C₂×C₄×C₁₈₁

C₂×C₈

yes

—

C₂×C₄×C₁₈₁

C₂²×C₄

yes

characteristic

C₂²×C₁₈₁

—

C₂²×C₁₈₁

C₄×C₈

yes

—

C₂²×C₁₈₁

C₂²×C₈

yes

characteristic

C₄×C₁₈₁

—

C₄×C₁₈₁

C₄×C₈

yes

—

C₄×C₁₈₁

C₂×C₄²

yes

characteristic

C₄×C₁₈₁

C₂²×C₈

yes

characteristic

C₂×C₁₈₁

—

C₂×C₁₈₁

C₂×C₄×C₈

yes

characteristic

C₂×C₁₈₁

#504

yes

—

C₁₈₁

#2108

yes

characteristic, complemented, Sylow

#2108

—

181

maximal, Sylow

C₂×M₃₂

—

181

—

C₂²×C₁₆

—

181

—

#405

—

181

—

#346

—

181

—

C₄×C₁₆

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

—

181

—

#117

#10624382

yes

characteristic

M₃₂

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

C₂×C₁₆

—

181

—

#97

—

181

—

C₄×C₈

—

181

—

C₂²×C₄

C₂×#10624382

yes

characteristic

M₁₆

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₄⋊C₄

#13089685

yes

—

C₂²⋊C₄

#13089685

yes

—

C₄²

C₂×#10624382

yes

—

C₁₆

—

181

—

C₁₆

—

181

—

C₁₆

—

181

—

C₂³

C₂×#13089685

yes

characteristic

C₂×C₄

C₄×#10624382

yes

—

C₂×C₄

C₂×#13089685

yes

—

C₂×C₄

C₂×#13089685

yes

characteristic

C₂×C₄

D₁₈₁⋊C₈

yes

—

C₂×C₄

C₂²×#10624382

yes

characteristic

C₈

—

181

—

C₈

—

181

—

C₈

—

181

—

C₈

—

181

—

C₂²

—

C₂²

C₄×#13089685

yes

—

C₂²

C₂²×#13089685

yes

characteristic

C₄

—

C₄

C₄×#13089685

yes

—

C₄

C₂×C₄×#10624382

yes

characteristic

C₄

C₂×D₁₈₁⋊C₈

yes

characteristic

C₂

—

C₂

C₂×C₄×#13089685

yes

characteristic

C₂

#26042337

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10624382
commutator	C₂×C₁₈₁	C₂×C₄×C₈
Fitting	#117×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂²×C₈
prime radical	C₂³×C₁₈₁	C₂×C₈
cosocle	C₂×#13089678	C₂³
hypercenter	#117	#10624382
hypocenter	C₁₈₁	#2108
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#10624382

commutator

C₂×C₁₈₁

C₂×C₄×C₈

Fitting

#117×C₁₈₁

C₄

socle

C₂²×C₁₈₁

C₂²×C₈

prime radical

C₂³×C₁₈₁

C₂×C₈

C₂³

C₁₈₁

G ▷ C₂×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
3. #26042167	C₂	semidirect
4. C₄×#15668452	C₂	semidirect
6. #19153890	C₄	semidirect
7. C₂×#15668452	C₄	semidirect
49. C₁₈₁	#2108	semidirect

H ≅ G/N

type

3. #26042167

C₂

semidirect

4. C₄×#15668452

C₂

semidirect

6. #19153890

C₄

semidirect

7. C₂×#15668452

C₄

semidirect

49. C₁₈₁

#2108

semidirect

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

subgroup	index
C₂×#19153890	2
C₂²×#15668452	2
#26042167	2
C₄×#15668452	2
#26041235	2
#2108	181

subgroup

index

181

Subgroups — #37549930

Conjugacy classes of subgroups

Complements

Maximal subgroups