Group #37508686 — subgroups

Subgroups — #37508686

Order 22912.

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×#19153024	C₂	1	1	yes	maximal, characteristic
2	C₂×#19153023	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₁₇₉	C₂	1	2	yes	maximal
4	#26038285	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₇₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₇₉	C₂²	1	2	yes	—
8	#19153024	C₄	1	4	yes	complemented
9	#19153023	C₄	1	8	yes	complemented
10	C₈×Dic₁₇₉	C₄	1	8	yes	complemented
11	C₁₇₉⋊#95	C₄	1	4	yes	—
12	C₂²×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₁₇₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₇₉	C₄	1	4	yes	complemented
16	C₂²×Dic₁₇₉	C₂×C₄	1	4	yes	—
17	C₂×C₁₇₉⋊C₈	C₂×C₄	1	4	yes	—
18	C₂×C₁₇₉⋊C₈	C₂×C₄	1	4	yes	—
19	C₂×C₁₇₉⋊C₈	C₂×C₄	1	4	yes	—
20	C₄×Dic₁₇₉	C₂×C₄	1	4	yes	—
21	C₄×Dic₁₇₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₇₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₇₉	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₁₇₉	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₁₇₉	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₁₇₉	C₂×C₄	1	2	yes	—
28	C₄²×C₁₇₉	C₂×C₄	1	2	yes	—
29	C₄²×C₁₇₉	C₂×C₄	1	2	yes	—
30	C₂×Dic₁₇₉	—	2	8	no	—
31	C₂×Dic₁₇₉	C₄²	1	8	yes	—
32	C₁₇₉⋊C₈	C₄²	1	8	yes	—
33	C₂³×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇₉	—	2	4	no	—
35	C₂×C₄×C₁₇₉	C₄²	1	4	yes	—
36	C₂×C₄×C₁₇₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₁₇₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₁₇₉	C₄²	1	4	yes	—
41	C₈×C₁₇₉	C₄²	1	4	yes	—
42	C₂²×C₁₇₉	C₂×C₄²	1	2	yes	—
43	C₂²×C₁₇₉	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₁₇₉	#131	1	4	yes	—
45	C₄×C₁₇₉	—	2	4	no	—
46	C₄×C₁₇₉	C₂×C₄²	1	2	yes	—
47	C₄×C₁₇₉	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₁₇₉	C₂×C₄²	1	1	yes	characteristic
49	Dic₁₇₉	—	2	8	no	—
50	C₂×C₁₇₉	C₄³	1	1	yes	characteristic
51	C₂×C₁₇₉	#405	1	4	yes	—
52	C₂×C₁₇₉	#405	1	2	yes	—
53	C₁₇₉	#1726	1	1	yes	characteristic, complemented, Sylow
54	#1726	—	179	1	no	maximal, Sylow
55	C₂×#97	—	179	2	no	—
56	C₂×#97	—	179	1	no	—
57	C₂×C₄×C₈	—	179	2	no	—
58	C₂×C₄×C₈	D₁₇₉	1	1	yes	characteristic
59	#376	—	179	1	no	—
60	C₂²×C₈	—	179	2	no	—
61	C₂²×C₈	C₂×D₁₇₉	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₁₇₉	1	1	yes	characteristic
63	C₂×C₄²	—	179	2	no	—
64	C₂×C₄²	C₂×D₁₇₉	1	1	yes	characteristic
65	#97	—	179	8	no	—
66	#97	—	179	4	no	—
67	C₄×C₈	—	179	8	no	—
68	C₄×C₈	Dic₁₇₉	1	4	yes	complemented
69	#95	—	179	4	no	—
70	C₂²×C₄	—	179	4	no	—
71	C₂²×C₄	C₄×D₁₇₉	1	2	yes	—
72	C₂²×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
73	C₂×C₈	—	179	4	no	—
74	C₂×C₈	—	179	4	no	—
75	C₂×C₈	—	179	4	no	—
76	C₂×C₈	C₄×D₁₇₉	1	4	yes	—
77	C₂×C₈	C₄×D₁₇₉	1	4	yes	—
78	C₂×C₈	C₂×Dic₁₇₉	1	2	yes	—
79	C₂×C₈	C₂×Dic₁₇₉	1	2	yes	—
80	C₄²	—	179	4	no	—
81	C₄²	—	179	4	no	—
82	C₄²	C₄×D₁₇₉	1	2	yes	—
83	C₄²	C₂×Dic₁₇₉	1	2	yes	—
84	C₂³	C₂×C₄×D₁₇₉	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	358	8	no	—
87	C₂×C₄	—	179	8	no	—
88	C₂×C₄	C₄×Dic₁₇₉	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₁₇₉	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₁₇₉	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₁₇₉	1	2	yes	—
92	C₂×C₄	C₂²×Dic₁₇₉	1	1	yes	characteristic
93	C₈	—	179	8	no	—
94	C₈	C₄×Dic₁₇₉	1	4	yes	—
95	C₈	C₄×Dic₁₇₉	1	4	yes	—
96	C₂²	C₄²×D₁₇₉	1	2	yes	—
97	C₂²	C₂×C₄×Dic₁₇₉	1	1	yes	characteristic
98	C₂²	#19153119	1	4	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	358	8	no	—
101	C₄	C₄²×D₁₇₉	1	2	yes	—
102	C₄	C₂×C₄×Dic₁₇₉	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₁₇₉	1	1	yes	characteristic
104	C₂	C₄²×Dic₁₇₉	1	1	yes	characteristic
105	C₂	#26038393	1	4	yes	—
106	C₂	#26038394	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153024

C₂

yes

maximal, characteristic

C₂×#19153023

C₂

yes

maximal

C₂×C₈×Dic₁₇₉

C₂

yes

maximal

#26038285

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₇₉

C₂

yes

maximal, characteristic

C₂²×C₁₇₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₁₇₉

C₂²

yes

—

#19153024

C₄

yes

complemented

#19153023

C₄

yes

complemented

C₈×Dic₁₇₉

C₄

yes

complemented

C₁₇₉⋊#95

C₄

yes

—

C₂²×C₈×C₁₇₉

C₂²

yes

characteristic

C₂²×C₈×C₁₇₉

C₂²

yes

characteristic

C₂×C₄²×C₁₇₉

C₂²

yes

characteristic

C₄×C₈×C₁₇₉

C₄

yes

complemented

C₂²×Dic₁₇₉

C₂×C₄

yes

—

C₂×C₁₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₇₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₇₉

C₂×C₄

yes

—

C₄×Dic₁₇₉

C₂×C₄

yes

—

C₂²×C₄×C₁₇₉

C₂×C₄

yes

—

C₂²×C₄×C₁₇₉

C₂³

yes

characteristic

C₂×C₈×C₁₇₉

C₂×C₄

yes

—

C₂×C₈×C₁₇₉

C₂×C₄

yes

—

C₂×C₈×C₁₇₉

C₂×C₄

yes

—

C₂×C₈×C₁₇₉

C₂×C₄

yes

—

C₄²×C₁₇₉

C₂×C₄

yes

—

C₄²×C₁₇₉

C₂×C₄

yes

—

C₂×Dic₁₇₉

—

C₂×Dic₁₇₉

C₄²

yes

—

C₁₇₉⋊C₈

C₄²

yes

—

C₂³×C₁₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₉

—

C₂×C₄×C₁₇₉

C₄²

yes

—

C₂×C₄×C₁₇₉

C₂²×C₄

yes

—

C₂×C₄×C₁₇₉

C₂²×C₄

yes

—

C₂×C₄×C₁₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₉

C₂²×C₄

yes

characteristic

C₈×C₁₇₉

C₄²

yes

—

C₈×C₁₇₉

C₄²

yes

—

C₂²×C₁₇₉

C₂×C₄²

yes

—

C₂²×C₁₇₉

C₂×C₄²

yes

characteristic

C₂²×C₁₇₉

#131

yes

—

C₄×C₁₇₉

—

C₄×C₁₇₉

C₂×C₄²

yes

—

C₄×C₁₇₉

C₂×C₄²

yes

characteristic

C₄×C₁₇₉

C₂×C₄²

yes

characteristic

Dic₁₇₉

—

C₂×C₁₇₉

C₄³

yes

characteristic

C₂×C₁₇₉

#405

yes

—

C₂×C₁₇₉

#405

yes

—

C₁₇₉

#1726

yes

characteristic, complemented, Sylow

#1726

—

179

maximal, Sylow

C₂×#97

—

179

—

C₂×#97

—

179

—

C₂×C₄×C₈

—

179

—

C₂×C₄×C₈

D₁₇₉

yes

characteristic

#376

—

179

—

C₂²×C₈

—

179

—

C₂²×C₈

C₂×D₁₇₉

yes

characteristic

C₂²×C₈

C₂×D₁₇₉

yes

characteristic

C₂×C₄²

—

179

—

C₂×C₄²

C₂×D₁₇₉

yes

characteristic

#97

—

179

—

#97

—

179

—

C₄×C₈

—

179

—

C₄×C₈

Dic₁₇₉

yes

complemented

#95

—

179

—

C₂²×C₄

—

179

—

C₂²×C₄

C₄×D₁₇₉

yes

—

C₂²×C₄

C₂²×D₁₇₉

yes

characteristic

C₂×C₈

—

179

—

C₂×C₈

—

179

—

C₂×C₈

—

179

—

C₂×C₈

C₄×D₁₇₉

yes

—

C₂×C₈

C₄×D₁₇₉

yes

—

C₂×C₈

C₂×Dic₁₇₉

yes

—

C₂×C₈

C₂×Dic₁₇₉

yes

—

C₄²

—

179

—

C₄²

—

179

—

C₄²

C₄×D₁₇₉

yes

—

C₄²

C₂×Dic₁₇₉

yes

—

C₂³

C₂×C₄×D₁₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

358

—

C₂×C₄

—

179

—

C₂×C₄

C₄×Dic₁₇₉

yes

—

C₂×C₄

C₂×C₄×D₁₇₉

yes

characteristic

C₂×C₄

C₂×C₄×D₁₇₉

yes

—

C₂×C₄

C₂×C₄×D₁₇₉

yes

—

C₂×C₄

C₂²×Dic₁₇₉

yes

characteristic

C₈

—

179

—

C₈

C₄×Dic₁₇₉

yes

—

C₈

C₄×Dic₁₇₉

yes

—

C₂²

C₄²×D₁₇₉

yes

—

C₂²

C₂×C₄×Dic₁₇₉

yes

characteristic

C₂²

#19153119

yes

—

C₄

—

100

C₄

—

358

—

101

C₄

C₄²×D₁₇₉

yes

—

102

C₄

C₂×C₄×Dic₁₇₉

yes

characteristic

103

C₄

C₂×C₄×Dic₁₇₉

yes

characteristic

104

C₂

C₄²×Dic₁₇₉

yes

characteristic

105

C₂

#26038393

yes

—

106

C₂

#26038394

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₇₉
commutator	C₂×C₁₇₉	C₄³
Frattini	C₂²×C₄	C₂²×D₁₇₉
Fitting	C₂×C₄×C₈×C₁₇₉	C₂
socle, prime radical	C₂³×C₁₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₇₉
hypocenter	C₁₇₉	#1726
LCS	G ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₁₇₉

commutator

C₂×C₁₇₉

C₄³

Frattini

C₂²×C₄

C₂²×D₁₇₉

Fitting

C₂×C₄×C₈×C₁₇₉

C₂

socle, prime radical

C₂³×C₁₇₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₇₉

C₁₇₉

G ▷ C₂×C₁₇₉ ▷ C₁₇₉

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
8. #19153024	C₄	semidirect
9. #19153023	C₄	semidirect
10. C₈×Dic₁₇₉	C₄	semidirect
15. C₄×C₈×C₁₇₉	C₄	semidirect
53. C₁₇₉	#1726	semidirect
68. C₄×C₈	Dic₁₇₉	semidirect

H ≅ G/N

type

8. #19153024

C₄

semidirect

9. #19153023

C₄

semidirect

10. C₈×Dic₁₇₉

C₄

semidirect

15. C₄×C₈×C₁₇₉

C₄

semidirect

53. C₁₇₉

#1726

semidirect

68. C₄×C₈

Dic₁₇₉

semidirect

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

subgroup	index
C₂×#19153024	2
C₂×#19153023	2
C₂×C₈×Dic₁₇₉	2
#26038285	2
C₂×C₄×C₈×C₁₇₉	2
#1726	179

subgroup

index

C₂×C₈×Dic₁₇₉

C₂×C₄×C₈×C₁₇₉

179

Subgroups — #37508686

Conjugacy classes of subgroups

Complements

Maximal subgroups