Group #37509965 — subgroups

Subgroups — #37509965

Order 22912.

252 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19153105	C₂	1	1	yes	maximal, characteristic
2	#26038305	C₂	1	1	yes	maximal, characteristic
3	#26038202	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₁₇₉	C₂	1	1	yes	maximal, characteristic
5	#19153105	—	2	2	no	—
6	#19153105	C₄	1	4	yes	complemented
7	C₂×C₄⋊Dic₁₇₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₇₉	C₂²	1	2	yes	—
9	C₂×Dic₁₇₉⋊C₄	—	2	2	no	—
10	C₁₇₉⋊#95	—	2	2	no	—
11	C₂²×C₈×C₁₇₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₇₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₇₉	—	2	2	no	—
14	C₂²×Dic₁₇₉	—	2	2	no	—
15	C₂²×Dic₁₇₉	—	2	2	no	—
16	C₄⋊Dic₁₇₉	—	2	2	no	—
17	C₄⋊Dic₁₇₉	—	2	4	no	—
18	C₄⋊Dic₁₇₉	C₂×C₄	1	4	yes	—
19	Dic₁₇₉⋊C₄	—	2	8	no	—
20	C₂²×C₄×C₁₇₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₁₇₉	—	2	2	no	—
23	C₂×C₈×C₁₇₉	—	2	2	no	—
24	C₂×C₈×C₁₇₉	Q₈	1	4	yes	—
25	C₄²×C₁₇₉	C₂×C₄	1	2	yes	—
26	C₄²×C₁₇₉	D₄	1	2	yes	—
27	C₂×Dic₁₇₉	—	2	4	no	—
28	C₂×Dic₁₇₉	—	4	4	no	—
29	C₂×Dic₁₇₉	—	4	2	no	—
30	C₂×Dic₁₇₉	—	4	4	no	—
31	C₂³×C₁₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₇₉	—	2	4	no	—
33	C₂×C₄×C₁₇₉	C₂²⋊C₄	1	4	yes	—
34	C₂×C₄×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₇₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₇₉	C₂×Q₈	1	2	yes	—
37	C₂×C₄×C₁₇₉	#41	1	2	yes	—
38	C₈×C₁₇₉	—	2	4	no	—
39	C₂²×C₁₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₁₇₉	#124	1	1	yes	characteristic
41	C₂²×C₁₇₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₁₇₉	#135	1	4	yes	—
43	C₄×C₁₇₉	—	2	4	no	—
44	C₄×C₁₇₉	C₄×Q₈	1	2	yes	—
45	C₄×C₁₇₉	C₂²⋊Q₈	1	2	yes	—
46	Dic₁₇₉	—	4	4	no	—
47	Dic₁₇₉	—	8	2	no	—
48	C₂×C₁₇₉	#391	1	1	yes	characteristic
49	C₂×C₁₇₉	#416	1	2	yes	—
50	C₂×C₁₇₉	#488	1	2	yes	—
51	C₂×C₁₇₉	#499	1	2	yes	—
52	C₁₇₉	#1991	1	1	yes	characteristic, complemented, Sylow
53	#1991	—	179	1	no	maximal, Sylow
54	C₂×#125	—	179	1	no	—
55	C₂×C₄×C₈	D₁₇₉	1	1	yes	characteristic
56	#382	—	179	1	no	—
57	#340	—	179	4	no	—
58	C₂²×C₈	C₂×D₁₇₉	1	2	yes	—
59	#125	—	358	2	no	—
60	#125	—	179	4	no	—
61	C₂×C₄⋊C₄	—	358	2	no	—
62	C₂×C₄⋊C₄	—	179	2	no	—
63	C₂×C₄⋊C₄	—	179	2	no	—
64	C₂×C₄²	C₂×D₁₇₉	1	1	yes	characteristic
65	C₄×C₈	—	2	2	no	—
66	#95	—	358	2	no	—
67	C₂²×C₄	—	358	2	no	—
68	C₂²×C₄	—	358	2	no	—
69	C₂²×C₄	D₇₁₆	1	2	yes	—
70	C₂²×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₃₅₈	1	4	yes	—
74	C₄⋊C₄	—	358	8	no	—
75	C₄⋊C₄	—	358	2	no	—
76	C₄⋊C₄	—	358	4	no	—
77	C₄⋊C₄	—	179	4	no	—
78	C₄²	C₄×D₁₇₉	1	2	yes	—
79	C₄²	C₂²⋊D₁₇₉	1	2	yes	—
80	C₂³	C₂×D₇₁₆	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	358	4	no	—
83	C₂×C₄	—	716	2	no	—
84	C₂×C₄	—	716	4	no	—
85	C₂×C₄	—	716	4	no	—
86	C₂×C₄	(C₂×D₁₇₉)⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₁₇₉	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₁₇₉	1	1	yes	characteristic
89	C₂×C₄	C₂×Dic₃₅₈	1	2	yes	—
90	C₂×C₄	#15668259	1	2	yes	—
91	C₈	—	2	4	no	—
92	C₂²	C₂×(C₂×D₁₇₉)⋊C₄	1	1	yes	characteristic
93	C₂²	#19153101	1	1	yes	characteristic
94	C₂²	#19153113	1	1	yes	characteristic
95	C₂²	#19153135	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	1432	2	no	—
98	C₄	—	716	4	no	—
99	C₄	C₄×Dic₃₅₈	1	2	yes	—
100	C₄	#19153092	1	2	yes	—
101	C₂	#26038345	1	1	yes	characteristic
102	C₂	#26038436	1	2	yes	—
103	C₂	#26038794	1	2	yes	—
104	C₂	#26038841	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19153105

C₂

yes

maximal, characteristic

#26038305

C₂

yes

maximal, characteristic

#26038202

C₂

yes

maximal

C₂×C₄×C₈×C₁₇₉

C₂

yes

maximal, characteristic

#19153105

—

#19153105

C₄

yes

complemented

C₂×C₄⋊Dic₁₇₉

C₂²

yes

—

C₂×C₄⋊Dic₁₇₉

C₂²

yes

—

C₂×Dic₁₇₉⋊C₄

—

C₁₇₉⋊#95

—

C₂²×C₈×C₁₇₉

C₂²

yes

—

C₂×C₄²×C₁₇₉

C₂²

yes

characteristic

C₄×C₈×C₁₇₉

—

C₂²×Dic₁₇₉

—

C₂²×Dic₁₇₉

—

C₄⋊Dic₁₇₉

—

C₄⋊Dic₁₇₉

—

C₄⋊Dic₁₇₉

C₂×C₄

yes

—

Dic₁₇₉⋊C₄

—

C₂²×C₄×C₁₇₉

D₄

yes

—

C₂²×C₄×C₁₇₉

C₂³

yes

characteristic

C₂×C₈×C₁₇₉

—

C₂×C₈×C₁₇₉

—

C₂×C₈×C₁₇₉

Q₈

yes

—

C₄²×C₁₇₉

C₂×C₄

yes

—

C₄²×C₁₇₉

D₄

yes

—

C₂×Dic₁₇₉

—

C₂×Dic₁₇₉

—

C₂×Dic₁₇₉

—

C₂×Dic₁₇₉

—

C₂³×C₁₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇₉

—

C₂×C₄×C₁₇₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇₉

C₂×Q₈

yes

—

C₂×C₄×C₁₇₉

#41

yes

—

C₈×C₁₇₉

—

C₂²×C₁₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₇₉

#124

yes

characteristic

C₂²×C₁₇₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₇₉

#135

yes

—

C₄×C₁₇₉

—

C₄×C₁₇₉

C₄×Q₈

yes

—

C₄×C₁₇₉

C₂²⋊Q₈

yes

—

Dic₁₇₉

—

Dic₁₇₉

—

C₂×C₁₇₉

#391

yes

characteristic

C₂×C₁₇₉

#416

yes

—

C₂×C₁₇₉

#488

yes

—

C₂×C₁₇₉

#499

yes

—

C₁₇₉

#1991

yes

characteristic, complemented, Sylow

#1991

—

179

maximal, Sylow

C₂×#125

—

179

—

C₂×C₄×C₈

D₁₇₉

yes

characteristic

#382

—

179

—

#340

—

179

—

C₂²×C₈

C₂×D₁₇₉

yes

—

#125

—

358

—

#125

—

179

—

C₂×C₄⋊C₄

—

358

—

C₂×C₄⋊C₄

—

179

—

C₂×C₄⋊C₄

—

179

—

C₂×C₄²

C₂×D₁₇₉

yes

characteristic

C₄×C₈

—

#95

—

358

—

C₂²×C₄

—

358

—

C₂²×C₄

—

358

—

C₂²×C₄

D₇₁₆

yes

—

C₂²×C₄

C₂²×D₁₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₅₈

yes

—

C₄⋊C₄

—

358

—

C₄⋊C₄

—

358

—

C₄⋊C₄

—

358

—

C₄⋊C₄

—

179

—

C₄²

C₄×D₁₇₉

yes

—

C₄²

C₂²⋊D₁₇₉

yes

—

C₂³

C₂×D₇₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

358

—

C₂×C₄

—

716

—

C₂×C₄

—

716

—

C₂×C₄

—

716

—

C₂×C₄

(C₂×D₁₇₉)⋊C₄

yes

—

C₂×C₄

C₂×C₄×D₁₇₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₇₉

yes

characteristic

C₂×C₄

C₂×Dic₃₅₈

yes

—

C₂×C₄

#15668259

yes

—

C₈

—

C₂²

C₂×(C₂×D₁₇₉)⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

1432

—

C₄

—

716

—

C₄

C₄×Dic₃₅₈

yes

—

100

C₄

#19153092

yes

—

101

C₂

#26038345

yes

characteristic

102

C₂

#26038436

yes

—

103

C₂

#26038794

yes

—

104

C₂

#26038841

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₁₆
commutator	C₂×C₄×C₁₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₇₉
Fitting	C₂×C₄×C₈×C₁₇₉	C₂
socle, prime radical	C₂³×C₁₇₉	C₂×D₄
cosocle	C₂²×C₄×C₁₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₇₉
hypocenter	C₁₇₉	#1991
LCS	G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₇₁₆

commutator

C₂×C₄×C₁₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₇₉

Fitting

C₂×C₄×C₈×C₁₇₉

C₂

socle, prime radical

C₂³×C₁₇₉

C₂×D₄

cosocle

C₂²×C₄×C₁₇₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₇₉

hypocenter

C₁₇₉

#1991

LCS

G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
6. #19153105	C₄	semidirect
52. C₁₇₉	#1991	semidirect

H ≅ G/N

type

6. #19153105

C₄

semidirect

52. C₁₇₉

#1991

semidirect

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

subgroup	index
C₂×#19153105	2
#26038305	2
#26038202	2
C₂×C₄×C₈×C₁₇₉	2
#1991	179

subgroup

index

C₂×C₄×C₈×C₁₇₉

179

Subgroups — #37509965

Conjugacy classes of subgroups

Complements

Maximal subgroups