Group #37509136 — subgroups

Subgroups — #37509136

Order 22912.

188 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 81 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	#26038462	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₁₇₉	C₂	1	1	yes	maximal, characteristic
3	#26038204	C₂	1	1	yes	maximal, characteristic
4	#26038203	C₂	1	2	yes	maximal
5	#341×C₁₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668243	C₂²	1	2	yes	—
7	C₂²×C₁₇₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇₉	C₂²	1	1	yes	characteristic
9	Dic₁₇₉⋊C₈	—	2	4	no	—
10	C₈×Dic₁₇₉	C₄	1	2	yes	—
11	C₈×Dic₁₇₉	C₄	1	2	yes	—
12	C₂×M₁₆×C₁₇₉	C₂²	1	2	yes	—
13	C₂²×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₇₉	Q₈	1	2	yes	—
15	#15668243	—	2	2	no	—
16	#15668243	—	2	2	no	—
17	C₂×C₁₇₉⋊C₈	—	2	2	no	—
18	C₂×C₁₇₉⋊C₈	—	2	2	no	—
19	C₂×C₁₇₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₄×Dic₁₇₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₇₉	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₇₉	D₄	1	2	yes	—
23	C₂²×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
24	M₁₆×C₁₇₉	—	2	2	no	—
25	M₁₆×C₁₇₉	—	2	2	no	—
26	C₂×C₈×C₁₇₉	—	2	2	no	—
27	C₂×C₈×C₁₇₉	—	2	2	no	—
28	C₂×C₈×C₁₇₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₇₉	—	2	4	no	—
30	C₂×Dic₁₇₉	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₁₇₉	C₄⋊C₄	1	2	yes	—
32	C₁₇₉⋊C₈	—	2	2	no	—
33	C₁₇₉⋊C₈	—	4	2	no	—
34	C₂³×C₁₇₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₇₉	#41	1	2	yes	—
38	C₂×C₄×C₁₇₉	#41	1	2	yes	—
39	C₈×C₁₇₉	—	2	2	no	—
40	C₈×C₁₇₉	—	4	2	no	—
41	C₂²×C₁₇₉	—	2	2	no	—
42	C₂²×C₁₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₁₇₉	#125	1	2	yes	—
44	C₄×C₁₇₉	#117	1	1	yes	characteristic
45	C₄×C₁₇₉	#117	1	1	yes	characteristic
46	C₄×C₁₇₉	#124	1	2	yes	—
47	Dic₁₇₉	—	2	2	no	—
48	Dic₁₇₉	#108	1	4	yes	—
49	C₂×C₁₇₉	—	2	2	no	—
50	C₂×C₁₇₉	#382	1	1	yes	characteristic
51	C₂×C₁₇₉	C₂×#108	1	2	yes	—
52	C₁₇₉	#1837	1	1	yes	characteristic, complemented, Sylow
53	#1837	—	179	1	no	maximal, Sylow
54	#423	—	179	2	no	—
55	C₂×C₄×C₈	—	179	1	no	—
56	#341	—	179	2	no	—
57	#341	—	179	1	no	—
58	#341	D₁₇₉	1	1	yes	characteristic
59	C₂×M₁₆	—	179	2	no	—
60	C₂×M₁₆	C₂×D₁₇₉	1	2	yes	—
61	C₂²×C₈	—	179	1	no	—
62	C₂²×C₈	C₂×D₁₇₉	1	1	yes	characteristic
63	C₂×C₄²	—	179	1	no	—
64	C₄⋊C₈	—	358	4	no	—
65	C₄×C₈	—	179	2	no	—
66	C₄×C₈	—	179	2	no	—
67	C₂²×C₄	—	179	2	no	—
68	C₂²×C₄	C₂²×D₁₇₉	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	358	2	no	—
72	M₁₆	—	358	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	358	2	no	—
76	C₂×C₈	—	358	2	no	—
77	C₂×C₈	—	179	2	no	—
78	C₂×C₈	C₄×D₁₇₉	1	2	yes	—
79	C₄²	—	179	1	no	—
80	C₄²	—	179	1	no	—
81	C₄²	—	179	2	no	—
82	C₂³	Q₈×D₁₇₉	1	1	yes	characteristic
83	C₂×C₄	—	358	4	no	—
84	C₂×C₄	—	179	2	no	—
85	C₂×C₄	—	179	2	no	—
86	C₂×C₄	C₂×C₄×D₁₇₉	1	1	yes	characteristic
87	C₂×C₄	D₄×D₁₇₉	1	1	yes	characteristic
88	C₂×C₄	#15668258	1	2	yes	—
89	C₂×C₄	#15668259	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	358	2	no	—
93	C₈	—	716	2	no	—
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊C₄×D₁₇₉	1	1	yes	characteristic
96	C₂²	#19153103	1	2	yes	—
97	C₄	—	358	2	no	—
98	C₄	—	179	4	no	—
99	C₄	#19153069	1	1	yes	characteristic
100	C₄	#19153070	1	1	yes	characteristic
101	C₄	#19153099	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	#26038303	1	1	yes	characteristic
104	C₂	#108×D₁₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26038462

C₂

yes

maximal

C₂×C₈×Dic₁₇₉

C₂

yes

maximal, characteristic

#26038204

C₂

yes

maximal, characteristic

#26038203

C₂

yes

maximal

#341×C₁₇₉

C₂

yes

maximal, characteristic

C₂×#15668243

C₂²

yes

—

C₂²×C₁₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₁₇₉

C₂²

yes

characteristic

Dic₁₇₉⋊C₈

—

C₈×Dic₁₇₉

C₄

yes

—

C₈×Dic₁₇₉

C₄

yes

—

C₂×M₁₆×C₁₇₉

C₂²

yes

—

C₂²×C₈×C₁₇₉

C₂²

yes

characteristic

C₂²×Dic₁₇₉

Q₈

yes

—

#15668243

—

#15668243

—

C₂×C₁₇₉⋊C₈

—

C₂×C₁₇₉⋊C₈

—

C₂×C₁₇₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₁₇₉

C₂×C₄

yes

characteristic

C₄×Dic₁₇₉

C₂×C₄

yes

characteristic

C₄×Dic₁₇₉

D₄

yes

—

C₂²×C₄×C₁₇₉

C₂³

yes

characteristic

M₁₆×C₁₇₉

—

M₁₆×C₁₇₉

—

C₂×C₈×C₁₇₉

—

C₂×C₈×C₁₇₉

—

C₂×C₈×C₁₇₉

C₂×C₄

yes

—

C₂×Dic₁₇₉

—

C₂×Dic₁₇₉

C₄⋊C₄

yes

—

C₂×Dic₁₇₉

C₄⋊C₄

yes

—

C₁₇₉⋊C₈

—

C₁₇₉⋊C₈

—

C₂³×C₁₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇₉

#41

yes

—

C₂×C₄×C₁₇₉

#41

yes

—

C₈×C₁₇₉

—

C₈×C₁₇₉

—

C₂²×C₁₇₉

—

C₂²×C₁₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₇₉

#125

yes

—

C₄×C₁₇₉

yes

C₄×C₁₇₉

yes

C₄×C₁₇₉

yes

—

Dic₁₇₉

—

Dic₁₇₉

#108

yes

—

C₂×C₁₇₉

—

C₂×C₁₇₉

#382

yes

characteristic

C₂×C₁₇₉

C₂×#108

yes

—

C₁₇₉

#1837

yes

characteristic, complemented, Sylow

#1837

—

179

maximal, Sylow

#423

—

179

—

C₂×C₄×C₈

—

179

—

#341

—

179

—

#341

—

179

—

#341

D₁₇₉

yes

characteristic

C₂×M₁₆

—

179

—

C₂×M₁₆

C₂×D₁₇₉

yes

—

C₂²×C₈

—

179

—

C₂²×C₈

C₂×D₁₇₉

yes

characteristic

C₂×C₄²

—

179

—

C₄⋊C₈

—

358

—

C₄×C₈

—

179

—

C₄×C₈

—

179

—

C₂²×C₄

—

179

—

C₂²×C₄

C₂²×D₁₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

358

—

M₁₆

—

358

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

358

—

C₂×C₈

—

358

—

C₂×C₈

—

179

—

C₂×C₈

C₄×D₁₇₉

yes

—

C₄²

—

179

—

C₄²

—

179

—

C₄²

—

179

—

C₂³

Q₈×D₁₇₉

yes

characteristic

C₂×C₄

—

358

—

C₂×C₄

—

179

—

C₂×C₄

—

179

—

C₂×C₄

C₂×C₄×D₁₇₉

yes

characteristic

C₂×C₄

D₄×D₁₇₉

yes

characteristic

C₂×C₄

#15668258

yes

—

C₂×C₄

#15668259

yes

—

C₈

—

C₈

—

C₈

—

358

—

C₈

—

716

—

C₂²

—

C₂²

C₄⋊C₄×D₁₇₉

yes

characteristic

C₂²

#19153103

yes

—

C₄

—

358

—

C₄

—

179

—

C₄

#19153069

yes

characteristic

100

C₄

#19153070

yes

characteristic

101

C₄

#19153099

yes

—

102

C₂

—

103

C₂

#26038303

yes

characteristic

104

C₂

#108×D₁₇₉

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₇₉
commutator	C₂×C₄×C₁₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₇₉
Fitting	#341×C₁₇₉	C₂
socle	C₂²×C₁₇₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₇₉	C₂³
hypercenter	#341	D₁₇₉
hypocenter	C₁₇₉	#1837
LCS	G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₁₇₉

commutator

C₂×C₄×C₁₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₇₉

Fitting

#341×C₁₇₉

C₂

socle

C₂²×C₁₇₉

C₂×C₄⋊C₄

prime radical

C₂³×C₁₇₉

C₂×Q₈

cosocle

C₂²×C₄×C₁₇₉

C₂³

D₁₇₉

C₁₇₉

G ▷ C₂×C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
52. C₁₇₉	#1837	semidirect

H ≅ G/N

type

52. C₁₇₉

#1837

semidirect

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

subgroup	index
#26038462	2
C₂×C₈×Dic₁₇₉	2
#26038204	2
#26038203	2
#341×C₁₇₉	2
#1837	179

subgroup

index

C₂×C₈×Dic₁₇₉

#341×C₁₇₉

179

Subgroups — #37509136

Conjugacy classes of subgroups

Complements

Maximal subgroups