Group #36361838 — subgroups

Subgroups — #36361838

Order 22144.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	#26011425	C₂	1	4	yes	maximal
2	#26011424	C₂	1	4	yes	maximal
3	#26011423	C₂	1	4	yes	maximal
4	#26011357	C₂	1	2	yes	maximal
5	#382×C₁₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₁₇₃	C₂²	1	4	yes	—
7	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	—
9	C₂×#14583805	C₂²	1	4	yes	—
10	C₂×#14583805	C₂²	1	4	yes	—
11	#19149586	C₂²	1	4	yes	—
12	#19149586	C₂²	1	4	yes	—
13	#19149586	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
16	#95×C₁₇₃	C₂²	1	4	yes	—
17	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
18	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
19	C₄⋊Dic₁₇₃	—	4	2	no	—
20	C₄⋊Dic₁₇₃	—	4	2	no	—
21	C₄⋊Dic₁₇₃	—	4	4	no	—
22	#14583805	—	4	4	no	—
23	#14583805	—	4	4	no	—
24	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
27	C₄⋊C₄×C₁₇₃	—	4	2	no	—
28	C₄²×C₁₇₃	Q₈	1	4	yes	—
29	C₂×Dic₁₇₃	—	2	4	no	—
30	C₂×Dic₁₇₃	—	2	4	no	—
31	C₂×Dic₁₇₃	—	2	4	no	—
32	C₂×Dic₁₇₃	—	2	4	no	—
33	C₂×Dic₁₇₃	—	2	4	no	—
34	C₂×Dic₁₇₃	—	2	4	no	—
35	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₁₇₃	—	2	1	no	—
37	C₂×C₄×C₁₇₃	—	2	2	no	—
38	C₂×C₄×C₁₇₃	—	2	2	no	—
39	C₂×C₄×C₁₇₃	—	2	1	no	—
40	C₂×C₄×C₁₇₃	—	2	4	no	—
41	C₂×C₄×C₁₇₃	—	2	4	no	—
42	C₂×C₄×C₁₇₃	—	2	4	no	—
43	C₂×C₄×C₁₇₃	C₂×Q₈	1	2	yes	—
44	C₂×C₄×C₁₇₃	C₂×Q₈	1	4	yes	—
45	C₂²×C₁₇₃	C₂²×Q₈	1	1	yes	characteristic
46	C₂²×C₁₇₃	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₁₇₃	H(5,𝔽₂)	1	2	yes	—
48	C₂²×C₁₇₃	2₋¹⁺⁴	1	2	yes	—
49	C₂²×C₁₇₃	2₋¹⁺⁴	1	1	yes	characteristic
50	C₄×C₁₇₃	—	2	4	no	—
51	C₄×C₁₇₃	—	2	2	no	—
52	C₄×C₁₇₃	—	4	4	no	—
53	Dic₁₇₃	—	4	4	no	—
54	Dic₁₇₃	—	4	4	no	—
55	C₂×C₁₇₃	#544	1	2	yes	—
56	C₂×C₁₇₃	#544	1	1	yes	characteristic
57	C₂×C₁₇₃	#562	1	2	yes	—
58	C₂×C₁₇₃	#562	1	1	yes	characteristic
59	C₂×C₁₇₃	#564	1	1	yes	characteristic
60	C₁₇₃	#2845	1	1	yes	characteristic, complemented, Sylow
61	#2845	—	173	1	no	maximal, Sylow
62	#398	—	173	4	no	—
63	#398	—	173	4	no	—
64	#398	—	173	4	no	—
65	#382	—	173	2	no	—
66	#382	D₁₇₃	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	173	4	no	—
68	C₂×C₄⋊C₄	—	173	4	no	—
69	C₂×C₄⋊C₄	—	173	2	no	—
70	C₂×C₄⋊C₄	—	173	2	no	—
71	C₂×C₄⋊C₄	—	173	4	no	—
72	C₂×C₄⋊C₄	C₂×D₁₇₃	1	2	yes	—
73	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
74	#95	—	173	4	no	—
75	#95	—	173	4	no	—
76	#95	—	173	4	no	—
77	#95	C₂×D₁₇₃	1	4	yes	—
78	C₂²×C₄	—	173	4	no	—
79	C₂²×C₄	—	173	4	no	—
80	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
81	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
83	C₄⋊C₄	—	4	2	no	—
84	C₄⋊C₄	—	692	4	no	—
85	C₄⋊C₄	—	692	4	no	—
86	C₄⋊C₄	—	692	2	no	—
87	C₄⋊C₄	—	692	2	no	—
88	C₄⋊C₄	—	692	4	no	—
89	C₄²	Dic₃₄₆	1	4	yes	—
90	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	346	4	no	—
99	C₂×C₄	—	346	4	no	—
100	C₂×C₄	—	346	4	no	—
101	C₂×C₄	—	346	4	no	—
102	C₂×C₄	—	346	4	no	—
103	C₂×C₄	—	346	4	no	—
104	C₂×C₄	C₂×Dic₃₄₆	1	4	yes	—
105	C₂×C₄	C₂×Dic₃₄₆	1	2	yes	—
106	C₂²	C₂²×Dic₃₄₆	1	1	yes	characteristic
107	C₂²	#19149724	1	1	yes	characteristic
108	C₂²	#19149725	1	2	yes	—
109	C₂²	#19149726	1	2	yes	—
110	C₂²	#19149727	1	1	yes	characteristic
111	C₄	—	2	4	no	—
112	C₄	—	2	2	no	—
113	C₄	—	4	4	no	—
114	C₄	—	692	4	no	—
115	C₄	—	692	4	no	—
116	C₂	#26012119	1	2	yes	—
117	C₂	#26012122	1	1	yes	characteristic
118	C₂	#26012235	1	2	yes	—
119	C₂	#26012239	1	1	yes	characteristic
120	C₂	C₁₇₃⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26011425

C₂

yes

maximal

#26011424

C₂

yes

maximal

#26011423

C₂

yes

maximal

#26011357

C₂

yes

maximal

#382×C₁₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₁₇₃

C₂²

yes

—

C₂×C₄⋊Dic₁₇₃

C₂²

yes

—

C₂×C₄⋊Dic₁₇₃

C₂²

yes

—

C₂×#14583805

C₂²

yes

—

C₂×#14583805

C₂²

yes

—

#19149586

C₂²

yes

—

#19149586

C₂²

yes

—

#19149586

C₂²

yes

—

C₂×C₄⋊C₄×C₁₇₃

C₂²

yes

—

C₂×C₄²×C₁₇₃

C₂²

yes

characteristic

#95×C₁₇₃

C₂²

yes

—

C₂²×Dic₁₇₃

C₂³

yes

—

C₂²×Dic₁₇₃

C₂³

yes

—

C₄⋊Dic₁₇₃

—

C₄⋊Dic₁₇₃

—

C₄⋊Dic₁₇₃

—

#14583805

—

#14583805

—

C₂²×C₄×C₁₇₃

C₂³

yes

—

C₂²×C₄×C₁₇₃

C₂³

yes

characteristic

C₂²×C₄×C₁₇₃

C₂³

yes

—

C₄⋊C₄×C₁₇₃

—

C₄²×C₁₇₃

Q₈

yes

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂³×C₁₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂²×C₁₇₃

C₂²×Q₈

yes

C₂²×C₁₇₃

yes

C₂²×C₁₇₃

yes

—

C₂²×C₁₇₃

2₋¹⁺⁴

yes

—

C₂²×C₁₇₃

2₋¹⁺⁴

yes

characteristic

C₄×C₁₇₃

—

C₄×C₁₇₃

—

C₄×C₁₇₃

—

Dic₁₇₃

—

Dic₁₇₃

—

C₂×C₁₇₃

#544

yes

—

C₂×C₁₇₃

#544

yes

characteristic

C₂×C₁₇₃

#562

yes

—

C₂×C₁₇₃

yes

C₂×C₁₇₃

yes

C₁₇₃

yes

characteristic, complemented, Sylow

#2845

—

173

maximal, Sylow

#398

—

173

—

#398

—

173

—

#398

—

173

—

#382

—

173

—

#382

D₁₇₃

yes

characteristic

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

C₂×D₁₇₃

yes

—

C₂×C₄²

C₂×D₁₇₃

yes

characteristic

#95

—

173

—

#95

—

173

—

#95

—

173

—

#95

C₂×D₁₇₃

yes

—

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₂²×D₁₇₃

yes

—

C₂²×C₄

C₂²×D₁₇₃

yes

characteristic

C₂²×C₄

C₂²×D₁₇₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

692

—

C₄⋊C₄

—

692

—

C₄⋊C₄

—

692

—

C₄⋊C₄

—

692

—

C₄⋊C₄

—

692

—

C₄²

Dic₃₄₆

yes

—

C₂³

C₂³×D₁₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

100

C₂×C₄

—

346

—

101

C₂×C₄

—

346

—

102

C₂×C₄

—

346

—

103

C₂×C₄

—

346

—

104

C₂×C₄

C₂×Dic₃₄₆

yes

—

105

C₂×C₄

C₂×Dic₃₄₆

yes

—

106

C₂²

C₂²×Dic₃₄₆

yes

characteristic

107

C₂²

#19149724

yes

characteristic

108

C₂²

#19149725

yes

—

109

C₂²

#19149726

yes

—

110

C₂²

#19149727

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

692

—

115

C₄

—

692

—

116

C₂

#26012119

yes

—

117

C₂

#26012122

yes

characteristic

118

C₂

#26012235

yes

—

119

C₂

#26012239

yes

characteristic

120

C₂

C₁₇₃⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₇₃
commutator, socle, prime radical, cosocle	C₂³×C₁₇₃	C₂⁴
Fitting	#382×C₁₇₃	C₂
hypercenter	#382	D₁₇₃
hypocenter	C₁₇₃	#2845
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₇₃

commutator, socle, prime radical, cosocle

C₂³×C₁₇₃

C₂⁴

Fitting

#382×C₁₇₃

C₂

D₁₇₃

C₁₇₃

G ▷ C₂³×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
60. C₁₇₃	#2845	semidirect

H ≅ G/N

type

60. C₁₇₃

#2845

semidirect

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

subgroup	index
#26011425	2
#26011424	2
#26011423	2
#26011357	2
#382×C₁₇₃	2
#2845	173

subgroup

index

#382×C₁₇₃

173

Subgroups — #36361838

Conjugacy classes of subgroups

Complements

Maximal subgroups