Group #36369481 — subgroups

Subgroups — #36369481

Order 22144.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#19149746	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#13063443	C₂	1	1	yes	maximal, characteristic
3	#26012357	C₂	1	4	yes	maximal
4	#26011336	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13063443	C₂²	1	2	yes	—
6	C₂²×#13063443	C₂²	1	2	yes	—
7	#19149746	—	2	2	no	—
8	C₄⋊#13063443	—	2	2	no	—
9	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
11	#19149586	C₄	1	1	yes	characteristic
12	#19149586	C₄	1	2	yes	—
13	#95×C₁₇₃	C₄	1	1	yes	characteristic
14	C₂×#13063443	—	2	2	no	—
15	C₂×#13063443	—	2	2	no	—
16	C₂×#13063443	—	2	4	no	—
17	C₂×#13063443	—	2	4	no	—
18	C₂²×Dic₁₇₃	C₂×C₄	1	2	yes	—
19	C₂²×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
21	C₄×Dic₁₇₃	—	2	2	no	—
22	C₄×Dic₁₇₃	—	2	2	no	—
23	C₄×Dic₁₇₃	D₄	1	2	yes	—
24	C₄×Dic₁₇₃	Q₈	1	2	yes	—
25	C₂²×C₄×C₁₇₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
27	#13063443	—	4	2	no	—
28	#13063443	—	4	2	no	—
29	C₂×Dic₁₇₃	—	2	1	no	—
30	C₂×Dic₁₇₃	—	2	1	no	—
31	C₂×Dic₁₇₃	—	2	2	no	—
32	C₂×Dic₁₇₃	—	2	2	no	—
33	C₂×Dic₁₇₃	—	2	2	no	—
34	C₂×Dic₁₇₃	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₁₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₁₇₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×Dic₁₇₃	#41	1	2	yes	—
38	C₂×Dic₁₇₃	#41	1	2	yes	—
39	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₇₃	—	2	2	no	—
41	C₂×C₄×C₁₇₃	—	2	2	no	—
42	C₂×C₄×C₁₇₃	—	2	2	no	—
43	C₂×C₄×C₁₇₃	—	2	2	no	—
44	C₂×C₄×C₁₇₃	C₄⋊C₄	1	2	yes	—
45	C₂²×C₁₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₁₇₃	#117	1	2	yes	—
47	C₂²×C₁₇₃	#131	1	2	yes	—
48	C₂²×C₁₇₃	#131	1	1	yes	characteristic
49	C₂²×C₁₇₃	#131	1	1	yes	characteristic
50	C₄×C₁₇₃	—	2	2	no	—
51	C₄×C₁₇₃	—	4	2	no	—
52	Dic₁₇₃	—	2	2	no	—
53	Dic₁₇₃	—	4	2	no	—
54	Dic₁₇₃	#124	1	1	yes	characteristic
55	Dic₁₇₃	#124	1	1	yes	characteristic
56	Dic₁₇₃	#125	1	2	yes	—
57	C₂×C₁₇₃	#382	1	1	yes	characteristic
58	C₂×C₁₇₃	#424	1	1	yes	characteristic
59	C₂×C₁₇₃	#424	1	1	yes	characteristic
60	C₂×C₁₇₃	#433	1	2	yes	—
61	C₂×C₁₇₃	#433	1	2	yes	—
62	C₁₇₃	#1832	1	1	yes	characteristic, complemented, Sylow
63	#1832	—	173	1	no	maximal, Sylow
64	C₂×C₄⋊C₈	—	173	1	no	—
65	C₂×C₄⋊C₈	—	173	1	no	—
66	#376	—	173	1	no	—
67	#336	—	173	4	no	—
68	C₂²×C₈	—	173	2	no	—
69	C₂²×C₈	—	173	2	no	—
70	C₂×C₄²	—	173	2	no	—
71	C₂×C₄²	—	173	1	no	—
72	C₄⋊C₈	—	346	2	no	—
73	C₄⋊C₈	—	346	2	no	—
74	#95	—	173	1	no	—
75	#95	—	173	2	no	—
76	#95	#10621924	1	1	yes	characteristic
77	C₂²×C₄	—	173	2	no	—
78	C₂²×C₄	—	173	1	no	—
79	C₂²×C₄	—	173	1	no	—
80	C₂²×C₄	C₂×#10621924	1	2	yes	—
81	C₂²×C₄	C₂×#10621924	1	1	yes	characteristic
82	C₂×C₈	—	346	2	no	—
83	C₂×C₈	—	346	2	no	—
84	C₂×C₈	—	346	4	no	—
85	C₂×C₈	—	346	4	no	—
86	C₄²	—	346	2	no	—
87	C₄²	—	346	2	no	—
88	C₄²	—	173	2	no	—
89	C₄²	—	173	2	no	—
90	C₂³	C₂²×#10621924	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	346	1	no	—
96	C₂×C₄	—	346	1	no	—
97	C₂×C₄	—	346	2	no	—
98	C₂×C₄	—	346	2	no	—
99	C₂×C₄	—	346	2	no	—
100	C₂×C₄	—	173	2	no	—
101	C₂×C₄	—	173	1	no	—
102	C₂×C₄	—	173	1	no	—
103	C₂×C₄	—	173	2	no	—
104	C₂×C₄	—	173	2	no	—
105	C₂×C₄	C₄⋊#10621924	1	2	yes	—
106	C₈	—	692	2	no	—
107	C₈	—	692	2	no	—
108	C₂²	C₂×C₄⋊#10621924	1	1	yes	characteristic
109	C₂²	#19149758	1	2	yes	—
110	C₂²	#19149766	1	2	yes	—
111	C₂²	#19149766	1	1	yes	characteristic
112	C₂²	#19149767	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	346	2	no	—
116	C₄	—	173	1	no	—
117	C₄	—	173	1	no	—
118	C₄	—	173	2	no	—
119	C₄	—	692	2	no	—
120	C₂	#26012435	1	1	yes	characteristic
121	C₂	#26012497	1	1	yes	characteristic
122	C₂	#26012498	1	1	yes	characteristic
123	C₂	#26012515	1	2	yes	—
124	C₂	#26012516	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149746

C₂

yes

maximal, characteristic

C₂×C₄⋊#13063443

C₂

yes

maximal, characteristic

#26012357

C₂

yes

maximal

#26011336

C₂

yes

maximal, characteristic

C₂²×#13063443

C₂²

yes

—

C₂²×#13063443

C₂²

yes

—

#19149746

—

C₄⋊#13063443

—

C₂×C₄×Dic₁₇₃

C₂²

yes

—

C₂×C₄×Dic₁₇₃

C₂²

yes

characteristic

#19149586

C₄

yes

characteristic

#19149586

C₄

yes

—

#95×C₁₇₃

C₄

yes

—

—

—

—

C₂²×Dic₁₇₃

C₂×C₄

yes

—

C₂²×Dic₁₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₇₃

C₂³

yes

characteristic

C₄×Dic₁₇₃

—

C₄×Dic₁₇₃

—

C₄×Dic₁₇₃

D₄

yes

—

C₄×Dic₁₇₃

Q₈

yes

—

C₂²×C₄×C₁₇₃

C₂×C₄

yes

—

C₂²×C₄×C₁₇₃

C₂×C₄

yes

characteristic

#13063443

—

#13063443

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

C₄⋊C₄

yes

—

C₂×Dic₁₇₃

C₂×D₄

yes

characteristic

C₂×Dic₁₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₁₇₃

#41

yes

—

C₂×Dic₁₇₃

#41

yes

—

C₂³×C₁₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

C₄⋊C₄

yes

—

C₂²×C₁₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₇₃

#117

yes

—

C₂²×C₁₇₃

#131

yes

—

C₂²×C₁₇₃

yes

C₂²×C₁₇₃

yes

C₄×C₁₇₃

—

C₄×C₁₇₃

—

Dic₁₇₃

—

Dic₁₇₃

—

Dic₁₇₃

yes

Dic₁₇₃

yes

Dic₁₇₃

yes

—

C₂×C₁₇₃

yes

C₂×C₁₇₃

yes

C₂×C₁₇₃

yes

C₂×C₁₇₃

yes

—

C₂×C₁₇₃

#433

yes

—

C₁₇₃

#1832

yes

characteristic, complemented, Sylow

#1832

—

173

maximal, Sylow

C₂×C₄⋊C₈

—

173

—

C₂×C₄⋊C₈

—

173

—

#376

—

173

—

#336

—

173

—

C₂²×C₈

—

173

—

C₂²×C₈

—

173

—

C₂×C₄²

—

173

—

C₂×C₄²

—

173

—

C₄⋊C₈

—

346

—

C₄⋊C₈

—

346

—

#95

—

173

—

#95

—

173

—

#95

#10621924

yes

characteristic

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₂×#10621924

yes

—

C₂²×C₄

C₂×#10621924

yes

characteristic

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₄²

—

346

—

C₄²

—

346

—

C₄²

—

173

—

C₄²

—

173

—

C₂³

C₂²×#10621924

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

100

C₂×C₄

—

173

—

101

C₂×C₄

—

173

—

102

C₂×C₄

—

173

—

103

C₂×C₄

—

173

—

104

C₂×C₄

—

173

—

105

C₂×C₄

C₄⋊#10621924

yes

—

106

C₈

—

692

—

107

C₈

—

692

—

108

C₂²

C₂×C₄⋊#10621924

yes

characteristic

109

C₂²

#19149758

yes

—

110

C₂²

#19149766

yes

—

111

C₂²

#19149766

yes

characteristic

112

C₂²

#19149767

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

346

—

116

C₄

—

173

—

117

C₄

—

173

—

118

C₄

—

173

—

119

C₄

—

692

—

120

C₂

#26012435

yes

characteristic

121

C₂

#26012497

yes

characteristic

122

C₂

#26012498

yes

characteristic

123

C₂

#26012515

yes

—

124

C₂

#26012516

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10621924
commutator, socle, prime radical	C₂³×C₁₇₃	C₂²×C₄
Fitting	#95×C₁₇₃	C₄
cosocle	C₂²×Dic₁₇₃	C₂³
hypercenter	#95	#10621924
hypocenter	C₁₇₃	#1832
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#10621924

commutator, socle, prime radical

C₂³×C₁₇₃

C₂²×C₄

Fitting

#95×C₁₇₃

C₄

cosocle

C₂²×Dic₁₇₃

C₂³

C₁₇₃

G ▷ C₂³×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
62. C₁₇₃	#1832	semidirect

H ≅ G/N

type

62. C₁₇₃

#1832

semidirect

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

subgroup	index
C₂×#19149746	2
C₂×C₄⋊#13063443	2
#26012357	2
#26011336	2
#1832	173

subgroup

index

173

Subgroups — #36369481

Conjugacy classes of subgroups

Complements

Maximal subgroups