Group #22625501 — subgroups

Subgroups — #22625501

Order 9344.

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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	#17989591	C₂	1	1	yes	maximal, characteristic
2	#17989588	C₂	1	1	yes	maximal, characteristic
3	#17989451	C₂	1	2	yes	maximal, complemented
4	#17989450	C₂	1	2	yes	maximal, complemented
5	#17988639	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924038	—	2	1	no	—
7	C₂×#11924036	—	2	1	no	—
8	#14556658	—	2	1	no	—
9	C₄⋊#10596833	—	2	1	no	—
10	C₄⋊#10596833	C₂²	1	1	yes	characteristic
11	C₄⋊#10596833	C₂²	1	2	yes	—
12	C₄⋊#10596833	C₂²	1	1	yes	characteristic
13	C₄²×D₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊#10596831	C₄	1	1	yes	characteristic
15	#14556503	C₄	1	2	yes	—
16	C₈×Dic₇₃	C₂²	1	2	yes	—
17	C₄⋊C₈×C₇₃	C₄	1	1	yes	characteristic
18	#11924038	—	4	2	no	—
19	#11924036	—	4	2	no	—
20	C₂×#10596833	—	2	1	no	—
21	C₂×#10596833	—	2	1	no	—
22	C₂×#10596833	—	2	2	no	—
23	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
25	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
26	C₂×#10596831	C₂×C₄	1	2	yes	—
27	C₄×Dic₇₃	D₄	1	1	yes	characteristic
28	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
29	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
31	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₄×D₇₃	—	2	1	no	—
40	C₄×D₇₃	—	2	1	no	—
41	C₄×D₇₃	—	4	1	no	—
42	C₄×D₇₃	D₈	1	2	yes	—
43	C₄×D₇₃	Q₁₆	1	2	yes	—
44	#10596833	—	4	1	no	—
45	#10596833	—	4	1	no	—
46	#10596833	—	4	2	no	—
47	C₈×C₇₃	—	2	2	no	—
48	#10596831	—	2	2	no	—
49	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×D₇₃	—	2	1	no	—
51	C₂×D₇₃	—	2	1	no	—
52	C₂×D₇₃	#107	1	2	yes	—
53	C₄×C₇₃	—	2	1	no	—
54	C₄×C₇₃	#107	1	2	yes	—
55	C₄×C₇₃	#131	1	1	yes	characteristic
56	C₄×C₇₃	#131	1	1	yes	characteristic
57	Dic₇₃	—	2	1	no	—
58	Dic₇₃	—	2	1	no	—
59	Dic₇₃	C₂×D₈	1	1	yes	characteristic
60	Dic₇₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₂×C₇₃	#424	1	1	yes	characteristic
62	C₂×C₇₃	C₂×#107	1	1	yes	characteristic
63	C₂×C₇₃	#430	1	1	yes	characteristic
64	D₇₃	—	2	2	no	—
65	#1571	—	73	1	no	maximal, Sylow
66	C₇₃	#1571	1	1	yes	characteristic, complemented, Sylow
67	#431	—	73	1	no	—
68	#423	—	73	1	no	—
69	C₂×C₄⋊C₈	—	73	1	no	—
70	#335	—	73	2	no	—
71	#335	—	73	2	no	—
72	C₂×M₁₆	—	146	1	no	—
73	C₂²×C₈	—	146	1	no	—
74	C₂×C₄²	—	73	1	no	—
75	C₄⋊C₈	—	73	1	no	—
76	C₄⋊C₈	—	73	1	no	—
77	C₄⋊C₈	—	73	2	no	—
78	C₄⋊C₈	—	73	1	no	—
79	C₄⋊C₈	—	146	1	no	—
80	C₄⋊C₈	—	146	1	no	—
81	C₄⋊C₈	#64408	1	1	yes	characteristic
82	C₂²⋊C₈	—	73	2	no	—
83	C₄×C₈	—	73	2	no	—
84	C₂²×C₄	—	73	1	no	—
85	C₂²×C₄	—	73	1	no	—
86	C₂²×C₄	—	73	1	no	—
87	M₁₆	—	292	2	no	—
88	C₂×C₈	—	292	2	no	—
89	C₂×C₈	—	73	2	no	—
90	C₂×C₈	—	146	1	no	—
91	C₂×C₈	—	146	1	no	—
92	C₂×C₈	—	146	2	no	—
93	C₂×C₈	C₂×#64408	1	2	yes	—
94	C₄²	—	73	1	no	—
95	C₄²	—	73	1	no	—
96	C₄²	—	73	1	no	—
97	C₄²	C₂×#64408	1	1	yes	characteristic
98	C₂³	—	73	1	no	—
99	C₂×C₄	—	292	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	2	no	—
102	C₂×C₄	—	73	2	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	73	1	no	—
105	C₂×C₄	—	146	1	no	—
106	C₂×C₄	—	146	1	no	—
107	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
108	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
109	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	292	1	no	—
112	C₈	—	292	1	no	—
113	C₈	—	292	2	no	—
114	C₈	—	146	2	no	—
115	C₂²	—	73	2	no	—
116	C₂²	—	146	1	no	—
117	C₂²	—	146	1	no	—
118	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
119	C₄	—	2	1	no	—
120	C₄	—	73	1	no	—
121	C₄	—	73	1	no	—
122	C₄	—	146	1	no	—
123	C₄	—	146	1	no	—
124	C₄	#14556660	1	2	yes	—
125	C₄	#14556678	1	1	yes	characteristic
126	C₄	#14556679	1	1	yes	characteristic
127	C₂	—	146	2	no	—
128	C₂	#17989594	1	1	yes	characteristic
129	C₂	C₂×#14556660	1	1	yes	characteristic
130	C₂	#17989602	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989591

C₂

yes

maximal, characteristic

#17989588

C₂

yes

maximal, characteristic

#17989451

C₂

yes

maximal, complemented

#17989450

C₂

yes

maximal, complemented

#17988639

C₂

yes

maximal, characteristic

—

—

—

—

C₂²

yes

characteristic

C₄⋊#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

C₄⋊#10596831

C₄

yes

characteristic

#14556503

C₄

yes

—

C₈×Dic₇₃

C₂²

yes

—

C₄⋊C₈×C₇₃

C₄

yes

—

—

—

—

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

D₈

yes

—

C₄×D₇₃

Q₁₆

yes

—

#10596833

—

#10596833

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#107

yes

—

C₄×C₇₃

—

C₄×C₇₃

#107

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

C₂×D₈

yes

characteristic

Dic₇₃

C₂×Q₁₆

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1571

—

maximal, Sylow

C₇₃

#1571

yes

characteristic, complemented, Sylow

#431

—

#423

—

C₂×C₄⋊C₈

—

#335

—

#335

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

C₄⋊C₈

#64408

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

292

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

146

—

106

C₂×C₄

—

146

—

107

C₂×C₄

C₄⋊#64408

yes

characteristic

108

C₂×C₄

C₄⋊#64408

yes

characteristic

109

C₂×C₄

C₂²×#64408

yes

characteristic

110

C₈

—

111

C₈

—

292

—

112

C₈

—

292

—

113

C₈

—

292

—

114

C₈

—

146

—

115

C₂²

—

116

C₂²

—

146

—

117

C₂²

—

146

—

118

C₂²

C₂×C₄⋊#64408

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

146

—

123

C₄

—

146

—

124

C₄

#14556660

yes

—

125

C₄

#14556678

yes

characteristic

126

C₄

#14556679

yes

characteristic

127

C₂

—

146

—

128

C₂

#17989594

yes

characteristic

129

C₂

C₂×#14556660

yes

characteristic

130

C₂

#17989602

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₄⋊C₈	#64408
hypocenter	C₇₃	#1571
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄⋊C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₄⋊C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #17989451	C₂	semidirect
4. #17989450	C₂	semidirect
66. C₇₃	#1571	semidirect

H ≅ G/N

type

3. #17989451

C₂

semidirect

4. #17989450

C₂

semidirect

66. C₇₃

#1571

semidirect

Subgroups — #22625501

Conjugacy classes of subgroups

Complements