Group #22608693 — subgroups

Subgroups — #22608693

Order 9344.

168 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 73 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	#17988643	C₂	1	2	yes	maximal
2	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#17988340	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988337	C₂	1	2	yes	maximal, complemented
5	#335×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
8	C₄²×D₇₃	C₂²	1	1	yes	characteristic
9	C₄⋊#10596831	C₂²	1	2	yes	—
10	#14556503	—	2	2	no	—
11	#14556501	—	2	2	no	—
12	C₄×#10596831	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₄	1	1	yes	characteristic
14	C₈×Dic₇₃	C₄	1	1	yes	characteristic
15	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
20	C₂×#10596831	—	2	2	no	—
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
23	C₈×D₇₃	—	2	2	no	—
24	C₈×D₇₃	—	2	2	no	—
25	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₇₃	D₄	1	1	yes	characteristic
27	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	—	2	2	no	—
40	C₄×D₇₃	—	2	1	no	—
41	C₄×D₇₃	—	2	1	no	—
42	C₄×D₇₃	—	2	1	no	—
43	C₄×D₇₃	—	2	1	no	—
44	C₈×C₇₃	—	2	1	no	—
45	C₈×C₇₃	—	4	2	no	—
46	C₈×C₇₃	M₁₆	1	2	yes	—
47	#10596831	—	2	1	no	—
48	#10596831	—	4	2	no	—
49	#10596831	M₁₆	1	2	yes	—
50	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×D₇₃	—	2	1	no	—
52	C₂×D₇₃	—	2	1	no	—
53	C₂×D₇₃	#108	1	2	yes	—
54	C₄×C₇₃	—	2	1	no	—
55	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
56	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
57	C₄×C₇₃	#135	1	1	yes	characteristic
58	C₄×C₇₃	#135	1	1	yes	characteristic
59	Dic₇₃	—	2	1	no	—
60	Dic₇₃	—	2	1	no	—
61	Dic₇₃	—	2	1	no	—
62	C₂×C₇₃	#423	1	1	yes	characteristic
63	C₂×C₇₃	#427	1	1	yes	characteristic
64	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
65	D₇₃	—	2	2	no	—
66	#1568	—	73	1	no	maximal, Sylow
67	C₇₃	#1568	1	1	yes	characteristic, complemented, Sylow
68	#432	—	73	2	no	—
69	C₂×C₄×C₈	—	73	1	no	—
70	#335	—	73	1	no	—
71	#335	D₇₃	1	1	yes	characteristic, complemented
72	#334	—	73	2	no	—
73	C₂²×C₈	—	73	1	no	—
74	C₂²×C₈	—	73	1	no	—
75	C₂×C₄²	—	73	1	no	—
76	C₄⋊C₈	—	73	2	no	—
77	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
78	C₂²⋊C₈	—	146	2	no	—
79	#97	—	146	2	no	—
80	C₄×C₈	—	73	1	no	—
81	C₄×C₈	—	73	1	no	—
82	C₄×C₈	—	73	1	no	—
83	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
84	C₂²×C₄	—	73	1	no	—
85	C₂²×C₄	—	73	1	no	—
86	C₂²×C₄	—	73	1	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	73	1	no	—
89	C₂×C₈	—	73	1	no	—
90	C₂×C₈	—	146	2	no	—
91	C₂×C₈	—	146	2	no	—
92	C₂×C₈	—	146	2	no	—
93	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
94	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
95	C₄²	—	73	1	no	—
96	C₄²	—	73	1	no	—
97	C₄²	—	73	1	no	—
98	C₄²	C₂²×D₇₃	1	1	yes	characteristic
99	C₂³	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	—	146	1	no	—
105	C₂×C₄	—	146	1	no	—
106	C₂×C₄	—	146	1	no	—
107	C₂×C₄	—	146	1	no	—
108	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
109	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
110	C₂×C₄	Q₈×D₇₃	1	1	yes	characteristic
111	C₈	—	2	1	no	—
112	C₈	—	4	2	no	—
113	C₈	—	292	2	no	—
114	C₈	—	73	2	no	—
115	C₈	—	146	1	no	—
116	C₈	#11924011	1	2	yes	—
117	C₂²	—	73	2	no	—
118	C₂²	—	146	1	no	—
119	C₂²	—	146	1	no	—
120	C₂²	C₄⋊C₄×D₇₃	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	146	1	no	—
123	C₄	—	146	1	no	—
124	C₄	—	146	1	no	—
125	C₄	M₁₆×D₇₃	1	1	yes	characteristic
126	C₄	C₂×#11924011	1	1	yes	characteristic
127	C₄	#14556610	1	1	yes	characteristic
128	C₄	#14556614	1	1	yes	characteristic
129	C₂	—	146	2	no	—
130	C₂	#17988609	1	1	yes	characteristic
131	C₂	#17988624	1	1	yes	characteristic
132	C₂	#108×D₇₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988643

C₂

yes

maximal

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

#17988340

C₂

yes

maximal, characteristic, complemented

#17988337

C₂

yes

maximal, complemented

#335×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

#14556503

—

#14556501

—

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

M₁₆

yes

—

#10596831

—

#10596831

—

#10596831

M₁₆

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#108

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1568

—

maximal, Sylow

C₇₃

#1568

yes

characteristic, complemented, Sylow

#432

—

C₂×C₄×C₈

—

#335

—

#335

D₇₃

yes

characteristic, complemented

#334

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

—

C₂²⋊C₈

—

146

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

146

—

104

C₂×C₄

—

146

—

105

C₂×C₄

—

146

—

106

C₂×C₄

—

146

—

107

C₂×C₄

—

146

—

108

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

109

C₂×C₄

D₄×D₇₃

yes

characteristic

110

C₂×C₄

Q₈×D₇₃

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

292

—

114

C₈

—

115

C₈

—

146

—

116

C₈

#11924011

yes

—

117

C₂²

—

118

C₂²

—

146

—

119

C₂²

—

146

—

120

C₂²

C₄⋊C₄×D₇₃

yes

characteristic

121

C₄

—

122

C₄

—

146

—

123

C₄

—

146

—

124

C₄

—

146

—

125

C₄

M₁₆×D₇₃

yes

characteristic

126

C₄

C₂×#11924011

yes

characteristic

127

C₄

#14556610

yes

characteristic

128

C₄

#14556614

yes

characteristic

129

C₂

—

146

—

130

C₂

#17988609

yes

characteristic

131

C₂

#17988624

yes

characteristic

132

C₂

#108×D₇₃

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#335×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#335	D₇₃
hypocenter	C₇₃	#1568
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#335×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
3. #17988340	C₂	semidirect
4. #17988337	C₂	semidirect
5. #335×C₇₃	C₂	semidirect
67. C₇₃	#1568	semidirect
71. #335	D₇₃	semidirect

H ≅ G/N

type

3. #17988340

C₂

semidirect

4. #17988337

C₂

semidirect

5. #335×C₇₃

C₂

semidirect

67. C₇₃

#1568

semidirect

71. #335

D₇₃

semidirect

Subgroups — #22608693

Conjugacy classes of subgroups

Complements