Group #22612059 — subgroups

Subgroups — #22612059

Order 9344.

144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14556535	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989004	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988862	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988416	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988402	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988400	C₂	1	1	yes	maximal, characteristic, complemented
7	#472×C₇₃	C₂	1	1	yes	maximal, characteristic
8	#14556621	—	2	1	no	—
9	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
10	#14556535	—	2	1	no	—
11	#14556535	—	2	1	no	—
12	#14556531	—	2	1	no	—
13	#14556531	C₂²	1	1	yes	characteristic
14	C₂×#11924003	—	2	1	no	—
15	C₂×#11924003	C₂²	1	1	yes	characteristic
16	#14556527	C₂²	1	1	yes	characteristic
17	#14556509	—	2	1	no	—
18	AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
19	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
20	#131×C₇₃	C₂²	1	1	yes	characteristic
21	#108×C₇₃	C₂²	1	1	yes	characteristic
22	#100×C₇₃	—	2	1	no	—
23	C₂×Dic₁₄₆	—	2	1	no	—
24	Dic₂₉₂	—	2	1	no	—
25	Dic₂₉₂	—	2	1	no	—
26	#11924018	—	4	1	no	—
27	#11924016	—	4	1	no	—
28	#11924012	—	2	1	no	—
29	#11924003	—	2	1	no	—
30	#11924003	D₄	1	1	yes	characteristic
31	#11924003	D₄	1	1	yes	characteristic
32	#41×C₇₃	D₄	1	1	yes	characteristic
33	C₂×D₄×C₇₃	—	2	1	no	—
34	SD₁₆×C₇₃	—	4	1	no	—
35	D₈×C₇₃	—	2	1	no	—
36	D₈×C₇₃	—	2	1	no	—
37	D₈×C₇₃	—	4	1	no	—
38	M₁₆×C₇₃	—	2	1	no	—
39	M₁₆×C₇₃	—	2	1	no	—
40	M₁₆×C₇₃	D₄	1	1	yes	characteristic
41	C₂×C₈×C₇₃	—	2	1	no	—
42	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂³×C₇₃	—	4	1	no	—
44	Q₈×C₇₃	D₈	1	1	yes	characteristic
45	D₄×C₇₃	—	2	1	no	—
46	D₄×C₇₃	—	4	1	no	—
47	D₄×C₇₃	—	4	1	no	—
48	D₄×C₇₃	D₈	1	1	yes	characteristic
49	C₂×C₄×C₇₃	—	2	1	no	—
50	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₇₃	—	4	1	no	—
52	Dic₁₄₆	—	4	1	no	—
53	Dic₁₄₆	—	4	1	no	—
54	C₈×C₇₃	—	2	1	no	—
55	C₈×C₇₃	—	4	1	no	—
56	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₃	#41	1	1	yes	characteristic
58	#10596831	—	4	1	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	—	8	1	no	—
61	C₂²×C₇₃	—	16	1	no	—
62	C₂²×C₇₃	#135	1	1	yes	characteristic
63	C₄×C₇₃	—	2	1	no	—
64	C₄×C₇₃	#121	1	1	yes	characteristic
65	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
66	Dic₇₃	—	8	1	no	—
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	—	4	1	no	—
69	C₂×C₇₃	—	16	1	no	—
70	C₂×C₇₃	#466	1	1	yes	characteristic
71	#2223	—	73	1	no	maximal, Sylow
72	C₇₃	#2223	1	1	yes	characteristic, complemented, Sylow
73	C₂×SD₃₂	—	73	1	no	—
74	#504	—	73	1	no	—
75	#473	—	73	1	no	—
76	#472	D₇₃	1	1	yes	characteristic
77	#368	—	73	1	no	—
78	#362	—	73	1	no	—
79	#361	—	73	1	no	—
80	#137	—	146	1	no	—
81	AGL(1,ℤ/8)	—	2	1	no	—
82	C₂×Q₁₆	—	73	1	no	—
83	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
84	#131	C₂×D₇₃	1	1	yes	characteristic
85	SD₃₂	—	146	1	no	—
86	SD₃₂	—	146	1	no	—
87	M₃₂	—	73	1	no	—
88	M₃₂	—	146	1	no	—
89	C₂×C₁₆	—	73	1	no	—
90	C₂×C₁₆	—	146	1	no	—
91	#108	—	73	1	no	—
92	#108	C₂×D₇₃	1	1	yes	characteristic
93	#101	—	146	1	no	—
94	#100	—	2	1	no	—
95	#41	C₂²⋊D₇₃	1	1	yes	characteristic
96	C₂×Q₈	—	146	1	no	—
97	C₂×D₄	—	2	1	no	—
98	Q₁₆	—	292	1	no	—
99	Q₁₆	—	146	1	no	—
100	Q₁₆	—	146	1	no	—
101	SD₁₆	—	4	1	no	—
102	SD₁₆	—	292	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	D₈	—	4	1	no	—
106	M₁₆	—	2	1	no	—
107	M₁₆	—	2	1	no	—
108	M₁₆	—	146	1	no	—
109	M₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
112	C₁₆	—	73	1	no	—
113	C₁₆	—	73	1	no	—
114	C₁₆	—	146	1	no	—
115	C₂³	—	4	1	no	—
116	Q₈	—	292	1	no	—
117	Q₈	—	292	1	no	—
118	Q₈	#11924013	1	1	yes	characteristic
119	D₄	—	2	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	#11924013	1	1	yes	characteristic
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	292	1	no	—
125	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
126	C₈	—	2	1	no	—
127	C₈	—	4	1	no	—
128	C₈	—	292	1	no	—
129	C₈	D₄×D₇₃	1	1	yes	characteristic
130	C₈	#11924027	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	—	16	1	no	—
134	C₂²	#14556611	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	584	1	no	—
137	C₄	#14556563	1	1	yes	characteristic
138	C₄	C₂×#11924013	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	16	1	no	—
142	C₂	#17988821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556535

C₂

yes

maximal, characteristic, complemented

#17989004

C₂

yes

maximal, characteristic, complemented

#17988862

C₂

yes

maximal, characteristic, complemented

#17988416

C₂

yes

maximal, characteristic, complemented

#17988402

C₂

yes

maximal, characteristic, complemented

#17988400

C₂

yes

maximal, characteristic, complemented

#472×C₇₃

C₂

yes

maximal, characteristic

#14556621

—

C₂×Dic₂₉₂

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#11924003

—

C₂×#11924003

C₂²

yes

characteristic

#14556527

C₂²

yes

characteristic

#14556509

—

AGL(1,ℤ/8)×C₇₃

—

C₂×D₈×C₇₃

C₂²

yes

characteristic

#131×C₇₃

C₂²

yes

characteristic

#108×C₇₃

C₂²

yes

characteristic

#100×C₇₃

—

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

—

—

—

—

D₄

yes

characteristic

#11924003

D₄

yes

characteristic

#41×C₇₃

D₄

yes

characteristic

C₂×D₄×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

Q₈×C₇₃

D₈

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#135

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#121

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

#504

—

#473

—

#472

D₇₃

yes

—

—

—

—

146

—

AGL(1,ℤ/8)

—

C₂×Q₁₆

—

C₂×D₈

C₂×D₇₃

yes

characteristic

#131

C₂×D₇₃

yes

characteristic

SD₃₂

—

146

—

SD₃₂

—

146

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#108

—

#108

C₂×D₇₃

yes

characteristic

#101

—

146

—

#100

—

#41

C₂²⋊D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

—

Q₁₆

—

292

—

Q₁₆

—

146

—

100

Q₁₆

—

146

—

101

SD₁₆

—

102

SD₁₆

—

292

—

103

D₈

—

104

D₈

—

105

D₈

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

146

—

109

M₁₆

C₂²⋊D₇₃

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

C₂²×D₇₃

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

146

—

115

C₂³

—

116

Q₈

—

292

—

117

Q₈

—

292

—

118

Q₈

#11924013

yes

characteristic

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

#11924013

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

292

—

125

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

292

—

129

C₈

D₄×D₇₃

yes

characteristic

130

C₈

#11924027

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

#14556611

yes

characteristic

135

C₄

—

136

C₄

—

584

—

137

C₄

#14556563

yes

characteristic

138

C₄

C₂×#11924013

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#17988821

yes

characteristic

	subgroup	G/H
center	C₂	#17988821
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#472×C₇₃	C₂
socle	C₂×C₇₃	#466
hypercenter	#472	D₇₃
hypocenter	C₇₃	#2223
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

subgroup

G/H

center

C₂

#17988821

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#472×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

N	H ≅ G/N	type
1. C₂×#14556535	C₂	semidirect
2. #17989004	C₂	semidirect
3. #17988862	C₂	semidirect
4. #17988416	C₂	semidirect
5. #17988402	C₂	semidirect
6. #17988400	C₂	semidirect
72. C₇₃	#2223	semidirect

H ≅ G/N

type

1. C₂×#14556535

C₂

semidirect

2. #17989004

C₂

semidirect

3. #17988862

C₂

semidirect

4. #17988416

C₂

semidirect

5. #17988402

C₂

semidirect

6. #17988400

C₂

semidirect

72. C₇₃

#2223

semidirect

Subgroups — #22612059

Conjugacy classes of subgroups

Complements