Group #22612147 — subgroups

Subgroups — #22612147

Order 9344.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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	#17988841	C₂	1	1	yes	maximal, characteristic
2	#17988634	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988409	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988401	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988399	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988368	C₂	1	1	yes	maximal, characteristic, complemented
7	#365×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
9	C₂×#11924011	C₂²	1	1	yes	characteristic
10	M₁₆×D₇₃	—	2	1	no	—
11	#14556566	—	2	1	no	—
12	#14556531	C₂²	1	1	yes	characteristic
13	#14556527	C₂²	1	1	yes	characteristic
14	#14556526	—	2	1	no	—
15	#14556511	—	2	1	no	—
16	M₃₂×C₇₃	C₂²	1	1	yes	characteristic
17	#108×C₇₃	C₂²	1	1	yes	characteristic
18	#106×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×D₂₉₂	—	2	1	no	—
20	C₂×D₂₉₂	—	4	1	no	—
21	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
22	D₅₈₄	—	2	1	no	—
23	D₅₈₄	—	2	1	no	—
24	#11924012	—	2	1	no	—
25	#11924011	—	2	1	no	—
26	#11924011	—	2	1	no	—
27	#11924011	—	4	1	no	—
28	C₂×#10596831	D₄	1	1	yes	characteristic
29	C₈×D₇₃	—	4	1	no	—
30	#11924005	—	4	1	no	—
31	#11924003	—	2	1	no	—
32	M₁₆×C₇₃	—	2	1	no	—
33	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₇₃	—	2	1	no	—
35	C₁₆×C₇₃	—	2	1	no	—
36	C₂²×D₇₃	—	4	1	no	—
37	C₂²×D₇₃	SD₁₆	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	4	1	no	—
39	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
41	D₂₉₂	—	4	1	no	—
42	D₂₉₂	—	4	1	no	—
43	D₂₉₂	—	8	2	no	—
44	C₄×D₇₃	—	2	1	no	—
45	C₄×D₇₃	—	2	1	no	—
46	C₈×C₇₃	—	4	1	no	—
47	C₈×C₇₃	#41	1	1	yes	characteristic
48	C₈×C₇₃	#41	1	1	yes	characteristic
49	#10596831	—	2	1	no	—
50	#10596831	—	4	1	no	—
51	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
52	C₂×D₇₃	—	2	1	no	—
53	C₂×D₇₃	—	4	1	no	—
54	C₂×D₇₃	—	8	1	no	—
55	C₂×D₇₃	—	8	1	no	—
56	C₂×D₇₃	—	8	1	no	—
57	C₄×C₇₃	—	8	1	no	—
58	C₄×C₇₃	#123	1	1	yes	characteristic
59	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
60	Dic₇₃	—	2	1	no	—
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	#481	1	1	yes	characteristic
63	D₇₃	—	4	1	no	—
64	D₇₃	—	16	1	no	—
65	#2238	—	73	1	no	maximal, Sylow
66	C₇₃	#2238	1	1	yes	characteristic, complemented, Sylow
67	#469	—	73	1	no	—
68	#430	—	73	1	no	—
69	#365	—	73	1	no	—
70	#365	D₇₃	1	1	yes	characteristic, complemented
71	#361	—	73	1	no	—
72	#361	—	73	1	no	—
73	#349	—	73	1	no	—
74	C₂×D₈	—	73	1	no	—
75	C₂×M₁₆	—	73	1	no	—
76	C₂×M₁₆	—	146	1	no	—
77	#121	—	146	1	no	—
78	M₃₂	—	73	1	no	—
79	M₃₂	C₂×D₇₃	1	1	yes	characteristic
80	#108	—	73	1	no	—
81	#108	—	146	1	no	—
82	#108	C₂×D₇₃	1	1	yes	characteristic
83	#106	C₂×D₇₃	1	1	yes	characteristic
84	#102	—	146	1	no	—
85	C₂×D₄	—	292	1	no	—
86	C₂×D₄	—	146	1	no	—
87	C₂²×C₄	—	73	1	no	—
88	D₈	—	146	1	no	—
89	D₈	—	146	1	no	—
90	M₁₆	—	2	1	no	—
91	M₁₆	—	292	1	no	—
92	M₁₆	—	146	1	no	—
93	M₁₆	—	146	1	no	—
94	M₁₆	—	146	1	no	—
95	C₂×C₈	—	292	1	no	—
96	C₂×C₈	—	73	1	no	—
97	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
98	C₄⋊C₄	—	2	1	no	—
99	C₂²⋊C₄	—	292	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	146	1	no	—
102	C₂³	—	292	1	no	—
103	C₂³	—	73	1	no	—
104	D₄	—	292	1	no	—
105	D₄	—	292	1	no	—
106	D₄	—	584	2	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	73	1	no	—
109	C₂×C₄	—	146	1	no	—
110	C₂×C₄	—	146	1	no	—
111	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
112	C₈	—	4	1	no	—
113	C₈	—	292	1	no	—
114	C₈	—	146	1	no	—
115	C₈	#11924028	1	1	yes	characteristic
116	C₈	#11924029	1	1	yes	characteristic
117	C₂²	—	292	1	no	—
118	C₂²	—	584	1	no	—
119	C₂²	—	584	1	no	—
120	C₂²	—	584	1	no	—
121	C₂²	—	146	1	no	—
122	C₂²	SD₁₆×D₇₃	1	1	yes	characteristic
123	C₄	—	8	1	no	—
124	C₄	—	146	1	no	—
125	C₄	#14556576	1	1	yes	characteristic
126	C₄	#14556618	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	292	1	no	—
129	C₂	—	1168	1	no	—
130	C₂	#17988907	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988841

C₂

yes

maximal, characteristic

#17988634

C₂

yes

maximal, characteristic, complemented

#17988409

C₂

yes

maximal, characteristic, complemented

#17988401

C₂

yes

maximal, characteristic, complemented

#17988399

C₂

yes

maximal, characteristic, complemented

#17988368

C₂

yes

maximal, characteristic, complemented

#365×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×D₅₈₄

C₂²

yes

characteristic

C₂×#11924011

C₂²

yes

characteristic

M₁₆×D₇₃

—

#14556566

—

#14556531

C₂²

yes

characteristic

#14556527

C₂²

yes

characteristic

#14556526

—

#14556511

—

M₃₂×C₇₃

C₂²

yes

characteristic

#108×C₇₃

C₂²

yes

characteristic

#106×C₇₃

C₂²

yes

characteristic

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×C₄×D₇₃

D₄

yes

characteristic

D₅₈₄

—

D₅₈₄

—

—

—

—

—

D₄

yes

characteristic

C₈×D₇₃

—

#11924005

—

#11924003

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

—

—

C₂²×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#481

yes

characteristic

D₇₃

—

D₇₃

—

#2238

—

maximal, Sylow

C₇₃

#2238

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#361

—

#361

—

#349

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

#121

—

146

—

M₃₂

—

M₃₂

C₂×D₇₃

yes

characteristic

#108

—

#108

—

146

—

#108

C₂×D₇₃

yes

characteristic

#106

C₂×D₇₃

yes

characteristic

#102

—

146

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂²×C₄

—

D₈

—

146

—

D₈

—

146

—

M₁₆

—

M₁₆

—

292

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

292

—

100

C₁₆

—

101

C₁₆

—

146

—

102

C₂³

—

292

—

103

C₂³

—

104

D₄

—

292

—

105

D₄

—

292

—

106

D₄

—

584

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

146

—

110

C₂×C₄

—

146

—

111

C₂×C₄

D₄×D₇₃

yes

characteristic

112

C₈

—

113

C₈

—

292

—

114

C₈

—

146

—

115

C₈

#11924028

yes

characteristic

116

C₈

#11924029

yes

characteristic

117

C₂²

—

292

—

118

C₂²

—

584

—

119

C₂²

—

584

—

120

C₂²

—

584

—

121

C₂²

—

146

—

122

C₂²

SD₁₆×D₇₃

yes

characteristic

123

C₄

—

124

C₄

—

146

—

125

C₄

#14556576

yes

characteristic

126

C₄

#14556618

yes

characteristic

127

C₂

—

128

C₂

—

292

—

129

C₂

—

1168

—

130

C₂

#17988907

yes

characteristic

	subgroup	G/H
center	C₂	#17988907
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#365×C₇₃	C₂
socle	C₂×C₇₃	#481
hypercenter	#365	D₇₃
hypocenter	C₇₃	#2238
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#17988907

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#365×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

N	H ≅ G/N	type
2. #17988634	C₂	semidirect
3. #17988409	C₂	semidirect
4. #17988401	C₂	semidirect
5. #17988399	C₂	semidirect
6. #17988368	C₂	semidirect
7. #365×C₇₃	C₂	semidirect
66. C₇₃	#2238	semidirect
70. #365	D₇₃	semidirect

H ≅ G/N

type

2. #17988634

C₂

semidirect

3. #17988409

C₂

semidirect

4. #17988401

C₂

semidirect

5. #17988399

C₂

semidirect

6. #17988368

C₂

semidirect

7. #365×C₇₃

C₂

semidirect

66. C₇₃

#2238

semidirect

70. #365

D₇₃

semidirect

Subgroups — #22612147

Conjugacy classes of subgroups

Complements