Group #22611529 — subgroups

Subgroups — #22611529

Order 9344.

184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14556530	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#17988541	C₂	1	1	yes	maximal, characteristic
4	#17988362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#11924003	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924011	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
10	#14556548	C₄	1	1	yes	characteristic
11	#14556530	C₄	1	4	yes	complemented
12	C₂×#11924003	C₂²	1	1	yes	characteristic
13	C₂×#11924003	C₂²	1	1	yes	characteristic
14	C₁₆×D₇₃	C₄	1	4	yes	complemented
15	#14556502	C₄	1	1	yes	characteristic
16	#14556501	C₄	1	1	yes	characteristic
17	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
22	#11924011	C₈	1	4	yes	—
23	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
24	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	C₂×C₄	1	2	yes	—
26	C₈×D₇₃	C₂×C₄	1	2	yes	—
27	#11924007	C₈	1	2	yes	—
28	#11924005	C₈	1	2	yes	—
29	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	#11924003	C₂×C₄	1	2	yes	—
31	#11924003	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
34	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₁₆×C₇₃	C₂×C₄	1	2	yes	—
36	C₁₆×C₇₃	C₂×C₄	1	2	yes	—
37	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
41	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
42	C₄×D₇₃	C₄²	1	2	yes	—
43	C₄×D₇₃	C₂×C₈	1	2	yes	—
44	C₈×C₇₃	C₂×C₈	1	2	yes	—
45	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	#10596831	C₄²	1	2	yes	—
48	#10596831	C₂×C₈	1	2	yes	—
49	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₇₃	—	2	2	no	—
51	C₂×D₇₃	C₄×C₈	1	2	yes	—
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
55	Dic₇₃	—	2	2	no	—
56	Dic₇₃	C₄×C₈	1	2	yes	—
57	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
58	C₂×C₇₃	#504	1	2	yes	—
59	D₇₃	—	2	2	no	—
60	#2108	—	73	1	no	maximal, Sylow
61	C₇₃	#2108	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₃₂	—	73	1	no	—
63	C₂²×C₁₆	—	73	1	no	—
64	#405	—	73	1	no	—
65	#346	—	73	1	no	—
66	#346	D₇₃	1	1	yes	characteristic, complemented
67	C₄×C₁₆	—	73	1	no	—
68	C₄×C₁₆	—	73	1	no	—
69	C₂×M₁₆	—	73	1	no	—
70	C₂²×C₈	—	73	1	no	—
71	#117	—	73	1	no	—
72	M₃₂	—	73	4	no	—
73	C₂×C₁₆	—	73	1	no	—
74	C₂×C₁₆	—	73	1	no	—
75	C₂×C₁₆	—	73	4	no	—
76	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
77	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
78	#97	—	73	1	no	—
79	#97	—	73	1	no	—
80	C₄×C₈	—	73	1	no	—
81	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
82	C₂²×C₄	—	73	1	no	—
83	M₁₆	—	73	4	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	—	73	2	no	—
88	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
90	C₄⋊C₄	—	73	2	no	—
91	C₂²⋊C₄	—	73	2	no	—
92	C₄²	—	73	1	no	—
93	C₄²	C₄×D₇₃	1	1	yes	characteristic
94	C₁₆	—	73	2	no	—
95	C₁₆	—	73	2	no	—
96	C₁₆	C₄×D₇₃	1	2	yes	—
97	C₁₆	C₄×D₇₃	1	2	yes	—
98	C₂³	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	73	2	no	—
102	C₂×C₄	—	73	2	no	—
103	C₂×C₄	C₈×D₇₃	1	2	yes	—
104	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
105	C₈	—	73	2	no	—
106	C₈	—	73	2	no	—
107	C₈	C₈×D₇₃	1	2	yes	—
108	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
109	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
110	C₂²	—	73	2	no	—
111	C₂²	—	146	2	no	—
112	C₂²	C₂×C₈×D₇₃	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	146	2	no	—
116	C₄	C₄²×D₇₃	1	1	yes	characteristic
117	C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
118	C₂	—	146	2	no	—
119	C₂	C₄×C₈×D₇₃	1	1	yes	characteristic
120	C₂	#17989005	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556530

C₂

yes

maximal, characteristic

C₂×C₁₆×D₇₃

C₂

yes

maximal, characteristic

#17988541

C₂

yes

maximal, characteristic

#17988362

C₂

yes

maximal, characteristic, complemented

C₄×#11924003

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₇₃

C₂

yes

maximal, characteristic, complemented

#346×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924011

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₄

yes

characteristic

#14556530

C₄

yes

complemented

C₂×#11924003

C₂²

yes

characteristic

C₂×#11924003

C₂²

yes

characteristic

C₁₆×D₇₃

C₄

yes

complemented

#14556502

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924011

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

#11924007

C₈

yes

—

#11924005

C₈

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

#11924003

C₂×C₄

yes

—

#11924003

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

—

C₁₆×C₇₃

C₂×C₄

yes

—

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₄²

yes

—

C₄×D₇₃

C₂×C₈

yes

—

C₈×C₇₃

C₂×C₈

yes

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

characteristic

#10596831

C₄²

yes

—

#10596831

C₂×C₈

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄×C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄×C₈

yes

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#504

yes

—

D₇₃

—

#2108

—

maximal, Sylow

C₇₃

#2108

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

D₇₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₇₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₄×D₇₃

yes

—

C₁₆

C₄×D₇₃

yes

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₈×D₇₃

yes

—

104

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

C₈×D₇₃

yes

—

108

C₈

C₂×C₄×D₇₃

yes

characteristic

109

C₈

C₂×C₄×D₇₃

yes

characteristic

110

C₂²

—

111

C₂²

—

146

—

112

C₂²

C₂×C₈×D₇₃

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

146

—

116

C₄

C₄²×D₇₃

yes

characteristic

117

C₄

C₂×C₈×D₇₃

yes

characteristic

118

C₂

—

146

—

119

C₂

C₄×C₈×D₇₃

yes

characteristic

120

C₂

#17989005

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₃
commutator	C₂×C₇₃	C₂×C₄×C₈
Fitting	#346×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2108
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₃

commutator

C₂×C₇₃

C₂×C₄×C₈

Fitting

#346×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×C₈

D₇₃

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
4. #17988362	C₂	semidirect
5. C₄×#11924003	C₂	semidirect
6. C₁₆×Dic₇₃	C₂	semidirect
7. #346×C₇₃	C₂	semidirect
11. #14556530	C₄	semidirect
14. C₁₆×D₇₃	C₄	semidirect
61. C₇₃	#2108	semidirect
66. #346	D₇₃	semidirect

H ≅ G/N

type

4. #17988362

C₂

semidirect

5. C₄×#11924003

C₂

semidirect

6. C₁₆×Dic₇₃

C₂

semidirect

7. #346×C₇₃

C₂

semidirect

11. #14556530

C₄

semidirect

14. C₁₆×D₇₃

C₄

semidirect

61. C₇₃

#2108

semidirect

66. #346

D₇₃

semidirect

Subgroups — #22611529

Conjugacy classes of subgroups

Complements