Group #22610043 — subgroups

Subgroups — #22610043

Order 9344.

236 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 81 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	#17989065	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556510	C₂	1	1	yes	maximal, characteristic
3	#17988359	C₂	1	2	yes	maximal
4	#17988358	C₂	1	2	yes	maximal
5	C₂×#101×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924012	C₂²	1	2	yes	—
7	Q₈×Dic₇₃	—	2	2	no	—
8	Q₈×Dic₇₃	—	2	2	no	—
9	#14556550	C₄	1	4	yes	—
10	#14556550	C₂²	1	1	yes	characteristic
11	#14556550	C₂²	1	1	yes	characteristic
12	#14556510	—	2	2	no	—
13	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
15	#101×C₇₃	—	2	2	no	—
16	#11924012	—	2	2	no	—
17	#11924012	—	2	2	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	4	no	—
20	C₄⋊Dic₇₃	—	2	1	no	—
21	C₄⋊Dic₇₃	—	2	1	no	—
22	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
23	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₇₃	—	2	4	no	—
25	C₄×Dic₇₃	—	2	1	no	—
26	C₄×Dic₇₃	—	2	1	no	—
27	C₂×Q₈×C₇₃	—	2	2	no	—
28	C₂×Q₈×C₇₃	—	2	2	no	—
29	C₂×Q₈×C₇₃	D₄	1	2	yes	—
30	C₂×Q₈×C₇₃	D₄	1	2	yes	—
31	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
33	M₁₆×C₇₃	—	2	2	no	—
34	M₁₆×C₇₃	—	2	2	no	—
35	C₂×C₈×C₇₃	—	2	2	no	—
36	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₇₃	—	2	4	no	—
38	Q₈×C₇₃	—	2	4	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
42	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₃	#41	1	2	yes	—
45	C₂×C₄×C₇₃	#41	1	2	yes	—
46	C₂×Dic₇₃	—	2	2	no	—
47	C₂×Dic₇₃	—	2	2	no	—
48	C₈×C₇₃	—	4	2	no	—
49	#10596831	—	4	2	no	—
50	C₂²×C₇₃	—	4	1	no	—
51	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₇₃	#117	1	1	yes	characteristic
53	C₂²×C₇₃	#117	1	1	yes	characteristic
54	C₄×C₇₃	—	2	4	no	—
55	C₄×C₇₃	#123	1	2	yes	—
56	C₄×C₇₃	#123	1	2	yes	—
57	Dic₇₃	—	4	2	no	—
58	Dic₇₃	—	4	2	no	—
59	C₂×C₇₃	—	2	1	no	—
60	C₂×C₇₃	—	2	1	no	—
61	C₂×C₇₃	—	2	1	no	—
62	C₂×C₇₃	#381	1	1	yes	characteristic
63	#1830	—	73	1	no	maximal, Sylow
64	C₇₃	#1830	1	1	yes	characteristic, complemented, Sylow
65	#519	—	73	1	no	—
66	C₂×#101	—	73	1	no	—
67	C₂×#101	D₇₃	1	1	yes	characteristic
68	#344	—	73	2	no	—
69	#344	—	73	2	no	—
70	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
71	C₂×M₁₆	—	73	2	no	—
72	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
73	C₄×Q₈	—	146	2	no	—
74	C₄×Q₈	—	146	2	no	—
75	#117	—	73	4	no	—
76	#117	—	73	1	no	—
77	#117	—	73	1	no	—
78	#101	—	2	2	no	—
79	#101	—	146	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	D₂₉₂	1	2	yes	—
83	C₂×Q₈	C₂²⋊D₇₃	1	2	yes	—
84	C₂²×C₄	C₄×D₇₃	1	2	yes	—
85	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	146	2	no	—
89	M₁₆	—	146	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	146	2	no	—
92	C₄⋊C₄	—	146	4	no	—
93	C₄⋊C₄	—	146	1	no	—
94	C₄⋊C₄	—	146	1	no	—
95	C₂²⋊C₄	—	73	2	no	—
96	C₂²⋊C₄	—	73	2	no	—
97	C₄²	—	146	4	no	—
98	C₄²	—	146	1	no	—
99	C₄²	—	146	1	no	—
100	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
101	Q₈	—	2	4	no	—
102	Q₈	—	2	4	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	146	2	no	—
106	C₂×C₄	—	146	2	no	—
107	C₂×C₄	#11924005	1	4	yes	—
108	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
109	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
110	C₂×C₄	#11924027	1	2	yes	—
111	C₂×C₄	#11924027	1	2	yes	—
112	C₈	—	4	2	no	—
113	C₈	—	292	2	no	—
114	C₂²	—	4	1	no	—
115	C₂²	C₂×#11924005	1	1	yes	characteristic
116	C₂²	#14556547	1	1	yes	characteristic
117	C₂²	#14556547	1	1	yes	characteristic
118	C₄	—	2	4	no	—
119	C₄	—	292	2	no	—
120	C₄	—	292	2	no	—
121	C₄	#14556572	1	2	yes	—
122	C₄	#14556575	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	2	1	no	—
126	C₂	#17988448	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989065

C₂

yes

maximal, characteristic

C₂×#14556510

C₂

yes

maximal, characteristic

#17988359

C₂

yes

maximal

#17988358

C₂

yes

maximal

C₂×#101×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

Q₈×Dic₇₃

—

Q₈×Dic₇₃

—

#14556550

C₄

yes

—

#14556550

C₂²

yes

characteristic

#14556550

C₂²

yes

characteristic

#14556510

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

—

#101×C₇₃

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

C₂×C₄

yes

—

C₂²⋊Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#123

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#519

—

C₂×#101

—

C₂×#101

D₇₃

yes

characteristic

#344

—

#344

—

C₂²×Q₈

C₂×D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₄×Q₈

—

146

—

C₄×Q₈

—

146

—

—

—

—

—

—

146

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₂₉₂

yes

—

C₂×Q₈

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

—

146

—

100

C₂³

C₂×C₄×D₇₃

yes

characteristic

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

146

—

106

C₂×C₄

—

146

—

107

C₂×C₄

#11924005

yes

—

108

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

109

C₂×C₄

C₂×D₂₉₂

yes

characteristic

110

C₂×C₄

#11924027

yes

—

111

C₂×C₄

#11924027

yes

—

112

C₈

—

113

C₈

—

292

—

114

C₂²

—

115

C₂²

C₂×#11924005

yes

characteristic

116

C₂²

#14556547

yes

characteristic

117

C₂²

#14556547

yes

characteristic

118

C₄

—

119

C₄

—

292

—

120

C₄

—

292

—

121

C₄

#14556572

yes

—

122

C₄

#14556575

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

#17988448

yes

characteristic

	subgroup	G/H
center	C₂	#17988448
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×#101×C₇₃	C₂
socle	C₂×C₇₃	#381
hypercenter	C₂×#101	D₇₃
hypocenter	C₇₃	#1830
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂

#17988448

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×#101×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
64. C₇₃	#1830	semidirect

H ≅ G/N

type

64. C₇₃

#1830

semidirect

Subgroups — #22610043

Conjugacy classes of subgroups

Complements