Group #22625485 — subgroups

Subgroups — #22625485

Order 9344.

184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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	#17989590	C₂	1	2	yes	maximal
2	#17989449	C₂	1	2	yes	maximal, complemented
3	#17989448	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924037	—	2	2	no	—
6	#14556658	—	2	2	no	—
7	C₄⋊#10596833	C₂²	1	4	yes	—
8	C₂²×#10596831	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₈×Dic₇₃	C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₄	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
15	#11924037	—	4	4	no	—
16	C₂×#10596833	—	2	4	no	—
17	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
19	C₂×#10596831	—	2	2	no	—
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₇₃	D₄	1	1	yes	characteristic
24	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	SD₁₆	1	4	yes	—
39	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
41	#10596833	—	4	4	no	—
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	M₁₆	1	2	yes	complemented
44	#10596831	—	2	1	no	—
45	#10596831	M₁₆	1	2	yes	complemented
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	#106	1	2	yes	—
49	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₇₃	—	2	1	no	—
51	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
52	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
53	Dic₇₃	—	2	1	no	—
54	Dic₇₃	#106	1	2	yes	—
55	Dic₇₃	#108	1	2	yes	—
56	Dic₇₃	C₂×SD₁₆	1	2	yes	—
57	C₂×C₇₃	—	2	2	no	—
58	C₂×C₇₃	#423	1	1	yes	characteristic
59	C₂×C₇₃	C₂×#106	1	1	yes	characteristic
60	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
61	#1566	—	73	1	no	maximal, Sylow
62	C₇₃	#1566	1	1	yes	characteristic, complemented, Sylow
63	#423	—	73	2	no	—
64	C₂×C₄×C₈	—	73	1	no	—
65	#334	—	73	2	no	—
66	#334	—	73	2	no	—
67	C₂×M₁₆	—	146	2	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂²×C₈	#64408	1	1	yes	characteristic
70	C₂×C₄²	—	73	1	no	—
71	C₄⋊C₈	—	73	4	no	—
72	C₄⋊C₈	—	146	2	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₄×C₈	—	73	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	73	1	no	—
79	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
80	M₁₆	—	292	4	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	146	4	no	—
85	C₂×C₈	—	146	2	no	—
86	C₂×C₈	C₂×#64408	1	1	yes	characteristic
87	C₂×C₈	C₂×#64408	1	1	yes	characteristic
88	C₄²	—	73	1	no	—
89	C₄²	—	73	1	no	—
90	C₄²	—	73	1	no	—
91	C₄²	—	73	1	no	—
92	C₂³	C₄⋊#64408	1	1	yes	characteristic
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	73	4	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	146	2	no	—
101	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
102	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	292	4	no	—
105	C₈	—	73	2	no	—
106	C₈	—	146	1	no	—
107	C₈	#11924037	1	2	yes	complemented
108	C₂²	—	2	1	no	—
109	C₂²	—	2	1	no	—
110	C₂²	#14556659	1	2	yes	—
111	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	73	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	73	2	no	—
116	C₄	—	146	1	no	—
117	C₄	C₂×#11924037	1	1	yes	characteristic
118	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
119	C₂	—	2	2	no	—
120	C₂	#17989590	1	1	yes	characteristic
121	C₂	C₂×#14556659	1	1	yes	characteristic
122	C₂	D₇₃⋊#108	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989590

C₂

yes

maximal

#17989449

C₂

yes

maximal, complemented

#17989448

C₂

yes

maximal, complemented

C₂×C₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂×#11924037

—

#14556658

—

C₄⋊#10596833

C₂²

yes

—

C₂²×#10596831

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₄

yes

characteristic

#11924037

—

C₂×#10596833

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

M₁₆

yes

complemented

#10596831

—

#10596831

M₁₆

yes

complemented

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#106

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

#106

yes

—

Dic₇₃

#108

yes

—

Dic₇₃

C₂×SD₁₆

yes

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#423

—

C₂×C₄×C₈

—

#334

—

#334

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

#64408

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

C₄⋊#64408

yes

characteristic

102

C₂×C₄

C₂²×#64408

yes

characteristic

103

C₈

—

104

C₈

—

292

—

105

C₈

—

106

C₈

—

146

—

107

C₈

#11924037

yes

complemented

108

C₂²

—

109

C₂²

—

110

C₂²

#14556659

yes

—

111

C₂²

C₂×C₄⋊#64408

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

146

—

117

C₄

C₂×#11924037

yes

characteristic

118

C₄

D₇₃⋊M₁₆

yes

characteristic

119

C₂

—

120

C₂

#17989590

yes

characteristic

121

C₂

C₂×#14556659

yes

characteristic

122

C₂

D₇₃⋊#108

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1566
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₂²×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #17989449	C₂	semidirect
3. #17989448	C₂	semidirect
43. C₈×C₇₃	M₁₆	semidirect
45. #10596831	M₁₆	semidirect
62. C₇₃	#1566	semidirect
107. C₈	#11924037	semidirect

H ≅ G/N

type

2. #17989449

C₂

semidirect

3. #17989448

C₂

semidirect

43. C₈×C₇₃

M₁₆

semidirect

45. #10596831

M₁₆

semidirect

62. C₇₃

#1566

semidirect

107. C₈

#11924037

semidirect

Subgroups — #22625485

Conjugacy classes of subgroups

Complements