Group #22625504 — subgroups

Subgroups — #22625504

Order 9344.

160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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	#17989608	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989451	C₂	1	2	yes	maximal, complemented
4	#17989448	C₂	1	2	yes	maximal, complemented
5	#17988637	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596833	—	2	1	no	—
7	C₄⋊#10596833	—	2	1	no	—
8	C₄⋊#10596833	C₂²	1	1	yes	characteristic
9	C₄⋊#10596833	C₂²	1	2	yes	—
10	C₄⋊#10596833	C₂²	1	1	yes	characteristic
11	C₂²⋊#10596833	—	2	1	no	—
12	#14556646	—	2	1	no	—
13	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
14	#14556520	C₄	1	2	yes	—
15	C₂²⋊#10596831	C₄	1	1	yes	characteristic
16	C₈×Dic₇₃	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₇₃	C₄	1	1	yes	characteristic
18	C₂×#10596833	—	2	2	no	—
19	C₂×#10596833	—	2	1	no	—
20	C₂×#10596833	—	2	1	no	—
21	C₂×#10596833	—	4	2	no	—
22	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
23	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
24	C₂×#10596831	C₂×C₄	1	2	yes	—
25	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₇₃	D₄	1	1	yes	characteristic
27	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
28	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
31	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	2	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	—	2	1	no	—
37	C₂×Dic₇₃	—	2	1	no	—
38	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
42	#10596833	—	4	1	no	—
43	#10596833	—	4	2	no	—
44	#10596833	—	4	1	no	—
45	C₈×C₇₃	—	2	2	no	—
46	#10596831	—	2	2	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	—	2	1	no	—
49	C₂²×C₇₃	#108	1	2	yes	—
50	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	#131	1	2	yes	—
53	Dic₇₃	—	2	1	no	—
54	Dic₇₃	—	2	1	no	—
55	Dic₇₃	—	2	1	no	—
56	Dic₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
57	Dic₇₃	#137	1	1	yes	characteristic
58	C₂×C₇₃	—	2	2	no	—
59	C₂×C₇₃	#424	1	1	yes	characteristic
60	C₂×C₇₃	#428	1	1	yes	characteristic
61	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
62	#1573	—	73	1	no	maximal, Sylow
63	C₇₃	#1573	1	1	yes	characteristic, complemented, Sylow
64	#432	—	73	1	no	—
65	#431	—	73	1	no	—
66	C₂×C₄⋊C₈	—	73	1	no	—
67	#335	—	73	2	no	—
68	#334	—	73	2	no	—
69	C₂²×C₈	—	146	1	no	—
70	C₂×C₄²	—	73	1	no	—
71	C₄⋊C₈	—	73	2	no	—
72	C₄⋊C₈	—	73	1	no	—
73	C₄⋊C₈	—	73	2	no	—
74	C₄⋊C₈	—	73	1	no	—
75	C₄⋊C₈	—	146	1	no	—
76	C₂²⋊C₈	—	73	1	no	—
77	C₂²⋊C₈	—	146	1	no	—
78	C₂²⋊C₈	#64408	1	1	yes	characteristic
79	#97	—	146	1	no	—
80	C₄×C₈	—	73	2	no	—
81	C₂²×C₄	—	73	1	no	—
82	C₂²×C₄	—	73	1	no	—
83	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
84	C₂×C₈	—	292	2	no	—
85	C₂×C₈	—	73	2	no	—
86	C₂×C₈	—	146	1	no	—
87	C₂×C₈	—	146	1	no	—
88	C₂×C₈	—	146	2	no	—
89	C₂×C₈	C₂×#64408	1	2	yes	—
90	C₄²	—	73	1	no	—
91	C₄²	—	73	1	no	—
92	C₄²	—	73	1	no	—
93	C₄²	—	73	1	no	—
94	C₂³	C₄⋊#64408	1	1	yes	characteristic
95	C₂×C₄	—	2	2	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	1	no	—
101	C₂×C₄	—	146	1	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
104	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	292	2	no	—
107	C₈	—	292	1	no	—
108	C₈	—	292	1	no	—
109	C₈	—	146	2	no	—
110	C₂²	—	2	1	no	—
111	C₂²	—	2	1	no	—
112	C₂²	#14556661	1	2	yes	—
113	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	73	1	no	—
116	C₄	—	73	1	no	—
117	C₄	—	146	1	no	—
118	C₄	—	146	1	no	—
119	C₄	—	146	1	no	—
120	C₄	#14556678	1	2	yes	—
121	C₂	—	2	2	no	—
122	C₂	#17989593	1	1	yes	characteristic
123	C₂	#17989598	1	1	yes	characteristic
124	C₂	C₂×#14556661	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989608

C₂

yes

maximal, characteristic

C₂×C₄⋊#10596833

C₂

yes

maximal, characteristic

#17989451

C₂

yes

maximal, complemented

#17989448

C₂

yes

maximal, complemented

#17988637

C₂

yes

maximal, characteristic

C₂²×#10596833

—

C₄⋊#10596833

—

C₄⋊#10596833

C₂²

yes

characteristic

C₄⋊#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

characteristic

C₂²⋊#10596833

—

#14556646

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556520

C₄

yes

—

C₂²⋊#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

C₄

yes

—

—

—

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

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×C₄

yes

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

—

—

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#108

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#131

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#432

—

#431

—

C₂×C₄⋊C₈

—

#335

—

#334

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₂²⋊C₈

#64408

yes

characteristic

#97

—

146

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

—

146

—

103

C₂×C₄

C₄⋊#64408

yes

characteristic

104

C₂×C₄

C₂²×#64408

yes

characteristic

105

C₈

—

106

C₈

—

292

—

107

C₈

—

292

—

108

C₈

—

292

—

109

C₈

—

146

—

110

C₂²

—

111

C₂²

—

112

C₂²

#14556661

yes

—

113

C₂²

C₂×C₄⋊#64408

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

146

—

118

C₄

—

146

—

119

C₄

—

146

—

120

C₄

#14556678

yes

—

121

C₂

—

122

C₂

#17989593

yes

characteristic

123

C₂

#17989598

yes

characteristic

124

C₂

C₂×#14556661

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	#1573
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
3. #17989451	C₂	semidirect
4. #17989448	C₂	semidirect
63. C₇₃	#1573	semidirect

H ≅ G/N

type

3. #17989451

C₂

semidirect

4. #17989448

C₂

semidirect

63. C₇₃

#1573

semidirect

Subgroups — #22625504

Conjugacy classes of subgroups

Complements