Group #22625136 — subgroups

Subgroups — #22625136

Order 9344.

212 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 104 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	#17989604	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989429	C₂	1	2	yes	maximal, complemented
4	C₈×#10596833	C₂	1	2	yes	maximal, complemented
5	#17988637	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596833	C₄	1	2	yes	—
7	#14556658	C₄	1	2	yes	—
8	C₂²⋊#10596833	C₄	1	2	yes	—
9	C₄×#10596833	C₄	1	2	yes	—
10	C₄×#10596833	C₂²	1	1	yes	characteristic
11	C₄×#10596833	C₂²	1	2	yes	—
12	C₄×#10596833	C₂²	1	1	yes	characteristic
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	C₈	1	8	yes	complemented
19	C₂×#10596833	C₂×C₄	1	4	yes	—
20	C₂×#10596833	C₂×C₄	1	2	yes	—
21	C₂×#10596833	C₂×C₄	1	2	yes	—
22	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#10596831	C₂×C₄	1	2	yes	—
25	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	C₂×C₄	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	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
38	C₂×Dic₇₃	C₂×C₈	1	4	yes	—
39	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
41	#10596833	—	2	4	no	—
42	#10596833	C₂×C₈	1	4	yes	—
43	#10596833	C₂×C₈	1	4	yes	—
44	C₈×C₇₃	—	2	2	no	—
45	#10596831	—	2	2	no	—
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	—	2	1	no	—
48	C₂²×C₇₃	C₄×C₈	1	2	yes	—
49	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₇₃	—	2	1	no	—
51	C₄×C₇₃	#131	1	2	yes	—
52	Dic₇₃	—	2	1	no	—
53	Dic₇₃	C₄×C₈	1	2	yes	—
54	Dic₇₃	C₂²×C₈	1	2	yes	—
55	Dic₇₃	#131	1	2	yes	—
56	C₂×C₇₃	—	2	2	no	—
57	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
58	C₂×C₇₃	#405	1	1	yes	characteristic
59	C₂×C₇₃	#405	1	1	yes	characteristic
60	#1450	—	73	1	no	maximal, Sylow
61	C₇₃	#1450	1	1	yes	characteristic, complemented, Sylow
62	#431	—	73	1	no	—
63	#431	—	73	1	no	—
64	C₂×C₄×C₈	—	73	1	no	—
65	#322	—	73	2	no	—
66	C₈²	—	73	2	no	—
67	C₂²×C₈	—	73	2	no	—
68	C₂×C₄²	—	73	1	no	—
69	C₄⋊C₈	—	73	2	no	—
70	C₄⋊C₈	—	73	2	no	—
71	C₂²⋊C₈	—	73	2	no	—
72	C₂²⋊C₈	—	73	1	no	—
73	C₂²⋊C₈	#64408	1	1	yes	characteristic
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	2	no	—
76	C₄×C₈	—	73	1	no	—
77	C₄×C₈	—	73	2	no	—
78	C₄×C₈	—	73	2	no	—
79	C₂²×C₄	—	73	1	no	—
80	C₂²×C₄	—	73	1	no	—
81	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
82	C₂×C₈	—	73	8	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	73	2	no	—
85	C₂×C₈	—	73	4	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	C₂×#64408	1	2	yes	—
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	2	no	—
94	C₂×C₄	—	73	4	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	C₄×#64408	1	1	yes	characteristic
101	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
102	C₈	—	2	2	no	—
103	C₈	—	73	4	no	—
104	C₈	—	73	4	no	—
105	C₈	—	146	4	no	—
106	C₈	—	146	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	C₈×#64408	1	2	yes	—
110	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	73	2	no	—
113	C₄	—	73	2	no	—
114	C₄	—	73	2	no	—
115	C₄	—	146	1	no	—
116	C₄	#14556678	1	2	yes	—
117	C₂	—	2	2	no	—
118	C₂	C₂×C₈×#64408	1	1	yes	characteristic
119	C₂	#17989551	1	1	yes	characteristic
120	C₂	#17989553	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989604

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

#17989429

C₂

yes

maximal, complemented

C₈×#10596833

C₂

yes

maximal, complemented

#17988637

C₂

yes

maximal, characteristic

C₂²×#10596833

C₄

yes

—

#14556658

C₄

yes

—

C₂²⋊#10596833

C₄

yes

—

C₄×#10596833

C₄

yes

—

C₄×#10596833

C₂²

yes

characteristic

C₄×#10596833

C₂²

yes

—

C₄×#10596833

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556520

C₄

yes

—

C₂²⋊#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

C₈

yes

complemented

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

#10596833

—

#10596833

C₂×C₈

yes

—

#10596833

C₂×C₈

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×C₈

yes

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#131

yes

—

Dic₇₃

—

Dic₇₃

C₄×C₈

yes

—

Dic₇₃

C₂²×C₈

yes

—

Dic₇₃

#131

yes

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄×C₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

#64408

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

100

C₂×C₄

C₄×#64408

yes

characteristic

101

C₂×C₄

C₂²×#64408

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

146

—

106

C₈

—

146

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₈×#64408

yes

—

110

C₂²

C₂×C₄×#64408

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

146

—

116

C₄

#14556678

yes

—

117

C₂

—

118

C₂

C₂×C₈×#64408

yes

characteristic

119

C₂

#17989551

yes

characteristic

120

C₂

#17989553

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Fitting	C₂²⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄²
hypercenter	C₂²⋊C₈	#64408
hypocenter	C₇₃	#1450
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator

C₂×C₇₃

C₂×C₄×C₈

Fitting

C₂²⋊C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄²

C₂²⋊C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
3. #17989429	C₂	semidirect
4. C₈×#10596833	C₂	semidirect
18. C₂×#10596833	C₈	semidirect
61. C₇₃	#1450	semidirect

H ≅ G/N

type

3. #17989429

C₂

semidirect

4. C₈×#10596833

C₂

semidirect

18. C₂×#10596833

C₈

semidirect

61. C₇₃

#1450

semidirect

Subgroups — #22625136

Conjugacy classes of subgroups

Complements