Group #22626270 — subgroups

Subgroups — #22626270

Order 9344.

168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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	#17989643	C₂	1	2	yes	maximal
2	#17989510	C₂	1	2	yes	maximal, complemented
3	#17989509	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#14556666	—	2	2	no	—
6	#14556665	C₂²	1	4	yes	—
7	#14556664	—	2	2	no	—
8	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
10	C₄²×D₇₃	C₄	1	1	yes	characteristic
11	C₄×#10596831	C₂²	1	1	yes	characteristic
12	C₈×Dic₇₃	C₄	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
15	#11924031	—	2	4	no	—
16	C₂×C₄×D₇₃	—	2	1	no	—
17	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₈×D₇₃	C₈	1	2	yes	—
21	C₈×D₇₃	C₈	1	2	yes	—
22	C₈×D₇₃	D₄	1	1	yes	characteristic
23	C₈×D₇₃	D₄	1	1	yes	characteristic
24	C₈×D₇₃	Q₈	1	1	yes	characteristic
25	C₈×D₇₃	Q₈	1	1	yes	characteristic
26	C₄×Dic₇₃	—	2	1	no	—
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₃	—	2	1	no	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	1	no	—
35	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
36	C₄×D₇₃	—	2	4	no	—
37	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
40	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
43	C₈×C₇₃	C₂×C₈	1	2	yes	—
44	#10596831	C₂×C₈	1	2	yes	—
45	#10596831	C₂×D₄	1	1	yes	characteristic
46	#10596831	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂×D₇₃	—	2	2	no	—
49	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
50	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
51	C₄×C₇₃	—	2	2	no	—
52	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
54	Dic₇₃	—	2	2	no	—
55	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
56	Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	—	2	1	no	—
58	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
59	D₇₃	—	2	1	no	—
60	D₇₃	#364	1	2	yes	complemented
61	C₂×#364	—	73	1	no	maximal, Sylow
62	C₇₃	C₂×#364	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	73	2	no	—
64	C₂×C₄×C₈	—	73	1	no	—
65	#364	—	73	2	no	—
66	#364	—	73	2	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	73	1	no	—
69	C₂×C₄²	—	73	1	no	—
70	M₃₂	—	73	4	no	—
71	M₃₂	—	146	2	no	—
72	C₂×C₁₆	—	146	2	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₄×C₈	#64408	1	1	yes	characteristic
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	—	146	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	2	no	—
86	C₂×C₈	—	73	2	no	—
87	C₂×C₈	C₂×#64408	1	1	yes	characteristic
88	C₂×C₈	C₂×#64408	1	1	yes	characteristic
89	C₄²	—	73	1	no	—
90	C₄²	—	146	1	no	—
91	C₄²	C₂×#64408	1	1	yes	characteristic
92	C₁₆	—	146	4	no	—
93	C₂³	—	73	1	no	—
94	C₂×C₄	—	2	1	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	—	73	1	no	—
100	C₂×C₄	—	146	4	no	—
101	C₂×C₄	—	146	1	no	—
102	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
103	C₈	—	73	2	no	—
104	C₈	—	73	1	no	—
105	C₈	—	73	1	no	—
106	C₈	C₄⋊#64408	1	1	yes	characteristic
107	C₈	C₄⋊#64408	1	1	yes	characteristic
108	C₈	#11924036	1	2	yes	—
109	C₂²	—	73	1	no	—
110	C₂²	—	73	1	no	—
111	C₂²	—	146	2	no	—
112	C₂²	D₇₃⋊M₁₆	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	73	1	no	—
115	C₄	—	73	1	no	—
116	C₄	—	146	2	no	—
117	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
118	C₄	C₂×#11924036	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	73	2	no	—
121	C₂	—	146	1	no	—
122	C₂	#17989588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989643

C₂

yes

maximal

#17989510

C₂

yes

maximal, complemented

#17989509

C₂

yes

maximal, complemented

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

#14556666

—

#14556665

C₂²

yes

—

#14556664

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₄²×D₇₃

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₄

yes

characteristic

#11924031

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

C₈

yes

—

C₈×D₇₃

C₈

yes

—

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂×C₈

yes

—

#10596831

C₂×C₈

yes

—

#10596831

C₂×D₄

yes

characteristic

#10596831

C₂×Q₈

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

D₇₃

—

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

146

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

146

—

101

C₂×C₄

—

146

—

102

C₂×C₄

C₂²×#64408

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

C₄⋊#64408

yes

characteristic

107

C₈

C₄⋊#64408

yes

characteristic

108

C₈

#11924036

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

146

—

112

C₂²

D₇₃⋊M₁₆

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

146

—

117

C₄

C₂×C₄⋊#64408

yes

characteristic

118

C₄

C₂×#11924036

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

146

—

122

C₂

#17989588

yes

characteristic

	subgroup	G/H
center	C₈	C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₄⋊C₈
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	C₂×#364
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₈

C₄⋊#64408

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄×C₈×C₇₃

C₄

socle

C₂×C₇₃

C₂×C₄⋊C₈

C₄×C₈

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #17989510	C₂	semidirect
3. #17989509	C₂	semidirect
60. D₇₃	#364	semidirect
62. C₇₃	C₂×#364	semidirect

H ≅ G/N

type

2. #17989510

C₂

semidirect

3. #17989509

C₂

semidirect

60. D₇₃

#364

semidirect

62. C₇₃

C₂×#364

semidirect

Subgroups — #22626270

Conjugacy classes of subgroups

Complements