Group #22607828 — subgroups

Subgroups — #22607828

Order 9344.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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	#17988640	C₂	1	1	yes	maximal, characteristic
2	#17988611	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924012	—	2	1	no	—
5	C₄⋊#10596831	—	2	1	no	—
6	C₄⋊#10596831	—	2	1	no	—
7	C₄⋊#10596831	C₄	1	2	yes	—
8	C₂²⋊#10596831	C₄	1	2	yes	—
9	C₄×#10596831	—	2	1	no	—
10	C₂²×C₈×C₇₃	—	2	1	no	—
11	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₇₃	—	2	1	no	—
13	C₄⋊C₈×C₇₃	C₄	1	2	yes	—
14	#11924012	—	4	1	no	—
15	#11924012	—	4	1	no	—
16	C₂×#10596831	—	2	2	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₇₃	—	2	2	no	—
22	C₂×C₈×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	—	4	1	no	—
24	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₇₃	D₄	1	1	yes	characteristic
27	C₄²×C₇₃	D₄	1	1	yes	characteristic
28	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	2	no	—
30	C₂×C₄×C₇₃	—	4	1	no	—
31	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
39	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
40	C₂×C₄×C₇₃	Q₁₆	1	1	yes	characteristic
41	C₈×C₇₃	—	4	2	no	—
42	#10596831	—	4	2	no	—
43	#10596831	—	4	2	no	—
44	C₂²×C₇₃	—	2	1	no	—
45	C₂²×C₇₃	—	2	1	no	—
46	C₂²×C₇₃	#95	1	1	yes	characteristic
47	C₂²×C₇₃	#106	1	1	yes	characteristic
48	C₂²×C₇₃	#107	1	1	yes	characteristic
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	—	2	1	no	—
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	#102	1	1	yes	characteristic
53	C₄×C₇₃	#102	1	1	yes	characteristic
54	C₄×C₇₃	#103	1	1	yes	characteristic
55	C₄×C₇₃	#103	1	1	yes	characteristic
56	C₄×C₇₃	#108	1	2	yes	—
57	C₂×C₇₃	—	2	1	no	—
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	#340	1	1	yes	characteristic
60	C₂×C₇₃	#341	1	1	yes	characteristic
61	C₂×C₇₃	#344	1	1	yes	characteristic
62	#1301	—	73	1	no	maximal, Sylow
63	C₇₃	#1301	1	1	yes	characteristic, complemented, Sylow
64	#431	—	73	1	no	—
65	#423	—	73	1	no	—
66	C₂×C₄⋊C₈	D₇₃	1	1	yes	characteristic
67	C₂×M₁₆	—	146	1	no	—
68	C₂²×C₈	—	2	1	no	—
69	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
70	C₄⋊C₈	—	2	1	no	—
71	C₄⋊C₈	—	73	2	no	—
72	C₄⋊C₈	—	146	1	no	—
73	C₄⋊C₈	—	146	1	no	—
74	C₄⋊C₈	Dic₇₃	1	2	yes	—
75	C₂²⋊C₈	—	73	2	no	—
76	C₄×C₈	—	146	1	no	—
77	C₂²×C₄	Dic₁₄₆	1	1	yes	characteristic
78	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
79	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
80	M₁₆	—	292	1	no	—
81	M₁₆	—	292	1	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	4	1	no	—
84	C₂×C₈	—	4	1	no	—
85	C₂×C₈	—	146	2	no	—
86	C₂×C₈	—	146	2	no	—
87	C₄²	C₄×D₇₃	1	1	yes	characteristic
88	C₄²	D₂₉₂	1	1	yes	characteristic
89	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
90	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂³	#11924007	1	1	yes	characteristic
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	C₄×Dic₇₃	1	1	yes	characteristic
95	C₂×C₄	#11924005	1	1	yes	characteristic
96	C₂×C₄	#11924005	1	1	yes	characteristic
97	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
98	C₂×C₄	#11924007	1	1	yes	characteristic
99	C₂×C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
100	C₂×C₄	#11924013	1	1	yes	characteristic
101	C₂×C₄	#11924015	1	1	yes	characteristic
102	C₂×C₄	#11924016	1	1	yes	characteristic
103	C₂×C₄	#11924018	1	1	yes	characteristic
104	C₈	—	4	2	no	—
105	C₈	—	292	2	no	—
106	C₈	—	292	2	no	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	#14556498	1	1	yes	characteristic
110	C₂²	#14556522	1	1	yes	characteristic
111	C₂²	#14556524	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	#14556511	1	1	yes	characteristic
116	C₄	#14556512	1	1	yes	characteristic
117	C₄	#14556514	1	1	yes	characteristic
118	C₄	#14556515	1	1	yes	characteristic
119	C₄	#14556527	1	2	yes	—
120	C₂	—	2	1	no	—
121	C₂	—	2	1	no	—
122	C₂	#17988349	1	1	yes	characteristic
123	C₂	#17988352	1	1	yes	characteristic
124	C₂	#17988359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988640

C₂

yes

maximal, characteristic

#17988611

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₇₃

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

—

C₂²⋊#10596831

C₄

yes

—

C₄×#10596831

—

C₂²×C₈×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₄

yes

—

—

—

—

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

Q₈

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

Q₁₆

yes

characteristic

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

#423

—

C₂×C₄⋊C₈

D₇₃

yes

characteristic

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

C₄⋊C₈

Dic₇₃

yes

—

C₂²⋊C₈

—

C₄×C₈

—

146

—

C₂²×C₄

Dic₁₄₆

yes

characteristic

C₂²×C₄

C₄×D₇₃

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

M₁₆

—

292

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

C₄×D₇₃

yes

characteristic

C₄²

D₂₉₂

yes

characteristic

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

characteristic

C₂³

#11924007

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₇₃

yes

characteristic

C₂×C₄

#11924007

yes

characteristic

C₂×C₄

C₄⋊Dic₇₃

yes

characteristic

100

C₂×C₄

#11924013

yes

characteristic

101

C₂×C₄

#11924015

yes

characteristic

102

C₂×C₄

#11924016

yes

characteristic

103

C₂×C₄

#11924018

yes

characteristic

104

C₈

—

105

C₈

—

292

—

106

C₈

—

292

—

107

C₂²

—

108

C₂²

—

109

C₂²

#14556498

yes

characteristic

110

C₂²

#14556522

yes

characteristic

111

C₂²

#14556524

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#14556511

yes

characteristic

116

C₄

#14556512

yes

characteristic

117

C₄

#14556514

yes

characteristic

118

C₄

#14556515

yes

characteristic

119

C₄

#14556527

yes

—

120

C₂

—

121

C₂

—

122

C₂

#17988349

yes

characteristic

123

C₂

#17988352

yes

characteristic

124

C₂

#17988359

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#11924005
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₂×C₄²	C₂×D₇₃
Fitting	C₂×C₄⋊C₈×C₇₃	C₂
socle	C₂²×C₇₃	#95
hypercenter	C₂×C₄⋊C₈	D₇₃
hypocenter	C₇₃	#1301
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂×C₄

#11924005

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₂×C₄²

C₂×D₇₃

Fitting

C₂×C₄⋊C₈×C₇₃

C₂

socle

C₂²×C₇₃

#95

hypercenter

C₂×C₄⋊C₈

D₇₃

hypocenter

C₇₃

#1301

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
63. C₇₃	#1301	semidirect

H ≅ G/N

type

63. C₇₃

#1301

semidirect

Subgroups — #22607828

Conjugacy classes of subgroups

Complements