Group #22608686 — subgroups

Subgroups — #22608686

Order 9344.

184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 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	#17988611	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
3	#17988337	C₂	1	4	yes	maximal, complemented
4	#423×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	—	2	1	no	—
6	C₂²×#10596831	C₄	1	2	yes	—
7	C₄⋊#10596831	—	2	1	no	—
8	C₄⋊#10596831	C₂²	1	2	yes	—
9	C₄×#10596831	C₄	1	1	yes	characteristic
10	C₄×#10596831	C₄	1	1	yes	characteristic
11	C₄×#10596831	C₂²	1	2	yes	—
12	C₂×M₁₆×C₇₃	—	2	1	no	—
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₃	—	2	1	no	—
15	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
16	#11924012	—	4	2	no	—
17	C₂×#10596831	—	2	4	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	C₂×C₄	1	2	yes	—
20	C₂×#10596831	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₃	Q₈	1	1	yes	characteristic
24	M₁₆×C₇₃	—	4	2	no	—
25	C₂×C₈×C₇₃	—	2	2	no	—
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₇₃	D₄	1	1	yes	characteristic
28	C₄²×C₇₃	Q₈	1	1	yes	characteristic
29	C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
37	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
38	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₇₃	—	4	2	no	—
42	#10596831	—	2	2	no	—
43	#10596831	—	4	2	no	—
44	#10596831	M₁₆	1	4	yes	complemented
45	C₂²×C₇₃	—	2	1	no	—
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	#106	1	2	yes	—
48	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	—	2	1	no	—
51	C₄×C₇₃	#106	1	2	yes	—
52	C₄×C₇₃	#108	1	2	yes	—
53	C₄×C₇₃	C₂×M₁₆	1	2	yes	—
54	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
55	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
56	C₂×C₇₃	—	2	2	no	—
57	C₂×C₇₃	#423	1	1	yes	characteristic
58	C₂×C₇₃	C₂×#106	1	1	yes	characteristic
59	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
60	#1566	—	73	1	no	maximal, Sylow
61	C₇₃	#1566	1	1	yes	characteristic, complemented, Sylow
62	#423	—	73	1	no	—
63	#423	D₇₃	1	1	yes	characteristic
64	C₂×C₄×C₈	—	73	1	no	—
65	#334	—	73	4	no	—
66	C₂×M₁₆	—	2	1	no	—
67	C₂×M₁₆	—	146	1	no	—
68	C₂²×C₈	—	73	2	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	C₂×D₇₃	1	2	yes	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₄×C₈	—	73	2	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	—	4	2	no	—
81	M₁₆	—	292	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	73	2	no	—
84	C₂×C₈	—	73	2	no	—
85	C₂×C₈	—	146	2	no	—
86	C₂×C₈	—	146	4	no	—
87	C₄²	Dic₁₄₆	1	1	yes	characteristic
88	C₄²	C₄×D₇₃	1	1	yes	characteristic
89	C₄²	C₂²⋊D₇₃	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	—	2	2	no	—
94	C₂×C₄	#11924007	1	1	yes	characteristic
95	C₂×C₄	#11924007	1	1	yes	characteristic
96	C₂×C₄	#11924007	1	1	yes	characteristic
97	C₂×C₄	#11924015	1	2	yes	—
98	C₂×C₄	#11924016	1	2	yes	—
99	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
102	C₈	—	4	2	no	—
103	C₈	—	292	2	no	—
104	C₈	—	73	4	no	—
105	C₈	—	146	2	no	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#14556522	1	2	yes	—
109	C₂²	C₂×#11924007	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	#14556522	1	2	yes	—
113	C₄	#14556526	1	2	yes	—
114	C₄	M₁₆×D₇₃	1	2	yes	—
115	C₄	C₂×#11924015	1	1	yes	characteristic
116	C₄	C₂×#11924016	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#17988610	1	1	yes	characteristic
119	C₂	C₂×#14556522	1	1	yes	characteristic
120	C₂	C₂×#14556526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988611

C₂

yes

maximal, characteristic

C₂×C₄×#10596831

C₂

yes

maximal, characteristic

#17988337

C₂

yes

maximal, complemented

#423×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

—

C₂²×#10596831

C₄

yes

—

C₄⋊#10596831

—

C₄⋊#10596831

C₂²

yes

—

C₄×#10596831

C₄

yes

characteristic

C₄×#10596831

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

—

C₂×M₁₆×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₂²

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

Q₈

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

Q₈

yes

characteristic

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₈×C₇₃

—

#10596831

—

#10596831

—

#10596831

M₁₆

yes

complemented

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#106

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#106

yes

—

C₄×C₇₃

#108

yes

—

C₄×C₇₃

C₂×M₁₆

yes

—

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#423

—

#423

D₇₃

yes

characteristic

C₂×C₄×C₈

—

#334

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

Dic₁₄₆

yes

characteristic

C₂²×C₄

C₄×D₇₃

yes

characteristic

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

Dic₁₄₆

yes

characteristic

C₄²

C₄×D₇₃

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

characteristic

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

#11924007

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

#11924016

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

101

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

102

C₈

—

103

C₈

—

292

—

104

C₈

—

105

C₈

—

146

—

106

C₂²

—

107

C₂²

—

108

C₂²

#14556522

yes

—

109

C₂²

C₂×#11924007

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

#14556522

yes

—

113

C₄

#14556526

yes

—

114

C₄

M₁₆×D₇₃

yes

—

115

C₄

C₂×#11924015

yes

characteristic

116

C₄

C₂×#11924016

yes

characteristic

117

C₂

—

118

C₂

#17988610

yes

characteristic

119

C₂

C₂×#14556522

yes

characteristic

120

C₂

C₂×#14556526

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#423×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#423	D₇₃
hypocenter	C₇₃	#1566
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#423×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₄⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
3. #17988337	C₂	semidirect
44. #10596831	M₁₆	semidirect
61. C₇₃	#1566	semidirect

H ≅ G/N

type

3. #17988337

C₂

semidirect

44. #10596831

M₁₆

semidirect

61. C₇₃

#1566

semidirect

Subgroups — #22608686

Conjugacy classes of subgroups

Complements