Group #32975298 — subgroups

Subgroups — #32975298

Order 18688.

322 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 83 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	#22611494	C₂	1	3	yes	maximal
2	#22607754	C₂	1	3	yes	maximal
3	C₇₃×#2810	C₂	1	1	yes	maximal, characteristic
4	#17988457	C₂²	1	1	yes	characteristic
5	#17988349	—	2	3	no	—
6	#17988349	—	2	3	no	—
7	#17988342	C₂²	1	3	yes	—
8	#400×C₇₃	—	2	3	no	—
9	#389×C₇₃	C₂²	1	3	yes	—
10	#387×C₇₃	—	2	3	no	—
11	C₂²×#10596831	—	2	3	no	—
12	C₂×C₄⋊Dic₇₃	—	2	3	no	—
13	C₂×C₄⋊C₄×C₇₃	—	2	3	no	—
14	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
15	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
16	C₂×C₄²×C₇₃	—	2	1	no	—
17	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
18	#95×C₇₃	—	2	3	no	—
19	#95×C₇₃	—	2	3	no	—
20	#95×C₇₃	—	2	1	no	—
21	#95×C₇₃	—	2	3	no	—
22	C₂²×Dic₇₃	—	4	1	no	—
23	C₂×#10596831	—	4	3	no	—
24	C₂×#10596831	—	4	3	no	—
25	C₂×#10596831	—	4	3	no	—
26	C₄⋊Dic₇₃	—	4	6	no	—
27	C₂²×C₄×C₇₃	—	2	3	no	—
28	C₂²×C₄×C₇₃	—	2	3	no	—
29	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
30	C₄⋊C₄×C₇₃	—	2	3	no	—
31	C₄⋊C₄×C₇₃	—	2	3	no	—
32	C₄⋊C₄×C₇₃	—	4	3	no	—
33	C₄⋊C₄×C₇₃	—	4	3	no	—
34	C₄⋊C₄×C₇₃	—	4	3	no	—
35	C₄²×C₇₃	—	4	1	no	—
36	C₄²×C₇₃	—	8	1	no	—
37	C₂³×C₇₃	#120	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	3	no	—
39	C₂×C₄×C₇₃	—	2	3	no	—
40	C₂×C₄×C₇₃	—	4	3	no	—
41	C₂×C₄×C₇₃	—	4	3	no	—
42	C₂×C₄×C₇₃	—	4	3	no	—
43	C₂×C₄×C₇₃	—	4	3	no	—
44	C₂×C₄×C₇₃	—	4	3	no	—
45	C₂×C₄×C₇₃	—	4	3	no	—
46	C₂×C₄×C₇₃	#135	1	3	yes	—
47	C₂×C₄×C₇₃	#137	1	3	yes	—
48	C₂×Dic₇₃	—	8	3	no	—
49	#10596831	—	8	3	no	—
50	C₂²×C₇₃	#452	1	3	yes	—
51	C₂²×C₇₃	#454	1	3	yes	—
52	C₂²×C₇₃	#458	1	1	yes	characteristic
53	C₄×C₇₃	—	2	3	no	—
54	C₄×C₇₃	—	2	3	no	—
55	C₄×C₇₃	—	8	3	no	—
56	C₄×C₇₃	—	8	3	no	—
57	Dic₇₃	—	16	1	no	—
58	#7832	—	73	1	no	maximal, Sylow
59	C₂×C₇₃	#1615	1	3	yes	—
60	C₂×C₇₃	#1638	1	3	yes	—
61	C₂×C₇₃	#1658	1	1	yes	characteristic
62	#2810	D₇₃	1	1	yes	characteristic
63	#2100	—	73	3	no	—
64	#1271	—	73	3	no	—
65	C₇₃	#7832	1	1	yes	characteristic, complemented, Sylow
66	#400	—	2	3	no	—
67	#389	C₂×D₇₃	1	3	yes	—
68	#387	—	2	3	no	—
69	#384	—	73	1	no	—
70	#340	—	146	3	no	—
71	#340	—	146	3	no	—
72	#336	—	73	3	no	—
73	C₂²×C₈	—	146	3	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄⋊C₄	—	146	3	no	—
76	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
77	C₂×C₄⋊C₄	C₂²⋊D₇₃	1	3	yes	—
78	C₂×C₄²	—	2	1	no	—
79	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
80	#95	—	2	3	no	—
81	#95	—	2	3	no	—
82	#95	—	2	1	no	—
83	#95	—	2	3	no	—
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	2	3	no	—
86	C₂²×C₄	—	292	1	no	—
87	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
88	C₂×C₈	—	292	3	no	—
89	C₂×C₈	—	292	3	no	—
90	C₂×C₈	—	292	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	292	6	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	8	1	no	—
99	C₂³	#14556560	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	584	3	no	—
109	C₂×C₄	#14556611	1	3	yes	—
110	C₂×C₄	#14556621	1	3	yes	—
111	C₈	—	584	3	no	—
112	C₂²	#17988749	1	3	yes	—
113	C₂²	#17988760	1	3	yes	—
114	C₂²	#17988777	1	1	yes	characteristic
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	1168	1	no	—
120	C₂	#22608962	1	3	yes	—
121	C₂	#22609103	1	3	yes	—
122	C₂	#22609233	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611494

C₂

yes

maximal

#22607754

C₂

yes

maximal

C₇₃×#2810

C₂

yes

maximal, characteristic

#17988457

C₂²

yes

—

—

C₂²

yes

—

#400×C₇₃

—

#389×C₇₃

C₂²

yes

—

#387×C₇₃

—

C₂²×#10596831

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#95×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#120

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

#452

yes

—

C₂²×C₇₃

#454

yes

—

C₂²×C₇₃

#458

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

#7832

—

maximal, Sylow

C₂×C₇₃

#1615

yes

—

C₂×C₇₃

#1638

yes

—

C₂×C₇₃

#1658

yes

characteristic

#2810

D₇₃

yes

characteristic

#2100

—

#1271

—

C₇₃

#7832

yes

characteristic, complemented, Sylow

#400

—

#389

C₂×D₇₃

yes

—

#387

—

#384

—

#340

—

146

—

#340

—

146

—

#336

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄⋊C₄

C₂²⋊D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₇₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

292

—

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄²

—

C₄²

—

C₂³

#14556560

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

584

—

109

C₂×C₄

#14556611

yes

—

110

C₂×C₄

#14556621

yes

—

111

C₈

—

584

—

112

C₂²

#17988749

yes

—

113

C₂²

#17988760

yes

—

114

C₂²

#17988777

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

1168

—

120

C₂

#22608962

yes

—

121

C₂

#22609103

yes

—

122

C₂

#22609233

yes

characteristic

	subgroup	G/H
center	C₂³	#14556560
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#2810	C₂
socle, prime radical	C₂³×C₇₃	#120
hypercenter	#2810	D₇₃
hypocenter	C₇₃	#7832
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

subgroup

G/H

center

C₂³

#14556560

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#2810

C₂

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂³×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

N	H ≅ G/N	type
65. C₇₃	#7832	semidirect

H ≅ G/N

type

65. C₇₃

#7832

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22611494	2
#22607754	2
C₇₃×#2810	2
#7832	73

subgroup

index

#22611494

#22607754

C₇₃×#2810

#7832

Subgroups — #32975298

Conjugacy classes of subgroups

Complements

Maximal subgroups