Group #32973167 — subgroups

Subgroups — #32973167

Order 18688.

208 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₂×#17988408	C₂	1	2	yes	maximal
2	C₇₃×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556531	—	2	2	no	—
4	#17988408	—	2	2	no	—
5	#17988408	C₄	1	4	yes	—
6	C₂×#108×C₇₃	—	2	2	no	—
7	#423×C₇₃	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
9	#14556531	—	2	4	no	—
10	#14556531	—	4	2	no	—
11	C₂×#11924003	—	4	2	no	—
12	C₂×M₁₆×C₇₃	—	2	2	no	—
13	C₂²×C₈×C₇₃	D₄	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
15	#108×C₇₃	—	4	2	no	—
16	#108×C₇₃	—	4	2	no	—
17	C₄⋊C₈×C₇₃	—	4	2	no	—
18	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
20	C₄×C₈×C₇₃	Q₈	1	1	yes	characteristic
21	#11924003	—	4	4	no	—
22	C₂²×C₄×C₇₃	—	2	1	no	—
23	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₇₃	—	4	4	no	—
25	C₂×C₈×C₇₃	—	4	2	no	—
26	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₇₃	D₈	1	2	yes	—
29	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
30	C₂×C₈×C₇₃	SD₁₆	1	2	yes	—
31	C₂×C₈×C₇₃	Q₁₆	1	2	yes	—
32	C₄²×C₇₃	—	2	1	no	—
33	C₄²×C₇₃	C₄²	1	1	yes	characteristic
34	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂³×C₇₃	#101	1	1	yes	characteristic
36	C₂×C₄×C₇₃	—	2	1	no	—
37	C₂×C₄×C₇₃	—	2	1	no	—
38	C₂×C₄×C₇₃	—	4	2	no	—
39	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
40	C₂×C₄×C₇₃	#100	1	1	yes	characteristic
41	C₂×C₄×C₇₃	#102	1	2	yes	—
42	C₂×C₄×C₇₃	#103	1	2	yes	—
43	C₈×C₇₃	—	8	2	no	—
44	C₈×C₇₃	#102	1	2	yes	—
45	C₈×C₇₃	#103	1	2	yes	—
46	C₈×C₇₃	#106	1	2	yes	—
47	C₈×C₇₃	#107	1	2	yes	—
48	C₂²×C₇₃	—	4	1	no	—
49	C₂²×C₇₃	#332	1	2	yes	—
50	C₂²×C₇₃	#343	1	1	yes	characteristic
51	C₄×C₇₃	—	2	2	no	—
52	C₄×C₇₃	—	4	1	no	—
53	C₄×C₇₃	#331	1	1	yes	characteristic
54	C₄×C₇₃	#333	1	1	yes	characteristic
55	C₄×C₇₃	#340	1	2	yes	—
56	#7273	—	73	1	no	maximal, Sylow
57	C₂×C₇₃	—	2	1	no	—
58	C₂×C₇₃	—	2	2	no	—
59	C₂×C₇₃	#1296	1	1	yes	characteristic
60	C₂×#364	—	73	2	no	—
61	#1848	D₇₃	1	1	yes	characteristic
62	C₇₃	#7273	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	146	2	no	—
64	C₂×#108	—	2	2	no	—
65	#423	Dic₇₃	1	2	yes	—
66	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
67	#364	—	73	4	no	—
68	#364	—	146	2	no	—
69	C₂×M₁₆	—	2	2	no	—
70	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
71	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
72	M₃₂	—	292	2	no	—
73	M₃₂	—	146	4	no	—
74	C₂×C₁₆	—	292	2	no	—
75	#108	—	4	2	no	—
76	#108	—	4	2	no	—
77	C₄⋊C₈	—	4	2	no	—
78	C₄×C₈	Dic₁₄₆	1	1	yes	characteristic
79	C₄×C₈	C₄×D₇₃	1	2	yes	—
80	C₄×C₈	D₂₉₂	1	1	yes	characteristic
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
83	M₁₆	—	4	4	no	—
84	C₂×C₈	—	4	2	no	—
85	C₂×C₈	#11924005	1	2	yes	—
86	C₂×C₈	#11924007	1	2	yes	—
87	C₂×C₈	#11924013	1	2	yes	—
88	C₂×C₈	#11924015	1	2	yes	—
89	C₂×C₈	#11924016	1	2	yes	—
90	C₂×C₈	#11924018	1	2	yes	—
91	C₄²	—	2	1	no	—
92	C₄²	C₄×Dic₇₃	1	1	yes	characteristic
93	C₄²	C₄⋊Dic₇₃	1	1	yes	characteristic
94	C₁₆	—	292	4	no	—
95	C₂³	#14556510	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	#14556498	1	1	yes	characteristic
100	C₂×C₄	#14556508	1	1	yes	characteristic
101	C₂×C₄	#14556512	1	2	yes	—
102	C₂×C₄	#14556515	1	2	yes	—
103	C₈	—	8	2	no	—
104	C₈	#14556511	1	2	yes	—
105	C₈	#14556514	1	2	yes	—
106	C₈	#14556522	1	2	yes	—
107	C₈	#14556524	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#17988333	1	2	yes	—
110	C₂²	#17988356	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	4	1	no	—
113	C₄	#17988331	1	1	yes	characteristic
114	C₄	#17988336	1	1	yes	characteristic
115	C₄	#17988349	1	2	yes	—
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	#22607814	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988408

C₂

yes

maximal

C₇₃×#1848

C₂

yes

maximal, characteristic

C₂×#14556531

—

#17988408

—

#17988408

C₄

yes

—

C₂×#108×C₇₃

—

#423×C₇₃

C₄

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

—

—

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

Q₈

yes

characteristic

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

D₈

yes

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

Q₁₆

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

C₄²

yes

characteristic

C₄²×C₇₃

C₄⋊C₄

yes

characteristic

C₂³×C₇₃

#101

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#103

yes

—

C₈×C₇₃

—

C₈×C₇₃

#102

yes

—

C₈×C₇₃

#103

yes

—

C₈×C₇₃

#106

yes

—

C₈×C₇₃

#107

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

#332

yes

—

C₂²×C₇₃

#343

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

#7273

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

D₇₃

yes

characteristic

C₇₃

#7273

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

146

—

C₂×#108

—

#423

Dic₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#364

—

#364

—

146

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

M₃₂

—

292

—

M₃₂

—

146

—

C₂×C₁₆

—

292

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₁₄₆

yes

characteristic

C₄×C₈

C₄×D₇₃

yes

—

C₄×C₈

D₂₉₂

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₇₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

#11924005

yes

—

C₂×C₈

#11924007

yes

—

C₂×C₈

#11924013

yes

—

C₂×C₈

#11924015

yes

—

C₂×C₈

#11924016

yes

—

C₂×C₈

#11924018

yes

—

C₄²

—

C₄²

C₄×Dic₇₃

yes

characteristic

C₄²

C₄⋊Dic₇₃

yes

characteristic

C₁₆

—

292

—

C₂³

#14556510

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#14556498

yes

characteristic

100

C₂×C₄

#14556508

yes

characteristic

101

C₂×C₄

#14556512

yes

—

102

C₂×C₄

#14556515

yes

—

103

C₈

—

104

C₈

#14556511

yes

—

105

C₈

#14556514

yes

—

106

C₈

#14556522

yes

—

107

C₈

#14556524

yes

—

108

C₂²

—

109

C₂²

#17988333

yes

—

110

C₂²

#17988356

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

#17988331

yes

characteristic

114

C₄

#17988336

yes

characteristic

115

C₄

#17988349

yes

—

116

C₂

—

117

C₂

—

118

C₂

#22607814

yes

characteristic

	subgroup	G/H
center	C₄	#17988336
commutator	C₄²×C₇₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₇₃
Fitting	C₇₃×#1848	C₂
socle	C₂×C₇₃	#1296
prime radical	C₂³×C₇₃	#101
cosocle	C₂×C₄×C₈×C₇₃	C₂²
hypercenter	#1848	D₇₃
hypocenter	C₇₃	#7273
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₄

#17988336

commutator

C₄²×C₇₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₇₃

Fitting

C₇₃×#1848

C₂

C₂×C₇₃

C₂³×C₇₃

C₂×C₄×C₈×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

N	H ≅ G/N	type
62. C₇₃	#7273	semidirect

H ≅ G/N

type

62. C₇₃

#7273

semidirect

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

subgroup	index
C₂×#17988408	2
C₇₃×#1848	2
#7273	73

subgroup

index

C₂×#17988408

C₇₃×#1848

#7273

Subgroups — #32973167

Conjugacy classes of subgroups

Complements

Maximal subgroups