Group #33006957 — subgroups

Subgroups — #33006957

Order 18688.

182 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 75 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	#22612206	C₂	1	1	yes	maximal, characteristic
2	#22612184	C₂	1	1	yes	maximal, characteristic
3	#22608113	C₂	1	4	yes	maximal
4	C₄×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₅₈₄	—	2	1	no	—
6	C₂×Dic₅₈₄	C₂²	1	2	yes	—
7	#17988992	—	2	1	no	—
8	#17988967	—	2	1	no	—
9	#17988413	—	2	1	no	—
10	#17988413	C₂²	1	2	yes	—
11	C₂×C₃₂×C₇₃	C₂²	1	2	yes	—
12	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₉₂	—	2	2	no	—
14	C₂×Dic₂₉₂	—	4	1	no	—
15	#14556591	—	4	1	no	—
16	#14556591	—	4	1	no	—
17	Dic₅₈₄	—	2	4	no	—
18	Dic₅₈₄	—	4	2	no	—
19	#14556525	—	2	2	no	—
20	#14556525	—	4	1	no	—
21	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
23	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₃₂×C₇₃	—	2	2	no	—
25	C₂×Dic₁₄₆	—	4	2	no	—
26	C₂×Dic₁₄₆	—	8	1	no	—
27	Dic₂₉₂	—	4	2	no	—
28	Dic₂₉₂	—	4	2	no	—
29	Dic₂₉₂	—	8	2	no	—
30	C₄⋊Dic₇₃	—	4	2	no	—
31	C₄⋊Dic₇₃	—	8	1	no	—
32	C₄⋊Dic₇₃	—	8	1	no	—
33	C₄⋊Dic₇₃	—	8	1	no	—
34	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
35	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₄²×C₇₃	D₈	1	1	yes	characteristic
37	C₁₆×C₇₃	SD₁₆	1	2	yes	—
38	C₁₆×C₇₃	#41	1	2	yes	—
39	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
40	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
41	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
42	C₂×Dic₇₃	—	8	2	no	—
43	C₂×Dic₇₃	—	8	2	no	—
44	Dic₁₄₆	—	8	2	no	—
45	Dic₁₄₆	—	8	2	no	—
46	Dic₁₄₆	—	16	2	no	—
47	C₈×C₇₃	SD₃₂	1	2	yes	—
48	C₈×C₇₃	#124	1	1	yes	characteristic
49	C₈×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₂²×C₇₃	C₂×D₁₆	1	1	yes	characteristic
51	C₄×C₇₃	SD₆₄	1	2	yes	—
52	C₄×C₇₃	Q₆₄	1	2	yes	—
53	C₄×C₇₃	#486	1	1	yes	characteristic
54	C₄×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
55	Dic₇₃	—	16	2	no	—
56	Dic₇₃	—	16	2	no	—
57	#13720	—	73	1	no	maximal, Sylow
58	C₂×C₇₃	#2240	1	1	yes	characteristic
59	C₂×C₇₃	C₂×SD₆₄	1	1	yes	characteristic
60	C₂×C₇₃	C₂×Q₆₄	1	1	yes	characteristic
61	#2252	—	73	1	no	—
62	#2247	—	73	1	no	—
63	#1416	—	73	4	no	—
64	C₄×C₃₂	D₇₃	1	1	yes	characteristic
65	C₇₃	#13720	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₃₂	—	73	2	no	—
67	C₂×Q₃₂	—	146	1	no	—
68	#500	—	146	1	no	—
69	#494	—	146	1	no	—
70	C₂×C₃₂	C₂×D₇₃	1	2	yes	—
71	#366	—	73	2	no	—
72	#366	—	146	1	no	—
73	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
74	C₂×Q₁₆	—	292	1	no	—
75	C₂×Q₁₆	—	146	2	no	—
76	C₄⋊Q₈	—	292	1	no	—
77	C₄⋊Q₈	—	292	1	no	—
78	Q₃₂	—	292	2	no	—
79	Q₃₂	—	146	4	no	—
80	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
81	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
82	#107	—	292	1	no	—
83	#107	—	146	2	no	—
84	C₄×C₈	D₂₉₂	1	1	yes	characteristic
85	C₃₂	—	2	2	no	—
86	C₂×Q₈	—	292	2	no	—
87	C₂×Q₈	—	584	1	no	—
88	Q₁₆	—	292	2	no	—
89	Q₁₆	—	292	2	no	—
90	Q₁₆	—	584	2	no	—
91	C₂×C₈	D₅₈₄	1	1	yes	characteristic
92	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
93	C₄⋊C₄	—	292	2	no	—
94	C₄⋊C₄	—	584	1	no	—
95	C₄⋊C₄	—	584	1	no	—
96	C₄⋊C₄	—	584	1	no	—
97	C₄²	D₅₈₄	1	1	yes	characteristic
98	C₁₆	#11924017	1	2	yes	—
99	C₁₆	#11924028	1	2	yes	—
100	Q₈	—	584	2	no	—
101	Q₈	—	584	2	no	—
102	Q₈	—	1168	2	no	—
103	C₂×C₄	—	584	2	no	—
104	C₂×C₄	—	584	2	no	—
105	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
106	C₂×C₄	D₁₁₆₈	1	1	yes	characteristic
107	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
108	C₈	#14556536	1	2	yes	—
109	C₈	#14556579	1	1	yes	characteristic
110	C₈	C₂×#11924017	1	1	yes	characteristic
111	C₂²	C₂×D₁₁₆₈	1	1	yes	characteristic
112	C₄	—	1168	2	no	—
113	C₄	—	1168	2	no	—
114	C₄	#17988426	1	2	yes	—
115	C₄	Dic₁₁₆₈	1	2	yes	—
116	C₄	#17988934	1	1	yes	characteristic
117	C₄	C₂×#14556536	1	1	yes	characteristic
118	C₂	#22612155	1	1	yes	characteristic
119	C₂	C₂×#17988426	1	1	yes	characteristic
120	C₂	C₂×Dic₁₁₆₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22612206

C₂

yes

maximal, characteristic

#22612184

C₂

yes

maximal, characteristic

#22608113

C₂

yes

maximal

C₄×C₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×C₃₂×C₇₃

C₂²

yes

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

#14556591

—

#14556591

—

Dic₅₈₄

—

Dic₅₈₄

—

#14556525

—

#14556525

—

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

characteristic

C₃₂×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×C₈×C₇₃

D₈

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

D₈

yes

characteristic

C₁₆×C₇₃

SD₁₆

yes

—

C₁₆×C₇₃

#41

yes

—

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

SD₃₂

yes

—

C₈×C₇₃

#124

yes

characteristic

C₈×C₇₃

C₂×SD₁₆

yes

characteristic

C₂²×C₇₃

C₂×D₁₆

yes

characteristic

C₄×C₇₃

SD₆₄

yes

—

C₄×C₇₃

Q₆₄

yes

—

C₄×C₇₃

#486

yes

characteristic

C₄×C₇₃

C₂×SD₃₂

yes

characteristic

Dic₇₃

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

C₂×SD₆₄

yes

characteristic

C₂×C₇₃

C₂×Q₆₄

yes

—

—

—

C₄×C₃₂

D₇₃

yes

characteristic

C₇₃

#13720

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

—

146

—

#500

—

146

—

#494

—

146

—

C₂×C₃₂

C₂×D₇₃

yes

—

#366

—

#366

—

146

—

C₄×C₁₆

C₂×D₇₃

yes

characteristic

C₂×Q₁₆

—

292

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

292

—

C₄⋊Q₈

—

292

—

Q₃₂

—

292

—

Q₃₂

—

146

—

C₂×C₁₆

D₂₉₂

yes

characteristic

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

#107

—

292

—

#107

—

146

—

C₄×C₈

D₂₉₂

yes

characteristic

C₃₂

—

C₂×Q₈

—

292

—

C₂×Q₈

—

584

—

Q₁₆

—

292

—

Q₁₆

—

292

—

Q₁₆

—

584

—

C₂×C₈

D₅₈₄

yes

characteristic

C₂×C₈

C₂×D₂₉₂

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

584

—

C₄⋊C₄

—

584

—

C₄⋊C₄

—

584

—

C₄²

D₅₈₄

yes

characteristic

C₁₆

#11924017

yes

—

C₁₆

#11924028

yes

—

100

Q₈

—

584

—

101

Q₈

—

584

—

102

Q₈

—

1168

—

103

C₂×C₄

—

584

—

104

C₂×C₄

—

584

—

105

C₂×C₄

D₁₁₆₈

yes

characteristic

106

C₂×C₄

D₁₁₆₈

yes

characteristic

107

C₂×C₄

C₂×D₅₈₄

yes

characteristic

108

C₈

#14556536

yes

—

109

C₈

#14556579

yes

characteristic

110

C₈

C₂×#11924017

yes

characteristic

111

C₂²

C₂×D₁₁₆₈

yes

characteristic

112

C₄

—

1168

—

113

C₄

—

1168

—

114

C₄

#17988426

yes

—

115

C₄

Dic₁₁₆₈

yes

—

116

C₄

#17988934

yes

characteristic

117

C₄

C₂×#14556536

yes

characteristic

118

C₂

#22612155

yes

characteristic

119

C₂

C₂×#17988426

yes

characteristic

120

C₂

C₂×Dic₁₁₆₈

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆₈
commutator, cosocle	C₂×C₁₆×C₇₃	C₂³
Frattini	C₂×C₁₆	C₂²×D₇₃
Fitting	C₄×C₃₂×C₇₃	C₂
socle, prime radical	C₂²×C₇₃	C₂×D₁₆
hypercenter	C₄×C₃₂	D₇₃
hypocenter	C₇₃	#13720
LCS	G ▷ C₂×C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

subgroup

G/H

center

C₂²

C₂×D₁₁₆₈

commutator, cosocle

C₂×C₁₆×C₇₃

C₂³

Frattini

C₂×C₁₆

C₂²×D₇₃

Fitting

C₄×C₃₂×C₇₃

C₂

socle, prime radical

C₂²×C₇₃

C₂×D₁₆

hypercenter

C₄×C₃₂

D₇₃

hypocenter

C₇₃

#13720

LCS

G ▷ C₂×C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

N	H ≅ G/N	type
65. C₇₃	#13720	semidirect

H ≅ G/N

type

65. C₇₃

#13720

semidirect

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

subgroup	index
#22612206	2
#22612184	2
#22608113	2
C₄×C₃₂×C₇₃	2
#13720	73

subgroup

index

C₄×C₃₂×C₇₃

Subgroups — #33006957

Conjugacy classes of subgroups

Complements

Maximal subgroups