Group #33006466 — subgroups

Subgroups — #33006466

Order 18688.

218 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 127 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×#17988421	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#22608126	C₂	1	4	yes	maximal, complemented
4	C₂×M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11924003	C₄	1	1	yes	characteristic
6	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
7	#17988421	—	2	2	no	—
8	C₂×#14556497	C₂²	1	2	yes	—
9	C₁₆×Dic₇₃	C₄	1	2	yes	—
10	C₁₆×Dic₇₃	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	M₆₄×C₇₃	—	2	2	no	—
13	C₂×C₃₂×C₇₃	C₂²	1	2	yes	—
14	C₂²×#10596831	C₈	1	1	yes	characteristic
15	C₂×C₄×Dic₇₃	C₈	1	1	yes	characteristic
16	C₂×#11924003	—	2	2	no	—
17	C₂×#11924003	C₂×C₄	1	2	yes	—
18	C₈×Dic₇₃	C₈	1	2	yes	—
19	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
20	#14556497	—	2	2	no	—
21	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
24	C₂×C₁₆×C₇₃	Q₈	1	2	yes	—
25	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
26	C₃₂×C₇₃	—	2	2	no	—
27	C₂²×Dic₇₃	C₁₆	1	2	yes	—
28	C₂×#10596831	—	2	2	no	—
29	C₂×#10596831	C₂×C₈	1	2	yes	—
30	C₄×Dic₇₃	C₁₆	1	1	yes	characteristic
31	C₄×Dic₇₃	C₁₆	1	1	yes	characteristic
32	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
33	#11924003	—	2	2	no	—
34	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
38	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₁₆×C₇₃	C₄⋊C₄	1	2	yes	—
40	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
41	C₁₆×C₇₃	C₂×Q₈	1	1	yes	characteristic
42	C₂³×C₇₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₄×C₇₃	M₃₂	1	2	yes	—
46	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
47	C₂×Dic₇₃	—	2	4	no	—
48	C₂×Dic₇₃	C₂×C₁₆	1	2	yes	—
49	C₂×Dic₇₃	C₂×C₁₆	1	2	yes	—
50	C₈×C₇₃	C₄⋊C₈	1	2	yes	—
51	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₈×C₇₃	C₂×M₁₆	1	1	yes	characteristic
53	#10596831	—	2	2	no	—
54	C₂²×C₇₃	—	2	2	no	—
55	C₂²×C₇₃	C₄⋊C₁₆	1	2	yes	—
56	C₂²×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
57	C₄×C₇₃	C₄⋊C₁₆	1	2	yes	—
58	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₄×C₇₃	C₂×M₃₂	1	1	yes	characteristic
60	Dic₇₃	—	2	2	no	—
61	Dic₇₃	M₆₄	1	4	yes	complemented
62	#13627	—	73	1	no	maximal, Sylow
63	C₂×C₇₃	—	2	2	no	—
64	C₂×C₇₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
65	C₂×C₇₃	C₂×M₆₄	1	2	yes	—
66	C₂×M₆₄	—	73	1	no	—
67	C₂×M₆₄	D₇₃	1	1	yes	characteristic
68	C₂×C₄×C₁₆	—	73	1	no	—
69	C₄⋊C₃₂	—	73	4	no	—
70	C₇₃	#13627	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₁₆	—	73	1	no	—
72	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
73	C₂×C₄×C₈	—	73	1	no	—
74	M₆₄	—	2	2	no	—
75	M₆₄	—	146	2	no	—
76	C₂×C₃₂	—	73	2	no	—
77	C₂×C₃₂	C₂×D₇₃	1	2	yes	—
78	C₄×C₁₆	—	73	2	no	—
79	C₄×C₁₆	—	73	2	no	—
80	C₂²×C₈	—	73	1	no	—
81	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
82	C₂×C₄²	—	73	1	no	—
83	C₂×C₁₆	—	73	2	no	—
84	C₂×C₁₆	—	146	2	no	—
85	C₂×C₁₆	Dic₁₄₆	1	2	yes	—
86	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
87	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
88	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
89	C₄×C₈	—	73	2	no	—
90	C₄×C₈	—	73	2	no	—
91	C₃₂	—	2	2	no	—
92	C₃₂	—	146	2	no	—
93	C₂²×C₄	—	73	2	no	—
94	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
95	C₂×C₈	—	73	2	no	—
96	C₂×C₈	—	146	2	no	—
97	C₂×C₈	#11924007	1	2	yes	—
98	C₂×C₈	C₈×D₇₃	1	1	yes	characteristic
99	C₂×C₈	#11924011	1	2	yes	—
100	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
101	C₄²	—	73	1	no	—
102	C₄²	—	73	1	no	—
103	C₄²	—	73	2	no	—
104	C₁₆	—	146	2	no	—
105	C₁₆	#11924007	1	2	yes	—
106	C₁₆	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
107	C₁₆	C₂×Dic₁₄₆	1	1	yes	characteristic
108	C₂³	C₁₆×D₇₃	1	1	yes	characteristic
109	C₂×C₄	—	73	2	no	—
110	C₂×C₄	—	73	2	no	—
111	C₂×C₄	—	146	4	no	—
112	C₂×C₄	#14556520	1	2	yes	—
113	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
114	C₂×C₄	#14556530	1	2	yes	—
115	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
116	C₈	—	146	2	no	—
117	C₈	#14556520	1	2	yes	—
118	C₈	C₂×#11924007	1	1	yes	characteristic
119	C₈	C₂×#11924011	1	1	yes	characteristic
120	C₂²	—	2	2	no	—
121	C₂²	#17988405	1	2	yes	—
122	C₂²	C₂×C₁₆×D₇₃	1	1	yes	characteristic
123	C₄	—	73	4	no	—
124	C₄	—	146	2	no	—
125	C₄	#17988405	1	2	yes	—
126	C₄	C₂×#14556520	1	1	yes	characteristic
127	C₄	C₂×#14556530	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	C₂×#17988405	1	1	yes	characteristic
130	C₂	M₆₄×D₇₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988421

C₂

yes

maximal, characteristic

C₂×C₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#22608126

C₂

yes

maximal, complemented

C₂×M₆₄×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924003

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₄

yes

characteristic

#17988421

—

C₂×#14556497

C₂²

yes

—

C₁₆×Dic₇₃

C₄

yes

—

C₁₆×Dic₇₃

C₂²

yes

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

M₆₄×C₇₃

—

C₂×C₃₂×C₇₃

C₂²

yes

—

C₂²×#10596831

C₈

yes

characteristic

C₂×C₄×Dic₇₃

C₈

yes

characteristic

C₂×#11924003

—

C₂×#11924003

C₂×C₄

yes

—

C₈×Dic₇₃

C₈

yes

—

C₈×Dic₇₃

C₂×C₄

yes

—

#14556497

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×C₁₆×C₇₃

Q₈

yes

—

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

C₃₂×C₇₃

—

C₂²×Dic₇₃

C₁₆

yes

—

C₂×#10596831

—

C₂×#10596831

C₂×C₈

yes

—

C₄×Dic₇₃

C₁₆

yes

characteristic

C₄×Dic₇₃

C₁₆

yes

characteristic

C₄×Dic₇₃

C₂×C₈

yes

—

#11924003

—

C₂²×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

M₁₆

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

—

C₁₆×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

C₂×Q₈

yes

characteristic

C₂³×C₇₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₃

M₃₂

yes

—

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×C₁₆

yes

—

C₂×Dic₇₃

C₂×C₁₆

yes

—

C₈×C₇₃

C₄⋊C₈

yes

—

C₈×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂×M₁₆

yes

characteristic

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄⋊C₁₆

yes

—

C₂²×C₇₃

C₂²×C₁₆

yes

characteristic

C₄×C₇₃

C₄⋊C₁₆

yes

—

C₄×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₇₃

C₂×M₃₂

yes

characteristic

Dic₇₃

—

Dic₇₃

M₆₄

yes

complemented

#13627

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₇₃

C₂×M₆₄

yes

—

C₂×M₆₄

—

C₂×M₆₄

D₇₃

yes

characteristic

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₇₃

#13627

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₄×C₈

—

M₆₄

—

M₆₄

—

146

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₇₃

yes

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

C₄×D₇₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

Dic₁₄₆

yes

—

C₂×C₁₆

C₄×D₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

—

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

146

—

C₂²×C₄

—

C₂²×C₄

C₈×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

#11924007

yes

—

C₂×C₈

C₈×D₇₃

yes

characteristic

C₂×C₈

#11924011

yes

—

100

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₁₆

—

146

—

105

C₁₆

#11924007

yes

—

106

C₁₆

C₂×C₂²⋊D₇₃

yes

characteristic

107

C₁₆

C₂×Dic₁₄₆

yes

characteristic

108

C₂³

C₁₆×D₇₃

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

#14556520

yes

—

113

C₂×C₄

C₁₆×D₇₃

yes

characteristic

114

C₂×C₄

#14556530

yes

—

115

C₂×C₄

C₂×C₈×D₇₃

yes

characteristic

116

C₈

—

146

—

117

C₈

#14556520

yes

—

118

C₈

C₂×#11924007

yes

characteristic

119

C₈

C₂×#11924011

yes

characteristic

120

C₂²

—

121

C₂²

#17988405

yes

—

122

C₂²

C₂×C₁₆×D₇₃

yes

characteristic

123

C₄

—

124

C₄

—

146

—

125

C₄

#17988405

yes

—

126

C₄

C₂×#14556520

yes

characteristic

127

C₄

C₂×#14556530

yes

characteristic

128

C₂

—

129

C₂

C₂×#17988405

yes

characteristic

130

C₂

M₆₄×D₇₃

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂²×C₁₆
Fitting	C₂×M₆₄×C₇₃	C₂
prime radical	C₂³×C₇₃	C₂×C₁₆
cosocle	C₂×C₁₆×C₇₃	C₂³
hypercenter	C₂×M₆₄	D₇₃
hypocenter	C₇₃	#13627
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₇₃

commutator, socle

C₂²×C₇₃

C₂²×C₁₆

Fitting

C₂×M₆₄×C₇₃

C₂

prime radical

C₂³×C₇₃

C₂×C₁₆

cosocle

C₂×C₁₆×C₇₃

C₂³

hypercenter

C₂×M₆₄

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

N	H ≅ G/N	type
3. #22608126	C₂	semidirect
61. Dic₇₃	M₆₄	semidirect
70. C₇₃	#13627	semidirect

H ≅ G/N

type

3. #22608126

C₂

semidirect

61. Dic₇₃

M₆₄

semidirect

70. C₇₃

#13627

semidirect

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

subgroup	index
C₂×#17988421	2
C₂×C₁₆×Dic₇₃	2
#22608126	2
C₂×M₆₄×C₇₃	2
#13627	73

subgroup

index

C₂×#17988421

C₂×C₁₆×Dic₇₃

#22608126

C₂×M₆₄×C₇₃

#13627

Subgroups — #33006466

Conjugacy classes of subgroups

Complements

Maximal subgroups