Group #33006463 — subgroups

Subgroups — C₂×#22608126 #33006463

Order 18688.

230 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂²×#14556497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#22608126	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃₂×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	C₂×#14556497	—	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	C₂×C₃₂×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	1	yes	characteristic
28	C₂²×Dic₇₃	C₁₆	1	1	yes	characteristic
29	C₂×#10596831	—	2	2	no	—
30	C₂×#10596831	C₂×C₈	1	2	yes	—
31	C₄×Dic₇₃	C₁₆	1	2	yes	—
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	2	no	—
48	C₂×Dic₇₃	C₃₂	1	4	yes	complemented
49	C₂×Dic₇₃	C₂×C₁₆	1	2	yes	—
50	C₂×Dic₇₃	C₂×C₁₆	1	2	yes	—
51	C₈×C₇₃	C₄⋊C₈	1	2	yes	—
52	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₇₃	C₂×M₁₆	1	1	yes	characteristic
54	#10596831	—	2	2	no	—
55	C₂²×C₇₃	C₄⋊C₁₆	1	2	yes	—
56	C₂²×C₇₃	C₂×C₃₂	1	2	yes	—
57	C₂²×C₇₃	M₆₄	1	2	yes	—
58	C₂²×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
59	C₄×C₇₃	C₄⋊C₁₆	1	2	yes	—
60	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
61	C₄×C₇₃	C₂×M₃₂	1	1	yes	characteristic
62	Dic₇₃	—	2	2	no	—
63	Dic₇₃	C₂×C₃₂	1	4	yes	complemented
64	C₂×C₄⋊C₃₂	—	73	1	no	maximal, Sylow
65	C₂×C₇₃	C₄⋊C₃₂	1	4	yes	complemented
66	C₂×C₇₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
67	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
68	C₂×C₇₃	C₂×M₆₄	1	1	yes	characteristic
69	C₂²×C₃₂	—	73	1	no	—
70	C₂²×C₃₂	D₇₃	1	1	yes	characteristic
71	C₂×C₄×C₁₆	—	73	1	no	—
72	C₄⋊C₃₂	—	73	4	no	—
73	C₇₃	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₁₆	—	73	1	no	—
75	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
76	C₂×C₄×C₈	—	73	1	no	—
77	C₂×C₃₂	—	2	2	no	—
78	C₂×C₃₂	—	73	2	no	—
79	C₂×C₃₂	—	146	2	no	—
80	C₂×C₃₂	C₂×D₇₃	1	2	yes	—
81	C₄×C₁₆	—	73	2	no	—
82	C₄×C₁₆	—	73	2	no	—
83	C₂²×C₈	—	73	1	no	—
84	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
85	C₂×C₄²	—	73	1	no	—
86	C₂×C₁₆	—	73	2	no	—
87	C₂×C₁₆	—	146	2	no	—
88	C₂×C₁₆	Dic₁₄₆	1	2	yes	—
89	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
90	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
91	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
92	C₄×C₈	—	73	2	no	—
93	C₄×C₈	—	73	2	no	—
94	C₃₂	—	2	2	no	—
95	C₃₂	—	146	2	no	—
96	C₂²×C₄	—	73	1	no	—
97	C₂²×C₄	—	73	1	no	—
98	C₂²×C₄	C₈×D₇₃	1	1	yes	characteristic
99	C₂×C₈	—	73	2	no	—
100	C₂×C₈	—	146	2	no	—
101	C₂×C₈	#11924007	1	2	yes	—
102	C₂×C₈	C₈×D₇₃	1	1	yes	characteristic
103	C₂×C₈	#11924011	1	2	yes	—
104	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
105	C₄²	—	73	2	no	—
106	C₄²	—	73	2	no	—
107	C₁₆	—	146	2	no	—
108	C₁₆	#11924007	1	2	yes	—
109	C₁₆	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
110	C₁₆	C₂×Dic₁₄₆	1	1	yes	characteristic
111	C₂³	C₁₆×D₇₃	1	1	yes	characteristic
112	C₂×C₄	—	73	4	no	—
113	C₂×C₄	—	73	2	no	—
114	C₂×C₄	—	73	2	no	—
115	C₂×C₄	—	146	2	no	—
116	C₂×C₄	#14556520	1	2	yes	—
117	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
118	C₂×C₄	#14556530	1	2	yes	—
119	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
120	C₈	—	146	2	no	—
121	C₈	#14556520	1	2	yes	—
122	C₈	C₂×#11924007	1	1	yes	characteristic
123	C₈	C₂×#11924011	1	1	yes	characteristic
124	C₂²	#17988405	1	2	yes	—
125	C₂²	C₃₂×D₇₃	1	2	yes	—
126	C₂²	#17988420	1	2	yes	—
127	C₂²	C₂×C₁₆×D₇₃	1	1	yes	characteristic
128	C₄	—	73	4	no	—
129	C₄	—	146	2	no	—
130	C₄	#17988405	1	2	yes	—
131	C₄	C₂×#14556520	1	1	yes	characteristic
132	C₄	C₂×#14556530	1	1	yes	characteristic
133	C₂	#22608126	1	4	yes	direct product factor
134	C₂	C₂×#17988405	1	1	yes	characteristic
135	C₂	C₂×C₃₂×D₇₃	1	1	yes	characteristic
136	C₂	C₂×#17988420	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556497

C₂

yes

maximal, characteristic

C₂×C₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#22608126

C₂

yes

maximal, direct product factor

C₂²×C₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924003

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₄

yes

characteristic

C₂×#14556497

—

C₂×#14556497

C₂²

yes

—

C₁₆×Dic₇₃

C₄

yes

—

C₁₆×Dic₇₃

C₂²

yes

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₃₂×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

characteristic

C₂²×Dic₇₃

C₁₆

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂×C₈

yes

—

C₄×Dic₇₃

C₁₆

yes

—

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

C₃₂

yes

complemented

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

C₄⋊C₁₆

yes

—

C₂²×C₇₃

C₂×C₃₂

yes

—

C₂²×C₇₃

M₆₄

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

C₂×C₃₂

yes

complemented

C₂×C₄⋊C₃₂

—

maximal, Sylow

C₂×C₇₃

C₄⋊C₃₂

yes

complemented

C₂×C₇₃

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₇₃

C₂²×C₃₂

yes

characteristic

C₂×C₇₃

C₂×M₆₄

yes

characteristic

C₂²×C₃₂

—

C₂²×C₃₂

D₇₃

yes

characteristic

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₇₃

C₂×C₄⋊C₃₂

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

C₂×C₄×C₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

146

—

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

—

C₂²×C₄

C₈×D₇₃

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

146

—

101

C₂×C₈

#11924007

yes

—

102

C₂×C₈

C₈×D₇₃

yes

characteristic

103

C₂×C₈

#11924011

yes

—

104

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

105

C₄²

—

106

C₄²

—

107

C₁₆

—

146

—

108

C₁₆

#11924007

yes

—

109

C₁₆

C₂×C₂²⋊D₇₃

yes

characteristic

110

C₁₆

C₂×Dic₁₄₆

yes

characteristic

111

C₂³

C₁₆×D₇₃

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

146

—

116

C₂×C₄

#14556520

yes

—

117

C₂×C₄

C₁₆×D₇₃

yes

characteristic

118

C₂×C₄

#14556530

yes

—

119

C₂×C₄

C₂×C₈×D₇₃

yes

characteristic

120

C₈

—

146

—

121

C₈

#14556520

yes

—

122

C₈

C₂×#11924007

yes

characteristic

123

C₈

C₂×#11924011

yes

characteristic

124

C₂²

#17988405

yes

—

125

C₂²

C₃₂×D₇₃

yes

—

126

C₂²

#17988420

yes

—

127

C₂²

C₂×C₁₆×D₇₃

yes

characteristic

128

C₄

—

129

C₄

—

146

—

130

C₄

#17988405

yes

—

131

C₄

C₂×#14556520

yes

characteristic

132

C₄

C₂×#14556530

yes

characteristic

133

C₂

#22608126

yes

direct product factor

134

C₂

C₂×#17988405

yes

characteristic

135

C₂

C₂×C₃₂×D₇₃

yes

characteristic

136

C₂

C₂×#17988420

yes

characteristic

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

subgroup

G/H

center

C₂²×C₁₆

C₂×D₇₃

commutator

C₂×C₇₃

C₂²×C₃₂

Frattini

C₂×C₁₆

C₂²×D₇₃

Fitting

C₂²×C₃₂×C₇₃

C₂

socle, prime radical

C₂³×C₇₃

C₂×C₁₆

cosocle

C₂×C₁₆×C₇₃

C₂³

hypercenter

C₂²×C₃₂

D₇₃

hypocenter

C₇₃

C₂×C₄⋊C₃₂

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

N	H ≅ G/N	type
3. #22608126	C₂	direct (N × H)
48. C₂×Dic₇₃	C₃₂	semidirect
63. Dic₇₃	C₂×C₃₂	semidirect
65. C₂×C₇₃	C₄⋊C₃₂	semidirect
73. C₇₃	C₂×C₄⋊C₃₂	semidirect
133. C₂	#22608126	direct (N × H)

H ≅ G/N

type

3. #22608126

C₂

direct (N × H)

48. C₂×Dic₇₃

C₃₂

semidirect

63. Dic₇₃

C₂×C₃₂

semidirect

65. C₂×C₇₃

C₄⋊C₃₂

semidirect

73. C₇₃

C₂×C₄⋊C₃₂

semidirect

133. C₂

#22608126

direct (N × H)

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

subgroup	index
C₂²×#14556497	2
C₂×C₁₆×Dic₇₃	2
#22608126	2
C₂²×C₃₂×C₇₃	2
C₂×C₄⋊C₃₂	73

subgroup

index

C₂²×#14556497

C₂×C₁₆×Dic₇₃

#22608126

C₂²×C₃₂×C₇₃

C₂×C₄⋊C₃₂

Subgroups — C₂×#22608126 #33006463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#22608126 #33006463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22608126 #33006463