Group #33006948 — subgroups

Subgroups — #33006948

Order 18688.

160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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	#22612039	C₂	1	1	yes	maximal, characteristic
2	#22608138	C₂	1	2	yes	maximal, complemented
3	#22608123	C₂	1	2	yes	maximal, complemented
4	#22608071	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2161	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₈₄	C₂²	1	1	yes	characteristic
7	#17988828	—	2	1	no	—
8	#17988421	C₂²	1	2	yes	—
9	#17988415	C₂²	1	1	yes	characteristic
10	#17988392	—	2	1	no	—
11	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×#108×C₇₃	—	2	1	no	—
13	#368×C₇₃	—	2	1	no	—
14	#368×C₇₃	C₂²	1	2	yes	—
15	C₂×Dic₂₉₂	—	2	1	no	—
16	#14556570	—	4	1	no	—
17	Dic₅₈₄	—	2	2	no	—
18	#14556525	—	2	1	no	—
19	#14556516	—	4	1	no	—
20	#14556497	—	2	2	no	—
21	C₂×M₁₆×C₇₃	—	4	1	no	—
22	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
23	M₃₂×C₇₃	—	2	2	no	—
24	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
25	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
26	#108×C₇₃	—	2	2	no	—
27	#108×C₇₃	—	4	1	no	—
28	C₂×Dic₁₄₆	—	4	1	no	—
29	Dic₂₉₂	—	4	1	no	—
30	Dic₂₉₂	—	4	1	no	—
31	C₄⋊Dic₇₃	—	4	1	no	—
32	#11924007	—	8	1	no	—
33	C₂²⋊Dic₇₃	—	8	1	no	—
34	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
35	M₁₆×C₇₃	—	4	2	no	—
36	M₁₆×C₇₃	—	8	1	no	—
37	C₂×C₈×C₇₃	—	2	1	no	—
38	C₂×C₈×C₇₃	—	2	1	no	—
39	C₂×C₈×C₇₃	—	8	1	no	—
40	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
41	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
42	C₁₆×C₇₃	—	2	1	no	—
43	C₁₆×C₇₃	#41	1	2	yes	—
44	C₂³×C₇₃	SD₃₂	1	1	yes	characteristic
45	C₂×C₄×C₇₃	—	2	1	no	—
46	C₂×C₄×C₇₃	—	2	1	no	—
47	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
49	C₂×Dic₇₃	—	8	1	no	—
50	C₂×Dic₇₃	—	8	1	no	—
51	Dic₁₄₆	—	8	1	no	—
52	Dic₁₄₆	—	8	1	no	—
53	C₈×C₇₃	—	2	1	no	—
54	C₈×C₇₃	—	8	2	no	—
55	C₈×C₇₃	#123	1	1	yes	characteristic
56	C₈×C₇₃	#137	1	1	yes	characteristic
57	C₂²×C₇₃	—	2	1	no	—
58	C₂²×C₇₃	—	4	1	no	—
59	C₂²×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
60	C₄×C₇₃	—	2	1	no	—
61	C₄×C₇₃	#480	1	1	yes	characteristic
62	C₄×C₇₃	#509	1	1	yes	characteristic
63	Dic₇₃	—	16	1	no	—
64	Dic₇₃	—	16	1	no	—
65	#13718	—	73	1	no	maximal, Sylow
66	C₂×C₇₃	—	2	1	no	—
67	C₂×C₇₃	—	4	1	no	—
68	C₂×C₇₃	#2233	1	1	yes	characteristic
69	#2219	—	73	1	no	—
70	#2161	D₇₃	1	1	yes	characteristic
71	#1426	—	73	2	no	—
72	#1420	—	73	2	no	—
73	#1400	—	73	1	no	—
74	C₇₃	#13718	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₃₂	—	73	1	no	—
76	C₂×M₃₂	C₂×D₇₃	1	1	yes	characteristic
77	#467	—	146	1	no	—
78	C₂×#108	—	2	1	no	—
79	M₆₄	—	73	2	no	—
80	#368	—	2	1	no	—
81	#368	C₂×D₇₃	1	2	yes	—
82	#367	—	73	1	no	—
83	#358	—	146	1	no	—
84	C₂×Q₁₆	—	146	1	no	—
85	C₂×M₁₆	—	4	1	no	—
86	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
87	C₂²⋊Q₈	—	292	1	no	—
88	Q₃₂	—	146	2	no	—
89	M₃₂	—	2	2	no	—
90	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
92	#108	—	2	2	no	—
93	#108	—	4	1	no	—
94	#107	—	146	1	no	—
95	#103	—	292	1	no	—
96	C₃₂	—	146	2	no	—
97	C₂×Q₈	—	292	1	no	—
98	C₂²×C₄	#11924013	1	1	yes	characteristic
99	Q₁₆	—	292	1	no	—
100	Q₁₆	—	292	1	no	—
101	M₁₆	—	4	2	no	—
102	M₁₆	—	8	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	8	1	no	—
106	C₂×C₈	#11924013	1	1	yes	characteristic
107	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
108	C₄⋊C₄	—	292	1	no	—
109	C₄⋊C₄	—	584	1	no	—
110	C₂²⋊C₄	—	584	1	no	—
111	C₁₆	—	2	1	no	—
112	C₁₆	#11924028	1	2	yes	—
113	C₂³	#14556534	1	1	yes	characteristic
114	Q₈	—	584	1	no	—
115	Q₈	—	584	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	584	1	no	—
119	C₂×C₄	—	584	1	no	—
120	C₂×C₄	#14556534	1	1	yes	characteristic
121	C₂×C₄	C₂×#11924013	1	1	yes	characteristic
122	C₈	—	2	1	no	—
123	C₈	—	8	2	no	—
124	C₈	#14556574	1	1	yes	characteristic
125	C₈	#14556622	1	1	yes	characteristic
126	C₂²	—	2	1	no	—
127	C₂²	—	4	1	no	—
128	C₂²	C₂×#14556534	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	1168	1	no	—
131	C₄	—	1168	1	no	—
132	C₄	#17988900	1	1	yes	characteristic
133	C₄	#17989023	1	1	yes	characteristic
134	C₂	—	2	1	no	—
135	C₂	—	4	1	no	—
136	C₂	#22612116	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22612039

C₂

yes

maximal, characteristic

#22608138

C₂

yes

maximal, complemented

#22608123

C₂

yes

maximal, complemented

#22608071

C₂

yes

maximal, characteristic

C₇₃×#2161

C₂

yes

maximal, characteristic

C₂×Dic₅₈₄

C₂²

yes

characteristic

#17988828

—

#17988421

C₂²

yes

—

#17988415

C₂²

yes

characteristic

#17988392

—

C₂×M₃₂×C₇₃

C₂²

yes

characteristic

C₂×#108×C₇₃

—

#368×C₇₃

—

#368×C₇₃

C₂²

yes

—

C₂×Dic₂₉₂

—

#14556570

—

Dic₅₈₄

—

#14556525

—

#14556516

—

#14556497

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₈

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

#41

yes

—

C₂³×C₇₃

SD₃₂

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×SD₃₂

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

#13718

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

D₇₃

yes

—

—

—

C₇₃

#13718

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×M₃₂

C₂×D₇₃

yes

characteristic

#467

—

146

—

C₂×#108

—

M₆₄

—

#368

—

#368

C₂×D₇₃

yes

—

#367

—

#358

—

146

—

C₂×Q₁₆

—

146

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

C₂²⋊Q₈

—

292

—

Q₃₂

—

146

—

M₃₂

—

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

C₂×C₁₆

C₂²×D₇₃

yes

—

—

—

146

—

#103

—

292

—

C₃₂

—

146

—

C₂×Q₈

—

292

—

C₂²×C₄

#11924013

yes

characteristic

Q₁₆

—

292

—

100

Q₁₆

—

292

—

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

#11924013

yes

characteristic

107

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

108

C₄⋊C₄

—

292

—

109

C₄⋊C₄

—

584

—

110

C₂²⋊C₄

—

584

—

111

C₁₆

—

112

C₁₆

#11924028

yes

—

113

C₂³

#14556534

yes

characteristic

114

Q₈

—

584

—

115

Q₈

—

584

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

584

—

119

C₂×C₄

—

584

—

120

C₂×C₄

#14556534

yes

characteristic

121

C₂×C₄

C₂×#11924013

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

#14556574

yes

characteristic

125

C₈

#14556622

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

C₂×#14556534

yes

characteristic

129

C₄

—

130

C₄

—

1168

—

131

C₄

—

1168

—

132

C₄

#17988900

yes

characteristic

133

C₄

#17989023

yes

characteristic

134

C₂

—

135

C₂

—

136

C₂

#22612116

yes

characteristic

	subgroup	G/H
center	C₂	#22612116
commutator, cosocle	C₂×C₁₆×C₇₃	C₂³
Frattini	C₂×C₁₆	C₂²×D₇₃
Fitting	C₇₃×#2161	C₂
socle	C₂×C₇₃	#2233
prime radical	C₂³×C₇₃	SD₃₂
hypercenter	#2161	D₇₃
hypocenter	C₇₃	#13718
LCS	G ▷ C₂×C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2161

subgroup

G/H

center

C₂

#22612116

commutator, cosocle

C₂×C₁₆×C₇₃

C₂³

Frattini

C₂×C₁₆

C₂²×D₇₃

Fitting

C₇₃×#2161

C₂

socle

C₂×C₇₃

#2233

prime radical

C₂³×C₇₃

SD₃₂

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2161

N	H ≅ G/N	type
2. #22608138	C₂	semidirect
3. #22608123	C₂	semidirect
74. C₇₃	#13718	semidirect

H ≅ G/N

type

2. #22608138

C₂

semidirect

3. #22608123

C₂

semidirect

74. C₇₃

#13718

semidirect

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

subgroup	index
#22612039	2
#22608138	2
#22608123	2
#22608071	2
C₇₃×#2161	2
#13718	73

subgroup

index

C₇₃×#2161

Subgroups — #33006948

Conjugacy classes of subgroups

Complements

Maximal subgroups