Finite Group Databasebeta

← #45692434

Subgroups — #45692434

Order 33516.

248 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#19150298C211yesmaximal, characteristic, complemented
2C19×C3⋊#64423C211yesmaximal, characteristic, complemented
3C3×#19150288C211yesmaximal, characteristic, complemented
4D21⋊D133C311yesmaximal, characteristic, complemented
5#64423⋊D19—31nomaximal
6C3×C19×#3861C2211yescharacteristic, complemented, Hall
7C7×D399C2×C311yescharacteristic, complemented
8C7×C19×D21C2×C311yescharacteristic, complemented
9C3×C7⋊D133C2×C311yescharacteristic, complemented
10#19150298—31no—
11C19×#64423—31no—
12#19150288—21no—
13#19150288D311yescharacteristic, complemented
14(C3⋊AGL(1,𝔽7))⋊D19—71nomaximal
15D3×ΓL(1,𝔽8)⋊D19—71nomaximal
16D7×D133—31noHall
17C19×#3861—21no—
18C19×#3861C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20ΓL(1,𝔽8)×D57—71no—
21D3×C19×ΓL(1,𝔽8)—71no—
22C3⋊(ΓL(1,𝔽8)⋊D19)—71no—
23C19×C3⋊AGL(1,𝔽7)—71no—
24C3×ΓL(1,𝔽8)⋊D19—71no—
25C3×ΓL(1,𝔽8)⋊D19—71no—
26C3×ΓL(1,𝔽8)⋊D19—143no—
27C7⋊D133C3×D311yescharacteristic, complemented
28C7×D133—31no—
29C7×D7×C19—31no—
30#13183634—191nomaximal, Hall
31D21⋊D19—71no—
32D3×D133—71no—
33C2×ΓL(1,𝔽8)⋊D19—211no—
34D19×AGL(1,𝔽7)—211no—
35C3×C19×ΓL(1,𝔽8)—71no—
36C3×C19×ΓL(1,𝔽8)—71no—
37C3×C19×ΓL(1,𝔽8)—143no—
38C72×C19C2×C3×D311yescharacteristic, complemented, Hall
39C3⋊#64423—191no—
40C3⋊#64423D1911yescharacteristic, complemented
41C3×#64424—191no—
42D399AGL(1,𝔽7)11yescharacteristic, complemented
43C19×D21AGL(1,𝔽7)11yescharacteristic, complemented
44C7×D57—71no—
45D3×C7×C19—71no—
46C3×D133—71no—
47C3×D133—71no—
48C3×D133—143no—
49C2×C19×ΓL(1,𝔽8)—211no—
50ΓL(1,𝔽8)⋊D19—71no—
51ΓL(1,𝔽8)⋊D19—71no—
52ΓL(1,𝔽8)⋊D19—143no—
53ΓL(1,𝔽8)⋊D19—141no—
54ΓL(1,𝔽8)⋊D19—141no—
55ΓL(1,𝔽8)⋊D19—146no—
56ΓL(1,𝔽8)⋊D19—211no—
57C19×AGL(1,𝔽7)—211no—
58ΓL(1,𝔽8)×D19—211no—
59C3×D3×D19—491noHall
60D21⋊D7—191no—
61#64423⋊C2—571no—
62C2×D133—211no—
63D7×D19—211no—
64C3×#3861C2×D1911yescharacteristic, complemented, Hall
65C3×C7×C19—23no—
66C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
68C19×ΓL(1,𝔽8)—71no—
69C19×ΓL(1,𝔽8)—71no—
70C19×ΓL(1,𝔽8)—143no—
71C19×ΓL(1,𝔽8)—146no—
72C19×ΓL(1,𝔽8)—141no—
73C19×ΓL(1,𝔽8)—141no—
74C3×D57—491no—
75C3×D3×C19—491no—
76C32×D19—491no—
77C7×D21—191no—
78C7×D21C3×D1911yescharacteristic, complemented
79C3×C7⋊D7—191no—
80#64424—191no—
81#64424—381no—
82#64423—31no—
83#64423—571no—
84C2×C7×C19—211no—
85D133—31no—
86D133—71no—
87D133—71no—
88D133—143no—
89C7×D19—211no—
90D7×C19—31no—
91D3×AGL(1,𝔽7)—1331no—
92D3×AGL(1,𝔽7)—1331no—
93C2×C3×D19—1471no—
94D3×D19—491no—
95D72—571noHall
96C32×C19—491noHall
97C3×C72C2×C3×D1911yescharacteristic, complemented
98#3861—21no—
99#3861D3×D1911yescharacteristic, complemented
100C7×C19—23no—
101C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
102C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
103C3⋊AGL(1,𝔽7)—71no—
104C3⋊AGL(1,𝔽7)—1331no—
105D3×ΓL(1,𝔽8)—71no—
106D3×ΓL(1,𝔽8)—1331no—
107C3×AGL(1,𝔽7)—2663no—
108C3×AGL(1,𝔽7)—1331no—
109C3×AGL(1,𝔽7)—1331no—
110C2×C3×C19—1471no—
111D57—71no—
112C3×D19—491no—
113C3×D19—491no—
114C3×D19—981no—
115C3×D19—1471no—
116D3×C19—71no—
117C7⋊D7—191no—
118C7×D7—31no—
119C7×D7—571no—
120D3×D7—1331no—
121D3×D7—1331no—
122C2×AGL(1,𝔽7)—3991no—
123C2×AGL(1,𝔽7)—3991no—
124C2×D19—1471noHall
125C3×ΓL(1,𝔽8)—71no—
126C3×ΓL(1,𝔽8)—71no—
127C3×ΓL(1,𝔽8)—143no—
128C3×C19—491no—
129C3×C19—981no—
130C3×C19#64423⋊C211yescharacteristic, complemented
131C72C3×D3×D1911yescharacteristic, complemented, Sylow
132D21—191no—
133D21ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
134C3×D7—2663no—
135C3×D7—1331no—
136C3×D7—1331no—
137D3×C7—71no—
138D3×C7—1331no—
139C2×ΓL(1,𝔽8)—211no—
140C2×ΓL(1,𝔽8)—3991no—
141AGL(1,𝔽7)—2666no—
142AGL(1,𝔽7)—2661no—
143AGL(1,𝔽7)—2661no—
144AGL(1,𝔽7)—2663no—
145AGL(1,𝔽7)—211no—
146AGL(1,𝔽7)—1331no—
147AGL(1,𝔽7)—1331no—
148AGL(1,𝔽7)—3991no—
149C2×C19—211no—
150D19—211no—
151D19—491no—
152C2×C3×D3—9311noHall
153C2×D7—3991no—
154C2×D7—3991no—
155C3×C7—23no—
156C3×C7D19×AGL(1,𝔽7)11yescharacteristic, complemented
157C3×C7C2×ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
158ΓL(1,𝔽8)—71no—
159ΓL(1,𝔽8)—71no—
160ΓL(1,𝔽8)—143no—
161ΓL(1,𝔽8)—146no—
162ΓL(1,𝔽8)—141no—
163ΓL(1,𝔽8)—141no—
164C19#1318363411yescharacteristic, complemented, Sylow
165C2×C32—9311no—
166C3×D3—491no—
167C3×D3—9311no—
168C2×C7—211no—
169C2×C7—3991no—
170D7—31no—
171D7—2663no—
172D7—571no—
173D7—1331no—
174D7—1331no—
175C22×C3—27931no—
176C2×D3—9311no—
177C32—491noSylow
178C7—23no—
179C7D3×ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
180C7(C3⋊AGL(1,𝔽7))⋊D1911yescharacteristic, complemented
181C2×C3—18621no—
182C2×C3—1471no—
183C2×C3—9311no—
184C2×C3—9311no—
185C2×C3—27931no—
186D3—71no—
187D3—1331no—
188C22—27931noSylow
189C3—491no—
190C3—981no—
191C3#64423⋊D1911yescharacteristic, complemented
192C2—211no—
193C2—3991no—
194C2—9311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C19C22×C3
LCSG ▷ C3×C72×C19
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3⋊#19150298C2semidirect
2. C19×C3⋊#64423C2semidirect
3. C3×#19150288C2semidirect
4. D21⋊D133C3semidirect
6. C3×C19×#3861C22semidirect
7. C7×D399C2×C3semidirect
8. C7×C19×D21C2×C3semidirect
9. C3×C7⋊D133C2×C3semidirect
13. #19150288D3semidirect
18. C19×#3861C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
27. C7⋊D133C3×D3semidirect
38. C72×C19C2×C3×D3semidirect
40. C3⋊#64423D19semidirect
42. D399AGL(1,𝔽7)semidirect
43. C19×D21AGL(1,𝔽7)semidirect
64. C3×#3861C2×D19semidirect
66. C3×C7×C19C2×AGL(1,𝔽7)semidirect
67. C3×C7×C19C2×AGL(1,𝔽7)semidirect
78. C7×D21C3×D19semidirect
97. C3×C72C2×C3×D19semidirect
99. #3861D3×D19semidirect
101. C7×C19D3×AGL(1,𝔽7)semidirect
102. C7×C19D3×AGL(1,𝔽7)semidirect
130. C3×C19#64423⋊C2semidirect
131. C72C3×D3×D19semidirect
133. D21ΓL(1,𝔽8)⋊D19semidirect
156. C3×C7D19×AGL(1,𝔽7)semidirect
157. C3×C7C2×ΓL(1,𝔽8)⋊D19semidirect
164. C19#13183634semidirect
179. C7D3×ΓL(1,𝔽8)⋊D19semidirect
180. C7(C3⋊AGL(1,𝔽7))⋊D19semidirect
191. C3#64423⋊D19semidirect

Maximal subgroups

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

subgroupindex
C3⋊#191502982
C19×C3⋊#644232
C3×#191502882
D21⋊D1333
#64423⋊D193
(C3⋊AGL(1,𝔽7))⋊D197
D3×ΓL(1,𝔽8)⋊D197
#1318363419