Finite Group Databasebeta

← #45692424

Subgroups — #45692424

Order 33516.

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

normal subgroups only

This group has 230 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⋊#64424C211yesmaximal, characteristic, complemented
3C3×#19150298C211yesmaximal, characteristic, complemented
4D133⋊D21C311yesmaximal, characteristic, complemented
5#64424⋊D19—31nomaximal
6C3×C19×#3861C2211yescharacteristic, complemented, Hall
7C19×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C7×D399C2×C311yescharacteristic, complemented
9C3×C7×D133C2×C311yescharacteristic, complemented
10#19150298—21no—
11#19150298—31no—
12#19150298D311yescharacteristic, complemented
13C19×#64424—31no—
14(C3⋊AGL(1,𝔽7))⋊D19—71nomaximal
15D19×C3⋊AGL(1,𝔽7)—71nomaximal
16(C7⋊D7)⋊D19—31noHall
17C19×#3861—21no—
18C19×#3861C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20ΓL(1,𝔽8)×D57—71no—
21C3⋊(ΓL(1,𝔽8)⋊D19)—71no—
22C19×C3⋊AGL(1,𝔽7)—71no—
23C19×C3⋊AGL(1,𝔽7)—71no—
24C19×C3⋊AGL(1,𝔽7)—143no—
25C3×ΓL(1,𝔽8)×D19—71no—
26C3×ΓL(1,𝔽8)⋊D19—71no—
27C19×C7⋊D7—31no—
28C7×D133—31no—
29C7×D133C3×D311yescharacteristic, complemented
30#64423⋊D3—191nomaximal, Hall
31D21⋊D19—71no—
32D19×D21—71no—
33D19×AGL(1,𝔽7)—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⋊#64424D1911yescharacteristic, complemented
40C3⋊#64423—191no—
41C3×#64423—191no—
42D399AGL(1,𝔽7)11yescharacteristic, complemented
43C19×D21—71no—
44C19×D21—71no—
45C19×D21—143no—
46C7×D57—71no—
47C3×D133AGL(1,𝔽7)11yescharacteristic, complemented
48C3×C7×D19—71no—
49ΓL(1,𝔽8)⋊D19—71no—
50ΓL(1,𝔽8)⋊D19—141no—
51ΓL(1,𝔽8)⋊D19—211no—
52C19×AGL(1,𝔽7)—211no—
53C19×AGL(1,𝔽7)—211no—
54C19×AGL(1,𝔽7)—423no—
55ΓL(1,𝔽8)×D19—71no—
56ΓL(1,𝔽8)×D19—141no—
57ΓL(1,𝔽8)×D19—211no—
58C3×D3×D19—491noHall
59D7×D21—191no—
60#64423⋊C2—571no—
61D7×D19—211no—
62D7×D19—211no—
63C3×#3861C2×D1911yescharacteristic, complemented, Hall
64C3×C7×C19—23no—
65C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
66C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C19×ΓL(1,𝔽8)—71no—
68C19×ΓL(1,𝔽8)—71no—
69C19×ΓL(1,𝔽8)—143no—
70C19×ΓL(1,𝔽8)—141no—
71C19×ΓL(1,𝔽8)—141no—
72C19×ΓL(1,𝔽8)—283no—
73C3×D57—491no—
74C3×D3×C19—491no—
75C32×D19—491no—
76C3⋊(C7⋊D7)C3×D1911yescharacteristic, complemented
77C7×D21—191no—
78C3×C7×D7—191no—
79#64424—31no—
80#64423—191no—
81#64423—381no—
82#64423—571no—
83D133—31no—
84D133C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
85C7×D19—71no—
86C7×D19—211no—
87D7×C19—211no—
88D7×C19—211no—
89D7×C19—423no—
90C2×C3⋊AGL(1,𝔽7)—1331no—
91D3×AGL(1,𝔽7)—1331no—
92C2×C3×D19—1471no—
93D3×D19—491no—
94D72—571noHall
95C32×C19—491noHall
96C3×C72C2×C3×D1911yescharacteristic, complemented
97#3861—21no—
98#3861D3×D1911yescharacteristic, complemented
99C7×C19—23no—
100C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
101C7×C19C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
102C2×C3×ΓL(1,𝔽8)—1331no—
103C3⋊AGL(1,𝔽7)—71no—
104C3⋊AGL(1,𝔽7)—71no—
105C3⋊AGL(1,𝔽7)—143no—
106C3⋊AGL(1,𝔽7)—1331no—
107D3×ΓL(1,𝔽8)—1331no—
108C3×AGL(1,𝔽7)—1331no—
109C2×C3×C19—1471no—
110D57—71no—
111C3×D19—71no—
112C3×D19—491no—
113C3×D19—981no—
114C3×D19—1471no—
115D3×C19—491no—
116C7⋊D7—31no—
117C7×D7—191no—
118C7×D7—571no—
119C2×D21—1331no—
120D3×D7—1331no—
121C2×AGL(1,𝔽7)—3991no—
122C2×AGL(1,𝔽7)—3991no—
123C2×D19—1471noHall
124C3×ΓL(1,𝔽8)—71no—
125C3×ΓL(1,𝔽8)—71no—
126C3×ΓL(1,𝔽8)—143no—
127C3×C19—491no—
128C3×C19—981no—
129C3×C19#64423⋊C211yescharacteristic, complemented
130C72C3×D3×D1911yescharacteristic, complemented, Sylow
131C2×C3×C7—1331no—
132D21—71no—
133D21—71no—
134D21—143no—
135D21—191no—
136C3×D7—191no—
137D3×C7—1331no—
138C2×ΓL(1,𝔽8)—2661no—
139C2×ΓL(1,𝔽8)—1331no—
140C2×ΓL(1,𝔽8)—3991no—
141AGL(1,𝔽7)—2661no—
142AGL(1,𝔽7)—211no—
143AGL(1,𝔽7)—211no—
144AGL(1,𝔽7)—423no—
145AGL(1,𝔽7)—1331no—
146AGL(1,𝔽7)—3991no—
147C2×C19—1471no—
148D19—71no—
149D19—211no—
150C2×C3×D3—9311noHall
151C2×D7—3991no—
152C2×D7—3991no—
153C3×C7—23no—
154C3×C7D19×AGL(1,𝔽7)11yescharacteristic, complemented
155C3×C7D19×AGL(1,𝔽7)11yescharacteristic, complemented
156ΓL(1,𝔽8)—71no—
157ΓL(1,𝔽8)—71no—
158ΓL(1,𝔽8)—143no—
159ΓL(1,𝔽8)—141no—
160ΓL(1,𝔽8)—141no—
161ΓL(1,𝔽8)—283no—
162C19#64423⋊D311yescharacteristic, complemented, Sylow
163C2×C32—9311no—
164C3×D3—491no—
165C3×D3—9311no—
166C2×C7—1331no—
167C2×C7—3991no—
168D7—191no—
169D7—211no—
170D7—211no—
171D7—423no—
172D7—571no—
173C22×C3—27931no—
174C2×D3—9311no—
175C32—491noSylow
176C7—23no—
177C7D19×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
178C7(C3⋊AGL(1,𝔽7))⋊D1911yescharacteristic, complemented
179C2×C3—18621no—
180C2×C3—1331no—
181C2×C3—1471no—
182C2×C3—9311no—
183C2×C3—27931no—
184D3—491no—
185D3—1331no—
186C22—27931noSylow
187C3—491no—
188C3—981no—
189C3#64424⋊D1911yescharacteristic, complemented
190C2—1331no—
191C2—3991no—
192C2—1471no—
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⋊#64424C2semidirect
3. C3×#19150298C2semidirect
4. D133⋊D21C3semidirect
6. C3×C19×#3861C22semidirect
7. C19×C3⋊(C7⋊D7)C2×C3semidirect
8. C7×D399C2×C3semidirect
9. C3×C7×D133C2×C3semidirect
12. #19150298D3semidirect
18. C19×#3861C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
29. C7×D133C3×D3semidirect
38. C72×C19C2×C3×D3semidirect
39. C3⋊#64424D19semidirect
42. D399AGL(1,𝔽7)semidirect
47. C3×D133AGL(1,𝔽7)semidirect
63. C3×#3861C2×D19semidirect
65. C3×C7×C19C2×AGL(1,𝔽7)semidirect
66. C3×C7×C19C2×AGL(1,𝔽7)semidirect
76. C3⋊(C7⋊D7)C3×D19semidirect
84. D133C3⋊AGL(1,𝔽7)semidirect
96. C3×C72C2×C3×D19semidirect
98. #3861D3×D19semidirect
100. C7×C19D3×AGL(1,𝔽7)semidirect
101. C7×C19C2×C3⋊AGL(1,𝔽7)semidirect
129. C3×C19#64423⋊C2semidirect
130. C72C3×D3×D19semidirect
154. C3×C7D19×AGL(1,𝔽7)semidirect
155. C3×C7D19×AGL(1,𝔽7)semidirect
162. C19#64423⋊D3semidirect
177. C7D19×C3⋊AGL(1,𝔽7)semidirect
178. C7(C3⋊AGL(1,𝔽7))⋊D19semidirect
189. C3#64424⋊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⋊#644242
C3×#191502982
D133⋊D213
#64424⋊D193
(C3⋊AGL(1,𝔽7))⋊D197
D19×C3⋊AGL(1,𝔽7)7
#64423⋊D319