Finite Group Databasebeta

← D3×#19150290 #45692475

Subgroups — D3×#19150290 #45692475

Order 33516.

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

normal subgroups only

This group has 216 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
1D3×C19⋊#3862C211yesmaximal, characteristic, complemented
2C3⋊#19150290C211yesmaximal, characteristic, complemented
3C3×#19150290C211yesmaximal, characteristic, complemented
4D3×C7⋊D133C311yesmaximal, characteristic, complemented
5C2×#19150290—31nomaximal
6C3×C19⋊#3862C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8D3×C72×C19C2×C311yescharacteristic, complemented
9C3×C7⋊D133C2×C311yescharacteristic, complemented
10C2×C19⋊#3862—31no—
11#19150290—21no—
12#19150290—31no—
13#19150290D311yescharacteristic, direct product factor
14D3×#11716328—71nomaximal
15D3×#11716327—71nomaximal
16C2×C7⋊D133—31noHall
17C19⋊#3862—21no—
18C19⋊#3862C2×D311yescharacteristic, complemented
19C3×C72×C19C22×C311yescharacteristic, complemented
20D3×#87705—71no—
21D3×#87704—71no—
22C3⋊#11716328—71no—
23C3⋊#11716327—71no—
24C3×#11716328—71no—
25C3×#11716327—71no—
26C2×C72×C19—31no—
27C7⋊D133—31no—
28C7⋊D133C3×D311yescharacteristic, complemented
29D3×#64425—191nomaximal, Hall
30D3×D133—71no—
31D3×D133—71no—
32D3×D133—212no—
33C2×#11716328—211no—
34C2×#11716327—211no—
35C3×#87704—71no—
36C3×#87705—71no—
37C72×C19C2×C3×D311yescharacteristic, complemented, Hall
38C3⋊#64425—191no—
39D3×#3862—191no—
40C3×#64425—191no—
41D399—71no—
42D399—71no—
43D399—212no—
44D3×C7×C19—32no—
45D3×C7×C19AGL(1,𝔽7)11yescharacteristic, complemented
46D3×C7×C19AGL(1,𝔽7)11yescharacteristic, complemented
47C3×D133—71no—
48C3×D133—71no—
49C3×D133—212no—
50C2×#87705—211no—
51C2×#87704—211no—
52#11716328—71no—
53#11716328—141no—
54#11716328—211no—
55#11716327—71no—
56#11716327—141no—
57#11716327—211no—
58D3×D19⋊C3—491noHall
59D3×C7⋊D7—191no—
60C2×#64425—571no—
61C2×D133—211no—
62C2×D133—211no—
63C2×D133—632no—
64C3×#3862—191noHall
65C3×C7×C19—32no—
66C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
67C3×C7×C19C2×AGL(1,𝔽7)11yescharacteristic, complemented
68#87705—71no—
69#87705—141no—
70#87704—71no—
71#87704—141no—
72C3⋊(D19⋊C3)—491no—
73D3×C19⋊C3—491no—
74C3×D19⋊C3—491no—
75C3⋊(C7⋊D7)—191no—
76D3×C72D19⋊C311yescharacteristic, complemented
77C3×C7⋊D7—191no—
78C2×#3862—571no—
79#64425—191no—
80#64425—381no—
81#64425—571no—
82C2×C7×C19—31no—
83C2×C7×C19—31no—
84C2×C7×C19—92no—
85D133—71no—
86D133—71no—
87D133—212no—
88D133—211no—
89D133—211no—
90D133—632no—
91D3×AGL(1,𝔽7)—1331no—
92D3×AGL(1,𝔽7)—1331no—
93D3×D19—491no—
94C2×D19⋊C3—1471no—
95C2×C7⋊D7—571noHall
96C3×C19⋊C3—491noHall
97C3×C72C2×D19⋊C311yescharacteristic, complemented
98#3862—191no—
99#3862—381no—
100C7×C19—32no—
101C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
102C7×C19D3×AGL(1,𝔽7)11yescharacteristic, complemented
103C3⋊AGL(1,𝔽7)—1331no—
104C3⋊AGL(1,𝔽7)—1331no—
105D3×ΓL(1,𝔽8)—1331no—
106D3×ΓL(1,𝔽8)—1331no—
107C3×AGL(1,𝔽7)—1331no—
108C3×AGL(1,𝔽7)—1331no—
109D57—491no—
110C3×D19—491no—
111D3×C19#6442511yescharacteristic, complemented
112C2×C19⋊C3—1471no—
113D19⋊C3—491no—
114D19⋊C3—981no—
115D19⋊C3—1471no—
116C2×C72—31no—
117C7⋊D7—191no—
118C7⋊D7—571no—
119D3×D7—1331no—
120D3×D7—1331no—
121D3×D7—3992no—
122C2×AGL(1,𝔽7)—3991no—
123C2×AGL(1,𝔽7)—3991no—
124C2×D19—1471noHall
125C3×ΓL(1,𝔽8)—1331no—
126C3×ΓL(1,𝔽8)—1331no—
127C3×C19C2×#6442511yescharacteristic, complemented
128C19⋊C3—491no—
129C19⋊C3—981no—
130C72D3×D19⋊C311yescharacteristic, complemented, Sylow
131D21—1331no—
132D21—1331no—
133D21—3992no—
134C3×D7—1331no—
135C3×D7—1331no—
136C3×D7—3992no—
137D3×C7—32no—
138D3×C7#1171632711yescharacteristic, complemented
139D3×C7#1171632811yescharacteristic, complemented
140C2×ΓL(1,𝔽8)—3991no—
141C2×ΓL(1,𝔽8)—3991no—
142AGL(1,𝔽7)—2661no—
143AGL(1,𝔽7)—2661no—
144AGL(1,𝔽7)—1331no—
145AGL(1,𝔽7)—1331no—
146AGL(1,𝔽7)—3991no—
147AGL(1,𝔽7)—3991no—
148C2×C19—31no—
149D19—491no—
150D19—1471no—
151C2×C3×D3—9311noHall
152C2×D7—3991no—
153C2×D7—3991no—
154C2×D7—11972no—
155C3×C7—32no—
156C3×C7C2×#1171632711yescharacteristic, complemented
157C3×C7C2×#1171632811yescharacteristic, complemented
158ΓL(1,𝔽8)—2661no—
159ΓL(1,𝔽8)—2661no—
160ΓL(1,𝔽8)—1331no—
161ΓL(1,𝔽8)—1331no—
162C19D3×#6442511yescharacteristic, complemented, Sylow
163C2×C32—9311no—
164C3×D3—9311no—
165C3×D3—9311no—
166C2×C7—31no—
167C2×C7—31no—
168C2×C7—92no—
169D7—1331no—
170D7—1331no—
171D7—3992no—
172D7—3991no—
173D7—3991no—
174D7—11972no—
175C22×C3—27931no—
176C2×D3—9311no—
177C32—9311noSylow
178C7—32no—
179C7D3×#1171632711yescharacteristic, complemented
180C7D3×#1171632811yescharacteristic, complemented
181C2×C3—18621no—
182C2×C3—9311no—
183C2×C3—9311no—
184C2×C3—27931no—
185C2×C3—27931no—
186D3—9311no—
187D3#1915029011yescharacteristic, direct product factor
188C22—27931noSylow
189C3—18621no—
190C3—9311no—
191C3C2×#1915029011yescharacteristic, complemented
192C2—31no—
193C2—9311no—
194C2—27931no—
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. D3×C19⋊#3862C2semidirect
2. C3⋊#19150290C2semidirect
3. C3×#19150290C2semidirect
4. D3×C7⋊D133C3semidirect
6. C3×C19⋊#3862C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. D3×C72×C19C2×C3semidirect
9. C3×C7⋊D133C2×C3semidirect
13. #19150290D3direct (N × H)
18. C19⋊#3862C2×D3semidirect
19. C3×C72×C19C22×C3semidirect
28. C7⋊D133C3×D3semidirect
37. C72×C19C2×C3×D3semidirect
45. D3×C7×C19AGL(1,𝔽7)semidirect
46. D3×C7×C19AGL(1,𝔽7)semidirect
66. C3×C7×C19C2×AGL(1,𝔽7)semidirect
67. C3×C7×C19C2×AGL(1,𝔽7)semidirect
76. D3×C72D19⋊C3semidirect
97. C3×C72C2×D19⋊C3semidirect
101. C7×C19D3×AGL(1,𝔽7)semidirect
102. C7×C19D3×AGL(1,𝔽7)semidirect
111. D3×C19#64425semidirect
127. C3×C19C2×#64425semidirect
130. C72D3×D19⋊C3semidirect
138. D3×C7#11716327semidirect
139. D3×C7#11716328semidirect
156. C3×C7C2×#11716327semidirect
157. C3×C7C2×#11716328semidirect
162. C19D3×#64425semidirect
179. C7D3×#11716327semidirect
180. C7D3×#11716328semidirect
187. D3#19150290direct (N × H)
191. C3C2×#19150290semidirect

Maximal subgroups

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

subgroupindex
D3×C19⋊#38622
C3⋊#191502902
C3×#191502902
D3×C7⋊D1333
C2×#191502903
D3×#117163287
D3×#117163277
D3×#6442519