Finite Group Databasebeta

← C3×D3×C7×D91 #37525587

Subgroups — C3×D3×C7×D91 #37525587

Order 22932.

230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C32×C7×D91C211yesmaximal, characteristic, complemented
2C3×D3×C72×C13C211yesmaximal, characteristic, complemented
3C3×C7×D273C211yesmaximal, characteristic, complemented
4C2×C3×C7×D91—31nomaximal
5D3×C7×D91C311yesmaximal, characteristic, direct product factor
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C7×D273C2×C311yescharacteristic, complemented
8D3×C72×C13C2×C311yescharacteristic, complemented
9C3×C7×D91—21no—
10C3×C7×D91—31no—
11C3×C7×D91D311yescharacteristic, direct product factor
12C3×C7×D91C2×C311yescharacteristic, complemented
13C2×C3×C72×C13—31no—
14C3×D3×D91C711yesmaximal, characteristic, direct product factor
15C3×D3×C7×D13—71nomaximal
16C2×C7×D91—31noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C22×C311yescharacteristic, complemented
20C3×D3×C7×D7—131nomaximal, Hall
21C3×D273C2×C711yescharacteristic, complemented
22C3×C7×D39—71no—
23C3×D3×C7×C13—23no—
24C3×D3×C7×C13D711yescharacteristic, complemented
25C3×D3×C7×C13C2×C711yescharacteristic, complemented
26C32×D91C2×C711yescharacteristic, complemented
27C32×C7×D13—71no—
28C2×C72×C13—31no—
29C7×D91—31no—
30C7×D91C3×D311yescharacteristic, direct product factor
31C2×C3×D91—31no—
32C2×C3×C7×D13—211no—
33D3×D91C3×C711yescharacteristic, direct product factor
34D3×C7×D13—71no—
35C3×C7×D21—131no—
36C3×D3×C72D1311yescharacteristic, complemented
37C32×C7×D7—131no—
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C22×C711yescharacteristic, complemented
41C72×C13C2×C3×D311yescharacteristic, complemented, Hall
42C2×C3×C7×D7—391no—
43D3×C7×D7—131no—
44C2×C3×C7×C13—31no—
45C2×C3×C7×C13—31no—
46C2×C3×C7×C13—63no—
47D273C2×C3×C711yescharacteristic, complemented
48C7×D39—71no—
49D3×C7×C13—23no—
50D3×C7×C13C3×D711yescharacteristic, complemented
51D3×C7×C13C2×C3×C711yescharacteristic, complemented
52C3×D91—21no—
53C3×D91—31no—
54C3×D91D3×C711yescharacteristic, direct product factor
55C3×D91C2×C3×C711yescharacteristic, complemented
56C3×C7×D13—71no—
57C3×C7×D13—71no—
58C3×C7×D13—141no—
59C3×C7×D13—211no—
60C3×D3×D13—71noHall
61C32×C72C2×D1311yescharacteristic, complemented, Hall
62C2×D91—31no—
63C2×C7×D13—211no—
64C2×C3×C72—31no—
65C7×D21—131no—
66D3×C72C3×D1311yescharacteristic, complemented
67C3×C7×D7—131no—
68C3×C7×D7—131no—
69C3×C7×D7—261no—
70C3×C7×D7—391no—
71C3×C7×C13—23no—
72C3×C7×C13—23no—
73C3×C7×C13—21no—
74C3×C7×C13—21no—
75C3×C7×C13—43no—
76C3×C7×C13D3×D711yescharacteristic, complemented
77C3×C7×C13C2×C3×D711yescharacteristic, complemented
78C3×C7×C13C2×D3×C711yescharacteristic, complemented
79C3×C7×C13C22×C3×C711yescharacteristic, complemented
80C2×C3×D3×C7—911no—
81C3×D3×D7—131no—
82C3×D39—71no—
83C3×D3×C13C7×D711yescharacteristic, complemented
84C32×D13—71no—
85C2×C7×D7—391noHall
86C2×C7×C13—31no—
87C2×C7×C13—31no—
88C2×C7×C13—63no—
89D91—31no—
90D91C3×D3×C711yescharacteristic, direct product factor
91C7×D13—71no—
92C7×D13—211no—
93C2×C3×D13—211no—
94D3×D13—71no—
95C3×C72—21no—
96C3×C72D3×D1311yescharacteristic, complemented
97C3×C72C2×C3×D1311yescharacteristic, complemented
98C2×C32×C7—911no—
99C3×D21—131no—
100C3×D3×C7—23no—
101C3×D3×C7—911no—
102C3×D3×C7C7×D1311yescharacteristic, complemented
103C3×D3×C7D9111yescharacteristic, direct product factor
104C32×D7—131no—
105C32×C13C2×C7×D711yescharacteristic, complemented, Hall
106C2×C72—31no—
107C7×D7—131no—
108C7×D7—391no—
109C7×C13—23no—
110C7×C13C3×D3×D711yescharacteristic, complemented
111C7×C13C2×C3×D3×C711yescharacteristic, complemented
112C22×C3×C7—2731no—
113C2×D3×C7—911no—
114C2×C3×D7—391no—
115D3×D7—131no—
116C2×C3×C13—31no—
117D39—71no—
118C3×D13—71no—
119C3×D13—71no—
120C3×D13—141no—
121C3×D13—211no—
122D3×C13C3×C7×D711yescharacteristic, complemented
123C32×C7—23no—
124C32×C7C2×C7×D1311yescharacteristic, complemented
125C32×C7C2×D9111yescharacteristic, complemented
126C2×D13—211noHall
127C72C3×D3×D1311yescharacteristic, complemented, Sylow
128C2×C3×C7—31no—
129C2×C3×C7—31no—
130C2×C3×C7—63no—
131C2×C3×C7—2731no—
132C2×C3×C7—911no—
133C2×C3×C7—911no—
134C2×C3×C7—1821no—
135D21—131no—
136C3×D7—131no—
137C3×D7—131no—
138C3×D7—261no—
139C3×D7—391no—
140D3×C7—23no—
141D3×C7—911no—
142D3×C7C3×C7×D1311yescharacteristic, complemented
143D3×C7C3×D9111yescharacteristic, direct product factor
144C3×C13—21no—
145C3×C13D3×C7×D711yescharacteristic, complemented
146C3×C13C2×C3×C7×D711yescharacteristic, complemented
147C2×C3×D3—911noHall
148C22×C7—2731no—
149C2×D7—391no—
150C2×C13—31no—
151D13—71no—
152D13—211no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D3×C7×D1311yescharacteristic, complemented
159C3×C7D3×D9111yescharacteristic, direct product factor
160C3×C7C2×C3×C7×D1311yescharacteristic, complemented
161C3×C7C2×C3×D9111yescharacteristic, complemented
162C2×C32—911no—
163C3×D3—911no—
164C3×D3C7×D9111yescharacteristic, direct product factor
165C2×C7—31no—
166C2×C7—31no—
167C2×C7—63no—
168C2×C7—2731no—
169C2×C7—911no—
170D7—131no—
171D7—391no—
172C13C3×D3×C7×D711yescharacteristic, complemented, Sylow
173C22×C3—2731no—
174C2×D3—911no—
175C32C2×C7×D9111yescharacteristic, complemented, Sylow
176C7—23no—
177C7C3×D3×C7×D1311yescharacteristic, complemented
178C7C3×D3×D9111yescharacteristic, direct product factor
179C2×C3—31no—
180C2×C3—2731no—
181C2×C3—911no—
182C2×C3—911no—
183C2×C3—1821no—
184D3—911no—
185D3C3×C7×D9111yescharacteristic, direct product factor
186C22—2731noSylow
187C3—21no—
188C3D3×C7×D9111yescharacteristic, direct product factor
189C3C2×C3×C7×D9111yescharacteristic, complemented
190C2—31no—
191C2—2731no—
192C2—911no—
subgroupG/H
center, hypercenterC3×C7D3×D91
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D91C2semidirect
2. C3×D3×C72×C13C2semidirect
3. C3×C7×D273C2semidirect
5. D3×C7×D91C3direct (N × H)
6. C32×C72×C13C22semidirect
7. C7×D273C2×C3semidirect
8. D3×C72×C13C2×C3semidirect
11. C3×C7×D91D3direct (N × H)
12. C3×C7×D91C2×C3semidirect
14. C3×D3×D91C7direct (N × H)
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C22×C3semidirect
21. C3×D273C2×C7semidirect
24. C3×D3×C7×C13D7semidirect
25. C3×D3×C7×C13C2×C7semidirect
26. C32×D91C2×C7semidirect
30. C7×D91C3×D3direct (N × H)
33. D3×D91C3×C7direct (N × H)
36. C3×D3×C72D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C22×C7semidirect
41. C72×C13C2×C3×D3semidirect
47. D273C2×C3×C7semidirect
50. D3×C7×C13C3×D7semidirect
51. D3×C7×C13C2×C3×C7semidirect
54. C3×D91D3×C7direct (N × H)
55. C3×D91C2×C3×C7semidirect
61. C32×C72C2×D13semidirect
66. D3×C72C3×D13semidirect
76. C3×C7×C13D3×D7semidirect
77. C3×C7×C13C2×C3×D7semidirect
78. C3×C7×C13C2×D3×C7semidirect
79. C3×C7×C13C22×C3×C7semidirect
83. C3×D3×C13C7×D7semidirect
90. D91C3×D3×C7direct (N × H)
96. C3×C72D3×D13semidirect
97. C3×C72C2×C3×D13semidirect
102. C3×D3×C7C7×D13semidirect
103. C3×D3×C7D91direct (N × H)
105. C32×C13C2×C7×D7semidirect
110. C7×C13C3×D3×D7semidirect
111. C7×C13C2×C3×D3×C7semidirect
122. D3×C13C3×C7×D7semidirect
124. C32×C7C2×C7×D13semidirect
125. C32×C7C2×D91semidirect
127. C72C3×D3×D13semidirect
142. D3×C7C3×C7×D13semidirect
143. D3×C7C3×D91direct (N × H)
145. C3×C13D3×C7×D7semidirect
146. C3×C13C2×C3×C7×D7semidirect
158. C3×C7D3×C7×D13semidirect
159. C3×C7D3×D91direct (N × H)
160. C3×C7C2×C3×C7×D13semidirect
161. C3×C7C2×C3×D91semidirect
164. C3×D3C7×D91direct (N × H)
172. C13C3×D3×C7×D7semidirect
175. C32C2×C7×D91semidirect
177. C7C3×D3×C7×D13semidirect
178. C7C3×D3×D91direct (N × H)
185. D3C3×C7×D91direct (N × H)
188. C3D3×C7×D91direct (N × H)
189. C3C2×C3×C7×D91semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D912
C3×D3×C72×C132
C3×C7×D2732
C2×C3×C7×D913
D3×C7×D913
C3×D3×D917
C3×D3×C7×D137
C3×D3×C7×D713