Finite Group Databasebeta

← C7×D21⋊D39 #37525610

Subgroups — C7×D21⋊D39 #37525610

Order 22932.

248 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 50 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×C7×C13×D21C211yesmaximal, characteristic, complemented
2C3×C7×D273C211yesmaximal, characteristic, complemented
3C72×C3⋊D39C211yesmaximal, characteristic, complemented
4C7×D21⋊D13—31nomaximal
5C7×D7×D39—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C7×D273D311yescharacteristic, complemented
8C7×C13×D21D311yescharacteristic, complemented
9C72×D39—31no—
10C72×D39—31no—
11C72×D39—61no—
12C3×C7×D91—31no—
13C3×C7×C13×D7—31no—
14D21⋊D39C711yesmaximal, characteristic, direct product factor
15D3×C7×D39—71nomaximal
16C7×D7×D13—91noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C2×D311yescharacteristic, complemented
20C7×(C3⋊D3)⋊D7—131nomaximal, Hall
21C7×C3⋊D39—23no—
22C7×C3⋊D39D711yescharacteristic, complemented
23C7×C3⋊D39C2×C711yescharacteristic, complemented
24C3×D273C2×C711yescharacteristic, complemented
25C3×C13×D21C2×C711yescharacteristic, complemented
26C3×C7×D39—71no—
27C3×D3×C7×C13—71no—
28C7×D91—31no—
29C7×C13×D7—31no—
30C72×D13—91no—
31C2×C7×D39—211no—
32D21⋊D13—31no—
33D7×D39—31no—
34D3×C7×D13—211no—
35C72×C3⋊D3—131no—
36C3×C7×D21—131no—
37C3×C7×D21D1311yescharacteristic, complemented
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C22×C711yescharacteristic, complemented
41C72×C13D3211yescharacteristic, complemented, Hall
42D3×C7×D7—391no—
43D3×C7×D7—391no—
44C2×C3×C7×C13—211no—
45D273D3×C711yescharacteristic, complemented
46C13×D21D3×C711yescharacteristic, complemented
47C7×D39—31no—
48C7×D39—31no—
49C7×D39—31no—
50C7×D39—31no—
51C7×D39—61no—
52C7×D39—61no—
53C7×D39—63no—
54C7×D39—63no—
55C7×D39—66no—
56C7×D39—71no—
57D3×C7×C13—71no—
58C3×D91—31no—
59C3×C13×D7—31no—
60C3×C7×D13—211no—
61D3×D39—71noHall
62C32×C72C2×D1311yescharacteristic, complemented, Hall
63C2×C7×D13—631no—
64D7×D13—91no—
65C7×D21—131no—
66C7×D21D3911yescharacteristic, complemented
67D3×C72—391no—
68D3×C72—391no—
69D3×C72—781no—
70C3×C7×D7—31no—
71C3×C7×D7—391no—
72C3×C7×C13—26no—
73C3×C7×C13—23no—
74C3×C7×C13—23no—
75C3×C7×C13—21no—
76C3×C7×C13—21no—
77C3×C7×C13D3×D711yescharacteristic, complemented
78C3×C7×C13D3×D711yescharacteristic, complemented
79C3×C7×C13C2×D3×C711yescharacteristic, complemented
80C3×C7×C13C2×D3×C711yescharacteristic, complemented
81(C3⋊D3)⋊D7—131no—
82D32×C7—911no—
83C3⋊D39C7×D711yescharacteristic, complemented
84C3×D39—71no—
85C3×D3×C13—71no—
86C2×C7×D7—1171noHall
87C2×C7×C13—211no—
88D91—31no—
89C7×D13—91no—
90C7×D13—91no—
91C7×D13—183no—
92C7×D13—211no—
93C13×D7—31no—
94C2×D39—211no—
95D3×D13—211no—
96C3×C72—21no—
97C3×C72D3×D1311yescharacteristic, complemented
98C3×C72C2×D3911yescharacteristic, complemented
99C7×C3⋊D3—131no—
100C7×C3⋊D3—131no—
101C7×C3⋊D3—263no—
102C3×D21—131no—
103C3×D21C7×D1311yescharacteristic, complemented
104C3×D3×C7—71no—
105C3×D3×C7—911no—
106C32×C13C2×C7×D711yescharacteristic, complemented, Hall
107C2×C72—1171no—
108C7×D7—31no—
109C7×D7—391no—
110C7×C13—23no—
111C7×C13D32×C711yescharacteristic, complemented
112C7×C13(C3⋊D3)⋊D711yescharacteristic, complemented
113C2×D3×C7—2731no—
114C2×D3×C7—2731no—
115D3×D7—391no—
116D3×D7—391no—
117C2×C3×C13—211no—
118D39—31no—
119D39—31no—
120D39—61no—
121D39—71no—
122C3×D13—211no—
123D3×C13—71no—
124C32×C7—23no—
125C32×C7D7×D1311yescharacteristic, complemented
126C32×C7C2×C7×D1311yescharacteristic, complemented
127C2×D13—631noHall
128C72D3×D3911yescharacteristic, complemented, Sylow
129C2×C3×C7—2731no—
130C2×C3×C7—211no—
131D21—131no—
132D21C7×D3911yescharacteristic, complemented
133C3×D7—31no—
134C3×D7—391no—
135D3×C7—71no—
136D3×C7—391no—
137D3×C7—391no—
138D3×C7—391no—
139D3×C7—391no—
140D3×C7—783no—
141D3×C7—783no—
142D3×C7—781no—
143D3×C7—781no—
144D3×C7—786no—
145D3×C7—911no—
146C3×C13—21no—
147C3×C13D3×C7×D711yescharacteristic, complemented
148C3×C13D3×C7×D711yescharacteristic, complemented
149D32—911noHall
150C22×C7—8191no—
151C2×D7—1171no—
152C2×C13—211no—
153D13—91no—
154D13—211no—
155C3×C7—26no—
156C3×C7—21no—
157C3×C7—21no—
158C3×C7—23no—
159C3×C7—23no—
160C3×C7D3×C7×D1311yescharacteristic, complemented
161C3×C7D7×D3911yescharacteristic, complemented
162C3×C7D21⋊D1311yescharacteristic, complemented
163C3×C7C2×C7×D3911yescharacteristic, complemented
164C3⋊D3—131no—
165C3×D3—71no—
166C3×D3—911no—
167C2×C7—2731no—
168C2×C7—211no—
169C2×C7—1171no—
170C2×C7—1171no—
171C2×C7—2343no—
172D7—31no—
173D7—391no—
174C13C7×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
175C2×D3—2731no—
176C2×D3—2731no—
177C32C7×D7×D1311yescharacteristic, complemented, Sylow
178C7—23no—
179C7D3×C7×D3911yescharacteristic, complemented
180C7D21⋊D3911yescharacteristic, direct product factor
181C2×C3—2731no—
182C2×C3—211no—
183D3—71no—
184D3—391no—
185D3—391no—
186D3—781no—
187D3—911no—
188C22—8191noSylow
189C3—21no—
190C3C7×D7×D3911yescharacteristic, complemented
191C3C7×D21⋊D1311yescharacteristic, complemented
192C2—2731no—
193C2—211no—
194C2—1171no—
subgroupG/H
center, hypercenterC7D21⋊D39
commutator, cosocle, hypocenterC32×C7×C13C22×C7
FrattiniC1G
Fitting, socleC32×C72×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D21C2semidirect
2. C3×C7×D273C2semidirect
3. C72×C3⋊D39C2semidirect
6. C32×C72×C13C22semidirect
7. C7×D273D3semidirect
8. C7×C13×D21D3semidirect
14. D21⋊D39C7direct (N × H)
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C2×D3semidirect
22. C7×C3⋊D39D7semidirect
23. C7×C3⋊D39C2×C7semidirect
24. C3×D273C2×C7semidirect
25. C3×C13×D21C2×C7semidirect
37. C3×C7×D21D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C22×C7semidirect
41. C72×C13D32semidirect
45. D273D3×C7semidirect
46. C13×D21D3×C7semidirect
62. C32×C72C2×D13semidirect
66. C7×D21D39semidirect
77. C3×C7×C13D3×D7semidirect
78. C3×C7×C13D3×D7semidirect
79. C3×C7×C13C2×D3×C7semidirect
80. C3×C7×C13C2×D3×C7semidirect
83. C3⋊D39C7×D7semidirect
97. C3×C72D3×D13semidirect
98. C3×C72C2×D39semidirect
103. C3×D21C7×D13semidirect
106. C32×C13C2×C7×D7semidirect
111. C7×C13D32×C7semidirect
112. C7×C13(C3⋊D3)⋊D7semidirect
125. C32×C7D7×D13semidirect
126. C32×C7C2×C7×D13semidirect
128. C72D3×D39semidirect
132. D21C7×D39semidirect
147. C3×C13D3×C7×D7semidirect
148. C3×C13D3×C7×D7semidirect
160. C3×C7D3×C7×D13semidirect
161. C3×C7D7×D39semidirect
162. C3×C7D21⋊D13semidirect
163. C3×C7C2×C7×D39semidirect
174. C13C7×(C3⋊D3)⋊D7semidirect
177. C32C7×D7×D13semidirect
179. C7D3×C7×D39semidirect
180. C7D21⋊D39direct (N × H)
190. C3C7×D7×D39semidirect
191. C3C7×D21⋊D13semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D212
C3×C7×D2732
C72×C3⋊D392
C7×D21⋊D133
C7×D7×D393
D21⋊D397
D3×C7×D397
C7×(C3⋊D3)⋊D713