Finite Group Databasebeta

← C7×D21×D39 #37525608

Subgroups — C7×D21×D39 #37525608

Order 22932.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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×C72×D39C211yesmaximal, characteristic, complemented
2C3×C7×C13×D21C211yesmaximal, characteristic, complemented
3C7×C3⋊D273C211yesmaximal, characteristic, complemented
4C7×D7×D39—31nomaximal
5C7×D13×D21—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C7×D273—31no—
8C7×D273—31no—
9C7×D273—61no—
10C7×C13×D21D311yescharacteristic, complemented
11C72×D39D311yescharacteristic, complemented
12C3×C7×C13×D7—31no—
13C3×C72×D13—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
20D3×C7×D21—131nomaximal, Hall
21C3⋊D273C2×C711yescharacteristic, complemented
22C7×C3⋊D39—71no—
23C3×C13×D21C2×C711yescharacteristic, complemented
24C3×C7×D39—23no—
25C3×C7×D39D711yescharacteristic, complemented
26C3×C7×D39C2×C711yescharacteristic, complemented
27C3×D3×C7×C13—71no—
28C7×D91—91no—
29C7×C13×D7—31no—
30C72×D13—31no—
31C2×C7×D39—211no—
32D7×D39—31no—
33D13×D21—31no—
34D3×C7×D13—211no—
35C7×C3⋊D21—131no—
36C3×C7×D21D1311yescharacteristic, complemented
37C3×D3×C72—131no—
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C22×C711yescharacteristic, complemented
41C72×C13D3211yescharacteristic, complemented, Hall
42C2×C7×D21—391no—
43D3×C7×D7—391no—
44C2×C3×C7×C13—211no—
45D273—31no—
46D273—31no—
47D273—61no—
48C13×D21D3×C711yescharacteristic, complemented
49C7×D39—23no—
50C7×D39—211no—
51C7×D39—211no—
52C7×D39—421no—
53C7×D39D3×C711yescharacteristic, complemented
54C7×D39D2111yescharacteristic, direct product factor
55D3×C7×C13—71no—
56C3×C13×D7—31no—
57C3×C7×D13—31no—
58C3×C7×D13—31no—
59C3×C7×D13—63no—
60D3×D39—71noHall
61C32×C72C2×D1311yescharacteristic, complemented, Hall
62C2×C7×D13—631no—
63D7×D13—91no—
64C2×C3×C72—391no—
65C7×D21—391no—
66C7×D21—391no—
67C7×D21—781no—
68C7×D21D3911yescharacteristic, direct product factor
69D3×C72—131no—
70C3×C7×D7—31no—
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×D3×C711yescharacteristic, complemented
78C3×C7×C13C2×D3×C711yescharacteristic, complemented
79C3×C7×C13C2×D2111yescharacteristic, complemented
80D3×D21—131no—
81D32×C7—911no—
82C3⋊D39—71no—
83C3×D39C7×D711yescharacteristic, complemented
84C3×D3×C13—71no—
85C2×C7×D7—1171noHall
86C2×C7×C13—211no—
87D91—91no—
88C7×D13—31no—
89C7×D13—31no—
90C7×D13—63no—
91C7×D13—631no—
92C13×D7—31no—
93C2×D39—211no—
94D3×D13—211no—
95C3×C72—21no—
96C3×C72D3×D1311yescharacteristic, complemented
97C3×C72C2×D3911yescharacteristic, complemented
98C3⋊D21—131no—
99C7×C3⋊D3—911no—
100C3×D21C7×D1311yescharacteristic, complemented
101C3×D3×C7—71no—
102C3×D3×C7—131no—
103C3×D3×C7—131no—
104C3×D3×C7—263no—
105C32×C13C2×C7×D711yescharacteristic, complemented, Hall
106C2×C72—391no—
107C7×D7—31no—
108C7×D7—1171no—
109C7×C13—23no—
110C7×C13D32×C711yescharacteristic, complemented
111C7×C13D3×D2111yescharacteristic, complemented
112C2×D21—391no—
113C2×D3×C7—2731no—
114C2×D3×C7—2731no—
115D3×D7—391no—
116C2×C3×C13—211no—
117D39—211no—
118D39—211no—
119D39—421no—
120D39C7×D2111yescharacteristic, direct product factor
121C3×D13—31no—
122D3×C13—71no—
123C32×C7—23no—
124C32×C7D7×D1311yescharacteristic, complemented
125C32×C7C2×C7×D1311yescharacteristic, complemented
126C2×D13—631noHall
127C72D3×D3911yescharacteristic, complemented, Sylow
128C2×C3×C7—211no—
129C2×C3×C7—391no—
130C2×C3×C7—391no—
131C2×C3×C7—783no—
132D21—391no—
133D21—391no—
134D21—781no—
135D21C7×D3911yescharacteristic, direct product factor
136C3×D7—31no—
137D3×C7—71no—
138D3×C7—131no—
139D3×C7—131no—
140D3×C7—2731no—
141D3×C7—2731no—
142D3×C7—263no—
143D3×C7—5461no—
144C3×C13—21no—
145C3×C13D3×C7×D711yescharacteristic, complemented
146C3×C13C2×C7×D2111yescharacteristic, complemented
147D32—911noHall
148C22×C7—8191no—
149C2×D7—1171no—
150C2×C13—211no—
151D13—31no—
152D13—631no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D3×C7×D1311yescharacteristic, complemented
159C3×C7D13×D2111yescharacteristic, complemented
160C3×C7D7×D3911yescharacteristic, complemented
161C3×C7C2×C7×D3911yescharacteristic, complemented
162C3⋊D3—911no—
163C3×D3—71no—
164C3×D3—131no—
165C2×C7—211no—
166C2×C7—391no—
167C2×C7—391no—
168C2×C7—8191no—
169C2×C7—783no—
170D7—31no—
171D7—1171no—
172C13D3×C7×D2111yescharacteristic, complemented, Sylow
173C2×D3—2731no—
174C2×D3—2731no—
175C32C7×D7×D1311yescharacteristic, complemented, Sylow
176C7—23no—
177C7D3×C7×D3911yescharacteristic, complemented
178C7D21×D3911yescharacteristic, direct product factor
179C2×C3—211no—
180C2×C3—391no—
181D3—71no—
182D3—131no—
183D3—2731no—
184D3—2731no—
185D3—5461no—
186C22—8191noSylow
187C3—21no—
188C3C7×D13×D2111yescharacteristic, complemented
189C3C7×D7×D3911yescharacteristic, complemented
190C2—211no—
191C2—391no—
192C2—8191no—
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×C72×D39C2semidirect
2. C3×C7×C13×D21C2semidirect
3. C7×C3⋊D273C2semidirect
6. C32×C72×C13C22semidirect
10. C7×C13×D21D3semidirect
11. C72×D39D3semidirect
14. D21×D39C7direct (N × H)
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C2×D3semidirect
21. C3⋊D273C2×C7semidirect
23. C3×C13×D21C2×C7semidirect
25. C3×C7×D39D7semidirect
26. C3×C7×D39C2×C7semidirect
36. C3×C7×D21D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C22×C7semidirect
41. C72×C13D32semidirect
48. C13×D21D3×C7semidirect
53. C7×D39D3×C7semidirect
54. C7×D39D21direct (N × H)
61. C32×C72C2×D13semidirect
68. C7×D21D39direct (N × H)
76. C3×C7×C13D3×D7semidirect
77. C3×C7×C13C2×D3×C7semidirect
78. C3×C7×C13C2×D3×C7semidirect
79. C3×C7×C13C2×D21semidirect
83. C3×D39C7×D7semidirect
96. C3×C72D3×D13semidirect
97. C3×C72C2×D39semidirect
100. C3×D21C7×D13semidirect
105. C32×C13C2×C7×D7semidirect
110. C7×C13D32×C7semidirect
111. C7×C13D3×D21semidirect
120. D39C7×D21direct (N × H)
124. C32×C7D7×D13semidirect
125. C32×C7C2×C7×D13semidirect
127. C72D3×D39semidirect
135. D21C7×D39direct (N × H)
145. C3×C13D3×C7×D7semidirect
146. C3×C13C2×C7×D21semidirect
158. C3×C7D3×C7×D13semidirect
159. C3×C7D13×D21semidirect
160. C3×C7D7×D39semidirect
161. C3×C7C2×C7×D39semidirect
172. C13D3×C7×D21semidirect
175. C32C7×D7×D13semidirect
177. C7D3×C7×D39semidirect
178. C7D21×D39direct (N × H)
188. C3C7×D13×D21semidirect
189. C3C7×D7×D39semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D392
C3×C7×C13×D212
C7×C3⋊D2732
C7×D7×D393
C7×D13×D213
D21×D397
D3×C7×D397
D3×C7×D2113