Finite Group Databasebeta

← D21×D273 #37525613

Subgroups — D21×D273 #37525613

Order 22932.

248 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 46 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
3C3⋊(C3⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4D21×D91—31nomaximal
5D7×D273—31nomaximal
6C32×C72×C13C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D91)—31no—
8C3⋊(C7⋊D91)—31no—
9C3⋊(C7⋊D91)—61no—
10C7×D273D311yescharacteristic, complemented
11C7×C13×D21D311yescharacteristic, complemented
12C3×C7×D91—31no—
13C3×C7×C13×D7—31no—
14D21×D39—71nomaximal
15D3×D273—71nomaximal
16D7×D91—91noHall
17C3×C72×C13—21no—
18C3×C72×C13C2×D311yescharacteristic, complemented
19C3×C72×C13C2×D311yescharacteristic, complemented
20D212—131nomaximal, Hall
21C3⋊D273—71no—
22C3⋊D273—71no—
23C3⋊D273—143no—
24C3×D273D711yescharacteristic, complemented
25C3×C13×D21D711yescharacteristic, complemented
26C3×C7×D39—71no—
27C3×D3×C7×C13—71no—
28C7⋊D91—91no—
29C7×D91—31no—
30C7×C13×D7—31no—
31C2×D273—211no—
32D3×D91—211no—
33D7×D39—211no—
34D13×D21—211no—
35C3⋊(C3⋊(C7⋊D7))—131no—
36C3×C7×D21—131no—
37C3×C7×D21D1311yescharacteristic, complemented
38C32×C7×C13—23no—
39C32×C7×C13C2×D711yescharacteristic, complemented
40C32×C7×C13C2×D711yescharacteristic, complemented
41C72×C13D3211yescharacteristic, complemented, Hall
42D7×D21—391no—
43D7×D21—391no—
44C2×C3×C7×C13—211no—
45D273—211no—
46D273—211no—
47D273—211no—
48D273—211no—
49D273—421no—
50D273—421no—
51D273—426no—
52D273—423no—
53D273—423no—
54D273D2111yescharacteristic, direct product factor
55C13×D21D2111yescharacteristic, complemented
56C7×D39—71no—
57D3×C7×C13—71no—
58C3×D91—31no—
59C3×C13×D7—31no—
60C3×C7×D13—211no—
61D3×D39—491noHall
62C32×C72C2×D1311yescharacteristic, complemented, Hall
63C2×D91—631no—
64D7×D13—631no—
65C3⋊(C7⋊D7)—391no—
66C3⋊(C7⋊D7)—391no—
67C3⋊(C7⋊D7)—781no—
68C7×D21—131no—
69C7×D21D3911yescharacteristic, complemented
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×D2111yescharacteristic, complemented
80C3×C7×C13C2×D2111yescharacteristic, complemented
81D3×D21—911no—
82D3×D21—911no—
83C3⋊D39—491no—
84C3×D39—71no—
85C3×D3×C13—71no—
86D72—1171noHall
87C2×C7×C13—211no—
88D91—31no—
89D91—631no—
90D91—631no—
91D91—1263no—
92C7×D13—211no—
93C13×D7—31no—
94C2×D39—1471no—
95D3×D13—1471no—
96C3×C72—21no—
97C3×C72D3×D1311yescharacteristic, complemented
98C3×C72C2×D3911yescharacteristic, complemented
99C3⋊D21—911no—
100C3⋊D21—911no—
101C3⋊D21—1823no—
102C3×D21—131no—
103C3×D21D9111yescharacteristic, complemented
104C3×D3×C7—71no—
105C3×D3×C7—911no—
106C32×C13D7211yescharacteristic, complemented, Hall
107C7⋊D7—1171no—
108C7×D7—31no—
109C7×D7—391no—
110C7×C13—23no—
111C7×C13D3×D2111yescharacteristic, complemented
112C7×C13D3×D2111yescharacteristic, complemented
113C2×D21—2731no—
114C2×D21—2731no—
115D3×D7—2731no—
116D3×D7—2731no—
117C2×C3×C13—211no—
118D39—71no—
119D39—2941no—
120D39—1471no—
121D39—1471no—
122C3×D13—211no—
123D3×C13—71no—
124C32×C7—23no—
125C32×C7D7×D1311yescharacteristic, complemented
126C32×C7C2×D9111yescharacteristic, complemented
127C2×D13—4411noHall
128C72D3×D3911yescharacteristic, complemented, Sylow
129C2×C3×C7—2731no—
130C2×C3×C7—211no—
131D21—131no—
132D21—2731no—
133D21—2731no—
134D21—2731no—
135D21—2731no—
136D21—5463no—
137D21—5463no—
138D21—5461no—
139D21—5461no—
140D21—5466no—
141D21D27311yescharacteristic, direct product factor
142C3×D7—31no—
143C3×D7—391no—
144D3×C7—71no—
145D3×C7—911no—
146C3×C13—21no—
147C3×C13D7×D2111yescharacteristic, complemented
148C3×C13D7×D2111yescharacteristic, complemented
149D32—6371noHall
150C2×D7—8191no—
151C2×D7—8191no—
152C2×C13—211no—
153D13—211no—
154D13—4411no—
155C3×C7—26no—
156C3×C7—21no—
157C3×C7—21no—
158C3×C7—23no—
159C3×C7—23no—
160C3×C7D13×D2111yescharacteristic, complemented
161C3×C7D7×D3911yescharacteristic, complemented
162C3×C7D3×D9111yescharacteristic, complemented
163C3×C7C2×D27311yescharacteristic, complemented
164C3⋊D3—6371no—
165C3×D3—71no—
166C3×D3—911no—
167C2×C7—2731no—
168C2×C7—211no—
169D7—31no—
170D7—391no—
171D7—8191no—
172D7—8191no—
173D7—16383no—
174C13D21211yescharacteristic, complemented, Sylow
175C2×D3—19111no—
176C2×D3—19111no—
177C32D7×D9111yescharacteristic, complemented, Sylow
178C7—23no—
179C7D3×D27311yescharacteristic, complemented
180C7D21×D3911yescharacteristic, complemented
181C2×C3—2731no—
182C2×C3—211no—
183D3—71no—
184D3—911no—
185D3—19111no—
186D3—19111no—
187D3—38221no—
188C22—57331noSylow
189C3—21no—
190C3D7×D27311yescharacteristic, complemented
191C3D21×D9111yescharacteristic, complemented
192C2—2731no—
193C2—211no—
194C2—57331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C13C22
LCSG ▷ C32×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D21C2semidirect
2. C3×C7×D273C2semidirect
3. C3⋊(C3⋊(C7⋊D91))C2semidirect
6. C32×C72×C13C22semidirect
10. C7×D273D3semidirect
11. C7×C13×D21D3semidirect
18. C3×C72×C13C2×D3semidirect
19. C3×C72×C13C2×D3semidirect
24. C3×D273D7semidirect
25. C3×C13×D21D7semidirect
37. C3×C7×D21D13semidirect
39. C32×C7×C13C2×D7semidirect
40. C32×C7×C13C2×D7semidirect
41. C72×C13D32semidirect
54. D273D21direct (N × H)
55. C13×D21D21semidirect
62. C32×C72C2×D13semidirect
69. C7×D21D39semidirect
77. C3×C7×C13D3×D7semidirect
78. C3×C7×C13D3×D7semidirect
79. C3×C7×C13C2×D21semidirect
80. C3×C7×C13C2×D21semidirect
97. C3×C72D3×D13semidirect
98. C3×C72C2×D39semidirect
103. C3×D21D91semidirect
106. C32×C13D72semidirect
111. C7×C13D3×D21semidirect
112. C7×C13D3×D21semidirect
125. C32×C7D7×D13semidirect
126. C32×C7C2×D91semidirect
128. C72D3×D39semidirect
141. D21D273direct (N × H)
147. C3×C13D7×D21semidirect
148. C3×C13D7×D21semidirect
160. C3×C7D13×D21semidirect
161. C3×C7D7×D39semidirect
162. C3×C7D3×D91semidirect
163. C3×C7C2×D273semidirect
174. C13D212semidirect
177. C32D7×D91semidirect
179. C7D3×D273semidirect
180. C7D21×D39semidirect
190. C3D7×D273semidirect
191. C3D21×D91semidirect

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
C3⋊(C3⋊(C7⋊D91))2
D21×D913
D7×D2733
D21×D397
D3×D2737
D21213