Finite Group Databasebeta

← D21×D357 #44472965

Subgroups — D21×D357 #44472965

Order 29988.

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×C17×D21C211yesmaximal, characteristic, complemented
2C3×C7×D357C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C7⋊D119))C211yesmaximal, characteristic, complemented
4D21×D119—31nomaximal
5D7×D357—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D119)—31no—
8C3⋊(C7⋊D119)—31no—
9C3⋊(C7⋊D119)—61no—
10C7×D357D311yescharacteristic, complemented
11C7×C17×D21D311yescharacteristic, complemented
12C3×C7×D119—31no—
13C3×C7×D7×C17—31no—
14D21×D51—71nomaximal
15D3×D357—71nomaximal
16D7×D119—91noHall
17C3×C72×C17—21no—
18C3×C72×C17C2×D311yescharacteristic, complemented
19C3×C72×C17C2×D311yescharacteristic, complemented
20C3⋊D357—71no—
21C3⋊D357—71no—
22C3⋊D357—143no—
23C3×D357D711yescharacteristic, complemented
24C3×C17×D21D711yescharacteristic, complemented
25C3×C7×D51—71no—
26C3×D3×C7×C17—71no—
27D212—171nomaximal, Hall
28C7⋊D119—91no—
29C7×D119—31no—
30C7×D7×C17—31no—
31C2×D357—211no—
32D3×D119—211no—
33D7×D51—211no—
34D17×D21—211no—
35C32×C7×C17—23no—
36C32×C7×C17C2×D711yescharacteristic, complemented
37C32×C7×C17C2×D711yescharacteristic, complemented
38C3⋊(C3⋊(C7⋊D7))—171no—
39C3×C7×D21—171no—
40C3×C7×D21D1711yescharacteristic, complemented
41C72×C17D3211yescharacteristic, complemented, Hall
42C2×C3×C7×C17—211no—
43D357—211no—
44D357—211no—
45D357—211no—
46D357—211no—
47D357—421no—
48D357—421no—
49D357—426no—
50D357—423no—
51D357—423no—
52D357D2111yescharacteristic, direct product factor
53C17×D21D2111yescharacteristic, complemented
54C7×D51—71no—
55D3×C7×C17—71no—
56C3×D119—31no—
57C3×D7×C17—31no—
58C3×C7×D17—211no—
59D3×D51—491noHall
60D7×D21—511no—
61D7×D21—511no—
62C2×D119—631no—
63D7×D17—631no—
64C32×C72C2×D1711yescharacteristic, complemented, Hall
65C3×C7×C17—26no—
66C3×C7×C17—21no—
67C3×C7×C17—21no—
68C3×C7×C17—23no—
69C3×C7×C17—23no—
70C3×C7×C17D3×D711yescharacteristic, complemented
71C3×C7×C17D3×D711yescharacteristic, complemented
72C3×C7×C17C2×D2111yescharacteristic, complemented
73C3×C7×C17C2×D2111yescharacteristic, complemented
74C3⋊D51—491no—
75C3×D51—71no—
76C3×D3×C17—71no—
77C3⋊(C7⋊D7)—511no—
78C3⋊(C7⋊D7)—511no—
79C3⋊(C7⋊D7)—1021no—
80C7×D21—171no—
81C7×D21D5111yescharacteristic, complemented
82C3×C7×D7—31no—
83C3×C7×D7—511no—
84D3×D21—1191no—
85D3×D21—1191no—
86C2×C7×C17—211no—
87D119—31no—
88D119—631no—
89D119—631no—
90D119—1263no—
91C7×D17—211no—
92D7×C17—31no—
93C2×D51—1471no—
94D3×D17—1471no—
95D72—1531noHall
96C32×C17D7211yescharacteristic, complemented, Hall
97C3×C72—21no—
98C3×C72D3×D1711yescharacteristic, complemented
99C3×C72C2×D5111yescharacteristic, complemented
100C3⋊D21—1191no—
101C3⋊D21—1191no—
102C3⋊D21—2383no—
103C3×D21—171no—
104C3×D21D11911yescharacteristic, complemented
105C3×D3×C7—71no—
106C3×D3×C7—1191no—
107C7×C17—23no—
108C7×C17D3×D2111yescharacteristic, complemented
109C7×C17D3×D2111yescharacteristic, complemented
110C2×C3×C17—211no—
111D51—71no—
112D51—2941no—
113D51—1471no—
114D51—1471no—
115C3×D17—211no—
116D3×C17—71no—
117C7⋊D7—1531no—
118C7×D7—31no—
119C7×D7—511no—
120C2×D21—3571no—
121C2×D21—3571no—
122D3×D7—3571no—
123D3×D7—3571no—
124C2×D17—4411noHall
125C32×C7—23no—
126C32×C7D7×D1711yescharacteristic, complemented
127C32×C7C2×D11911yescharacteristic, complemented
128C3×C17—21no—
129C3×C17D7×D2111yescharacteristic, complemented
130C3×C17D7×D2111yescharacteristic, complemented
131C72D3×D5111yescharacteristic, complemented, Sylow
132C2×C3×C7—211no—
133C2×C3×C7—3571no—
134D21—171no—
135D21—3571no—
136D21—3571no—
137D21—3571no—
138D21—3571no—
139D21—7141no—
140D21—7141no—
141D21—7146no—
142D21—7143no—
143D21—7143no—
144D21D35711yescharacteristic, direct product factor
145C3×D7—31no—
146C3×D7—511no—
147D3×C7—71no—
148D3×C7—1191no—
149D32—8331noHall
150C2×C17—211no—
151D17—211no—
152D17—4411no—
153C2×D7—10711no—
154C2×D7—10711no—
155C3×C7—26no—
156C3×C7—21no—
157C3×C7—21no—
158C3×C7—23no—
159C3×C7—23no—
160C3×C7D17×D2111yescharacteristic, complemented
161C3×C7D7×D5111yescharacteristic, complemented
162C3×C7D3×D11911yescharacteristic, complemented
163C3×C7C2×D35711yescharacteristic, complemented
164C3⋊D3—8331no—
165C3×D3—71no—
166C3×D3—1191no—
167C17D21211yescharacteristic, complemented, Sylow
168C2×C7—211no—
169C2×C7—3571no—
170D7—31no—
171D7—10711no—
172D7—10711no—
173D7—511no—
174D7—21423no—
175C2×D3—24991no—
176C2×D3—24991no—
177C32D7×D11911yescharacteristic, complemented, Sylow
178C7—23no—
179C7D3×D35711yescharacteristic, complemented
180C7D21×D5111yescharacteristic, complemented
181C2×C3—211no—
182C2×C3—3571no—
183D3—71no—
184D3—1191no—
185D3—49981no—
186D3—24991no—
187D3—24991no—
188C22—74971noSylow
189C3—21no—
190C3D7×D35711yescharacteristic, complemented
191C3D21×D11911yescharacteristic, complemented
192C2—211no—
193C2—74971no—
194C2—3571no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C17C22
LCSG ▷ C32×C72×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C17×D21C2semidirect
2. C3×C7×D357C2semidirect
3. C3⋊(C3⋊(C7⋊D119))C2semidirect
6. C32×C72×C17C22semidirect
10. C7×D357D3semidirect
11. C7×C17×D21D3semidirect
18. C3×C72×C17C2×D3semidirect
19. C3×C72×C17C2×D3semidirect
23. C3×D357D7semidirect
24. C3×C17×D21D7semidirect
36. C32×C7×C17C2×D7semidirect
37. C32×C7×C17C2×D7semidirect
40. C3×C7×D21D17semidirect
41. C72×C17D32semidirect
52. D357D21direct (N × H)
53. C17×D21D21semidirect
64. C32×C72C2×D17semidirect
70. C3×C7×C17D3×D7semidirect
71. C3×C7×C17D3×D7semidirect
72. C3×C7×C17C2×D21semidirect
73. C3×C7×C17C2×D21semidirect
81. C7×D21D51semidirect
96. C32×C17D72semidirect
98. C3×C72D3×D17semidirect
99. C3×C72C2×D51semidirect
104. C3×D21D119semidirect
108. C7×C17D3×D21semidirect
109. C7×C17D3×D21semidirect
126. C32×C7D7×D17semidirect
127. C32×C7C2×D119semidirect
129. C3×C17D7×D21semidirect
130. C3×C17D7×D21semidirect
131. C72D3×D51semidirect
144. D21D357direct (N × H)
160. C3×C7D17×D21semidirect
161. C3×C7D7×D51semidirect
162. C3×C7D3×D119semidirect
163. C3×C7C2×D357semidirect
167. C17D212semidirect
177. C32D7×D119semidirect
179. C7D3×D357semidirect
180. C7D21×D51semidirect
190. C3D7×D357semidirect
191. C3D21×D119semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C17×D212
C3×C7×D3572
C3⋊(C3⋊(C7⋊D119))2
D21×D1193
D7×D3573
D21×D517
D3×D3577
D21217