Finite Group Databasebeta

← #44472970

Subgroups — #44472970

Order 29988.

230 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 43 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×D357C211yesmaximal, characteristic, complemented
2C3×C17×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C7×C3⋊D357C211yesmaximal, characteristic, complemented
4#23756260—31nomaximal
5D119⋊D21—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C17×C3⋊(C7⋊D7)D311yescharacteristic, complemented
8C7×D357—31no—
9C7×D357—31no—
10C7×D357—61no—
11C7×D357D311yescharacteristic, complemented
12C3×C17×C7⋊D7—31no—
13C3×C7×D119—31no—
14D21⋊D51—71nomaximal
15D21×D51—71nomaximal
16(C7⋊D7)⋊D17—91noHall
17C3×C72×C17—21no—
18C3×C72×C17C2×D311yescharacteristic, complemented
19C3×C72×C17C2×D311yescharacteristic, complemented
20C3⋊D357D711yescharacteristic, complemented
21C7×C3⋊D51—71no—
22C3×D357D711yescharacteristic, complemented
23C3×C17×D21—71no—
24C3×C17×D21—71no—
25C3×C17×D21—143no—
26C3×C7×D51—71no—
27D21⋊D21—171nomaximal, Hall
28C17×C7⋊D7—31no—
29C7×D119—31no—
30C7×D119—91no—
31D21⋊D17—211no—
32D7×D51—211no—
33D7×D51—211no—
34D17×D21—211no—
35C32×C7×C17—23no—
36C32×C7×C17C2×D711yescharacteristic, complemented
37C32×C7×C17C2×D711yescharacteristic, complemented
38C7×C3⋊D21—171no—
39C3×C3⋊(C7⋊D7)D1711yescharacteristic, complemented
40C3×C7×D21—171no—
41C72×C17D3211yescharacteristic, complemented, Hall
42D357—31no—
43D357—31no—
44D357—61no—
45D357D2111yescharacteristic, complemented
46C17×D21—71no—
47C17×D21—71no—
48C17×D21—143no—
49C7×D51—71no—
50C7×D51—211no—
51C7×D51—211no—
52C7×D51—421no—
53C3×D119—31no—
54C3×D7×C17—211no—
55C3×D7×C17—211no—
56C3×D7×C17—423no—
57C3×C7×D17—211no—
58D3×D51—491noHall
59D21⋊D7—511no—
60D7×D21—511no—
61D7×D17—631no—
62D7×D17—631no—
63C32×C72C2×D1711yescharacteristic, complemented, Hall
64C3×C7×C17—21no—
65C3×C7×C17—21no—
66C3×C7×C17—23no—
67C3×C7×C17—23no—
68C3×C7×C17—43no—
69C3×C7×C17D3×D711yescharacteristic, complemented
70C3×C7×C17D3×D711yescharacteristic, complemented
71C3×C7×C17D3×D711yescharacteristic, complemented
72C3×C7×C17C2×D2111yescharacteristic, complemented
73C3⋊D51—71no—
74C3×D51—71no—
75C3×D3×C17—491no—
76C3⋊(C7⋊D7)D5111yescharacteristic, complemented
77C7×D21—171no—
78C7×D21—511no—
79C7×D21—511no—
80C7×D21—1021no—
81C3×C7⋊D7—31no—
82C3×C7×D7—511no—
83(C3⋊D3)⋊D7—1191no—
84D3×D21—1191no—
85D119—31no—
86D119—91no—
87C7×D17—211no—
88C7×D17—631no—
89D7×C17—211no—
90D7×C17—211no—
91D7×C17—423no—
92C2×D51—1471no—
93D3×D17—1471no—
94D72—1531noHall
95C32×C17D7211yescharacteristic, complemented, Hall
96C3×C72—21no—
97C3×C72D3×D1711yescharacteristic, complemented
98C3×C72C2×D5111yescharacteristic, complemented
99C3⋊D21—171no—
100C7×C3⋊D3—1191no—
101C3×D21—71no—
102C3×D21—71no—
103C3×D21—143no—
104C3×D21—171no—
105C3×D3×C7—1191no—
106C7×C17—23no—
107C7×C17D3×D2111yescharacteristic, complemented
108C7×C17(C3⋊D3)⋊D711yescharacteristic, complemented
109C2×C3×C17—1471no—
110D51—71no—
111D51—211no—
112D51—211no—
113D51—421no—
114C3×D17—211no—
115D3×C17—491no—
116C7⋊D7—31no—
117C7×D7—511no—
118C7×D7—1531no—
119C2×D21—3571no—
120D3×D7—3571no—
121D3×D7—3571no—
122D3×D7—3571no—
123C2×D17—4411noHall
124C32×C7—23no—
125C32×C7D7×D1711yescharacteristic, complemented
126C32×C7D7×D1711yescharacteristic, complemented
127C3×C17—21no—
128C3×C17D7×D2111yescharacteristic, complemented
129C3×C17D21⋊D711yescharacteristic, complemented
130C72D3×D5111yescharacteristic, complemented, Sylow
131C2×C3×C7—3571no—
132D21—71no—
133D21—71no—
134D21—143no—
135D21—171no—
136D21—511no—
137D21—511no—
138D21—1021no—
139C3×D7—211no—
140C3×D7—211no—
141C3×D7—423no—
142C3×D7—511no—
143D3×C7—3571no—
144D3×C7—3571no—
145D3×C7—1191no—
146D3×C7—7141no—
147D32—8331noHall
148C2×C17—1471no—
149D17—211no—
150D17—631no—
151C2×D7—10711no—
152C2×D7—10711no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7D17×D2111yescharacteristic, complemented
159C3×C7D7×D5111yescharacteristic, complemented
160C3×C7D7×D5111yescharacteristic, complemented
161C3×C7D21⋊D1711yescharacteristic, complemented
162C3⋊D3—1191no—
163C3×D3—491no—
164C3×D3—1191no—
165C17D21⋊D2111yescharacteristic, complemented, Sylow
166C2×C7—10711no—
167C2×C7—3571no—
168D7—211no—
169D7—211no—
170D7—423no—
171D7—511no—
172D7—1531no—
173C2×D3—24991no—
174C2×D3—24991no—
175C32(C7⋊D7)⋊D1711yescharacteristic, complemented, Sylow
176C7—23no—
177C7D21×D5111yescharacteristic, complemented
178C7D21⋊D5111yescharacteristic, complemented
179C2×C3—3571no—
180C2×C3—1471no—
181D3—491no—
182D3—3571no—
183D3—3571no—
184D3—1191no—
185D3—7141no—
186C22—74971noSylow
187C3—21no—
188C3D119⋊D2111yescharacteristic, complemented
189C3#2375626011yescharacteristic, complemented
190C2—10711no—
191C2—3571no—
192C2—1471no—
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×D357C2semidirect
2. C3×C17×C3⋊(C7⋊D7)C2semidirect
3. C7×C3⋊D357C2semidirect
6. C32×C72×C17C22semidirect
7. C17×C3⋊(C7⋊D7)D3semidirect
11. C7×D357D3semidirect
18. C3×C72×C17C2×D3semidirect
19. C3×C72×C17C2×D3semidirect
20. C3⋊D357D7semidirect
22. C3×D357D7semidirect
36. C32×C7×C17C2×D7semidirect
37. C32×C7×C17C2×D7semidirect
39. C3×C3⋊(C7⋊D7)D17semidirect
41. C72×C17D32semidirect
45. D357D21semidirect
63. C32×C72C2×D17semidirect
69. C3×C7×C17D3×D7semidirect
70. C3×C7×C17D3×D7semidirect
71. C3×C7×C17D3×D7semidirect
72. C3×C7×C17C2×D21semidirect
76. C3⋊(C7⋊D7)D51semidirect
95. C32×C17D72semidirect
97. C3×C72D3×D17semidirect
98. C3×C72C2×D51semidirect
107. C7×C17D3×D21semidirect
108. C7×C17(C3⋊D3)⋊D7semidirect
125. C32×C7D7×D17semidirect
126. C32×C7D7×D17semidirect
128. C3×C17D7×D21semidirect
129. C3×C17D21⋊D7semidirect
130. C72D3×D51semidirect
158. C3×C7D17×D21semidirect
159. C3×C7D7×D51semidirect
160. C3×C7D7×D51semidirect
161. C3×C7D21⋊D17semidirect
165. C17D21⋊D21semidirect
175. C32(C7⋊D7)⋊D17semidirect
177. C7D21×D51semidirect
178. C7D21⋊D51semidirect
188. C3D119⋊D21semidirect
189. C3#23756260semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3572
C3×C17×C3⋊(C7⋊D7)2
C7×C3⋊D3572
#237562603
D119⋊D213
D21⋊D517
D21×D517
D21⋊D2117