Finite Group Databasebeta

← C3×C7×D21⋊D17 #44472940

Subgroups — C3×C7×D21⋊D17 #44472940

Order 29988.

230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C32×C7×D119C211yesmaximal, characteristic, complemented
2C3×C72×D51C211yesmaximal, characteristic, complemented
3C3×C7×C17×D21C211yesmaximal, characteristic, complemented
4C7×D21⋊D17C311yesmaximal, characteristic, direct product factor
5C3×C7×D7×D17—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C7×C17×D21C2×C311yescharacteristic, complemented
8C72×D51C2×C311yescharacteristic, complemented
9C3×C7×D119—21no—
10C3×C7×D119D311yescharacteristic, complemented
11C3×C7×D119C2×C311yescharacteristic, complemented
12C3×C7×D7×C17—31no—
13C3×C72×D17—31no—
14C3×D21⋊D17C711yesmaximal, characteristic, direct product factor
15C3×D3×C7×D17—71nomaximal
16C7×D7×D17—31noHall
17C3×C72×C17—21no—
18C3×C72×C17C2×D311yescharacteristic, complemented
19C3×C72×C17C22×C311yescharacteristic, complemented
20C3×C17×D21C2×C711yescharacteristic, complemented
21C3×C7×D51—23no—
22C3×C7×D51D711yescharacteristic, complemented
23C3×C7×D51C2×C711yescharacteristic, complemented
24C3×D3×C7×C17—71no—
25C32×D119C2×C711yescharacteristic, complemented
26C32×C7×D17—71no—
27C3×D3×C7×D7—171nomaximal, Hall
28C7×D119C3×D311yescharacteristic, complemented
29C7×D7×C17—31no—
30C72×D17—31no—
31C2×C3×C7×D17—211no—
32D21⋊D17C3×C711yescharacteristic, direct product factor
33D3×C7×D17—71no—
34C3×D7×D17—31no—
35C32×C7×C17—23no—
36C32×C7×C17C2×D711yescharacteristic, complemented
37C32×C7×C17C22×C711yescharacteristic, complemented
38C3×C7×D21D1711yescharacteristic, complemented
39C3×D3×C72—171no—
40C32×C7×D7—171no—
41C72×C17C2×C3×D311yescharacteristic, complemented, Hall
42C2×C3×C7×C17—211no—
43C17×D21C2×C3×C711yescharacteristic, complemented
44C7×D51—23no—
45C7×D51C3×D711yescharacteristic, complemented
46C7×D51C2×C3×C711yescharacteristic, complemented
47D3×C7×C17—71no—
48C3×D119—21no—
49C3×D119D3×C711yescharacteristic, complemented
50C3×D119C2×C3×C711yescharacteristic, complemented
51C3×D7×C17—31no—
52C3×C7×D17—31no—
53C3×C7×D17—31no—
54C3×C7×D17—63no—
55C3×C7×D17—71no—
56C3×C7×D17—71no—
57C3×C7×D17—141no—
58C3×D3×D17—71noHall
59C2×C3×C7×D7—511no—
60D3×C7×D7—171no—
61C2×C7×D17—211no—
62D7×D17—31no—
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×C17C2×C3×D711yescharacteristic, complemented
71C3×C7×C17C2×D3×C711yescharacteristic, complemented
72C3×C7×C17C22×C3×C711yescharacteristic, complemented
73C3×D51C7×D711yescharacteristic, complemented
74C3×D3×C17—71no—
75C32×D17—71no—
76C2×C3×C72—511no—
77C7×D21C3×D1711yescharacteristic, complemented
78D3×C72—171no—
79C3×C7×D7—31no—
80C3×C7×D7—171no—
81C3×C7×D7—171no—
82C3×C7×D7—341no—
83C2×C3×D3×C7—1191no—
84C3×D3×D7—171no—
85C2×C7×C17—211no—
86D119C3×D3×C711yescharacteristic, complemented
87C7×D17—31no—
88C7×D17—31no—
89C7×D17—63no—
90C7×D17—71no—
91D7×C17—31no—
92C2×C3×D17—211no—
93D3×D17—71no—
94C2×C7×D7—511noHall
95C32×C17C2×C7×D711yescharacteristic, complemented, Hall
96C3×C72—21no—
97C3×C72D3×D1711yescharacteristic, complemented
98C3×C72C2×C3×D1711yescharacteristic, complemented
99C2×C32×C7—1191no—
100C3×D21C7×D1711yescharacteristic, complemented
101C3×D3×C7—71no—
102C3×D3×C7—171no—
103C3×D3×C7—171no—
104C3×D3×C7—343no—
105C32×D7—171no—
106C7×C17—23no—
107C7×C17C3×D3×D711yescharacteristic, complemented
108C7×C17C2×C3×D3×C711yescharacteristic, complemented
109C2×C3×C17—211no—
110D51C3×C7×D711yescharacteristic, complemented
111C3×D17—31no—
112C3×D17—71no—
113C3×D17—71no—
114C3×D17—141no—
115D3×C17—71no—
116C2×C72—511no—
117C7×D7—31no—
118C7×D7—171no—
119C22×C3×C7—3571no—
120C2×D3×C7—1191no—
121C2×C3×D7—511no—
122D3×D7—171no—
123C2×D17—211noHall
124C32×C7—23no—
125C32×C7D7×D1711yescharacteristic, complemented
126C32×C7C2×C7×D1711yescharacteristic, complemented
127C3×C17—21no—
128C3×C17D3×C7×D711yescharacteristic, complemented
129C3×C17C2×C3×C7×D711yescharacteristic, complemented
130C72C3×D3×D1711yescharacteristic, complemented, Sylow
131C2×C3×C7—211no—
132C2×C3×C7—511no—
133C2×C3×C7—511no—
134C2×C3×C7—1023no—
135C2×C3×C7—1191no—
136C2×C3×C7—1191no—
137C2×C3×C7—2381no—
138D21C3×C7×D1711yescharacteristic, complemented
139C3×D7—31no—
140C3×D7—171no—
141C3×D7—171no—
142C3×D7—341no—
143D3×C7—71no—
144D3×C7—171no—
145D3×C7—171no—
146D3×C7—343no—
147C2×C3×D3—1191noHall
148C2×C17—211no—
149D17—31no—
150D17—71no—
151C22×C7—3571no—
152C2×D7—511no—
153C3×C7—21no—
154C3×C7—21no—
155C3×C7—23no—
156C3×C7—23no—
157C3×C7—43no—
158C3×C7C3×D7×D1711yescharacteristic, complemented
159C3×C7D3×C7×D1711yescharacteristic, complemented
160C3×C7D21⋊D1711yescharacteristic, direct product factor
161C3×C7C2×C3×C7×D1711yescharacteristic, complemented
162C2×C32—1191no—
163C3×D3—71no—
164C3×D3—171no—
165C17C3×D3×C7×D711yescharacteristic, complemented, Sylow
166C2×C7—211no—
167C2×C7—511no—
168C2×C7—511no—
169C2×C7—1023no—
170C2×C7—1191no—
171D7—31no—
172D7—171no—
173C22×C3—3571no—
174C2×D3—1191no—
175C32C7×D7×D1711yescharacteristic, complemented, Sylow
176C7—23no—
177C7C3×D3×C7×D1711yescharacteristic, complemented
178C7C3×D21⋊D1711yescharacteristic, direct product factor
179C2×C3—211no—
180C2×C3—511no—
181C2×C3—1191no—
182C2×C3—1191no—
183C2×C3—2381no—
184D3—71no—
185D3—171no—
186C22—3571noSylow
187C3—21no—
188C3C3×C7×D7×D1711yescharacteristic, complemented
189C3C7×D21⋊D1711yescharacteristic, direct product factor
190C2—211no—
191C2—511no—
192C2—1191no—
subgroupG/H
center, hypercenterC3×C7D21⋊D17
commutator, cosocle, hypocenterC3×C7×C17C22×C3×C7
FrattiniC1G
Fitting, socleC32×C72×C17C22
LCSG ▷ C3×C7×C17
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D119C2semidirect
2. C3×C72×D51C2semidirect
3. C3×C7×C17×D21C2semidirect
4. C7×D21⋊D17C3direct (N × H)
6. C32×C72×C17C22semidirect
7. C7×C17×D21C2×C3semidirect
8. C72×D51C2×C3semidirect
10. C3×C7×D119D3semidirect
11. C3×C7×D119C2×C3semidirect
14. C3×D21⋊D17C7direct (N × H)
18. C3×C72×C17C2×D3semidirect
19. C3×C72×C17C22×C3semidirect
20. C3×C17×D21C2×C7semidirect
22. C3×C7×D51D7semidirect
23. C3×C7×D51C2×C7semidirect
25. C32×D119C2×C7semidirect
28. C7×D119C3×D3semidirect
32. D21⋊D17C3×C7direct (N × H)
36. C32×C7×C17C2×D7semidirect
37. C32×C7×C17C22×C7semidirect
38. C3×C7×D21D17semidirect
41. C72×C17C2×C3×D3semidirect
43. C17×D21C2×C3×C7semidirect
45. C7×D51C3×D7semidirect
46. C7×D51C2×C3×C7semidirect
49. C3×D119D3×C7semidirect
50. C3×D119C2×C3×C7semidirect
63. C32×C72C2×D17semidirect
69. C3×C7×C17D3×D7semidirect
70. C3×C7×C17C2×C3×D7semidirect
71. C3×C7×C17C2×D3×C7semidirect
72. C3×C7×C17C22×C3×C7semidirect
73. C3×D51C7×D7semidirect
77. C7×D21C3×D17semidirect
86. D119C3×D3×C7semidirect
95. C32×C17C2×C7×D7semidirect
97. C3×C72D3×D17semidirect
98. C3×C72C2×C3×D17semidirect
100. C3×D21C7×D17semidirect
107. C7×C17C3×D3×D7semidirect
108. C7×C17C2×C3×D3×C7semidirect
110. D51C3×C7×D7semidirect
125. C32×C7D7×D17semidirect
126. C32×C7C2×C7×D17semidirect
128. C3×C17D3×C7×D7semidirect
129. C3×C17C2×C3×C7×D7semidirect
130. C72C3×D3×D17semidirect
138. D21C3×C7×D17semidirect
158. C3×C7C3×D7×D17semidirect
159. C3×C7D3×C7×D17semidirect
160. C3×C7D21⋊D17direct (N × H)
161. C3×C7C2×C3×C7×D17semidirect
165. C17C3×D3×C7×D7semidirect
175. C32C7×D7×D17semidirect
177. C7C3×D3×C7×D17semidirect
178. C7C3×D21⋊D17direct (N × H)
188. C3C3×C7×D7×D17semidirect
189. C3C7×D21⋊D17direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D1192
C3×C72×D512
C3×C7×C17×D212
C7×D21⋊D173
C3×C7×D7×D173
C3×D21⋊D177
C3×D3×C7×D177
C3×D3×C7×D717