Finite Group Databasebeta

← C3×D21⋊D85 #36339490

Subgroups — C3×D21⋊D85 #36339490

Order 21420.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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×D595C211yesmaximal, characteristic, complemented
2C3×C5×C17×D21C211yesmaximal, characteristic, complemented
3C3×C7×D255C211yesmaximal, characteristic, complemented
4D21⋊D85C311yesmaximal, characteristic, direct product factor
5C3×D7×D85—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7C3×D21⋊D17—51nomaximal, Hall
8C7×D255C2×C311yescharacteristic, complemented
9C5×C17×D21C2×C311yescharacteristic, complemented
10C3×D595—21no—
11C3×D595D311yescharacteristic, complemented
12C3×D595C2×C311yescharacteristic, complemented
13C3×C7×D85—31no—
14C3×C5×D7×C17—31no—
15C3×D3×D85—71nomaximal, Hall
16D7×D85—31noHall
17C3×C17×D21D511yescharacteristic, complemented
18C3×C7×D51—51no—
19C32×D119—51no—
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C22×C311yescharacteristic, complemented
23C3×D255D711yescharacteristic, complemented
24C3×C5×D3×C17—71no—
25C32×D85—71no—
26D21⋊D17—51no—
27C3×D7×D17—151no—
28C3×D15⋊D7—171nomaximal, Hall
29D595C3×D311yescharacteristic, complemented
30C7×D85—31no—
31C5×D7×C17—31no—
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33C2×C3×D85—211no—
34D3×D85—71no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36C17×D21C3×D511yescharacteristic, complemented
37C7×D51—51no—
38C3×D119—51no—
39C3×D119—51no—
40C3×D119—101no—
41C3×D7×C17—31no—
42C3×C7×D17—151no—
43C3×C7×D15—171no—
44C3×C5×D21D1711yescharacteristic, complemented
45C32×D35—171no—
46C3×D3×D17—351noHall
47C5×C7×C17C2×C3×D311yescharacteristic, complemented, Hall
48C2×C3×C5×C17—211no—
49D255C3×D711yescharacteristic, complemented
50C5×D3×C17—71no—
51C3×D85—31no—
52C3×D85—71no—
53C3×D85—71no—
54C3×D85—141no—
55D7×D17—151noHall
56D15⋊D7—171no—
57C3×D5×D7—511no—
58C3×C7×C17—21no—
59C3×C7×C17D3×D511yescharacteristic, complemented
60C3×C7×C17C2×C3×D511yescharacteristic, complemented
61C2×D85—211noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3×D51—51no—
64C3×D3×C17—71no—
65C32×D17—351no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17C2×C3×D711yescharacteristic, complemented
69C3×D3×D7—851noHall
70D119—51no—
71C7×D17—151no—
72D7×C17—31no—
73C7×D15—171no—
74C5×D21C3×D1711yescharacteristic, complemented
75C3×D35—171no—
76C3×D35—171no—
77C3×D35—341no—
78C3×C7×D5—511no—
79C3×C5×D7—31no—
80C2×C3×D17—1051no—
81D3×D17—351no—
82C3×D3×D5—1191noHall
83C2×C5×C17—211no—
84D85—31no—
85D85—71no—
86C32×C17D5×D711yescharacteristic, complemented, Hall
87D5×D7—511noHall
88C3×D21D8511yescharacteristic, complemented
89C3×D3×C7—851no—
90C32×D7—851no—
91C7×C17C3×D3×D511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×C3×D1711yescharacteristic, complemented
95C2×C3×C17—211no—
96D51—51no—
97C3×D17—151no—
98C3×D17—351no—
99C3×D17—351no—
100C3×D17—701no—
101D3×C17—71no—
102C3×D15—171no—
103C3×C5×D3—71no—
104C32×D5—1191no—
105C5×C17C3×D3×D711yescharacteristic, complemented, Hall
106C2×C3×D7—2551no—
107D3×D7—851no—
108D35—171no—
109C5×D7—31no—
110C7×D5—511no—
111C2×D17—1051noHall
112C32×C7C2×D8511yescharacteristic, complemented, Hall
113C2×C3×D5—3571no—
114D3×D5—1191no—
115C3×C17—21no—
116C3×C17C3×D5×D711yescharacteristic, complemented
117C3×C17D15⋊D711yescharacteristic, complemented
118C32×C5D7×D1711yescharacteristic, complemented, Hall
119C2×C3×C7—2551no—
120D21C3×D8511yescharacteristic, complemented
121C3×D7—31no—
122C3×D7—851no—
123C3×D7—851no—
124C3×D7—1701no—
125D3×C7—851no—
126C2×C3×D3—5951noHall
127C5×C7C3×D3×D1711yescharacteristic, complemented, Hall
128C2×C17—211no—
129D17—151no—
130D17—351no—
131C2×C3×C5—211no—
132D15—171no—
133C3×D5—511no—
134C3×D5—1191no—
135C3×D5—1191no—
136C3×D5—2381no—
137C5×D3—71no—
138C2×D7—2551noHall
139C3×C7—21no—
140C3×C7D3×D8511yescharacteristic, complemented
141C3×C7C2×C3×D8511yescharacteristic, complemented
142C2×D5—3571noHall
143C2×C32—5951no—
144C3×D3—71no—
145C3×D3—851no—
146C17C3×D15⋊D711yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5C3×D7×D1711yescharacteristic, complemented
149C3×C5D21⋊D1711yescharacteristic, complemented
150C2×C7—2551no—
151D7—31no—
152D7—851no—
153C22×C3—17851no—
154C2×D3—5951no—
155C2×C5—211no—
156D5—511no—
157D5—1191no—
158C32D7×D8511yescharacteristic, complemented, Sylow
159C7C3×D3×D8511yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—5951no—
162C2×C3—5951no—
163C2×C3—11901no—
164C2×C3—2551no—
165D3—71no—
166D3—851no—
167C5C3×D21⋊D1711yescharacteristic, complemented, Sylow
168C22—17851noSylow
169C3—21no—
170C3C3×D7×D8511yescharacteristic, complemented
171C3D21⋊D8511yescharacteristic, direct product factor
172C2—211no—
173C2—5951no—
174C2—2551no—
subgroupG/H
center, hypercenterC3D21⋊D85
commutator, cosocle, hypocenterC3×C5×C7×C17C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C5×C7×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×D595C2semidirect
2. C3×C5×C17×D21C2semidirect
3. C3×C7×D255C2semidirect
4. D21⋊D85C3direct (N × H)
6. C32×C5×C7×C17C22semidirect
8. C7×D255C2×C3semidirect
9. C5×C17×D21C2×C3semidirect
11. C3×D595D3semidirect
12. C3×D595C2×C3semidirect
17. C3×C17×D21D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C22×C3semidirect
23. C3×D255D7semidirect
29. D595C3×D3semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
36. C17×D21C3×D5semidirect
44. C3×C5×D21D17semidirect
47. C5×C7×C17C2×C3×D3semidirect
49. D255C3×D7semidirect
59. C3×C7×C17D3×D5semidirect
60. C3×C7×C17C2×C3×D5semidirect
62. C32×C5×C7C2×D17semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17C2×C3×D7semidirect
74. C5×D21C3×D17semidirect
86. C32×C17D5×D7semidirect
88. C3×D21D85semidirect
91. C7×C17C3×D3×D5semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×C3×D17semidirect
105. C5×C17C3×D3×D7semidirect
112. C32×C7C2×D85semidirect
116. C3×C17C3×D5×D7semidirect
117. C3×C17D15⋊D7semidirect
118. C32×C5D7×D17semidirect
120. D21C3×D85semidirect
127. C5×C7C3×D3×D17semidirect
140. C3×C7D3×D85semidirect
141. C3×C7C2×C3×D85semidirect
146. C17C3×D15⋊D7semidirect
148. C3×C5C3×D7×D17semidirect
149. C3×C5D21⋊D17semidirect
158. C32D7×D85semidirect
159. C7C3×D3×D85semidirect
167. C5C3×D21⋊D17semidirect
170. C3C3×D7×D85semidirect
171. C3D21⋊D85direct (N × H)

Maximal subgroups

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

subgroupindex
C32×D5952
C3×C5×C17×D212
C3×C7×D2552
D21⋊D853
C3×D7×D853
C3×D21⋊D175
C3×D3×D857
C3×D15⋊D717