Finite Group Databasebeta

← D21⋊D255 #36339511

Subgroups — D21⋊D255 #36339511

Order 21420.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×C5×C17×D21C211yesmaximal, characteristic, complemented
2C3×D1785C211yesmaximal, characteristic, complemented
3C7×C3⋊D255C211yesmaximal, characteristic, complemented
4D21⋊D85—31nomaximal
5D7×D255—31nomaximal
6C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
7D21⋊D51—51nomaximal, Hall
8D1785D311yescharacteristic, complemented
9C7×D255—31no—
10C7×D255—31no—
11C7×D255—61no—
12C5×C17×D21D311yescharacteristic, complemented
13C3×D595—31no—
14C3×C5×D7×C17—31no—
15D3×D255—71nomaximal, Hall
16D7×D85—91noHall
17C7×C3⋊D51—51no—
18C3×D357—51no—
19C3×C17×D21D511yescharacteristic, complemented
20C3×C5×C7×C17—21no—
21C3×C5×C7×C17C2×D311yescharacteristic, complemented
22C3×C5×C7×C17C2×D311yescharacteristic, complemented
23C3⋊D255D711yescharacteristic, complemented
24C3×D255—71no—
25C3×C5×D3×C17—71no—
26D21⋊D17—151no—
27D7×D51—151no—
28D21⋊D15—171nomaximal, Hall
29D595—31no—
30C7×D85—91no—
31C5×D7×C17—31no—
32C32×C7×C17C2×D511yescharacteristic, complemented, Hall
33C2×D255—211no—
34D3×D85—211no—
35C32×C5×C17C2×D711yescharacteristic, complemented, Hall
36D357—51no—
37C17×D21D1511yescharacteristic, complemented
38C7×D51—151no—
39C7×D51—151no—
40C7×D51—301no—
41C3×D119—151no—
42C3×D7×C17—31no—
43C7×C3⋊D15—171no—
44C3×D105—171no—
45C3×C5×D21D1711yescharacteristic, complemented
46D3×D51—351noHall
47C5×C7×C17D3211yescharacteristic, complemented, Hall
48C2×C3×C5×C17—211no—
49D255—31no—
50D255—31no—
51D255—61no—
52D255—71no—
53C5×D3×C17—71no—
54C3×D85—211no—
55D7×D17—451noHall
56D15⋊D7—511no—
57D7×D15—511no—
58C3×C7×C17—21no—
59C3×C7×C17D3×D511yescharacteristic, complemented
60C3×C7×C17C2×D1511yescharacteristic, complemented
61C2×D85—631noHall
62C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
63C3⋊D51—51no—
64C3×D51—351no—
65C3×D3×C17—71no—
66C3×C5×C17—21no—
67C3×C5×C17D3×D711yescharacteristic, complemented
68C3×C5×C17D3×D711yescharacteristic, complemented
69(C3⋊D3)⋊D7—851noHall
70D119—151no—
71C7×D17—451no—
72D7×C17—31no—
73D105—171no—
74C7×D15—511no—
75C7×D15—511no—
76C7×D15—1021no—
77C5×D21D5111yescharacteristic, complemented
78C3×D35—511no—
79C3×C5×D7—31no—
80C2×D51—1051no—
81D3×D17—1051no—
82D3×D15—1191noHall
83C2×C5×C17—211no—
84D85—91no—
85D85—211no—
86C32×C17D5×D711yescharacteristic, complemented, Hall
87D5×D7—1531noHall
88C7×C3⋊D3—851no—
89C3×D21—851no—
90C3×D21D8511yescharacteristic, complemented
91C7×C17D3×D1511yescharacteristic, complemented, Hall
92C3×C5×C7—21no—
93C3×C5×C7D3×D1711yescharacteristic, complemented
94C3×C5×C7C2×D5111yescharacteristic, complemented
95C2×C3×C17—211no—
96D51—151no—
97D51—151no—
98D51—301no—
99D51—351no—
100C3×D17—1051no—
101D3×C17—71no—
102C3⋊D15—171no—
103C3×D15—1191no—
104C3×C5×D3—71no—
105C5×C17(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
106D3×D7—2551no—
107D3×D7—2551no—
108D35—511no—
109C5×D7—31no—
110C7×D5—1531no—
111C2×D17—3151noHall
112C32×C7C2×D8511yescharacteristic, complemented, Hall
113C2×D15—3571no—
114D3×D5—3571no—
115C3×C17—21no—
116C3×C17D7×D1511yescharacteristic, complemented
117C3×C17D15⋊D711yescharacteristic, complemented
118C32×C5D7×D1711yescharacteristic, complemented, Hall
119D21—851no—
120D21D25511yescharacteristic, complemented
121C3×D7—31no—
122C3×D7—2551no—
123D3×C7—5101no—
124D3×C7—2551no—
125D3×C7—2551no—
126D32—5951noHall
127C5×C7D3×D5111yescharacteristic, complemented, Hall
128C2×C17—211no—
129D17—451no—
130D17—1051no—
131C2×C3×C5—211no—
132D15—511no—
133D15—511no—
134D15—1021no—
135D15—1191no—
136C3×D5—3571no—
137C5×D3—71no—
138C2×D7—7651noHall
139C3×C7—21no—
140C3×C7D3×D8511yescharacteristic, complemented
141C3×C7C2×D25511yescharacteristic, complemented
142C2×D5—10711noHall
143C3⋊D3—851no—
144C3×D3—71no—
145C3×D3—5951no—
146C17D21⋊D1511yescharacteristic, complemented, Sylow
147C3×C5—21no—
148C3×C5D7×D5111yescharacteristic, complemented
149C3×C5D21⋊D1711yescharacteristic, complemented
150C2×C7—7651no—
151D7—31no—
152D7—2551no—
153C2×D3—17851no—
154C2×D3—17851no—
155C2×C5—211no—
156D5—3571no—
157D5—1531no—
158C32D7×D8511yescharacteristic, complemented, Sylow
159C7D3×D25511yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—17851no—
162D3—71no—
163D3—5951no—
164D3—5101no—
165D3—2551no—
166D3—2551no—
167C5D21⋊D5111yescharacteristic, complemented, Sylow
168C22—53551noSylow
169C3—21no—
170C3D7×D25511yescharacteristic, complemented
171C3D21⋊D8511yescharacteristic, complemented
172C2—211no—
173C2—17851no—
174C2—7651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C17C22
LCSG ▷ C32×C5×C7×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C17×D21C2semidirect
2. C3×D1785C2semidirect
3. C7×C3⋊D255C2semidirect
6. C32×C5×C7×C17C22semidirect
8. D1785D3semidirect
12. C5×C17×D21D3semidirect
19. C3×C17×D21D5semidirect
21. C3×C5×C7×C17C2×D3semidirect
22. C3×C5×C7×C17C2×D3semidirect
23. C3⋊D255D7semidirect
32. C32×C7×C17C2×D5semidirect
35. C32×C5×C17C2×D7semidirect
37. C17×D21D15semidirect
45. C3×C5×D21D17semidirect
47. C5×C7×C17D32semidirect
59. C3×C7×C17D3×D5semidirect
60. C3×C7×C17C2×D15semidirect
62. C32×C5×C7C2×D17semidirect
67. C3×C5×C17D3×D7semidirect
68. C3×C5×C17D3×D7semidirect
77. C5×D21D51semidirect
86. C32×C17D5×D7semidirect
90. C3×D21D85semidirect
91. C7×C17D3×D15semidirect
93. C3×C5×C7D3×D17semidirect
94. C3×C5×C7C2×D51semidirect
105. C5×C17(C3⋊D3)⋊D7semidirect
112. C32×C7C2×D85semidirect
116. C3×C17D7×D15semidirect
117. C3×C17D15⋊D7semidirect
118. C32×C5D7×D17semidirect
120. D21D255semidirect
127. C5×C7D3×D51semidirect
140. C3×C7D3×D85semidirect
141. C3×C7C2×D255semidirect
146. C17D21⋊D15semidirect
148. C3×C5D7×D51semidirect
149. C3×C5D21⋊D17semidirect
158. C32D7×D85semidirect
159. C7D3×D255semidirect
167. C5D21⋊D51semidirect
170. C3D7×D255semidirect
171. C3D21⋊D85semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C17×D212
C3×D17852
C7×C3⋊D2552
D21⋊D853
D7×D2553
D21⋊D515
D3×D2557
D21⋊D1517