Finite Group Databasebeta

← D21⋊D435 #49141613

Subgroups — D21⋊D435 #49141613

Order 36540.

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×C29×D21C211yesmaximal, characteristic, complemented
2C3×D3045C211yesmaximal, characteristic, complemented
3C7×C3⋊D435C211yesmaximal, characteristic, complemented
4D21⋊D145—31nomaximal
5D7×D435—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D21⋊D87—51nomaximal, Hall
8D3045D311yescharacteristic, complemented
9C7×D435—31no—
10C7×D435—31no—
11C7×D435—61no—
12C5×C29×D21D311yescharacteristic, complemented
13C3×D1015—31no—
14C3×C5×D7×C29—31no—
15D3×D435—71nomaximal, Hall
16D7×D145—91noHall
17C7×C3⋊D87—51no—
18C3×D609—51no—
19C3×C29×D21D511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C3⋊D435D711yescharacteristic, complemented
24C3×D435—71no—
25C3×C5×D3×C29—71no—
26D21⋊D29—151no—
27D7×D87—151no—
28D1015—31no—
29C7×D145—91no—
30C5×D7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×D435—211no—
33D3×D145—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D21⋊D15—291nomaximal, Hall
36D609—51no—
37C29×D21D1511yescharacteristic, complemented
38C7×D87—151no—
39C7×D87—151no—
40C7×D87—301no—
41C3×D203—151no—
42C3×D7×C29—31no—
43D3×D87—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45C2×C3×C5×C29—211no—
46D435—31no—
47D435—31no—
48D435—61no—
49D435—71no—
50C5×D3×C29—71no—
51C3×D145—211no—
52D7×D29—451noHall
53C7×C3⋊D15—291no—
54C3×D105—291no—
55C3×C5×D21D2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×D1511yescharacteristic, complemented
59C2×D145—631noHall
60C3⋊D87—51no—
61C3×D87—351no—
62C3×D3×C29—71no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29D3×D711yescharacteristic, complemented
66D15⋊D7—871no—
67D7×D15—871no—
68D203—151no—
69C7×D29—451no—
70D7×C29—31no—
71C2×D87—1051no—
72D3×D29—1051no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74C2×C5×C29—211no—
75D145—91no—
76D145—211no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78(C3⋊D3)⋊D7—1451noHall
79D105—291no—
80C7×D15—871no—
81C7×D15—871no—
82C7×D15—1741no—
83C5×D21D8711yescharacteristic, complemented
84C3×D35—871no—
85C3×C5×D7—31no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—2031noHall
88C2×C3×C29—211no—
89D87—151no—
90D87—151no—
91D87—301no—
92D87—351no—
93C3×D29—1051no—
94D3×C29—71no—
95C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
96D5×D7—2611noHall
97C7×C3⋊D3—1451no—
98C3×D21—1451no—
99C3×D21D14511yescharacteristic, complemented
100C2×D29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C3⋊D15—291no—
105C3×D15—2031no—
106C3×C5×D3—71no—
107C3×C29—21no—
108C3×C29D7×D1511yescharacteristic, complemented
109C3×C29D15⋊D711yescharacteristic, complemented
110D3×D7—4351no—
111D3×D7—4351no—
112D35—871no—
113C5×D7—31no—
114C7×D5—2611no—
115C32×C7C2×D14511yescharacteristic, complemented, Hall
116C2×D15—6091no—
117D3×D5—6091no—
118C2×C29—211no—
119D29—451no—
120D29—1051no—
121C32×C5D7×D2911yescharacteristic, complemented, Hall
122D21—1451no—
123D21D43511yescharacteristic, complemented
124C3×D7—31no—
125C3×D7—4351no—
126D3×C7—8701no—
127D3×C7—4351no—
128D3×C7—4351no—
129D32—10151noHall
130C5×C7D3×D8711yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132D15—871no—
133D15—871no—
134D15—1741no—
135D15—2031no—
136C3×D5—6091no—
137C5×D3—71no—
138C29D21⋊D1511yescharacteristic, complemented, Sylow
139C2×D7—13051noHall
140C3×C7—21no—
141C3×C7D3×D14511yescharacteristic, complemented
142C3×C7C2×D43511yescharacteristic, complemented
143C2×D5—18271noHall
144C3⋊D3—1451no—
145C3×D3—71no—
146C3×D3—10151no—
147C3×C5—21no—
148C3×C5D7×D8711yescharacteristic, complemented
149C3×C5D21⋊D2911yescharacteristic, complemented
150C2×C7—13051no—
151D7—31no—
152D7—4351no—
153C2×D3—30451no—
154C2×D3—30451no—
155C2×C5—211no—
156D5—2611no—
157D5—6091no—
158C32D7×D14511yescharacteristic, complemented, Sylow
159C7D3×D43511yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—30451no—
162D3—71no—
163D3—8701no—
164D3—4351no—
165D3—4351no—
166D3—10151no—
167C5D21⋊D8711yescharacteristic, complemented, Sylow
168C22—91351noSylow
169C3—21no—
170C3D7×D43511yescharacteristic, complemented
171C3D21⋊D14511yescharacteristic, complemented
172C2—211no—
173C2—13051no—
174C2—30451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C29×D21C2semidirect
2. C3×D3045C2semidirect
3. C7×C3⋊D435C2semidirect
6. C32×C5×C7×C29C22semidirect
8. D3045D3semidirect
12. C5×C29×D21D3semidirect
19. C3×C29×D21D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
23. C3⋊D435D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
37. C29×D21D15semidirect
44. C5×C7×C29D32semidirect
55. C3×C5×D21D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29D3×D7semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29D5×D7semidirect
83. C5×D21D87semidirect
86. C7×C29D3×D15semidirect
95. C5×C29(C3⋊D3)⋊D7semidirect
99. C3×D21D145semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×D87semidirect
108. C3×C29D7×D15semidirect
109. C3×C29D15⋊D7semidirect
115. C32×C7C2×D145semidirect
121. C32×C5D7×D29semidirect
123. D21D435semidirect
130. C5×C7D3×D87semidirect
138. C29D21⋊D15semidirect
141. C3×C7D3×D145semidirect
142. C3×C7C2×D435semidirect
148. C3×C5D7×D87semidirect
149. C3×C5D21⋊D29semidirect
158. C32D7×D145semidirect
159. C7D3×D435semidirect
167. C5D21⋊D87semidirect
170. C3D7×D435semidirect
171. C3D21⋊D145semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C29×D212
C3×D30452
C7×C3⋊D4352
D21⋊D1453
D7×D4353
D21⋊D875
D3×D4357
D21⋊D1529