Finite Group Databasebeta

← C7×D15⋊D87 #49141621

Subgroups — C7×D15⋊D87 #49141621

Order 36540.

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
1C3×C7×C29×D15C211yesmaximal, characteristic, complemented
2C3×C7×D435C211yesmaximal, characteristic, complemented
3C5×C7×C3⋊D87C211yesmaximal, characteristic, complemented
4C7×D15⋊D29—31nomaximal
5C7×D5×D87—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×C7×D87—51nomaximal, Hall
8C7×D435D311yescharacteristic, complemented
9C7×C29×D15D311yescharacteristic, complemented
10C5×C7×D87—31no—
11C5×C7×D87—31no—
12C5×C7×D87—61no—
13C3×C7×D145—31no—
14C3×C7×D5×C29—31no—
15D15⋊D87C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D29—91noHall
17C7×C3⋊D87D511yescharacteristic, complemented
18C3×C7×D87—51no—
19C3×D3×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C5×C3⋊D87C2×C711yescharacteristic, complemented
24C3×D435C2×C711yescharacteristic, complemented
25C3×C29×D15C2×C711yescharacteristic, complemented
26C2×C7×D87—151no—
27D3×C7×D29—151no—
28C7×D145—31no—
29C7×D5×C29—31no—
30C5×C7×D29—91no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D15⋊D29—31no—
33D5×D87—31no—
34C32×C5×C29C22×C711yescharacteristic, complemented, Hall
35C7×(C3⋊D3)⋊D5—291nomaximal, Hall
36C2×C3×C7×C29—151no—
37C7×D87—31no—
38C7×D87—31no—
39C7×D87—51no—
40C7×D87—61no—
41D3×C7×C29—51no—
42C3×C7×D29—151no—
43D3×D87—51noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45D435D3×C711yescharacteristic, complemented
46C29×D15D3×C711yescharacteristic, complemented
47C5×D87—31no—
48C5×D87—31no—
49C5×D87—61no—
50C3×D145—31no—
51C3×D5×C29—31no—
52C2×C7×D29—451noHall
53C5×C7×C3⋊D3—291no—
54C3×C7×D15—291no—
55C3×C7×D15D2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29D3×D511yescharacteristic, complemented
59D5×D29—91noHall
60C3⋊D87C7×D511yescharacteristic, complemented
61C3×D87—51no—
62C3×D3×C29—51no—
63C3×C5×C29—21no—
64C3×C5×C29C2×D3×C711yescharacteristic, complemented
65C3×C5×C29C2×D3×C711yescharacteristic, complemented
66D3×C7×D5—871no—
67D3×C7×D5—871no—
68C2×C7×C29—151no—
69C7×D29—91no—
70C7×D29—151no—
71C2×D87—151no—
72D3×D29—151no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74D145—31no—
75C5×D29—91no—
76D5×C29—31no—
77C32×C29C2×C7×D511yescharacteristic, complemented, Hall
78D32×C7—1451noHall
79C7×D15—291no—
80C7×D15D8711yescharacteristic, complemented
81C5×D3×C7—871no—
82C5×D3×C7—871no—
83C5×D3×C7—1741no—
84C3×C7×D5—31no—
85C3×C7×D5—871no—
86C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
87(C3⋊D3)⋊D5—291noHall
88C2×C3×C29—151no—
89D87—31no—
90D87—31no—
91D87—51no—
92D87—61no—
93C3×D29—151no—
94D3×C29—51no—
95C5×C29D32×C711yescharacteristic, complemented, Hall
96C2×C7×D5—2611noHall
97C7×C3⋊D3—291no—
98C3×D3×C7—51no—
99C3×D3×C7—1451no—
100C2×D29—451noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C5×C3⋊D3—291no—
105C3×D15—291no—
106C3×D15C7×D2911yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D3×C7×D511yescharacteristic, complemented
109C3×C29D3×C7×D511yescharacteristic, complemented
110C2×D3×C7—4351no—
111C2×D3×C7—4351no—
112C2×C5×C7—2611no—
113C7×D5—31no—
114C7×D5—871no—
115C32×C7D5×D2911yescharacteristic, complemented, Hall
116D3×D5—871no—
117D3×D5—871no—
118C2×C29—151no—
119D29—91no—
120D29—151no—
121C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
122C2×C3×C7—151no—
123C2×C3×C7—4351no—
124D3×C7—51no—
125D3×C7—871no—
126D3×C7—871no—
127D3×C7—1451no—
128D3×C7—1741no—
129D32—1451noHall
130C5×C7D3×D8711yescharacteristic, complemented, Hall
131D15—291no—
132D15C7×D8711yescharacteristic, complemented
133C3×D5—31no—
134C3×D5—871no—
135C5×D3—871no—
136C5×D3—871no—
137C5×D3—1741no—
138C29C7×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
139C22×C7—13051noHall
140C3×C7—21no—
141C3×C7D5×D8711yescharacteristic, complemented
142C3×C7D15⋊D2911yescharacteristic, complemented
143C2×D5—2611noHall
144C3⋊D3—291no—
145C3×D3—51no—
146C3×D3—1451no—
147C3×C5—21no—
148C3×C5D3×C7×D2911yescharacteristic, complemented
149C3×C5C2×C7×D8711yescharacteristic, complemented
150C2×C7—2611no—
151C2×C7—151no—
152C2×C7—4351no—
153C2×D3—4351no—
154C2×D3—4351no—
155C2×C5—2611no—
156D5—31no—
157D5—871no—
158C32C7×D5×D2911yescharacteristic, complemented, Sylow
159C7D15⋊D8711yescharacteristic, direct product factor, Sylow
160C2×C3—151no—
161C2×C3—4351no—
162D3—51no—
163D3—871no—
164D3—871no—
165D3—1451no—
166D3—1741no—
167C5D3×C7×D8711yescharacteristic, complemented, Sylow
168C22—13051noSylow
169C3—21no—
170C3C7×D5×D8711yescharacteristic, complemented
171C3C7×D15⋊D2911yescharacteristic, complemented
172C2—2611no—
173C2—151no—
174C2—4351no—
subgroupG/H
center, hypercenterC7D15⋊D87
commutator, cosocle, hypocenterC32×C5×C29C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C29×D15C2semidirect
2. C3×C7×D435C2semidirect
3. C5×C7×C3⋊D87C2semidirect
6. C32×C5×C7×C29C22semidirect
8. C7×D435D3semidirect
9. C7×C29×D15D3semidirect
15. D15⋊D87C7direct (N × H)
17. C7×C3⋊D87D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
23. C5×C3⋊D87C2×C7semidirect
24. C3×D435C2×C7semidirect
25. C3×C29×D15C2×C7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C22×C7semidirect
44. C5×C7×C29D32semidirect
45. D435D3×C7semidirect
46. C29×D15D3×C7semidirect
55. C3×C7×D15D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29D3×D5semidirect
60. C3⋊D87C7×D5semidirect
64. C3×C5×C29C2×D3×C7semidirect
65. C3×C5×C29C2×D3×C7semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29C2×C7×D5semidirect
80. C7×D15D87semidirect
86. C7×C29(C3⋊D3)⋊D5semidirect
95. C5×C29D32×C7semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×D87semidirect
106. C3×D15C7×D29semidirect
108. C3×C29D3×C7×D5semidirect
109. C3×C29D3×C7×D5semidirect
115. C32×C7D5×D29semidirect
121. C32×C5C2×C7×D29semidirect
130. C5×C7D3×D87semidirect
132. D15C7×D87semidirect
138. C29C7×(C3⋊D3)⋊D5semidirect
141. C3×C7D5×D87semidirect
142. C3×C7D15⋊D29semidirect
148. C3×C5D3×C7×D29semidirect
149. C3×C5C2×C7×D87semidirect
158. C32C7×D5×D29semidirect
159. C7D15⋊D87direct (N × H)
167. C5D3×C7×D87semidirect
170. C3C7×D5×D87semidirect
171. C3C7×D15⋊D29semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C29×D152
C3×C7×D4352
C5×C7×C3⋊D872
C7×D15⋊D293
C7×D5×D873
D3×C7×D875
D15⋊D877
C7×(C3⋊D3)⋊D529