Finite Group Databasebeta

← C7×D87⋊D15 #49141606

Subgroups — C7×D87⋊D15 #49141606

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×C5×C7×D87C211yesmaximal, characteristic, complemented
2C3×C7×D435C211yesmaximal, characteristic, complemented
3C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4C7×D15⋊D29—31nomaximal
5C7×D15×D29—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C7×(C3⋊D3)⋊D29—51nomaximal, Hall
8C7×D435D311yescharacteristic, complemented
9C7×C29×D15—31no—
10C7×C29×D15—31no—
11C7×C29×D15—61no—
12C5×C7×D87D311yescharacteristic, complemented
13C3×C7×D145—31no—
14C3×C5×C7×D29—31no—
15D87⋊D15C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D29—91noHall
17C7×C3⋊D3×C29—51no—
18C3×C7×D87—51no—
19C3×C7×D87D511yescharacteristic, complemented
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C29×C3⋊D15C2×C711yescharacteristic, complemented
24C3×D435C2×C711yescharacteristic, complemented
25C3×C5×D87C2×C711yescharacteristic, complemented
26D3×C7×D29—151no—
27D3×C7×D29—151no—
28C7×D145—31no—
29C7×D5×C29—91no—
30C5×C7×D29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D15⋊D29—31no—
33D15×D29—31no—
34C32×C5×C29C22×C711yescharacteristic, complemented, Hall
35D3×C7×D15—291nomaximal, Hall
36C7×D87—51no—
37C7×D87D1511yescharacteristic, complemented
38D3×C7×C29—151no—
39D3×C7×C29—151no—
40D3×C7×C29—301no—
41C3×C7×D29—31no—
42C3×C7×D29—151no—
43(C3⋊D3)⋊D29—51noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45D435D3×C711yescharacteristic, complemented
46C29×D15—31no—
47C29×D15—31no—
48C29×D15—61no—
49C5×D87D3×C711yescharacteristic, complemented
50C3×D145—31no—
51C3×C5×D29—31no—
52C2×C7×D29—451noHall
53C7×C3⋊D15D2911yescharacteristic, complemented
54C3×C7×D15—291no—
55C3×C5×D3×C7—291no—
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×D1511yescharacteristic, complemented
59D5×D29—91noHall
60C3⋊D3×C29—51no—
61C3×D87—51no—
62C3×D87C7×D511yescharacteristic, complemented
63C3×C5×C29—21no—
64C3×C5×C29C2×D3×C711yescharacteristic, complemented
65C3×C5×C29C2×D3×C711yescharacteristic, complemented
66C2×C7×D15—871no—
67D3×C7×D5—871no—
68C2×C7×C29—451no—
69C7×D29—31no—
70C7×D29—151no—
71D3×D29—151no—
72D3×D29—151no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74D145—31no—
75C5×D29—31no—
76D5×C29—91no—
77C32×C29C2×C7×D511yescharacteristic, complemented, Hall
78D32×C7—1451noHall
79C2×C3×C5×C7—871no—
80C7×D15—31no—
81C7×D15—31no—
82C7×D15—61no—
83C7×D15—291no—
84C5×D3×C7—291no—
85C3×C7×D5—871no—
86C7×C29D3×D1511yescharacteristic, complemented, Hall
87D3×D15—291noHall
88D87—51no—
89D87C7×D1511yescharacteristic, complemented
90C3×D29—31no—
91C3×D29—151no—
92D3×C29—151no—
93D3×C29—151no—
94D3×C29—301no—
95C5×C29D32×C711yescharacteristic, complemented, Hall
96C2×C7×D5—2611noHall
97C7×C3⋊D3—51no—
98C3×D3×C7—291no—
99C3×D3×C7—1451no—
100C2×D29—451noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7D3×D2911yescharacteristic, complemented
104C3⋊D15C7×D2911yescharacteristic, complemented
105C3×D15—291no—
106C3×C5×D3—291no—
107C3×C29—21no—
108C3×C29D3×C7×D511yescharacteristic, complemented
109C3×C29C2×C7×D1511yescharacteristic, complemented
110C2×D3×C7—4351no—
111C2×D3×C7—4351no—
112C2×C5×C7—871no—
113C7×D5—91no—
114C7×D5—871no—
115C32×C7D5×D2911yescharacteristic, complemented, Hall
116C2×D15—871no—
117D3×D5—871no—
118C2×C29—451no—
119D29—31no—
120D29—151no—
121C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
122C2×C3×C7—871no—
123C2×C3×C7—4351no—
124D3×C7—151no—
125D3×C7—151no—
126D3×C7—291no—
127D3×C7—301no—
128D3×C7—1451no—
129D32—1451noHall
130C5×C7(C3⋊D3)⋊D2911yescharacteristic, complemented, Hall
131C2×C3×C5—871no—
132D15—31no—
133D15—31no—
134D15—61no—
135D15—291no—
136C3×D5—871no—
137C5×D3—291no—
138C29D3×C7×D1511yescharacteristic, complemented, Sylow
139C22×C7—13051noHall
140C3×C7—21no—
141C3×C7D15×D2911yescharacteristic, complemented
142C3×C7D15⋊D2911yescharacteristic, complemented
143C2×D5—2611noHall
144C3⋊D3—51no—
145C3×D3—291no—
146C3×D3—1451no—
147C3×C5—21no—
148C3×C5D3×C7×D2911yescharacteristic, complemented
149C3×C5D3×C7×D2911yescharacteristic, complemented
150C2×C7—451no—
151C2×C7—871no—
152C2×C7—4351no—
153C2×D3—4351no—
154C2×D3—4351no—
155C2×C5—871no—
156D5—91no—
157D5—871no—
158C32C7×D5×D2911yescharacteristic, complemented, Sylow
159C7D87⋊D1511yescharacteristic, direct product factor, Sylow
160C2×C3—871no—
161C2×C3—4351no—
162D3—151no—
163D3—151no—
164D3—291no—
165D3—301no—
166D3—1451no—
167C5C7×(C3⋊D3)⋊D2911yescharacteristic, complemented, Sylow
168C22—13051noSylow
169C3—21no—
170C3C7×D15×D2911yescharacteristic, complemented
171C3C7×D15⋊D2911yescharacteristic, complemented
172C2—451no—
173C2—871no—
174C2—4351no—
subgroupG/H
center, hypercenterC7D87⋊D15
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×C5×C7×D87C2semidirect
2. C3×C7×D435C2semidirect
3. C7×C29×C3⋊D15C2semidirect
6. C32×C5×C7×C29C22semidirect
8. C7×D435D3semidirect
12. C5×C7×D87D3semidirect
15. D87⋊D15C7direct (N × H)
19. C3×C7×D87D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
23. C29×C3⋊D15C2×C7semidirect
24. C3×D435C2×C7semidirect
25. C3×C5×D87C2×C7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C22×C7semidirect
37. C7×D87D15semidirect
44. C5×C7×C29D32semidirect
45. D435D3×C7semidirect
49. C5×D87D3×C7semidirect
53. C7×C3⋊D15D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×D15semidirect
62. 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
86. C7×C29D3×D15semidirect
89. D87C7×D15semidirect
95. C5×C29D32×C7semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7D3×D29semidirect
104. C3⋊D15C7×D29semidirect
108. C3×C29D3×C7×D5semidirect
109. C3×C29C2×C7×D15semidirect
115. C32×C7D5×D29semidirect
121. C32×C5C2×C7×D29semidirect
130. C5×C7(C3⋊D3)⋊D29semidirect
138. C29D3×C7×D15semidirect
141. C3×C7D15×D29semidirect
142. C3×C7D15⋊D29semidirect
148. C3×C5D3×C7×D29semidirect
149. C3×C5D3×C7×D29semidirect
158. C32C7×D5×D29semidirect
159. C7D87⋊D15direct (N × H)
167. C5C7×(C3⋊D3)⋊D29semidirect
170. C3C7×D15×D29semidirect
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×C5×C7×D872
C3×C7×D4352
C7×C29×C3⋊D152
C7×D15⋊D293
C7×D15×D293
C7×(C3⋊D3)⋊D295
D87⋊D157
D3×C7×D1529