Finite Group Databasebeta

← C7×D57⋊D15 #37561564

Subgroups — C7×D57⋊D15 #37561564

Order 23940.

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×D57C211yesmaximal, characteristic, complemented
2C3×C7×D285C211yesmaximal, characteristic, complemented
3C7×C19×C3⋊D15C211yesmaximal, characteristic, complemented
4C7×D15⋊D19—31nomaximal
5C7×D15×D19—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7C7×(C3⋊D3)⋊D19—51nomaximal, Hall
8C7×D285D311yescharacteristic, complemented
9C7×C19×D15—31no—
10C7×C19×D15—31no—
11C7×C19×D15—61no—
12C5×C7×D57D311yescharacteristic, complemented
13C3×C7×D95—31no—
14C3×C5×C7×D19—31no—
15D57⋊D15C711yesmaximal, characteristic, direct product factor, Hall
16C7×D5×D19—91noHall
17C7×C3⋊D3×C19—51no—
18C3×C7×D57—51no—
19C3×C7×D57D511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C2×D311yescharacteristic, complemented
23C19×C3⋊D15C2×C711yescharacteristic, complemented
24C3×D285C2×C711yescharacteristic, complemented
25C3×C5×D57C2×C711yescharacteristic, complemented
26D3×C7×D19—151no—
27D3×C7×D19—151no—
28C7×D95—31no—
29C7×D5×C19—91no—
30C5×C7×D19—31no—
31D3×C7×D15—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33D15⋊D19—31no—
34D15×D19—31no—
35C32×C5×C19C22×C711yescharacteristic, complemented, Hall
36C7×D57—51no—
37C7×D57D1511yescharacteristic, complemented
38D3×C7×C19—151no—
39D3×C7×C19—151no—
40D3×C7×C19—301no—
41C3×C7×D19—31no—
42C3×C7×D19—151no—
43(C3⋊D3)⋊D19—51noHall
44C5×C7×C19D3211yescharacteristic, complemented, Hall
45C7×C3⋊D15D1911yescharacteristic, complemented
46C3×C7×D15—191no—
47C3×C5×D3×C7—191no—
48D285D3×C711yescharacteristic, complemented
49C19×D15—31no—
50C19×D15—31no—
51C19×D15—61no—
52C5×D57D3×C711yescharacteristic, complemented
53C3×D95—31no—
54C3×C5×D19—31no—
55C2×C7×D19—451noHall
56C2×C7×D15—571no—
57D3×C7×D5—571no—
58C3×C7×C19—21no—
59C3×C7×C19D3×D511yescharacteristic, complemented
60C3×C7×C19C2×D1511yescharacteristic, complemented
61D5×D19—91noHall
62C3⋊D3×C19—51no—
63C3×D57—51no—
64C3×D57C7×D511yescharacteristic, complemented
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19C2×D3×C711yescharacteristic, complemented
68C3×C5×C19C2×D3×C711yescharacteristic, complemented
69C2×C7×C19—451no—
70C7×D19—31no—
71C7×D19—151no—
72D32×C7—951noHall
73D3×D19—151no—
74D3×D19—151no—
75C2×C3×C5×C7—571no—
76C7×D15—31no—
77C7×D15—31no—
78C7×D15—61no—
79C7×D15—191no—
80C5×D3×C7—191no—
81C3×C7×D5—571no—
82D95—31no—
83C5×D19—31no—
84D5×C19—91no—
85D3×D15—191noHall
86C32×C19C2×C7×D511yescharacteristic, complemented, Hall
87C2×C7×D5—1711noHall
88C7×C19D3×D1511yescharacteristic, complemented, Hall
89C7×C3⋊D3—51no—
90C3×D3×C7—191no—
91C3×D3×C7—951no—
92D57—51no—
93D57C7×D1511yescharacteristic, complemented
94C3×D19—31no—
95C3×D19—151no—
96D3×C19—151no—
97D3×C19—151no—
98D3×C19—301no—
99C3×C5×C7—21no—
100C3×C5×C7D3×D1911yescharacteristic, complemented
101C3×C5×C7D3×D1911yescharacteristic, complemented
102C5×C19D32×C711yescharacteristic, complemented, Hall
103C3⋊D15C7×D1911yescharacteristic, complemented
104C3×D15—191no—
105C3×C5×D3—191no—
106C2×D3×C7—2851no—
107C2×D3×C7—2851no—
108C2×D19—451noHall
109C2×C5×C7—571no—
110C7×D5—91no—
111C7×D5—571no—
112C32×C7D5×D1911yescharacteristic, complemented, Hall
113C2×D15—571no—
114D3×D5—571no—
115C3×C19—21no—
116C3×C19D3×C7×D511yescharacteristic, complemented
117C3×C19C2×C7×D1511yescharacteristic, complemented
118C32×C5C2×C7×D1911yescharacteristic, complemented, Hall
119C2×C3×C7—2851no—
120C2×C3×C7—571no—
121D3×C7—151no—
122D3×C7—151no—
123D3×C7—191no—
124D3×C7—301no—
125D3×C7—951no—
126C2×C19—451no—
127D19—31no—
128D19—151no—
129D32—951noHall
130C5×C7(C3⋊D3)⋊D1911yescharacteristic, complemented, Hall
131C2×C3×C5—571no—
132D15—31no—
133D15—31no—
134D15—61no—
135D15—191no—
136C3×D5—571no—
137C5×D3—191no—
138C22×C7—8551noHall
139C3×C7—21no—
140C3×C7D15×D1911yescharacteristic, complemented
141C3×C7D15⋊D1911yescharacteristic, complemented
142C2×D5—1711noHall
143C19D3×C7×D1511yescharacteristic, complemented, Sylow
144C3⋊D3—51no—
145C3×D3—191no—
146C3×D3—951no—
147C3×C5—21no—
148C3×C5D3×C7×D1911yescharacteristic, complemented
149C3×C5D3×C7×D1911yescharacteristic, complemented
150C2×C7—2851no—
151C2×C7—451no—
152C2×C7—571no—
153C2×D3—2851no—
154C2×D3—2851no—
155C2×C5—571no—
156D5—91no—
157D5—571no—
158C32C7×D5×D1911yescharacteristic, complemented, Sylow
159C7D57⋊D1511yescharacteristic, direct product factor, Sylow
160C2×C3—2851no—
161C2×C3—571no—
162D3—151no—
163D3—151no—
164D3—191no—
165D3—301no—
166D3—951no—
167C5C7×(C3⋊D3)⋊D1911yescharacteristic, complemented, Sylow
168C22—8551noSylow
169C3—21no—
170C3C7×D15×D1911yescharacteristic, complemented
171C3C7×D15⋊D1911yescharacteristic, complemented
172C2—2851no—
173C2—451no—
174C2—571no—
subgroupG/H
center, hypercenterC7D57⋊D15
commutator, cosocle, hypocenterC32×C5×C19C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D57C2semidirect
2. C3×C7×D285C2semidirect
3. C7×C19×C3⋊D15C2semidirect
6. C32×C5×C7×C19C22semidirect
8. C7×D285D3semidirect
12. C5×C7×D57D3semidirect
15. D57⋊D15C7direct (N × H)
19. C3×C7×D57D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C2×D3semidirect
23. C19×C3⋊D15C2×C7semidirect
24. C3×D285C2×C7semidirect
25. C3×C5×D57C2×C7semidirect
32. C32×C7×C19C2×D5semidirect
35. C32×C5×C19C22×C7semidirect
37. C7×D57D15semidirect
44. C5×C7×C19D32semidirect
45. C7×C3⋊D15D19semidirect
48. D285D3×C7semidirect
52. C5×D57D3×C7semidirect
59. C3×C7×C19D3×D5semidirect
60. C3×C7×C19C2×D15semidirect
64. C3×D57C7×D5semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19C2×D3×C7semidirect
68. C3×C5×C19C2×D3×C7semidirect
86. C32×C19C2×C7×D5semidirect
88. C7×C19D3×D15semidirect
93. D57C7×D15semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7D3×D19semidirect
102. C5×C19D32×C7semidirect
103. C3⋊D15C7×D19semidirect
112. C32×C7D5×D19semidirect
116. C3×C19D3×C7×D5semidirect
117. C3×C19C2×C7×D15semidirect
118. C32×C5C2×C7×D19semidirect
130. C5×C7(C3⋊D3)⋊D19semidirect
140. C3×C7D15×D19semidirect
141. C3×C7D15⋊D19semidirect
143. C19D3×C7×D15semidirect
148. C3×C5D3×C7×D19semidirect
149. C3×C5D3×C7×D19semidirect
158. C32C7×D5×D19semidirect
159. C7D57⋊D15direct (N × H)
167. C5C7×(C3⋊D3)⋊D19semidirect
170. C3C7×D15×D19semidirect
171. C3C7×D15⋊D19semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D572
C3×C7×D2852
C7×C19×C3⋊D152
C7×D15⋊D193
C7×D15×D193
C7×(C3⋊D3)⋊D195
D57⋊D157
D3×C7×D1519