Finite Group Databasebeta

← C22×#41×D157 #34114932

Subgroups — C22×#41×D157 #34114932

Order 20096.

6520 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14578955C211yesmaximal, characteristic, complemented
2C22×#14578954C213yesmaximal, complemented
3C22×#14578953C213yesmaximal, complemented
4C2×#41×D157C2148yesmaximal, direct product factor
5C22×Q8×D157C211yesmaximal, characteristic, complemented
6C22×D4×D157C213yesmaximal, complemented
7C23×C4×D157C213yesmaximal, complemented
8C22×#41×C157C211yesmaximal, characteristic, complemented
9C24×D157C2213yes—
10C2×#14578955C22124yescomplemented
11C2×#14578954C22172yescomplemented
12C2×#14578953C22172yescomplemented
13#41×D157C221256yesdirect product factor
14C22×Dic314C2213yescomplemented
15C2×Q8×D157C22124yescomplemented
16C22×D628C2213yescomplemented
17C22×C22⋊D157C2216yescomplemented
18C2×D4×D157C22172yescomplemented
19C23×Dic157C2213yescomplemented
20C22×C4×D157C2211yescharacteristic
21C22×C4×D157C2213yes—
22C22×C4×D157C22172yescomplemented
23C22×C4×D157C2213yescomplemented
24C22×C4×D157C2213yescomplemented
25C2×#41×C157C22124yescomplemented
26C22×Q8×C157C2211yescharacteristic, complemented
27C22×D4×C157C2213yescomplemented
28C23×C4×C157C2213yescomplemented
29C23×D157—224no—
30C23×D157C23136yes—
31C23×D157C2313yes—
32C23×D157C2311yescharacteristic
33#14578955C23164yescomplemented
34#14578954C231192yescomplemented
35#14578953C231192yescomplemented
36C2×Dic314C23136yescomplemented
37Q8×D157C23164yescomplemented
38C2×D628C23136yescomplemented
39C2×C22⋊D157C23172yescomplemented
40D4×D157C231192yescomplemented
41C22×Dic157C2311yescharacteristic
42C22×Dic157C2313yes—
43C22×Dic157C23136yescomplemented
44C2×C4×D157C23112yes—
45C2×C4×D157C23136yes—
46C2×C4×D157C23136yescomplemented
47C2×C4×D157C23136yescomplemented
48C2×C4×D157C231192yescomplemented
49C24×C157C2313yes—
50#41×C157C23164yescomplemented
51C2×Q8×C157C23112yescomplemented
52C2×D4×C157C23136yescomplemented
53C22×C4×C157C2313yes—
54C22×C4×C157C2311yescharacteristic
55C22×C4×C157C23136yescomplemented
56C22×D157—212no—
57C22×D157—2144no—
58C22×D157#4118yesdirect product factor
59C22×D157C24148yes—
60C22×D157C24118yes—
61C22×D157C2416yes—
62Dic314C24148yescomplemented
63D628C24148yescomplemented
64C22⋊D157C24196yescomplemented
65C2×Dic157C2416yes—
66C2×Dic157C24118yes—
67C2×Dic157C24148yescomplemented
68C4×D157C24116yes—
69C4×D157C24148yes—
70C4×D157C24148yescomplemented
71C4×D157C24148yescomplemented
72C23×C157—212no—
73C23×C157C24118yes—
74C23×C157C2411yescharacteristic
75Q8×C157C24116yescomplemented
76D4×C157C24148yescomplemented
77C2×C4×C157C2416yes—
78C2×C4×C157C24118yes—
79C2×C4×C157C24148yescomplemented
80C22×C157—236no—
81C22×C157C2×#4114yescomplemented
82C22×C157C25112yes—
83C22×C157C2513yes—
84C2×D157—236no—
85C2×D157—296no—
86C2×D157C2×#41124yesdirect product factor
87C2×D157C25112yes—
88C2×D157C2514yes—
89C4×C157C2514yes—
90C4×C157C25112yes—
91Dic157C2514yes—
92Dic157C25112yes—
93C2×C157—212no—
94C2×C157C22×#4116yescomplemented
95C2×C157C2611yescharacteristic
96D157—212no—
97D157C22×#4118yesdirect product factor
98C157C23×#4111yescharacteristic, complemented, Sylow
99C23×#41—1571nomaximal, Sylow
100C22×#41—15748no—
101C22×#41—1571no—
102C22×#41—1573no—
103C22×#41—1573no—
104C22×#41D15711yescharacteristic, direct product factor
105C23×Q8—1571no—
106C23×D4—1573no—
107C24×C4—1573no—
108C25—1573no—
109C2×#41—157256no—
110C2×#41—15724no—
111C2×#41—15772no—
112C2×#41—15772no—
113C2×#41C2×D157124yesdirect product factor
114C22×Q8—15724no—
115C22×Q8—1573no—
116C22×Q8C2×D15711yescharacteristic, complemented
117C22×D4—1576no—
118C22×D4—15772no—
119C22×D4—1573no—
120C22×D4C2×D15713yescomplemented
121C23×C4—1573no—
122C23×C4—1573no—
123C23×C4—1573no—
124C23×C4—1571no—
125C23×C4—1573no—
126C23×C4—15772no—
127C23×C4C2×D15713yescomplemented
128C24—31424no—
129C24—15736no—
130C24—1573no—
131C24—1571no—
132C24C22×D15713yes—
133#41—15764no—
134#41—157192no—
135#41—157192no—
136#41C22×D157164yesdirect product factor
137C2×Q8—15764no—
138C2×Q8—15736no—
139C2×Q8C22×D157112yescomplemented
140C2×D4—15772no—
141C2×D4—157192no—
142C2×D4—15736no—
143C2×D4C22×D157136yescomplemented
144C22×C4—1571no—
145C22×C4—1573no—
146C22×C4—15736no—
147C22×C4—15712no—
148C22×C4—15736no—
149C22×C4—15736no—
150C22×C4—15736no—
151C22×C4—157192no—
152C22×C4C22×D15713yes—
153C22×C4C22×D15711yescharacteristic
154C22×C4C22×D157136yescomplemented
155C23—212no—
156C23—314144no—
157C23—31412no—
158C23—15748no—
159C23—15718no—
160C23—1578no—
161C23—1576no—
162C23C23×D157118yes—
163C23C23×D15711yescharacteristic
164Q8—15748no—
165Q8C23×D157116yescomplemented
166D4—15796no—
167D4—15748no—
168D4C23×D157148yescomplemented
169C2×C4—1576no—
170C2×C4—15718no—
171C2×C4—15748no—
172C2×C4—15716no—
173C2×C4—15748no—
174C2×C4—15748no—
175C2×C4—15748no—
176C2×C4C23×D15716yes—
177C2×C4C23×D157118yes—
178C2×C4C23×D157148yescomplemented
179C22—236no—
180C22—31496no—
181C22—31436no—
182C22—15712no—
183C22—15724no—
184C22—1574no—
185C22#41×D15714yesdirect product factor
186C22C24×D157112yes—
187C22C24×D15713yes—
188C4—1574no—
189C4—15712no—
190C4C24×D15714yes—
191C4C24×D157112yes—
192C2—212no—
193C2—31412no—
194C2—1578no—
195C2C2×#41×D15716yesdirect product factor
196C2C25×D15711yescharacteristic
subgroupG/H
centerC22×C4C22×D157
commutator, cosocleC2×C157C26
FrattiniC2C25×D157
FittingC22×#41×C157C2
socleC23×C157C24
hypercenterC22×#41D157
hypocenterC157C23×#41
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C22×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#14578955C2semidirect
2. C22×#14578954C2semidirect
3. C22×#14578953C2semidirect
4. C2×#41×D157C2direct (N × H)
5. C22×Q8×D157C2semidirect
6. C22×D4×D157C2semidirect
7. C23×C4×D157C2semidirect
8. C22×#41×C157C2semidirect
10. C2×#14578955C22semidirect
11. C2×#14578954C22semidirect
12. C2×#14578953C22semidirect
13. #41×D157C22direct (N × H)
14. C22×Dic314C22semidirect
15. C2×Q8×D157C22semidirect
16. C22×D628C22semidirect
17. C22×C22⋊D157C22semidirect
18. C2×D4×D157C22semidirect
19. C23×Dic157C22semidirect
22. C22×C4×D157C22semidirect
23. C22×C4×D157C22semidirect
24. C22×C4×D157C22semidirect
25. C2×#41×C157C22semidirect
26. C22×Q8×C157C22semidirect
27. C22×D4×C157C22semidirect
28. C23×C4×C157C22semidirect
33. #14578955C23semidirect
34. #14578954C23semidirect
35. #14578953C23semidirect
36. C2×Dic314C23semidirect
37. Q8×D157C23semidirect
38. C2×D628C23semidirect
39. C2×C22⋊D157C23semidirect
40. D4×D157C23semidirect
43. C22×Dic157C23semidirect
46. C2×C4×D157C23semidirect
47. C2×C4×D157C23semidirect
48. C2×C4×D157C23semidirect
50. #41×C157C23semidirect
51. C2×Q8×C157C23semidirect
52. C2×D4×C157C23semidirect
55. C22×C4×C157C23semidirect
58. C22×D157#41direct (N × H)
62. Dic314C24semidirect
63. D628C24semidirect
64. C22⋊D157C24semidirect
67. C2×Dic157C24semidirect
70. C4×D157C24semidirect
71. C4×D157C24semidirect
75. Q8×C157C24semidirect
76. D4×C157C24semidirect
79. C2×C4×C157C24semidirect
81. C22×C157C2×#41semidirect
86. C2×D157C2×#41direct (N × H)
94. C2×C157C22×#41semidirect
97. D157C22×#41direct (N × H)
98. C157C23×#41semidirect
104. C22×#41D157direct (N × H)
113. C2×#41C2×D157direct (N × H)
116. C22×Q8C2×D157semidirect
120. C22×D4C2×D157semidirect
127. C23×C4C2×D157semidirect
136. #41C22×D157direct (N × H)
139. C2×Q8C22×D157semidirect
143. C2×D4C22×D157semidirect
154. C22×C4C22×D157semidirect
165. Q8C23×D157semidirect
168. D4C23×D157semidirect
178. C2×C4C23×D157semidirect
185. C22#41×D157direct (N × H)
195. C2C2×#41×D157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145789552
C22×#145789542
C22×#145789532
C2×#41×D1572
C22×Q8×D1572
C22×D4×D1572
C23×C4×D1572
C22×#41×C1572
C23×#41157