Finite Group Databasebeta

← C22×C13×#568 #15749413

Subgroups — C22×C13×#568 #15749413

Order 3328.

11118 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×#41C211yesmaximal, characteristic
2C2×C13×#568C2148yesmaximal, direct product factor
3C22×C13×#131C218yesmaximal, complemented
4C23×C13×M16C216yesmaximal, complemented
5C22×C13×#41C414yes—
6C22×C13×#41C4124yes—
7C22×C13×#41C2214yes—
8C22×C13×#41C22124yes—
9C23×Q8×C13C411yescharacteristic
10C23×D4×C13C413yes—
11C24×C4×C13C2213yes—
12C13×#568C221256yesdirect product factor
13C2×C13×#131C221192yescomplemented
14C22×C13×M16C2214yes—
15C22×C13×M16C22112yescomplemented
16C22×C13×M16C221144yescomplemented
17C23×C8×C13C22112yescomplemented
18C25×C13C2×C413yes—
19C2×C13×#41C2×C4148yes—
20C2×C13×#41C2×C4196yes—
21C2×C13×#41C2×C41192yes—
22C2×C13×#41C23148yes—
23C2×C13×#41C23164yes—
24C22×Q8×C13C2×C414yes—
25C22×Q8×C13C2×C4124yes—
26C22×D4×C13C2×C4112yes—
27C22×D4×C13C2×C4172yes—
28C23×C4×C13C2×C413yes—
29C23×C4×C13C2×C416yes—
30C23×C4×C13C2×C4136yes—
31C23×C4×C13C23136yes—
32C23×C4×C13C2316yes—
33C23×C4×C13C2311yescharacteristic
34C13×#131C231512yescomplemented
35C2×C13×M16C23148yes—
36C2×C13×M16C231144yescomplemented
37C2×C13×M16C231384yescomplemented
38C22×C8×C13C2318yes—
39C22×C8×C13C231144yescomplemented
40C22×#568C1311yesmaximal, characteristic, direct product factor, Sylow
41C24×C13—412no—
42C24×C13C22×C411yescharacteristic
43C24×C13C22×C416yes—
44C24×C13C22×C4136yes—
45C13×#41C22×C41192yes—
46C13×#41C22×C41256yes—
47C13×#41C24164yes—
48C2×Q8×C13C22×C4148yes—
49C2×Q8×C13C22×C4164yes—
50C2×D4×C13C22×C41144yes—
51C2×D4×C13C22×C41192yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×C4×C13C22×C416yes—
54C22×C4×C13C22×C4136yes—
55C22×C4×C13C22×C416yes—
56C22×C4×C13C22×C4172yes—
57C22×C4×C13C22×C41144yes—
58C22×C4×C13C22×C4136yes—
59C22×C4×C13C24136yes—
60C22×C4×C13C2416yes—
61C22×C4×C13C24148yes—
62C22×C4×C13C2411yescharacteristic
63C13×M16C24164yes—
64C13×M16C241192yescomplemented
65C2×C8×C13C24148yes—
66C2×C8×C13C241192yescomplemented
67C23×#41C2×C1311yescharacteristic
68C2×#568C2×C13148yesdirect product factor
69C22×#131C2×C1318yescomplemented
70C23×M16C2×C1316yescomplemented
71C23×C13—24no—
72C23×C13—224no—
73C23×C13—472no—
74C23×C13C23×C416yes—
75C23×C13C23×C4136yes—
76C23×C13C23×C4148yes—
77C23×C13C23×C411yescharacteristic
78Q8×C13C23×C4164yes—
79D4×C13C23×C41192yes—
80C2×C4×C13C23×C4112yes—
81C2×C4×C13C23×C416yes—
82C2×C4×C13C23×C413yes—
83C2×C4×C13C23×C4148yes—
84C2×C4×C13C23×C4136yes—
85C2×C4×C13C23×C4172yes—
86C2×C4×C13C23×C4196yes—
87C2×C4×C13C2513yes—
88C2×C4×C13C25124yes—
89C2×C4×C13C2514yes—
90C8×C13C25132yes—
91C22×#41C4×C1314yes—
92C22×#41C4×C13124yes—
93C22×#41C22×C1314yes—
94C22×#41C22×C13124yes—
95C23×Q8C4×C1311yescharacteristic
96C23×D4C4×C1313yes—
97C24×C4C22×C1313yes—
98#568C22×C131256yesdirect product factor
99C2×#131C22×C131192yescomplemented
100C22×M16C22×C1314yes—
101C22×M16C22×C13112yescomplemented
102C22×M16C22×C131144yescomplemented
103C23×C8C22×C13112yescomplemented
104C22×C13—212no—
105C22×C13—272no—
106C22×C13—448no—
107C22×C13#56814yesdirect product factor
108C22×C13C24×C414yes—
109C22×C13C24×C4124yes—
110C22×C13C24×C413yes—
111C4×C13C24×C414yes—
112C4×C13C24×C413yes—
113C4×C13C24×C4124yes—
114C4×C13C2611yescharacteristic
115C25C2×C4×C1313yes—
116C2×#41C2×C4×C13148yes—
117C2×#41C2×C4×C13196yes—
118C2×#41C2×C4×C131192yes—
119C2×#41C23×C13148yes—
120C2×#41C23×C13164yes—
121C22×Q8C2×C4×C1314yes—
122C22×Q8C2×C4×C13124yes—
123C22×D4C2×C4×C13112yes—
124C22×D4C2×C4×C13172yes—
125C23×C4C2×C4×C1313yes—
126C23×C4C2×C4×C1316yes—
127C23×C4C2×C4×C13136yes—
128C23×C4C23×C1316yes—
129C23×C4C23×C1311yescharacteristic
130C23×C4C23×C13136yes—
131#131C23×C131512yescomplemented
132C2×M16C23×C13148yes—
133C2×M16C23×C131144yescomplemented
134C2×M16C23×C131384yescomplemented
135C22×C8C23×C1318yes—
136C22×C8C23×C131144yescomplemented
137C2×C13—24no—
138C2×C13—224no—
139C2×C13C2×#56816yesdirect product factor
140C2×C13C25×C411yescharacteristic
141C24—412no—
142C24C22×C4×C1311yescharacteristic
143C24C22×C4×C1316yes—
144C24C22×C4×C13136yes—
145#41C22×C4×C131192yes—
146#41C22×C4×C131256yes—
147#41C24×C13164yes—
148C2×Q8C22×C4×C13148yes—
149C2×Q8C22×C4×C13164yes—
150C2×D4C22×C4×C131144yes—
151C2×D4C22×C4×C131192yes—
152C22×C4C22×C4×C1316yes—
153C22×C4C22×C4×C1311yescharacteristic
154C22×C4C22×C4×C13136yes—
155C22×C4C22×C4×C1316yes—
156C22×C4C22×C4×C13136yes—
157C22×C4C22×C4×C13172yes—
158C22×C4C22×C4×C131144yes—
159C22×C4C24×C1311yescharacteristic
160C22×C4C24×C13136yes—
161C22×C4C24×C1316yes—
162C22×C4C24×C13148yes—
163M16C24×C13164yes—
164M16C24×C131192yescomplemented
165C2×C8C24×C13148yes—
166C2×C8C24×C131192yescomplemented
167C13C22×#56811yescharacteristic, direct product factor, Sylow
168C23—24no—
169C23—224no—
170C23—472no—
171C23C23×C4×C1316yes—
172C23C23×C4×C13136yes—
173C23C23×C4×C13148yes—
174C23C23×C4×C1311yescharacteristic
175Q8C23×C4×C13164yes—
176D4C23×C4×C131192yes—
177C2×C4C23×C4×C13112yes—
178C2×C4C23×C4×C1313yes—
179C2×C4C23×C4×C1316yes—
180C2×C4C23×C4×C13148yes—
181C2×C4C23×C4×C13136yes—
182C2×C4C23×C4×C13172yes—
183C2×C4C23×C4×C13196yes—
184C2×C4C25×C1313yes—
185C2×C4C25×C13124yes—
186C2×C4C25×C1314yes—
187C8C25×C13132yes—
188C22—212no—
189C22—272no—
190C22—448no—
191C22C13×#56814yesdirect product factor
192C22C24×C4×C1314yes—
193C22C24×C4×C13124yes—
194C22C24×C4×C1313yes—
195C4C24×C4×C1313yes—
196C4C24×C4×C1314yes—
197C4C24×C4×C13124yes—
198C4C26×C1311yescharacteristic
199C2—24no—
200C2—224no—
201C2C2×C13×#56816yesdirect product factor
202C2C25×C4×C1311yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutatorC2C25×C4×C13
Frattini, cosocleC4C26×C13
socleC23×C13C23×C4
prime radicalC23×C13×#41C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#568C2direct (N × H)
3. C22×C13×#131C2semidirect
4. C23×C13×M16C2semidirect
12. C13×#568C22direct (N × H)
13. C2×C13×#131C22semidirect
15. C22×C13×M16C22semidirect
16. C22×C13×M16C22semidirect
17. C23×C8×C13C22semidirect
34. C13×#131C23semidirect
36. C2×C13×M16C23semidirect
37. C2×C13×M16C23semidirect
39. C22×C8×C13C23semidirect
40. C22×#568C13direct (N × H)
64. C13×M16C24semidirect
66. C2×C8×C13C24semidirect
68. C2×#568C2×C13direct (N × H)
69. C22×#131C2×C13semidirect
70. C23×M16C2×C13semidirect
98. #568C22×C13direct (N × H)
99. C2×#131C22×C13semidirect
101. C22×M16C22×C13semidirect
102. C22×M16C22×C13semidirect
103. C23×C8C22×C13semidirect
107. C22×C13#568direct (N × H)
131. #131C23×C13semidirect
133. C2×M16C23×C13semidirect
134. C2×M16C23×C13semidirect
136. C22×C8C23×C13semidirect
139. C2×C13C2×#568direct (N × H)
164. M16C24×C13semidirect
166. C2×C8C24×C13semidirect
167. C13C22×#568direct (N × H)
191. C22C13×#568direct (N × H)
201. C2C2×C13×#568direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C13×#412
C2×C13×#5682
C22×C13×#1312
C23×C13×M162
C22×#56813