Finite Group Databasebeta

← C113×#20660 #43288680

Subgroups — C113×#20660 #43288680

Order 28928.

1518 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C113C211yesmaximal, characteristic
2C2×#427×C113C212yesmaximal, complemented
3C113×#2280C212yesmaximal
4C113×#1809C218yesmaximal, complemented
5C113×#1735C212yesmaximal, complemented
6C24×C4×C113C2211yescharacteristic
7C22×M16×C113—28no—
8C22×M16×C113C418yescomplemented
9C22×M16×C113C2214yes—
10C23×C8×C113C2211yescharacteristic
11C23×C8×C113C2211yescharacteristic
12C2×#117×C113C2214yes—
13#427×C113—28no—
14C2×#107×C113C2214yescomplemented
15C2×#106×C113C2214yescomplemented
16#381×C113—22no—
17#380×C113C2218yes—
18#379×C113—22no—
19C4×C22⋊C4×C113—24no—
20#340×C113C2218yescomplemented
21C25×C113D411yescharacteristic
22C23×C4×C113—24no—
23C23×C4×C113—24no—
24C23×C4×C113C2×C414yes—
25C23×C4×C113D411yescharacteristic
26C23×C4×C113D412yes—
27C23×C4×C113Q814yes—
28C23×C4×C113C2312yes—
29C23×C4×C113C2311yescharacteristic
30C2×M16×C113—232no—
31C2×M16×C113—28no—
32C2×M16×C113—28no—
33C2×M16×C113C2×C4116yes—
34C22×C8×C113—24no—
35C22×C8×C113C2×C414yes—
36C22×C8×C113C2×C414yes—
37C22×C8×C113D418yes—
38C22×C8×C113C2312yes—
39C22×C8×C113C2312yes—
40#117×C113—28no—
41#117×C113—28no—
42C2×C4⋊C4×C113C2318yes—
43C2×C22⋊C4×C113—24no—
44C2×C22⋊C4×C113—28no—
45C2×C42×C113—24no—
46#107×C113—28no—
47#106×C113—28no—
48#95×C113—28no—
49C24×C113—24no—
50C24×C113—44no—
51C24×C113C4⋊C414yes—
52C24×C113C2×D412yes—
53C24×C113C2×D411yescharacteristic
54C22×C4×C113—24no—
55C22×C4×C113—28no—
56C22×C4×C113—28no—
57C22×C4×C113—28no—
58C22×C4×C113—216no—
59C22×C4×C113—24no—
60C22×C4×C113—24no—
61C22×C4×C113—28no—
62C22×C4×C113C4⋊C414yes—
63C22×C4×C113C4⋊C418yes—
64C22×C4×C113C22×C414yes—
65C22×C4×C113C22×C412yes—
66C22×C4×C113C2×D412yes—
67C22×C4×C113C2×D414yes—
68C22×C4×C113C2×D411yescharacteristic
69C22×C4×C113C2×Q814yes—
70C22×C4×C113C2×Q812yes—
71C22×C4×C113#4114yes—
72C22×C4×C113C2411yescharacteristic
73M16×C113—232no—
74C2×C8×C113—28no—
75C2×C8×C113—24no—
76C2×C8×C113C22⋊C4116yescomplemented
77C2×C8×C113C22×C414yes—
78C2×C8×C113C22×C414yes—
79C2×C8×C113C2×D414yes—
80C2×C8×C113C2×D414yes—
81C4⋊C4×C113—28no—
82C4⋊C4×C113—28no—
83C22⋊C4×C113—416no—
84C22⋊C4×C113—48no—
85C42×C113—48no—
86C23×C113—24no—
87C23×C113—24no—
88C23×C113—28no—
89C23×C113—28no—
90C23×C113—48no—
91C23×C113—416no—
92C23×C113C2×C4⋊C414yes—
93C23×C113C2×C4⋊C412yes—
94C23×C113#12114yes—
95C23×C113C22×D411yescharacteristic
96C2×C4×C113—24no—
97C2×C4×C113—28no—
98C2×C4×C113—24no—
99C2×C4×C113—24no—
100C2×C4×C113—28no—
101C2×C4×C113—216no—
102C2×C4×C113—48no—
103C2×C4×C113—416no—
104C2×C4×C113C2×C22⋊C414yes—
105C2×C4×C113C2×C4⋊C414yes—
106C2×C4×C113C2×C4⋊C412yes—
107C2×C4×C113#11714yes—
108C2×C4×C113#12114yes—
109C2×C4×C113C22⋊Q818yes—
110C2×C4×C113C23×C411yescharacteristic
111C2×C4×C113C22×D412yes—
112C2×C4×C113C22×Q811yescharacteristic
113C2×C4×C113C2×#4112yes—
114C8×C113—24no—
115C8×C113C2×C22⋊C418yes—
116C22×C113—24no—
117C22×C113—28no—
118C22×C113—28no—
119C22×C113—24no—
120C22×C113—416no—
121C22×C113—48no—
122C22×C113#38014yes—
123C22×C113C22×C4⋊C411yescharacteristic
124C22×C113C2×#12112yes—
125C22×C113#57514yes—
126C4×C113—24no—
127C4×C113—88no—
128C4×C113#38014yes—
129C4×C113C22×C22⋊C411yescharacteristic
130C4×C113C2×#11711yescharacteristic
131C4×C113C2×C22⋊Q812yes—
132#20660C11311yesmaximal, characteristic, direct product factor, Sylow
133C2×C113—24no—
134C2×C113—44no—
135C2×C113C2×#38011yescharacteristic
136C2×C113#291112yes—
137C2×C113#305414yes—
138C23×M16C2×C11311yescharacteristic
139C2×#427C2×C11312yescomplemented
140#2280C2×C11312yes—
141#1809C2×C11318yescomplemented
142#1735C2×C11312yescomplemented
143C113#2066011yescharacteristic, direct product factor, Sylow
144C24×C4C22×C11311yescharacteristic
145C22×M16—28no—
146C22×M16C4×C11318yescomplemented
147C22×M16C22×C11314yes—
148C23×C8C22×C11311yescharacteristic
149C23×C8C22×C11311yescharacteristic
150C2×#117C22×C11314yes—
151#427—28no—
152C2×#107C22×C11314yescomplemented
153C2×#106C22×C11314yescomplemented
154#381—22no—
155#380C22×C11318yes—
156#379—22no—
157C4×C22⋊C4—24no—
158#340C22×C11318yescomplemented
159C25D4×C11311yescharacteristic
160C23×C4—24no—
161C23×C4—24no—
162C23×C4C2×C4×C11314yes—
163C23×C4D4×C11312yes—
164C23×C4D4×C11311yescharacteristic
165C23×C4Q8×C11314yes—
166C23×C4C23×C11312yes—
167C23×C4C23×C11311yescharacteristic
168C2×M16—232no—
169C2×M16—28no—
170C2×M16—28no—
171C2×M16C2×C4×C113116yes—
172C22×C8—24no—
173C22×C8C2×C4×C11314yes—
174C22×C8C2×C4×C11314yes—
175C22×C8D4×C11318yes—
176C22×C8C23×C11312yes—
177C22×C8C23×C11312yes—
178#117—28no—
179#117—28no—
180C2×C4⋊C4C23×C11318yes—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—28no—
183C2×C42—24no—
184#107—28no—
185#106—28no—
186#95—28no—
187C24—24no—
188C24—44no—
189C24C4⋊C4×C11314yes—
190C24C2×D4×C11312yes—
191C24C2×D4×C11311yescharacteristic
192C22×C4—24no—
193C22×C4—28no—
194C22×C4—28no—
195C22×C4—28no—
196C22×C4—216no—
197C22×C4—24no—
198C22×C4—24no—
199C22×C4—28no—
200C22×C4C4⋊C4×C11314yes—
201C22×C4C4⋊C4×C11318yes—
202C22×C4C22×C4×C11314yes—
203C22×C4C22×C4×C11312yes—
204C22×C4C2×D4×C11312yes—
205C22×C4C2×D4×C11314yes—
206C22×C4C2×D4×C11311yescharacteristic
207C22×C4C2×Q8×C11314yes—
208C22×C4C2×Q8×C11312yes—
209C22×C4#41×C11314yes—
210C22×C4C24×C11311yescharacteristic
211M16—232no—
212C2×C8—28no—
213C2×C8—24no—
214C2×C8C22⋊C4×C113116yescomplemented
215C2×C8C22×C4×C11314yes—
216C2×C8C22×C4×C11314yes—
217C2×C8C2×D4×C11314yes—
218C2×C8C2×D4×C11314yes—
219C4⋊C4—28no—
220C4⋊C4—28no—
221C22⋊C4—416no—
222C22⋊C4—48no—
223C42—48no—
224C23—24no—
225C23—24no—
226C23—28no—
227C23—28no—
228C23—48no—
229C23—416no—
230C23C2×C4⋊C4×C11314yes—
231C23C2×C4⋊C4×C11312yes—
232C23#121×C11314yes—
233C23C22×D4×C11311yescharacteristic
234C2×C4—24no—
235C2×C4—28no—
236C2×C4—24no—
237C2×C4—24no—
238C2×C4—28no—
239C2×C4—216no—
240C2×C4—48no—
241C2×C4—416no—
242C2×C4C2×C22⋊C4×C11314yes—
243C2×C4C2×C4⋊C4×C11314yes—
244C2×C4C2×C4⋊C4×C11312yes—
245C2×C4#117×C11314yes—
246C2×C4#121×C11314yes—
247C2×C4C22⋊Q8×C11318yes—
248C2×C4C23×C4×C11311yescharacteristic
249C2×C4C22×D4×C11312yes—
250C2×C4C22×Q8×C11311yescharacteristic
251C2×C4C2×#41×C11312yes—
252C8—24no—
253C8C2×C22⋊C4×C11318yes—
254C22—28no—
255C22—24no—
256C22—24no—
257C22—28no—
258C22—416no—
259C22—48no—
260C22#380×C11314yes—
261C22C22×C4⋊C4×C11311yescharacteristic
262C22C2×#121×C11312yes—
263C22#575×C11314yes—
264C4—24no—
265C4—88no—
266C4#380×C11314yes—
267C4C22×C22⋊C4×C11311yescharacteristic
268C4C2×#117×C11311yescharacteristic
269C4C2×C22⋊Q8×C11312yes—
270C2—24no—
271C2—44no—
272C2C2×#380×C11311yescharacteristic
273C2C113×#291112yes—
274C2C113×#305414yes—
subgroupG/H
centerC22×C4×C113C2×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC23×C113C22×D4
prime radicalC25×C113D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C113 ◁ C24×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#427×C113C2semidirect
4. C113×#1809C2semidirect
5. C113×#1735C2semidirect
8. C22×M16×C113C4semidirect
14. C2×#107×C113C22semidirect
15. C2×#106×C113C22semidirect
20. #340×C113C22semidirect
76. C2×C8×C113C22⋊C4semidirect
132. #20660C113direct (N × H)
139. C2×#427C2×C113semidirect
141. #1809C2×C113semidirect
142. #1735C2×C113semidirect
143. C113#20660direct (N × H)
146. C22×M16C4×C113semidirect
152. C2×#107C22×C113semidirect
153. C2×#106C22×C113semidirect
158. #340C22×C113semidirect
214. C2×C8C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C23×M16×C1132
C2×#427×C1132
C113×#22802
C113×#18092
C113×#17352
#20660113