Finite Group Databasebeta

← C113×#20354 #43288374

Subgroups — C113×#20354 #43288374

Order 28928.

2410 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C113C212yesmaximal
2C2×#518×C113C211yesmaximal, characteristic
3C113×#1740C214yesmaximal, complemented
4C2×#342×C113C218yesmaximal, complemented
5C23×D4×C113C2211yescharacteristic
6#518×C113—28no—
7#518×C113—28no—
8#518×C113C4116yescomplemented
9C2×C4×D4×C113—28no—
10C2×C4×D4×C113C418yescomplemented
11C2×#117×C113C2214yes—
12C2×#117×C113C2212yes—
13C22×C22⋊C4×C113C2214yes—
14C22×C22⋊C4×C113C2218yes—
15#342×C113C22116yes—
16C25×C113C2312yes—
17C22×D4×C113C2×C414yes—
18C22×D4×C113C2×C418yes—
19C22×D4×C113D418yes—
20C22×D4×C113D414yes—
21C22×D4×C113Q814yes—
22C23×C4×C113—28no—
23C23×C4×C113C2×C418yescomplemented
24C23×C4×C113C2311yescharacteristic
25C4×D4×C113—264no—
26C4×D4×C113—232no—
27#117×C113—28no—
28#117×C113—28no—
29#117×C113C2×C4116yescomplemented
30C2×C4⋊C4×C113—24no—
31C2×C4⋊C4×C113C2×C414yescomplemented
32C2×C22⋊C4×C113—28no—
33C2×C22⋊C4×C113—216no—
34C2×C22⋊C4×C113—216no—
35C2×C22⋊C4×C113C2×C418yescomplemented
36C2×C22⋊C4×C113C2×C4132yescomplemented
37C2×C22⋊C4×C113C2314yes—
38C2×C22⋊C4×C113C2318yes—
39C2×C42×C113—24no—
40C2×C42×C113C2×C414yescomplemented
41C24×C113—84no—
42C24×C113C22×C414yes—
43C24×C113C22×C418yes—
44C24×C113C2×D418yes—
45C24×C113C2×D414yes—
46C24×C113C2×Q814yes—
47C24×C113C2411yescharacteristic
48C2×D4×C113C42116yes—
49C2×D4×C113C22⋊C4132yes—
50C2×D4×C113C22⋊C4116yes—
51C2×D4×C113C4⋊C4116yes—
52C2×D4×C113C4⋊C4132yes—
53C22×C4×C113—28no—
54C22×C4×C113—216no—
55C22×C4×C113—232no—
56C22×C4×C113—816no—
57C22×C4×C113—88no—
58C22×C4×C113C22×C418yes—
59C22×C4×C113C22×C412yes—
60C22×C4×C113C22×C414yes—
61C22×C4×C113C2×D414yes—
62C22×C4×C113C2×D412yes—
63C22×C4×C113C2×Q812yes—
64C4⋊C4×C113—216no—
65C4⋊C4×C113—28no—
66C22⋊C4×C113—232no—
67C22⋊C4×C113—216no—
68C22⋊C4×C113—28no—
69C22⋊C4×C113—28no—
70C22⋊C4×C113C22×C4116yes—
71C42×C113—216no—
72C42×C113—28no—
73C23×C113—48no—
74C23×C113—416no—
75C23×C113—42no—
76C23×C113—88no—
77C23×C113—84no—
78C23×C113—84no—
79C23×C113C2×C4218yes—
80C23×C113C2×C22⋊C418yes—
81C23×C113C2×C22⋊C4116yes—
82C23×C113C2×C4⋊C418yes—
83C23×C113C2×C4⋊C4116yes—
84C23×C113C23×C411yescharacteristic
85C23×C113C23×C412yes—
86C23×C113C22×D412yes—
87C23×C113C22×D411yescharacteristic
88C23×C113C22×Q811yescharacteristic
89D4×C113#95164yes—
90C2×C4×C113—216no—
91C2×C4×C113—28no—
92C2×C4×C113—416no—
93C2×C4×C113—48no—
94C2×C4×C113—816no—
95C2×C4×C113—832no—
96C2×C4×C113C2×C4214yes—
97C2×C4×C113C2×C22⋊C418yes—
98C2×C4×C113C2×C22⋊C414yes—
99C2×C4×C113C2×C4⋊C414yes—
100C2×C4×C113C2×C4⋊C418yes—
101C22×C113—22no—
102C22×C113—24no—
103C22×C113—216no—
104C22×C113—416no—
105C22×C113—42no—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113—48no—
109C22×C113—48no—
110C22×C113—416no—
111C22×C113C2×#95116yes—
112C22×C113C22×C4211yescharacteristic
113C22×C113C22×C22⋊C412yes—
114C22×C113C22×C22⋊C411yescharacteristic
115C22×C113C22×C4⋊C411yescharacteristic
116C22×C113C22×C4⋊C412yes—
117C4×C113—416no—
118C4×C113—48no—
119C4×C113C2×#9518yes—
120#20354C11311yesmaximal, characteristic, direct product factor, Sylow
121C2×C113—22no—
122C2×C113—21no—
123C2×C113—22no—
124C2×C113—21no—
125C2×C113—216no—
126C2×C113C22×#9511yescharacteristic
127C2×C113#288312yes—
128C2×#518C2×C11312yes—
129C2×#518C2×C11311yescharacteristic
130#1740C2×C11314yescomplemented
131C2×#342C2×C11318yescomplemented
132C113#2035411yescharacteristic, direct product factor, Sylow
133C23×D4C22×C11311yescharacteristic
134#518—28no—
135#518—28no—
136#518C4×C113116yescomplemented
137C2×C4×D4—28no—
138C2×C4×D4C4×C11318yescomplemented
139C2×#117C22×C11314yes—
140C2×#117C22×C11312yes—
141C22×C22⋊C4C22×C11314yes—
142C22×C22⋊C4C22×C11318yes—
143#342C22×C113116yes—
144C25C23×C11312yes—
145C22×D4C2×C4×C11314yes—
146C22×D4C2×C4×C11318yes—
147C22×D4D4×C11318yes—
148C22×D4D4×C11314yes—
149C22×D4Q8×C11314yes—
150C23×C4—28no—
151C23×C4C2×C4×C11318yescomplemented
152C23×C4C23×C11311yescharacteristic
153C4×D4—264no—
154C4×D4—232no—
155#117—28no—
156#117—28no—
157#117C2×C4×C113116yescomplemented
158C2×C4⋊C4—24no—
159C2×C4⋊C4C2×C4×C11314yescomplemented
160C2×C22⋊C4—28no—
161C2×C22⋊C4—216no—
162C2×C22⋊C4—216no—
163C2×C22⋊C4C2×C4×C11318yescomplemented
164C2×C22⋊C4C2×C4×C113132yescomplemented
165C2×C22⋊C4C23×C11314yes—
166C2×C22⋊C4C23×C11318yes—
167C2×C42—24no—
168C2×C42C2×C4×C11314yescomplemented
169C24—84no—
170C24C22×C4×C11314yes—
171C24C22×C4×C11318yes—
172C24C2×D4×C11318yes—
173C24C2×D4×C11314yes—
174C24C2×Q8×C11314yes—
175C24C24×C11311yescharacteristic
176C2×D4C42×C113116yes—
177C2×D4C22⋊C4×C113116yes—
178C2×D4C22⋊C4×C113132yes—
179C2×D4C4⋊C4×C113116yes—
180C2×D4C4⋊C4×C113132yes—
181C22×C4—28no—
182C22×C4—216no—
183C22×C4—232no—
184C22×C4—816no—
185C22×C4—88no—
186C22×C4C22×C4×C11318yes—
187C22×C4C22×C4×C11312yes—
188C22×C4C22×C4×C11314yes—
189C22×C4C2×D4×C11314yes—
190C22×C4C2×D4×C11312yes—
191C22×C4C2×Q8×C11312yes—
192C4⋊C4—216no—
193C4⋊C4—28no—
194C22⋊C4—216no—
195C22⋊C4—232no—
196C22⋊C4—28no—
197C22⋊C4—28no—
198C22⋊C4C22×C4×C113116yes—
199C42—216no—
200C42—28no—
201C23—48no—
202C23—416no—
203C23—42no—
204C23—88no—
205C23—84no—
206C23—84no—
207C23C2×C42×C11318yes—
208C23C2×C22⋊C4×C11318yes—
209C23C2×C22⋊C4×C113116yes—
210C23C2×C4⋊C4×C11318yes—
211C23C2×C4⋊C4×C113116yes—
212C23C23×C4×C11311yescharacteristic
213C23C23×C4×C11312yes—
214C23C22×D4×C11312yes—
215C23C22×D4×C11311yescharacteristic
216C23C22×Q8×C11311yescharacteristic
217D4#95×C113164yes—
218C2×C4—28no—
219C2×C4—216no—
220C2×C4—416no—
221C2×C4—48no—
222C2×C4—816no—
223C2×C4—832no—
224C2×C4C2×C42×C11314yes—
225C2×C4C2×C22⋊C4×C11318yes—
226C2×C4C2×C22⋊C4×C11314yes—
227C2×C4C2×C4⋊C4×C11314yes—
228C2×C4C2×C4⋊C4×C11318yes—
229C22—22no—
230C22—24no—
231C22—216no—
232C22—416no—
233C22—42no—
234C22—41no—
235C22—41no—
236C22—48no—
237C22—48no—
238C22—416no—
239C22C2×#95×C113116yes—
240C22C22×C42×C11311yescharacteristic
241C22C22×C22⋊C4×C11312yes—
242C22C22×C22⋊C4×C11311yescharacteristic
243C22C22×C4⋊C4×C11311yescharacteristic
244C22C22×C4⋊C4×C11312yes—
245C4—416no—
246C4—48no—
247C4C2×#95×C11318yes—
248C2—22no—
249C2—21no—
250C2—21no—
251C2—22no—
252C2—216no—
253C2C22×#95×C11311yescharacteristic
254C2C113×#288312yes—
subgroupG/H
center, socleC22×C113C22×C22⋊C4
commutatorC22C22×C42×C113
Frattini, cosocleC24C24×C113
prime radicalC23×D4×C113C22
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1740C2semidirect
4. C2×#342×C113C2semidirect
8. #518×C113C4semidirect
10. C2×C4×D4×C113C4semidirect
23. C23×C4×C113C2×C4semidirect
29. #117×C113C2×C4semidirect
31. C2×C4⋊C4×C113C2×C4semidirect
35. C2×C22⋊C4×C113C2×C4semidirect
36. C2×C22⋊C4×C113C2×C4semidirect
40. C2×C42×C113C2×C4semidirect
120. #20354C113direct (N × H)
130. #1740C2×C113semidirect
131. C2×#342C2×C113semidirect
132. C113#20354direct (N × H)
136. #518C4×C113semidirect
138. C2×C4×D4C4×C113semidirect
151. C23×C4C2×C4×C113semidirect
157. #117C2×C4×C113semidirect
159. C2×C4⋊C4C2×C4×C113semidirect
163. C2×C22⋊C4C2×C4×C113semidirect
164. C2×C22⋊C4C2×C4×C113semidirect
168. C2×C42C2×C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1132
C113×#17402
C2×#342×C1132
#20354113