Finite Group Databasebeta

← C113×#9145 #43277165

Subgroups — C113×#9145 #43277165

Order 28928.

694 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2855C211yesmaximal, characteristic
2C2×#376×C113C211yesmaximal, characteristic
3C113×#1817C211yesmaximal, characteristic
4C2×#328×C113C212yesmaximal
5C113×#1294C212yesmaximal
6C2×C22⋊Q8×C113C2211yescharacteristic
7C22×C42×C113—21no—
8C22×C42×C113C2211yescharacteristic
9C2×C22⋊C8×C113C2212yes—
10#391×C113C412yescomplemented
11#389×C113C412yescomplemented
12#387×C113—22no—
13#385×C113—21no—
14#381×C113—21no—
15#380×C113C2211yescharacteristic
16#376×C113—24no—
17C2×#95×C113—21no—
18C2×#95×C113C2212yes—
19#336×C113—22no—
20#328×C113—24no—
21C22×Q8×C113C2×C411yescharacteristic
22C23×C4×C113—22no—
23C23×C4×C113D411yescharacteristic
24C23×C4×C113D411yescharacteristic
25C23×C4×C113C2311yescharacteristic
26C22×C8×C113—22no—
27C22⋊Q8×C113—22no—
28C22⋊Q8×C113—22no—
29C2×C4⋊C4×C113—22no—
30C2×C4⋊C4×C113—21no—
31C2×C4⋊C4×C113C2×C411yescharacteristic
32C2×C4⋊C4×C113C2×C412yes—
33C2×C22⋊C4×C113—21no—
34C2×C22⋊C4×C113—21no—
35C2×C42×C113—28no—
36C2×C42×C113—24no—
37C2×C42×C113—22no—
38C2×C42×C113—22no—
39C2×C42×C113C2×C412yes—
40C2×C42×C113D412yes—
41C22⋊C8×C113—22no—
42C22⋊C8×C113—22no—
43#95×C113—24no—
44#95×C113—22no—
45#95×C113—22no—
46#95×C113—22no—
47#95×C113—22no—
48#95×C113—21no—
49#95×C113D414yes—
50C24×C113C2×D411yescharacteristic
51C2×Q8×C113—22no—
52C2×Q8×C113—42no—
53C22×C4×C113—21no—
54C22×C4×C113—21no—
55C22×C4×C113—24no—
56C22×C4×C113—28no—
57C22×C4×C113—21no—
58C22×C4×C113—24no—
59C22×C4×C113—21no—
60C22×C4×C113—22no—
61C22×C4×C113—22no—
62C22×C4×C113—22no—
63C22×C4×C113—21no—
64C22×C4×C113—21no—
65C22×C4×C113—42no—
66C22×C4×C113—44no—
67C22×C4×C113—42no—
68C22×C4×C113—42no—
69C22×C4×C113C22⋊C412yes—
70C22×C4×C113C22⋊C412yes—
71C22×C4×C113C22×C411yescharacteristic
72C22×C4×C113C2×D411yescharacteristic
73C22×C4×C113C2×D412yes—
74C22×C4×C113#4112yes—
75C2×C8×C113—44no—
76C2×C8×C113—42no—
77C4⋊C4×C113—22no—
78C4⋊C4×C113—42no—
79C4⋊C4×C113—44no—
80C4⋊C4×C113—42no—
81C22⋊C4×C113—41no—
82C22⋊C4×C113—41no—
83C22⋊C4×C113—42no—
84C42×C113—216no—
85C42×C113—24no—
86C42×C113—24no—
87C23×C113—22no—
88C23×C113—22no—
89C23×C113C2×C22⋊C411yescharacteristic
90C23×C113#12011yescharacteristic
91C23×C113#12311yescharacteristic
92C23×C113#13512yes—
93C23×C113#13712yes—
94Q8×C113—82no—
95C2×C4×C113—24no—
96C2×C4×C113—24no—
97C2×C4×C113—22no—
98C2×C4×C113—22no—
99C2×C4×C113—22no—
100C2×C4×C113—22no—
101C2×C4×C113—28no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113—22no—
105C2×C4×C113—42no—
106C2×C4×C113—42no—
107C2×C4×C113—44no—
108C2×C4×C113—48no—
109C2×C4×C113—48no—
110C2×C4×C113—42no—
111C2×C4×C113—44no—
112C2×C4×C113—42no—
113C2×C4×C113—41no—
114C2×C4×C113—41no—
115C2×C4×C113—42no—
116C2×C4×C113—42no—
117C2×C4×C113—42no—
118C2×C4×C113—42no—
119C2×C4×C113—42no—
120C2×C4×C113#10414yes—
121C2×C4×C113C4×D412yes—
122C2×C4×C113#12112yes—
123C8×C113—82no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—21no—
128C22×C113—24no—
129C22×C113—24no—
130C22×C113#38611yescharacteristic
131C22×C113#41012yes—
132C22×C113#41611yescharacteristic
133C22×C113#41911yescharacteristic
134C22×C113C2×#10412yes—
135C22×C113#45212yes—
136C22×C113#48512yes—
137C4×C113—24no—
138C4×C113—22no—
139C4×C113—22no—
140C4×C113—48no—
141C4×C113—42no—
142C4×C113—81no—
143C4×C113—81no—
144C4×C113—82no—
145#9145C11311yesmaximal, characteristic, direct product factor, Sylow
146C2×C113—22no—
147C2×C113—22no—
148C2×C113#150012yes—
149C2×C113#150612yes—
150C2×C113#187311yescharacteristic
151C2×C113#189611yescharacteristic
152C2×C113#189911yescharacteristic
153#2855C2×C11311yescharacteristic
154C2×#376C2×C11311yescharacteristic
155#1817C2×C11311yescharacteristic
156C2×#328C2×C11312yes—
157#1294C2×C11312yes—
158C113#914511yescharacteristic, direct product factor, Sylow
159C2×C22⋊Q8C22×C11311yescharacteristic
160C22×C42—21no—
161C22×C42C22×C11311yescharacteristic
162C2×C22⋊C8C22×C11312yes—
163#391C4×C11312yescomplemented
164#389C4×C11312yescomplemented
165#387—22no—
166#385—21no—
167#381—21no—
168#380C22×C11311yescharacteristic
169#376—24no—
170C2×#95—21no—
171C2×#95C22×C11312yes—
172#336—22no—
173#328—24no—
174C22×Q8C2×C4×C11311yescharacteristic
175C23×C4—22no—
176C23×C4D4×C11311yescharacteristic
177C23×C4D4×C11311yescharacteristic
178C23×C4C23×C11311yescharacteristic
179C22×C8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×C4×C11311yescharacteristic
185C2×C4⋊C4C2×C4×C11312yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C42—24no—
189C2×C42—28no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C2×C4×C11312yes—
193C2×C42D4×C11312yes—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—24no—
197#95—22no—
198#95—22no—
199#95—22no—
200#95—22no—
201#95—21no—
202#95D4×C11314yes—
203C24C2×D4×C11311yescharacteristic
204C2×Q8—22no—
205C2×Q8—42no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—24no—
209C22×C4—28no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—44no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊C4×C11312yes—
223C22×C4C22⋊C4×C11312yes—
224C22×C4C22×C4×C11311yescharacteristic
225C22×C4C2×D4×C11311yescharacteristic
226C22×C4C2×D4×C11312yes—
227C22×C4#41×C11312yes—
228C2×C8—44no—
229C2×C8—42no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—42no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—42no—
237C42—216no—
238C42—24no—
239C42—24no—
240C23—22no—
241C23—22no—
242C23C2×C22⋊C4×C11311yescharacteristic
243C23#120×C11311yescharacteristic
244C23#123×C11311yescharacteristic
245C23#135×C11312yes—
246C23#137×C11312yes—
247Q8—82no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—28no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—48no—
262C2×C4—48no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4#104×C11314yes—
274C2×C4C4×D4×C11312yes—
275C2×C4#121×C11312yes—
276C8—82no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—24no—
282C22—24no—
283C22#386×C11311yescharacteristic
284C22#410×C11312yes—
285C22#416×C11311yescharacteristic
286C22#419×C11311yescharacteristic
287C22C2×#104×C11312yes—
288C22#452×C11312yes—
289C22#485×C11312yes—
290C4—24no—
291C4—22no—
292C4—22no—
293C4—48no—
294C4—42no—
295C4—81no—
296C4—81no—
297C4—82no—
298C2—22no—
299C2—22no—
300C2C113×#150012yes—
301C2C113×#150612yes—
302C2C113×#187311yescharacteristic
303C2C113×#189611yescharacteristic
304C2C113×#189911yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC24×C113C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
10. #391×C113C4semidirect
11. #389×C113C4semidirect
145. #9145C113direct (N × H)
158. C113#9145direct (N × H)
163. #391C4×C113semidirect
164. #389C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#28552
C2×#376×C1132
C113×#18172
C2×#328×C1132
C113×#12942
#9145113