Finite Group Databasebeta

← C131×#10326 #45696210

Subgroups — C131×#10326 #45696210

Order 33536.

1174 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3192×C131C211yesmaximal, characteristic, complemented
2#2433×C131C212yesmaximal, complemented
3#1783×C131C211yesmaximal, characteristic, complemented
4#1507×C131C212yesmaximal, complemented
5#1297×C131C211yesmaximal, characteristic, complemented
6C23×D4×C131C2211yescharacteristic
7C2×#127×C131—22no—
8C2×#121×C131C2212yes—
9C2×#120×C131—24no—
10#481×C131—22no—
11#469×C131—22no—
12#447×C131—22no—
13C2×#100×C131—22no—
14#407×C131C2211yescharacteristic
15#407×C131C2211yescharacteristic
16#392×C131—24no—
17#390×C131—22no—
18C4×C22⋊C4×C131C2212yes—
19#327×C131—24no—
20C25×C131D412yes—
21C22×D4×C131—22no—
22C22×D4×C131—28no—
23C22×D4×C131—22no—
24C22×D4×C131—21no—
25C22×D4×C131—22no—
26C22×D4×C131—21no—
27C22×D4×C131—44no—
28C22×D4×C131D412yescomplemented
29C23×C4×C131C2311yescharacteristic
30C2×D8×C131—22no—
31C2×M16×C131—21no—
32C2×M16×C131D412yescomplemented
33#127×C131—48no—
34#121×C131—22no—
35#121×C131—22no—
36#121×C131—22no—
37#121×C131—22no—
38#120×C131—416no—
39C2×C4⋊C4×C131D412yescomplemented
40C2×C22⋊C4×C131—22no—
41C2×C22⋊C4×C131—28no—
42C2×C22⋊C4×C131—22no—
43C2×C42×C131—22no—
44#106×C131—22no—
45#102×C131—24no—
46#100×C131—44no—
47C22⋊C8×C131—22no—
48C22⋊C8×C131—22no—
49#95×C131D414yescomplemented
50C24×C131—24no—
51C24×C131—22no—
52C24×C131—22no—
53C24×C131—44no—
54C24×C131—48no—
55C24×C131C2×D411yescharacteristic
56C2×D4×C131—24no—
57C2×D4×C131—28no—
58C2×D4×C131—22no—
59C2×D4×C131—22no—
60C2×D4×C131—44no—
61C2×D4×C131—42no—
62C2×D4×C131—44no—
63C2×D4×C131—416no—
64C2×D4×C131—48no—
65C2×D4×C131—44no—
66C2×D4×C131—48no—
67C2×D4×C131—416no—
68C2×D4×C131—42no—
69C2×D4×C131—42no—
70C2×D4×C131—41no—
71C2×D4×C131—42no—
72C2×D4×C131—41no—
73C2×D4×C131—88no—
74C22×C4×C131—24no—
75C22×C4×C131—22no—
76C22×C4×C131—42no—
77C22×C4×C131C2×D412yes—
78C22×C4×C131C2×D411yescharacteristic
79C22×C4×C131C2×D412yes—
80C22×C4×C131#4111yescharacteristic
81D8×C131—82no—
82M16×C131—42no—
83M16×C131—42no—
84C2×C8×C131—22no—
85C2×C8×C131—41no—
86C4⋊C4×C131—22no—
87C4⋊C4×C131—22no—
88C22⋊C4×C131—28no—
89C22⋊C4×C131—416no—
90C22⋊C4×C131—42no—
91C22⋊C4×C131—42no—
92C42×C131—44no—
93C23×C131—24no—
94C23×C131—28no—
95C23×C131—24no—
96C23×C131—41no—
97C23×C131—48no—
98C23×C131—44no—
99C23×C131—42no—
100C23×C131—44no—
101C23×C131—44no—
102C23×C131—42no—
103C23×C131—48no—
104C23×C131—42no—
105C23×C131—44no—
106C23×C131—84no—
107C23×C131—816no—
108C23×C131#12012yes—
109C23×C131#12111yescharacteristic
110D4×C131—44no—
111D4×C131—48no—
112D4×C131—44no—
113D4×C131—44no—
114D4×C131—82no—
115D4×C131—832no—
116D4×C131—84no—
117D4×C131—84no—
118C2×C4×C131—24no—
119C2×C4×C131—22no—
120C2×C4×C131—28no—
121C2×C4×C131—42no—
122C2×C4×C131—41no—
123C2×C4×C131—44no—
124C2×C4×C131—44no—
125C2×C4×C131—44no—
126C2×C4×C131—42no—
127C2×C4×C131#12011yescharacteristic
128C2×C4×C131#12112yes—
129C2×C4×C131#12711yescharacteristic
130C8×C131—42no—
131C8×C131—81no—
132C22×C131—22no—
133C22×C131—22no—
134C22×C131—22no—
135C22×C131—21no—
136C22×C131—44no—
137C22×C131—416no—
138C22×C131—44no—
139C22×C131—88no—
140C22×C131—88no—
141C22×C131—84no—
142C22×C131—84no—
143C22×C131—84no—
144C22×C131—82no—
145C22×C131—82no—
146C22×C131—82no—
147C22×C131#39211yescharacteristic
148C22×C131#45314yes—
149C4×C131—21no—
150C4×C131—22no—
151C4×C131—48no—
152C4×C131—82no—
153C4×C131B(4,𝔽2)12yes—
154C2×C131—24no—
155C2×C131—41no—
156C2×C131—84no—
157C2×C131—162no—
158C2×C131#200212yes—
159C2×C131#202111yescharacteristic
160#10326C13111yesmaximal, characteristic, direct product factor, Sylow
161C131#1032611yescharacteristic, direct product factor, Sylow
162#3192C2×C13111yescharacteristic, complemented
163#2433C2×C13112yescomplemented
164#1783C2×C13111yescharacteristic, complemented
165#1507C2×C13112yescomplemented
166#1297C2×C13111yescharacteristic, complemented
167C23×D4C22×C13111yescharacteristic
168C2×#127—22no—
169C2×#121C22×C13112yes—
170C2×#120—24no—
171#481—22no—
172#469—22no—
173#447—22no—
174C2×#100—22no—
175#407C22×C13111yescharacteristic
176#407C22×C13111yescharacteristic
177#392—24no—
178#390—22no—
179C4×C22⋊C4C22×C13112yes—
180#327—24no—
181C25D4×C13112yes—
182C22×D4—22no—
183C22×D4—28no—
184C22×D4—22no—
185C22×D4—21no—
186C22×D4—22no—
187C22×D4—21no—
188C22×D4—44no—
189C22×D4D4×C13112yescomplemented
190C23×C4C23×C13111yescharacteristic
191C2×D8—22no—
192C2×M16—21no—
193C2×M16D4×C13112yescomplemented
194#127—48no—
195#121—22no—
196#121—22no—
197#121—22no—
198#121—22no—
199#120—416no—
200C2×C4⋊C4D4×C13112yescomplemented
201C2×C22⋊C4—22no—
202C2×C22⋊C4—28no—
203C2×C22⋊C4—22no—
204C2×C42—22no—
205#106—22no—
206#102—24no—
207#100—44no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95D4×C13114yescomplemented
211C24—24no—
212C24—22no—
213C24—22no—
214C24—44no—
215C24—48no—
216C24C2×D4×C13111yescharacteristic
217C2×D4—24no—
218C2×D4—28no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—44no—
222C2×D4—42no—
223C2×D4—44no—
224C2×D4—416no—
225C2×D4—48no—
226C2×D4—44no—
227C2×D4—48no—
228C2×D4—416no—
229C2×D4—42no—
230C2×D4—42no—
231C2×D4—41no—
232C2×D4—42no—
233C2×D4—41no—
234C2×D4—88no—
235C22×C4—24no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4C2×D4×C13112yes—
239C22×C4C2×D4×C13111yescharacteristic
240C22×C4C2×D4×C13112yes—
241C22×C4#41×C13111yescharacteristic
242D8—82no—
243M16—42no—
244M16—42no—
245C2×C8—22no—
246C2×C8—41no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C22⋊C4—28no—
250C22⋊C4—416no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—44no—
254C23—24no—
255C23—28no—
256C23—24no—
257C23—41no—
258C23—48no—
259C23—44no—
260C23—42no—
261C23—44no—
262C23—44no—
263C23—42no—
264C23—48no—
265C23—42no—
266C23—44no—
267C23—84no—
268C23—816no—
269C23#120×C13112yes—
270C23#121×C13111yescharacteristic
271D4—44no—
272D4—48no—
273D4—44no—
274D4—44no—
275D4—82no—
276D4—832no—
277D4—84no—
278D4—84no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—28no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4#120×C13111yescharacteristic
289C2×C4#121×C13112yes—
290C2×C4#127×C13111yescharacteristic
291C8—42no—
292C8—81no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—21no—
297C22—44no—
298C22—416no—
299C22—44no—
300C22—88no—
301C22—88no—
302C22—84no—
303C22—84no—
304C22—84no—
305C22—82no—
306C22—82no—
307C22—82no—
308C22#392×C13111yescharacteristic
309C22#453×C13114yes—
310C4—21no—
311C4—22no—
312C4—48no—
313C4—82no—
314C4B(4,𝔽2)×C13112yes—
315C2—24no—
316C2—41no—
317C2—84no—
318C2—162no—
319C2#2002×C13112yes—
320C2#2021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC23×C4C23×C131
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3192×C131C2semidirect
2. #2433×C131C2semidirect
3. #1783×C131C2semidirect
4. #1507×C131C2semidirect
5. #1297×C131C2semidirect
28. C22×D4×C131D4semidirect
32. C2×M16×C131D4semidirect
39. C2×C4⋊C4×C131D4semidirect
49. #95×C131D4semidirect
160. #10326C131direct (N × H)
161. C131#10326direct (N × H)
162. #3192C2×C131semidirect
163. #2433C2×C131semidirect
164. #1783C2×C131semidirect
165. #1507C2×C131semidirect
166. #1297C2×C131semidirect
189. C22×D4D4×C131semidirect
193. C2×M16D4×C131semidirect
200. C2×C4⋊C4D4×C131semidirect
210. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3192×C1312
#2433×C1312
#1783×C1312
#1507×C1312
#1297×C1312
#10326131