Finite Group Databasebeta

← C131×#9387 #45695271

Subgroups — C131×#9387 #45695271

Order 33536.

582 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2873×C131C211yesmaximal, characteristic, complemented
2#2610×C131C211yesmaximal, characteristic
3#1527×C131C212yesmaximal, complemented
4#1464×C131C211yesmaximal, characteristic, complemented
5#1300×C131C212yesmaximal, complemented
6C22×M16×C131—21no—
7C2×#124×C131C2211yescharacteristic
8C2×#117×C131C2211yescharacteristic
9#432×C131C2212yes—
10#405×C131—24no—
11C4×M16×C131—21no—
12C4×M16×C131C2212yes—
13#395×C131C411yescharacteristic
14#394×C131C411yescharacteristic
15#393×C131C411yescharacteristic
16#392×C131C411yescharacteristic
17#390×C131—21no—
18#388×C131—21no—
19#388×C131—21no—
20#386×C131—21no—
21#376×C131C2211yescharacteristic
22#329×C131—24no—
23#324×C131—21no—
24#323×C131—21no—
25C22×Q8×C131C2×C411yescharacteristic
26C22×D4×C131—21no—
27C22×D4×C131C2×C411yescharacteristic
28C23×C4×C131D411yescharacteristic
29C2×M16×C131—22no—
30C2×M16×C131—24no—
31C2×M16×C131—24no—
32C2×M16×C131—22no—
33C22×C8×C131—22no—
34#124×C131—22no—
35#124×C131—22no—
36#117×C131—22no—
37#117×C131—22no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131C2×C411yescharacteristic
40C2×C4⋊C4×C131D411yescharacteristic
41C2×C22⋊C4×C131—21no—
42C2×C22⋊C4×C131—21no—
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131C2×C411yescharacteristic
48C2×C22⋊C4×C131D411yescharacteristic
49C2×C42×C131—21no—
50C2×C42×C131D411yescharacteristic
51C2×C42×C131C2311yescharacteristic
52C4⋊C8×C131—22no—
53C22⋊C8×C131—22no—
54#97×C131—22no—
55#97×C131—22no—
56#97×C131D414yescomplemented
57C4×C8×C131—22no—
58C4×C8×C131—22no—
59#95×C131—21no—
60#95×C131—21no—
61#95×C131—21no—
62#95×C131C2×C411yescharacteristic
63#95×C131C2×C411yescharacteristic
64C24×C131—21no—
65C24×C131C22⋊C411yescharacteristic
66C2×Q8×C131—22no—
67C2×Q8×C131—81no—
68C2×D4×C131—22no—
69C2×D4×C131—42no—
70C2×D4×C131—42no—
71C2×D4×C131—81no—
72C2×D4×C131—81no—
73C22×C4×C131—22no—
74C22×C4×C131—22no—
75C22×C4×C131—21no—
76C22×C4×C131—21no—
77C22×C4×C131—21no—
78C22×C4×C131—21no—
79C22×C4×C131—21no—
80C22×C4×C131C22⋊C411yescharacteristic
81C22×C4×C131C22⋊C411yescharacteristic
82C22×C4×C131C22⋊C411yescharacteristic
83C22×C4×C131C22×C411yescharacteristic
84C22×C4×C131C2×D411yescharacteristic
85C22×C4×C131C2×D411yescharacteristic
86M16×C131—28no—
87M16×C131—24no—
88M16×C131—24no—
89C2×C8×C131—28no—
90C2×C8×C131—24no—
91C2×C8×C131—42no—
92C4⋊C4×C131—22no—
93C4⋊C4×C131—22no—
94C4⋊C4×C131—81no—
95C22⋊C4×C131—22no—
96C22⋊C4×C131—22no—
97C22⋊C4×C131—42no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—41no—
100C22⋊C4×C131—42no—
101C22⋊C4×C131—41no—
102C22⋊C4×C131—81no—
103C22⋊C4×C131—81no—
104C42×C131—21no—
105C42×C131—21no—
106C42×C131—42no—
107C42×C131C2×D412yes—
108C42×C131#4112yes—
109C23×C131—21no—
110C23×C131—21no—
111C23×C131—41no—
112C23×C131—41no—
113C23×C131—41no—
114C23×C131—41no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—41no—
119C23×C131—41no—
120C23×C131#10412yes—
121C23×C131C2×C22⋊C411yescharacteristic
122Q8×C131—82no—
123D4×C131—82no—
124D4×C131—84no—
125C2×C4×C131—22no—
126C2×C4×C131—22no—
127C2×C4×C131—24no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—22no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
137C2×C4×C131—41no—
138C2×C4×C131—41no—
139C2×C4×C131—41no—
140C2×C4×C131—41no—
141C2×C4×C131—41no—
142C2×C4×C131—41no—
143C2×C4×C131—41no—
144C2×C4×C131—41no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131#10412yes—
148C2×C4×C131C4×D412yes—
149C2×C4×C131#12011yescharacteristic
150C2×C4×C131#12112yes—
151C2×C4×C131#12311yescharacteristic
152C8×C131—28no—
153C8×C131—82no—
154C22×C131—21no—
155C22×C131—21no—
156C22×C131—22no—
157C22×C131—42no—
158C22×C131—41no—
159C22×C131—41no—
160C22×C131—81no—
161C22×C131—81no—
162C22×C131—81no—
163C22×C131—81no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131—81no—
167C22×C131—81no—
168C22×C131#38611yescharacteristic
169C22×C131C2×#10411yescharacteristic
170C22×C131C2×#10411yescharacteristic
171C4×C131—22no—
172C4×C131—21no—
173C4×C131—22no—
174C4×C131—21no—
175C4×C131—22no—
176C4×C131—42no—
177C4×C131—41no—
178C4×C131—41no—
179C4×C131—81no—
180C4×C131—81no—
181C2×C131—21no—
182C2×C131—21no—
183C2×C131—42no—
184C2×C131—161no—
185C2×C131#188411yescharacteristic
186C2×C131#189611yescharacteristic
187C2×C131#191411yescharacteristic
188#9387C13111yesmaximal, characteristic, direct product factor, Sylow
189C131#938711yescharacteristic, direct product factor, Sylow
190#2873C2×C13111yescharacteristic, complemented
191#2610C2×C13111yescharacteristic
192#1527C2×C13112yescomplemented
193#1464C2×C13111yescharacteristic, complemented
194#1300C2×C13112yescomplemented
195C22×M16—21no—
196C2×#124C22×C13111yescharacteristic
197C2×#117C22×C13111yescharacteristic
198#432C22×C13112yes—
199#405—24no—
200C4×M16—21no—
201C4×M16C22×C13112yes—
202#395C4×C13111yescharacteristic
203#394C4×C13111yescharacteristic
204#393C4×C13111yescharacteristic
205#392C4×C13111yescharacteristic
206#390—21no—
207#388—21no—
208#388—21no—
209#386—21no—
210#376C22×C13111yescharacteristic
211#329—24no—
212#324—21no—
213#323—21no—
214C22×Q8C2×C4×C13111yescharacteristic
215C22×D4—21no—
216C22×D4C2×C4×C13111yescharacteristic
217C23×C4D4×C13111yescharacteristic
218C2×M16—22no—
219C2×M16—24no—
220C2×M16—24no—
221C2×M16—22no—
222C22×C8—22no—
223#124—22no—
224#124—22no—
225#117—22no—
226#117—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C13111yescharacteristic
229C2×C4⋊C4D4×C13111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C2×C4×C13111yescharacteristic
237C2×C22⋊C4D4×C13111yescharacteristic
238C2×C42—21no—
239C2×C42D4×C13111yescharacteristic
240C2×C42C23×C13111yescharacteristic
241C4⋊C8—22no—
242C22⋊C8—22no—
243#97—22no—
244#97—22no—
245#97D4×C13114yescomplemented
246C4×C8—22no—
247C4×C8—22no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95C2×C4×C13111yescharacteristic
252#95C2×C4×C13111yescharacteristic
253C24—21no—
254C24C22⋊C4×C13111yescharacteristic
255C2×Q8—22no—
256C2×Q8—81no—
257C2×D4—22no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C2×D4—81no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22⋊C4×C13111yescharacteristic
270C22×C4C22⋊C4×C13111yescharacteristic
271C22×C4C22⋊C4×C13111yescharacteristic
272C22×C4C22×C4×C13111yescharacteristic
273C22×C4C2×D4×C13111yescharacteristic
274C22×C4C2×D4×C13111yescharacteristic
275M16—28no—
276M16—24no—
277M16—24no—
278C2×C8—28no—
279C2×C8—24no—
280C2×C8—42no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—81no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—21no—
294C42—21no—
295C42—42no—
296C42C2×D4×C13112yes—
297C42#41×C13112yes—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#104×C13112yes—
310C23C2×C22⋊C4×C13111yescharacteristic
311Q8—82no—
312D4—82no—
313D4—84no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4#104×C13112yes—
337C2×C4C4×D4×C13112yes—
338C2×C4#120×C13111yescharacteristic
339C2×C4#121×C13112yes—
340C2×C4#123×C13111yescharacteristic
341C8—28no—
342C8—82no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#386×C13111yescharacteristic
358C22C2×#104×C13111yescharacteristic
359C22C2×#104×C13111yescharacteristic
360C4—22no—
361C4—21no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1884×C13111yescharacteristic
375C2#1896×C13111yescharacteristic
376C2#1914×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#392×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2873×C131C2semidirect
3. #1527×C131C2semidirect
4. #1464×C131C2semidirect
5. #1300×C131C2semidirect
56. #97×C131D4semidirect
188. #9387C131direct (N × H)
189. C131#9387direct (N × H)
190. #2873C2×C131semidirect
192. #1527C2×C131semidirect
193. #1464C2×C131semidirect
194. #1300C2×C131semidirect
245. #97D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2873×C1312
#2610×C1312
#1527×C1312
#1464×C1312
#1300×C1312
#9387131