Finite Group Databasebeta

← C131×#9199 #45695083

Subgroups — C131×#9199 #45695083

Order 33536.

684 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2626×C131C211yesmaximal, characteristic
2#2315×C131C211yesmaximal, characteristic
3#1520×C131C212yesmaximal, complemented
4C2×#323×C131C211yesmaximal, characteristic
5#1289×C131C212yesmaximal, complemented
6C2×C22⋊Q8×C131C2211yescharacteristic
7C22×C22⋊C4×C131—21no—
8C22×C22⋊C4×C131C2211yescharacteristic
9C2×C22⋊C8×C131C2212yes—
10#399×C131C412yescomplemented
11#396×C131—22no—
12#393×C131C412yescomplemented
13#385×C131—21no—
14#385×C131—24no—
15#380×C131—21no—
16#380×C131C2211yescharacteristic
17#380×C131C2212yes—
18#379×C131—21no—
19#328×C131—24no—
20#323×C131—22no—
21C25×C131D411yescharacteristic
22C22×Q8×C131C2×C411yescharacteristic, complemented
23C23×C4×C131—22no—
24C23×C4×C131D411yescharacteristic
25C23×C4×C131C2311yescharacteristic
26C22×C8×C131—22no—
27C22⋊Q8×C131—22no—
28C22⋊Q8×C131—22no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131—22no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—22no—
34C2×C4⋊C4×C131C2×C411yescharacteristic, complemented
35C2×C22⋊C4×C131—22no—
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131—22no—
38C2×C22⋊C4×C131—22no—
39C2×C22⋊C4×C131—21no—
40C2×C22⋊C4×C131—21no—
41C2×C22⋊C4×C131—22no—
42C2×C22⋊C4×C131—22no—
43C2×C22⋊C4×C131—42no—
44C2×C22⋊C4×C131—42no—
45C2×C22⋊C4×C131C2×C412yes—
46C2×C22⋊C4×C131D412yes—
47C22⋊C8×C131—22no—
48C22⋊C8×C131—22no—
49#95×C131—22no—
50#95×C131—22no—
51#95×C131C2×C412yescomplemented
52#95×C131D414yes—
53C24×C131—21no—
54C24×C131—21no—
55C24×C131—21no—
56C24×C131—21no—
57C24×C131—81no—
58C24×C131—81no—
59C24×C131C22⋊C412yes—
60C24×C131SD1612yes—
61C24×C131Q1612yes—
62C24×C131C2×D411yescharacteristic
63C2×Q8×C131—22no—
64C2×Q8×C131—81no—
65C22×C4×C131—21no—
66C22×C4×C131—21no—
67C22×C4×C131—21no—
68C22×C4×C131—22no—
69C22×C4×C131—21no—
70C22×C4×C131—24no—
71C22×C4×C131—44no—
72C22×C4×C131—81no—
73C22×C4×C131—81no—
74C22×C4×C131—82no—
75C22×C4×C131—82no—
76C22×C4×C131C22⋊C412yes—
77C22×C4×C131C22×C411yescharacteristic
78C22×C4×C131C2×D412yes—
79C22×C4×C131C2×D411yescharacteristic
80C22×C4×C131#4112yes—
81C2×C8×C131—42no—
82C2×C8×C131—82no—
83C4⋊C4×C131—22no—
84C4⋊C4×C131—42no—
85C4⋊C4×C131—81no—
86C4⋊C4×C131—82no—
87C4⋊C4×C131—82no—
88C4⋊C4×C131—82no—
89C22⋊C4×C131—24no—
90C22⋊C4×C131—24no—
91C22⋊C4×C131—44no—
92C22⋊C4×C131—41no—
93C22⋊C4×C131—41no—
94C22⋊C4×C131—42no—
95C22⋊C4×C131—41no—
96C22⋊C4×C131—42no—
97C22⋊C4×C131—41no—
98C22⋊C4×C131—82no—
99C22⋊C4×C131—82no—
100C23×C131—22no—
101C23×C131—22no—
102C23×C131—22no—
103C23×C131—22no—
104C23×C131—22no—
105C23×C131—22no—
106C23×C131—41no—
107C23×C131—41no—
108C23×C131—42no—
109C23×C131—42no—
110C23×C131—42no—
111C23×C131—42no—
112C23×C131—81no—
113C23×C131—81no—
114C23×C131—82no—
115C23×C131—82no—
116C23×C131—82no—
117C23×C131—82no—
118C23×C131#10314yes—
119C23×C131C2×C22⋊C411yescharacteristic
120C23×C131#12011yescharacteristic
121C23×C131#12311yescharacteristic
122C23×C131C2×SD1611yescharacteristic
123C23×C131C2×Q1611yescharacteristic
124C23×C131AGL(1,ℤ/8)11yescharacteristic
125C23×C131#13711yescharacteristic
126Q8×C131—82no—
127C2×C4×C131—22no—
128C2×C4×C131—41no—
129C2×C4×C131—42no—
130C2×C4×C131—42no—
131C2×C4×C131—41no—
132C2×C4×C131—42no—
133C2×C4×C131—42no—
134C2×C4×C131—42no—
135C2×C4×C131—42no—
136C2×C4×C131—42no—
137C2×C4×C131—42no—
138C2×C4×C131—44no—
139C2×C4×C131—44no—
140C2×C4×C131—41no—
141C2×C4×C131—41no—
142C2×C4×C131—42no—
143C2×C4×C131—44no—
144C2×C4×C131—81no—
145C2×C4×C131—88no—
146C2×C4×C131C4×D412yes—
147C2×C4×C131#12112yes—
148C8×C131—82no—
149C22×C131—21no—
150C22×C131—21no—
151C22×C131—21no—
152C22×C131—21no—
153C22×C131—21no—
154C22×C131—21no—
155C22×C131—24no—
156C22×C131—41no—
157C22×C131—41no—
158C22×C131—41no—
159C22×C131—41no—
160C22×C131—44no—
161C22×C131—44no—
162C22×C131—44no—
163C22×C131—42no—
164C22×C131—42no—
165C22×C131—82no—
166C22×C131—82no—
167C22×C131—82no—
168C22×C131#38611yescharacteristic
169C22×C131C2×#10311yescharacteristic
170C22×C131#41711yescharacteristic
171C22×C131#45011yescharacteristic
172C22×C131#45111yescharacteristic
173C22×C131#48311yescharacteristic
174C22×C131#48411yescharacteristic
175C4×C131—22no—
176C4×C131—22no—
177C4×C131—42no—
178C4×C131—82no—
179C4×C131—84no—
180C4×C131—81no—
181C4×C131—81no—
182C2×C131—21no—
183C2×C131—21no—
184C2×C131—21no—
185C2×C131—21no—
186C2×C131—21no—
187C2×C131—21no—
188C2×C131—44no—
189C2×C131#187211yescharacteristic
190C2×C131#191111yescharacteristic
191C2×C131#191311yescharacteristic
192#9199C13111yesmaximal, characteristic, direct product factor, Sylow
193C131#919911yescharacteristic, direct product factor, Sylow
194#2626C2×C13111yescharacteristic
195#2315C2×C13111yescharacteristic
196#1520C2×C13112yescomplemented
197C2×#323C2×C13111yescharacteristic
198#1289C2×C13112yescomplemented
199C2×C22⋊Q8C22×C13111yescharacteristic
200C22×C22⋊C4—21no—
201C22×C22⋊C4C22×C13111yescharacteristic
202C2×C22⋊C8C22×C13112yes—
203#399C4×C13112yescomplemented
204#396—22no—
205#393C4×C13112yescomplemented
206#385—21no—
207#385—24no—
208#380—21no—
209#380C22×C13111yescharacteristic
210#380C22×C13112yes—
211#379—21no—
212#328—24no—
213#323—22no—
214C25D4×C13111yescharacteristic
215C22×Q8C2×C4×C13111yescharacteristic, complemented
216C23×C4—22no—
217C23×C4D4×C13111yescharacteristic
218C23×C4C23×C13111yescharacteristic
219C22×C8—22no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C13111yescharacteristic, complemented
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—42no—
237C2×C22⋊C4—42no—
238C2×C22⋊C4C2×C4×C13112yes—
239C2×C22⋊C4D4×C13112yes—
240C22⋊C8—22no—
241C22⋊C8—22no—
242#95—22no—
243#95—22no—
244#95C2×C4×C13112yescomplemented
245#95D4×C13114yes—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—21no—
250C24—81no—
251C24—81no—
252C24C22⋊C4×C13112yes—
253C24SD16×C13112yes—
254C24Q16×C13112yes—
255C24C2×D4×C13111yescharacteristic
256C2×Q8—22no—
257C2×Q8—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—24no—
264C22×C4—44no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4C22⋊C4×C13112yes—
270C22×C4C22×C4×C13111yescharacteristic
271C22×C4C2×D4×C13112yes—
272C22×C4C2×D4×C13111yescharacteristic
273C22×C4#41×C13112yes—
274C2×C8—42no—
275C2×C8—82no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—81no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—44no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—82no—
292C22⋊C4—82no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23#103×C13114yes—
312C23C2×C22⋊C4×C13111yescharacteristic
313C23#120×C13111yescharacteristic
314C23#123×C13111yescharacteristic
315C23C2×SD16×C13111yescharacteristic
316C23C2×Q16×C13111yescharacteristic
317C23AGL(1,ℤ/8)×C13111yescharacteristic
318C23#137×C13111yescharacteristic
319Q8—82no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—88no—
339C2×C4C4×D4×C13112yes—
340C2×C4#121×C13112yes—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22#386×C13111yescharacteristic
362C22C2×#103×C13111yescharacteristic
363C22#417×C13111yescharacteristic
364C22#450×C13111yescharacteristic
365C22#451×C13111yescharacteristic
366C22#483×C13111yescharacteristic
367C22#484×C13111yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—84no—
372C4—82no—
373C4—81no—
374C4—81no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1872×C13111yescharacteristic
383C2#1911×C13111yescharacteristic
384C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC25×C131D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1520×C131C2semidirect
5. #1289×C131C2semidirect
10. #399×C131C4semidirect
12. #393×C131C4semidirect
22. C22×Q8×C131C2×C4semidirect
34. C2×C4⋊C4×C131C2×C4semidirect
51. #95×C131C2×C4semidirect
192. #9199C131direct (N × H)
193. C131#9199direct (N × H)
196. #1520C2×C131semidirect
198. #1289C2×C131semidirect
203. #399C4×C131semidirect
205. #393C4×C131semidirect
215. C22×Q8C2×C4×C131semidirect
227. C2×C4⋊C4C2×C4×C131semidirect
244. #95C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
#2626×C1312
#2315×C1312
#1520×C1312
C2×#323×C1312
#1289×C1312
#9199131