Finite Group Databasebeta

← C131×#9225 #45695109

Subgroups — C131×#9225 #45695109

Order 33536.

578 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C131C211yesmaximal, characteristic
2C2×#436×C131C211yesmaximal, characteristic
3#1990×C131C211yesmaximal, characteristic, complemented
4#1802×C131C211yesmaximal, characteristic
5C2×#332×C131C211yesmaximal, characteristic, complemented
6#1296×C131C211yesmaximal, characteristic, complemented
7#1277×C131C211yesmaximal, characteristic, complemented
8C22×SD16×C131—21no—
9C22×M16×C131—21no—
10C2×C4⋊Q8×C131C2211yescharacteristic
11C2×C4×D4×C131C2211yescharacteristic
12#461×C131—22no—
13#461×C131C414yescomplemented
14#436×C131—22no—
15#436×C131—22no—
16C2×C4⋊C8×C131C2211yescharacteristic
17C2×C4⋊C8×C131C2211yescharacteristic
18C2×C4⋊C8×C131C2211yescharacteristic
19C2×#103×C131—21no—
20C2×#102×C131—21no—
21C2×C22⋊C8×C131—21no—
22C2×C4×C8×C131C2211yescharacteristic
23#384×C131C2211yescharacteristic
24#340×C131—21no—
25#340×C131—21no—
26#340×C131—21no—
27#332×C131—22no—
28C22×Q8×C131—21no—
29C22×D4×C131D411yescharacteristic
30C23×C4×C131—21no—
31C2×SD16×C131—24no—
32C2×SD16×C131—42no—
33C2×SD16×C131—42no—
34C2×M16×C131—24no—
35C2×M16×C131—42no—
36C2×M16×C131—42no—
37C22×C8×C131—21no—
38C22×C8×C131—21no—
39C22×C8×C131—21no—
40C22×C8×C131D411yescharacteristic
41C22×C8×C131D411yescharacteristic
42C4⋊Q8×C131—21no—
43C4⋊Q8×C131—21no—
44C4⋊Q8×C131—21no—
45C4⋊Q8×C131C2×C412yes—
46C4×D4×C131—21no—
47C4×D4×C131—21no—
48C4×D4×C131C2×C412yes—
49C4×D4×C131D412yes—
50C2×C4⋊C4×C131—21no—
51C2×C4⋊C4×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131D411yescharacteristic
56C2×C22⋊C4×C131—21no—
57C2×C42×C131C2311yescharacteristic
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131C2×C412yes—
63C4⋊C8×C131D412yes—
64#103×C131—24no—
65#102×C131—42no—
66C22⋊C8×C131—24no—
67C4×C8×C131—21no—
68C4×C8×C131—21no—
69C24×C131—21no—
70C2×Q8×C131—22no—
71C2×Q8×C131—41no—
72C2×Q8×C131—41no—
73C2×Q8×C131—41no—
74C2×Q8×C131—41no—
75C2×Q8×C131—41no—
76C2×D4×C131—21no—
77C2×D4×C131—21no—
78C2×D4×C131—21no—
79C2×D4×C131—21no—
80C2×D4×C131—21no—
81C2×D4×C131C22⋊C412yes—
82C22×C4×C131—21no—
83C22×C4×C131—22no—
84C22×C4×C131—22no—
85C22×C4×C131—41no—
86C22×C4×C131—41no—
87C22×C4×C131—41no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131—41no—
91C22×C4×C131C2×D411yescharacteristic
92C22×C4×C131C2×D411yescharacteristic
93C22×C4×C131#4111yescharacteristic
94SD16×C131—48no—
95M16×C131—48no—
96C2×C8×C131—21no—
97C2×C8×C131—21no—
98C2×C8×C131—22no—
99C2×C8×C131—21no—
100C2×C8×C131—22no—
101C2×C8×C131—21no—
102C2×C8×C131—21no—
103C2×C8×C131—41no—
104C2×C8×C131—41no—
105C2×C8×C131—41no—
106C2×C8×C131—41no—
107C2×C8×C131—41no—
108C2×C8×C131—41no—
109C2×C8×C131—41no—
110C2×C8×C131SD1612yescomplemented
111C4⋊C4×C131—21no—
112C4⋊C4×C131—22no—
113C4⋊C4×C131—22no—
114C4⋊C4×C131—41no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—41no—
118C4⋊C4×C131—41no—
119C4⋊C4×C131—41no—
120C4⋊C4×C131—81no—
121C4⋊C4×C131C22⋊C412yes—
122C22⋊C4×C131—22no—
123C22⋊C4×C131—22no—
124C42×C131C22×C411yescharacteristic
125C42×C131C2×D411yescharacteristic
126C42×C131C2×D411yescharacteristic
127C42×C131#4111yescharacteristic
128C23×C131—22no—
129C23×C131—41no—
130C23×C131—41no—
131C23×C131—41no—
132C23×C131—41no—
133C23×C131—41no—
134C23×C131—41no—
135C23×C131#12111yescharacteristic
136Q8×C131—42no—
137Q8×C131—42no—
138Q8×C131—81no—
139Q8×C131—81no—
140D4×C131—22no—
141D4×C131—22no—
142D4×C131—41no—
143D4×C131—41no—
144C2×C4×C131—21no—
145C2×C4×C131—21no—
146C2×C4×C131—22no—
147C2×C4×C131—41no—
148C2×C4×C131—41no—
149C2×C4×C131—42no—
150C2×C4×C131—42no—
151C2×C4×C131—42no—
152C2×C4×C131—42no—
153C2×C4×C131—42no—
154C2×C4×C131—81no—
155C2×C4×C131—81no—
156C2×C4×C131—81no—
157C2×C4×C131—81no—
158C2×C4×C131—81no—
159C2×C4×C131C2×C22⋊C411yescharacteristic
160C2×C4×C131C4×D411yescharacteristic
161C2×C4×C131C4×D411yescharacteristic
162C2×C4×C131#12011yescharacteristic
163C2×C4×C131#12111yescharacteristic
164C2×C4×C131#12311yescharacteristic
165C2×C4×C131C2×SD1611yescharacteristic
166C2×C4×C131#13511yescharacteristic
167C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C131#13711yescharacteristic
172C2×C4×C131#13711yescharacteristic
173C8×C131—22no—
174C8×C131—42no—
175C8×C131—42no—
176C8×C131—41no—
177C8×C131—81no—
178C22×C131—42no—
179C22×C131—42no—
180C22×C131—42no—
181C22×C131—81no—
182C22×C131—81no—
183C22×C131—81no—
184C22×C131—81no—
185C22×C131#38611yescharacteristic
186C22×C131#46111yescharacteristic
187C22×C131#46311yescharacteristic
188C22×C131#46811yescharacteristic
189C22×C131#46911yescharacteristic
190C22×C131#47111yescharacteristic
191C22×C131#47311yescharacteristic
192C4×C131—21no—
193C4×C131—21no—
194C4×C131—42no—
195C4×C131—82no—
196C4×C131—161no—
197C4×C131#41711yescharacteristic
198C4×C131#41811yescharacteristic
199C4×C131C4×SD1611yescharacteristic
200C4×C131#44011yescharacteristic
201C4×C131#45011yescharacteristic
202C4×C131#45211yescharacteristic
203C4×C131#46811yescharacteristic
204C4×C131#46911yescharacteristic
205C2×C131—82no—
206C2×C131#169111yescharacteristic
207C2×C131#169311yescharacteristic
208C2×C131#169911yescharacteristic
209C2×C131#170111yescharacteristic
210C2×C131#187711yescharacteristic
211C2×C131#189511yescharacteristic
212C2×C131#190811yescharacteristic
213#9225C13111yesmaximal, characteristic, direct product factor, Sylow
214C131#922511yescharacteristic, direct product factor, Sylow
215C2×#461C2×C13111yescharacteristic
216C2×#436C2×C13111yescharacteristic
217#1990C2×C13111yescharacteristic, complemented
218#1802C2×C13111yescharacteristic
219C2×#332C2×C13111yescharacteristic, complemented
220#1296C2×C13111yescharacteristic, complemented
221#1277C2×C13111yescharacteristic, complemented
222C22×SD16—21no—
223C22×M16—21no—
224C2×C4⋊Q8C22×C13111yescharacteristic
225C2×C4×D4C22×C13111yescharacteristic
226#461—22no—
227#461C4×C13114yescomplemented
228#436—22no—
229#436—22no—
230C2×C4⋊C8C22×C13111yescharacteristic
231C2×C4⋊C8C22×C13111yescharacteristic
232C2×C4⋊C8C22×C13111yescharacteristic
233C2×#103—21no—
234C2×#102—21no—
235C2×C22⋊C8—21no—
236C2×C4×C8C22×C13111yescharacteristic
237#384C22×C13111yescharacteristic
238#340—21no—
239#340—21no—
240#340—21no—
241#332—22no—
242C22×Q8—21no—
243C22×D4D4×C13111yescharacteristic
244C23×C4—21no—
245C2×SD16—24no—
246C2×SD16—42no—
247C2×SD16—42no—
248C2×M16—24no—
249C2×M16—42no—
250C2×M16—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8D4×C13111yescharacteristic
255C22×C8D4×C13111yescharacteristic
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C2×C4×C13112yes—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4C2×C4×C13112yes—
263C4×D4D4×C13112yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C13111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C42C23×C13111yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C13112yes—
277C4⋊C8D4×C13112yes—
278#103—24no—
279#102—42no—
280C22⋊C8—24no—
281C4×C8—21no—
282C4×C8—21no—
283C24—21no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4C22⋊C4×C13112yes—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C2×D4×C13111yescharacteristic
306C22×C4C2×D4×C13111yescharacteristic
307C22×C4#41×C13111yescharacteristic
308SD16—48no—
309M16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C13112yescomplemented
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—81no—
335C4⋊C4C22⋊C4×C13112yes—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C42C22×C4×C13111yescharacteristic
339C42C2×D4×C13111yescharacteristic
340C42C2×D4×C13111yescharacteristic
341C42#41×C13111yescharacteristic
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23#121×C13111yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354D4—22no—
355D4—22no—
356D4—41no—
357D4—41no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C2×C22⋊C4×C13111yescharacteristic
374C2×C4C4×D4×C13111yescharacteristic
375C2×C4C4×D4×C13111yescharacteristic
376C2×C4#120×C13111yescharacteristic
377C2×C4#121×C13111yescharacteristic
378C2×C4#123×C13111yescharacteristic
379C2×C4C2×SD16×C13111yescharacteristic
380C2×C4#135×C13111yescharacteristic
381C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
382C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
383C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
384C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
385C2×C4#137×C13111yescharacteristic
386C2×C4#137×C13111yescharacteristic
387C8—22no—
388C8—42no—
389C8—42no—
390C8—41no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22#386×C13111yescharacteristic
400C22#461×C13111yescharacteristic
401C22#463×C13111yescharacteristic
402C22#468×C13111yescharacteristic
403C22#469×C13111yescharacteristic
404C22#471×C13111yescharacteristic
405C22#473×C13111yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—82no—
410C4—161no—
411C4#417×C13111yescharacteristic
412C4#418×C13111yescharacteristic
413C4C4×SD16×C13111yescharacteristic
414C4#440×C13111yescharacteristic
415C4#450×C13111yescharacteristic
416C4#452×C13111yescharacteristic
417C4#468×C13111yescharacteristic
418C4#469×C13111yescharacteristic
419C2—82no—
420C2#1691×C13111yescharacteristic
421C2#1693×C13111yescharacteristic
422C2#1699×C13111yescharacteristic
423C2#1701×C13111yescharacteristic
424C2#1877×C13111yescharacteristic
425C2#1895×C13111yescharacteristic
426C2#1908×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#121
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1990×C131C2semidirect
5. C2×#332×C131C2semidirect
6. #1296×C131C2semidirect
7. #1277×C131C2semidirect
13. #461×C131C4semidirect
110. C2×C8×C131SD16semidirect
213. #9225C131direct (N × H)
214. C131#9225direct (N × H)
217. #1990C2×C131semidirect
219. C2×#332C2×C131semidirect
220. #1296C2×C131semidirect
221. #1277C2×C131semidirect
227. #461C4×C131semidirect
324. C2×C8SD16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1312
C2×#436×C1312
#1990×C1312
#1802×C1312
C2×#332×C1312
#1296×C1312
#1277×C1312
#9225131