Finite Group Databasebeta

← C131×#9278 #45695162

Subgroups — C131×#9278 #45695162

Order 33536.

564 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3187×C131C211yesmaximal, characteristic
2#2368×C131C211yesmaximal, characteristic, complemented
3#1964×C131C211yesmaximal, characteristic
4#1520×C131C211yesmaximal, characteristic, complemented
5C2×#327×C131C211yesmaximal, characteristic
6#1294×C131C211yesmaximal, characteristic, complemented
7#1282×C131C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C131C2211yescharacteristic
9C2×#121×C131C2211yescharacteristic
10#483×C131C412yescomplemented
11#481×C131—21no—
12#465×C131—22no—
13#450×C131C412yescomplemented
14#448×C131—21no—
15C2×#99×C131—21no—
16C2×#99×C131—21no—
17C2×C22⋊C8×C131C2211yescharacteristic
18C2×C22⋊C8×C131C2211yescharacteristic
19#391×C131—21no—
20#387×C131—21no—
21#387×C131—21no—
22#385×C131—21no—
23#380×C131C2211yescharacteristic
24C4×C4⋊C4×C131—21no—
25C4×C22⋊C4×C131—21no—
26C4×C22⋊C4×C131C2211yescharacteristic
27C2×#95×C131C2211yescharacteristic
28#328×C131—22no—
29#327×C131—21no—
30#327×C131—21no—
31C22×Q8×C131D411yescharacteristic
32C22×D4×C131—21no—
33C22×D4×C131C2×C411yescharacteristic
34C23×C4×C131—21no—
35C23×C4×C131C2311yescharacteristic
36C2×SD16×C131—22no—
37C22×C8×C131—21no—
38C22×C8×C131—21no—
39C22⋊Q8×C131—21no—
40C22⋊Q8×C131—21no—
41C22⋊Q8×C131C2×C412yes—
42C22⋊Q8×C131D412yes—
43#121×C131—21no—
44#121×C131—21no—
45#121×C131—21no—
46#121×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131—21no—
51C2×C4⋊C4×C131C2×C411yescharacteristic
52C2×C4⋊C4×C131D411yescharacteristic
53C2×C22⋊C4×C131—21no—
54C2×C22⋊C4×C131—21no—
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131D411yescharacteristic
57C2×C22⋊C4×C131D411yescharacteristic
58C2×C42×C131—21no—
59C2×C42×C131—21no—
60C2×C42×C131—21no—
61#106×C131—22no—
62#103×C131—22no—
63#102×C131—22no—
64#99×C131—42no—
65#99×C131—42no—
66C22⋊C8×C131—21no—
67C22⋊C8×C131—21no—
68C22⋊C8×C131—21no—
69C22⋊C8×C131C2×C412yes—
70#95×C131—21no—
71#95×C131—21no—
72#95×C131—21no—
73#95×C131—21no—
74#95×C131—21no—
75#95×C131—21no—
76#95×C131—21no—
77#95×C131D411yescharacteristic
78#95×C131D411yescharacteristic
79C24×C131—21no—
80C24×C131C2×D411yescharacteristic
81C2×Q8×C131—21no—
82C2×Q8×C131—81no—
83C2×Q8×C131C22⋊C412yes—
84C2×D4×C131—21no—
85C2×D4×C131—21no—
86C2×D4×C131—41no—
87C2×D4×C131—41no—
88C2×D4×C131—41no—
89C2×D4×C131—41no—
90C2×D4×C131—41no—
91C2×D4×C131—41no—
92C2×D4×C131—81no—
93C22×C4×C131—21no—
94C22×C4×C131—21no—
95C22×C4×C131—21no—
96C22×C4×C131—21no—
97C22×C4×C131—21no—
98C22×C4×C131—21no—
99C22×C4×C131—21no—
100C22×C4×C131—42no—
101C22×C4×C131—41no—
102C22×C4×C131—41no—
103C22×C4×C131—41no—
104C22×C4×C131—81no—
105C22×C4×C131—81no—
106C22×C4×C131C22×C411yescharacteristic
107C22×C4×C131C2×D411yescharacteristic
108C22×C4×C131C2×D411yescharacteristic
109C22×C4×C131C2×D411yescharacteristic
110C22×C4×C131#4111yescharacteristic
111C22×C4×C131#4111yescharacteristic
112SD16×C131—82no—
113C2×C8×C131—22no—
114C2×C8×C131—41no—
115C2×C8×C131—81no—
116C2×C8×C131—81no—
117C4⋊C4×C131—22no—
118C4⋊C4×C131—22no—
119C4⋊C4×C131—21no—
120C4⋊C4×C131—21no—
121C4⋊C4×C131—21no—
122C4⋊C4×C131—42no—
123C4⋊C4×C131—81no—
124C4⋊C4×C131—81no—
125C4⋊C4×C131C22⋊C412yes—
126C22⋊C4×C131—22no—
127C22⋊C4×C131—22no—
128C22⋊C4×C131—21no—
129C22⋊C4×C131—21no—
130C22⋊C4×C131—21no—
131C22⋊C4×C131—41no—
132C22⋊C4×C131—41no—
133C22⋊C4×C131—41no—
134C22⋊C4×C131—41no—
135C22⋊C4×C131SD1612yescomplemented
136C42×C131—42no—
137C42×C131—81no—
138C42×C131—81no—
139C23×C131—41no—
140C23×C131—41no—
141C23×C131—41no—
142C23×C131—41no—
143C23×C131—41no—
144C23×C131—81no—
145C23×C131—81no—
146C23×C131C4×D411yescharacteristic
147C23×C131#12011yescharacteristic
148C23×C131#12111yescharacteristic
149C23×C131C2×SD1611yescharacteristic
150C23×C131#13511yescharacteristic
151C23×C131AGL(1,ℤ/8)11yescharacteristic
152C23×C131#13711yescharacteristic
153Q8×C131—42no—
154Q8×C131—81no—
155D4×C131—42no—
156D4×C131—81no—
157D4×C131—81no—
158D4×C131—81no—
159D4×C131—81no—
160D4×C131—81no—
161C2×C4×C131—22no—
162C2×C4×C131—22no—
163C2×C4×C131—22no—
164C2×C4×C131—22no—
165C2×C4×C131—41no—
166C2×C4×C131—41no—
167C2×C4×C131—41no—
168C2×C4×C131—41no—
169C2×C4×C131—41no—
170C2×C4×C131—41no—
171C2×C4×C131—41no—
172C2×C4×C131—41no—
173C2×C4×C131—41no—
174C2×C4×C131—41no—
175C2×C4×C131—41no—
176C2×C4×C131—41no—
177C2×C4×C131—41no—
178C2×C4×C131—41no—
179C2×C4×C131—41no—
180C2×C4×C131—41no—
181C2×C4×C131—41no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—82no—
189C2×C4×C131—82no—
190C2×C4×C131—81no—
191C2×C4×C131—81no—
192C2×C4×C131—81no—
193C2×C4×C131C2×C22⋊C411yescharacteristic
194C2×C4×C131C4×D411yescharacteristic
195C2×C4×C131#12111yescharacteristic
196C2×C4×C131#12311yescharacteristic
197C8×C131—42no—
198C8×C131—81no—
199C22×C131—21no—
200C22×C131—21no—
201C22×C131—21no—
202C22×C131—21no—
203C22×C131—21no—
204C22×C131—21no—
205C22×C131—41no—
206C22×C131—41no—
207C22×C131—41no—
208C22×C131—41no—
209C22×C131—81no—
210C22×C131—81no—
211C22×C131—81no—
212C22×C131—161no—
213C22×C131—161no—
214C22×C131#38611yescharacteristic
215C22×C131C4×SD1611yescharacteristic
216C22×C131#44011yescharacteristic
217C22×C131#44811yescharacteristic
218C22×C131#44911yescharacteristic
219C22×C131#46011yescharacteristic
220C22×C131#46411yescharacteristic
221C4×C131—21no—
222C4×C131—21no—
223C4×C131—21no—
224C4×C131—21no—
225C4×C131—42no—
226C4×C131—42no—
227C4×C131—42no—
228C4×C131—42no—
229C4×C131—81no—
230C4×C131—81no—
231C4×C131—81no—
232C4×C131—161no—
233C2×C131—21no—
234C2×C131—21no—
235C2×C131—21no—
236C2×C131—21no—
237C2×C131—21no—
238C2×C131—21no—
239C2×C131—161no—
240C2×C131#188011yescharacteristic
241C2×C131#190611yescharacteristic
242C2×C131#191311yescharacteristic
243#9278C13111yesmaximal, characteristic, direct product factor, Sylow
244C131#927811yescharacteristic, direct product factor, Sylow
245#3187C2×C13111yescharacteristic
246#2368C2×C13111yescharacteristic, complemented
247#1964C2×C13111yescharacteristic
248#1520C2×C13111yescharacteristic, complemented
249C2×#327C2×C13111yescharacteristic
250#1294C2×C13111yescharacteristic, complemented
251#1282C2×C13111yescharacteristic, complemented
252C2×C22⋊Q8C22×C13111yescharacteristic
253C2×#121C22×C13111yescharacteristic
254#483C4×C13112yescomplemented
255#481—21no—
256#465—22no—
257#450C4×C13112yescomplemented
258#448—21no—
259C2×#99—21no—
260C2×#99—21no—
261C2×C22⋊C8C22×C13111yescharacteristic
262C2×C22⋊C8C22×C13111yescharacteristic
263#391—21no—
264#387—21no—
265#387—21no—
266#385—21no—
267#380C22×C13111yescharacteristic
268C4×C4⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4C22×C13111yescharacteristic
271C2×#95C22×C13111yescharacteristic
272#328—22no—
273#327—21no—
274#327—21no—
275C22×Q8D4×C13111yescharacteristic
276C22×D4—21no—
277C22×D4C2×C4×C13111yescharacteristic
278C23×C4—21no—
279C23×C4C23×C13111yescharacteristic
280C2×SD16—22no—
281C22×C8—21no—
282C22×C8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8C2×C4×C13112yes—
286C22⋊Q8D4×C13112yes—
287#121—21no—
288#121—21no—
289#121—21no—
290#121—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4C2×C4×C13111yescharacteristic
296C2×C4⋊C4D4×C13111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4D4×C13111yescharacteristic
301C2×C22⋊C4D4×C13111yescharacteristic
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305#106—22no—
306#103—22no—
307#102—22no—
308#99—42no—
309#99—42no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8C2×C4×C13112yes—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319#95—21no—
320#95—21no—
321#95D4×C13111yescharacteristic
322#95D4×C13111yescharacteristic
323C24—21no—
324C24C2×D4×C13111yescharacteristic
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8C22⋊C4×C13112yes—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—81no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—81no—
349C22×C4—81no—
350C22×C4C22×C4×C13111yescharacteristic
351C22×C4C2×D4×C13111yescharacteristic
352C22×C4C2×D4×C13111yescharacteristic
353C22×C4C2×D4×C13111yescharacteristic
354C22×C4#41×C13111yescharacteristic
355C22×C4#41×C13111yescharacteristic
356SD16—82no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—81no—
360C2×C8—81no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—42no—
367C4⋊C4—81no—
368C4⋊C4—81no—
369C4⋊C4C22⋊C4×C13112yes—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4SD16×C13112yescomplemented
380C42—42no—
381C42—81no—
382C42—81no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—81no—
389C23—81no—
390C23C4×D4×C13111yescharacteristic
391C23#120×C13111yescharacteristic
392C23#121×C13111yescharacteristic
393C23C2×SD16×C13111yescharacteristic
394C23#135×C13111yescharacteristic
395C23AGL(1,ℤ/8)×C13111yescharacteristic
396C23#137×C13111yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—42no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404D4—81no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4C2×C22⋊C4×C13111yescharacteristic
438C2×C4C4×D4×C13111yescharacteristic
439C2×C4#121×C13111yescharacteristic
440C2×C4#123×C13111yescharacteristic
441C8—42no—
442C8—81no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—161no—
457C22—161no—
458C22#386×C13111yescharacteristic
459C22C4×SD16×C13111yescharacteristic
460C22#440×C13111yescharacteristic
461C22#448×C13111yescharacteristic
462C22#449×C13111yescharacteristic
463C22#460×C13111yescharacteristic
464C22#464×C13111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—81no—
475C4—81no—
476C4—161no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—161no—
484C2#1880×C13111yescharacteristic
485C2#1906×C13111yescharacteristic
486C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC2×#121×C131C22
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
2. #2368×C131C2semidirect
4. #1520×C131C2semidirect
6. #1294×C131C2semidirect
7. #1282×C131C2semidirect
10. #483×C131C4semidirect
13. #450×C131C4semidirect
135. C22⋊C4×C131SD16semidirect
243. #9278C131direct (N × H)
244. C131#9278direct (N × H)
246. #2368C2×C131semidirect
248. #1520C2×C131semidirect
250. #1294C2×C131semidirect
251. #1282C2×C131semidirect
254. #483C4×C131semidirect
257. #450C4×C131semidirect
379. C22⋊C4SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3187×C1312
#2368×C1312
#1964×C1312
#1520×C1312
C2×#327×C1312
#1294×C1312
#1282×C1312
#9278131