Finite Group Databasebeta

← C131×#8513 #45694397

Subgroups — C131×#8513 #45694397

Order 33536.

724 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559×C131C211yesmaximal, characteristic
2#1989×C131C211yesmaximal, characteristic, complemented
3#1980×C131C211yesmaximal, characteristic, complemented
4#1551×C131C211yesmaximal, characteristic, complemented
5#1528×C131C211yesmaximal, characteristic, complemented
6#1509×C131C211yesmaximal, characteristic, complemented
7#1483×C131C211yesmaximal, characteristic, complemented
8#563×C131C412yescomplemented
9#562×C131C412yescomplemented
10#554×C131—21no—
11#553×C131—21no—
12#553×C131—21no—
13#547×C131—22no—
14#547×C131—21no—
15#544×C131—21no—
16#540×C131—21no—
17#539×C131—22no—
18#539×C131—21no—
19#537×C131—21no—
20#532×C131C2211yescharacteristic
21#529×C131C2211yescharacteristic
22C2×#125×C131C2211yescharacteristic
23#432×C131C2211yescharacteristic
24C2×C4⋊C8×C131C2211yescharacteristic
25C2×#104×C131—22no—
26C4×M16×C131C2211yescharacteristic
27C4×C4⋊C4×C131C2211yescharacteristic
28#340×C131—21no—
29#340×C131—21no—
30#333×C131—21no—
31#331×C131—21no—
32#330×C131—22no—
33#328×C131—21no—
34#327×C131—21no—
35Q8⋊C8×C131—21no—
36D4⋊C8×C131—21no—
37C2×#41×C131—22no—
38C2×#41×C131D412yes—
39C2×M16×C131—21no—
40C22×C8×C131—21no—
41C4⋊Q8×C131—21no—
42C4⋊Q8×C131—22no—
43C4⋊Q8×C131D411yescharacteristic
44#127×C131D411yescharacteristic
45#126×C131—22no—
46#126×C131—22no—
47#126×C131—21no—
48#125×C131—22no—
49#125×C131—21no—
50#125×C131—21no—
51#125×C131—21no—
52#125×C131C2×C412yes—
53#125×C131C2×C411yescharacteristic
54#125×C131D412yes—
55#124×C131C2×C411yescharacteristic
56#124×C131C2×C412yes—
57#123×C131—22no—
58#123×C131—22no—
59#123×C131—22no—
60#123×C131—22no—
61#123×C131—21no—
62#123×C131—22no—
63#123×C131—22no—
64C22⋊Q8×C131—22no—
65C22⋊Q8×C131—22no—
66C22⋊Q8×C131—22no—
67C22⋊Q8×C131—22no—
68C22⋊Q8×C131—22no—
69C22⋊Q8×C131—22no—
70C22⋊Q8×C131D411yescharacteristic
71#121×C131—22no—
72#121×C131—22no—
73#121×C131—21no—
74#121×C131—21no—
75#121×C131—22no—
76#121×C131—22no—
77#121×C131—21no—
78#121×C131—21no—
79#121×C131D411yescharacteristic
80C4×Q8×C131D411yescharacteristic
81C4×D4×C131—22no—
82C4×D4×C131—22no—
83C4×D4×C131—21no—
84C4×D4×C131—21no—
85C4×D4×C131—21no—
86C4×D4×C131—21no—
87C4×D4×C131—21no—
88C4×D4×C131D411yescharacteristic
89#117×C131—21no—
90#117×C131—21no—
91C2×C4⋊C4×C131—22no—
92C2×C4⋊C4×C131—21no—
93C2×C4⋊C4×C131—21no—
94C2×C4⋊C4×C131—21no—
95C2×C4⋊C4×C131—21no—
96C2×C4⋊C4×C131D411yescharacteristic
97C2×C4⋊C4×C131D411yescharacteristic
98C2×C42×C131—21no—
99C2×C42×C131C2311yescharacteristic
100C4⋊C8×C131—21no—
101C4⋊C8×C131—21no—
102C4⋊C8×C131—21no—
103#104×C131—44no—
104C22⋊C8×C131—21no—
105#97×C131—21no—
106#97×C131—21no—
107C4×C8×C131—21no—
108#95×C131—21no—
109#41×C131—42no—
110#41×C131—42no—
111#41×C131—82no—
112#41×C131—82no—
113C2×Q8×C131—22no—
114C2×Q8×C131C22⋊C411yescharacteristic
115C2×Q8×C131C22⋊C412yes—
116C2×D4×C131—22no—
117C2×D4×C131—21no—
118C2×D4×C131—22no—
119C2×D4×C131—22no—
120C2×D4×C131—21no—
121C2×D4×C131—21no—
122C2×D4×C131C22⋊C411yescharacteristic
123C2×D4×C131C22⋊C412yes—
124C22×C4×C131—21no—
125C22×C4×C131—22no—
126C22×C4×C131—22no—
127C22×C4×C131—22no—
128C22×C4×C131—21no—
129C22×C4×C131—21no—
130C22×C4×C131—22no—
131C22×C4×C131—41no—
132C22×C4×C131C2×D411yescharacteristic
133C22×C4×C131C2×D411yescharacteristic
134C22×C4×C131C2×D411yescharacteristic
135M16×C131—22no—
136M16×C131—41no—
137C2×C8×C131—41no—
138C2×C8×C131—42no—
139C2×C8×C131—41no—
140C2×C8×C131—41no—
141C4⋊C4×C131—22no—
142C4⋊C4×C131—22no—
143C4⋊C4×C131—22no—
144C4⋊C4×C131—22no—
145C4⋊C4×C131—22no—
146C4⋊C4×C131—22no—
147C4⋊C4×C131—21no—
148C4⋊C4×C131—21no—
149C4⋊C4×C131—22no—
150C4⋊C4×C131—21no—
151C4⋊C4×C131—21no—
152C4⋊C4×C131—21no—
153C4⋊C4×C131—22no—
154C4⋊C4×C131—21no—
155C4⋊C4×C131—21no—
156C4⋊C4×C131—21no—
157C4⋊C4×C131—22no—
158C4⋊C4×C131—41no—
159C4⋊C4×C131C22⋊C412yes—
160C4⋊C4×C131C22⋊C412yes—
161C4⋊C4×C131C22⋊C411yescharacteristic
162C4⋊C4×C131C22⋊C411yescharacteristic
163C22⋊C4×C131—22no—
164C22⋊C4×C131—22no—
165C22⋊C4×C131—22no—
166C22⋊C4×C131—22no—
167C22⋊C4×C131—22no—
168C22⋊C4×C131—21no—
169C22⋊C4×C131—21no—
170C22⋊C4×C131—22no—
171C22⋊C4×C131—22no—
172C22⋊C4×C131—21no—
173C22⋊C4×C131—21no—
174C22⋊C4×C131—21no—
175C42×C131—22no—
176C42×C131—21no—
177C42×C131—42no—
178C42×C131C22×C411yescharacteristic
179C42×C131C2×D411yescharacteristic
180C42×C131C2×D411yescharacteristic
181C42×C131C2×D411yescharacteristic
182C23×C131—22no—
183C23×C131—21no—
184C23×C131#12011yescharacteristic
185Q8×C131—41no—
186Q8×C131—42no—
187Q8×C131—82no—
188D4×C131—41no—
189D4×C131—42no—
190D4×C131—42no—
191D4×C131—41no—
192D4×C131—42no—
193D4×C131—41no—
194D4×C131—41no—
195D4×C131—41no—
196D4×C131—81no—
197D4×C131—82no—
198D4×C131—82no—
199C2×C4×C131—21no—
200C2×C4×C131—21no—
201C2×C4×C131—21no—
202C2×C4×C131—21no—
203C2×C4×C131—21no—
204C2×C4×C131—21no—
205C2×C4×C131—22no—
206C2×C4×C131—22no—
207C2×C4×C131—21no—
208C2×C4×C131—22no—
209C2×C4×C131—41no—
210C2×C4×C131—41no—
211C2×C4×C131—41no—
212C2×C4×C131—41no—
213C2×C4×C131—41no—
214C2×C4×C131—42no—
215C2×C4×C131—82no—
216C2×C4×C131—81no—
217C2×C4×C131—82no—
218C2×C4×C131—82no—
219C2×C4×C131—82no—
220C2×C4×C131—81no—
221C2×C4×C131—81no—
222C2×C4×C131C2×C22⋊C411yescharacteristic
223C2×C4×C131C2×C22⋊C411yescharacteristic
224C2×C4×C131C2×C22⋊C411yescharacteristic
225C2×C4×C131#12011yescharacteristic
226C2×C4×C131#12011yescharacteristic
227C2×C4×C131#12011yescharacteristic
228C8×C131—42no—
229C8×C131—81no—
230C8×C131—81no—
231C22×C131—21no—
232C22×C131—21no—
233C22×C131—42no—
234C22×C131—41no—
235C22×C131—41no—
236C22×C131—42no—
237C22×C131—42no—
238C22×C131—41no—
239C22×C131#37911yescharacteristic
240C22×C131#45311yescharacteristic
241C22×C131#45511yescharacteristic
242C4×C131—21no—
243C4×C131—21no—
244C4×C131—21no—
245C4×C131—21no—
246C4×C131—21no—
247C4×C131—42no—
248C4×C131—42no—
249C4×C131—41no—
250C4×C131—41no—
251C4×C131—42no—
252C4×C131—41no—
253C4×C131—82no—
254C4×C131#45411yescharacteristic
255C4×C131#45611yescharacteristic
256C2×C131—21no—
257C2×C131—21no—
258C2×C131—82no—
259C2×C131—81no—
260C2×C131#179211yescharacteristic
261C2×C131#179311yescharacteristic
262C2×C131#179411yescharacteristic
263#8513C13111yesmaximal, characteristic, direct product factor, Sylow
264C131#851311yescharacteristic, direct product factor, Sylow
265#3559C2×C13111yescharacteristic
266#1989C2×C13111yescharacteristic, complemented
267#1980C2×C13111yescharacteristic, complemented
268#1551C2×C13111yescharacteristic, complemented
269#1528C2×C13111yescharacteristic, complemented
270#1509C2×C13111yescharacteristic, complemented
271#1483C2×C13111yescharacteristic, complemented
272#563C4×C13112yescomplemented
273#562C4×C13112yescomplemented
274#554—21no—
275#553—21no—
276#553—21no—
277#547—22no—
278#547—21no—
279#544—21no—
280#540—21no—
281#539—22no—
282#539—21no—
283#537—21no—
284#532C22×C13111yescharacteristic
285#529C22×C13111yescharacteristic
286C2×#125C22×C13111yescharacteristic
287#432C22×C13111yescharacteristic
288C2×C4⋊C8C22×C13111yescharacteristic
289C2×#104—22no—
290C4×M16C22×C13111yescharacteristic
291C4×C4⋊C4C22×C13111yescharacteristic
292#340—21no—
293#340—21no—
294#333—21no—
295#331—21no—
296#330—22no—
297#328—21no—
298#327—21no—
299Q8⋊C8—21no—
300D4⋊C8—21no—
301C2×#41—22no—
302C2×#41D4×C13112yes—
303C2×M16—21no—
304C22×C8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—22no—
307C4⋊Q8D4×C13111yescharacteristic
308#127D4×C13111yescharacteristic
309#126—22no—
310#126—22no—
311#126—21no—
312#125—22no—
313#125—21no—
314#125—21no—
315#125—21no—
316#125C2×C4×C13112yes—
317#125C2×C4×C13111yescharacteristic
318#125D4×C13112yes—
319#124C2×C4×C13111yescharacteristic
320#124C2×C4×C13112yes—
321#123—22no—
322#123—22no—
323#123—22no—
324#123—22no—
325#123—21no—
326#123—22no—
327#123—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C13111yescharacteristic
335#121—22no—
336#121—22no—
337#121—21no—
338#121—21no—
339#121—22no—
340#121—22no—
341#121—21no—
342#121—21no—
343#121D4×C13111yescharacteristic
344C4×Q8D4×C13111yescharacteristic
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4D4×C13111yescharacteristic
353#117—21no—
354#117—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4D4×C13111yescharacteristic
361C2×C4⋊C4D4×C13111yescharacteristic
362C2×C42—21no—
363C2×C42C23×C13111yescharacteristic
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367#104—44no—
368C22⋊C8—21no—
369#97—21no—
370#97—21no—
371C4×C8—21no—
372#95—21no—
373#41—42no—
374#41—42no—
375#41—82no—
376#41—82no—
377C2×Q8—22no—
378C2×Q8C22⋊C4×C13111yescharacteristic
379C2×Q8C22⋊C4×C13112yes—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4C22⋊C4×C13111yescharacteristic
387C2×D4C22⋊C4×C13112yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—41no—
396C22×C4C2×D4×C13111yescharacteristic
397C22×C4C2×D4×C13111yescharacteristic
398C22×C4C2×D4×C13111yescharacteristic
399M16—22no—
400M16—41no—
401C2×C8—41no—
402C2×C8—42no—
403C2×C8—41no—
404C2×C8—41no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—41no—
423C4⋊C4C22⋊C4×C13112yes—
424C4⋊C4C22⋊C4×C13112yes—
425C4⋊C4C22⋊C4×C13111yescharacteristic
426C4⋊C4C22⋊C4×C13111yescharacteristic
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C42—22no—
440C42—21no—
441C42—42no—
442C42C22×C4×C13111yescharacteristic
443C42C2×D4×C13111yescharacteristic
444C42C2×D4×C13111yescharacteristic
445C42C2×D4×C13111yescharacteristic
446C23—22no—
447C23—21no—
448C23#120×C13111yescharacteristic
449Q8—42no—
450Q8—41no—
451Q8—82no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—41no—
456D4—42no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—81no—
461D4—82no—
462D4—82no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—82no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4C2×C22⋊C4×C13111yescharacteristic
487C2×C4C2×C22⋊C4×C13111yescharacteristic
488C2×C4C2×C22⋊C4×C13111yescharacteristic
489C2×C4#120×C13111yescharacteristic
490C2×C4#120×C13111yescharacteristic
491C2×C4#120×C13111yescharacteristic
492C8—42no—
493C8—81no—
494C8—81no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—42no—
502C22—41no—
503C22#379×C13111yescharacteristic
504C22#453×C13111yescharacteristic
505C22#455×C13111yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—42no—
512C4—42no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—82no—
518C4#454×C13111yescharacteristic
519C4#456×C13111yescharacteristic
520C2—21no—
521C2—21no—
522C2—82no—
523C2—81no—
524C2#1792×C13111yescharacteristic
525C2#1793×C13111yescharacteristic
526C2#1794×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#379
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3559×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1989×C131C2semidirect
3. #1980×C131C2semidirect
4. #1551×C131C2semidirect
5. #1528×C131C2semidirect
6. #1509×C131C2semidirect
7. #1483×C131C2semidirect
8. #563×C131C4semidirect
9. #562×C131C4semidirect
263. #8513C131direct (N × H)
264. C131#8513direct (N × H)
266. #1989C2×C131semidirect
267. #1980C2×C131semidirect
268. #1551C2×C131semidirect
269. #1528C2×C131semidirect
270. #1509C2×C131semidirect
271. #1483C2×C131semidirect
272. #563C4×C131semidirect
273. #562C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3559×C1312
#1989×C1312
#1980×C1312
#1551×C1312
#1528×C1312
#1509×C1312
#1483×C1312
#8513131