Finite Group Databasebeta

← C131×#29678 #45715562

Subgroups — C131×#29678 #45715562

Order 33536.

1274 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C131C211yesmaximal, characteristic, complemented
2#3038×C131C212yesmaximal, complemented
3#2541×C131C211yesmaximal, characteristic, complemented
4#2027×C131C212yesmaximal, complemented
5#2006×C131C212yesmaximal, complemented
6#2002×C131C214yesmaximal, complemented
7#1806×C131C212yesmaximal, complemented
8#1800×C131C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C131C2214yes—
10#544×C131C2211yescharacteristic
11#542×C131—22no—
12#540×C131—22no—
13#538×C131—22no—
14#537×C131C2211yescharacteristic
15#535×C131C2212yes—
16#532×C131—22no—
17C2×#127×C131C2212yes—
18C2×#127×C131C2211yescharacteristic
19#529×C131—22no—
20#525×C131—22no—
21C2×#121×C131—22no—
22C4×#41×C131C2212yes—
23C2×C4×D4×C131C2211yescharacteristic
24#460×C131—22no—
25#460×C131—22no—
26#459×C131—22no—
27#459×C131—22no—
28#423×C131C2212yes—
29C2×#104×C131C2214yes—
30#418×C131C2214yes—
31C2×#100×C131C2212yes—
32#392×C131—22no—
33#390×C131C2212yes—
34C4×C4⋊C4×C131C2211yescharacteristic
35#343×C131C2212yes—
36#339×C131C2214yes—
37C2×#41×C131—22no—
38C2×#41×C131C2312yes—
39C22×D4×C131—24no—
40C22×D4×C131—21no—
41C22×D4×C131—21no—
42C22×D4×C131C2312yes—
43C22×D4×C131C2311yescharacteristic
44C23×C4×C131D412yes—
45AGL(1,ℤ/8)×C131—44no—
46AGL(1,ℤ/8)×C131—44no—
47C2×SD16×C131—24no—
48C2×D8×C131—24no—
49C2×M16×C131C2314yes—
50C4⋊Q8×C131—22no—
51#127×C131—22no—
52#127×C131—22no—
53#127×C131—22no—
54#127×C131—44no—
55#126×C131—24no—
56#125×C131—22no—
57#124×C131—24no—
58#124×C131—22no—
59#123×C131—24no—
60#123×C131—24no—
61C22⋊Q8×C131—22no—
62C22⋊Q8×C131—22no—
63C22⋊Q8×C131—22no—
64#121×C131—22no—
65#121×C131—24no—
66#121×C131—22no—
67#121×C131—22no—
68#121×C131—22no—
69#121×C131—22no—
70#121×C131—48no—
71#120×C131—24no—
72C4×Q8×C131D412yescomplemented
73C4×Q8×C131D412yescomplemented
74C4×D4×C131—24no—
75C4×D4×C131—22no—
76C4×D4×C131—22no—
77C4×D4×C131—22no—
78C4×D4×C131—22no—
79C4×D4×C131D412yescomplemented
80C4×D4×C131D412yescomplemented
81#117×C131—22no—
82#117×C131—22no—
83#117×C131C2312yes—
84C2×C4⋊C4×C131—21no—
85C2×C4⋊C4×C131C2311yescharacteristic
86C2×C22⋊C4×C131—24no—
87C2×C22⋊C4×C131D412yes—
88C2×C42×C131—22no—
89C2×C42×C131C2312yes—
90C2×C42×C131C2311yescharacteristic
91C4⋊C8×C131—22no—
92C4⋊C8×C131—22no—
93#104×C131—44no—
94#102×C131—24no—
95#102×C131—24no—
96#100×C131—42no—
97#95×C131—21no—
98C24×C131—22no—
99C24×C131C2×D412yes—
100#41×C131—22no—
101#41×C131—22no—
102#41×C131—22no—
103#41×C131—22no—
104#41×C131—84no—
105C2×Q8×C131—22no—
106C2×Q8×C131C2×D412yes—
107C2×D4×C131—22no—
108C2×D4×C131—24no—
109C2×D4×C131—24no—
110C2×D4×C131—22no—
111C2×D4×C131—22no—
112C2×D4×C131—24no—
113C2×D4×C131—21no—
114C2×D4×C131—22no—
115C2×D4×C131—24no—
116C2×D4×C131—22no—
117C2×D4×C131—21no—
118C2×D4×C131—22no—
119C2×D4×C131—44no—
120C2×D4×C131—48no—
121C2×D4×C131—48no—
122C2×D4×C131—42no—
123C2×D4×C131—41no—
124C2×D4×C131—41no—
125C2×D4×C131—82no—
126C2×D4×C131—84no—
127C2×D4×C131C2×D412yes—
128C22×C4×C131—22no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—22no—
133C22×C4×C131—22no—
134C22×C4×C131—44no—
135C22×C4×C131C2×D411yescharacteristic
136C22×C4×C131C2×D412yes—
137C22×C4×C131C2×D411yescharacteristic
138C22×C4×C131C2411yescharacteristic
139SD16×C131—48no—
140D8×C131—48no—
141M16×C131—24no—
142M16×C131—24no—
143C2×C8×C131—24no—
144C4⋊C4×C131—24no—
145C4⋊C4×C131—22no—
146C4⋊C4×C131—22no—
147C4⋊C4×C131—24no—
148C4⋊C4×C131—22no—
149C4⋊C4×C131—22no—
150C4⋊C4×C131—22no—
151C4⋊C4×C131C2×D412yes—
152C4⋊C4×C131C2×D412yes—
153C22⋊C4×C131—24no—
154C22⋊C4×C131—24no—
155C22⋊C4×C131—24no—
156C22⋊C4×C131—22no—
157C22⋊C4×C131—24no—
158C22⋊C4×C131—22no—
159C22⋊C4×C131—22no—
160C22⋊C4×C131—48no—
161C42×C131—22no—
162C42×C131—22no—
163C42×C131—22no—
164C42×C131—24no—
165C42×C131C2×D412yes—
166C42×C131C2×D412yes—
167C23×C131—22no—
168C23×C131—22no—
169C23×C131—22no—
170C23×C131—22no—
171C23×C131—42no—
172C23×C131—42no—
173C23×C131—44no—
174C23×C131—44no—
175C23×C131—42no—
176C23×C131—42no—
177C23×C131—42no—
178C23×C131C22×D411yescharacteristic
179Q8×C131—22no—
180Q8×C131—22no—
181Q8×C131—82no—
182D4×C131—22no—
183D4×C131—22no—
184D4×C131—42no—
185D4×C131—42no—
186D4×C131—42no—
187D4×C131—44no—
188D4×C131—42no—
189D4×C131—44no—
190D4×C131—82no—
191D4×C131—84no—
192D4×C131—84no—
193D4×C131—82no—
194D4×C131—84no—
195D4×C131—816no—
196D4×C131—82no—
197C2×C4×C131—22no—
198C2×C4×C131—24no—
199C2×C4×C131—22no—
200C2×C4×C131—22no—
201C2×C4×C131—22no—
202C2×C4×C131—22no—
203C2×C4×C131—41no—
204C2×C4×C131—42no—
205C2×C4×C131—42no—
206C2×C4×C131—42no—
207C2×C4×C131—42no—
208C2×C4×C131—44no—
209C2×C4×C131—44no—
210C2×C4×C131—42no—
211C2×C4×C131—82no—
212C2×C4×C131—82no—
213C2×C4×C131#12012yes—
214C2×C4×C131#12011yescharacteristic
215C2×C4×C131#12011yescharacteristic
216C2×C4×C131C22×D412yes—
217C2×C4×C131H(5,𝔽2)11yescharacteristic
218C2×C4×C131H(5,𝔽2)12yes—
219C2×C4×C1312−1+411yescharacteristic
220C8×C131—44no—
221C22×C131—21no—
222C22×C131—21no—
223C22×C131—44no—
224C22×C131—42no—
225C22×C131—42no—
226C22×C131—42no—
227C22×C131—42no—
228C22×C131—42no—
229C22×C131—42no—
230C22×C131—82no—
231C22×C131—84no—
232C22×C131—84no—
233C22×C131—82no—
234C22×C131—82no—
235C22×C131—82no—
236C22×C131C2×#12011yescharacteristic
237C22×C131#53511yescharacteristic
238C22×C131#53711yescharacteristic
239C4×C131—21no—
240C4×C131—22no—
241C4×C131—44no—
242C4×C131—42no—
243C4×C131—42no—
244C4×C131—42no—
245C4×C131—42no—
246C4×C131#45312yes—
247C4×C131#53512yes—
248C4×C131#53712yes—
249C2×C131—21no—
250C2×C131—21no—
251C2×C131—82no—
252C2×C131—82no—
253C2×C131—162no—
254C2×C131#261511yescharacteristic
255C2×C131C2×#45311yescharacteristic
256C2×C131#302111yescharacteristic
257#29678C13111yesmaximal, characteristic, direct product factor, Sylow
258C131#2967811yescharacteristic, direct product factor, Sylow
259#3460C2×C13111yescharacteristic, complemented
260#3038C2×C13112yescomplemented
261#2541C2×C13111yescharacteristic, complemented
262#2027C2×C13112yescomplemented
263#2006C2×C13112yescomplemented
264#2002C2×C13114yescomplemented
265#1806C2×C13112yescomplemented
266#1800C2×C13111yescharacteristic, complemented
267C2×AGL(1,ℤ/8)C22×C13114yes—
268#544C22×C13111yescharacteristic
269#542—22no—
270#540—22no—
271#538—22no—
272#537C22×C13111yescharacteristic
273#535C22×C13112yes—
274#532—22no—
275C2×#127C22×C13111yescharacteristic
276C2×#127C22×C13112yes—
277#529—22no—
278#525—22no—
279C2×#121—22no—
280C4×#41C22×C13112yes—
281C2×C4×D4C22×C13111yescharacteristic
282#460—22no—
283#460—22no—
284#459—22no—
285#459—22no—
286#423C22×C13112yes—
287C2×#104C22×C13114yes—
288#418C22×C13114yes—
289C2×#100C22×C13112yes—
290#392—22no—
291#390C22×C13112yes—
292C4×C4⋊C4C22×C13111yescharacteristic
293#343C22×C13112yes—
294#339C22×C13114yes—
295C2×#41—22no—
296C2×#41C23×C13112yes—
297C22×D4—24no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C23×C13112yes—
301C22×D4C23×C13111yescharacteristic
302C23×C4D4×C13112yes—
303AGL(1,ℤ/8)—44no—
304AGL(1,ℤ/8)—44no—
305C2×SD16—24no—
306C2×D8—24no—
307C2×M16C23×C13114yes—
308C4⋊Q8—22no—
309#127—22no—
310#127—22no—
311#127—22no—
312#127—44no—
313#126—24no—
314#125—22no—
315#124—24no—
316#124—22no—
317#123—24no—
318#123—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322#121—22no—
323#121—24no—
324#121—22no—
325#121—22no—
326#121—22no—
327#121—22no—
328#121—48no—
329#120—24no—
330C4×Q8D4×C13112yescomplemented
331C4×Q8D4×C13112yescomplemented
332C4×D4—24no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4D4×C13112yescomplemented
338C4×D4D4×C13112yescomplemented
339#117—22no—
340#117—22no—
341#117C23×C13112yes—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C23×C13111yescharacteristic
344C2×C22⋊C4—24no—
345C2×C22⋊C4D4×C13112yes—
346C2×C42—22no—
347C2×C42C23×C13112yes—
348C2×C42C23×C13111yescharacteristic
349C4⋊C8—22no—
350C4⋊C8—22no—
351#104—44no—
352#102—24no—
353#102—24no—
354#100—42no—
355#95—21no—
356C24—22no—
357C24C2×D4×C13112yes—
358#41—22no—
359#41—22no—
360#41—22no—
361#41—22no—
362#41—84no—
363C2×Q8—22no—
364C2×Q8C2×D4×C13112yes—
365C2×D4—22no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—22no—
377C2×D4—44no—
378C2×D4—48no—
379C2×D4—48no—
380C2×D4—42no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—82no—
384C2×D4—84no—
385C2×D4C2×D4×C13112yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—44no—
393C22×C4C2×D4×C13111yescharacteristic
394C22×C4C2×D4×C13112yes—
395C22×C4C2×D4×C13111yescharacteristic
396C22×C4C24×C13111yescharacteristic
397SD16—48no—
398D8—48no—
399M16—24no—
400M16—24no—
401C2×C8—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4C2×D4×C13112yes—
410C4⋊C4C2×D4×C13112yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—48no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—24no—
423C42C2×D4×C13112yes—
424C42C2×D4×C13112yes—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23C22×D4×C13111yescharacteristic
437Q8—22no—
438Q8—22no—
439Q8—82no—
440D4—22no—
441D4—22no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—42no—
447D4—44no—
448D4—82no—
449D4—84no—
450D4—82no—
451D4—84no—
452D4—84no—
453D4—816no—
454D4—82no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4#120×C13112yes—
472C2×C4#120×C13111yescharacteristic
473C2×C4#120×C13111yescharacteristic
474C2×C4C22×D4×C13112yes—
475C2×C4H(5,𝔽2)×C13111yescharacteristic
476C2×C4H(5,𝔽2)×C13112yes—
477C2×C42−1+4×C13111yescharacteristic
478C8—44no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—82no—
489C22—84no—
490C22—84no—
491C22—82no—
492C22—82no—
493C22—82no—
494C22C2×#120×C13111yescharacteristic
495C22#535×C13111yescharacteristic
496C22#537×C13111yescharacteristic
497C4—21no—
498C4—22no—
499C4—44no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4#453×C13112yes—
505C4#535×C13112yes—
506C4#537×C13112yes—
507C2—21no—
508C2—21no—
509C2—82no—
510C2—82no—
511C2—162no—
512C2#2615×C13111yescharacteristic
513C2C2×#453×C13111yescharacteristic
514C2#3021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3460×C131C2semidirect
2. #3038×C131C2semidirect
3. #2541×C131C2semidirect
4. #2027×C131C2semidirect
5. #2006×C131C2semidirect
6. #2002×C131C2semidirect
7. #1806×C131C2semidirect
8. #1800×C131C2semidirect
72. C4×Q8×C131D4semidirect
73. C4×Q8×C131D4semidirect
79. C4×D4×C131D4semidirect
80. C4×D4×C131D4semidirect
257. #29678C131direct (N × H)
258. C131#29678direct (N × H)
259. #3460C2×C131semidirect
260. #3038C2×C131semidirect
261. #2541C2×C131semidirect
262. #2027C2×C131semidirect
263. #2006C2×C131semidirect
264. #2002C2×C131semidirect
265. #1806C2×C131semidirect
266. #1800C2×C131semidirect
330. C4×Q8D4×C131semidirect
331. C4×Q8D4×C131semidirect
337. C4×D4D4×C131semidirect
338. C4×D4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3460×C1312
#3038×C1312
#2541×C1312
#2027×C1312
#2006×C1312
#2002×C1312
#1806×C1312
#1800×C1312
#29678131