Finite Group Databasebeta

← C131×#25615 #45711499

Subgroups — C131×#25615 #45711499

Order 33536.

1116 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C131C211yesmaximal, characteristic
2#3152×C131C211yesmaximal, characteristic, complemented
3#3039×C131C211yesmaximal, characteristic, complemented
4#2862×C131C211yesmaximal, characteristic, complemented
5#2007×C131C214yesmaximal, complemented
6#1997×C131C211yesmaximal, characteristic, complemented
7#1962×C131C211yesmaximal, characteristic, complemented
8#1882×C131C214yesmaximal, complemented
9C4×#104×C131C211yesmaximal, characteristic, complemented
10C2×#137×C131C2214yes—
11C2×#137×C131C2212yes—
12#556×C131—21no—
13#555×C131—21no—
14#554×C131—21no—
15#553×C131—22no—
16#548×C131—22no—
17#547×C131—21no—
18#542×C131—22no—
19#537×C131C2212yes—
20#533×C131—21no—
21#532×C131—21no—
22#532×C131C2211yescharacteristic
23C2×C4⋊Q8×C131C2211yescharacteristic
24C2×C4⋊Q8×C131C2211yescharacteristic
25#520×C131C2212yes—
26C4×#41×C131C2211yescharacteristic
27#497×C131—22no—
28#494×C131—21no—
29#492×C131—21no—
30#462×C131—21no—
31#462×C131—21no—
32#461×C131—21no—
33#461×C131—21no—
34#423×C131C2211yescharacteristic
35C2×#104×C131C2212yes—
36C2×#104×C131C2214yes—
37#419×C131C2212yes—
38C4×M16×C131C2211yescharacteristic
39#391×C131—22no—
40#391×C131C2214yes—
41#382×C131—22no—
42C43×C131C2211yescharacteristic
43#343×C131C2214yes—
44#339×C131C2212yes—
45C2×#41×C131—22no—
46C2×#41×C131C2311yescharacteristic
47C2×#41×C131C2312yes—
48C22×Q8×C131D412yes—
49C22×Q8×C131C2312yes—
50#137×C131—28no—
51#137×C131—44no—
52#137×C131—44no—
53C2×Q16×C131—22no—
54C2×Q16×C131—24no—
55C2×SD16×C131—22no—
56C2×SD16×C131—24no—
57C2×M16×C131C2312yes—
58C2×M16×C131C2312yes—
59C4⋊Q8×C131—21no—
60C4⋊Q8×C131—21no—
61C4⋊Q8×C131—21no—
62C4⋊Q8×C131—21no—
63C4⋊Q8×C131—21no—
64C4⋊Q8×C131—21no—
65C4⋊Q8×C131—21no—
66C4⋊Q8×C131—21no—
67C4⋊Q8×C131D411yescharacteristic
68#127×C131D411yescharacteristic
69#126×C131—24no—
70#125×C131—22no—
71#124×C131—22no—
72#124×C131—24no—
73#124×C131D412yes—
74#123×C131—24no—
75C22⋊Q8×C131—22no—
76C22⋊Q8×C131—24no—
77C22⋊Q8×C131—22no—
78C22⋊Q8×C131—22no—
79#121×C131—22no—
80#121×C131—22no—
81#121×C131—22no—
82#121×C131—21no—
83#121×C131—21no—
84#121×C131—24no—
85C4×Q8×C131—22no—
86C4×Q8×C131—22no—
87C4×Q8×C131D411yescharacteristic
88C4×Q8×C131D411yescharacteristic
89C4×D4×C131—22no—
90C4×D4×C131—22no—
91C4×D4×C131—21no—
92C4×D4×C131—21no—
93C4×D4×C131—24no—
94C4×D4×C131—21no—
95C4×D4×C131—21no—
96C4×D4×C131D411yescharacteristic
97C4×D4×C131D411yescharacteristic
98#117×C131—22no—
99#117×C131—22no—
100#117×C131—21no—
101#117×C131C2311yescharacteristic
102C2×C4⋊C4×C131—22no—
103C2×C4⋊C4×C131—21no—
104C2×C4⋊C4×C131—21no—
105C2×C4⋊C4×C131D412yes—
106C2×C4⋊C4×C131C2312yes—
107C2×C42×C131—21no—
108C2×C42×C131—21no—
109C2×C42×C131—21no—
110C2×C42×C131C2312yes—
111C2×C42×C131C2311yescharacteristic
112C4⋊C8×C131—21no—
113C4⋊C8×C131—21no—
114#104×C131—24no—
115#104×C131—44no—
116#103×C131—22no—
117#103×C131—22no—
118#97×C131—21no—
119C4×C8×C131—21no—
120#95×C131—28no—
121#41×C131—22no—
122#41×C131—24no—
123#41×C131—24no—
124#41×C131—22no—
125#41×C131—84no—
126C2×Q8×C131—22no—
127C2×Q8×C131—22no—
128C2×Q8×C131—22no—
129C2×Q8×C131—22no—
130C2×Q8×C131—24no—
131C2×Q8×C131—24no—
132C2×Q8×C131—44no—
133C2×Q8×C131C2×D412yes—
134C2×Q8×C131C2×D411yescharacteristic
135C2×D4×C131—21no—
136C2×D4×C131—22no—
137C2×D4×C131—24no—
138C2×D4×C131—21no—
139C2×D4×C131—21no—
140C2×D4×C131C2×D412yes—
141C2×D4×C131C2×D411yescharacteristic
142C22×C4×C131—22no—
143C22×C4×C131—24no—
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—21no—
147C22×C4×C131—22no—
148C22×C4×C131—22no—
149C22×C4×C131C2×D411yescharacteristic
150C22×C4×C131C2×D411yescharacteristic
151C22×C4×C131C2×D414yes—
152C22×C4×C131C2411yescharacteristic
153Q16×C131—48no—
154Q16×C131—44no—
155SD16×C131—48no—
156SD16×C131—44no—
157M16×C131—22no—
158M16×C131—24no—
159M16×C131#4114yescomplemented
160C2×C8×C131—22no—
161C2×C8×C131—22no—
162C4⋊C4×C131—24no—
163C4⋊C4×C131—24no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131—22no—
166C4⋊C4×C131—21no—
167C4⋊C4×C131—21no—
168C4⋊C4×C131—21no—
169C4⋊C4×C131—21no—
170C4⋊C4×C131—22no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—41no—
173C4⋊C4×C131—41no—
174C4⋊C4×C131—41no—
175C4⋊C4×C131—41no—
176C4⋊C4×C131C2×D411yescharacteristic
177C4⋊C4×C131C2×D411yescharacteristic
178C22⋊C4×C131—24no—
179C22⋊C4×C131—24no—
180C22⋊C4×C131—24no—
181C22⋊C4×C131—21no—
182C22⋊C4×C131—21no—
183C22⋊C4×C131—21no—
184C22⋊C4×C131—22no—
185C22⋊C4×C131—22no—
186C42×C131—24no—
187C42×C131—24no—
188C42×C131—21no—
189C42×C131—21no—
190C42×C131—21no—
191C42×C131—22no—
192C42×C131—22no—
193C42×C131—42no—
194C42×C131C2×D411yescharacteristic
195C42×C131C2×D411yescharacteristic
196C42×C131C2×D411yescharacteristic
197C42×C131C2×D411yescharacteristic
198C23×C131—21no—
199C23×C131—22no—
200C23×C131C22×D411yescharacteristic
201Q8×C131—21no—
202Q8×C131—21no—
203Q8×C131—24no—
204Q8×C131—44no—
205Q8×C131—42no—
206Q8×C131—42no—
207Q8×C131—44no—
208Q8×C131—82no—
209D4×C131—21no—
210D4×C131—21no—
211D4×C131—24no—
212D4×C131—42no—
213D4×C131—44no—
214D4×C131—42no—
215D4×C131—42no—
216D4×C131—84no—
217C2×C4×C131—22no—
218C2×C4×C131—22no—
219C2×C4×C131—24no—
220C2×C4×C131—21no—
221C2×C4×C131—22no—
222C2×C4×C131—21no—
223C2×C4×C131—21no—
224C2×C4×C131—24no—
225C2×C4×C131—42no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—42no—
231C2×C4×C131—42no—
232C2×C4×C131—44no—
233C2×C4×C131—42no—
234C2×C4×C131—44no—
235C2×C4×C131—84no—
236C2×C4×C131#12011yescharacteristic
237C2×C4×C131#12011yescharacteristic
238C2×C4×C131#12011yescharacteristic
239C2×C4×C131#12011yescharacteristic
240C2×C4×C131C22×D411yescharacteristic
241C2×C4×C131C22×D411yescharacteristic
242C2×C4×C131C2×#4112yes—
243C2×C4×C131H(5,𝔽2)12yes—
244C8×C131—24no—
245C8×C131—42no—
246C22×C131—21no—
247C22×C131—21no—
248C22×C131—42no—
249C22×C131—41no—
250C22×C131—41no—
251C22×C131—42no—
252C22×C131—41no—
253C22×C131—42no—
254C22×C131C2×#12011yescharacteristic
255C22×C131#55012yes—
256C4×C131—21no—
257C4×C131—21no—
258C4×C131—44no—
259C4×C131—42no—
260C4×C131—41no—
261C4×C131—41no—
262C4×C131—44no—
263C4×C131—41no—
264C4×C131—82no—
265C4×C131#45512yes—
266C4×C131#45612yes—
267C4×C131#53211yescharacteristic
268C4×C131#53511yescharacteristic
269C4×C131#54612yes—
270C2×C131—22no—
271C2×C131—81no—
272C2×C131—82no—
273C2×C131#243111yescharacteristic
274C2×C131C2×#45511yescharacteristic
275C2×C131C2×#45611yescharacteristic
276#25615C13111yesmaximal, characteristic, direct product factor, Sylow
277C131#2561511yescharacteristic, direct product factor, Sylow
278#3511C2×C13111yescharacteristic
279#3152C2×C13111yescharacteristic, complemented
280#3039C2×C13111yescharacteristic, complemented
281#2862C2×C13111yescharacteristic, complemented
282#2007C2×C13114yescomplemented
283#1997C2×C13111yescharacteristic, complemented
284#1962C2×C13111yescharacteristic, complemented
285#1882C2×C13114yescomplemented
286C4×#104C2×C13111yescharacteristic, complemented
287C2×#137C22×C13114yes—
288C2×#137C22×C13112yes—
289#556—21no—
290#555—21no—
291#554—21no—
292#553—22no—
293#548—22no—
294#547—21no—
295#542—22no—
296#537C22×C13112yes—
297#533—21no—
298#532—21no—
299#532C22×C13111yescharacteristic
300C2×C4⋊Q8C22×C13111yescharacteristic
301C2×C4⋊Q8C22×C13111yescharacteristic
302#520C22×C13112yes—
303C4×#41C22×C13111yescharacteristic
304#497—22no—
305#494—21no—
306#492—21no—
307#462—21no—
308#462—21no—
309#461—21no—
310#461—21no—
311#423C22×C13111yescharacteristic
312C2×#104C22×C13112yes—
313C2×#104C22×C13114yes—
314#419C22×C13112yes—
315C4×M16C22×C13111yescharacteristic
316#391—22no—
317#391C22×C13114yes—
318#382—22no—
319C43C22×C13111yescharacteristic
320#343C22×C13114yes—
321#339C22×C13112yes—
322C2×#41—22no—
323C2×#41C23×C13111yescharacteristic
324C2×#41C23×C13112yes—
325C22×Q8D4×C13112yes—
326C22×Q8C23×C13112yes—
327#137—28no—
328#137—44no—
329#137—44no—
330C2×Q16—22no—
331C2×Q16—24no—
332C2×SD16—22no—
333C2×SD16—24no—
334C2×M16C23×C13112yes—
335C2×M16C23×C13112yes—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8D4×C13111yescharacteristic
345#127D4×C13111yescharacteristic
346#126—24no—
347#125—22no—
348#124—22no—
349#124—24no—
350#124D4×C13112yes—
351#123—24no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—21no—
360#121—21no—
361#121—24no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8D4×C13111yescharacteristic
365C4×Q8D4×C13111yescharacteristic
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—24no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D4×C13111yescharacteristic
374C4×D4D4×C13111yescharacteristic
375#117—22no—
376#117—22no—
377#117—21no—
378#117C23×C13111yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4D4×C13112yes—
383C2×C4⋊C4C23×C13112yes—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C13112yes—
388C2×C42C23×C13111yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391#104—24no—
392#104—44no—
393#103—22no—
394#103—22no—
395#97—21no—
396C4×C8—21no—
397#95—28no—
398#41—22no—
399#41—24no—
400#41—24no—
401#41—22no—
402#41—84no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—44no—
410C2×Q8C2×D4×C13112yes—
411C2×Q8C2×D4×C13111yescharacteristic
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×D4×C13112yes—
418C2×D4C2×D4×C13111yescharacteristic
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4C2×D4×C13111yescharacteristic
427C22×C4C2×D4×C13111yescharacteristic
428C22×C4C2×D4×C13114yes—
429C22×C4C24×C13111yescharacteristic
430Q16—48no—
431Q16—44no—
432SD16—48no—
433SD16—44no—
434M16—22no—
435M16—24no—
436M16#41×C13114yescomplemented
437C2×C8—22no—
438C2×C8—22no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4C2×D4×C13111yescharacteristic
454C4⋊C4C2×D4×C13111yescharacteristic
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C42—24no—
464C42—24no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—22no—
469C42—22no—
470C42—42no—
471C42C2×D4×C13111yescharacteristic
472C42C2×D4×C13111yescharacteristic
473C42C2×D4×C13111yescharacteristic
474C42C2×D4×C13111yescharacteristic
475C23—21no—
476C23—22no—
477C23C22×D4×C13111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—24no—
481Q8—44no—
482Q8—42no—
483Q8—42no—
484Q8—44no—
485Q8—82no—
486D4—21no—
487D4—21no—
488D4—24no—
489D4—42no—
490D4—44no—
491D4—42no—
492D4—42no—
493D4—84no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—84no—
513C2×C4#120×C13111yescharacteristic
514C2×C4#120×C13111yescharacteristic
515C2×C4#120×C13111yescharacteristic
516C2×C4#120×C13111yescharacteristic
517C2×C4C22×D4×C13111yescharacteristic
518C2×C4C22×D4×C13111yescharacteristic
519C2×C4C2×#41×C13112yes—
520C2×C4H(5,𝔽2)×C13112yes—
521C8—24no—
522C8—42no—
523C22—21no—
524C22—21no—
525C22—41no—
526C22—42no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22C2×#120×C13111yescharacteristic
532C22#550×C13112yes—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—41no—
537C4—44no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4—82no—
542C4#455×C13112yes—
543C4#456×C13112yes—
544C4#532×C13111yescharacteristic
545C4#535×C13111yescharacteristic
546C4#546×C13112yes—
547C2—22no—
548C2—81no—
549C2—82no—
550C2#2431×C13111yescharacteristic
551C2C2×#455×C13111yescharacteristic
552C2C2×#456×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3511×C131C2
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
2. #3152×C131C2semidirect
3. #3039×C131C2semidirect
4. #2862×C131C2semidirect
5. #2007×C131C2semidirect
6. #1997×C131C2semidirect
7. #1962×C131C2semidirect
8. #1882×C131C2semidirect
9. C4×#104×C131C2semidirect
159. M16×C131#41semidirect
276. #25615C131direct (N × H)
277. C131#25615direct (N × H)
279. #3152C2×C131semidirect
280. #3039C2×C131semidirect
281. #2862C2×C131semidirect
282. #2007C2×C131semidirect
283. #1997C2×C131semidirect
284. #1962C2×C131semidirect
285. #1882C2×C131semidirect
286. C4×#104C2×C131semidirect
436. M16#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3511×C1312
#3152×C1312
#3039×C1312
#2862×C1312
#2007×C1312
#1997×C1312
#1962×C1312
#1882×C1312
C4×#104×C1312
#25615131