Finite Group Databasebeta

← C131×#25924 #45711808

Subgroups — C131×#25924 #45711808

Order 33536.

1138 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C131C211yesmaximal, characteristic, complemented
2#3138×C131C211yesmaximal, characteristic, complemented
3#3038×C131C211yesmaximal, characteristic
4#2858×C131C211yesmaximal, characteristic, complemented
5#2027×C131C214yesmaximal, complemented
6#1997×C131C211yesmaximal, characteristic, complemented
7#1994×C131C211yesmaximal, characteristic, complemented
8#1883×C131C214yesmaximal, complemented
9C4×#104×C131C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C131C2212yes—
11Q82×C131—21no—
12#557×C131—21no—
13#554×C131—21no—
14#554×C131—22no—
15D4×Q8×C131—22no—
16D4×Q8×C131—21no—
17#544×C131—22no—
18#544×C131C2212yes—
19#533×C131—21no—
20#533×C131C2211yescharacteristic
21C2×C4⋊Q8×C131—21no—
22C2×C4⋊Q8×C131C2211yescharacteristic
23C2×#127×C131C2211yescharacteristic
24C2×#124×C131—22no—
25#520×C131C2212yes—
26C4×#41×C131C2211yescharacteristic
27#490×C131—22no—
28#486×C131—21no—
29#486×C131—21no—
30#460×C131—21no—
31#460×C131—21no—
32#459×C131—21no—
33#459×C131—21no—
34#423×C131C2211yescharacteristic
35C2×#104×C131C2212yes—
36#418×C131C2212yes—
37#418×C131C2214yes—
38C4×M16×C131C2211yescharacteristic
39#390×C131—22no—
40#390×C131C2214yes—
41C43×C131C2211yescharacteristic
42#343×C131C2214yes—
43#339×C131C2214yes—
44#339×C131C2212yes—
45C2×#41×C131C2311yescharacteristic
46C22×Q8×C131—22no—
47C22×Q8×C131D412yes—
48C22×D4×C131—21no—
49C22×D4×C131—21no—
50C22×D4×C131C2312yes—
51AGL(1,ℤ/8)×C131—28no—
52C2×SD16×C131—22no—
53C2×D8×C131—22no—
54C2×M16×C131C2312yes—
55C2×M16×C131C2312yes—
56C4⋊Q8×C131—22no—
57C4⋊Q8×C131—22no—
58C4⋊Q8×C131—24no—
59C4⋊Q8×C131—22no—
60C4⋊Q8×C131—22no—
61C4⋊Q8×C131—21no—
62C4⋊Q8×C131—21no—
63C4⋊Q8×C131—21no—
64C4⋊Q8×C131—21no—
65C4⋊Q8×C131D411yescharacteristic
66C4⋊Q8×C131D411yescharacteristic
67#127×C131—21no—
68#127×C131—21no—
69#127×C131—21no—
70#127×C131—21no—
71#125×C131—24no—
72#125×C131—22no—
73#125×C131—22no—
74#125×C131D412yes—
75#124×C131—48no—
76C22⋊Q8×C131—22no—
77C22⋊Q8×C131—22no—
78C22⋊Q8×C131—24no—
79C22⋊Q8×C131—24no—
80C22⋊Q8×C131—21no—
81C22⋊Q8×C131—21no—
82C22⋊Q8×C131—24no—
83C4×Q8×C131—22no—
84C4×Q8×C131—22no—
85C4×Q8×C131—22no—
86C4×Q8×C131—21no—
87C4×Q8×C131—21no—
88C4×Q8×C131D411yescharacteristic
89C4×Q8×C131D411yescharacteristic
90C4×D4×C131—22no—
91C4×D4×C131—21no—
92C4×D4×C131—21no—
93C4×D4×C131—24no—
94C4×D4×C131D411yescharacteristic
95C4×D4×C131D411yescharacteristic
96#117×C131—22no—
97#117×C131—21no—
98#117×C131C2311yescharacteristic
99#117×C131C2312yes—
100C2×C4⋊C4×C131—22no—
101C2×C4⋊C4×C131—22no—
102C2×C4⋊C4×C131D412yes—
103C2×C4⋊C4×C131C2312yes—
104C2×C22⋊C4×C131—28no—
105C2×C42×C131—21no—
106C2×C42×C131—21no—
107C2×C42×C131—21no—
108C2×C42×C131C2312yes—
109C2×C42×C131C2311yescharacteristic
110C4⋊C8×C131—21no—
111C4⋊C8×C131—21no—
112#104×C131—24no—
113#102×C131—22no—
114#102×C131—22no—
115#102×C131—24no—
116#102×C131—24no—
117#97×C131—21no—
118C4×C8×C131—21no—
119C24×C131—22no—
120#41×C131—22no—
121#41×C131#4114yes—
122C2×Q8×C131—24no—
123C2×Q8×C131—21no—
124C2×Q8×C131—22no—
125C2×Q8×C131—21no—
126C2×Q8×C131—22no—
127C2×Q8×C131—44no—
128C2×Q8×C131—84no—
129C2×Q8×C131C2×D411yescharacteristic
130C2×D4×C131—21no—
131C2×D4×C131—22no—
132C2×D4×C131—22no—
133C2×D4×C131—24no—
134C2×D4×C131—24no—
135C2×D4×C131—44no—
136C2×D4×C131—44no—
137C2×D4×C131—41no—
138C2×D4×C131—41no—
139C2×D4×C131—41no—
140C2×D4×C131—41no—
141C2×D4×C131C2×D411yescharacteristic
142C22×C4×C131—21no—
143C22×C4×C131—22no—
144C22×C4×C131—24no—
145C22×C4×C131—21no—
146C22×C4×C131—21no—
147C22×C4×C131C2×D411yescharacteristic
148C22×C4×C131C2×D411yescharacteristic
149C22×C4×C131C2×D414yes—
150C22×C4×C131C2411yescharacteristic
151SD16×C131—44no—
152D8×C131—44no—
153M16×C131—22no—
154M16×C131—24no—
155M16×C131—22no—
156C2×C8×C131—22no—
157C2×C8×C131—22no—
158C4⋊C4×C131—24no—
159C4⋊C4×C131—24no—
160C4⋊C4×C131—24no—
161C4⋊C4×C131—24no—
162C4⋊C4×C131—21no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131—21no—
166C4⋊C4×C131—21no—
167C4⋊C4×C131—21no—
168C4⋊C4×C131—22no—
169C4⋊C4×C131—22no—
170C4⋊C4×C131—22no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131C2×D412yes—
173C4⋊C4×C131C2×D412yes—
174C4⋊C4×C131C2×D411yescharacteristic
175C4⋊C4×C131C2×D411yescharacteristic
176C22⋊C4×C131—24no—
177C22⋊C4×C131—22no—
178C22⋊C4×C131—21no—
179C22⋊C4×C131—21no—
180C22⋊C4×C131—21no—
181C22⋊C4×C131—416no—
182C42×C131—24no—
183C42×C131—24no—
184C42×C131—21no—
185C42×C131—21no—
186C42×C131—21no—
187C42×C131—22no—
188C42×C131—22no—
189C42×C131—22no—
190C42×C131—42no—
191C42×C131C2×D411yescharacteristic
192C42×C131C2×D411yescharacteristic
193C42×C131C2×D411yescharacteristic
194C42×C131C2×D411yescharacteristic
195C23×C131—21no—
196C23×C131—44no—
197C23×C131—44no—
198C23×C131—42no—
199C23×C131—44no—
200C23×C131C22×D411yescharacteristic
201Q8×C131—21no—
202Q8×C131—44no—
203Q8×C131—42no—
204Q8×C131—42no—
205Q8×C131—82no—
206Q8×C131—84no—
207Q8×C131#12412yescomplemented
208D4×C131—24no—
209D4×C131—21no—
210D4×C131—42no—
211D4×C131—42no—
212D4×C131—44no—
213D4×C131—82no—
214D4×C131—82no—
215D4×C131—82no—
216D4×C131—82no—
217D4×C131#12412yescomplemented
218C2×C4×C131—21no—
219C2×C4×C131—24no—
220C2×C4×C131—22no—
221C2×C4×C131—22no—
222C2×C4×C131—24no—
223C2×C4×C131—22no—
224C2×C4×C131—21no—
225C2×C4×C131—21no—
226C2×C4×C131—24no—
227C2×C4×C131—22no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—42no—
231C2×C4×C131—42no—
232C2×C4×C131—44no—
233C2×C4×C131—84no—
234C2×C4×C131#12011yescharacteristic
235C2×C4×C131#12011yescharacteristic
236C2×C4×C131#12011yescharacteristic
237C2×C4×C131#12011yescharacteristic
238C2×C4×C131C22×D411yescharacteristic
239C2×C4×C131C22×D411yescharacteristic
240C2×C4×C131C2×#4112yes—
241C2×C4×C1312−1+412yes—
242C8×C131—42no—
243C8×C131—42no—
244C22×C131—21no—
245C22×C131—21no—
246C22×C131—22no—
247C22×C131—41no—
248C22×C131—41no—
249C22×C131—88no—
250C22×C131—82no—
251C22×C131—82no—
252C22×C131—82no—
253C22×C131C2×#12011yescharacteristic
254C22×C131#54812yes—
255C4×C131—22no—
256C4×C131—21no—
257C4×C131—21no—
258C4×C131—44no—
259C4×C131—41no—
260C4×C131—44no—
261C4×C131—42no—
262C4×C131—41no—
263C4×C131—42no—
264C4×C131#45312yes—
265C4×C131#45412yes—
266C4×C131C2×#12411yescharacteristic
267C4×C131#53611yescharacteristic
268C4×C131#54812yes—
269C2×C131—22no—
270C2×C131—42no—
271C2×C131—162no—
272C2×C131#243611yescharacteristic
273C2×C131C2×#45311yescharacteristic
274C2×C131C2×#45411yescharacteristic
275#25924C13111yesmaximal, characteristic, direct product factor, Sylow
276C131#2592411yescharacteristic, direct product factor, Sylow
277#3503C2×C13111yescharacteristic, complemented
278#3138C2×C13111yescharacteristic, complemented
279#3038C2×C13111yescharacteristic
280#2858C2×C13111yescharacteristic, complemented
281#2027C2×C13114yescomplemented
282#1997C2×C13111yescharacteristic, complemented
283#1994C2×C13111yescharacteristic, complemented
284#1883C2×C13114yescomplemented
285C4×#104C2×C13111yescharacteristic, complemented
286C2×AGL(1,ℤ/8)C22×C13112yes—
287Q82—21no—
288#557—21no—
289#554—21no—
290#554—22no—
291D4×Q8—22no—
292D4×Q8—21no—
293#544—22no—
294#544C22×C13112yes—
295#533—21no—
296#533C22×C13111yescharacteristic
297C2×C4⋊Q8—21no—
298C2×C4⋊Q8C22×C13111yescharacteristic
299C2×#127C22×C13111yescharacteristic
300C2×#124—22no—
301#520C22×C13112yes—
302C4×#41C22×C13111yescharacteristic
303#490—22no—
304#486—21no—
305#486—21no—
306#460—21no—
307#460—21no—
308#459—21no—
309#459—21no—
310#423C22×C13111yescharacteristic
311C2×#104C22×C13112yes—
312#418C22×C13114yes—
313#418C22×C13112yes—
314C4×M16C22×C13111yescharacteristic
315#390—22no—
316#390C22×C13114yes—
317C43C22×C13111yescharacteristic
318#343C22×C13114yes—
319#339C22×C13114yes—
320#339C22×C13112yes—
321C2×#41C23×C13111yescharacteristic
322C22×Q8—22no—
323C22×Q8D4×C13112yes—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C23×C13112yes—
327AGL(1,ℤ/8)—28no—
328C2×SD16—22no—
329C2×D8—22no—
330C2×M16C23×C13112yes—
331C2×M16C23×C13112yes—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—24no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8D4×C13111yescharacteristic
342C4⋊Q8D4×C13111yescharacteristic
343#127—21no—
344#127—21no—
345#127—21no—
346#127—21no—
347#125—24no—
348#125—22no—
349#125—22no—
350#125D4×C13112yes—
351#124—48no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—24no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8D4×C13111yescharacteristic
365C4×Q8D4×C13111yescharacteristic
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—24no—
370C4×D4D4×C13111yescharacteristic
371C4×D4D4×C13111yescharacteristic
372#117—22no—
373#117—21no—
374#117C23×C13111yescharacteristic
375#117C23×C13112yes—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4D4×C13112yes—
379C2×C4⋊C4C23×C13112yes—
380C2×C22⋊C4—28no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C13112yes—
385C2×C42C23×C13111yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388#104—24no—
389#102—22no—
390#102—22no—
391#102—24no—
392#102—24no—
393#97—21no—
394C4×C8—21no—
395C24—22no—
396#41—22no—
397#41#41×C13114yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8—84no—
405C2×Q8C2×D4×C13111yescharacteristic
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4C2×D4×C13111yescharacteristic
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4C2×D4×C13111yescharacteristic
424C22×C4C2×D4×C13111yescharacteristic
425C22×C4C2×D4×C13114yes—
426C22×C4C24×C13111yescharacteristic
427SD16—44no—
428D8—44no—
429M16—22no—
430M16—24no—
431M16—22no—
432C2×C8—22no—
433C2×C8—22no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4C2×D4×C13112yes—
449C4⋊C4C2×D4×C13112yes—
450C4⋊C4C2×D4×C13111yescharacteristic
451C4⋊C4C2×D4×C13111yescharacteristic
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—416no—
458C42—24no—
459C42—24no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—22no—
464C42—22no—
465C42—22no—
466C42—42no—
467C42C2×D4×C13111yescharacteristic
468C42C2×D4×C13111yescharacteristic
469C42C2×D4×C13111yescharacteristic
470C42C2×D4×C13111yescharacteristic
471C23—21no—
472C23—44no—
473C23—44no—
474C23—42no—
475C23—44no—
476C23C22×D4×C13111yescharacteristic
477Q8—21no—
478Q8—44no—
479Q8—42no—
480Q8—42no—
481Q8—82no—
482Q8—84no—
483Q8#124×C13112yescomplemented
484D4—24no—
485D4—21no—
486D4—42no—
487D4—42no—
488D4—44no—
489D4—82no—
490D4—82no—
491D4—82no—
492D4—82no—
493D4#124×C13112yescomplemented
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—84no—
510C2×C4#120×C13111yescharacteristic
511C2×C4#120×C13111yescharacteristic
512C2×C4#120×C13111yescharacteristic
513C2×C4#120×C13111yescharacteristic
514C2×C4C22×D4×C13111yescharacteristic
515C2×C4C22×D4×C13111yescharacteristic
516C2×C4C2×#41×C13112yes—
517C2×C42−1+4×C13112yes—
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—88no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22C2×#120×C13111yescharacteristic
530C22#548×C13112yes—
531C4—21no—
532C4—21no—
533C4—22no—
534C4—44no—
535C4—41no—
536C4—44no—
537C4—42no—
538C4—41no—
539C4—42no—
540C4#453×C13112yes—
541C4#454×C13112yes—
542C4C2×#124×C13111yescharacteristic
543C4#536×C13111yescharacteristic
544C4#548×C13112yes—
545C2—22no—
546C2—42no—
547C2—162no—
548C2#2436×C13111yescharacteristic
549C2C2×#453×C13111yescharacteristic
550C2C2×#454×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3038×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
1. #3503×C131C2semidirect
2. #3138×C131C2semidirect
4. #2858×C131C2semidirect
5. #2027×C131C2semidirect
6. #1997×C131C2semidirect
7. #1994×C131C2semidirect
8. #1883×C131C2semidirect
9. C4×#104×C131C2semidirect
207. Q8×C131#124semidirect
217. D4×C131#124semidirect
275. #25924C131direct (N × H)
276. C131#25924direct (N × H)
277. #3503C2×C131semidirect
278. #3138C2×C131semidirect
280. #2858C2×C131semidirect
281. #2027C2×C131semidirect
282. #1997C2×C131semidirect
283. #1994C2×C131semidirect
284. #1883C2×C131semidirect
285. C4×#104C2×C131semidirect
483. Q8#124×C131semidirect
493. D4#124×C131semidirect

Maximal subgroups

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

subgroupindex
#3503×C1312
#3138×C1312
#3038×C1312
#2858×C1312
#2027×C1312
#1997×C1312
#1994×C1312
#1883×C1312
C4×#104×C1312
#25924131