Finite Group Databasebeta

← C131×#19459 #45705343

Subgroups — C131×#19459 #45705343

Order 33536.

638 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3209×C131C211yesmaximal, characteristic, complemented
2#3110×C131C211yesmaximal, characteristic
3C2×#474×C131C211yesmaximal, characteristic
4#2974×C131C211yesmaximal, characteristic
5#1699×C131C212yesmaximal, complemented
6#1689×C131C212yesmaximal, complemented
7#1679×C131C212yesmaximal, complemented
8#1669×C131C212yesmaximal, complemented
9#1573×C131C211yesmaximal, characteristic, complemented
10#1556×C131C211yesmaximal, characteristic, complemented
11#1552×C131C211yesmaximal, characteristic, complemented
12#533×C131C2211yescharacteristic
13C2×C4⋊Q8×C131C2211yescharacteristic
14C2×C4×D4×C131C2211yescharacteristic
15#494×C131C2212yescomplemented
16#487×C131C2212yescomplemented
17#484×C131—21no—
18#474×C131—21no—
19#474×C131—21no—
20#474×C131C2212yes—
21#474×C131C2212yes—
22#474×C131C2211yescharacteristic
23#474×C131C2211yescharacteristic
24#462×C131—22no—
25#461×C131C2211yescharacteristic
26#461×C131C2211yescharacteristic
27#451×C131—21no—
28#451×C131—21no—
29#450×C131—21no—
30#440×C131—21no—
31#440×C131—21no—
32#436×C131C2212yes—
33#435×C131—22no—
34C8×D4×C131C2212yes—
35#432×C131C2211yescharacteristic
36#432×C131C2211yescharacteristic
37#431×C131C2211yescharacteristic
38C2×#107×C131—21no—
39C2×C4⋊C8×C131C2211yescharacteristic
40C2×#102×C131—21no—
41#407×C131—21no—
42C2×C22⋊C8×C131—21no—
43#335×C131C2212yescomplemented
44#334×C131C2212yescomplemented
45#332×C131C2212yescomplemented
46#332×C131C2212yescomplemented
47#332×C131C2212yescomplemented
48#332×C131C2212yescomplemented
49C22×Q8×C131—21no—
50C22×D4×C131D411yescharacteristic
51C23×C4×C131—21no—
52C2×Q16×C131—22no—
53C2×Q16×C131—22no—
54C2×SD16×C131—21no—
55C2×SD16×C131—21no—
56C2×M16×C131—22no—
57C22×C8×C131—21no—
58C22×C8×C131—22no—
59C4⋊Q8×C131—21no—
60C4⋊Q8×C131—21no—
61C4⋊Q8×C131—21no—
62C4⋊Q8×C131C2311yescharacteristic
63C4⋊Q8×C131C2312yes—
64C4⋊Q8×C131C2311yescharacteristic
65#125×C131—21no—
66C22⋊Q8×C131—21no—
67C22⋊Q8×C131—21no—
68C4×Q8×C131—21no—
69C4×Q8×C131—21no—
70C4×D4×C131—21no—
71C4×D4×C131—21no—
72C4×D4×C131D411yescharacteristic
73C4×D4×C131D411yescharacteristic
74C4×D4×C131C2311yescharacteristic
75C4×D4×C131C2311yescharacteristic
76#117×C131—21no—
77C2×C4⋊C4×C131—21no—
78C2×C4⋊C4×C131—21no—
79C2×C4⋊C4×C131D411yescharacteristic
80C2×C22⋊C4×C131—21no—
81C2×C42×C131C2311yescharacteristic
82#107×C131—22no—
83#107×C131—22no—
84#107×C131—21no—
85#107×C131—21no—
86C4⋊C8×C131—21no—
87C4⋊C8×C131D412yes—
88C4⋊C8×C131C2312yes—
89C4⋊C8×C131C2312yes—
90C4⋊C8×C131C2311yescharacteristic
91C4⋊C8×C131C2311yescharacteristic
92#103×C131—22no—
93#103×C131—22no—
94#103×C131—21no—
95#103×C131—21no—
96#102×C131—22no—
97#102×C131—22no—
98#102×C131—21no—
99#102×C131—21no—
100C22⋊C8×C131—21no—
101C22⋊C8×C131—21no—
102C22⋊C8×C131—22no—
103C22⋊C8×C131—22no—
104C22⋊C8×C131D411yescharacteristic
105C22⋊C8×C131D411yescharacteristic
106#97×C131—21no—
107#97×C131—21no—
108C4×C8×C131C2312yes—
109C24×C131—21no—
110C2×Q8×C131—21no—
111C2×Q8×C131—22no—
112C2×Q8×C131—21no—
113C2×Q8×C131—41no—
114C2×Q8×C131—82no—
115C2×D4×C131—22no—
116C2×D4×C131—21no—
117C2×D4×C131—41no—
118C2×D4×C131C2×D411yescharacteristic
119C2×D4×C131C2×D411yescharacteristic
120C22×C4×C131—21no—
121C22×C4×C131—21no—
122C22×C4×C131—21no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—41no—
126C22×C4×C131—82no—
127C22×C4×C131C2×D411yescharacteristic
128C22×C4×C131C2×D411yescharacteristic
129C22×C4×C131#4111yescharacteristic
130Q16×C131—82no—
131Q16×C131—82no—
132SD16×C131—42no—
133SD16×C131—42no—
134M16×C131—82no—
135C2×C8×C131—22no—
136C2×C8×C131—21no—
137C2×C8×C131—21no—
138C2×C8×C131—22no—
139C2×C8×C131—42no—
140C2×C8×C131—82no—
141C2×C8×C131C2×D412yes—
142C2×C8×C131C2×D412yes—
143C4⋊C4×C131—21no—
144C4⋊C4×C131—22no—
145C4⋊C4×C131—21no—
146C4⋊C4×C131—21no—
147C4⋊C4×C131—22no—
148C4⋊C4×C131—21no—
149C4⋊C4×C131—21no—
150C4⋊C4×C131—41no—
151C4⋊C4×C131—41no—
152C4⋊C4×C131—41no—
153C4⋊C4×C131—41no—
154C4⋊C4×C131C2×D411yescharacteristic
155C4⋊C4×C131C2×D411yescharacteristic
156C22⋊C4×C131—21no—
157C22⋊C4×C131—21no—
158C22⋊C4×C131—21no—
159C22⋊C4×C131—21no—
160C22⋊C4×C131—41no—
161C42×C131—41no—
162C42×C131C2×D411yescharacteristic
163C42×C131C2×D411yescharacteristic
164C42×C131#4111yescharacteristic
165C42×C131C2411yescharacteristic
166C23×C131—21no—
167C23×C131—21no—
168C23×C131—42no—
169C23×C131—42no—
170C23×C131—81no—
171C23×C131#12111yescharacteristic
172Q8×C131—41no—
173Q8×C131—41no—
174Q8×C131—42no—
175Q8×C131—42no—
176Q8×C131—42no—
177Q8×C131—82no—
178D4×C131—21no—
179D4×C131—21no—
180D4×C131—21no—
181D4×C131—42no—
182D4×C131#13712yes—
183C2×C4×C131—22no—
184C2×C4×C131—21no—
185C2×C4×C131—21no—
186C2×C4×C131—22no—
187C2×C4×C131—21no—
188C2×C4×C131—21no—
189C2×C4×C131—42no—
190C2×C4×C131—42no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—42no—
194C2×C4×C131—81no—
195C2×C4×C131—81no—
196C2×C4×C131—81no—
197C2×C4×C131—82no—
198C2×C4×C131#12111yescharacteristic
199C2×C4×C131#12111yescharacteristic
200C2×C4×C131#12111yescharacteristic
201C2×C4×C131C22×D411yescharacteristic
202C2×C4×C131C22×D411yescharacteristic
203C2×C4×C131C2×#4111yescharacteristic
204C8×C131—22no—
205C8×C131—22no—
206C8×C131—41no—
207C8×C131—42no—
208C8×C131—41no—
209C8×C131—42no—
210C22×C131—21no—
211C22×C131—21no—
212C22×C131—22no—
213C22×C131—41no—
214C22×C131—41no—
215C22×C131—41no—
216C22×C131—41no—
217C22×C131—41no—
218C22×C131—84no—
219C22×C131#47312yes—
220C22×C131C2×#12111yescharacteristic
221C4×C131—21no—
222C4×C131—21no—
223C4×C131—21no—
224C4×C131—21no—
225C4×C131—41no—
226C4×C131—41no—
227C4×C131—82no—
228C4×C131—81no—
229C4×C131—81no—
230C4×C131C2×#13711yescharacteristic
231C4×C131#57511yescharacteristic
232C4×C131#57612yes—
233C2×C131—22no—
234C2×C131—42no—
235C2×C131—81no—
236C2×C131#304111yescharacteristic
237C2×C131#305611yescharacteristic
238C2×C131C2×#47311yescharacteristic
239#19459C13111yesmaximal, characteristic, direct product factor, Sylow
240C131#1945911yescharacteristic, direct product factor, Sylow
241#3209C2×C13111yescharacteristic, complemented
242#3110C2×C13111yescharacteristic
243C2×#474C2×C13111yescharacteristic
244#2974C2×C13111yescharacteristic
245#1699C2×C13112yescomplemented
246#1689C2×C13112yescomplemented
247#1679C2×C13112yescomplemented
248#1669C2×C13112yescomplemented
249#1573C2×C13111yescharacteristic, complemented
250#1556C2×C13111yescharacteristic, complemented
251#1552C2×C13111yescharacteristic, complemented
252#533C22×C13111yescharacteristic
253C2×C4⋊Q8C22×C13111yescharacteristic
254C2×C4×D4C22×C13111yescharacteristic
255#494C22×C13112yescomplemented
256#487C22×C13112yescomplemented
257#484—21no—
258#474—21no—
259#474—21no—
260#474C22×C13111yescharacteristic
261#474C22×C13111yescharacteristic
262#474C22×C13112yes—
263#474C22×C13112yes—
264#462—22no—
265#461C22×C13111yescharacteristic
266#461C22×C13111yescharacteristic
267#451—21no—
268#451—21no—
269#450—21no—
270#440—21no—
271#440—21no—
272#436C22×C13112yes—
273#435—22no—
274C8×D4C22×C13112yes—
275#432C22×C13111yescharacteristic
276#432C22×C13111yescharacteristic
277#431C22×C13111yescharacteristic
278C2×#107—21no—
279C2×C4⋊C8C22×C13111yescharacteristic
280C2×#102—21no—
281#407—21no—
282C2×C22⋊C8—21no—
283#335C22×C13112yescomplemented
284#334C22×C13112yescomplemented
285#332C22×C13112yescomplemented
286#332C22×C13112yescomplemented
287#332C22×C13112yescomplemented
288#332C22×C13112yescomplemented
289C22×Q8—21no—
290C22×D4D4×C13111yescharacteristic
291C23×C4—21no—
292C2×Q16—22no—
293C2×Q16—22no—
294C2×SD16—21no—
295C2×SD16—21no—
296C2×M16—22no—
297C22×C8—21no—
298C22×C8—22no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8C23×C13112yes—
303C4⋊Q8C23×C13111yescharacteristic
304C4⋊Q8C23×C13111yescharacteristic
305#125—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4D4×C13111yescharacteristic
313C4×D4D4×C13111yescharacteristic
314C4×D4C23×C13111yescharacteristic
315C4×D4C23×C13111yescharacteristic
316#117—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C13111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C42C23×C13111yescharacteristic
322#107—22no—
323#107—22no—
324#107—21no—
325#107—21no—
326C4⋊C8—21no—
327C4⋊C8D4×C13112yes—
328C4⋊C8C23×C13112yes—
329C4⋊C8C23×C13111yescharacteristic
330C4⋊C8C23×C13112yes—
331C4⋊C8C23×C13111yescharacteristic
332#103—22no—
333#103—22no—
334#103—21no—
335#103—21no—
336#102—22no—
337#102—22no—
338#102—21no—
339#102—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—22no—
343C22⋊C8—22no—
344C22⋊C8D4×C13111yescharacteristic
345C22⋊C8D4×C13111yescharacteristic
346#97—21no—
347#97—21no—
348C4×C8C23×C13112yes—
349C24—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4C2×D4×C13111yescharacteristic
359C2×D4C2×D4×C13111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—82no—
367C22×C4C2×D4×C13111yescharacteristic
368C22×C4C2×D4×C13111yescharacteristic
369C22×C4#41×C13111yescharacteristic
370Q16—82no—
371Q16—82no—
372SD16—42no—
373SD16—42no—
374M16—82no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8—82no—
381C2×C8C2×D4×C13112yes—
382C2×C8C2×D4×C13112yes—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C13111yescharacteristic
395C4⋊C4C2×D4×C13111yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—41no—
401C42—41no—
402C42C2×D4×C13111yescharacteristic
403C42C2×D4×C13111yescharacteristic
404C42#41×C13111yescharacteristic
405C42C24×C13111yescharacteristic
406C23—21no—
407C23—21no—
408C23—42no—
409C23—42no—
410C23—81no—
411C23#121×C13111yescharacteristic
412Q8—41no—
413Q8—41no—
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—82no—
418D4—21no—
419D4—21no—
420D4—21no—
421D4—42no—
422D4#137×C13112yes—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4#121×C13111yescharacteristic
439C2×C4#121×C13111yescharacteristic
440C2×C4#121×C13111yescharacteristic
441C2×C4C22×D4×C13111yescharacteristic
442C2×C4C22×D4×C13111yescharacteristic
443C2×C4C2×#41×C13111yescharacteristic
444C8—22no—
445C8—22no—
446C8—41no—
447C8—42no—
448C8—41no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—84no—
459C22#473×C13112yes—
460C22C2×#121×C13111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—82no—
468C4—81no—
469C4—81no—
470C4C2×#137×C13111yescharacteristic
471C4#575×C13111yescharacteristic
472C4#576×C13112yes—
473C2—22no—
474C2—42no—
475C2—81no—
476C2#3041×C13111yescharacteristic
477C2#3056×C13111yescharacteristic
478C2C2×#473×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC42C24×C131
prime radicalC22×D4×C131D4
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
1. #3209×C131C2semidirect
5. #1699×C131C2semidirect
6. #1689×C131C2semidirect
7. #1679×C131C2semidirect
8. #1669×C131C2semidirect
9. #1573×C131C2semidirect
10. #1556×C131C2semidirect
11. #1552×C131C2semidirect
15. #494×C131C22semidirect
16. #487×C131C22semidirect
43. #335×C131C22semidirect
44. #334×C131C22semidirect
45. #332×C131C22semidirect
46. #332×C131C22semidirect
47. #332×C131C22semidirect
48. #332×C131C22semidirect
239. #19459C131direct (N × H)
240. C131#19459direct (N × H)
241. #3209C2×C131semidirect
245. #1699C2×C131semidirect
246. #1689C2×C131semidirect
247. #1679C2×C131semidirect
248. #1669C2×C131semidirect
249. #1573C2×C131semidirect
250. #1556C2×C131semidirect
251. #1552C2×C131semidirect
255. #494C22×C131semidirect
256. #487C22×C131semidirect
283. #335C22×C131semidirect
284. #334C22×C131semidirect
285. #332C22×C131semidirect
286. #332C22×C131semidirect
287. #332C22×C131semidirect
288. #332C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3209×C1312
#3110×C1312
C2×#474×C1312
#2974×C1312
#1699×C1312
#1689×C1312
#1679×C1312
#1669×C1312
#1573×C1312
#1556×C1312
#1552×C1312
#19459131