Finite Group Databasebeta

← C131×#29852 #45715736

Subgroups — C131×#29852 #45715736

Order 33536.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#491×C131C211yesmaximal, characteristic, complemented
2C2×#432×C131C211yesmaximal, characteristic
3#2857×C131C211yesmaximal, characteristic
4#2851×C131C211yesmaximal, characteristic
5#2068×C131C212yesmaximal, complemented
6#2066×C131C212yesmaximal, complemented
7#2036×C131C212yesmaximal
8#2035×C131C212yesmaximal
9#1992×C131C211yesmaximal, characteristic, complemented
10#1960×C131C211yesmaximal, characteristic, complemented
11#1847×C131C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C131C2211yescharacteristic
13C2×#125×C131C2211yescharacteristic
14C2×C22⋊Q8×C131C2212yes—
15C22×C42×C131C2211yescharacteristic
16#491×C131—24no—
17#432×C131—24no—
18C2×#107×C131C2212yes—
19C2×#106×C131C2212yes—
20C2×C4⋊C8×C131C2212yes—
21C2×#103×C131C2212yes—
22C2×#103×C131C2212yes—
23C2×#103×C131C2212yes—
24C2×#103×C131C2212yes—
25C2×C22⋊C8×C131C2212yes—
26C2×#97×C131C2211yescharacteristic
27C2×#97×C131C2211yescharacteristic
28#391×C131C2212yes—
29#389×C131—21no—
30#389×C131—21no—
31#389×C131C2211yescharacteristic
32#389×C131C2211yescharacteristic
33#387×C131—21no—
34#387×C131—21no—
35#385×C131—21no—
36#385×C131—21no—
37#384×C131C2211yescharacteristic
38#382×C131C2211yescharacteristic
39#380×C131—21no—
40#380×C131—21no—
41#380×C131C2211yescharacteristic
42#380×C131C2211yescharacteristic
43#340×C131C2212yes—
44#340×C131C2212yes—
45C22×Q8×C131C2312yes—
46C23×C4×C131D411yescharacteristic
47C23×C4×C131D411yescharacteristic
48C23×C4×C131C2311yescharacteristic
49C22×C8×C131C2312yes—
50C22×C8×C131C2312yes—
51C4⋊Q8×C131—22no—
52C4⋊Q8×C131—22no—
53#125×C131—22no—
54#125×C131—22no—
55C22⋊Q8×C131—42no—
56C22⋊Q8×C131—42no—
57C2×C4⋊C4×C131—22no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131—21no—
60C2×C4⋊C4×C131—21no—
61C2×C4⋊C4×C131—21no—
62C2×C4⋊C4×C131—21no—
63C2×C4⋊C4×C131—21no—
64C2×C4⋊C4×C131—21no—
65C2×C4⋊C4×C131—21no—
66C2×C4⋊C4×C131C2311yescharacteristic
67C2×C4⋊C4×C131C2311yescharacteristic
68C2×C4⋊C4×C131C2311yescharacteristic
69C2×C4⋊C4×C131C2311yescharacteristic
70C2×C4⋊C4×C131C2312yes—
71C2×C22⋊C4×C131—22no—
72C2×C22⋊C4×C131—21no—
73C2×C22⋊C4×C131—21no—
74C2×C42×C131—22no—
75C2×C42×C131—22no—
76C2×C42×C131D411yescharacteristic
77C2×C42×C131D411yescharacteristic
78C2×C42×C131C2311yescharacteristic
79C2×C42×C131C2311yescharacteristic
80#107×C131—42no—
81#106×C131—42no—
82C4⋊C8×C131—24no—
83#103×C131—24no—
84#103×C131—24no—
85#103×C131—42no—
86#103×C131—42no—
87C22⋊C8×C131—24no—
88#97×C131—22no—
89#97×C131D414yes—
90#95×C131—22no—
91#95×C131—22no—
92#95×C131—21no—
93#95×C131—21no—
94#95×C131—21no—
95#95×C131—21no—
96#95×C131—21no—
97#95×C131—21no—
98C24×C131C2×D411yescharacteristic
99C2×Q8×C131—22no—
100C2×Q8×C131—22no—
101C2×Q8×C131—22no—
102C2×Q8×C131—22no—
103C2×Q8×C131—22no—
104C2×Q8×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—22no—
107C22×C4×C131—22no—
108C22×C4×C131—22no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—21no—
114C22×C4×C131—21no—
115C22×C4×C131—21no—
116C22×C4×C131—21no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—41no—
120C22×C4×C131—41no—
121C22×C4×C131C2×D411yescharacteristic
122C22×C4×C131C2×D411yescharacteristic
123C22×C4×C131C2×D411yescharacteristic
124C22×C4×C131C2×D411yescharacteristic
125C22×C4×C131C2×D411yescharacteristic
126C22×C4×C131C2411yescharacteristic
127C2×C8×C131—22no—
128C2×C8×C131—22no—
129C2×C8×C131—22no—
130C2×C8×C131—22no—
131C2×C8×C131—22no—
132C2×C8×C131C2×D414yes—
133C4⋊C4×C131—21no—
134C4⋊C4×C131—21no—
135C4⋊C4×C131—21no—
136C4⋊C4×C131—21no—
137C4⋊C4×C131—22no—
138C4⋊C4×C131—22no—
139C4⋊C4×C131—22no—
140C4⋊C4×C131—22no—
141C4⋊C4×C131—42no—
142C4⋊C4×C131—42no—
143C4⋊C4×C131—42no—
144C4⋊C4×C131—44no—
145C4⋊C4×C131—42no—
146C4⋊C4×C131—42no—
147C4⋊C4×C131—42no—
148C4⋊C4×C131—42no—
149C4⋊C4×C131—42no—
150C22⋊C4×C131—42no—
151C22⋊C4×C131—44no—
152C22⋊C4×C131—42no—
153C42×C131—22no—
154C42×C131—22no—
155C42×C131—21no—
156C42×C131—21no—
157C42×C131C2×D412yes—
158C42×C131#4112yes—
159C23×C131—21no—
160C23×C131—21no—
161C23×C131—21no—
162C23×C131—21no—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131#13712yes—
166C23×C131C22×D411yescharacteristic
167Q8×C131—42no—
168Q8×C131—42no—
169Q8×C131—42no—
170Q8×C131—42no—
171C2×C4×C131—21no—
172C2×C4×C131—21no—
173C2×C4×C131—21no—
174C2×C4×C131—21no—
175C2×C4×C131—21no—
176C2×C4×C131—21no—
177C2×C4×C131—21no—
178C2×C4×C131—21no—
179C2×C4×C131—21no—
180C2×C4×C131—21no—
181C2×C4×C131—21no—
182C2×C4×C131—21no—
183C2×C4×C131—44no—
184C2×C4×C131—44no—
185C2×C4×C131—42no—
186C2×C4×C131—42no—
187C2×C4×C131—41no—
188C2×C4×C131—41no—
189C2×C4×C131—42no—
190C2×C4×C131—42no—
191C2×C4×C131—42no—
192C2×C4×C131—41no—
193C2×C4×C131—41no—
194C2×C4×C131—42no—
195C2×C4×C131—41no—
196C2×C4×C131—41no—
197C2×C4×C131—41no—
198C2×C4×C131—41no—
199C2×C4×C131—41no—
200C2×C4×C131—41no—
201C2×C4×C131—42no—
202C2×C4×C131—41no—
203C2×C4×C131—42no—
204C2×C4×C131—41no—
205C2×C4×C131#12112yes—
206C2×C4×C131#12112yes—
207C2×C4×C131#13712yes—
208C2×C4×C131C22×D411yescharacteristic
209C2×C4×C131C2×#4111yescharacteristic
210C2×C4×C131H(5,𝔽2)12yes—
211C2×C4×C1312−1+412yes—
212C8×C131—24no—
213C8×C131—42no—
214C22×C131—22no—
215C22×C131—22no—
216C22×C131—22no—
217C22×C131—41no—
218C22×C131—41no—
219C22×C131—41no—
220C22×C131—41no—
221C22×C131C2×#12111yescharacteristic
222C22×C131#53511yescharacteristic
223C22×C131#53611yescharacteristic
224C22×C131C2×#13711yescharacteristic
225C22×C131C2×#13711yescharacteristic
226C22×C131#57511yescharacteristic
227C22×C131#57511yescharacteristic
228C4×C131—22no—
229C4×C131—22no—
230C4×C131—22no—
231C4×C131—41no—
232C4×C131—41no—
233C4×C131—82no—
234C4×C131—81no—
235C4×C131—82no—
236C4×C131—81no—
237C4×C131—81no—
238C4×C131—81no—
239C4×C131#53712yes—
240C4×C131#54212yes—
241C2×C131—42no—
242C2×C131#262011yescharacteristic
243C2×C131#305611yescharacteristic
244C2×C131#305611yescharacteristic
245C2×C131#321811yescharacteristic
246C2×C131#321911yescharacteristic
247C2×C131#323611yescharacteristic
248C2×C131#323711yescharacteristic
249#29852C13111yesmaximal, characteristic, direct product factor, Sylow
250C131#2985211yescharacteristic, direct product factor, Sylow
251C2×#491C2×C13111yescharacteristic, complemented
252C2×#432C2×C13111yescharacteristic
253#2857C2×C13111yescharacteristic
254#2851C2×C13111yescharacteristic
255#2068C2×C13112yescomplemented
256#2066C2×C13112yescomplemented
257#2036C2×C13112yes—
258#2035C2×C13112yes—
259#1992C2×C13111yescharacteristic, complemented
260#1960C2×C13111yescharacteristic, complemented
261#1847C2×C13111yescharacteristic, complemented
262C2×C4⋊Q8C22×C13111yescharacteristic
263C2×#125C22×C13111yescharacteristic
264C2×C22⋊Q8C22×C13112yes—
265C22×C42C22×C13111yescharacteristic
266#491—24no—
267#432—24no—
268C2×#107C22×C13112yes—
269C2×#106C22×C13112yes—
270C2×C4⋊C8C22×C13112yes—
271C2×#103C22×C13112yes—
272C2×#103C22×C13112yes—
273C2×#103C22×C13112yes—
274C2×#103C22×C13112yes—
275C2×C22⋊C8C22×C13112yes—
276C2×#97C22×C13111yescharacteristic
277C2×#97C22×C13111yescharacteristic
278#391C22×C13112yes—
279#389—21no—
280#389—21no—
281#389C22×C13111yescharacteristic
282#389C22×C13111yescharacteristic
283#387—21no—
284#387—21no—
285#385—21no—
286#385—21no—
287#384C22×C13111yescharacteristic
288#382C22×C13111yescharacteristic
289#380—21no—
290#380—21no—
291#380C22×C13111yescharacteristic
292#380C22×C13111yescharacteristic
293#340C22×C13112yes—
294#340C22×C13112yes—
295C22×Q8C23×C13112yes—
296C23×C4D4×C13111yescharacteristic
297C23×C4D4×C13111yescharacteristic
298C23×C4C23×C13111yescharacteristic
299C22×C8C23×C13112yes—
300C22×C8C23×C13112yes—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303#125—22no—
304#125—22no—
305C22⋊Q8—42no—
306C22⋊Q8—42no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4C23×C13112yes—
317C2×C4⋊C4C23×C13111yescharacteristic
318C2×C4⋊C4C23×C13111yescharacteristic
319C2×C4⋊C4C23×C13111yescharacteristic
320C2×C4⋊C4C23×C13111yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42D4×C13111yescharacteristic
327C2×C42D4×C13111yescharacteristic
328C2×C42C23×C13111yescharacteristic
329C2×C42C23×C13111yescharacteristic
330#107—42no—
331#106—42no—
332C4⋊C8—24no—
333#103—24no—
334#103—24no—
335#103—42no—
336#103—42no—
337C22⋊C8—24no—
338#97—22no—
339#97D4×C13114yes—
340#95—22no—
341#95—22no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348C24C2×D4×C13111yescharacteristic
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4C2×D4×C13111yescharacteristic
372C22×C4C2×D4×C13111yescharacteristic
373C22×C4C2×D4×C13111yescharacteristic
374C22×C4C2×D4×C13111yescharacteristic
375C22×C4C2×D4×C13111yescharacteristic
376C22×C4C24×C13111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8C2×D4×C13114yes—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—42no—
400C22⋊C4—42no—
401C22⋊C4—44no—
402C22⋊C4—42no—
403C42—22no—
404C42—22no—
405C42—21no—
406C42—21no—
407C42C2×D4×C13112yes—
408C42#41×C13112yes—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23#137×C13112yes—
416C23C22×D4×C13111yescharacteristic
417Q8—42no—
418Q8—42no—
419Q8—42no—
420Q8—42no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4#121×C13112yes—
456C2×C4#121×C13112yes—
457C2×C4#137×C13112yes—
458C2×C4C22×D4×C13111yescharacteristic
459C2×C4C2×#41×C13111yescharacteristic
460C2×C4H(5,𝔽2)×C13112yes—
461C2×C42−1+4×C13112yes—
462C8—24no—
463C8—42no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22C2×#121×C13111yescharacteristic
472C22#535×C13111yescharacteristic
473C22#536×C13111yescharacteristic
474C22C2×#137×C13111yescharacteristic
475C22C2×#137×C13111yescharacteristic
476C22#575×C13111yescharacteristic
477C22#575×C13111yescharacteristic
478C4—22no—
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—81no—
484C4—81no—
485C4—82no—
486C4—81no—
487C4—82no—
488C4—81no—
489C4#537×C13112yes—
490C4#542×C13112yes—
491C2—42no—
492C2#2620×C13111yescharacteristic
493C2#3056×C13111yescharacteristic
494C2#3056×C13111yescharacteristic
495C2#3218×C13111yescharacteristic
496C2#3219×C13111yescharacteristic
497C2#3236×C13111yescharacteristic
498C2#3237×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#491×C131C2semidirect
5. #2068×C131C2semidirect
6. #2066×C131C2semidirect
9. #1992×C131C2semidirect
10. #1960×C131C2semidirect
11. #1847×C131C2semidirect
249. #29852C131direct (N × H)
250. C131#29852direct (N × H)
251. C2×#491C2×C131semidirect
255. #2068C2×C131semidirect
256. #2066C2×C131semidirect
259. #1992C2×C131semidirect
260. #1960C2×C131semidirect
261. #1847C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#491×C1312
C2×#432×C1312
#2857×C1312
#2851×C1312
#2068×C1312
#2066×C1312
#2036×C1312
#2035×C1312
#1992×C1312
#1960×C1312
#1847×C1312
#29852131