Finite Group Databasebeta

← C131×#29927 #45715811

Subgroups — C131×#29927 #45715811

Order 33536.

798 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C131C211yesmaximal, characteristic
2#2285×C131C211yesmaximal, characteristic, complemented
3#2096×C131C211yesmaximal, characteristic, complemented
4#2093×C131C211yesmaximal, characteristic, complemented
5#2072×C131C211yesmaximal, characteristic, complemented
6#2071×C131C211yesmaximal, characteristic, complemented
7#2036×C131C212yesmaximal, complemented
8#2034×C131C212yesmaximal
9#1983×C131C212yesmaximal, complemented
10#1949×C131C212yesmaximal, complemented
11#1797×C131C211yesmaximal, characteristic, complemented
12C2×#124×C131C2211yescharacteristic
13C2×C22⋊Q8×C131C2211yescharacteristic
14C2×#121×C131C2211yescharacteristic
15C2×#117×C131—21no—
16C22×C42×C131C2211yescharacteristic
17C2×#107×C131C2212yes—
18C2×#106×C131C2212yes—
19C2×C4⋊C8×C131C2212yes—
20C2×#103×C131C2212yes—
21C2×#103×C131C2212yes—
22C2×#102×C131C2212yes—
23C2×#102×C131C2212yes—
24C2×C22⋊C8×C131C2212yes—
25#391×C131C2211yescharacteristic
26#390×C131C2211yescharacteristic
27#388×C131—21no—
28#388×C131—21no—
29#386×C131—21no—
30#386×C131—21no—
31#384×C131C2211yescharacteristic
32#384×C131C2211yescharacteristic
33#382×C131—21no—
34#382×C131C2211yescharacteristic
35#380×C131—21no—
36#380×C131C2212yes—
37C4×C4⋊C4×C131—21no—
38C4×C4⋊C4×C131C2212yes—
39#340×C131C2212yes—
40#340×C131C2212yes—
41#336×C131C2211yescharacteristic
42#336×C131C2211yescharacteristic
43C22×Q8×C131C2311yescharacteristic
44C22×D4×C131—21no—
45C22×D4×C131C2311yescharacteristic
46C23×C4×C131D411yescharacteristic
47C23×C4×C131D411yescharacteristic
48C23×C4×C131C2311yescharacteristic
49C22×C8×C131C2312yes—
50C22×C8×C131C2312yes—
51#124×C131—24no—
52C22⋊Q8×C131—42no—
53#121×C131—42no—
54#117×C131—44no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131—21no—
60C2×C4⋊C4×C131C2311yescharacteristic
61C2×C4⋊C4×C131C2311yescharacteristic
62C2×C4⋊C4×C131C2312yes—
63C2×C4⋊C4×C131C2312yes—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—21no—
67C2×C22⋊C4×C131—21no—
68C2×C22⋊C4×C131—21no—
69C2×C22⋊C4×C131—21no—
70C2×C22⋊C4×C131—21no—
71C2×C42×C131—24no—
72C2×C42×C131—22no—
73C2×C42×C131D411yescharacteristic
74C2×C42×C131D411yescharacteristic
75C2×C42×C131C2311yescharacteristic
76C2×C42×C131C2311yescharacteristic
77#107×C131—42no—
78#106×C131—42no—
79C4⋊C8×C131—24no—
80#103×C131—42no—
81#103×C131—42no—
82#102×C131—42no—
83#102×C131—42no—
84C22⋊C8×C131—42no—
85#95×C131—21no—
86#95×C131—21no—
87#95×C131—21no—
88#95×C131—21no—
89#95×C131—22no—
90#95×C131—22no—
91C24×C131—21no—
92C24×C131C2×D411yescharacteristic
93C2×Q8×C131—22no—
94C2×Q8×C131—21no—
95C2×Q8×C131—22no—
96C2×Q8×C131—21no—
97C2×D4×C131—22no—
98C2×D4×C131—21no—
99C2×D4×C131—22no—
100C2×D4×C131—21no—
101C2×D4×C131—42no—
102C2×D4×C131—42no—
103C2×D4×C131—42no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—22no—
107C22×C4×C131—22no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—21no—
111C22×C4×C131—22no—
112C22×C4×C131—21no—
113C22×C4×C131—21no—
114C22×C4×C131—22no—
115C22×C4×C131—22no—
116C22×C4×C131—21no—
117C22×C4×C131—21no—
118C22×C4×C131—41no—
119C22×C4×C131C2×D411yescharacteristic
120C22×C4×C131C2×D411yescharacteristic
121C22×C4×C131C2×D411yescharacteristic
122C22×C4×C131C2×D411yescharacteristic
123C22×C4×C131C2×D411yescharacteristic
124C22×C4×C131C2411yescharacteristic
125C2×C8×C131—22no—
126C2×C8×C131—22no—
127C2×C8×C131—22no—
128C2×C8×C131—22no—
129C2×C8×C131—22no—
130C2×C8×C131—22no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—22no—
134C4⋊C4×C131—22no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—22no—
137C4⋊C4×C131—42no—
138C4⋊C4×C131—42no—
139C4⋊C4×C131—42no—
140C4⋊C4×C131—42no—
141C4⋊C4×C131—42no—
142C22⋊C4×C131—42no—
143C22⋊C4×C131—44no—
144C22⋊C4×C131—42no—
145C22⋊C4×C131—42no—
146C22⋊C4×C131—42no—
147C22⋊C4×C131—42no—
148C22⋊C4×C131—42no—
149C42×C131—22no—
150C42×C131—22no—
151C42×C131—22no—
152C42×C131—44no—
153C42×C131#4114yes—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—21no—
157C23×C131—21no—
158C23×C131—21no—
159C23×C131—21no—
160C23×C131—41no—
161C23×C131—41no—
162C23×C131—41no—
163C23×C131—41no—
164C23×C131—41no—
165C23×C131—41no—
166C23×C131—41no—
167C23×C131#13712yes—
168C23×C131C22×D411yescharacteristic
169Q8×C131—42no—
170Q8×C131—42no—
171D4×C131—42no—
172D4×C131—42no—
173D4×C131—84no—
174C2×C4×C131—28no—
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—21no—
184C2×C4×C131—21no—
185C2×C4×C131—21no—
186C2×C4×C131—44no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—41no—
190C2×C4×C131—41no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—42no—
194C2×C4×C131—42no—
195C2×C4×C131—41no—
196C2×C4×C131—41no—
197C2×C4×C131—42no—
198C2×C4×C131—42no—
199C2×C4×C131—42no—
200C2×C4×C131—41no—
201C2×C4×C131—41no—
202C2×C4×C131—42no—
203C2×C4×C131—41no—
204C2×C4×C131#12312yes—
205C2×C4×C131#12312yes—
206C2×C4×C131#13512yes—
207C2×C4×C131AGL(1,ℤ/8)12yes—
208C2×C4×C131C2×#4112yes—
209C2×C4×C131H(5,𝔽2)11yescharacteristic
210C2×C4×C131H(5,𝔽2)12yes—
211C2×C4×C1312−1+411yescharacteristic
212C8×C131—42no—
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×C131—81no—
222C22×C131—81no—
223C22×C131—81no—
224C22×C131—81no—
225C22×C131—81no—
226C22×C131—81no—
227C22×C131—81no—
228C22×C131C2×#12311yescharacteristic
229C22×C131#53511yescharacteristic
230C22×C131#53711yescharacteristic
231C22×C131C2×#13511yescharacteristic
232C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
233C22×C131C2×#13711yescharacteristic
234C22×C131#57511yescharacteristic
235C4×C131—22no—
236C4×C131—22no—
237C4×C131—22no—
238C4×C131—22no—
239C4×C131—41no—
240C4×C131—81no—
241C4×C131—81no—
242C4×C131—82no—
243C4×C131—81no—
244C4×C131—82no—
245C4×C131#54012yes—
246C4×C131#54212yes—
247C2×C131—42no—
248C2×C131—161no—
249C2×C131#262411yescharacteristic
250C2×C131#309111yescharacteristic
251C2×C131#309211yescharacteristic
252C2×C131#320711yescharacteristic
253C2×C131#321511yescharacteristic
254C2×C131#324811yescharacteristic
255C2×C131#325111yescharacteristic
256#29927C13111yesmaximal, characteristic, direct product factor, Sylow
257C131#2992711yescharacteristic, direct product factor, Sylow
258#2850C2×C13111yescharacteristic
259#2285C2×C13111yescharacteristic, complemented
260#2096C2×C13111yescharacteristic, complemented
261#2093C2×C13111yescharacteristic, complemented
262#2072C2×C13111yescharacteristic, complemented
263#2071C2×C13111yescharacteristic, complemented
264#2036C2×C13112yescomplemented
265#2034C2×C13112yes—
266#1983C2×C13112yescomplemented
267#1949C2×C13112yescomplemented
268#1797C2×C13111yescharacteristic, complemented
269C2×#124C22×C13111yescharacteristic
270C2×C22⋊Q8C22×C13111yescharacteristic
271C2×#121C22×C13111yescharacteristic
272C2×#117—21no—
273C22×C42C22×C13111yescharacteristic
274C2×#107C22×C13112yes—
275C2×#106C22×C13112yes—
276C2×C4⋊C8C22×C13112yes—
277C2×#103C22×C13112yes—
278C2×#103C22×C13112yes—
279C2×#102C22×C13112yes—
280C2×#102C22×C13112yes—
281C2×C22⋊C8C22×C13112yes—
282#391C22×C13111yescharacteristic
283#390C22×C13111yescharacteristic
284#388—21no—
285#388—21no—
286#386—21no—
287#386—21no—
288#384C22×C13111yescharacteristic
289#384C22×C13111yescharacteristic
290#382—21no—
291#382C22×C13111yescharacteristic
292#380—21no—
293#380C22×C13112yes—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C22×C13112yes—
296#340C22×C13112yes—
297#340C22×C13112yes—
298#336C22×C13111yescharacteristic
299#336C22×C13111yescharacteristic
300C22×Q8C23×C13111yescharacteristic
301C22×D4—21no—
302C22×D4C23×C13111yescharacteristic
303C23×C4D4×C13111yescharacteristic
304C23×C4D4×C13111yescharacteristic
305C23×C4C23×C13111yescharacteristic
306C22×C8C23×C13112yes—
307C22×C8C23×C13112yes—
308#124—24no—
309C22⋊Q8—42no—
310#121—42no—
311#117—44no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4C23×C13111yescharacteristic
318C2×C4⋊C4C23×C13111yescharacteristic
319C2×C4⋊C4C23×C13112yes—
320C2×C4⋊C4C23×C13112yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—24no—
329C2×C42—22no—
330C2×C42D4×C13111yescharacteristic
331C2×C42D4×C13111yescharacteristic
332C2×C42C23×C13111yescharacteristic
333C2×C42C23×C13111yescharacteristic
334#107—42no—
335#106—42no—
336C4⋊C8—24no—
337#103—42no—
338#103—42no—
339#102—42no—
340#102—42no—
341C22⋊C8—42no—
342#95—22no—
343#95—22no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348C24—21no—
349C24C2×D4×C13111yescharacteristic
350C2×Q8—22no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—21no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4C2×D4×C13111yescharacteristic
377C22×C4C2×D4×C13111yescharacteristic
378C22×C4C2×D4×C13111yescharacteristic
379C22×C4C2×D4×C13111yescharacteristic
380C22×C4C2×D4×C13111yescharacteristic
381C22×C4C24×C13111yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C22⋊C4—42no—
400C22⋊C4—44no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C22⋊C4—42no—
404C22⋊C4—42no—
405C22⋊C4—42no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—44no—
410C42#41×C13114yes—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23#137×C13112yes—
425C23C22×D4×C13111yescharacteristic
426Q8—42no—
427Q8—42no—
428D4—42no—
429D4—42no—
430D4—84no—
431C2×C4—28no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4#123×C13112yes—
462C2×C4#123×C13112yes—
463C2×C4#135×C13112yes—
464C2×C4AGL(1,ℤ/8)×C13112yes—
465C2×C4C2×#41×C13112yes—
466C2×C4H(5,𝔽2)×C13111yescharacteristic
467C2×C4H(5,𝔽2)×C13112yes—
468C2×C42−1+4×C13111yescharacteristic
469C8—42no—
470C8—42no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22C2×#123×C13111yescharacteristic
486C22#535×C13111yescharacteristic
487C22#537×C13111yescharacteristic
488C22C2×#135×C13111yescharacteristic
489C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
490C22C2×#137×C13111yescharacteristic
491C22#575×C13111yescharacteristic
492C4—22no—
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—82no—
498C4—81no—
499C4—81no—
500C4—82no—
501C4—81no—
502C4#540×C13112yes—
503C4#542×C13112yes—
504C2—42no—
505C2—161no—
506C2#2624×C13111yescharacteristic
507C2#3091×C13111yescharacteristic
508C2#3092×C13111yescharacteristic
509C2#3207×C13111yescharacteristic
510C2#3215×C13111yescharacteristic
511C2#3248×C13111yescharacteristic
512C2#3251×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
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
2. #2285×C131C2semidirect
3. #2096×C131C2semidirect
4. #2093×C131C2semidirect
5. #2072×C131C2semidirect
6. #2071×C131C2semidirect
7. #2036×C131C2semidirect
9. #1983×C131C2semidirect
10. #1949×C131C2semidirect
11. #1797×C131C2semidirect
256. #29927C131direct (N × H)
257. C131#29927direct (N × H)
259. #2285C2×C131semidirect
260. #2096C2×C131semidirect
261. #2093C2×C131semidirect
262. #2072C2×C131semidirect
263. #2071C2×C131semidirect
264. #2036C2×C131semidirect
266. #1983C2×C131semidirect
267. #1949C2×C131semidirect
268. #1797C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2850×C1312
#2285×C1312
#2096×C1312
#2093×C1312
#2072×C1312
#2071×C1312
#2036×C1312
#2034×C1312
#1983×C1312
#1949×C1312
#1797×C1312
#29927131