Finite Group Databasebeta

← C131×#29912 #45715796

Subgroups — C131×#29912 #45715796

Order 33536.

796 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C131C211yesmaximal, characteristic
2C2×#382×C131C211yesmaximal, characteristic, complemented
3#2101×C131C212yesmaximal, complemented
4#2092×C131C212yesmaximal, complemented
5#2085×C131C212yesmaximal, complemented
6#2073×C131C212yesmaximal, complemented
7#1874×C131C211yesmaximal, characteristic
8#1874×C131C211yesmaximal, characteristic
9#1853×C131C211yesmaximal, characteristic, complemented
10#1852×C131C211yesmaximal, characteristic, complemented
11#1817×C131C211yesmaximal, characteristic, complemented
12C2×#123×C131—21no—
13C2×#121×C131C2211yescharacteristic
14C22×C4⋊C4×C131C2211yescharacteristic
15C22×C4⋊C4×C131C2211yescharacteristic
16C22×C42×C131C2211yescharacteristic
17C2×#107×C131C2212yes—
18C2×#106×C131C2212yes—
19C2×#102×C131C2212yes—
20C2×#102×C131C2212yes—
21C2×C22⋊C8×C131C2211yescharacteristic
22C2×C22⋊C8×C131C2211yescharacteristic
23#390×C131C2211yescharacteristic
24#390×C131C2211yescharacteristic
25#389×C131C2211yescharacteristic
26#389×C131C2211yescharacteristic
27#388×C131—21no—
28#388×C131—21no—
29#386×C131—21no—
30#382×C131—21no—
31#382×C131—21no—
32#382×C131C2212yes—
33#382×C131C2212yes—
34#380×C131C2211yescharacteristic
35C2×#95×C131—21no—
36C2×#95×C131—21no—
37#340×C131C2212yes—
38#340×C131C2212yes—
39#340×C131C2212yes—
40#340×C131C2212yes—
41#336×C131C2212yes—
42#336×C131C2212yes—
43C22×D4×C131—21no—
44C22×D4×C131C2311yescharacteristic
45C23×C4×C131—21no—
46C23×C4×C131—21no—
47C23×C4×C131D411yescharacteristic
48C23×C4×C131D411yescharacteristic
49C23×C4×C131C2311yescharacteristic
50C22×C8×C131C2312yes—
51C22×C8×C131C2312yes—
52#123×C131—44no—
53#121×C131—22no—
54#121×C131—22no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131—42no—
60C2×C4⋊C4×C131—42no—
61C2×C4⋊C4×C131C2311yescharacteristic
62C2×C4⋊C4×C131C2311yescharacteristic
63C2×C4⋊C4×C131C2311yescharacteristic
64C2×C4⋊C4×C131C2312yes—
65C2×C4⋊C4×C131C2312yes—
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×C22⋊C4×C131—21no—
72C2×C42×C131—22no—
73C2×C42×C131—22no—
74C2×C42×C131D411yescharacteristic
75C2×C42×C131D411yescharacteristic
76C2×C42×C131C2311yescharacteristic
77C2×C42×C131C2311yescharacteristic
78#107×C131—42no—
79#106×C131—42no—
80#102×C131—42no—
81#102×C131—42no—
82C22⋊C8×C131—22no—
83C22⋊C8×C131—22no—
84#95×C131—21no—
85#95×C131—21no—
86#95×C131—21no—
87#95×C131—22no—
88#95×C131—22no—
89#95×C131—22no—
90#95×C131—22no—
91C24×C131—21no—
92C24×C131C2×D411yescharacteristic
93C2×D4×C131—21no—
94C2×D4×C131—21no—
95C2×D4×C131—22no—
96C2×D4×C131—22no—
97C2×D4×C131—42no—
98C2×D4×C131—42no—
99C2×D4×C131—42no—
100C22×C4×C131—22no—
101C22×C4×C131—22no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—22no—
107C22×C4×C131—22no—
108C22×C4×C131—21no—
109C22×C4×C131—21no—
110C22×C4×C131—21no—
111C22×C4×C131—41no—
112C22×C4×C131—41no—
113C22×C4×C131—42no—
114C22×C4×C131—42no—
115C22×C4×C131—42no—
116C22×C4×C131—42no—
117C22×C4×C131—42no—
118C22×C4×C131—42no—
119C22×C4×C131C2×D411yescharacteristic
120C22×C4×C131C2×D411yescharacteristic
121C22×C4×C131C2×D411yescharacteristic
122C22×C4×C131C2×D411yescharacteristic
123C22×C4×C131C2×D411yescharacteristic
124C22×C4×C131#4112yes—
125C22×C4×C131#4112yes—
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×C131—22no—
133C4⋊C4×C131—21no—
134C4⋊C4×C131—21no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—22no—
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—42no—
145C22⋊C4×C131—42no—
146C22⋊C4×C131—42no—
147C22⋊C4×C131—42no—
148C22⋊C4×C131—42no—
149C22⋊C4×C131—42no—
150C22⋊C4×C131—42no—
151C42×C131—22no—
152C42×C131—22no—
153C42×C131—21no—
154C42×C131—21no—
155C42×C131—21no—
156C42×C131—21no—
157C23×C131—21no—
158C23×C131—21no—
159C23×C131—21no—
160C23×C131—21no—
161C23×C131—41no—
162C23×C131—41no—
163C23×C131—41no—
164C23×C131—41no—
165C23×C131—41no—
166C23×C131—41no—
167C23×C131—41no—
168C23×C131#12312yes—
169C23×C131#13512yes—
170C23×C131AGL(1,ℤ/8)12yes—
171C23×C131C22×D411yescharacteristic
172D4×C131—42no—
173D4×C131—42no—
174D4×C131—84no—
175C2×C4×C131—21no—
176C2×C4×C131—21no—
177C2×C4×C131—24no—
178C2×C4×C131—24no—
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—21no—
187C2×C4×C131—21no—
188C2×C4×C131—21no—
189C2×C4×C131—21no—
190C2×C4×C131—21no—
191C2×C4×C131—44no—
192C2×C4×C131—44no—
193C2×C4×C131—41no—
194C2×C4×C131—42no—
195C2×C4×C131—42no—
196C2×C4×C131—41no—
197C2×C4×C131—41no—
198C2×C4×C131—42no—
199C2×C4×C131—41no—
200C2×C4×C131—41no—
201C2×C4×C131—41no—
202C2×C4×C131—41no—
203C2×C4×C131—42no—
204C2×C4×C131—41no—
205C2×C4×C131—41no—
206C2×C4×C131—42no—
207C2×C4×C131—42no—
208C2×C4×C131—84no—
209C2×C4×C131—84no—
210C2×C4×C131#12312yes—
211C2×C4×C131C2×#4111yescharacteristic
212C2×C4×C131C2×#4111yescharacteristic
213C2×C4×C131H(5,𝔽2)12yes—
214C2×C4×C1312−1+412yes—
215C8×C131—42no—
216C8×C131—42no—
217C22×C131—22no—
218C22×C131—22no—
219C22×C131—22no—
220C22×C131—22no—
221C22×C131—22no—
222C22×C131—22no—
223C22×C131—81no—
224C22×C131—81no—
225C22×C131—81no—
226C22×C131—81no—
227C22×C131—81no—
228C22×C131—81no—
229C22×C131—81no—
230C22×C131#48214yes—
231C22×C131C2×#12311yescharacteristic
232C22×C131#53511yescharacteristic
233C22×C131#53611yescharacteristic
234C22×C131C2×#13511yescharacteristic
235C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
236C22×C131#57511yescharacteristic
237C22×C131#57511yescharacteristic
238C4×C131—22no—
239C4×C131—41no—
240C4×C131—41no—
241C4×C131—41no—
242C4×C131—41no—
243C4×C131—81no—
244C4×C131—82no—
245C4×C131—81no—
246C4×C131—82no—
247C4×C131—81no—
248C4×C131#53912yes—
249C4×C131#53912yes—
250C2×C131—24no—
251C2×C131—161no—
252C2×C131#262311yescharacteristic
253C2×C131C2×#48211yescharacteristic
254C2×C131#309311yescharacteristic
255C2×C131#321111yescharacteristic
256C2×C131#321311yescharacteristic
257C2×C131#323211yescharacteristic
258C2×C131#323411yescharacteristic
259#29912C13111yesmaximal, characteristic, direct product factor, Sylow
260C131#2991211yescharacteristic, direct product factor, Sylow
261#2854C2×C13111yescharacteristic
262C2×#382C2×C13111yescharacteristic, complemented
263#2101C2×C13112yescomplemented
264#2092C2×C13112yescomplemented
265#2085C2×C13112yescomplemented
266#2073C2×C13112yescomplemented
267#1874C2×C13111yescharacteristic
268#1874C2×C13111yescharacteristic
269#1853C2×C13111yescharacteristic, complemented
270#1852C2×C13111yescharacteristic, complemented
271#1817C2×C13111yescharacteristic, complemented
272C2×#123—21no—
273C2×#121C22×C13111yescharacteristic
274C22×C4⋊C4C22×C13111yescharacteristic
275C22×C4⋊C4C22×C13111yescharacteristic
276C22×C42C22×C13111yescharacteristic
277C2×#107C22×C13112yes—
278C2×#106C22×C13112yes—
279C2×#102C22×C13112yes—
280C2×#102C22×C13112yes—
281C2×C22⋊C8C22×C13111yescharacteristic
282C2×C22⋊C8C22×C13111yescharacteristic
283#390C22×C13111yescharacteristic
284#390C22×C13111yescharacteristic
285#389C22×C13111yescharacteristic
286#389C22×C13111yescharacteristic
287#388—21no—
288#388—21no—
289#386—21no—
290#382—21no—
291#382—21no—
292#382C22×C13112yes—
293#382C22×C13112yes—
294#380C22×C13111yescharacteristic
295C2×#95—21no—
296C2×#95—21no—
297#340C22×C13112yes—
298#340C22×C13112yes—
299#340C22×C13112yes—
300#340C22×C13112yes—
301#336C22×C13112yes—
302#336C22×C13112yes—
303C22×D4—21no—
304C22×D4C23×C13111yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C23×C4D4×C13111yescharacteristic
308C23×C4D4×C13111yescharacteristic
309C23×C4C23×C13111yescharacteristic
310C22×C8C23×C13112yes—
311C22×C8C23×C13112yes—
312#123—44no—
313#121—22no—
314#121—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4C23×C13112yes—
322C2×C4⋊C4C23×C13112yes—
323C2×C4⋊C4C23×C13111yescharacteristic
324C2×C4⋊C4C23×C13111yescharacteristic
325C2×C4⋊C4C23×C13111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42D4×C13111yescharacteristic
335C2×C42D4×C13111yescharacteristic
336C2×C42C23×C13111yescharacteristic
337C2×C42C23×C13111yescharacteristic
338#107—42no—
339#106—42no—
340#102—42no—
341#102—42no—
342C22⋊C8—22no—
343C22⋊C8—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—21no—
349#95—21no—
350#95—21no—
351C24—21no—
352C24C2×D4×C13111yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4C2×D4×C13111yescharacteristic
380C22×C4C2×D4×C13111yescharacteristic
381C22×C4C2×D4×C13111yescharacteristic
382C22×C4C2×D4×C13111yescharacteristic
383C22×C4C2×D4×C13111yescharacteristic
384C22×C4#41×C13112yes—
385C22×C4#41×C13112yes—
386C22×C4C24×C13111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C42—22no—
412C42—22no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23#123×C13112yes—
429C23#135×C13112yes—
430C23AGL(1,ℤ/8)×C13112yes—
431C23C22×D4×C13111yescharacteristic
432D4—42no—
433D4—42no—
434D4—84no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4#123×C13112yes—
471C2×C4C2×#41×C13111yescharacteristic
472C2×C4C2×#41×C13111yescharacteristic
473C2×C4H(5,𝔽2)×C13112yes—
474C2×C42−1+4×C13112yes—
475C8—42no—
476C8—42no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22#482×C13114yes—
491C22C2×#123×C13111yescharacteristic
492C22#535×C13111yescharacteristic
493C22#536×C13111yescharacteristic
494C22C2×#135×C13111yescharacteristic
495C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
496C22#575×C13111yescharacteristic
497C22#575×C13111yescharacteristic
498C4—22no—
499C4—41no—
500C4—41no—
501C4—41no—
502C4—41no—
503C4—81no—
504C4—82no—
505C4—82no—
506C4—81no—
507C4—81no—
508C4#539×C13112yes—
509C4#539×C13112yes—
510C2—24no—
511C2—161no—
512C2#2623×C13111yescharacteristic
513C2C2×#482×C13111yescharacteristic
514C2#3093×C13111yescharacteristic
515C2#3211×C13111yescharacteristic
516C2#3213×C13111yescharacteristic
517C2#3232×C13111yescharacteristic
518C2#3234×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. C2×#382×C131C2semidirect
3. #2101×C131C2semidirect
4. #2092×C131C2semidirect
5. #2085×C131C2semidirect
6. #2073×C131C2semidirect
9. #1853×C131C2semidirect
10. #1852×C131C2semidirect
11. #1817×C131C2semidirect
259. #29912C131direct (N × H)
260. C131#29912direct (N × H)
262. C2×#382C2×C131semidirect
263. #2101C2×C131semidirect
264. #2092C2×C131semidirect
265. #2085C2×C131semidirect
266. #2073C2×C131semidirect
269. #1853C2×C131semidirect
270. #1852C2×C131semidirect
271. #1817C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2854×C1312
C2×#382×C1312
#2101×C1312
#2092×C1312
#2085×C1312
#2073×C1312
#1874×C1312
#1853×C1312
#1852×C1312
#1817×C1312
#29912131