Finite Group Databasebeta

← C131×#29883 #45715767

Subgroups — C131×#29883 #45715767

Order 33536.

754 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#501×C131C211yesmaximal, characteristic, complemented
2C2×#432×C131C211yesmaximal, characteristic
3#2857×C131C211yesmaximal, characteristic
4#2851×C131C211yesmaximal, characteristic
5#2088×C131C212yesmaximal, complemented
6#2087×C131C212yesmaximal, complemented
7#2077×C131C212yesmaximal
8#2075×C131C212yesmaximal
9#1993×C131C211yesmaximal, characteristic, complemented
10#1992×C131C211yesmaximal, characteristic, complemented
11#1836×C131C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C131C2211yescharacteristic
13C2×#125×C131C2211yescharacteristic
14C2×C22⋊Q8×C131—21no—
15C22×C42×C131C2211yescharacteristic
16#501×C131—24no—
17#432×C131—24no—
18C2×#107×C131C2212yes—
19C2×#106×C131C2212yes—
20C2×C4⋊C8×C131C2212yes—
21C2×C22⋊C8×C131C2212yes—
22C2×#97×C131C2211yescharacteristic
23C2×#97×C131C2211yescharacteristic
24#391×C131—21no—
25#389×C131—21no—
26#389×C131C2211yescharacteristic
27#389×C131C2211yescharacteristic
28#389×C131C2212yes—
29#387×C131—21no—
30#387×C131—21no—
31#385×C131—21no—
32#385×C131—21no—
33#384×C131C2211yescharacteristic
34#382×C131C2211yescharacteristic
35#380×C131—21no—
36#380×C131C2211yescharacteristic
37#380×C131C2212yes—
38#380×C131C2211yescharacteristic
39#340×C131C2212yes—
40#340×C131C2212yes—
41#340×C131C2212yes—
42#340×C131C2212yes—
43#340×C131C2212yes—
44#340×C131C2212yes—
45C22×Q8×C131—21no—
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—44no—
56C2×C4⋊C4×C131—22no—
57C2×C4⋊C4×C131—21no—
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×C131C2311yescharacteristic
65C2×C4⋊C4×C131C2312yes—
66C2×C4⋊C4×C131C2311yescharacteristic
67C2×C4⋊C4×C131C2311yescharacteristic
68C2×C4⋊C4×C131C2311yescharacteristic
69C2×C4⋊C4×C131C2312yes—
70C2×C22⋊C4×C131—22no—
71C2×C22⋊C4×C131—21no—
72C2×C22⋊C4×C131—21no—
73C2×C42×C131—22no—
74C2×C42×C131—22no—
75C2×C42×C131D411yescharacteristic
76C2×C42×C131D411yescharacteristic
77C2×C42×C131C2311yescharacteristic
78C2×C42×C131C2311yescharacteristic
79#107×C131—24no—
80#106×C131—24no—
81C4⋊C8×C131—24no—
82C22⋊C8×C131—24no—
83#97×C131—22no—
84#97×C131D414yes—
85#95×C131—22no—
86#95×C131—22no—
87#95×C131—21no—
88#95×C131—21no—
89#95×C131—21no—
90#95×C131—21no—
91#95×C131—21no—
92#95×C131—21no—
93C24×C131C2×D411yescharacteristic
94C2×Q8×C131—42no—
95C2×Q8×C131—42no—
96C2×Q8×C131—42no—
97C22×C4×C131—22no—
98C22×C4×C131—22no—
99C22×C4×C131—22no—
100C22×C4×C131—22no—
101C22×C4×C131—21no—
102C22×C4×C131—21no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—21no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—21no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—41no—
112C22×C4×C131—41no—
113C22×C4×C131C2×D411yescharacteristic
114C22×C4×C131C2×D411yescharacteristic
115C22×C4×C131C2×D411yescharacteristic
116C22×C4×C131C2×D411yescharacteristic
117C22×C4×C131C2×D411yescharacteristic
118C22×C4×C131C2411yescharacteristic
119C2×C8×C131—22no—
120C2×C8×C131—22no—
121C2×C8×C131—22no—
122C2×C8×C131—22no—
123C2×C8×C131—22no—
124C2×C8×C131C2×D414yes—
125C4⋊C4×C131—21no—
126C4⋊C4×C131—22no—
127C4⋊C4×C131—21no—
128C4⋊C4×C131—21no—
129C4⋊C4×C131—21no—
130C4⋊C4×C131—22no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—24no—
134C4⋊C4×C131—42no—
135C4⋊C4×C131—42no—
136C4⋊C4×C131—42no—
137C4⋊C4×C131—44no—
138C4⋊C4×C131—42no—
139C4⋊C4×C131—42no—
140C4⋊C4×C131—42no—
141C4⋊C4×C131—42no—
142C22⋊C4×C131—42no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—44no—
145C42×C131—22no—
146C42×C131—22no—
147C42×C131—21no—
148C42×C131—21no—
149C42×C131C2×D412yes—
150C42×C131#4112yes—
151C23×C131—21no—
152C23×C131—21no—
153C23×C131—21no—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—21no—
157C23×C131AGL(1,ℤ/8)12yes—
158C23×C131C22×D411yescharacteristic
159Q8×C131—84no—
160C2×C4×C131—21no—
161C2×C4×C131—21no—
162C2×C4×C131—21no—
163C2×C4×C131—21no—
164C2×C4×C131—21no—
165C2×C4×C131—21no—
166C2×C4×C131—21no—
167C2×C4×C131—21no—
168C2×C4×C131—21no—
169C2×C4×C131—21no—
170C2×C4×C131—21no—
171C2×C4×C131—21no—
172C2×C4×C131—44no—
173C2×C4×C131—44no—
174C2×C4×C131—42no—
175C2×C4×C131—42no—
176C2×C4×C131—41no—
177C2×C4×C131—41no—
178C2×C4×C131—42no—
179C2×C4×C131—42no—
180C2×C4×C131—41no—
181C2×C4×C131—41no—
182C2×C4×C131—42no—
183C2×C4×C131—42no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—41no—
189C2×C4×C131—41no—
190C2×C4×C131—42no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—42no—
194C2×C4×C131#12112yes—
195C2×C4×C131#12112yes—
196C2×C4×C131#13712yes—
197C2×C4×C131C22×D411yescharacteristic
198C2×C4×C131C2×#4111yescharacteristic
199C2×C4×C1312−1+412yes—
200C2×C4×C1312−1+412yes—
201C8×C131—24no—
202C8×C131—42no—
203C22×C131—22no—
204C22×C131—22no—
205C22×C131—22no—
206C22×C131—41no—
207C22×C131—41no—
208C22×C131—41no—
209C22×C131—41no—
210C22×C131C2×#12111yescharacteristic
211C22×C131#53611yescharacteristic
212C22×C131#53611yescharacteristic
213C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
214C22×C131C2×#13711yescharacteristic
215C22×C131#57511yescharacteristic
216C22×C131#57511yescharacteristic
217C4×C131—22no—
218C4×C131—22no—
219C4×C131—22no—
220C4×C131—41no—
221C4×C131—41no—
222C4×C131—82no—
223C4×C131—81no—
224C4×C131—81no—
225C4×C131—81no—
226C4×C131—82no—
227C4×C131—81no—
228C4×C131#53612yes—
229C4×C131#54112yes—
230C2×C131—42no—
231C2×C131#262111yescharacteristic
232C2×C131#305511yescharacteristic
233C2×C131#305611yescharacteristic
234C2×C131#323411yescharacteristic
235C2×C131#323711yescharacteristic
236C2×C131#323811yescharacteristic
237C2×C131#324011yescharacteristic
238#29883C13111yesmaximal, characteristic, direct product factor, Sylow
239C131#2988311yescharacteristic, direct product factor, Sylow
240C2×#501C2×C13111yescharacteristic, complemented
241C2×#432C2×C13111yescharacteristic
242#2857C2×C13111yescharacteristic
243#2851C2×C13111yescharacteristic
244#2088C2×C13112yescomplemented
245#2087C2×C13112yescomplemented
246#2077C2×C13112yes—
247#2075C2×C13112yes—
248#1993C2×C13111yescharacteristic, complemented
249#1992C2×C13111yescharacteristic, complemented
250#1836C2×C13111yescharacteristic, complemented
251C2×C4⋊Q8C22×C13111yescharacteristic
252C2×#125C22×C13111yescharacteristic
253C2×C22⋊Q8—21no—
254C22×C42C22×C13111yescharacteristic
255#501—24no—
256#432—24no—
257C2×#107C22×C13112yes—
258C2×#106C22×C13112yes—
259C2×C4⋊C8C22×C13112yes—
260C2×C22⋊C8C22×C13112yes—
261C2×#97C22×C13111yescharacteristic
262C2×#97C22×C13111yescharacteristic
263#391—21no—
264#389—21no—
265#389C22×C13111yescharacteristic
266#389C22×C13111yescharacteristic
267#389C22×C13112yes—
268#387—21no—
269#387—21no—
270#385—21no—
271#385—21no—
272#384C22×C13111yescharacteristic
273#382C22×C13111yescharacteristic
274#380—21no—
275#380C22×C13111yescharacteristic
276#380C22×C13112yes—
277#380C22×C13111yescharacteristic
278#340C22×C13112yes—
279#340C22×C13112yes—
280#340C22×C13112yes—
281#340C22×C13112yes—
282#340C22×C13112yes—
283#340C22×C13112yes—
284C22×Q8—21no—
285C23×C4D4×C13111yescharacteristic
286C23×C4D4×C13111yescharacteristic
287C23×C4C23×C13111yescharacteristic
288C22×C8C23×C13112yes—
289C22×C8C23×C13112yes—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292#125—22no—
293#125—22no—
294C22⋊Q8—44no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4C23×C13111yescharacteristic
304C2×C4⋊C4C23×C13111yescharacteristic
305C2×C4⋊C4C23×C13112yes—
306C2×C4⋊C4C23×C13111yescharacteristic
307C2×C4⋊C4C23×C13111yescharacteristic
308C2×C4⋊C4C23×C13112yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42D4×C13111yescharacteristic
315C2×C42D4×C13111yescharacteristic
316C2×C42C23×C13111yescharacteristic
317C2×C42C23×C13111yescharacteristic
318#107—24no—
319#106—24no—
320C4⋊C8—24no—
321C22⋊C8—24no—
322#97—22no—
323#97D4×C13114yes—
324#95—22no—
325#95—21no—
326#95—21no—
327#95—22no—
328#95—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332C24C2×D4×C13111yescharacteristic
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—42no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×D4×C13111yescharacteristic
353C22×C4C2×D4×C13111yescharacteristic
354C22×C4C2×D4×C13111yescharacteristic
355C22×C4C2×D4×C13111yescharacteristic
356C22×C4C2×D4×C13111yescharacteristic
357C22×C4C24×C13111yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8C2×D4×C13114yes—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—24no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—44no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—44no—
384C42—22no—
385C42—22no—
386C42—21no—
387C42—21no—
388C42C2×D4×C13112yes—
389C42#41×C13112yes—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23AGL(1,ℤ/8)×C13112yes—
397C23C22×D4×C13111yescharacteristic
398Q8—84no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4#121×C13112yes—
434C2×C4#121×C13112yes—
435C2×C4#137×C13112yes—
436C2×C4C22×D4×C13111yescharacteristic
437C2×C4C2×#41×C13111yescharacteristic
438C2×C42−1+4×C13112yes—
439C2×C42−1+4×C13112yes—
440C8—24no—
441C8—42no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22C2×#121×C13111yescharacteristic
450C22#536×C13111yescharacteristic
451C22#536×C13111yescharacteristic
452C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
453C22C2×#137×C13111yescharacteristic
454C22#575×C13111yescharacteristic
455C22#575×C13111yescharacteristic
456C4—22no—
457C4—22no—
458C4—22no—
459C4—41no—
460C4—41no—
461C4—82no—
462C4—81no—
463C4—81no—
464C4—82no—
465C4—81no—
466C4—81no—
467C4#536×C13112yes—
468C4#541×C13112yes—
469C2—42no—
470C2#2621×C13111yescharacteristic
471C2#3055×C13111yescharacteristic
472C2#3056×C13111yescharacteristic
473C2#3234×C13111yescharacteristic
474C2#3237×C13111yescharacteristic
475C2#3238×C13111yescharacteristic
476C2#3240×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×#501×C131C2semidirect
5. #2088×C131C2semidirect
6. #2087×C131C2semidirect
9. #1993×C131C2semidirect
10. #1992×C131C2semidirect
11. #1836×C131C2semidirect
238. #29883C131direct (N × H)
239. C131#29883direct (N × H)
240. C2×#501C2×C131semidirect
244. #2088C2×C131semidirect
245. #2087C2×C131semidirect
248. #1993C2×C131semidirect
249. #1992C2×C131semidirect
250. #1836C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#501×C1312
C2×#432×C1312
#2857×C1312
#2851×C1312
#2088×C1312
#2087×C1312
#2077×C1312
#2075×C1312
#1993×C1312
#1992×C1312
#1836×C1312
#29883131