Finite Group Databasebeta

← C131×#33671 #45719555

Subgroups — C131×#33671 #45719555

Order 33536.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3168×C131C211yesmaximal, characteristic, complemented
2C4×#135×C131C211yesmaximal, characteristic, complemented
3#2237×C131C211yesmaximal, characteristic, complemented
4#2234×C131C211yesmaximal, characteristic, complemented
5#2229×C131C211yesmaximal, characteristic, complemented
6#2228×C131C211yesmaximal, characteristic, complemented
7#2211×C131C211yesmaximal, characteristic, complemented
8#2210×C131C211yesmaximal, characteristic, complemented
9#2189×C131C211yesmaximal, characteristic, complemented
10#2186×C131C211yesmaximal, characteristic
11#2177×C131C211yesmaximal, characteristic, complemented
12#2176×C131C211yesmaximal, characteristic, complemented
13#2175×C131C211yesmaximal, characteristic, complemented
14#2175×C131C211yesmaximal, characteristic, complemented
15#2163×C131C211yesmaximal, characteristic, complemented
16C2×#135×C131C2211yescharacteristic
17#529×C131—21no—
18C4×#41×C131—21no—
19C2×Q32×C131C2211yescharacteristic
20C2×SD32×C131C2211yescharacteristic
21C2×SD32×C131C2211yescharacteristic
22C2×D16×C131C2211yescharacteristic
23#499×C131C2211yescharacteristic
24#495×C131C2211yescharacteristic
25#488×C131—21no—
26#467×C131C2211yescharacteristic
27#466×C131C2211yescharacteristic
28#465×C131—21no—
29C4×Q16×C131C2211yescharacteristic
30C4×Q16×C131C2211yescharacteristic
31C4×Q16×C131C2211yescharacteristic
32C4×SD16×C131—21no—
33C4×SD16×C131—21no—
34C4×SD16×C131—21no—
35C4×D8×C131C2211yescharacteristic
36C4×D8×C131C2211yescharacteristic
37C4×D8×C131C2211yescharacteristic
38#427×C131C2211yescharacteristic
39#416×C131—21no—
40C2×C4×C8×C131C2211yescharacteristic
41#367×C131C2211yescharacteristic
42#367×C131C2211yescharacteristic
43#366×C131C2211yescharacteristic
44#366×C131C2211yescharacteristic
45C4⋊C16×C131C2211yescharacteristic
46C4⋊C16×C131C2211yescharacteristic
47#358×C131C2211yescharacteristic
48#358×C131C2211yescharacteristic
49#358×C131C2211yescharacteristic
50#358×C131C2211yescharacteristic
51#357×C131C2211yescharacteristic
52#357×C131C2211yescharacteristic
53#357×C131C2211yescharacteristic
54#357×C131C2211yescharacteristic
55C22⋊C16×C131C2211yescharacteristic
56C22⋊C16×C131C2211yescharacteristic
57#346×C131C2211yescharacteristic
58#346×C131C2211yescharacteristic
59C2×#41×C131—21no—
60#135×C131—22no—
61#135×C131—22no—
62C2×Q16×C131C2311yescharacteristic
63C2×Q16×C131C2311yescharacteristic
64C2×SD16×C131—21no—
65C2×SD16×C131—21no—
66C2×D8×C131C2311yescharacteristic
67C2×D8×C131C2311yescharacteristic
68C22×C8×C131D411yescharacteristic
69C22×C8×C131C2311yescharacteristic
70#126×C131—41no—
71#125×C131—21no—
72#124×C131—21no—
73#123×C131—41no—
74C22⋊Q8×C131—21no—
75#121×C131—21no—
76C4×Q8×C131—21no—
77C4×Q8×C131—21no—
78C4×Q8×C131—21no—
79C4×D4×C131—21no—
80C4×D4×C131—21no—
81C4×D4×C131—21no—
82C4×D4×C131—41no—
83C4×D4×C131—41no—
84C4×D4×C131—41no—
85#117×C131—21no—
86#117×C131—41no—
87#117×C131—41no—
88C2×C42×C131—41no—
89C2×C42×C131D411yescharacteristic
90Q32×C131—22no—
91SD32×C131—22no—
92SD32×C131—22no—
93D16×C131—22no—
94C2×C16×C131C2311yescharacteristic
95C2×C16×C131C2311yescharacteristic
96C2×C16×C131C2311yescharacteristic
97C2×C16×C131C2311yescharacteristic
98#107×C131C2311yescharacteristic
99#107×C131C2311yescharacteristic
100#107×C131C2311yescharacteristic
101#107×C131C2311yescharacteristic
102#106×C131—21no—
103#106×C131—21no—
104#103×C131—21no—
105#103×C131—21no—
106#103×C131—21no—
107#103×C131—21no—
108#102×C131—21no—
109#102×C131—21no—
110#102×C131—21no—
111#102×C131—21no—
112C4×C8×C131D411yescharacteristic
113C4×C8×C131D411yescharacteristic
114C4×C8×C131C2311yescharacteristic
115C4×C8×C131C2311yescharacteristic
116#41×C131—24no—
117#41×C131—42no—
118C2×Q8×C131—21no—
119C2×Q8×C131—21no—
120C2×D4×C131—21no—
121C2×D4×C131—21no—
122C2×D4×C131—41no—
123C2×D4×C131—41no—
124C22×C4×C131—41no—
125C22×C4×C131—41no—
126C22×C4×C131—41no—
127C22×C4×C131—41no—
128C22×C4×C131D811yescharacteristic
129C22×C4×C131D811yescharacteristic
130C22×C4×C131C2×D411yescharacteristic
131Q16×C131—21no—
132Q16×C131—21no—
133Q16×C131—21no—
134Q16×C131#4112yes—
135SD16×C131—24no—
136SD16×C131—42no—
137D8×C131—21no—
138D8×C131—21no—
139D8×C131—21no—
140D8×C131#4112yes—
141C2×C8×C131—21no—
142C2×C8×C131—21no—
143C2×C8×C131—41no—
144C2×C8×C131C2×D411yescharacteristic
145C2×C8×C131C2×D411yescharacteristic
146C2×C8×C131C2×D411yescharacteristic
147C2×C8×C131C2411yescharacteristic
148C4⋊C4×C131—21no—
149C4⋊C4×C131—21no—
150C4⋊C4×C131—21no—
151C4⋊C4×C131—21no—
152C4⋊C4×C131—41no—
153C4⋊C4×C131—41no—
154C4⋊C4×C131—41no—
155C4⋊C4×C131—41no—
156C4⋊C4×C131—41no—
157C4⋊C4×C131—41no—
158C22⋊C4×C131—41no—
159C22⋊C4×C131—41no—
160C22⋊C4×C131—41no—
161C22⋊C4×C131—41no—
162C22⋊C4×C131—41no—
163C22⋊C4×C131—41no—
164C22⋊C4×C131—41no—
165C22⋊C4×C131—41no—
166C42×C131—41no—
167C42×C131—41no—
168C42×C131—41no—
169C42×C131—41no—
170C42×C131D811yescharacteristic
171C42×C131D811yescharacteristic
172C42×C131C2×D411yescharacteristic
173C42×C131C2×D411yescharacteristic
174C16×C131—21no—
175C16×C131—21no—
176C16×C131—21no—
177C16×C131—21no—
178C23×C131—41no—
179C23×C131—41no—
180C23×C131C2×D811yescharacteristic
181Q8×C131—22no—
182Q8×C131—41no—
183Q8×C131—41no—
184Q8×C131—41no—
185D4×C131—22no—
186D4×C131—44no—
187D4×C131—41no—
188D4×C131—41no—
189D4×C131—41no—
190D4×C131—82no—
191C2×C4×C131—21no—
192C2×C4×C131—21no—
193C2×C4×C131—41no—
194C2×C4×C131—41no—
195C2×C4×C131—44no—
196C2×C4×C131—41no—
197C2×C4×C131—41no—
198C2×C4×C131—41no—
199C2×C4×C131—41no—
200C2×C4×C131—41no—
201C2×C4×C131—41no—
202C2×C4×C131—82no—
203C2×C4×C131—82no—
204C2×C4×C131—82no—
205C2×C4×C131C2×D811yescharacteristic
206C2×C4×C131C2×D811yescharacteristic
207C2×C4×C131C2×D811yescharacteristic
208C2×C4×C131C2×D811yescharacteristic
209C2×C4×C131C2×D811yescharacteristic
210C2×C4×C131C22×D411yescharacteristic
211C8×C131—21no—
212C8×C131—21no—
213C8×C131—21no—
214C8×C131C2×#4111yescharacteristic
215C8×C131C2×#4111yescharacteristic
216C22×C131—21no—
217C22×C131—21no—
218C22×C131—21no—
219C22×C131—42no—
220C22×C131—81no—
221C22×C131—81no—
222C22×C131—81no—
223C22×C131—81no—
224C22×C131—81no—
225C22×C131C22×D811yescharacteristic
226C4×C131—21no—
227C4×C131—21no—
228C4×C131—21no—
229C4×C131—21no—
230C4×C131—21no—
231C4×C131—42no—
232C4×C131—81no—
233C4×C131—81no—
234C4×C131—81no—
235C4×C131—81no—
236C4×C131—81no—
237C4×C131#52511yescharacteristic
238C4×C131#57511yescharacteristic
239C2×C131—41no—
240C2×C131—82no—
241C2×C131—161no—
242C2×C131#310011yescharacteristic
243C2×C131#341411yescharacteristic
244C2×C131#341411yescharacteristic
245#33671C13111yesmaximal, characteristic, direct product factor, Sylow
246C131#3367111yescharacteristic, direct product factor, Sylow
247#3168C2×C13111yescharacteristic, complemented
248C4×#135C2×C13111yescharacteristic, complemented
249#2237C2×C13111yescharacteristic, complemented
250#2234C2×C13111yescharacteristic, complemented
251#2229C2×C13111yescharacteristic, complemented
252#2228C2×C13111yescharacteristic, complemented
253#2211C2×C13111yescharacteristic, complemented
254#2210C2×C13111yescharacteristic, complemented
255#2189C2×C13111yescharacteristic, complemented
256#2186C2×C13111yescharacteristic
257#2177C2×C13111yescharacteristic, complemented
258#2176C2×C13111yescharacteristic, complemented
259#2175C2×C13111yescharacteristic, complemented
260#2175C2×C13111yescharacteristic, complemented
261#2163C2×C13111yescharacteristic, complemented
262C2×#135C22×C13111yescharacteristic
263#529—21no—
264C4×#41—21no—
265C2×Q32C22×C13111yescharacteristic
266C2×SD32C22×C13111yescharacteristic
267C2×SD32C22×C13111yescharacteristic
268C2×D16C22×C13111yescharacteristic
269#499C22×C13111yescharacteristic
270#495C22×C13111yescharacteristic
271#488—21no—
272#467C22×C13111yescharacteristic
273#466C22×C13111yescharacteristic
274#465—21no—
275C4×Q16C22×C13111yescharacteristic
276C4×Q16C22×C13111yescharacteristic
277C4×Q16C22×C13111yescharacteristic
278C4×SD16—21no—
279C4×SD16—21no—
280C4×SD16—21no—
281C4×D8C22×C13111yescharacteristic
282C4×D8C22×C13111yescharacteristic
283C4×D8C22×C13111yescharacteristic
284#427C22×C13111yescharacteristic
285#416—21no—
286C2×C4×C8C22×C13111yescharacteristic
287#367C22×C13111yescharacteristic
288#367C22×C13111yescharacteristic
289#366C22×C13111yescharacteristic
290#366C22×C13111yescharacteristic
291C4⋊C16C22×C13111yescharacteristic
292C4⋊C16C22×C13111yescharacteristic
293#358C22×C13111yescharacteristic
294#358C22×C13111yescharacteristic
295#358C22×C13111yescharacteristic
296#358C22×C13111yescharacteristic
297#357C22×C13111yescharacteristic
298#357C22×C13111yescharacteristic
299#357C22×C13111yescharacteristic
300#357C22×C13111yescharacteristic
301C22⋊C16C22×C13111yescharacteristic
302C22⋊C16C22×C13111yescharacteristic
303#346C22×C13111yescharacteristic
304#346C22×C13111yescharacteristic
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16C23×C13111yescharacteristic
309C2×Q16C23×C13111yescharacteristic
310C2×SD16—21no—
311C2×SD16—21no—
312C2×D8C23×C13111yescharacteristic
313C2×D8C23×C13111yescharacteristic
314C22×C8D4×C13111yescharacteristic
315C22×C8C23×C13111yescharacteristic
316#126—41no—
317#125—21no—
318#124—21no—
319#123—41no—
320C22⋊Q8—21no—
321#121—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—41no—
329C4×D4—41no—
330C4×D4—41no—
331#117—21no—
332#117—41no—
333#117—41no—
334C2×C42—41no—
335C2×C42D4×C13111yescharacteristic
336Q32—22no—
337SD32—22no—
338SD32—22no—
339D16—22no—
340C2×C16C23×C13111yescharacteristic
341C2×C16C23×C13111yescharacteristic
342C2×C16C23×C13111yescharacteristic
343C2×C16C23×C13111yescharacteristic
344#107C23×C13111yescharacteristic
345#107C23×C13111yescharacteristic
346#107C23×C13111yescharacteristic
347#107C23×C13111yescharacteristic
348#106—21no—
349#106—21no—
350#103—21no—
351#103—21no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—21no—
358C4×C8D4×C13111yescharacteristic
359C4×C8D4×C13111yescharacteristic
360C4×C8C23×C13111yescharacteristic
361C4×C8C23×C13111yescharacteristic
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4D8×C13111yescharacteristic
375C22×C4D8×C13111yescharacteristic
376C22×C4C2×D4×C13111yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—21no—
380Q16#41×C13112yes—
381SD16—24no—
382SD16—42no—
383D8—21no—
384D8—21no—
385D8—21no—
386D8#41×C13112yes—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8C2×D4×C13111yescharacteristic
391C2×C8C2×D4×C13111yescharacteristic
392C2×C8C2×D4×C13111yescharacteristic
393C2×C8C24×C13111yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42—41no—
416C42D8×C13111yescharacteristic
417C42D8×C13111yescharacteristic
418C42C2×D4×C13111yescharacteristic
419C42C2×D4×C13111yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—41no—
425C23—41no—
426C23C2×D8×C13111yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4C2×D8×C13111yescharacteristic
452C2×C4C2×D8×C13111yescharacteristic
453C2×C4C2×D8×C13111yescharacteristic
454C2×C4C2×D8×C13111yescharacteristic
455C2×C4C2×D8×C13111yescharacteristic
456C2×C4C22×D4×C13111yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#41×C13111yescharacteristic
461C8C2×#41×C13111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×D8×C13111yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4#525×C13111yescharacteristic
484C4#575×C13111yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2#3100×C13111yescharacteristic
489C2#3414×C13111yescharacteristic
490C2#3414×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C22×D8
commutator, Frattini, cosocleC2×C8C24×C131
prime radical#2186×C131C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3168×C131C2semidirect
2. C4×#135×C131C2semidirect
3. #2237×C131C2semidirect
4. #2234×C131C2semidirect
5. #2229×C131C2semidirect
6. #2228×C131C2semidirect
7. #2211×C131C2semidirect
8. #2210×C131C2semidirect
9. #2189×C131C2semidirect
11. #2177×C131C2semidirect
12. #2176×C131C2semidirect
13. #2175×C131C2semidirect
14. #2175×C131C2semidirect
15. #2163×C131C2semidirect
245. #33671C131direct (N × H)
246. C131#33671direct (N × H)
247. #3168C2×C131semidirect
248. C4×#135C2×C131semidirect
249. #2237C2×C131semidirect
250. #2234C2×C131semidirect
251. #2229C2×C131semidirect
252. #2228C2×C131semidirect
253. #2211C2×C131semidirect
254. #2210C2×C131semidirect
255. #2189C2×C131semidirect
257. #2177C2×C131semidirect
258. #2176C2×C131semidirect
259. #2175C2×C131semidirect
260. #2175C2×C131semidirect
261. #2163C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3168×C1312
C4×#135×C1312
#2237×C1312
#2234×C1312
#2229×C1312
#2228×C1312
#2211×C1312
#2210×C1312
#2189×C1312
#2186×C1312
#2177×C1312
#2176×C1312
#2175×C1312
#2163×C1312
#33671131