Finite Group Databasebeta

← C131×#23594 #45709478

Subgroups — C131×#23594 #45709478

Order 33536.

1038 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461×C131C211yesmaximal, characteristic
2C4×#137×C131C212yesmaximal, complemented
3#2327×C131C211yesmaximal, characteristic, complemented
4#2061×C131C211yesmaximal, characteristic, complemented
5#2040×C131C211yesmaximal, characteristic
6#2038×C131C212yesmaximal, complemented
7#2028×C131C211yesmaximal, characteristic, complemented
8#2007×C131C211yesmaximal, characteristic
9#2005×C131C212yesmaximal, complemented
10#1759×C131C212yesmaximal, complemented
11C4×#101×C131C211yesmaximal, characteristic, complemented
12C2×#137×C131C2212yes—
13#544×C131C2211yescharacteristic
14#542×C131—22no—
15#541×C131—22no—
16#539×C131—22no—
17#537×C131C2211yescharacteristic
18#536×C131C2212yes—
19#533×C131—22no—
20C2×C4⋊Q8×C131C2211yescharacteristic
21#529×C131—22no—
22#529×C131—22no—
23C4×#41×C131C2212yes—
24C2×C4×Q8×C131C2211yescharacteristic
25C2×C4×Q8×C131C2211yescharacteristic
26#441×C131—22no—
27#440×C131—22no—
28C4×Q16×C131—22no—
29C4×SD16×C131—22no—
30#428×C131C2212yes—
31C2×#104×C131C2212yes—
32C2×#104×C131C2212yes—
33#419×C131C2212yes—
34#417×C131C2212yes—
35C2×#101×C131C2212yes—
36C4×M16×C131C2212yes—
37#391×C131C2211yescharacteristic
38#391×C131C2211yescharacteristic
39#387×C131—22no—
40#387×C131—22no—
41#382×C131C2211yescharacteristic
42#376×C131C2211yescharacteristic
43#343×C131C2211yescharacteristic
44#343×C131C2211yescharacteristic
45#339×C131C2212yes—
46#339×C131C2212yes—
47C2×#41×C131C2312yes—
48C22×Q8×C131C2311yescharacteristic
49C22×Q8×C131C2311yescharacteristic
50#137×C131—24no—
51#137×C131—24no—
52C2×Q16×C131—22no—
53C2×SD16×C131—22no—
54C2×M16×C131C2312yes—
55C2×M16×C131C2312yes—
56C4⋊Q8×C131—22no—
57C4⋊Q8×C131—22no—
58C4⋊Q8×C131—22no—
59C4⋊Q8×C131—22no—
60#126×C131—24no—
61#126×C131—24no—
62#125×C131—22no—
63#125×C131—24no—
64#125×C131—22no—
65#124×C131—22no—
66#124×C131—22no—
67#123×C131—24no—
68#123×C131—24no—
69C22⋊Q8×C131—24no—
70C22⋊Q8×C131—22no—
71C22⋊Q8×C131—22no—
72C22⋊Q8×C131—22no—
73C22⋊Q8×C131—22no—
74#121×C131—22no—
75#121×C131—22no—
76C4×Q8×C131—22no—
77C4×Q8×C131—22no—
78C4×Q8×C131—22no—
79C4×Q8×C131—22no—
80C4×Q8×C131—22no—
81C4×Q8×C131D412yes—
82C4×Q8×C131D412yes—
83C4×D4×C131—22no—
84C4×D4×C131—22no—
85C4×D4×C131—22no—
86C4×D4×C131D412yes—
87C4×D4×C131D412yes—
88#117×C131—24no—
89#117×C131—22no—
90#117×C131C2312yes—
91C2×C4⋊C4×C131—22no—
92C2×C4⋊C4×C131—21no—
93C2×C4⋊C4×C131D412yes—
94C2×C4⋊C4×C131C2311yescharacteristic
95C2×C4⋊C4×C131C2311yescharacteristic
96C2×C42×C131—22no—
97C2×C42×C131—21no—
98C2×C42×C131D412yes—
99C2×C42×C131C2311yescharacteristic
100C2×C42×C131C2311yescharacteristic
101C2×C42×C131C2311yescharacteristic
102#107×C131—22no—
103#106×C131—22no—
104#104×C131—24no—
105#104×C131—24no—
106#103×C131—22no—
107#103×C131—22no—
108#103×C131—22no—
109#102×C131—22no—
110#101×C131—24no—
111#97×C131—22no—
112C4×C8×C131—22no—
113#95×C131—22no—
114#95×C131—22no—
115#95×C131—21no—
116#95×C131—21no—
117#95×C131—22no—
118#41×C131—22no—
119#41×C131—22no—
120#41×C131—22no—
121#41×C131—22no—
122C2×Q8×C131—22no—
123C2×Q8×C131—22no—
124C2×Q8×C131—22no—
125C2×Q8×C131—21no—
126C2×Q8×C131—21no—
127C2×Q8×C131—21no—
128C2×Q8×C131—22no—
129C2×Q8×C131—22no—
130C2×Q8×C131C2×D412yes—
131C2×Q8×C131#4112yes—
132C2×D4×C131—22no—
133C2×D4×C131—22no—
134C2×D4×C131C2×D412yes—
135C22×C4×C131—21no—
136C22×C4×C131—21no—
137C22×C4×C131—22no—
138C22×C4×C131—22no—
139C22×C4×C131—22no—
140C22×C4×C131—21no—
141C22×C4×C131—21no—
142C22×C4×C131C2×D412yes—
143C22×C4×C131C2×D412yes—
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131C2411yescharacteristic
147Q16×C131—28no—
148SD16×C131—28no—
149M16×C131—22no—
150M16×C131—22no—
151M16×C131—22no—
152M16×C131#4114yes—
153C2×C8×C131—22no—
154C2×C8×C131—22no—
155C4⋊C4×C131—28no—
156C4⋊C4×C131—24no—
157C4⋊C4×C131—24no—
158C4⋊C4×C131—22no—
159C4⋊C4×C131—22no—
160C4⋊C4×C131—24no—
161C4⋊C4×C131—24no—
162C4⋊C4×C131—22no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131—22no—
166C4⋊C4×C131—41no—
167C4⋊C4×C131—41no—
168C4⋊C4×C131C2×D412yes—
169C4⋊C4×C131C2×D412yes—
170C22⋊C4×C131—24no—
171C22⋊C4×C131—24no—
172C22⋊C4×C131—24no—
173C22⋊C4×C131—22no—
174C22⋊C4×C131—22no—
175C22⋊C4×C131—22no—
176C42×C131—22no—
177C42×C131—22no—
178C42×C131—22no—
179C42×C131—22no—
180C42×C131—22no—
181C42×C131—21no—
182C42×C131—22no—
183C42×C131—42no—
184C42×C131C2×D412yes—
185C42×C131C2×D412yes—
186C42×C131#4112yes—
187C23×C131—22no—
188C23×C131C22×D411yescharacteristic
189Q8×C131—24no—
190Q8×C131—22no—
191Q8×C131—22no—
192Q8×C131—42no—
193Q8×C131—42no—
194Q8×C131—42no—
195Q8×C131—82no—
196D4×C131—22no—
197D4×C131—22no—
198D4×C131—42no—
199D4×C131—42no—
200D4×C131—82no—
201C2×C4×C131—22no—
202C2×C4×C131—22no—
203C2×C4×C131—22no—
204C2×C4×C131—22no—
205C2×C4×C131—22no—
206C2×C4×C131—22no—
207C2×C4×C131—22no—
208C2×C4×C131—22no—
209C2×C4×C131—22no—
210C2×C4×C131—41no—
211C2×C4×C131—41no—
212C2×C4×C131—44no—
213C2×C4×C131—41no—
214C2×C4×C131—41no—
215C2×C4×C131—41no—
216C2×C4×C131—41no—
217C2×C4×C131—42no—
218C2×C4×C131—42no—
219C2×C4×C131—42no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—42no—
223C2×C4×C131—41no—
224C2×C4×C131—41no—
225C2×C4×C131—82no—
226C2×C4×C131#12011yescharacteristic
227C2×C4×C131#12011yescharacteristic
228C2×C4×C131#12012yes—
229C2×C4×C131C22×D412yes—
230C2×C4×C131C2×#4111yescharacteristic
231C2×C4×C131C2×#4112yes—
232C2×C4×C131C2×#4111yescharacteristic
233C8×C131—24no—
234C8×C131—42no—
235C22×C131—21no—
236C22×C131—21no—
237C22×C131—42no—
238C22×C131—42no—
239C22×C131—42no—
240C22×C131C2×#12011yescharacteristic
241C22×C131#52511yescharacteristic
242C22×C131#53211yescharacteristic
243C4×C131—21no—
244C4×C131—21no—
245C4×C131—22no—
246C4×C131—42no—
247C4×C131—42no—
248C4×C131—42no—
249C4×C131—42no—
250C4×C131—42no—
251C4×C131—42no—
252C4×C131—42no—
253C4×C131—81no—
254C4×C131—81no—
255C4×C131#52512yes—
256C4×C131#53212yes—
257C2×C131—21no—
258C2×C131—21no—
259C2×C131—82no—
260C2×C131#238811yescharacteristic
261C2×C131#302011yescharacteristic
262C2×C131#302211yescharacteristic
263#23594C13111yesmaximal, characteristic, direct product factor, Sylow
264C131#2359411yescharacteristic, direct product factor, Sylow
265#3461C2×C13111yescharacteristic
266C4×#137C2×C13112yescomplemented
267#2327C2×C13111yescharacteristic, complemented
268#2061C2×C13111yescharacteristic, complemented
269#2040C2×C13111yescharacteristic
270#2038C2×C13112yescomplemented
271#2028C2×C13111yescharacteristic, complemented
272#2007C2×C13111yescharacteristic
273#2005C2×C13112yescomplemented
274#1759C2×C13112yescomplemented
275C4×#101C2×C13111yescharacteristic, complemented
276C2×#137C22×C13112yes—
277#544C22×C13111yescharacteristic
278#542—22no—
279#541—22no—
280#539—22no—
281#537C22×C13111yescharacteristic
282#536C22×C13112yes—
283#533—22no—
284C2×C4⋊Q8C22×C13111yescharacteristic
285#529—22no—
286#529—22no—
287C4×#41C22×C13112yes—
288C2×C4×Q8C22×C13111yescharacteristic
289C2×C4×Q8C22×C13111yescharacteristic
290#441—22no—
291#440—22no—
292C4×Q16—22no—
293C4×SD16—22no—
294#428C22×C13112yes—
295C2×#104C22×C13112yes—
296C2×#104C22×C13112yes—
297#419C22×C13112yes—
298#417C22×C13112yes—
299C2×#101C22×C13112yes—
300C4×M16C22×C13112yes—
301#391C22×C13111yescharacteristic
302#391C22×C13111yescharacteristic
303#387—22no—
304#387—22no—
305#382C22×C13111yescharacteristic
306#376C22×C13111yescharacteristic
307#343C22×C13111yescharacteristic
308#343C22×C13111yescharacteristic
309#339C22×C13112yes—
310#339C22×C13112yes—
311C2×#41C23×C13112yes—
312C22×Q8C23×C13111yescharacteristic
313C22×Q8C23×C13111yescharacteristic
314#137—24no—
315#137—24no—
316C2×Q16—22no—
317C2×SD16—22no—
318C2×M16C23×C13112yes—
319C2×M16C23×C13112yes—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#126—24no—
325#126—24no—
326#125—22no—
327#125—24no—
328#125—22no—
329#124—22no—
330#124—22no—
331#123—24no—
332#123—24no—
333C22⋊Q8—24no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338#121—22no—
339#121—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8D4×C13112yes—
346C4×Q8D4×C13112yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4D4×C13112yes—
351C4×D4D4×C13112yes—
352#117—24no—
353#117—22no—
354#117C23×C13112yes—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C13112yes—
358C2×C4⋊C4C23×C13111yescharacteristic
359C2×C4⋊C4C23×C13111yescharacteristic
360C2×C42—22no—
361C2×C42—21no—
362C2×C42D4×C13112yes—
363C2×C42C23×C13111yescharacteristic
364C2×C42C23×C13111yescharacteristic
365C2×C42C23×C13111yescharacteristic
366#107—22no—
367#106—22no—
368#104—24no—
369#104—24no—
370#103—22no—
371#103—22no—
372#103—22no—
373#102—22no—
374#101—24no—
375#97—22no—
376C4×C8—22no—
377#95—21no—
378#95—21no—
379#95—22no—
380#95—22no—
381#95—22no—
382#41—22no—
383#41—22no—
384#41—22no—
385#41—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8C2×D4×C13112yes—
395C2×Q8#41×C13112yes—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4C2×D4×C13112yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4C2×D4×C13112yes—
407C22×C4C2×D4×C13112yes—
408C22×C4C2×D4×C13111yescharacteristic
409C22×C4C2×D4×C13111yescharacteristic
410C22×C4C24×C13111yescharacteristic
411Q16—28no—
412SD16—28no—
413M16—22no—
414M16—22no—
415M16—22no—
416M16#41×C13114yes—
417C2×C8—22no—
418C2×C8—22no—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4C2×D4×C13112yes—
433C4⋊C4C2×D4×C13112yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—21no—
446C42—22no—
447C42—42no—
448C42C2×D4×C13112yes—
449C42C2×D4×C13112yes—
450C42#41×C13112yes—
451C23—22no—
452C23C22×D4×C13111yescharacteristic
453Q8—24no—
454Q8—22no—
455Q8—22no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—42no—
464D4—82no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4#120×C13111yescharacteristic
491C2×C4#120×C13111yescharacteristic
492C2×C4#120×C13112yes—
493C2×C4C22×D4×C13112yes—
494C2×C4C2×#41×C13111yescharacteristic
495C2×C4C2×#41×C13112yes—
496C2×C4C2×#41×C13111yescharacteristic
497C8—24no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22C2×#120×C13111yescharacteristic
505C22#525×C13111yescharacteristic
506C22#532×C13111yescharacteristic
507C4—21no—
508C4—21no—
509C4—22no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4#525×C13112yes—
520C4#532×C13112yes—
521C2—21no—
522C2—21no—
523C2—82no—
524C2#2388×C13111yescharacteristic
525C2#3020×C13111yescharacteristic
526C2#3022×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#537×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#137×C131C2semidirect
3. #2327×C131C2semidirect
4. #2061×C131C2semidirect
6. #2038×C131C2semidirect
7. #2028×C131C2semidirect
9. #2005×C131C2semidirect
10. #1759×C131C2semidirect
11. C4×#101×C131C2semidirect
263. #23594C131direct (N × H)
264. C131#23594direct (N × H)
266. C4×#137C2×C131semidirect
267. #2327C2×C131semidirect
268. #2061C2×C131semidirect
270. #2038C2×C131semidirect
271. #2028C2×C131semidirect
273. #2005C2×C131semidirect
274. #1759C2×C131semidirect
275. C4×#101C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3461×C1312
C4×#137×C1312
#2327×C1312
#2061×C1312
#2040×C1312
#2038×C1312
#2028×C1312
#2007×C1312
#2005×C1312
#1759×C1312
C4×#101×C1312
#23594131