Finite Group Databasebeta

← C131×#13355 #45699239

Subgroups — C131×#13355 #45699239

Order 33536.

704 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3200×C131C211yesmaximal, characteristic, complemented
2#3027×C131C211yesmaximal, characteristic
3#3022×C131C211yesmaximal, characteristic, complemented
4#2134×C131C211yesmaximal, characteristic, complemented
5#2123×C131C211yesmaximal, characteristic, complemented
6#1791×C131C211yesmaximal, characteristic, complemented
7#1395×C131C211yesmaximal, characteristic, complemented
8#585×C131C2211yescharacteristic
9C2×#137×C131—21no—
10#536×C131C2211yescharacteristic
11#535×C131—21no—
12#535×C131C2211yescharacteristic
13#485×C131—21no—
14#482×C131—21no—
15#468×C131—21no—
16#465×C131—21no—
17B(4,𝔽2)×C131—22no—
18B(4,𝔽2)×C131—22no—
19#456×C131—22no—
20#455×C131—22no—
21#450×C131—21no—
22#448×C131—21no—
23#421×C131—21no—
24#413×C131—21no—
25#413×C131C2211yescharacteristic
26#413×C131C2211yescharacteristic
27#410×C131—21no—
28#410×C131C2211yescharacteristic
29#408×C131—21no—
30#408×C131C2211yescharacteristic
31#355×C131—22no—
32#352×C131—22no—
332−1+4×C131—21no—
342−1+4×C131—41no—
35H(5,𝔽2)×C131—21no—
36H(5,𝔽2)×C131—21no—
37H(5,𝔽2)×C131—41no—
38H(5,𝔽2)×C131D412yes—
39C2×#41×C131—21no—
40C2×#41×C131—21no—
41C2×#41×C131—21no—
42C2×#41×C131—42no—
43C2×#41×C131C2311yescharacteristic
44C22×Q8×C131D411yescharacteristic, complemented
45C22×D4×C131D411yescharacteristic
46#137×C131—24no—
47#137×C131—42no—
48C2×Q16×C131—41no—
49C2×SD16×C131—21no—
50C2×SD16×C131—21no—
51C2×SD16×C131—41no—
52C2×M16×C131—21no—
53C2×M16×C131—21no—
54C2×M16×C131D411yescharacteristic, complemented
55C22×C8×C131D411yescharacteristic, complemented
56C4⋊Q8×C131—21no—
57#127×C131—21no—
58#127×C131—41no—
59#124×C131—21no—
60#124×C131—21no—
61#124×C131—41no—
62#123×C131—21no—
63#123×C131—21no—
64C22⋊Q8×C131—21no—
65C22⋊Q8×C131—21no—
66#121×C131—21no—
67#121×C131—21no—
68#121×C131—42no—
69#120×C131—24no—
70#120×C131—21no—
71#120×C131—21no—
72#117×C131—21no—
73#117×C131D411yescharacteristic
74#117×C131D411yescharacteristic, complemented
75#107×C131—21no—
76#106×C131—21no—
77#104×C131—24no—
78#103×C131—21no—
79#103×C131—21no—
80#102×C131—21no—
81#102×C131—21no—
82#101×C131—21no—
83#101×C131—41no—
84#101×C131D412yescomplemented
85#100×C131—21no—
86#100×C131—21no—
87#100×C131—41no—
88#99×C131—24no—
89#99×C131—21no—
90#99×C131D412yes—
91C22⋊C8×C131—21no—
92C22⋊C8×C131—21no—
93C22⋊C8×C131—42no—
94C24×C131—21no—
95#41×C131—22no—
96#41×C131—22no—
97#41×C131—41no—
98#41×C131—41no—
99#41×C131—42no—
100#41×C131—41no—
101#41×C131—41no—
102#41×C131—41no—
103#41×C131—41no—
104#41×C131—41no—
105#41×C131—42no—
106#41×C131—42no—
107#41×C131—42no—
108#41×C131—41no—
109#41×C131—41no—
110#41×C131—41no—
111C2×Q8×C131—21no—
112C2×Q8×C131—21no—
113C2×Q8×C131—21no—
114C2×Q8×C131—21no—
115C2×Q8×C131—21no—
116C2×Q8×C131—41no—
117C2×Q8×C131—41no—
118C2×Q8×C131—42no—
119C2×Q8×C131C2×D411yescharacteristic
120C2×D4×C131—21no—
121C2×D4×C131—21no—
122C2×D4×C131—21no—
123C2×D4×C131—22no—
124C2×D4×C131—22no—
125C2×D4×C131—21no—
126C2×D4×C131—21no—
127C2×D4×C131—41no—
128C2×D4×C131—41no—
129C2×D4×C131—42no—
130C2×D4×C131—42no—
131C2×D4×C131—42no—
132C2×D4×C131—41no—
133C2×D4×C131—44no—
134C2×D4×C131—41no—
135C2×D4×C131—41no—
136C2×D4×C131C2×D411yescharacteristic
137C2×D4×C131C2×D411yescharacteristic
138C2×D4×C131#4111yescharacteristic
139C22×C4×C131—22no—
140C22×C4×C131—22no—
141C22×C4×C131—21no—
142C22×C4×C131—41no—
143C22×C4×C131C2×D411yescharacteristic
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146Q16×C131—44no—
147SD16×C131—44no—
148SD16×C131—81no—
149SD16×C131—81no—
150M16×C131—22no—
151M16×C131—41no—
152M16×C131—41no—
153M16×C131—41no—
154M16×C131—41no—
155C2×C8×C131—21no—
156C2×C8×C131—21no—
157C2×C8×C131—41no—
158C2×C8×C131—41no—
159C2×C8×C131—41no—
160C4⋊C4×C131—21no—
161C4⋊C4×C131—21no—
162C4⋊C4×C131—41no—
163C4⋊C4×C131—41no—
164C4⋊C4×C131—41no—
165C22⋊C4×C131—21no—
166C22⋊C4×C131—22no—
167C22⋊C4×C131—21no—
168C22⋊C4×C131—44no—
169C22⋊C4×C131—41no—
170C22⋊C4×C131—41no—
171C22⋊C4×C131—41no—
172C22⋊C4×C131—41no—
173C42×C131—21no—
174C42×C131—21no—
175C42×C131—41no—
176C23×C131—22no—
177C23×C131—22no—
178C23×C131—41no—
179C23×C131—42no—
180C23×C131—41no—
181C23×C131—161no—
182C23×C131#12011yescharacteristic
183C23×C131#12111yescharacteristic
184C23×C131#12111yescharacteristic
185Q8×C131—22no—
186Q8×C131—41no—
187Q8×C131—41no—
188Q8×C131—41no—
189Q8×C131—42no—
190Q8×C131—41no—
191Q8×C131—41no—
192Q8×C131—41no—
193D4×C131—22no—
194D4×C131—41no—
195D4×C131—41no—
196D4×C131—41no—
197D4×C131—41no—
198D4×C131—41no—
199D4×C131—42no—
200D4×C131—42no—
201D4×C131—42no—
202D4×C131—42no—
203D4×C131—41no—
204D4×C131—41no—
205D4×C131—41no—
206D4×C131—81no—
207D4×C131—161no—
208D4×C131—161no—
209D4×C131—164no—
210C2×C4×C131—21no—
211C2×C4×C131—21no—
212C2×C4×C131—21no—
213C2×C4×C131—21no—
214C2×C4×C131—21no—
215C2×C4×C131—21no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—42no—
219C2×C4×C131—42no—
220C2×C4×C131—42no—
221C2×C4×C131—41no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—41no—
225C2×C4×C131—41no—
226C2×C4×C131—41no—
227C2×C4×C131—81no—
228C2×C4×C131#12011yescharacteristic
229C2×C4×C131#12011yescharacteristic
230C2×C4×C131#12111yescharacteristic
231C2×C4×C131#12711yescharacteristic
232C8×C131—42no—
233C8×C131—41no—
234C8×C131—41no—
235C8×C131—81no—
236C22×C131—21no—
237C22×C131—21no—
238C22×C131—21no—
239C22×C131—41no—
240C22×C131—41no—
241C22×C131—41no—
242C22×C131—42no—
243C22×C131—81no—
244C22×C131—81no—
245C22×C131—82no—
246C22×C131—82no—
247C22×C131—84no—
248C22×C131—81no—
249C22×C131—161no—
250C22×C131#39211yescharacteristic
251C4×C131—21no—
252C4×C131—21no—
253C4×C131—21no—
254C4×C131—42no—
255C4×C131—81no—
256C4×C131—81no—
257C4×C131—82no—
258C4×C131—81no—
259C4×C131B(4,𝔽2)11yescharacteristic
260C4×C131B(4,𝔽2)11yescharacteristic
261C2×C131—21no—
262C2×C131—41no—
263C2×C131—41no—
264C2×C131—41no—
265C2×C131—82no—
266C2×C131—161no—
267C2×C131#202111yescharacteristic
268#13355C13111yesmaximal, characteristic, direct product factor, Sylow
269C131#1335511yescharacteristic, direct product factor, Sylow
270#3200C2×C13111yescharacteristic, complemented
271#3027C2×C13111yescharacteristic
272#3022C2×C13111yescharacteristic, complemented
273#2134C2×C13111yescharacteristic, complemented
274#2123C2×C13111yescharacteristic, complemented
275#1791C2×C13111yescharacteristic, complemented
276#1395C2×C13111yescharacteristic, complemented
277#585C22×C13111yescharacteristic
278C2×#137—21no—
279#536C22×C13111yescharacteristic
280#535—21no—
281#535C22×C13111yescharacteristic
282#485—21no—
283#482—21no—
284#468—21no—
285#465—21no—
286B(4,𝔽2)—22no—
287B(4,𝔽2)—22no—
288#456—22no—
289#455—22no—
290#450—21no—
291#448—21no—
292#421—21no—
293#413—21no—
294#413C22×C13111yescharacteristic
295#413C22×C13111yescharacteristic
296#410—21no—
297#410C22×C13111yescharacteristic
298#408—21no—
299#408C22×C13111yescharacteristic
300#355—22no—
301#352—22no—
3022−1+4—21no—
3032−1+4—41no—
304H(5,𝔽2)—21no—
305H(5,𝔽2)—21no—
306H(5,𝔽2)—41no—
307H(5,𝔽2)D4×C13112yes—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—42no—
312C2×#41C23×C13111yescharacteristic
313C22×Q8D4×C13111yescharacteristic, complemented
314C22×D4D4×C13111yescharacteristic
315#137—24no—
316#137—42no—
317C2×Q16—41no—
318C2×SD16—21no—
319C2×SD16—21no—
320C2×SD16—41no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16D4×C13111yescharacteristic, complemented
324C22×C8D4×C13111yescharacteristic, complemented
325C4⋊Q8—21no—
326#127—21no—
327#127—41no—
328#124—21no—
329#124—21no—
330#124—41no—
331#123—21no—
332#123—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335#121—21no—
336#121—21no—
337#121—42no—
338#120—24no—
339#120—21no—
340#120—21no—
341#117—21no—
342#117D4×C13111yescharacteristic
343#117D4×C13111yescharacteristic, complemented
344#107—21no—
345#106—21no—
346#104—24no—
347#103—21no—
348#103—21no—
349#102—21no—
350#102—21no—
351#101—21no—
352#101—41no—
353#101D4×C13112yescomplemented
354#100—21no—
355#100—21no—
356#100—41no—
357#99—24no—
358#99—21no—
359#99D4×C13112yes—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—42no—
363C24—21no—
364#41—22no—
365#41—22no—
366#41—41no—
367#41—41no—
368#41—42no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41—41no—
374#41—42no—
375#41—42no—
376#41—42no—
377#41—41no—
378#41—41no—
379#41—41no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—42no—
388C2×Q8C2×D4×C13111yescharacteristic
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—44no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4C2×D4×C13111yescharacteristic
406C2×D4C2×D4×C13111yescharacteristic
407C2×D4#41×C13111yescharacteristic
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4C2×D4×C13111yescharacteristic
413C22×C4C2×D4×C13111yescharacteristic
414C22×C4C2×D4×C13111yescharacteristic
415Q16—44no—
416SD16—44no—
417SD16—81no—
418SD16—81no—
419M16—22no—
420M16—41no—
421M16—41no—
422M16—41no—
423M16—41no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—21no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—44no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C42—21no—
443C42—21no—
444C42—41no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—42no—
449C23—41no—
450C23—161no—
451C23#120×C13111yescharacteristic
452C23#121×C13111yescharacteristic
453C23#121×C13111yescharacteristic
454Q8—22no—
455Q8—41no—
456Q8—41no—
457Q8—41no—
458Q8—42no—
459Q8—41no—
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—81no—
476D4—161no—
477D4—161no—
478D4—164no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—81no—
497C2×C4#120×C13111yescharacteristic
498C2×C4#120×C13111yescharacteristic
499C2×C4#121×C13111yescharacteristic
500C2×C4#127×C13111yescharacteristic
501C8—42no—
502C8—41no—
503C8—41no—
504C8—81no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—81no—
513C22—81no—
514C22—82no—
515C22—82no—
516C22—84no—
517C22—81no—
518C22—161no—
519C22#392×C13111yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—82no—
527C4—81no—
528C4B(4,𝔽2)×C13111yescharacteristic
529C4B(4,𝔽2)×C13111yescharacteristic
530C2—21no—
531C2—41no—
532C2—41no—
533C2—41no—
534C2—82no—
535C2—161no—
536C2#2021×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#2021
commutator, Frattini, cosocleC2×#41C23×C131
prime radical#3027×C131C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3200×C131C2semidirect
3. #3022×C131C2semidirect
4. #2134×C131C2semidirect
5. #2123×C131C2semidirect
6. #1791×C131C2semidirect
7. #1395×C131C2semidirect
44. C22×Q8×C131D4semidirect
54. C2×M16×C131D4semidirect
55. C22×C8×C131D4semidirect
74. #117×C131D4semidirect
84. #101×C131D4semidirect
268. #13355C131direct (N × H)
269. C131#13355direct (N × H)
270. #3200C2×C131semidirect
272. #3022C2×C131semidirect
273. #2134C2×C131semidirect
274. #2123C2×C131semidirect
275. #1791C2×C131semidirect
276. #1395C2×C131semidirect
313. C22×Q8D4×C131semidirect
323. C2×M16D4×C131semidirect
324. C22×C8D4×C131semidirect
343. #117D4×C131semidirect
353. #101D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3200×C1312
#3027×C1312
#3022×C1312
#2134×C1312
#2123×C1312
#1791×C1312
#1395×C1312
#13355131