Finite Group Databasebeta

← C131×#12705 #45698589

Subgroups — C131×#12705 #45698589

Order 33536.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 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#3484×C131C211yesmaximal, characteristic
2#2121×C131C214yesmaximal, complemented
3#1783×C131C211yesmaximal, characteristic, complemented
4#1781×C131C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C131C411yescharacteristic, complemented
6C23×D4×C131C2211yescharacteristic
7#546×C131—24no—
8D42×C131—24no—
9#535×C131—21no—
10#534×C131—21no—
11#534×C131C2212yes—
12#525×C131—21no—
13C2×#120×C131—21no—
14C2×#120×C131C412yescomplemented
15#518×C131C411yescharacteristic, complemented
16C2×#100×C131—21no—
17C2×#100×C131C2212yescomplemented
18C2×#99×C131—21no—
19C2×#99×C131C2212yescomplemented
20#407×C131—21no—
21#379×C131—21no—
22#352×C131—24no—
23AΣL(1,𝔽16)×C131—24no—
24C25×C131C2×C411yescharacteristic
25C25×C131D411yescharacteristic
26H(5,𝔽2)×C131—42no—
27H(5,𝔽2)×C131—42no—
28C2×#41×C131—21no—
29C2×#41×C131—22no—
30C22×D4×C131—21no—
31C22×D4×C131—22no—
32C22×D4×C131—22no—
33C22×D4×C131—22no—
34C22×D4×C131—24no—
35C22×D4×C131—42no—
36C22×D4×C131—42no—
37C22×D4×C131C2×C411yescharacteristic
38C22×D4×C131C2×C412yes—
39C22×D4×C131D411yescharacteristic
40C22×D4×C131D411yescharacteristic
41C22×D4×C131C2311yescharacteristic
42C23×C4×C131D411yescharacteristic
43C2×M16×C131—22no—
44#127×C131—22no—
45#124×C131—22no—
46#123×C131—22no—
47#123×C131—22no—
48#123×C131D414yes—
49C22⋊Q8×C131—22no—
50#121×C131—22no—
51#121×C131—24no—
52#121×C131—24no—
53#121×C131—24no—
54#120×C131—24no—
55#120×C131—22no—
56#120×C131—22no—
57#120×C131—22no—
58#120×C131—22no—
59#120×C131—24no—
60#120×C131D414yes—
61C4×D4×C131—24no—
62C4×D4×C131—24no—
63#117×C131—21no—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—22no—
67C2×C22⋊C4×C131—22no—
68C2×C22⋊C4×C131—42no—
69C2×C22⋊C4×C131C2×C412yes—
70#100×C131—24no—
71#100×C131—42no—
72#99×C131—24no—
73#99×C131—42no—
74C22⋊C8×C131—42no—
75C24×C131—21no—
76C24×C131—22no—
77C24×C131—22no—
78C24×C131—22no—
79C24×C131—41no—
80C24×C131—41no—
81C24×C131—41no—
82C24×C131—82no—
83C24×C131—82no—
84C24×C131C22⋊C411yescharacteristic
85C24×C131C22⋊C411yescharacteristic
86C24×C131C22⋊C411yescharacteristic
87C24×C131C22⋊C412yescomplemented
88C24×C131C22×C411yescharacteristic
89C24×C131C2×D411yescharacteristic
90#41×C131—42no—
91#41×C131—48no—
92#41×C131—42no—
93C2×Q8×C131—21no—
94C2×D4×C131—22no—
95C2×D4×C131—22no—
96C2×D4×C131—24no—
97C2×D4×C131—22no—
98C2×D4×C131—21no—
99C2×D4×C131—22no—
100C2×D4×C131—22no—
101C2×D4×C131—22no—
102C2×D4×C131—22no—
103C2×D4×C131—24no—
104C2×D4×C131—24no—
105C2×D4×C131—22no—
106C2×D4×C131—22no—
107C2×D4×C131—22no—
108C2×D4×C131—41no—
109C2×D4×C131—41no—
110C2×D4×C131—41no—
111C2×D4×C131—41no—
112C2×D4×C131—416no—
113C2×D4×C131—48no—
114C2×D4×C131—42no—
115C2×D4×C131—42no—
116C2×D4×C131—42no—
117C2×D4×C131—42no—
118C2×D4×C131—84no—
119C2×D4×C131—84no—
120C2×D4×C131C2×D414yes—
121C22×C4×C131—21no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131—22no—
125C22×C4×C131—22no—
126C22×C4×C131—22no—
127C22×C4×C131—41no—
128C22×C4×C131—42no—
129C22×C4×C131C22⋊C411yescharacteristic
130C22×C4×C131C22⋊C412yescomplemented
131C22×C4×C131C2×D411yescharacteristic
132M16×C131—42no—
133M16×C131—42no—
134C2×C8×C131—42no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—24no—
137C22⋊C4×C131—24no—
138C22⋊C4×C131—22no—
139C22⋊C4×C131—24no—
140C22⋊C4×C131—22no—
141C22⋊C4×C131—24no—
142C22⋊C4×C131—24no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—42no—
145C22⋊C4×C131—84no—
146C22⋊C4×C131C22⋊C414yescomplemented
147C42×C131—22no—
148C23×C131—21no—
149C23×C131—21no—
150C23×C131—21no—
151C23×C131—21no—
152C23×C131—21no—
153C23×C131—21no—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—21no—
157C23×C131—21no—
158C23×C131—22no—
159C23×C131—21no—
160C23×C131—21no—
161C23×C131—42no—
162C23×C131—44no—
163C23×C131—44no—
164C23×C131—44no—
165C23×C131—44no—
166C23×C131—44no—
167C23×C131—42no—
168C23×C131—42no—
169C23×C131—82no—
170C23×C131—82no—
171C23×C131—82no—
172C23×C131—81no—
173C23×C131—81no—
174C23×C131—81no—
175C23×C131—81no—
176C23×C131—82no—
177C23×C131—82no—
178C23×C131—82no—
179C23×C131—82no—
180C23×C131—82no—
181C23×C131—82no—
182C23×C131—82no—
183C23×C131—82no—
184C23×C131#9912yes—
185C23×C131C2×C22⋊C412yes—
186C23×C131C2×C22⋊C411yescharacteristic
187C23×C131#12012yes—
188Q8×C131—42no—
189D4×C131—28no—
190D4×C131—44no—
191D4×C131—44no—
192D4×C131—44no—
193D4×C131—42no—
194D4×C131—44no—
195D4×C131—44no—
196D4×C131—48no—
197D4×C131—42no—
198D4×C131—42no—
199D4×C131—84no—
200D4×C131—84no—
201C2×C4×C131—21no—
202C2×C4×C131—21no—
203C2×C4×C131—21no—
204C2×C4×C131—21no—
205C2×C4×C131—24no—
206C2×C4×C131—22no—
207C2×C4×C131—44no—
208C2×C4×C131—44no—
209C2×C4×C131—42no—
210C2×C4×C131—42no—
211C2×C4×C131—82no—
212C2×C4×C131—82no—
213C2×C4×C131—82no—
214C2×C4×C131—84no—
215C2×C4×C131#9912yes—
216C2×C4×C131#12012yes—
217C8×C131—82no—
218C22×C131—22no—
219C22×C131—22no—
220C22×C131—22no—
221C22×C131—22no—
222C22×C131—22no—
223C22×C131—22no—
224C22×C131—41no—
225C22×C131—42no—
226C22×C131—42no—
227C22×C131—42no—
228C22×C131—42no—
229C22×C131—42no—
230C22×C131—41no—
231C22×C131—41no—
232C22×C131—41no—
233C22×C131—44no—
234C22×C131—42no—
235C22×C131—41no—
236C22×C131—42no—
237C22×C131—41no—
238C22×C131—81no—
239C22×C131—81no—
240C22×C131—81no—
241C22×C131—81no—
242C22×C131—81no—
243C22×C131—81no—
244C22×C131—88no—
245C22×C131—88no—
246C22×C131—162no—
247C22×C131—162no—
248C22×C131#37911yescharacteristic
249C22×C131C2×#9911yescharacteristic
250C22×C131C2×#9911yescharacteristic
251C4×C131—22no—
252C4×C131—22no—
253C4×C131—44no—
254C4×C131—42no—
255C4×C131—162no—
256C2×C131—21no—
257C2×C131—21no—
258C2×C131—21no—
259C2×C131—42no—
260C2×C131—42no—
261C2×C131—42no—
262C2×C131—42no—
263C2×C131—81no—
264C2×C131—82no—
265C2×C131#178111yescharacteristic
266#12705C13111yesmaximal, characteristic, direct product factor, Sylow
267C131#1270511yescharacteristic, direct product factor, Sylow
268#3484C2×C13111yescharacteristic
269#2121C2×C13114yescomplemented
270#1783C2×C13111yescharacteristic, complemented
271#1781C2×C13111yescharacteristic, complemented
272C2×H(5,𝔽2)C4×C13111yescharacteristic, complemented
273C23×D4C22×C13111yescharacteristic
274#546—24no—
275D42—24no—
276#535—21no—
277#534—21no—
278#534C22×C13112yes—
279#525—21no—
280C2×#120—21no—
281C2×#120C4×C13112yescomplemented
282#518C4×C13111yescharacteristic, complemented
283C2×#100—21no—
284C2×#100C22×C13112yescomplemented
285C2×#99—21no—
286C2×#99C22×C13112yescomplemented
287#407—21no—
288#379—21no—
289#352—24no—
290AΣL(1,𝔽16)—24no—
291C25C2×C4×C13111yescharacteristic
292C25D4×C13111yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C13111yescharacteristic
305C22×D4C2×C4×C13112yes—
306C22×D4D4×C13111yescharacteristic
307C22×D4D4×C13111yescharacteristic
308C22×D4C23×C13111yescharacteristic
309C23×C4D4×C13111yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C13114yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C13114yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C13112yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C13111yescharacteristic
352C24C22⋊C4×C13111yescharacteristic
353C24C22⋊C4×C13111yescharacteristic
354C24C22⋊C4×C13112yescomplemented
355C24C22×C4×C13111yescharacteristic
356C24C2×D4×C13111yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C13114yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C13111yescharacteristic
397C22×C4C22⋊C4×C13112yescomplemented
398C22×C4C2×D4×C13111yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C13114yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C13112yes—
452C23C2×C22⋊C4×C13112yes—
453C23C2×C22⋊C4×C13111yescharacteristic
454C23#120×C13112yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C13112yes—
483C2×C4#120×C13112yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22#379×C13111yescharacteristic
516C22C2×#99×C13111yescharacteristic
517C22C2×#99×C13111yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2#1781×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1781
commutatorC24C22×C4×C131
Frattini, cosocleC22×D4C23×C131
prime radical#3484×C131C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C23×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2121×C131C2semidirect
3. #1783×C131C2semidirect
4. #1781×C131C2semidirect
5. C2×H(5,𝔽2)×C131C4semidirect
14. C2×#120×C131C4semidirect
15. #518×C131C4semidirect
17. C2×#100×C131C22semidirect
19. C2×#99×C131C22semidirect
87. C24×C131C22⋊C4semidirect
130. C22×C4×C131C22⋊C4semidirect
146. C22⋊C4×C131C22⋊C4semidirect
266. #12705C131direct (N × H)
267. C131#12705direct (N × H)
269. #2121C2×C131semidirect
270. #1783C2×C131semidirect
271. #1781C2×C131semidirect
272. C2×H(5,𝔽2)C4×C131semidirect
281. C2×#120C4×C131semidirect
282. #518C4×C131semidirect
284. C2×#100C22×C131semidirect
286. C2×#99C22×C131semidirect
354. C24C22⋊C4×C131semidirect
397. C22×C4C22⋊C4×C131semidirect
413. C22⋊C4C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
#2121×C1312
#1783×C1312
#1781×C1312
#12705131