Finite Group Databasebeta

← C131×#15068 #45700952

Subgroups — C131×#15068 #45700952

Order 33536.

1254 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C131C211yesmaximal, characteristic
2C2×#387×C131C211yesmaximal, characteristic
3#1444×C131C211yesmaximal, characteristic
4#1444×C131C212yesmaximal
5#1444×C131C211yesmaximal, characteristic
6#1442×C131C211yesmaximal, characteristic
7#1442×C131C211yesmaximal, characteristic
8#1441×C131C212yesmaximal
9#1436×C131C212yesmaximal
10C4⋊#95×C131C212yesmaximal
11C4×#95×C131C211yesmaximal, characteristic
12C22×C4⋊C4×C131C2211yescharacteristic
13C22×C4⋊C4×C131C2212yes—
14C22×C4⋊C4×C131C2211yescharacteristic
15C22×C4⋊C4×C131C2211yescharacteristic
16C22×C4⋊C4×C131C2212yes—
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2212yes—
19C22×C42×C131C2212yes—
20C22×C42×C131C2211yescharacteristic
21#389×C131—24no—
22#387×C131—24no—
23C2×#95×C131C2211yescharacteristic
24C2×#95×C131C2211yescharacteristic
25C2×#95×C131C2211yescharacteristic
26C2×#95×C131C2211yescharacteristic
27C2×#95×C131C2212yes—
28C2×#95×C131C2212yes—
29C2×#95×C131C2212yes—
30C2×#95×C131C2212yes—
31C2×#95×C131C2212yes—
32C2×#95×C131C2212yes—
33C2×#95×C131C2212yes—
34C2×#95×C131C2212yes—
35C2×#95×C131C2211yescharacteristic
36C2×#95×C131C2211yescharacteristic
37C23×C4×C131C2311yescharacteristic
38C23×C4×C131C2312yes—
39C23×C4×C131C2311yescharacteristic
40C23×C4×C131C2311yescharacteristic
41C23×C4×C131C2312yes—
42C23×C4×C131C2311yescharacteristic
43C23×C4×C131C2311yescharacteristic
44C23×C4×C131C2312yes—
45C23×C4×C131C2311yescharacteristic
46C23×C4×C131C2311yescharacteristic
47C23×C4×C131C2312yes—
48C2×C4⋊C4×C131—22no—
49C2×C4⋊C4×C131—22no—
50C2×C4⋊C4×C131—24no—
51C2×C4⋊C4×C131—22no—
52C2×C4⋊C4×C131—24no—
53C2×C4⋊C4×C131—22no—
54C2×C4⋊C4×C131—22no—
55C2×C4⋊C4×C131—24no—
56C2×C4⋊C4×C131—24no—
57C2×C4⋊C4×C131—24no—
58C2×C4⋊C4×C131—42no—
59C2×C4⋊C4×C131—42no—
60C2×C4⋊C4×C131—42no—
61C2×C4⋊C4×C131—42no—
62C2×C4⋊C4×C131—42no—
63C2×C4⋊C4×C131—42no—
64C2×C4⋊C4×C131—42no—
65C2×C4⋊C4×C131Q814yes—
66C2×C42×C131—24no—
67C2×C42×C131—24no—
68C2×C42×C131—42no—
69C2×C42×C131—42no—
70C2×C42×C131D414yes—
71#95×C131—24no—
72#95×C131—22no—
73#95×C131—22no—
74#95×C131—22no—
75#95×C131—22no—
76#95×C131—24no—
77#95×C131—24no—
78#95×C131—24no—
79#95×C131—24no—
80#95×C131—42no—
81#95×C131—42no—
82#95×C131—42no—
83#95×C131Q814yes—
84#95×C131Q814yes—
85C24×C131C2411yescharacteristic
86C22×C4×C131—22no—
87C22×C4×C131—22no—
88C22×C4×C131—22no—
89C22×C4×C131—22no—
90C22×C4×C131—22no—
91C22×C4×C131—22no—
92C22×C4×C131—22no—
93C22×C4×C131—22no—
94C22×C4×C131—21no—
95C22×C4×C131—21no—
96C22×C4×C131—22no—
97C22×C4×C131—22no—
98C22×C4×C131—22no—
99C22×C4×C131—22no—
100C22×C4×C131—22no—
101C22×C4×C131—22no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—22no—
115C22×C4×C131—21no—
116C22×C4×C131—21no—
117C22×C4×C131—22no—
118C22×C4×C131—21no—
119C22×C4×C131—21no—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131—22no—
125C22×C4×C131—22no—
126C22×C4×C131—21no—
127C22×C4×C131—21no—
128C22×C4×C131—22no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—22no—
133C22×C4×C131—21no—
134C22×C4×C131—21no—
135C22×C4×C131C2×D412yes—
136C22×C4×C131C2×D412yes—
137C22×C4×C131C2×D412yes—
138C22×C4×C131C2×Q814yes—
139C22×C4×C131C2×Q812yes—
140C22×C4×C131C2×Q812yes—
141C22×C4×C131C2×Q812yes—
142C22×C4×C131C2×Q814yes—
143C22×C4×C131C2×Q812yes—
144C22×C4×C131C2×Q812yes—
145C22×C4×C131#4114yes—
146C22×C4×C131#4112yes—
147C22×C4×C131#4114yes—
148C22×C4×C131#4114yes—
149C4⋊C4×C131—28no—
150C4⋊C4×C131—28no—
151C4⋊C4×C131—48no—
152C4⋊C4×C131—44no—
153C4⋊C4×C131—48no—
154C4⋊C4×C131—44no—
155C4⋊C4×C131—48no—
156C42×C131—44no—
157C42×C131—48no—
158C23×C131C22×D411yescharacteristic
159C23×C131C22×Q811yescharacteristic
160C23×C131C22×Q811yescharacteristic
161C23×C131C22×Q811yescharacteristic
162C23×C131C2×#4111yescharacteristic
163C23×C131C2×#4112yes—
164C23×C131C2×#4112yes—
165C23×C131C2×#4112yes—
166C23×C131H(5,𝔽2)12yes—
167C23×C131H(5,𝔽2)11yescharacteristic
168C23×C131H(5,𝔽2)11yescharacteristic
169C2×C4×C131—22no—
170C2×C4×C131—24no—
171C2×C4×C131—22no—
172C2×C4×C131—22no—
173C2×C4×C131—22no—
174C2×C4×C131—24no—
175C2×C4×C131—24no—
176C2×C4×C131—24no—
177C2×C4×C131—24no—
178C2×C4×C131—24no—
179C2×C4×C131—24no—
180C2×C4×C131—24no—
181C2×C4×C131—24no—
182C2×C4×C131—24no—
183C2×C4×C131—22no—
184C2×C4×C131—22no—
185C2×C4×C131—24no—
186C2×C4×C131—22no—
187C2×C4×C131—24no—
188C2×C4×C131—24no—
189C2×C4×C131—22no—
190C2×C4×C131—22no—
191C2×C4×C131—24no—
192C2×C4×C131—24no—
193C2×C4×C131—24no—
194C2×C4×C131—24no—
195C2×C4×C131—24no—
196C2×C4×C131—41no—
197C2×C4×C131—42no—
198C2×C4×C131—42no—
199C2×C4×C131—41no—
200C2×C4×C131—42no—
201C2×C4×C131—41no—
202C2×C4×C131—41no—
203C2×C4×C131—42no—
204C2×C4×C131—42no—
205C2×C4×C131—42no—
206C2×C4×C131—42no—
207C2×C4×C131—42no—
208C2×C4×C131—42no—
209C2×C4×C131—42no—
210C2×C4×C131—42no—
211C2×C4×C131—42no—
212C2×C4×C131—41no—
213C2×C4×C131—41no—
214C2×C4×C131—41no—
215C2×C4×C131—42no—
216C2×C4×C131—41no—
217C2×C4×C131—42no—
218C2×C4×C131—42no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—42no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—42no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131C22⋊Q814yes—
230C2×C4×C131#12518yes—
231C2×C4×C131C4⋊Q814yes—
232C22×C131C2×C22⋊Q811yescharacteristic
233C22×C131#52511yescharacteristic
234C22×C131C2×#12512yes—
235C22×C131#52912yes—
236C22×C131C2×C4⋊Q811yescharacteristic
237C22×C131#53211yescharacteristic
238C22×C131#53211yescharacteristic
239C22×C131#53312yes—
240C22×C131#53312yes—
241C22×C131#53411yescharacteristic
242C22×C131#53511yescharacteristic
243C22×C131#53812yes—
244C22×C131#54012yes—
245C22×C131#55112yes—
246C22×C131#55112yes—
247C22×C131#55312yes—
248C22×C131#55412yes—
249C22×C131#55411yescharacteristic
250C22×C131#55411yescharacteristic
251C22×C131#55412yes—
252C22×C131#55412yes—
253C22×C131Q8211yescharacteristic
254C22×C131Q8211yescharacteristic
255C4×C131—24no—
256C4×C131—24no—
257C4×C131—28no—
258C4×C131—42no—
259C4×C131—44no—
260C4×C131—42no—
261C4×C131—42no—
262C4×C131—44no—
263C4×C131—81no—
264C4×C131—82no—
265C4×C131—81no—
266C2×C131#239611yescharacteristic
267C2×C131#250512yes—
268C2×C131#250712yes—
269C2×C131#252212yes—
270C2×C131#256411yescharacteristic
271C2×C131#256711yescharacteristic
272C2×C131#258311yescharacteristic
273C2×C131#258612yes—
274C2×C131#260311yescharacteristic
275C2×C131#266111yescharacteristic
276C2×C131#285911yescharacteristic
277#15068C13111yesmaximal, characteristic, direct product factor, Sylow
278C131#1506811yescharacteristic, direct product factor, Sylow
279C2×#389C2×C13111yescharacteristic
280C2×#387C2×C13111yescharacteristic
281#1444C2×C13111yescharacteristic
282#1444C2×C13111yescharacteristic
283#1444C2×C13112yes—
284#1442C2×C13111yescharacteristic
285#1442C2×C13111yescharacteristic
286#1441C2×C13112yes—
287#1436C2×C13112yes—
288C4⋊#95C2×C13112yes—
289C4×#95C2×C13111yescharacteristic
290C22×C4⋊C4C22×C13111yescharacteristic
291C22×C4⋊C4C22×C13112yes—
292C22×C4⋊C4C22×C13111yescharacteristic
293C22×C4⋊C4C22×C13112yes—
294C22×C4⋊C4C22×C13112yes—
295C22×C4⋊C4C22×C13111yescharacteristic
296C22×C4⋊C4C22×C13111yescharacteristic
297C22×C42C22×C13112yes—
298C22×C42C22×C13111yescharacteristic
299#389—24no—
300#387—24no—
301C2×#95C22×C13112yes—
302C2×#95C22×C13111yescharacteristic
303C2×#95C22×C13112yes—
304C2×#95C22×C13112yes—
305C2×#95C22×C13112yes—
306C2×#95C22×C13112yes—
307C2×#95C22×C13111yescharacteristic
308C2×#95C22×C13111yescharacteristic
309C2×#95C22×C13111yescharacteristic
310C2×#95C22×C13112yes—
311C2×#95C22×C13112yes—
312C2×#95C22×C13112yes—
313C2×#95C22×C13111yescharacteristic
314C2×#95C22×C13111yescharacteristic
315C23×C4C23×C13111yescharacteristic
316C23×C4C23×C13112yes—
317C23×C4C23×C13111yescharacteristic
318C23×C4C23×C13111yescharacteristic
319C23×C4C23×C13111yescharacteristic
320C23×C4C23×C13111yescharacteristic
321C23×C4C23×C13112yes—
322C23×C4C23×C13112yes—
323C23×C4C23×C13111yescharacteristic
324C23×C4C23×C13111yescharacteristic
325C23×C4C23×C13112yes—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4Q8×C13114yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42D4×C13114yes—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95Q8×C13114yes—
362#95Q8×C13114yes—
363C24C24×C13111yescharacteristic
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×D4×C13112yes—
414C22×C4C2×D4×C13112yes—
415C22×C4C2×D4×C13112yes—
416C22×C4C2×Q8×C13114yes—
417C22×C4C2×Q8×C13112yes—
418C22×C4C2×Q8×C13112yes—
419C22×C4C2×Q8×C13112yes—
420C22×C4C2×Q8×C13114yes—
421C22×C4C2×Q8×C13112yes—
422C22×C4C2×Q8×C13112yes—
423C22×C4#41×C13114yes—
424C22×C4#41×C13112yes—
425C22×C4#41×C13114yes—
426C22×C4#41×C13114yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—48no—
430C4⋊C4—44no—
431C4⋊C4—48no—
432C4⋊C4—44no—
433C4⋊C4—48no—
434C42—44no—
435C42—48no—
436C23C22×D4×C13111yescharacteristic
437C23C22×Q8×C13111yescharacteristic
438C23C22×Q8×C13111yescharacteristic
439C23C22×Q8×C13111yescharacteristic
440C23C2×#41×C13111yescharacteristic
441C23C2×#41×C13112yes—
442C23C2×#41×C13112yes—
443C23C2×#41×C13112yes—
444C23H(5,𝔽2)×C13112yes—
445C23H(5,𝔽2)×C13111yescharacteristic
446C23H(5,𝔽2)×C13111yescharacteristic
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4C22⋊Q8×C13114yes—
508C2×C4#125×C13118yes—
509C2×C4C4⋊Q8×C13114yes—
510C22C2×C22⋊Q8×C13111yescharacteristic
511C22#525×C13111yescharacteristic
512C22C2×#125×C13112yes—
513C22#529×C13112yes—
514C22C2×C4⋊Q8×C13111yescharacteristic
515C22#532×C13111yescharacteristic
516C22#532×C13111yescharacteristic
517C22#533×C13112yes—
518C22#533×C13112yes—
519C22#534×C13111yescharacteristic
520C22#535×C13111yescharacteristic
521C22#538×C13112yes—
522C22#540×C13112yes—
523C22#551×C13112yes—
524C22#551×C13112yes—
525C22#553×C13112yes—
526C22#554×C13111yescharacteristic
527C22#554×C13112yes—
528C22#554×C13112yes—
529C22#554×C13111yescharacteristic
530C22#554×C13112yes—
531C22Q82×C13111yescharacteristic
532C22Q82×C13111yescharacteristic
533C4—28no—
534C4—24no—
535C4—24no—
536C4—44no—
537C4—42no—
538C4—44no—
539C4—42no—
540C4—42no—
541C4—81no—
542C4—82no—
543C4—81no—
544C2#2396×C13111yescharacteristic
545C2#2505×C13112yes—
546C2#2507×C13112yes—
547C2#2522×C13112yes—
548C2#2564×C13111yescharacteristic
549C2#2567×C13111yescharacteristic
550C2#2583×C13111yescharacteristic
551C2#2586×C13112yes—
552C2#2603×C13111yescharacteristic
553C2#2661×C13111yescharacteristic
554C2#2859×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C131C24
commutator, Frattini, cosocleC24C24×C131
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
277. #15068C131direct (N × H)
278. C131#15068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1312
C2×#387×C1312
#1444×C1312
#1442×C1312
#1441×C1312
#1436×C1312
C4⋊#95×C1312
C4×#95×C1312
#15068131