Finite Group Databasebeta

← C131×#25210 #45711094

Subgroups — C131×#25210 #45711094

Order 33536.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C131C211yesmaximal, characteristic, complemented
2C2×#465×C131C211yesmaximal, characteristic
3#2504×C131C211yesmaximal, characteristic
4#2360×C131C211yesmaximal, characteristic, complemented
5#2085×C131C211yesmaximal, characteristic, complemented
6#2074×C131C211yesmaximal, characteristic, complemented
7#2067×C131C211yesmaximal, characteristic, complemented
8#2055×C131C211yesmaximal, characteristic, complemented
9#1949×C131C211yesmaximal, characteristic, complemented
10#1925×C131C211yesmaximal, characteristic, complemented
11#1880×C131C211yesmaximal, characteristic, complemented
12#1874×C131C211yesmaximal, characteristic
13#1850×C131C211yesmaximal, characteristic, complemented
14#1805×C131C211yesmaximal, characteristic, complemented
15C2×#340×C131C211yesmaximal, characteristic, complemented
16C22×SD16×C131C2211yescharacteristic
17C23×C8×C131C2211yescharacteristic
18C2×C22⋊Q8×C131C2211yescharacteristic
19C2×#121×C131C2211yescharacteristic
20C2×C4×Q8×C131C2211yescharacteristic
21C22×C4⋊C4×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2211yescharacteristic
23#484×C131—24no—
24#465×C131—24no—
25C2×#107×C131C2211yescharacteristic
26C2×#107×C131C2211yescharacteristic
27C2×#106×C131C2211yescharacteristic
28C2×C4⋊C8×C131C2211yescharacteristic
29C2×C4⋊C8×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#102×C131C2211yescharacteristic
34C2×#102×C131C2211yescharacteristic
35C2×#102×C131C2211yescharacteristic
36C2×C22⋊C8×C131C2211yescharacteristic
37#397×C131—21no—
38#397×C131—21no—
39#391×C131C2211yescharacteristic
40#390×C131C2211yescharacteristic
41#390×C131C2211yescharacteristic
42#389×C131—21no—
43#389×C131C2211yescharacteristic
44#387×C131—21no—
45#386×C131—21no—
46#386×C131—21no—
47#385×C131—21no—
48#382×C131C2211yescharacteristic
49#382×C131C2211yescharacteristic
50C4×C4⋊C4×C131C2211yescharacteristic
51C4×C22⋊C4×C131—21no—
52C4×C22⋊C4×C131C2211yescharacteristic
53#340×C131C2211yescharacteristic
54#340×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61C22×Q8×C131C2311yescharacteristic
62C22×D4×C131—21no—
63C22×D4×C131C2311yescharacteristic
64C23×C4×C131—21no—
65C23×C4×C131—21no—
66C23×C4×C131C2311yescharacteristic
67C2×SD16×C131—22no—
68C2×SD16×C131—22no—
69C2×SD16×C131—41no—
70C22×C8×C131—22no—
71C22×C8×C131—22no—
72C22×C8×C131—41no—
73C22×C8×C131C2311yescharacteristic
74C22×C8×C131C2311yescharacteristic
75C22×C8×C131C2311yescharacteristic
76C22×C8×C131C2311yescharacteristic
77C22⋊Q8×C131—22no—
78C22⋊Q8×C131D414yes—
79#121×C131—22no—
80#121×C131—22no—
81C4×Q8×C131—22no—
82C4×Q8×C131—41no—
83C2×C4⋊C4×C131—21no—
84C2×C4⋊C4×C131—22no—
85C2×C4⋊C4×C131—22no—
86C2×C4⋊C4×C131—22no—
87C2×C4⋊C4×C131—21no—
88C2×C4⋊C4×C131—21no—
89C2×C4⋊C4×C131—21no—
90C2×C4⋊C4×C131—21no—
91C2×C4⋊C4×C131—41no—
92C2×C4⋊C4×C131C2311yescharacteristic
93C2×C4⋊C4×C131C2311yescharacteristic
94C2×C4⋊C4×C131C2311yescharacteristic
95C2×C4⋊C4×C131C2311yescharacteristic
96C2×C4⋊C4×C131C2311yescharacteristic
97C2×C4⋊C4×C131C2311yescharacteristic
98C2×C22⋊C4×C131—21no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—21no—
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—21no—
104C2×C22⋊C4×C131D411yescharacteristic
105C2×C22⋊C4×C131D411yescharacteristic
106C2×C42×C131—21no—
107C2×C42×C131—21no—
108C2×C42×C131C2311yescharacteristic
109C2×C42×C131C2311yescharacteristic
110#107×C131—22no—
111#107×C131—22no—
112#106×C131—22no—
113C4⋊C8×C131—22no—
114C4⋊C8×C131—41no—
115#103×C131—22no—
116#103×C131—22no—
117#103×C131—22no—
118#102×C131—22no—
119#102×C131—22no—
120#102×C131—41no—
121C22⋊C8×C131—22no—
122#95×C131—21no—
123#95×C131—21no—
124#95×C131—21no—
125#95×C131—21no—
126#95×C131—21no—
127#95×C131—21no—
128#95×C131—21no—
129#95×C131—21no—
130#95×C131D411yescharacteristic
131#95×C131D411yescharacteristic
132C24×C131—21no—
133C24×C131C2×D411yescharacteristic
134C2×Q8×C131—21no—
135C2×Q8×C131—21no—
136C2×Q8×C131—21no—
137C2×Q8×C131—21no—
138C2×Q8×C131—21no—
139C2×Q8×C131C2×D412yes—
140C2×D4×C131—21no—
141C2×D4×C131—21no—
142C2×D4×C131—21no—
143C2×D4×C131—21no—
144C2×D4×C131—21no—
145C2×D4×C131—21no—
146C2×D4×C131—42no—
147C2×D4×C131—42no—
148C2×D4×C131—42no—
149C22×C4×C131—21no—
150C22×C4×C131—21no—
151C22×C4×C131—21no—
152C22×C4×C131—21no—
153C22×C4×C131—21no—
154C22×C4×C131—21no—
155C22×C4×C131—21no—
156C22×C4×C131—21no—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—42no—
161C22×C4×C131—42no—
162C22×C4×C131—42no—
163C22×C4×C131—81no—
164C22×C4×C131—81no—
165C22×C4×C131—81no—
166C22×C4×C131C2×D411yescharacteristic
167C22×C4×C131C2×D411yescharacteristic
168C22×C4×C131C2×D411yescharacteristic
169C22×C4×C131C2×D411yescharacteristic
170C22×C4×C131C2×D411yescharacteristic
171C22×C4×C131C2×D412yes—
172C22×C4×C131#4112yes—
173C22×C4×C131C2411yescharacteristic
174SD16×C131—44no—
175C2×C8×C131—21no—
176C2×C8×C131—21no—
177C2×C8×C131—21no—
178C2×C8×C131—21no—
179C2×C8×C131—21no—
180C2×C8×C131—21no—
181C2×C8×C131—21no—
182C2×C8×C131—21no—
183C2×C8×C131—21no—
184C2×C8×C131—21no—
185C2×C8×C131—21no—
186C2×C8×C131—44no—
187C2×C8×C131#4112yes—
188C4⋊C4×C131—24no—
189C4⋊C4×C131—21no—
190C4⋊C4×C131—21no—
191C4⋊C4×C131—21no—
192C4⋊C4×C131—21no—
193C4⋊C4×C131—21no—
194C4⋊C4×C131—21no—
195C4⋊C4×C131—21no—
196C4⋊C4×C131—21no—
197C4⋊C4×C131—21no—
198C4⋊C4×C131—21no—
199C4⋊C4×C131—42no—
200C4⋊C4×C131—42no—
201C4⋊C4×C131—42no—
202C4⋊C4×C131—81no—
203C4⋊C4×C131C2×D412yes—
204C4⋊C4×C131#4112yes—
205C22⋊C4×C131—24no—
206C22⋊C4×C131—22no—
207C22⋊C4×C131—22no—
208C22⋊C4×C131—42no—
209C22⋊C4×C131—81no—
210C22⋊C4×C131—81no—
211C22⋊C4×C131—81no—
212C22⋊C4×C131—81no—
213C42×C131—21no—
214C42×C131—21no—
215C42×C131—21no—
216C42×C131—21no—
217C42×C131—42no—
218C42×C131—81no—
219C23×C131—21no—
220C23×C131—21no—
221C23×C131—21no—
222C23×C131—21no—
223C23×C131—41no—
224C23×C131—41no—
225C23×C131—41no—
226C23×C131—41no—
227C23×C131—41no—
228C23×C131—41no—
229C23×C131—41no—
230C23×C131#12112yes—
231C23×C131#13512yes—
232C23×C131#13712yes—
233C23×C131C22×D411yescharacteristic
234Q8×C131—22no—
235Q8×C131—22no—
236Q8×C131—41no—
237Q8×C131—41no—
238D4×C131—41no—
239D4×C131—41no—
240D4×C131—41no—
241D4×C131—41no—
242D4×C131—84no—
243C2×C4×C131—21no—
244C2×C4×C131—21no—
245C2×C4×C131—22no—
246C2×C4×C131—22no—
247C2×C4×C131—22no—
248C2×C4×C131—22no—
249C2×C4×C131—22no—
250C2×C4×C131—22no—
251C2×C4×C131—21no—
252C2×C4×C131—21no—
253C2×C4×C131—22no—
254C2×C4×C131—21no—
255C2×C4×C131—21no—
256C2×C4×C131—21no—
257C2×C4×C131—21no—
258C2×C4×C131—21no—
259C2×C4×C131—21no—
260C2×C4×C131—21no—
261C2×C4×C131—21no—
262C2×C4×C131—21no—
263C2×C4×C131—21no—
264C2×C4×C131—41no—
265C2×C4×C131—41no—
266C2×C4×C131—41no—
267C2×C4×C131—41no—
268C2×C4×C131—41no—
269C2×C4×C131—41no—
270C2×C4×C131—41no—
271C2×C4×C131—41no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—41no—
278C2×C4×C131—41no—
279C2×C4×C131—41no—
280C2×C4×C131—41no—
281C2×C4×C131—41no—
282C2×C4×C131—84no—
283C2×C4×C131—84no—
284C2×C4×C131#12112yes—
285C2×C4×C131C22×D411yescharacteristic
286C2×C4×C131C2×#4111yescharacteristic
287C2×C4×C131C2×#4111yescharacteristic
288C2×C4×C131C2×#4111yescharacteristic
289C2×C4×C131H(5,𝔽2)11yescharacteristic
290C2×C4×C1312−1+411yescharacteristic
291C8×C131—22no—
292C8×C131—41no—
293C8×C131—41no—
294C8×C131—41no—
295C22×C131—22no—
296C22×C131—22no—
297C22×C131—22no—
298C22×C131—22no—
299C22×C131—22no—
300C22×C131—22no—
301C22×C131—81no—
302C22×C131—81no—
303C22×C131—81no—
304C22×C131—81no—
305C22×C131—81no—
306C22×C131—81no—
307C22×C131—81no—
308C22×C131#46414yes—
309C22×C131C2×#12111yescharacteristic
310C22×C131#54611yescharacteristic
311C22×C131#54711yescharacteristic
312C22×C131C2×#13511yescharacteristic
313C22×C131C2×#13711yescharacteristic
314C22×C131#57611yescharacteristic
315C22×C131#57711yescharacteristic
316C4×C131—22no—
317C4×C131—41no—
318C4×C131—41no—
319C4×C131—42no—
320C4×C131—41no—
321C4×C131—42no—
322C4×C131—42no—
323C4×C131—41no—
324C4×C131—81no—
325C4×C131—81no—
326C4×C131—81no—
327C4×C131—81no—
328C4×C131#52911yescharacteristic
329C4×C131#53911yescharacteristic
330C4×C131#54611yescharacteristic
331C4×C131#54711yescharacteristic
332C2×C131—24no—
333C2×C131—161no—
334C2×C131#242511yescharacteristic
335C2×C131C2×#46411yescharacteristic
336C2×C131#304511yescharacteristic
337C2×C131#329711yescharacteristic
338C2×C131#332011yescharacteristic
339C2×C131#333711yescharacteristic
340C2×C131#334611yescharacteristic
341#25210C13111yesmaximal, characteristic, direct product factor, Sylow
342C131#2521011yescharacteristic, direct product factor, Sylow
343C2×#484C2×C13111yescharacteristic, complemented
344C2×#465C2×C13111yescharacteristic
345#2504C2×C13111yescharacteristic
346#2360C2×C13111yescharacteristic, complemented
347#2085C2×C13111yescharacteristic, complemented
348#2074C2×C13111yescharacteristic, complemented
349#2067C2×C13111yescharacteristic, complemented
350#2055C2×C13111yescharacteristic, complemented
351#1949C2×C13111yescharacteristic, complemented
352#1925C2×C13111yescharacteristic, complemented
353#1880C2×C13111yescharacteristic, complemented
354#1874C2×C13111yescharacteristic
355#1850C2×C13111yescharacteristic, complemented
356#1805C2×C13111yescharacteristic, complemented
357C2×#340C2×C13111yescharacteristic, complemented
358C22×SD16C22×C13111yescharacteristic
359C23×C8C22×C13111yescharacteristic
360C2×C22⋊Q8C22×C13111yescharacteristic
361C2×#121C22×C13111yescharacteristic
362C2×C4×Q8C22×C13111yescharacteristic
363C22×C4⋊C4C22×C13111yescharacteristic
364C22×C4⋊C4C22×C13111yescharacteristic
365#484—24no—
366#465—24no—
367C2×#107C22×C13111yescharacteristic
368C2×#107C22×C13111yescharacteristic
369C2×#106C22×C13111yescharacteristic
370C2×C4⋊C8C22×C13111yescharacteristic
371C2×C4⋊C8C22×C13111yescharacteristic
372C2×#103C22×C13111yescharacteristic
373C2×#103C22×C13111yescharacteristic
374C2×#103C22×C13111yescharacteristic
375C2×#102C22×C13111yescharacteristic
376C2×#102C22×C13111yescharacteristic
377C2×#102C22×C13111yescharacteristic
378C2×C22⋊C8C22×C13111yescharacteristic
379#397—21no—
380#397—21no—
381#391C22×C13111yescharacteristic
382#390C22×C13111yescharacteristic
383#390C22×C13111yescharacteristic
384#389—21no—
385#389C22×C13111yescharacteristic
386#387—21no—
387#386—21no—
388#386—21no—
389#385—21no—
390#382C22×C13111yescharacteristic
391#382C22×C13111yescharacteristic
392C4×C4⋊C4C22×C13111yescharacteristic
393C4×C22⋊C4—21no—
394C4×C22⋊C4C22×C13111yescharacteristic
395#340C22×C13111yescharacteristic
396#340C22×C13111yescharacteristic
397#340C22×C13111yescharacteristic
398#340C22×C13111yescharacteristic
399#340C22×C13111yescharacteristic
400#340C22×C13111yescharacteristic
401#336C22×C13111yescharacteristic
402#336C22×C13111yescharacteristic
403C22×Q8C23×C13111yescharacteristic
404C22×D4—21no—
405C22×D4C23×C13111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C13111yescharacteristic
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—41no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—41no—
415C22×C8C23×C13111yescharacteristic
416C22×C8C23×C13111yescharacteristic
417C22×C8C23×C13111yescharacteristic
418C22×C8C23×C13111yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8D4×C13114yes—
421#121—22no—
422#121—22no—
423C4×Q8—22no—
424C4×Q8—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4C23×C13111yescharacteristic
435C2×C4⋊C4C23×C13111yescharacteristic
436C2×C4⋊C4C23×C13111yescharacteristic
437C2×C4⋊C4C23×C13111yescharacteristic
438C2×C4⋊C4C23×C13111yescharacteristic
439C2×C4⋊C4C23×C13111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4D4×C13111yescharacteristic
447C2×C22⋊C4D4×C13111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C13111yescharacteristic
451C2×C42C23×C13111yescharacteristic
452#107—22no—
453#107—22no—
454#106—22no—
455C4⋊C8—22no—
456C4⋊C8—41no—
457#103—22no—
458#103—22no—
459#103—22no—
460#102—22no—
461#102—22no—
462#102—41no—
463C22⋊C8—22no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C13111yescharacteristic
473#95D4×C13111yescharacteristic
474C24—21no—
475C24C2×D4×C13111yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×D4×C13112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4C2×D4×C13111yescharacteristic
509C22×C4C2×D4×C13111yescharacteristic
510C22×C4C2×D4×C13111yescharacteristic
511C22×C4C2×D4×C13111yescharacteristic
512C22×C4C2×D4×C13111yescharacteristic
513C22×C4C2×D4×C13112yes—
514C22×C4#41×C13112yes—
515C22×C4C24×C13111yescharacteristic
516SD16—44no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—44no—
529C2×C8#41×C13112yes—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4C2×D4×C13112yes—
546C4⋊C4#41×C13112yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—81no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23#121×C13112yes—
573C23#135×C13112yes—
574C23#137×C13112yes—
575C23C22×D4×C13111yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—84no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4#121×C13112yes—
627C2×C4C22×D4×C13111yescharacteristic
628C2×C4C2×#41×C13111yescharacteristic
629C2×C4C2×#41×C13111yescharacteristic
630C2×C4C2×#41×C13111yescharacteristic
631C2×C4H(5,𝔽2)×C13111yescharacteristic
632C2×C42−1+4×C13111yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22#464×C13114yes—
651C22C2×#121×C13111yescharacteristic
652C22#546×C13111yescharacteristic
653C22#547×C13111yescharacteristic
654C22C2×#135×C13111yescharacteristic
655C22C2×#137×C13111yescharacteristic
656C22#576×C13111yescharacteristic
657C22#577×C13111yescharacteristic
658C4—22no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4#529×C13111yescharacteristic
671C4#539×C13111yescharacteristic
672C4#546×C13111yescharacteristic
673C4#547×C13111yescharacteristic
674C2—24no—
675C2—161no—
676C2#2425×C13111yescharacteristic
677C2C2×#464×C13111yescharacteristic
678C2#3045×C13111yescharacteristic
679C2#3297×C13111yescharacteristic
680C2#3320×C13111yescharacteristic
681C2#3337×C13111yescharacteristic
682C2#3346×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C131C2semidirect
4. #2360×C131C2semidirect
5. #2085×C131C2semidirect
6. #2074×C131C2semidirect
7. #2067×C131C2semidirect
8. #2055×C131C2semidirect
9. #1949×C131C2semidirect
10. #1925×C131C2semidirect
11. #1880×C131C2semidirect
13. #1850×C131C2semidirect
14. #1805×C131C2semidirect
15. C2×#340×C131C2semidirect
341. #25210C131direct (N × H)
342. C131#25210direct (N × H)
343. C2×#484C2×C131semidirect
346. #2360C2×C131semidirect
347. #2085C2×C131semidirect
348. #2074C2×C131semidirect
349. #2067C2×C131semidirect
350. #2055C2×C131semidirect
351. #1949C2×C131semidirect
352. #1925C2×C131semidirect
353. #1880C2×C131semidirect
355. #1850C2×C131semidirect
356. #1805C2×C131semidirect
357. C2×#340C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1312
C2×#465×C1312
#2504×C1312
#2360×C1312
#2085×C1312
#2074×C1312
#2067×C1312
#2055×C1312
#1949×C1312
#1925×C1312
#1880×C1312
#1874×C1312
#1850×C1312
#1805×C1312
C2×#340×C1312
#25210131