Finite Group Databasebeta

← C131×#25654 #45711538

Subgroups — C131×#25654 #45711538

Order 33536.

1018 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C131C211yesmaximal, characteristic
2C2×#488×C131C211yesmaximal, characteristic
3C2×#479×C131C211yesmaximal, characteristic, complemented
4#2584×C131C211yesmaximal, characteristic, complemented
5#2043×C131C211yesmaximal, characteristic, complemented
6#2043×C131C211yesmaximal, characteristic, complemented
7#2042×C131C211yesmaximal, characteristic
8#2042×C131C211yesmaximal, characteristic
9#1984×C131C211yesmaximal, characteristic, complemented
10#1983×C131C211yesmaximal, characteristic
11#1865×C131C211yesmaximal, characteristic, complemented
12#1864×C131C211yesmaximal, characteristic
13#1863×C131C211yesmaximal, characteristic, complemented
14#1862×C131C211yesmaximal, characteristic
15C4×#103×C131C211yesmaximal, characteristic, complemented
16#556×C131—24no—
17#556×C131—24no—
18C2×C4⋊Q8×C131C2211yescharacteristic
19C2×#126×C131—21no—
20C2×#126×C131—21no—
21C2×#125×C131C2211yescharacteristic
22C2×#124×C131C2211yescharacteristic
23C2×#124×C131C2211yescharacteristic
24C2×C22⋊Q8×C131—21no—
25C2×C4×Q8×C131C2211yescharacteristic
26C2×C4×Q8×C131C2211yescharacteristic
27C2×C4×Q8×C131C2211yescharacteristic
28C2×C4×D4×C131C2211yescharacteristic
29C2×#117×C131—21no—
30#488×C131—24no—
31#479×C131—24no—
32C2×#107×C131C2211yescharacteristic
33C2×#106×C131C2211yescharacteristic
34C2×C4⋊C8×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#103×C131C2211yescharacteristic
39C2×#103×C131C2211yescharacteristic
40C2×#103×C131C2211yescharacteristic
41C2×#103×C131C2211yescharacteristic
42C2×#103×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×C4×C8×C131C2211yescharacteristic
48#398×C131—21no—
49#395×C131—21no—
50#389×C131—21no—
51#389×C131—21no—
52#389×C131C2211yescharacteristic
53#389×C131C2211yescharacteristic
54#389×C131C2211yescharacteristic
55#389×C131C2211yescharacteristic
56C4×C4⋊C4×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C22×Q8×C131D411yescharacteristic
64C22×Q8×C131C2311yescharacteristic
65C22×Q8×C131C2311yescharacteristic
66C22×D4×C131C2311yescharacteristic
67C23×C4×C131—21no—
68C22×C8×C131C2311yescharacteristic
69C22×C8×C131C2311yescharacteristic
70C22×C8×C131C2311yescharacteristic
71C22×C8×C131C2311yescharacteristic
72C4⋊Q8×C131—22no—
73C4⋊Q8×C131—22no—
74#126×C131—28no—
75#126×C131—28no—
76#125×C131—22no—
77#125×C131—22no—
78#124×C131—22no—
79#124×C131—22no—
80#124×C131—22no—
81#124×C131D414yes—
82C22⋊Q8×C131—28no—
83C4×Q8×C131—22no—
84C4×Q8×C131—22no—
85C4×Q8×C131—22no—
86C4×Q8×C131—22no—
87C4×Q8×C131—22no—
88C4×Q8×C131D414yes—
89C4×D4×C131—22no—
90C4×D4×C131—22no—
91#117×C131—28no—
92C2×C4⋊C4×C131—21no—
93C2×C4⋊C4×C131—21no—
94C2×C4⋊C4×C131—21no—
95C2×C4⋊C4×C131—21no—
96C2×C4⋊C4×C131—21no—
97C2×C4⋊C4×C131—21no—
98C2×C4⋊C4×C131—21no—
99C2×C4⋊C4×C131—21no—
100C2×C4⋊C4×C131—21no—
101C2×C4⋊C4×C131—21no—
102C2×C4⋊C4×C131D411yescharacteristic
103C2×C4⋊C4×C131D411yescharacteristic
104C2×C4⋊C4×C131D411yescharacteristic
105C2×C4⋊C4×C131C2311yescharacteristic
106C2×C4⋊C4×C131C2311yescharacteristic
107C2×C4⋊C4×C131C2311yescharacteristic
108C2×C4⋊C4×C131C2311yescharacteristic
109C2×C4⋊C4×C131C2311yescharacteristic
110C2×C22⋊C4×C131—21no—
111C2×C22⋊C4×C131—21no—
112C2×C22⋊C4×C131—21no—
113C2×C22⋊C4×C131—21no—
114C2×C22⋊C4×C131—21no—
115C2×C42×C131—21no—
116C2×C42×C131—21no—
117C2×C42×C131—21no—
118C2×C42×C131C2311yescharacteristic
119C2×C42×C131C2311yescharacteristic
120C2×C42×C131C2311yescharacteristic
121#107×C131—22no—
122#106×C131—22no—
123C4⋊C8×C131—22no—
124#103×C131—22no—
125#103×C131—22no—
126#103×C131—22no—
127#103×C131—22no—
128#103×C131—22no—
129#103×C131—22no—
130#103×C131—22no—
131#103×C131—22no—
132#102×C131—22no—
133#102×C131—22no—
134#102×C131—22no—
135#102×C131—22no—
136C4×C8×C131—22no—
137#95×C131—21no—
138#95×C131—21no—
139#95×C131—21no—
140#95×C131—21no—
141#95×C131—21no—
142C24×C131—21no—
143C2×Q8×C131—22no—
144C2×Q8×C131—22no—
145C2×Q8×C131—21no—
146C2×Q8×C131—21no—
147C2×Q8×C131—21no—
148C2×Q8×C131—21no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131—21no—
152C2×Q8×C131—21no—
153C2×Q8×C131—21no—
154C2×Q8×C131—21no—
155C2×Q8×C131—41no—
156C2×Q8×C131C2×D412yes—
157C2×Q8×C131C2×D412yes—
158C2×D4×C131—21no—
159C2×D4×C131—21no—
160C2×D4×C131—21no—
161C2×D4×C131—21no—
162C2×D4×C131—21no—
163C2×D4×C131C2×D412yes—
164C22×C4×C131—24no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—21no—
172C22×C4×C131—42no—
173C22×C4×C131—42no—
174C22×C4×C131C2×D411yescharacteristic
175C22×C4×C131C2×D411yescharacteristic
176C22×C4×C131C2×D411yescharacteristic
177C22×C4×C131C2×D411yescharacteristic
178C22×C4×C131C2×D411yescharacteristic
179C22×C4×C131C2×D411yescharacteristic
180C22×C4×C131C2411yescharacteristic
181C2×C8×C131—21no—
182C2×C8×C131—21no—
183C2×C8×C131—21no—
184C2×C8×C131—21no—
185C2×C8×C131—21no—
186C2×C8×C131—21no—
187C2×C8×C131—21no—
188C2×C8×C131—21no—
189C2×C8×C131—21no—
190C2×C8×C131—21no—
191C2×C8×C131—21no—
192C2×C8×C131—21no—
193C4⋊C4×C131—24no—
194C4⋊C4×C131—24no—
195C4⋊C4×C131—24no—
196C4⋊C4×C131—24no—
197C4⋊C4×C131—22no—
198C4⋊C4×C131—22no—
199C4⋊C4×C131—22no—
200C4⋊C4×C131—21no—
201C4⋊C4×C131—21no—
202C4⋊C4×C131—21no—
203C4⋊C4×C131—21no—
204C4⋊C4×C131—21no—
205C4⋊C4×C131—21no—
206C4⋊C4×C131—21no—
207C4⋊C4×C131—42no—
208C4⋊C4×C131—42no—
209C4⋊C4×C131—42no—
210C4⋊C4×C131—42no—
211C4⋊C4×C131—81no—
212C4⋊C4×C131—81no—
213C4⋊C4×C131C2×D412yes—
214C4⋊C4×C131#4112yes—
215C4⋊C4×C131#4112yes—
216C22⋊C4×C131—24no—
217C22⋊C4×C131—24no—
218C22⋊C4×C131—24no—
219C22⋊C4×C131—24no—
220C22⋊C4×C131—24no—
221C42×C131—24no—
222C42×C131—24no—
223C42×C131—21no—
224C42×C131—21no—
225C42×C131—21no—
226C42×C131—21no—
227C42×C131—81no—
228C42×C131C2×D412yes—
229C42×C131C2×D412yes—
230C23×C131—22no—
231C23×C131—41no—
232C23×C131—41no—
233C23×C131—41no—
234C23×C131—41no—
235C23×C131—41no—
236C23×C131—41no—
237C23×C131C22×D411yescharacteristic
238Q8×C131—22no—
239Q8×C131—22no—
240Q8×C131—22no—
241Q8×C131—22no—
242Q8×C131—44no—
243Q8×C131—41no—
244Q8×C131—41no—
245Q8×C131—41no—
246Q8×C131—41no—
247D4×C131—22no—
248D4×C131—22no—
249D4×C131—41no—
250D4×C131—41no—
251C2×C4×C131—21no—
252C2×C4×C131—21no—
253C2×C4×C131—21no—
254C2×C4×C131—21no—
255C2×C4×C131—21no—
256C2×C4×C131—21no—
257C2×C4×C131—21no—
258C2×C4×C131—22no—
259C2×C4×C131—21no—
260C2×C4×C131—22no—
261C2×C4×C131—22no—
262C2×C4×C131—21no—
263C2×C4×C131—22no—
264C2×C4×C131—22no—
265C2×C4×C131—21no—
266C2×C4×C131—21no—
267C2×C4×C131—21no—
268C2×C4×C131—21no—
269C2×C4×C131—21no—
270C2×C4×C131—21no—
271C2×C4×C131—48no—
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—41no—
283C2×C4×C131—41no—
284C2×C4×C131—41no—
285C2×C4×C131—41no—
286C2×C4×C131—41no—
287C2×C4×C131—41no—
288C2×C4×C131#12012yes—
289C2×C4×C131#12012yes—
290C2×C4×C131#13512yes—
291C2×C4×C131C22×D411yescharacteristic
292C2×C4×C131C22×D411yescharacteristic
293C2×C4×C131C2×#4111yescharacteristic
294C2×C4×C131C2×#4111yescharacteristic
295C2×C4×C1312−1+411yescharacteristic
296C2×C4×C1312−1+411yescharacteristic
297C8×C131—41no—
298C8×C131—41no—
299C8×C131—41no—
300C8×C131—41no—
301C22×C131—42no—
302C22×C131—42no—
303C22×C131—42no—
304C22×C131—81no—
305C22×C131—81no—
306C22×C131—81no—
307C22×C131—81no—
308C22×C131C2×#12011yescharacteristic
309C22×C131#54811yescharacteristic
310C22×C131#54811yescharacteristic
311C22×C131C2×#13511yescharacteristic
312C22×C131#57511yescharacteristic
313C22×C131#57711yescharacteristic
314C22×C131#57811yescharacteristic
315C4×C131—22no—
316C4×C131—22no—
317C4×C131—22no—
318C4×C131—42no—
319C4×C131—42no—
320C4×C131—42no—
321C4×C131—42no—
322C4×C131—41no—
323C4×C131—42no—
324C4×C131—41no—
325C4×C131—41no—
326C4×C131—81no—
327C4×C131—81no—
328C4×C131#53211yescharacteristic
329C4×C131#53611yescharacteristic
330C4×C131#54711yescharacteristic
331C4×C131#54711yescharacteristic
332C2×C131—82no—
333C2×C131#243211yescharacteristic
334C2×C131#300211yescharacteristic
335C2×C131#301311yescharacteristic
336C2×C131#336011yescharacteristic
337C2×C131#336411yescharacteristic
338C2×C131#337611yescharacteristic
339C2×C131#337711yescharacteristic
340#25654C13111yesmaximal, characteristic, direct product factor, Sylow
341C131#2565411yescharacteristic, direct product factor, Sylow
342C2×#556C2×C13111yescharacteristic
343C2×#488C2×C13111yescharacteristic
344C2×#479C2×C13111yescharacteristic, complemented
345#2584C2×C13111yescharacteristic, complemented
346#2043C2×C13111yescharacteristic, complemented
347#2043C2×C13111yescharacteristic, complemented
348#2042C2×C13111yescharacteristic
349#2042C2×C13111yescharacteristic
350#1984C2×C13111yescharacteristic, complemented
351#1983C2×C13111yescharacteristic
352#1865C2×C13111yescharacteristic, complemented
353#1864C2×C13111yescharacteristic
354#1863C2×C13111yescharacteristic, complemented
355#1862C2×C13111yescharacteristic
356C4×#103C2×C13111yescharacteristic, complemented
357#556—24no—
358#556—24no—
359C2×C4⋊Q8C22×C13111yescharacteristic
360C2×#126—21no—
361C2×#126—21no—
362C2×#125C22×C13111yescharacteristic
363C2×#124C22×C13111yescharacteristic
364C2×#124C22×C13111yescharacteristic
365C2×C22⋊Q8—21no—
366C2×C4×Q8C22×C13111yescharacteristic
367C2×C4×Q8C22×C13111yescharacteristic
368C2×C4×Q8C22×C13111yescharacteristic
369C2×C4×D4C22×C13111yescharacteristic
370C2×#117—21no—
371#488—24no—
372#479—24no—
373C2×#107C22×C13111yescharacteristic
374C2×#106C22×C13111yescharacteristic
375C2×C4⋊C8C22×C13111yescharacteristic
376C2×#103C22×C13111yescharacteristic
377C2×#103C22×C13111yescharacteristic
378C2×#103C22×C13111yescharacteristic
379C2×#103C22×C13111yescharacteristic
380C2×#103C22×C13111yescharacteristic
381C2×#103C22×C13111yescharacteristic
382C2×#103C22×C13111yescharacteristic
383C2×#103C22×C13111yescharacteristic
384C2×#102C22×C13111yescharacteristic
385C2×#102C22×C13111yescharacteristic
386C2×#102C22×C13111yescharacteristic
387C2×#102C22×C13111yescharacteristic
388C2×C4×C8C22×C13111yescharacteristic
389#398—21no—
390#395—21no—
391#389—21no—
392#389—21no—
393#389C22×C13111yescharacteristic
394#389C22×C13111yescharacteristic
395#389C22×C13111yescharacteristic
396#389C22×C13111yescharacteristic
397C4×C4⋊C4C22×C13111yescharacteristic
398#340C22×C13111yescharacteristic
399#340C22×C13111yescharacteristic
400#336C22×C13111yescharacteristic
401#336C22×C13111yescharacteristic
402#336C22×C13111yescharacteristic
403#336C22×C13111yescharacteristic
404C22×Q8D4×C13111yescharacteristic
405C22×Q8C23×C13111yescharacteristic
406C22×Q8C23×C13111yescharacteristic
407C22×D4C23×C13111yescharacteristic
408C23×C4—21no—
409C22×C8C23×C13111yescharacteristic
410C22×C8C23×C13111yescharacteristic
411C22×C8C23×C13111yescharacteristic
412C22×C8C23×C13111yescharacteristic
413C4⋊Q8—22no—
414C4⋊Q8—22no—
415#126—28no—
416#126—28no—
417#125—22no—
418#125—22no—
419#124—22no—
420#124—22no—
421#124—22no—
422#124D4×C13114yes—
423C22⋊Q8—28no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8D4×C13114yes—
430C4×D4—22no—
431C4×D4—22no—
432#117—28no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C13111yescharacteristic
444C2×C4⋊C4D4×C13111yescharacteristic
445C2×C4⋊C4D4×C13111yescharacteristic
446C2×C4⋊C4C23×C13111yescharacteristic
447C2×C4⋊C4C23×C13111yescharacteristic
448C2×C4⋊C4C23×C13111yescharacteristic
449C2×C4⋊C4C23×C13111yescharacteristic
450C2×C4⋊C4C23×C13111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C13111yescharacteristic
460C2×C42C23×C13111yescharacteristic
461C2×C42C23×C13111yescharacteristic
462#107—22no—
463#106—22no—
464C4⋊C8—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477C4×C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483C24—21no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8C2×D4×C13112yes—
498C2×Q8C2×D4×C13112yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C13112yes—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4C2×D4×C13111yescharacteristic
516C22×C4C2×D4×C13111yescharacteristic
517C22×C4C2×D4×C13111yescharacteristic
518C22×C4C2×D4×C13111yescharacteristic
519C22×C4C2×D4×C13111yescharacteristic
520C22×C4C2×D4×C13111yescharacteristic
521C22×C4C24×C13111yescharacteristic
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C2×D4×C13112yes—
555C4⋊C4#41×C13112yes—
556C4⋊C4#41×C13112yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C42—24no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42C2×D4×C13112yes—
570C42C2×D4×C13112yes—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23C22×D4×C13111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—44no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—48no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4#120×C13112yes—
630C2×C4#120×C13112yes—
631C2×C4#135×C13112yes—
632C2×C4C22×D4×C13111yescharacteristic
633C2×C4C22×D4×C13111yescharacteristic
634C2×C4C2×#41×C13111yescharacteristic
635C2×C4C2×#41×C13111yescharacteristic
636C2×C42−1+4×C13111yescharacteristic
637C2×C42−1+4×C13111yescharacteristic
638C8—41no—
639C8—41no—
640C8—41no—
641C8—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×#120×C13111yescharacteristic
650C22#548×C13111yescharacteristic
651C22#548×C13111yescharacteristic
652C22C2×#135×C13111yescharacteristic
653C22#575×C13111yescharacteristic
654C22#577×C13111yescharacteristic
655C22#578×C13111yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—41no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4#532×C13111yescharacteristic
670C4#536×C13111yescharacteristic
671C4#547×C13111yescharacteristic
672C4#547×C13111yescharacteristic
673C2—82no—
674C2#2432×C13111yescharacteristic
675C2#3002×C13111yescharacteristic
676C2#3013×C13111yescharacteristic
677C2#3360×C13111yescharacteristic
678C2#3364×C13111yescharacteristic
679C2#3376×C13111yescharacteristic
680C2#3377×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×D4×C131C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#479×C131C2semidirect
4. #2584×C131C2semidirect
5. #2043×C131C2semidirect
6. #2043×C131C2semidirect
9. #1984×C131C2semidirect
11. #1865×C131C2semidirect
13. #1863×C131C2semidirect
15. C4×#103×C131C2semidirect
340. #25654C131direct (N × H)
341. C131#25654direct (N × H)
344. C2×#479C2×C131semidirect
345. #2584C2×C131semidirect
346. #2043C2×C131semidirect
347. #2043C2×C131semidirect
350. #1984C2×C131semidirect
352. #1865C2×C131semidirect
354. #1863C2×C131semidirect
356. C4×#103C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1312
C2×#488×C1312
C2×#479×C1312
#2584×C1312
#2043×C1312
#2042×C1312
#1984×C1312
#1983×C1312
#1865×C1312
#1864×C1312
#1863×C1312
#1862×C1312
C4×#103×C1312
#25654131