Finite Group Databasebeta

← C131×#25563 #45711447

Subgroups — C131×#25563 #45711447

Order 33536.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3490×C131C211yesmaximal, characteristic, complemented
2#2410×C131C212yesmaximal, complemented
3#2405×C131C211yesmaximal, characteristic, complemented
4#2062×C131C211yesmaximal, characteristic, complemented
5#2044×C131C211yesmaximal, characteristic, complemented
6#2029×C131C211yesmaximal, characteristic, complemented
7#2021×C131C211yesmaximal, characteristic, complemented
8#1898×C131C212yesmaximal, complemented
9#1889×C131C212yesmaximal, complemented
10#1867×C131C212yesmaximal, complemented
11C2×#342×C131C211yesmaximal, characteristic, complemented
12C23×D4×C131C2211yescharacteristic
13#551×C131—22no—
14#551×C131—22no—
15#546×C131—22no—
16#546×C131—22no—
17#543×C131C2211yescharacteristic
18#538×C131—21no—
19#538×C131—21no—
20#534×C131C2211yescharacteristic
21#525×C131—21no—
22#525×C131—21no—
23C2×#123×C131—21no—
24C2×#121×C131—22no—
25C2×#120×C131C2212yes—
26C2×#120×C131C2212yes—
27#518×C131C2212yes—
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2212yes—
30C2×#99×C131C2212yes—
31C2×#99×C131C2212yes—
32#394×C131—21no—
33#394×C131—21no—
34#394×C131—22no—
35#392×C131—22no—
36#386×C131—21no—
37#386×C131—22no—
38#386×C131C2212yes—
39#385×C131C2211yescharacteristic
40#385×C131C2212yes—
41#385×C131C2211yescharacteristic
42#379×C131C2211yescharacteristic
43#379×C131C2212yes—
44#379×C131C2211yescharacteristic
45#379×C131C2211yescharacteristic
46#342×C131C2211yescharacteristic
47#342×C131C2211yescharacteristic
48#342×C131C2212yes—
49#342×C131C2212yes—
50#342×C131C2212yes—
51C25×C131C2311yescharacteristic
52C25×C131C2311yescharacteristic
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C22×D4×C131—22no—
56C22×D4×C131—21no—
57C22×D4×C131—22no—
58C22×D4×C131—21no—
59C22×D4×C131—22no—
60C22×D4×C131—44no—
61C22×D4×C131D412yescomplemented
62C22×D4×C131D412yescomplemented
63C22×D4×C131C2312yes—
64C23×C4×C131—22no—
65C23×C4×C131D411yescharacteristic, complemented
66C23×C4×C131D411yescharacteristic, complemented
67C23×C4×C131C2311yescharacteristic
68#126×C131—22no—
69#126×C131—22no—
70#124×C131—22no—
71#124×C131—22no—
72#123×C131—22no—
73#123×C131—22no—
74#123×C131—22no—
75#123×C131—22no—
76#123×C131—22no—
77#123×C131—44no—
78C22⋊Q8×C131—21no—
79C22⋊Q8×C131—21no—
80C22⋊Q8×C131—21no—
81C22⋊Q8×C131—21no—
82C22⋊Q8×C131—22no—
83C22⋊Q8×C131—22no—
84#121×C131—21no—
85#121×C131—21no—
86#121×C131—22no—
87#121×C131—22no—
88#121×C131—21no—
89#121×C131—21no—
90#121×C131—48no—
91#120×C131—22no—
92#120×C131—22no—
93#120×C131—22no—
94#120×C131—22no—
95#120×C131—22no—
96#120×C131—24no—
97#120×C131—42no—
98C4×D4×C131—22no—
99C4×D4×C131—22no—
100C4×D4×C131—22no—
101C4×D4×C131—22no—
102C4×D4×C131—22no—
103C4×D4×C131—22no—
104#117×C131—21no—
105#117×C131—21no—
106#117×C131—22no—
107C2×C4⋊C4×C131—22no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C22⋊C4×C131—22no—
111C2×C22⋊C4×C131—22no—
112C2×C22⋊C4×C131—22no—
113C2×C22⋊C4×C131—24no—
114C2×C22⋊C4×C131—22no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—22no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—42no—
126C2×C22⋊C4×C131D411yescharacteristic, complemented
127C2×C22⋊C4×C131D411yescharacteristic, complemented
128C2×C22⋊C4×C131D412yescomplemented
129C2×C22⋊C4×C131D412yescomplemented
130C2×C22⋊C4×C131C2311yescharacteristic
131C2×C22⋊C4×C131C2311yescharacteristic
132C2×C22⋊C4×C131C2312yes—
133C2×C22⋊C4×C131C2311yescharacteristic
134C2×C22⋊C4×C131C2311yescharacteristic
135C2×C22⋊C4×C131C2312yes—
136C2×C22⋊C4×C131C2312yes—
137#99×C131—24no—
138#99×C131—42no—
139#95×C131—22no—
140#95×C131—21no—
141#95×C131—21no—
142#95×C131—22no—
143C24×C131—22no—
144C24×C131—21no—
145C24×C131—21no—
146C24×C131—21no—
147C24×C131—22no—
148C24×C131—22no—
149C24×C131—21no—
150C24×C131—21no—
151C24×C131—42no—
152C24×C131—42no—
153C24×C131—81no—
154C24×C131—81no—
155C24×C131C2×D412yes—
156C24×C131C2×D411yescharacteristic
157C24×C131C2×D412yes—
158C24×C131C2×D412yes—
159C24×C131C2×D411yescharacteristic
160C24×C131C2411yescharacteristic
161#41×C131—82no—
162#41×C131—82no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×D4×C131—28no—
166C2×D4×C131—24no—
167C2×D4×C131—22no—
168C2×D4×C131—22no—
169C2×D4×C131—22no—
170C2×D4×C131—22no—
171C2×D4×C131—22no—
172C2×D4×C131—22no—
173C2×D4×C131—22no—
174C2×D4×C131—22no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—22no—
178C2×D4×C131—22no—
179C2×D4×C131—44no—
180C2×D4×C131—42no—
181C2×D4×C131—44no—
182C2×D4×C131—42no—
183C2×D4×C131—44no—
184C2×D4×C131—42no—
185C2×D4×C131—44no—
186C2×D4×C131—42no—
187C2×D4×C131—41no—
188C2×D4×C131—41no—
189C2×D4×C131—44no—
190C2×D4×C131—44no—
191C2×D4×C131—82no—
192C2×D4×C131—82no—
193C22×C4×C131—21no—
194C22×C4×C131—21no—
195C22×C4×C131—22no—
196C22×C4×C131—21no—
197C22×C4×C131—22no—
198C22×C4×C131—22no—
199C22×C4×C131—22no—
200C22×C4×C131—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—22no—
205C22×C4×C131—42no—
206C22×C4×C131—44no—
207C22×C4×C131—42no—
208C22×C4×C131—44no—
209C22×C4×C131—81no—
210C22×C4×C131—82no—
211C22×C4×C131C2×D412yes—
212C22×C4×C131C2×D411yescharacteristic
213C22×C4×C131C2×D412yes—
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D412yes—
217C22×C4×C131C2×D411yescharacteristic
218C4⋊C4×C131—22no—
219C4⋊C4×C131—22no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—22no—
225C4⋊C4×C131—22no—
226C4⋊C4×C131—44no—
227C4⋊C4×C131—42no—
228C4⋊C4×C131—42no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—22no—
231C22⋊C4×C131—22no—
232C22⋊C4×C131—22no—
233C22⋊C4×C131—22no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—22no—
240C22⋊C4×C131—22no—
241C22⋊C4×C131—22no—
242C22⋊C4×C131—22no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—22no—
245C22⋊C4×C131—22no—
246C22⋊C4×C131—21no—
247C22⋊C4×C131—22no—
248C22⋊C4×C131—21no—
249C22⋊C4×C131—44no—
250C22⋊C4×C131—44no—
251C22⋊C4×C131—44no—
252C22⋊C4×C131—44no—
253C22⋊C4×C131—42no—
254C22⋊C4×C131—42no—
255C22⋊C4×C131—42no—
256C22⋊C4×C131—81no—
257C22⋊C4×C131—81no—
258C22⋊C4×C131—82no—
259C22⋊C4×C131—81no—
260C22⋊C4×C131#4114yescomplemented
261C42×C131—22no—
262C42×C131—22no—
263C23×C131—21no—
264C23×C131—21no—
265C23×C131—22no—
266C23×C131—22no—
267C23×C131—22no—
268C23×C131—24no—
269C23×C131—21no—
270C23×C131—21no—
271C23×C131—22no—
272C23×C131—22no—
273C23×C131—22no—
274C23×C131—24no—
275C23×C131—22no—
276C23×C131—22no—
277C23×C131—22no—
278C23×C131—41no—
279C23×C131—41no—
280C23×C131—42no—
281C23×C131—41no—
282C23×C131—41no—
283C23×C131—41no—
284C23×C131—42no—
285C23×C131—42no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—42no—
289C23×C131—41no—
290C23×C131—42no—
291C23×C131—42no—
292C23×C131—42no—
293C23×C131—42no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—42no—
298C23×C131—42no—
299C23×C131—84no—
300C23×C131—84no—
301C23×C131—82no—
302C23×C131—82no—
303C23×C131—82no—
304C23×C131—82no—
305C23×C131#12012yes—
306C23×C131#12011yescharacteristic
307C23×C131#12011yescharacteristic
308C23×C131C22×D411yescharacteristic
309C23×C131C22×D412yes—
310C23×C131C2×#4112yes—
311C23×C131H(5,𝔽2)11yescharacteristic
312C23×C1312−1+411yescharacteristic
313Q8×C131—81no—
314Q8×C131—81no—
315D4×C131—44no—
316D4×C131—48no—
317D4×C131—44no—
318D4×C131—42no—
319D4×C131—42no—
320D4×C131—42no—
321D4×C131—42no—
322D4×C131—44no—
323D4×C131—44no—
324D4×C131—82no—
325D4×C131—82no—
326D4×C131—81no—
327D4×C131—81no—
328D4×C131—88no—
329C2×C4×C131—24no—
330C2×C4×C131—22no—
331C2×C4×C131—22no—
332C2×C4×C131—21no—
333C2×C4×C131—21no—
334C2×C4×C131—22no—
335C2×C4×C131—22no—
336C2×C4×C131—21no—
337C2×C4×C131—21no—
338C2×C4×C131—24no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—42no—
342C2×C4×C131—41no—
343C2×C4×C131—42no—
344C2×C4×C131—42no—
345C2×C4×C131—42no—
346C2×C4×C131—41no—
347C2×C4×C131—42no—
348C2×C4×C131—41no—
349C2×C4×C131—41no—
350C2×C4×C131—42no—
351C2×C4×C131—41no—
352C2×C4×C131—41no—
353C2×C4×C131—42no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—42no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—42no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—42no—
363C2×C4×C131—81no—
364C2×C4×C131—81no—
365C2×C4×C131—82no—
366C2×C4×C131—82no—
367C2×C4×C131—88no—
368C22×C131—21no—
369C22×C131—21no—
370C22×C131—22no—
371C22×C131—21no—
372C22×C131—22no—
373C22×C131—21no—
374C22×C131—21no—
375C22×C131—22no—
376C22×C131—21no—
377C22×C131—22no—
378C22×C131—21no—
379C22×C131—22no—
380C22×C131—42no—
381C22×C131—41no—
382C22×C131—41no—
383C22×C131—44no—
384C22×C131—42no—
385C22×C131—42no—
386C22×C131—44no—
387C22×C131—44no—
388C22×C131—42no—
389C22×C131—42no—
390C22×C131—44no—
391C22×C131—42no—
392C22×C131—42no—
393C22×C131—42no—
394C22×C131—42no—
395C22×C131—82no—
396C22×C131—81no—
397C22×C131—81no—
398C22×C131—82no—
399C22×C131—82no—
400C22×C131—82no—
401C22×C131—82no—
402C22×C131—81no—
403C22×C131—81no—
404C22×C131—82no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131B(4,𝔽2)12yes—
408C22×C131C2×#12011yescharacteristic
409C22×C131#53211yescharacteristic
410C22×C131#53711yescharacteristic
411C22×C131#54612yes—
412C22×C131#54712yes—
413C4×C131—44no—
414C4×C131—42no—
415C4×C131—42no—
416C4×C131—41no—
417C4×C131—41no—
418C4×C131—42no—
419C4×C131—41no—
420C4×C131—41no—
421C4×C131—42no—
422C4×C131—81no—
423C4×C131—81no—
424C4×C131—82no—
425C2×C131—22no—
426C2×C131—21no—
427C2×C131—21no—
428C2×C131—22no—
429C2×C131—22no—
430C2×C131—41no—
431C2×C131—42no—
432C2×C131—82no—
433C2×C131—82no—
434C2×C131#243011yescharacteristic
435C2×C131C2×B(4,𝔽2)11yescharacteristic
436C2×C131#302611yescharacteristic
437#25563C13111yesmaximal, characteristic, direct product factor, Sylow
438C131#2556311yescharacteristic, direct product factor, Sylow
439#3490C2×C13111yescharacteristic, complemented
440#2410C2×C13112yescomplemented
441#2405C2×C13111yescharacteristic, complemented
442#2062C2×C13111yescharacteristic, complemented
443#2044C2×C13111yescharacteristic, complemented
444#2029C2×C13111yescharacteristic, complemented
445#2021C2×C13111yescharacteristic, complemented
446#1898C2×C13112yescomplemented
447#1889C2×C13112yescomplemented
448#1867C2×C13112yescomplemented
449C2×#342C2×C13111yescharacteristic, complemented
450C23×D4C22×C13111yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C13111yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C13111yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C13112yes—
464C2×#120C22×C13112yes—
465#518C22×C13112yes—
466C22×C22⋊C4C22×C13111yescharacteristic
467C22×C22⋊C4C22×C13112yes—
468C2×#99C22×C13112yes—
469C2×#99C22×C13112yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C13112yes—
477#385C22×C13112yes—
478#385C22×C13111yescharacteristic
479#385C22×C13111yescharacteristic
480#379C22×C13111yescharacteristic
481#379C22×C13112yes—
482#379C22×C13111yescharacteristic
483#379C22×C13111yescharacteristic
484#342C22×C13112yes—
485#342C22×C13111yescharacteristic
486#342C22×C13112yes—
487#342C22×C13112yes—
488#342C22×C13111yescharacteristic
489C25C23×C13111yescharacteristic
490C25C23×C13111yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C13112yescomplemented
500C22×D4D4×C13112yescomplemented
501C22×D4C23×C13112yes—
502C23×C4—22no—
503C23×C4D4×C13111yescharacteristic, complemented
504C23×C4D4×C13111yescharacteristic, complemented
505C23×C4C23×C13111yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C13111yescharacteristic, complemented
565C2×C22⋊C4D4×C13111yescharacteristic, complemented
566C2×C22⋊C4D4×C13112yescomplemented
567C2×C22⋊C4D4×C13112yescomplemented
568C2×C22⋊C4C23×C13112yes—
569C2×C22⋊C4C23×C13111yescharacteristic
570C2×C22⋊C4C23×C13111yescharacteristic
571C2×C22⋊C4C23×C13111yescharacteristic
572C2×C22⋊C4C23×C13111yescharacteristic
573C2×C22⋊C4C23×C13112yes—
574C2×C22⋊C4C23×C13112yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C13112yes—
594C24C2×D4×C13111yescharacteristic
595C24C2×D4×C13112yes—
596C24C2×D4×C13112yes—
597C24C2×D4×C13111yescharacteristic
598C24C24×C13111yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C13112yes—
650C22×C4C2×D4×C13111yescharacteristic
651C22×C4C2×D4×C13112yes—
652C22×C4C2×D4×C13111yescharacteristic
653C22×C4C2×D4×C13111yescharacteristic
654C22×C4C2×D4×C13112yes—
655C22×C4C2×D4×C13111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C13114yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C13112yes—
744C23#120×C13111yescharacteristic
745C23#120×C13111yescharacteristic
746C23C22×D4×C13111yescharacteristic
747C23C22×D4×C13112yes—
748C23C2×#41×C13112yes—
749C23H(5,𝔽2)×C13111yescharacteristic
750C232−1+4×C13111yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C13112yes—
846C22C2×#120×C13111yescharacteristic
847C22#532×C13111yescharacteristic
848C22#537×C13111yescharacteristic
849C22#546×C13112yes—
850C22#547×C13112yes—
851C4—44no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2#2430×C13111yescharacteristic
873C2C2×B(4,𝔽2)×C13111yescharacteristic
874C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3490×C131C2semidirect
2. #2410×C131C2semidirect
3. #2405×C131C2semidirect
4. #2062×C131C2semidirect
5. #2044×C131C2semidirect
6. #2029×C131C2semidirect
7. #2021×C131C2semidirect
8. #1898×C131C2semidirect
9. #1889×C131C2semidirect
10. #1867×C131C2semidirect
11. C2×#342×C131C2semidirect
61. C22×D4×C131D4semidirect
62. C22×D4×C131D4semidirect
65. C23×C4×C131D4semidirect
66. C23×C4×C131D4semidirect
126. C2×C22⋊C4×C131D4semidirect
127. C2×C22⋊C4×C131D4semidirect
128. C2×C22⋊C4×C131D4semidirect
129. C2×C22⋊C4×C131D4semidirect
260. C22⋊C4×C131#41semidirect
437. #25563C131direct (N × H)
438. C131#25563direct (N × H)
439. #3490C2×C131semidirect
440. #2410C2×C131semidirect
441. #2405C2×C131semidirect
442. #2062C2×C131semidirect
443. #2044C2×C131semidirect
444. #2029C2×C131semidirect
445. #2021C2×C131semidirect
446. #1898C2×C131semidirect
447. #1889C2×C131semidirect
448. #1867C2×C131semidirect
449. C2×#342C2×C131semidirect
499. C22×D4D4×C131semidirect
500. C22×D4D4×C131semidirect
503. C23×C4D4×C131semidirect
504. C23×C4D4×C131semidirect
564. C2×C22⋊C4D4×C131semidirect
565. C2×C22⋊C4D4×C131semidirect
566. C2×C22⋊C4D4×C131semidirect
567. C2×C22⋊C4D4×C131semidirect
698. C22⋊C4#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3490×C1312
#2410×C1312
#2405×C1312
#2062×C1312
#2044×C1312
#2029×C1312
#2021×C1312
#1898×C1312
#1889×C1312
#1867×C1312
C2×#342×C1312
#25563131