Finite Group Databasebeta

← C131×#24404 #45710288

Subgroups — C131×#24404 #45710288

Order 33536.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C131C211yesmaximal, characteristic, complemented
3C22×#99×C131C211yesmaximal, characteristic, complemented
4#2410×C131C212yesmaximal, complemented
5#2403×C131C211yesmaximal, characteristic, complemented
6#2044×C131C212yesmaximal, complemented
7#2021×C131C212yesmaximal, complemented
8#1898×C131C212yesmaximal, complemented
9#1889×C131C211yesmaximal, characteristic, complemented
10#1867×C131C211yesmaximal, characteristic, complemented
11#1790×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic
13C23×D4×C131C2211yescharacteristic
14C23×D4×C131C2211yescharacteristic, complemented
15#546×C131—22no—
16#546×C131—22no—
17D42×C131—22no—
18D42×C131—22no—
19#535×C131—21no—
20#534×C131—21no—
21#534×C131C2212yes—
22#525×C131—21no—
23C2×#121×C131—22no—
24C2×#120×C131—21no—
25C2×#120×C131—21no—
26C2×#120×C131C2211yescharacteristic
27C2×#120×C131C2212yes—
28C2×#120×C131C2212yescomplemented
29C2×#120×C131C2211yescharacteristic, complemented
30#518×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2212yescomplemented
32B(4,𝔽2)×C131—24no—
33C2×#99×C131—24no—
34C2×#99×C131C2211yescharacteristic
35C2×#99×C131C2211yescharacteristic
36C2×#99×C131C2212yescomplemented
37C2×#99×C131C2212yescomplemented
38C2×#99×C131C2212yescomplemented
39#394×C131—22no—
40#392×C131—21no—
41#392×C131—21no—
42#392×C131—22no—
43#386×C131—21no—
44#386×C131—22no—
45#386×C131C2211yescharacteristic
46#386×C131C2211yescharacteristic, complemented
47#386×C131C2212yescomplemented
48#385×C131C2212yescomplemented
49#379×C131C2212yescomplemented
50#379×C131C2211yescharacteristic, complemented
51#342×C131C2212yescomplemented
52#342×C131C2212yescomplemented
53C25×C131D411yescharacteristic, complemented
54C25×C131C2311yescharacteristic
55C25×C131C2311yescharacteristic
56H(5,𝔽2)×C131—22no—
57H(5,𝔽2)×C131—22no—
58H(5,𝔽2)×C131—42no—
59C2×#41×C131—21no—
60C2×#41×C131—22no—
61C22×D4×C131—21no—
62C22×D4×C131—21no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—21no—
68C22×D4×C131—21no—
69C22×D4×C131—22no—
70C22×D4×C131—22no—
71C22×D4×C131—21no—
72C22×D4×C131—22no—
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—22no—
76C22×D4×C131—44no—
77C22×D4×C131—42no—
78C22×D4×C131D411yescharacteristic, complemented
79C22×D4×C131D411yescharacteristic, complemented
80C22×D4×C131D412yescomplemented
81C22×D4×C131D412yescomplemented
82C22×D4×C131C2312yes—
83C22×D4×C131C2311yescharacteristic
84C22×D4×C131C2311yescharacteristic
85C23×C4×C131—22no—
86C23×C4×C131D411yescharacteristic, complemented
87C23×C4×C131C2311yescharacteristic
88#127×C131—22no—
89#124×C131—22no—
90#123×C131—22no—
91#123×C131—22no—
92#123×C131—22no—
93C22⋊Q8×C131—21no—
94C22⋊Q8×C131—21no—
95#121×C131—21no—
96#121×C131—21no—
97#121×C131—22no—
98#121×C131—22no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—48no—
104#120×C131—22no—
105#120×C131—22no—
106#120×C131—22no—
107#120×C131—22no—
108#120×C131—22no—
109#120×C131—22no—
110#120×C131—22no—
111#120×C131—22no—
112#120×C131—22no—
113#120×C131—22no—
114#120×C131—22no—
115#120×C131—24no—
116#120×C131—42no—
117#120×C131—42no—
118#120×C131—44no—
119C4×D4×C131—22no—
120C4×D4×C131—22no—
121C4×D4×C131—22no—
122C4×D4×C131—22no—
123#117×C131—21no—
124C2×C4⋊C4×C131—22no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—24no—
129C2×C22⋊C4×C131—22no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—22no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—21no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131—22no—
137C2×C22⋊C4×C131—22no—
138C2×C22⋊C4×C131—21no—
139C2×C22⋊C4×C131—22no—
140C2×C22⋊C4×C131—42no—
141C2×C22⋊C4×C131D412yescomplemented
142C2×C22⋊C4×C131D412yescomplemented
143C2×C22⋊C4×C131C2312yes—
144C2×C22⋊C4×C131C2311yescharacteristic
145C2×C22⋊C4×C131C2311yescharacteristic
146C2×C22⋊C4×C131C2312yes—
147C2×C22⋊C4×C131C2312yes—
148#99×C131—22no—
149#99×C131—24no—
150#99×C131—24no—
151#99×C131—42no—
152#99×C131D414yescomplemented
153#95×C131—22no—
154#95×C131—21no—
155#95×C131—21no—
156#95×C131—22no—
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—22no—
160C24×C131—21no—
161C24×C131—22no—
162C24×C131—21no—
163C24×C131—21no—
164C24×C131—21no—
165C24×C131—22no—
166C24×C131—21no—
167C24×C131—21no—
168C24×C131—22no—
169C24×C131—41no—
170C24×C131—42no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—81no—
174C24×C131—81no—
175C24×C131—81no—
176C24×C131C2×D411yescharacteristic
177C24×C131C2×D412yes—
178C24×C131C2×D411yescharacteristic
179C24×C131C2×D412yes—
180C24×C131C2×D412yes—
181C24×C131C2×D411yescharacteristic
182C24×C131C2×D411yescharacteristic
183C24×C131C2411yescharacteristic
184#41×C131—44no—
185#41×C131—44no—
186#41×C131—42no—
187#41×C131—42no—
188C2×Q8×C131—21no—
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—22no—
192C2×D4×C131—24no—
193C2×D4×C131—21no—
194C2×D4×C131—28no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
197C2×D4×C131—22no—
198C2×D4×C131—22no—
199C2×D4×C131—22no—
200C2×D4×C131—21no—
201C2×D4×C131—22no—
202C2×D4×C131—22no—
203C2×D4×C131—22no—
204C2×D4×C131—22no—
205C2×D4×C131—21no—
206C2×D4×C131—22no—
207C2×D4×C131—22no—
208C2×D4×C131—22no—
209C2×D4×C131—22no—
210C2×D4×C131—22no—
211C2×D4×C131—22no—
212C2×D4×C131—22no—
213C2×D4×C131—22no—
214C2×D4×C131—22no—
215C2×D4×C131—41no—
216C2×D4×C131—41no—
217C2×D4×C131—42no—
218C2×D4×C131—44no—
219C2×D4×C131—44no—
220C2×D4×C131—44no—
221C2×D4×C131—44no—
222C2×D4×C131—44no—
223C2×D4×C131—44no—
224C2×D4×C131—44no—
225C2×D4×C131—44no—
226C2×D4×C131—44no—
227C2×D4×C131—42no—
228C2×D4×C131—42no—
229C2×D4×C131—44no—
230C2×D4×C131—42no—
231C2×D4×C131—41no—
232C2×D4×C131—42no—
233C2×D4×C131—41no—
234C2×D4×C131—42no—
235C2×D4×C131—44no—
236C2×D4×C131—42no—
237C2×D4×C131—42no—
238C2×D4×C131—42no—
239C2×D4×C131—44no—
240C2×D4×C131—42no—
241C2×D4×C131—82no—
242C2×D4×C131—82no—
243C2×D4×C131—81no—
244C2×D4×C131—81no—
245C2×D4×C131—82no—
246C2×D4×C131—82no—
247C2×D4×C131C2×D412yes—
248C2×D4×C131#4112yes—
249C22×C4×C131—21no—
250C22×C4×C131—22no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—22no—
255C22×C4×C131—22no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—22no—
259C22×C4×C131—22no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—42no—
263C22×C4×C131—41no—
264C22×C4×C131—44no—
265C22×C4×C131—44no—
266C22×C4×C131—82no—
267C22×C4×C131C2×D412yes—
268C22×C4×C131C2×D411yescharacteristic
269C22×C4×C131C2×D411yescharacteristic
270C22×C4×C131C2×D412yes—
271C22×C4×C131C2×D412yes—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—22no—
275C4⋊C4×C131—22no—
276C4⋊C4×C131—44no—
277C22⋊C4×C131—22no—
278C22⋊C4×C131—22no—
279C22⋊C4×C131—22no—
280C22⋊C4×C131—22no—
281C22⋊C4×C131—22no—
282C22⋊C4×C131—22no—
283C22⋊C4×C131—22no—
284C22⋊C4×C131—22no—
285C22⋊C4×C131—22no—
286C22⋊C4×C131—22no—
287C22⋊C4×C131—22no—
288C22⋊C4×C131—22no—
289C22⋊C4×C131—22no—
290C22⋊C4×C131—21no—
291C22⋊C4×C131—21no—
292C22⋊C4×C131—22no—
293C22⋊C4×C131—22no—
294C22⋊C4×C131—44no—
295C22⋊C4×C131—44no—
296C22⋊C4×C131—42no—
297C22⋊C4×C131—42no—
298C22⋊C4×C131—42no—
299C22⋊C4×C131—44no—
300C22⋊C4×C131—42no—
301C22⋊C4×C131—44no—
302C22⋊C4×C131—42no—
303C22⋊C4×C131—82no—
304C22⋊C4×C131—81no—
305C22⋊C4×C131C2×D414yescomplemented
306C42×C131—22no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—22no—
311C23×C131—22no—
312C23×C131—22no—
313C23×C131—24no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—22no—
318C23×C131—22no—
319C23×C131—24no—
320C23×C131—22no—
321C23×C131—21no—
322C23×C131—22no—
323C23×C131—21no—
324C23×C131—21no—
325C23×C131—22no—
326C23×C131—22no—
327C23×C131—41no—
328C23×C131—42no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—42no—
333C23×C131—41no—
334C23×C131—42no—
335C23×C131—42no—
336C23×C131—42no—
337C23×C131—41no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—42no—
342C23×C131—42no—
343C23×C131—41no—
344C23×C131—42no—
345C23×C131—41no—
346C23×C131—41no—
347C23×C131—42no—
348C23×C131—42no—
349C23×C131—42no—
350C23×C131—42no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—41no—
354C23×C131—42no—
355C23×C131—42no—
356C23×C131—42no—
357C23×C131—81no—
358C23×C131—81no—
359C23×C131—82no—
360C23×C131—82no—
361C23×C131—82no—
362C23×C131—82no—
363C23×C131—84no—
364C23×C131—84no—
365C23×C131—81no—
366C23×C131—81no—
367C23×C131—84no—
368C23×C131—84no—
369C23×C131#12011yescharacteristic
370C23×C131#12012yes—
371C23×C131#12011yescharacteristic
372C23×C131#12112yescomplemented
373C23×C131C22×D411yescharacteristic
374C23×C131C22×D412yes—
375C23×C131C22×D411yescharacteristic
376C23×C131C2×#4111yescharacteristic
377C23×C131H(5,𝔽2)12yes—
378Q8×C131—42no—
379D4×C131—24no—
380D4×C131—24no—
381D4×C131—44no—
382D4×C131—42no—
383D4×C131—44no—
384D4×C131—48no—
385D4×C131—44no—
386D4×C131—44no—
387D4×C131—44no—
388D4×C131—42no—
389D4×C131—42no—
390D4×C131—42no—
391D4×C131—42no—
392D4×C131—42no—
393D4×C131—42no—
394D4×C131—44no—
395D4×C131—44no—
396D4×C131—82no—
397D4×C131—82no—
398D4×C131—82no—
399D4×C131—82no—
400D4×C131—88no—
401D4×C131—84no—
402D4×C131—84no—
403C2×C4×C131—21no—
404C2×C4×C131—21no—
405C2×C4×C131—22no—
406C2×C4×C131—24no—
407C2×C4×C131—22no—
408C2×C4×C131—22no—
409C2×C4×C131—22no—
410C2×C4×C131—21no—
411C2×C4×C131—21no—
412C2×C4×C131—21no—
413C2×C4×C131—24no—
414C2×C4×C131—22no—
415C2×C4×C131—22no—
416C2×C4×C131—42no—
417C2×C4×C131—42no—
418C2×C4×C131—44no—
419C2×C4×C131—42no—
420C2×C4×C131—42no—
421C2×C4×C131—41no—
422C2×C4×C131—42no—
423C2×C4×C131—42no—
424C2×C4×C131—41no—
425C2×C4×C131—42no—
426C2×C4×C131—42no—
427C2×C4×C131—42no—
428C2×C4×C131—41no—
429C2×C4×C131—41no—
430C2×C4×C131—42no—
431C2×C4×C131—41no—
432C2×C4×C131—41no—
433C2×C4×C131—41no—
434C2×C4×C131—41no—
435C2×C4×C131—42no—
436C2×C4×C131—81no—
437C2×C4×C131—81no—
438C2×C4×C131—88no—
439C2×C4×C131#12112yescomplemented
440C22×C131—21no—
441C22×C131—22no—
442C22×C131—21no—
443C22×C131—22no—
444C22×C131—21no—
445C22×C131—21no—
446C22×C131—21no—
447C22×C131—22no—
448C22×C131—22no—
449C22×C131—22no—
450C22×C131—21no—
451C22×C131—21no—
452C22×C131—22no—
453C22×C131—41no—
454C22×C131—41no—
455C22×C131—42no—
456C22×C131—44no—
457C22×C131—44no—
458C22×C131—42no—
459C22×C131—42no—
460C22×C131—42no—
461C22×C131—44no—
462C22×C131—42no—
463C22×C131—42no—
464C22×C131—42no—
465C22×C131—44no—
466C22×C131—41no—
467C22×C131—41no—
468C22×C131—42no—
469C22×C131—41no—
470C22×C131—42no—
471C22×C131—42no—
472C22×C131—41no—
473C22×C131—42no—
474C22×C131—41no—
475C22×C131—82no—
476C22×C131—81no—
477C22×C131—81no—
478C22×C131—81no—
479C22×C131—82no—
480C22×C131—84no—
481C22×C131—82no—
482C22×C131—82no—
483C22×C131—81no—
484C22×C131—82no—
485C22×C131—81no—
486C22×C131—81no—
487C22×C131—82no—
488C22×C131—84no—
489C22×C131—81no—
490C22×C131—81no—
491C22×C131—162no—
492C22×C131B(4,𝔽2)12yescomplemented
493C22×C131C2×#12011yescharacteristic
494C22×C131C2×#12111yescharacteristic
495C22×C131#53411yescharacteristic
496C22×C131D4212yes—
497C22×C131#54612yes—
498C4×C131—22no—
499C4×C131—44no—
500C4×C131—41no—
501C4×C131—42no—
502C4×C131—42no—
503C4×C131—42no—
504C4×C131—42no—
505C4×C131—82no—
506C4×C131—81no—
507C4×C131—81no—
508C2×C131—22no—
509C2×C131—21no—
510C2×C131—21no—
511C2×C131—22no—
512C2×C131—22no—
513C2×C131—42no—
514C2×C131—41no—
515C2×C131—42no—
516C2×C131—82no—
517C2×C131—81no—
518C2×C131—82no—
519C2×C131#241011yescharacteristic
520C2×C131C2×B(4,𝔽2)11yescharacteristic
521C2×C131#302611yescharacteristic
522#24404C13111yesmaximal, characteristic, direct product factor, Sylow
523C131#2440411yescharacteristic, direct product factor, Sylow
524#3484C2×C13111yescharacteristic, complemented
525C2×B(4,𝔽2)C2×C13111yescharacteristic, complemented
526C22×#99C2×C13111yescharacteristic, complemented
527#2410C2×C13112yescomplemented
528#2403C2×C13111yescharacteristic, complemented
529#2044C2×C13112yescomplemented
530#2021C2×C13112yescomplemented
531#1898C2×C13112yescomplemented
532#1889C2×C13111yescharacteristic, complemented
533#1867C2×C13111yescharacteristic, complemented
534#1790C2×C13111yescharacteristic, complemented
535C2×H(5,𝔽2)C22×C13111yescharacteristic
536C23×D4C22×C13111yescharacteristic
537C23×D4C22×C13111yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C13112yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C13111yescharacteristic
550C2×#120C22×C13112yes—
551C2×#120C22×C13112yescomplemented
552C2×#120C22×C13111yescharacteristic, complemented
553#518C22×C13111yescharacteristic
554C22×C22⋊C4C22×C13112yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C13111yescharacteristic
558C2×#99C22×C13111yescharacteristic
559C2×#99C22×C13112yescomplemented
560C2×#99C22×C13112yescomplemented
561C2×#99C22×C13112yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C13111yescharacteristic
569#386C22×C13111yescharacteristic, complemented
570#386C22×C13112yescomplemented
571#385C22×C13112yescomplemented
572#379C22×C13112yescomplemented
573#379C22×C13111yescharacteristic, complemented
574#342C22×C13112yescomplemented
575#342C22×C13112yescomplemented
576C25D4×C13111yescharacteristic, complemented
577C25C23×C13111yescharacteristic
578C25C23×C13111yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C13111yescharacteristic, complemented
602C22×D4D4×C13111yescharacteristic, complemented
603C22×D4D4×C13112yescomplemented
604C22×D4D4×C13112yescomplemented
605C22×D4C23×C13112yes—
606C22×D4C23×C13111yescharacteristic
607C22×D4C23×C13111yescharacteristic
608C23×C4—22no—
609C23×C4D4×C13111yescharacteristic, complemented
610C23×C4C23×C13111yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C13112yescomplemented
665C2×C22⋊C4D4×C13112yescomplemented
666C2×C22⋊C4C23×C13112yes—
667C2×C22⋊C4C23×C13111yescharacteristic
668C2×C22⋊C4C23×C13111yescharacteristic
669C2×C22⋊C4C23×C13112yes—
670C2×C22⋊C4C23×C13112yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C13114yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C13111yescharacteristic
700C24C2×D4×C13112yes—
701C24C2×D4×C13111yescharacteristic
702C24C2×D4×C13112yes—
703C24C2×D4×C13112yes—
704C24C2×D4×C13111yescharacteristic
705C24C2×D4×C13111yescharacteristic
706C24C24×C13111yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C13112yes—
771C2×D4#41×C13112yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C13112yes—
791C22×C4C2×D4×C13111yescharacteristic
792C22×C4C2×D4×C13111yescharacteristic
793C22×C4C2×D4×C13112yes—
794C22×C4C2×D4×C13112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C13114yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C13111yescharacteristic
893C23#120×C13112yes—
894C23#120×C13111yescharacteristic
895C23#121×C13112yescomplemented
896C23C22×D4×C13111yescharacteristic
897C23C22×D4×C13112yes—
898C23C22×D4×C13111yescharacteristic
899C23C2×#41×C13111yescharacteristic
900C23H(5,𝔽2)×C13112yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C13112yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C13112yescomplemented
1016C22C2×#120×C13111yescharacteristic
1017C22C2×#121×C13111yescharacteristic
1018C22#534×C13111yescharacteristic
1019C22D42×C13112yes—
1020C22#546×C13112yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2#2410×C13111yescharacteristic
1043C2C2×B(4,𝔽2)×C13111yescharacteristic
1044C2#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. #3484×C131C2semidirect
2. C2×B(4,𝔽2)×C131C2semidirect
3. C22×#99×C131C2semidirect
4. #2410×C131C2semidirect
5. #2403×C131C2semidirect
6. #2044×C131C2semidirect
7. #2021×C131C2semidirect
8. #1898×C131C2semidirect
9. #1889×C131C2semidirect
10. #1867×C131C2semidirect
11. #1790×C131C2semidirect
14. C23×D4×C131C22semidirect
28. C2×#120×C131C22semidirect
29. C2×#120×C131C22semidirect
31. C22×C22⋊C4×C131C22semidirect
36. C2×#99×C131C22semidirect
37. C2×#99×C131C22semidirect
38. C2×#99×C131C22semidirect
46. #386×C131C22semidirect
47. #386×C131C22semidirect
48. #385×C131C22semidirect
49. #379×C131C22semidirect
50. #379×C131C22semidirect
51. #342×C131C22semidirect
52. #342×C131C22semidirect
53. C25×C131D4semidirect
78. C22×D4×C131D4semidirect
79. C22×D4×C131D4semidirect
80. C22×D4×C131D4semidirect
81. C22×D4×C131D4semidirect
86. C23×C4×C131D4semidirect
141. C2×C22⋊C4×C131D4semidirect
142. C2×C22⋊C4×C131D4semidirect
152. #99×C131D4semidirect
305. C22⋊C4×C131C2×D4semidirect
372. C23×C131#121semidirect
439. C2×C4×C131#121semidirect
492. C22×C131B(4,𝔽2)semidirect
522. #24404C131direct (N × H)
523. C131#24404direct (N × H)
524. #3484C2×C131semidirect
525. C2×B(4,𝔽2)C2×C131semidirect
526. C22×#99C2×C131semidirect
527. #2410C2×C131semidirect
528. #2403C2×C131semidirect
529. #2044C2×C131semidirect
530. #2021C2×C131semidirect
531. #1898C2×C131semidirect
532. #1889C2×C131semidirect
533. #1867C2×C131semidirect
534. #1790C2×C131semidirect
537. C23×D4C22×C131semidirect
551. C2×#120C22×C131semidirect
552. C2×#120C22×C131semidirect
554. C22×C22⋊C4C22×C131semidirect
559. C2×#99C22×C131semidirect
560. C2×#99C22×C131semidirect
561. C2×#99C22×C131semidirect
569. #386C22×C131semidirect
570. #386C22×C131semidirect
571. #385C22×C131semidirect
572. #379C22×C131semidirect
573. #379C22×C131semidirect
574. #342C22×C131semidirect
575. #342C22×C131semidirect
576. C25D4×C131semidirect
601. C22×D4D4×C131semidirect
602. C22×D4D4×C131semidirect
603. C22×D4D4×C131semidirect
604. C22×D4D4×C131semidirect
609. C23×C4D4×C131semidirect
664. C2×C22⋊C4D4×C131semidirect
665. C2×C22⋊C4D4×C131semidirect
675. #99D4×C131semidirect
828. C22⋊C4C2×D4×C131semidirect
895. C23#121×C131semidirect
962. C2×C4#121×C131semidirect
1015. C22B(4,𝔽2)×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
C2×B(4,𝔽2)×C1312
C22×#99×C1312
#2410×C1312
#2403×C1312
#2044×C1312
#2021×C1312
#1898×C1312
#1889×C1312
#1867×C1312
#1790×C1312
#24404131