Finite Group Databasebeta

← C131×#23903 #45709787

Subgroups — C131×#23903 #45709787

Order 33536.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic, complemented
2C2×#534×C131C211yesmaximal, characteristic, complemented
3C2×#458×C131C211yesmaximal, characteristic, complemented
4C2×B(4,𝔽2)×C131C211yesmaximal, characteristic, complemented
5#2613×C131C212yesmaximal, complemented
6#2022×C131C212yesmaximal, complemented
7#2021×C131C212yesmaximal, complemented
8#1898×C131C212yesmaximal, complemented
9#1890×C131C211yesmaximal, characteristic, complemented
10#1889×C131C211yesmaximal, characteristic, complemented
11#1781×C131C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C131C2211yescharacteristic
13C23×D4×C131C2211yescharacteristic
14C23×D4×C131C2211yescharacteristic, complemented
15#546×C131—24no—
16D42×C131—24no—
17#535×C131—21no—
18#534×C131—21no—
19#534×C131—24no—
20#534×C131—24no—
21#534×C131C2212yes—
22#525×C131—21no—
23C2×#123×C131—21no—
24C2×#123×C131C2211yescharacteristic
25C2×#123×C131C2211yescharacteristic, complemented
26C2×#123×C131C2212yescomplemented
27C2×#121×C131—21no—
28C2×#121×C131—21no—
29C2×#120×C131—21no—
30C2×#120×C131—21no—
31C2×#120×C131C2211yescharacteristic
32C2×#120×C131C2212yes—
33C2×#120×C131C2211yescharacteristic, complemented
34C2×#120×C131C2212yescomplemented
35#518×C131C2211yescharacteristic
36C22×C22⋊C4×C131C2211yescharacteristic, complemented
37#458×C131—24no—
38B(4,𝔽2)×C131—24no—
39C2×#99×C131C2211yescharacteristic
40C2×#99×C131C2211yescharacteristic
41C2×#99×C131C2212yescomplemented
42C2×#99×C131C2212yescomplemented
43C2×#99×C131C2212yescomplemented
44#394×C131—24no—
45#392×C131—24no—
46#381×C131C2212yescomplemented
47#379×C131C2212yescomplemented
48#379×C131C2212yescomplemented
49#342×C131C2212yescomplemented
50#342×C131C2212yescomplemented
51C25×C131D411yescharacteristic, complemented
52C25×C131C2311yescharacteristic
53C25×C131C2311yescharacteristic
54H(5,𝔽2)×C131—22no—
55H(5,𝔽2)×C131—22no—
56H(5,𝔽2)×C131—42no—
57C2×#41×C131—21no—
58C2×#41×C131—22no—
59C22×D4×C131—21no—
60C22×D4×C131—21no—
61C22×D4×C131—21no—
62C22×D4×C131—22no—
63C22×D4×C131—24no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131—22no—
69C22×D4×C131—22no—
70C22×D4×C131—24no—
71C22×D4×C131—22no—
72C22×D4×C131—22no—
73C22×D4×C131—42no—
74C22×D4×C131—42no—
75C22×D4×C131D411yescharacteristic, complemented
76C22×D4×C131D411yescharacteristic, complemented
77C22×D4×C131D414yescomplemented
78C22×D4×C131C2312yes—
79C22×D4×C131C2311yescharacteristic
80C22×D4×C131C2311yescharacteristic
81C23×C4×C131—21no—
82C23×C4×C131D411yescharacteristic, complemented
83C23×C4×C131C2311yescharacteristic
84#127×C131—22no—
85#124×C131—22no—
86#123×C131—28no—
87#123×C131—22no—
88#123×C131—22no—
89#123×C131—22no—
90#123×C131—22no—
91#123×C131—22no—
92#123×C131—22no—
93#123×C131—24no—
94#123×C131—42no—
95#123×C131D414yescomplemented
96C22⋊Q8×C131—22no—
97#121×C131—28no—
98#121×C131—28no—
99#121×C131—22no—
100#121×C131—24no—
101#121×C131—24no—
102#121×C131—24no—
103#120×C131—28no—
104#120×C131—24no—
105#120×C131—22no—
106#120×C131—22no—
107#120×C131—22no—
108#120×C131—22no—
109#120×C131—24no—
110#120×C131—22no—
111#120×C131—22no—
112#120×C131—22no—
113#120×C131—22no—
114#120×C131—24no—
115#120×C131—42no—
116#120×C131D414yescomplemented
117C4×D4×C131—24no—
118C4×D4×C131—24no—
119#117×C131—21no—
120C2×C4⋊C4×C131—21no—
121C2×C4⋊C4×C131—21no—
122C2×C4⋊C4×C131—22no—
123C2×C22⋊C4×C131—22no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—22no—
131C2×C22⋊C4×C131—22no—
132C2×C22⋊C4×C131—22no—
133C2×C22⋊C4×C131—22no—
134C2×C22⋊C4×C131—24no—
135C2×C22⋊C4×C131—24no—
136C2×C22⋊C4×C131D414yescomplemented
137C2×C22⋊C4×C131C2312yes—
138C2×C22⋊C4×C131C2312yes—
139C2×C22⋊C4×C131C2312yes—
140C2×C22⋊C4×C131C2311yescharacteristic
141C2×C22⋊C4×C131C2311yescharacteristic
142#99×C131—22no—
143#99×C131—22no—
144#99×C131—24no—
145#99×C131—24no—
146#99×C131—42no—
147#95×C131—24no—
148C24×C131—21no—
149C24×C131—21no—
150C24×C131—22no—
151C24×C131—21no—
152C24×C131—22no—
153C24×C131—21no—
154C24×C131—22no—
155C24×C131—22no—
156C24×C131—21no—
157C24×C131—22no—
158C24×C131—41no—
159C24×C131—82no—
160C24×C131—82no—
161C24×C131—82no—
162C24×C131C2×D411yescharacteristic
163C24×C131C2×D412yes—
164C24×C131C2×D411yescharacteristic
165C24×C131C2×D414yes—
166C24×C131C2×D411yescharacteristic
167C24×C131C2×D411yescharacteristic
168C24×C131C2×D412yescomplemented
169C24×C131C2411yescharacteristic
170#41×C131—44no—
171#41×C131—44no—
172#41×C131—42no—
173#41×C131—42no—
174C2×Q8×C131—21no—
175C2×D4×C131—22no—
176C2×D4×C131—22no—
177C2×D4×C131—22no—
178C2×D4×C131—24no—
179C2×D4×C131—24no—
180C2×D4×C131—21no—
181C2×D4×C131—24no—
182C2×D4×C131—22no—
183C2×D4×C131—22no—
184C2×D4×C131—22no—
185C2×D4×C131—22no—
186C2×D4×C131—22no—
187C2×D4×C131—22no—
188C2×D4×C131—22no—
189C2×D4×C131—21no—
190C2×D4×C131—21no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—22no—
194C2×D4×C131—22no—
195C2×D4×C131—24no—
196C2×D4×C131—24no—
197C2×D4×C131—24no—
198C2×D4×C131—24no—
199C2×D4×C131—22no—
200C2×D4×C131—41no—
201C2×D4×C131—41no—
202C2×D4×C131—48no—
203C2×D4×C131—48no—
204C2×D4×C131—48no—
205C2×D4×C131—44no—
206C2×D4×C131—44no—
207C2×D4×C131—48no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—44no—
215C2×D4×C131—84no—
216C2×D4×C131—82no—
217C2×D4×C131—82no—
218C2×D4×C131—84no—
219C2×D4×C131—84no—
220C2×D4×C131C2×D412yes—
221C2×D4×C131C2×D412yes—
222C22×C4×C131—21no—
223C22×C4×C131—22no—
224C22×C4×C131—22no—
225C22×C4×C131—22no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—22no—
231C22×C4×C131—22no—
232C22×C4×C131—24no—
233C22×C4×C131—22no—
234C22×C4×C131—22no—
235C22×C4×C131—22no—
236C22×C4×C131—41no—
237C22×C4×C131—82no—
238C22×C4×C131C2×D412yes—
239C22×C4×C131C2×D411yescharacteristic
240C22×C4×C131C2×D411yescharacteristic
241C22×C4×C131C2×D414yes—
242C22×C4×C131C2×D412yescomplemented
243C4⋊C4×C131—24no—
244C4⋊C4×C131—22no—
245C4⋊C4×C131—24no—
246C4⋊C4×C131—24no—
247C4⋊C4×C131—44no—
248C22⋊C4×C131—24no—
249C22⋊C4×C131—22no—
250C22⋊C4×C131—24no—
251C22⋊C4×C131—24no—
252C22⋊C4×C131—24no—
253C22⋊C4×C131—24no—
254C22⋊C4×C131—24no—
255C22⋊C4×C131—24no—
256C22⋊C4×C131—24no—
257C22⋊C4×C131—21no—
258C22⋊C4×C131—21no—
259C22⋊C4×C131—22no—
260C22⋊C4×C131—22no—
261C22⋊C4×C131—24no—
262C22⋊C4×C131—22no—
263C22⋊C4×C131—22no—
264C22⋊C4×C131—22no—
265C22⋊C4×C131—22no—
266C22⋊C4×C131—44no—
267C22⋊C4×C131—44no—
268C22⋊C4×C131—84no—
269C22⋊C4×C131—84no—
270C22⋊C4×C131C2×D412yescomplemented
271C22⋊C4×C131C2×D412yescomplemented
272C42×C131—22no—
273C23×C131—21no—
274C23×C131—21no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—24no—
280C23×C131—24no—
281C23×C131—21no—
282C23×C131—22no—
283C23×C131—21no—
284C23×C131—22no—
285C23×C131—24no—
286C23×C131—21no—
287C23×C131—22no—
288C23×C131—22no—
289C23×C131—42no—
290C23×C131—42no—
291C23×C131—42no—
292C23×C131—44no—
293C23×C131—44no—
294C23×C131—44no—
295C23×C131—42no—
296C23×C131—42no—
297C23×C131—44no—
298C23×C131—44no—
299C23×C131—42no—
300C23×C131—42no—
301C23×C131—44no—
302C23×C131—42no—
303C23×C131—44no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—42no—
307C23×C131—82no—
308C23×C131—82no—
309C23×C131—82no—
310C23×C131—82no—
311C23×C131—82no—
312C23×C131—84no—
313C23×C131—84no—
314C23×C131—84no—
315C23×C131—82no—
316C23×C131—84no—
317C23×C131#12012yes—
318C23×C131#12012yes—
319C23×C131#12012yes—
320C23×C131C22×D411yescharacteristic
321C23×C131C22×D412yes—
322C23×C131C22×D411yescharacteristic
323C23×C131C22×D411yescharacteristic
324C23×C131H(5,𝔽2)12yes—
325Q8×C131—42no—
326D4×C131—24no—
327D4×C131—24no—
328D4×C131—44no—
329D4×C131—42no—
330D4×C131—44no—
331D4×C131—48no—
332D4×C131—48no—
333D4×C131—44no—
334D4×C131—48no—
335D4×C131—42no—
336D4×C131—42no—
337D4×C131—42no—
338D4×C131—42no—
339D4×C131—42no—
340D4×C131—42no—
341D4×C131—84no—
342D4×C131—84no—
343D4×C131—84no—
344D4×C131—84no—
345D4×C131—88no—
346C2×C4×C131—21no—
347C2×C4×C131—21no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—21no—
351C2×C4×C131—22no—
352C2×C4×C131—24no—
353C2×C4×C131—22no—
354C2×C4×C131—21no—
355C2×C4×C131—21no—
356C2×C4×C131—22no—
357C2×C4×C131—24no—
358C2×C4×C131—22no—
359C2×C4×C131—44no—
360C2×C4×C131—44no—
361C2×C4×C131—42no—
362C2×C4×C131—42no—
363C2×C4×C131—42no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—42no—
367C2×C4×C131—44no—
368C2×C4×C131—44no—
369C2×C4×C131—44no—
370C2×C4×C131—42no—
371C2×C4×C131—42no—
372C2×C4×C131—84no—
373C2×C4×C131—82no—
374C2×C4×C131#12012yes—
375C22×C131—24no—
376C22×C131—22no—
377C22×C131—22no—
378C22×C131—22no—
379C22×C131—22no—
380C22×C131—22no—
381C22×C131—24no—
382C22×C131—22no—
383C22×C131—41no—
384C22×C131—41no—
385C22×C131—42no—
386C22×C131—42no—
387C22×C131—42no—
388C22×C131—42no—
389C22×C131—42no—
390C22×C131—42no—
391C22×C131—42no—
392C22×C131—42no—
393C22×C131—42no—
394C22×C131—44no—
395C22×C131—44no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—41no—
400C22×C131—44no—
401C22×C131—42no—
402C22×C131—84no—
403C22×C131—84no—
404C22×C131—81no—
405C22×C131—82no—
406C22×C131—82no—
407C22×C131—81no—
408C22×C131—84no—
409C22×C131—82no—
410C22×C131—88no—
411C22×C131—82no—
412C22×C131—162no—
413C22×C131C2×#12011yescharacteristic
414C22×C131C2×#12011yescharacteristic
415C22×C131#53411yescharacteristic
416C22×C131D4212yes—
417C22×C131D4212yes—
418C4×C131—22no—
419C4×C131—42no—
420C4×C131—42no—
421C4×C131—41no—
422C4×C131—42no—
423C4×C131—42no—
424C4×C131—44no—
425C4×C131—82no—
426C4×C131—82no—
427C2×C131—21no—
428C2×C131—22no—
429C2×C131—22no—
430C2×C131—21no—
431C2×C131—42no—
432C2×C131—42no—
433C2×C131—42no—
434C2×C131—82no—
435C2×C131—81no—
436C2×C131—82no—
437C2×C131#240311yescharacteristic
438C2×C131#302612yes—
439#23903C13111yesmaximal, characteristic, direct product factor, Sylow
440C131#2390311yescharacteristic, direct product factor, Sylow
441#3484C2×C13111yescharacteristic, complemented
442C2×#534C2×C13111yescharacteristic, complemented
443C2×#458C2×C13111yescharacteristic, complemented
444C2×B(4,𝔽2)C2×C13111yescharacteristic, complemented
445#2613C2×C13112yescomplemented
446#2022C2×C13112yescomplemented
447#2021C2×C13112yescomplemented
448#1898C2×C13112yescomplemented
449#1890C2×C13111yescharacteristic, complemented
450#1889C2×C13111yescharacteristic, complemented
451#1781C2×C13111yescharacteristic, complemented
452C2×H(5,𝔽2)C22×C13111yescharacteristic
453C23×D4C22×C13111yescharacteristic
454C23×D4C22×C13111yescharacteristic, complemented
455#546—24no—
456D42—24no—
457#535—21no—
458#534—21no—
459#534—24no—
460#534—24no—
461#534C22×C13112yes—
462#525—21no—
463C2×#123—21no—
464C2×#123C22×C13111yescharacteristic
465C2×#123C22×C13111yescharacteristic, complemented
466C2×#123C22×C13112yescomplemented
467C2×#121—21no—
468C2×#121—21no—
469C2×#120—21no—
470C2×#120—21no—
471C2×#120C22×C13111yescharacteristic
472C2×#120C22×C13112yes—
473C2×#120C22×C13111yescharacteristic, complemented
474C2×#120C22×C13112yescomplemented
475#518C22×C13111yescharacteristic
476C22×C22⋊C4C22×C13111yescharacteristic, complemented
477#458—24no—
478B(4,𝔽2)—24no—
479C2×#99C22×C13111yescharacteristic
480C2×#99C22×C13111yescharacteristic
481C2×#99C22×C13112yescomplemented
482C2×#99C22×C13112yescomplemented
483C2×#99C22×C13112yescomplemented
484#394—24no—
485#392—24no—
486#381C22×C13112yescomplemented
487#379C22×C13112yescomplemented
488#379C22×C13112yescomplemented
489#342C22×C13112yescomplemented
490#342C22×C13112yescomplemented
491C25D4×C13111yescharacteristic, complemented
492C25C23×C13111yescharacteristic
493C25C23×C13111yescharacteristic
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—42no—
497C2×#41—21no—
498C2×#41—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—24no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—24no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4D4×C13111yescharacteristic, complemented
516C22×D4D4×C13111yescharacteristic, complemented
517C22×D4D4×C13114yescomplemented
518C22×D4C23×C13112yes—
519C22×D4C23×C13111yescharacteristic
520C22×D4C23×C13111yescharacteristic
521C23×C4—21no—
522C23×C4D4×C13111yescharacteristic, complemented
523C23×C4C23×C13111yescharacteristic
524#127—22no—
525#124—22no—
526#123—28no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—24no—
534#123—42no—
535#123D4×C13114yescomplemented
536C22⋊Q8—22no—
537#121—28no—
538#121—28no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#120—28no—
544#120—24no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—24no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—24no—
555#120—42no—
556#120D4×C13114yescomplemented
557C4×D4—24no—
558C4×D4—24no—
559#117—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4D4×C13114yescomplemented
577C2×C22⋊C4C23×C13112yes—
578C2×C22⋊C4C23×C13112yes—
579C2×C22⋊C4C23×C13112yes—
580C2×C22⋊C4C23×C13111yescharacteristic
581C2×C22⋊C4C23×C13111yescharacteristic
582#99—22no—
583#99—22no—
584#99—24no—
585#99—24no—
586#99—42no—
587#95—24no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C13111yescharacteristic
603C24C2×D4×C13112yes—
604C24C2×D4×C13111yescharacteristic
605C24C2×D4×C13114yes—
606C24C2×D4×C13111yescharacteristic
607C24C2×D4×C13111yescharacteristic
608C24C2×D4×C13112yescomplemented
609C24C24×C13111yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C13112yes—
661C2×D4C2×D4×C13112yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C13112yes—
679C22×C4C2×D4×C13111yescharacteristic
680C22×C4C2×D4×C13111yescharacteristic
681C22×C4C2×D4×C13114yes—
682C22×C4C2×D4×C13112yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C13112yescomplemented
711C22⋊C4C2×D4×C13112yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23#120×C13112yes—
758C23#120×C13112yes—
759C23#120×C13112yes—
760C23C22×D4×C13111yescharacteristic
761C23C22×D4×C13112yes—
762C23C22×D4×C13111yescharacteristic
763C23C22×D4×C13111yescharacteristic
764C23H(5,𝔽2)×C13112yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4#120×C13112yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—24no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—41no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×#120×C13111yescharacteristic
854C22C2×#120×C13111yescharacteristic
855C22#534×C13111yescharacteristic
856C22D42×C13112yes—
857C22D42×C13112yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—44no—
862C4—41no—
863C4—42no—
864C4—42no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2#2403×C13111yescharacteristic
878C2#3026×C13112yes—
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×#534×C131C2semidirect
3. C2×#458×C131C2semidirect
4. C2×B(4,𝔽2)×C131C2semidirect
5. #2613×C131C2semidirect
6. #2022×C131C2semidirect
7. #2021×C131C2semidirect
8. #1898×C131C2semidirect
9. #1890×C131C2semidirect
10. #1889×C131C2semidirect
11. #1781×C131C2semidirect
14. C23×D4×C131C22semidirect
25. C2×#123×C131C22semidirect
26. C2×#123×C131C22semidirect
33. C2×#120×C131C22semidirect
34. C2×#120×C131C22semidirect
36. C22×C22⋊C4×C131C22semidirect
41. C2×#99×C131C22semidirect
42. C2×#99×C131C22semidirect
43. C2×#99×C131C22semidirect
46. #381×C131C22semidirect
47. #379×C131C22semidirect
48. #379×C131C22semidirect
49. #342×C131C22semidirect
50. #342×C131C22semidirect
51. C25×C131D4semidirect
75. C22×D4×C131D4semidirect
76. C22×D4×C131D4semidirect
77. C22×D4×C131D4semidirect
82. C23×C4×C131D4semidirect
95. #123×C131D4semidirect
116. #120×C131D4semidirect
136. C2×C22⋊C4×C131D4semidirect
168. C24×C131C2×D4semidirect
242. C22×C4×C131C2×D4semidirect
270. C22⋊C4×C131C2×D4semidirect
271. C22⋊C4×C131C2×D4semidirect
439. #23903C131direct (N × H)
440. C131#23903direct (N × H)
441. #3484C2×C131semidirect
442. C2×#534C2×C131semidirect
443. C2×#458C2×C131semidirect
444. C2×B(4,𝔽2)C2×C131semidirect
445. #2613C2×C131semidirect
446. #2022C2×C131semidirect
447. #2021C2×C131semidirect
448. #1898C2×C131semidirect
449. #1890C2×C131semidirect
450. #1889C2×C131semidirect
451. #1781C2×C131semidirect
454. C23×D4C22×C131semidirect
465. C2×#123C22×C131semidirect
466. C2×#123C22×C131semidirect
473. C2×#120C22×C131semidirect
474. C2×#120C22×C131semidirect
476. C22×C22⋊C4C22×C131semidirect
481. C2×#99C22×C131semidirect
482. C2×#99C22×C131semidirect
483. C2×#99C22×C131semidirect
486. #381C22×C131semidirect
487. #379C22×C131semidirect
488. #379C22×C131semidirect
489. #342C22×C131semidirect
490. #342C22×C131semidirect
491. C25D4×C131semidirect
515. C22×D4D4×C131semidirect
516. C22×D4D4×C131semidirect
517. C22×D4D4×C131semidirect
522. C23×C4D4×C131semidirect
535. #123D4×C131semidirect
556. #120D4×C131semidirect
576. C2×C22⋊C4D4×C131semidirect
608. C24C2×D4×C131semidirect
682. C22×C4C2×D4×C131semidirect
710. C22⋊C4C2×D4×C131semidirect
711. C22⋊C4C2×D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
C2×#534×C1312
C2×#458×C1312
C2×B(4,𝔽2)×C1312
#2613×C1312
#2022×C1312
#2021×C1312
#1898×C1312
#1890×C1312
#1889×C1312
#1781×C1312
#23903131