Finite Group Databasebeta

← C131×#14725 #45700609

Subgroups — C131×#14725 #45700609

Order 33536.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C131C211yesmaximal, characteristic
2C23×C22⋊C4×C131C211yesmaximal, characteristic, complemented
3C2×#394×C131C212yesmaximal, complemented
4C2×#386×C131C211yesmaximal, characteristic, complemented
5C2×#386×C131C211yesmaximal, characteristic, complemented
6C2×#380×C131C211yesmaximal, characteristic, complemented
7C2×#379×C131C211yesmaximal, characteristic, complemented
8#1440×C131C212yesmaximal, complemented
9#1439×C131C212yesmaximal, complemented
10#1438×C131C212yesmaximal, complemented
11C22⋊#95×C131C211yesmaximal, characteristic, complemented
12C26×C131C2211yescharacteristic
13C23×D4×C131C2211yescharacteristic
14C23×D4×C131C2212yes—
15C24×C4×C131C2211yescharacteristic
16C24×C4×C131C2211yescharacteristic
17C2×#120×C131—24no—
18C2×#120×C131—24no—
19C2×#120×C131—24no—
20C22×C4⋊C4×C131C2212yescomplemented
21C22×C22⋊C4×C131—24no—
22C22×C22⋊C4×C131—28no—
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2212yes—
26C22×C22⋊C4×C131C2212yes—
27C22×C22⋊C4×C131C2212yes—
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2212yes—
30C22×C22⋊C4×C131C2212yes—
31C22×C22⋊C4×C131C2211yescharacteristic, complemented
32C22×C22⋊C4×C131C2212yescomplemented
33C22×C22⋊C4×C131C2211yescharacteristic, complemented
34#394×C131—28no—
35#386×C131—24no—
36#386×C131—24no—
37#380×C131—24no—
38#379×C131—24no—
39C2×#95×C131C2212yescomplemented
40C2×#95×C131C2211yescharacteristic, complemented
41C2×#95×C131C2212yescomplemented
42C2×#95×C131C2211yescharacteristic, complemented
43C2×#95×C131C2212yescomplemented
44C2×#95×C131C2212yescomplemented
45C25×C131—24no—
46C25×C131—22no—
47C25×C131—24no—
48C25×C131—22no—
49C25×C131—22no—
50C25×C131—22no—
51C25×C131—22no—
52C25×C131—22no—
53C25×C131—42no—
54C25×C131—42no—
55C25×C131D414yes—
56C25×C131C2311yescharacteristic
57C25×C131C2312yes—
58C25×C131C2311yescharacteristic
59C22×D4×C131—24no—
60C22×D4×C131—24no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—24no—
68C22×D4×C131—24no—
69C22×D4×C131—24no—
70C22×D4×C131—42no—
71C22×D4×C131—42no—
72C22×D4×C131D414yes—
73C23×C4×C131—22no—
74C23×C4×C131—22no—
75C23×C4×C131—22no—
76C23×C4×C131—24no—
77C23×C4×C131—24no—
78C23×C4×C131—22no—
79C23×C4×C131—22no—
80C23×C4×C131—42no—
81C23×C4×C131—42no—
82C23×C4×C131D414yescomplemented
83C23×C4×C131C2312yes—
84C23×C4×C131C2311yescharacteristic
85C23×C4×C131C2311yescharacteristic
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2312yes—
88C23×C4×C131C2312yes—
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91#120×C131—232no—
92C2×C4⋊C4×C131—24no—
93C2×C4⋊C4×C131—24no—
94C2×C4⋊C4×C131—42no—
95C2×C22⋊C4×C131—232no—
96C2×C22⋊C4×C131—24no—
97C2×C22⋊C4×C131—24no—
98C2×C22⋊C4×C131—22no—
99C2×C22⋊C4×C131—22no—
100C2×C22⋊C4×C131—24no—
101C2×C22⋊C4×C131—24no—
102C2×C22⋊C4×C131—24no—
103C2×C22⋊C4×C131—24no—
104C2×C22⋊C4×C131—24no—
105C2×C22⋊C4×C131—24no—
106C2×C22⋊C4×C131—24no—
107C2×C22⋊C4×C131—24no—
108C2×C22⋊C4×C131—22no—
109C2×C22⋊C4×C131—24no—
110C2×C22⋊C4×C131—22no—
111C2×C22⋊C4×C131—22no—
112C2×C22⋊C4×C131—22no—
113C2×C22⋊C4×C131—22no—
114C2×C22⋊C4×C131—24no—
115C2×C22⋊C4×C131—24no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—24no—
118C2×C22⋊C4×C131—24no—
119C2×C22⋊C4×C131—22no—
120C2×C22⋊C4×C131—22no—
121C2×C22⋊C4×C131—42no—
122C2×C22⋊C4×C131—42no—
123C2×C22⋊C4×C131—42no—
124C2×C22⋊C4×C131—42no—
125C2×C22⋊C4×C131D414yes—
126C2×C22⋊C4×C131D418yescomplemented
127#95×C131—24no—
128#95×C131—24no—
129#95×C131—22no—
130#95×C131—22no—
131#95×C131—24no—
132#95×C131—42no—
133C24×C131—22no—
134C24×C131—22no—
135C24×C131—22no—
136C24×C131—22no—
137C24×C131—28no—
138C24×C131—28no—
139C24×C131—216no—
140C24×C131—216no—
141C24×C131—28no—
142C24×C131—22no—
143C24×C131—22no—
144C24×C131—22no—
145C24×C131—22no—
146C24×C131—22no—
147C24×C131—22no—
148C24×C131—22no—
149C24×C131—22no—
150C24×C131—22no—
151C24×C131—22no—
152C24×C131—22no—
153C24×C131—22no—
154C24×C131—28no—
155C24×C131—28no—
156C24×C131—21no—
157C24×C131—22no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—21no—
161C24×C131—21no—
162C24×C131—21no—
163C24×C131—22no—
164C24×C131—22no—
165C24×C131—22no—
166C24×C131—48no—
167C24×C131—48no—
168C24×C131—48no—
169C24×C131—48no—
170C24×C131—48no—
171C24×C131—48no—
172C24×C131—48no—
173C24×C131—48no—
174C24×C131—48no—
175C24×C131—44no—
176C24×C131—44no—
177C24×C131—48no—
178C24×C131—44no—
179C24×C131—44no—
180C24×C131—44no—
181C24×C131—44no—
182C24×C131C2×D412yes—
183C24×C131C2×D414yes—
184C24×C131C2×D414yes—
185C24×C131C2×D412yes—
186C24×C131C2×D412yes—
187C24×C131C2×D412yes—
188C24×C131C2×D412yes—
189C24×C131#4114yes—
190C24×C131#4112yes—
191C24×C131#4112yes—
192C24×C131#4112yes—
193C24×C131C2411yescharacteristic
194C2×D4×C131—216no—
195C2×D4×C131—28no—
196C2×D4×C131—28no—
197C2×D4×C131—28no—
198C2×D4×C131—48no—
199C2×D4×C131—48no—
200C2×D4×C131—48no—
201C2×D4×C131—48no—
202C2×D4×C131—48no—
203C2×D4×C131—48no—
204C2×D4×C131—44no—
205C2×D4×C131—44no—
206C2×D4×C131—44no—
207C2×D4×C131—44no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—22no—
211C22×C4×C131—28no—
212C22×C4×C131—28no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—22no—
216C22×C4×C131—22no—
217C22×C4×C131—22no—
218C22×C4×C131—22no—
219C22×C4×C131—22no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—22no—
223C22×C4×C131—22no—
224C22×C4×C131—21no—
225C22×C4×C131—22no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
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—28no—
236C22×C4×C131—21no—
237C22×C4×C131—22no—
238C22×C4×C131—22no—
239C22×C4×C131—21no—
240C22×C4×C131—22no—
241C22×C4×C131—22no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—22no—
245C22×C4×C131—21no—
246C22×C4×C131—22no—
247C22×C4×C131—21no—
248C22×C4×C131—22no—
249C22×C4×C131—22no—
250C22×C4×C131—22no—
251C22×C4×C131—22no—
252C22×C4×C131—22no—
253C22×C4×C131—44no—
254C22×C4×C131—48no—
255C22×C4×C131—48no—
256C22×C4×C131—48no—
257C22×C4×C131—48no—
258C22×C4×C131—44no—
259C22×C4×C131—44no—
260C22×C4×C131C2×D412yes—
261C22×C4×C131C2×D412yes—
262C22×C4×C131C2×D414yes—
263C22×C4×C131C2×D414yes—
264C22×C4×C131C2×D412yes—
265C22×C4×C131C2×D414yes—
266C4⋊C4×C131—48no—
267C22⋊C4×C131—216no—
268C22⋊C4×C131—216no—
269C22⋊C4×C131—28no—
270C22⋊C4×C131—216no—
271C22⋊C4×C131—48no—
272C22⋊C4×C131—44no—
273C22⋊C4×C131—48no—
274C22⋊C4×C131—44no—
275C22⋊C4×C131—48no—
276C22⋊C4×C131—44no—
277C22⋊C4×C131—44no—
278C23×C131—22no—
279C23×C131—24no—
280C23×C131—22no—
281C23×C131—24no—
282C23×C131—22no—
283C23×C131—24no—
284C23×C131—22no—
285C23×C131—24no—
286C23×C131—24no—
287C23×C131—24no—
288C23×C131—24no—
289C23×C131—24no—
290C23×C131—24no—
291C23×C131—24no—
292C23×C131—24no—
293C23×C131—24no—
294C23×C131—232no—
295C23×C131—24no—
296C23×C131—24no—
297C23×C131—24no—
298C23×C131—24no—
299C23×C131—24no—
300C23×C131—24no—
301C23×C131—24no—
302C23×C131—24no—
303C23×C131—24no—
304C23×C131—24no—
305C23×C131—24no—
306C23×C131—24no—
307C23×C131—24no—
308C23×C131—24no—
309C23×C131—24no—
310C23×C131—24no—
311C23×C131—24no—
312C23×C131—24no—
313C23×C131—22no—
314C23×C131—22no—
315C23×C131—22no—
316C23×C131—24no—
317C23×C131—24no—
318C23×C131—432no—
319C23×C131—432no—
320C23×C131—416no—
321C23×C131—416no—
322C23×C131—416no—
323C23×C131—416no—
324C23×C131—432no—
325C23×C131—432no—
326C23×C131—416no—
327C23×C131—42no—
328C23×C131—42no—
329C23×C131—42no—
330C23×C131—42no—
331C23×C131—42no—
332C23×C131—42no—
333C23×C131—42no—
334C23×C131—42no—
335C23×C131—42no—
336C23×C131—42no—
337C23×C131—42no—
338C23×C131—42no—
339C23×C131—42no—
340C23×C131—42no—
341C23×C131—42no—
342C23×C131—42no—
343C23×C131—416no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—41no—
347C23×C131—42no—
348C23×C131—41no—
349C23×C131—42no—
350C23×C131—41no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—42no—
354C23×C131—41no—
355C23×C131—42no—
356C23×C131—42no—
357C23×C131—42no—
358C23×C131—42no—
359C23×C131—42no—
360C23×C131—42no—
361C23×C131—42no—
362C23×C131#12014yes—
363C23×C131#12118yes—
364C23×C131#12114yes—
365C23×C131#12114yes—
366C23×C131#12114yes—
367C23×C131#12314yes—
368C23×C131#12314yes—
369C23×C131#12414yes—
370C23×C131C22×D411yescharacteristic
371C23×C131C22×D411yescharacteristic
372C23×C131C22×D411yescharacteristic
373C23×C131C22×D412yes—
374C23×C131C22×D411yescharacteristic
375C23×C131C2×#4111yescharacteristic
376C23×C131C2×#4111yescharacteristic
377C23×C131C2×#4111yescharacteristic
378C23×C131C2×#4112yes—
379C23×C131H(5,𝔽2)12yes—
380C23×C131H(5,𝔽2)12yes—
381D4×C131—432no—
382D4×C131—416no—
383C2×C4×C131—22no—
384C2×C4×C131—22no—
385C2×C4×C131—24no—
386C2×C4×C131—24no—
387C2×C4×C131—24no—
388C2×C4×C131—22no—
389C2×C4×C131—22no—
390C2×C4×C131—24no—
391C2×C4×C131—22no—
392C2×C4×C131—22no—
393C2×C4×C131—22no—
394C2×C4×C131—22no—
395C2×C4×C131—24no—
396C2×C4×C131—24no—
397C2×C4×C131—24no—
398C2×C4×C131—24no—
399C2×C4×C131—416no—
400C2×C4×C131—416no—
401C2×C4×C131—42no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—42no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—42no—
408C2×C4×C131—42no—
409C2×C4×C131—42no—
410C2×C4×C131—42no—
411C2×C4×C131—42no—
412C2×C4×C131—42no—
413C2×C4×C131—42no—
414C2×C4×C131—42no—
415C2×C4×C131—41no—
416C2×C4×C131—42no—
417C2×C4×C131—41no—
418C2×C4×C131—42no—
419C2×C4×C131—41no—
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—41no—
427C2×C4×C131—42no—
428C2×C4×C131—42no—
429C2×C4×C131—42no—
430C2×C4×C131—42no—
431C2×C4×C131—42no—
432C2×C4×C131#12014yescomplemented
433C22×C131—24no—
434C22×C131—24no—
435C22×C131—24no—
436C22×C131—24no—
437C22×C131—28no—
438C22×C131—24no—
439C22×C131—28no—
440C22×C131—28no—
441C22×C131—28no—
442C22×C131—24no—
443C22×C131—28no—
444C22×C131—28no—
445C22×C131—28no—
446C22×C131—464no—
447C22×C131—44no—
448C22×C131—44no—
449C22×C131—44no—
450C22×C131—44no—
451C22×C131—44no—
452C22×C131—44no—
453C22×C131—44no—
454C22×C131—44no—
455C22×C131—44no—
456C22×C131—44no—
457C22×C131—44no—
458C22×C131—44no—
459C22×C131—42no—
460C22×C131—42no—
461C22×C131—44no—
462C22×C131—44no—
463C22×C131—42no—
464C22×C131—81no—
465C22×C131—81no—
466C22×C131—81no—
467C22×C131—81no—
468C22×C131—82no—
469C22×C131—82no—
470C22×C131#39418yescomplemented
471C22×C131C2×#12011yescharacteristic
472C22×C131C2×#12011yescharacteristic
473C22×C131C2×#12111yescharacteristic
474C22×C131C2×#12112yes—
475C22×C131C2×#12111yescharacteristic
476C22×C131C2×#12111yescharacteristic
477C22×C131C2×#12311yescharacteristic
478C22×C131C2×#12311yescharacteristic
479C22×C131#52511yescharacteristic
480C22×C131#52512yes—
481C22×C131C2×#12411yescharacteristic
482C22×C131#53412yes—
483C22×C131#53411yescharacteristic
484C22×C131#53511yescharacteristic
485C22×C131#53812yes—
486C22×C131D4212yes—
487C22×C131D4212yes—
488C22×C131#54612yes—
489C22×C131#54612yes—
490C22×C131#54612yes—
491C22×C131#54612yes—
492C22×C131#55112yes—
493C22×C131#55112yes—
494C4×C131—24no—
495C4×C131—42no—
496C4×C131—44no—
497C4×C131—42no—
498C4×C131—44no—
499C4×C131—81no—
500C4×C131—81no—
501C4×C131—82no—
502C2×C131—28no—
503C2×C131—48no—
504C2×C131—82no—
505C2×C131C2×#39411yescharacteristic
506C2×C131#240811yescharacteristic
507C2×C131#241011yescharacteristic
508C2×C131#241012yes—
509C2×C131#241111yescharacteristic
510C2×C131#241212yes—
511C2×C131#241812yes—
512C2×C131#247212yes—
513C2×C131#253411yescharacteristic
514C2×C131#261711yescharacteristic
515C2×C131#284711yescharacteristic
516#14725C13111yesmaximal, characteristic, direct product factor, Sylow
517C131#1472511yescharacteristic, direct product factor, Sylow
518C22×#120C2×C13111yescharacteristic
519C23×C22⋊C4C2×C13111yescharacteristic, complemented
520C2×#394C2×C13112yescomplemented
521C2×#386C2×C13111yescharacteristic, complemented
522C2×#386C2×C13111yescharacteristic, complemented
523C2×#380C2×C13111yescharacteristic, complemented
524C2×#379C2×C13111yescharacteristic, complemented
525#1440C2×C13112yescomplemented
526#1439C2×C13112yescomplemented
527#1438C2×C13112yescomplemented
528C22⋊#95C2×C13111yescharacteristic, complemented
529C26C22×C13111yescharacteristic
530C23×D4C22×C13111yescharacteristic
531C23×D4C22×C13112yes—
532C24×C4C22×C13111yescharacteristic
533C24×C4C22×C13111yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C13112yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C13112yes—
541C22×C22⋊C4C22×C13112yes—
542C22×C22⋊C4C22×C13112yes—
543C22×C22⋊C4C22×C13111yescharacteristic
544C22×C22⋊C4C22×C13111yescharacteristic
545C22×C22⋊C4C22×C13111yescharacteristic
546C22×C22⋊C4C22×C13112yes—
547C22×C22⋊C4C22×C13112yes—
548C22×C22⋊C4C22×C13111yescharacteristic, complemented
549C22×C22⋊C4C22×C13112yescomplemented
550C22×C22⋊C4C22×C13111yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C13112yescomplemented
557C2×#95C22×C13112yescomplemented
558C2×#95C22×C13111yescharacteristic, complemented
559C2×#95C22×C13112yescomplemented
560C2×#95C22×C13111yescharacteristic, complemented
561C2×#95C22×C13112yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C13114yes—
573C25C23×C13111yescharacteristic
574C25C23×C13112yes—
575C25C23×C13111yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C13114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C13114yescomplemented
600C23×C4C23×C13112yes—
601C23×C4C23×C13111yescharacteristic
602C23×C4C23×C13111yescharacteristic
603C23×C4C23×C13111yescharacteristic
604C23×C4C23×C13112yes—
605C23×C4C23×C13112yes—
606C23×C4C23×C13111yescharacteristic
607C23×C4C23×C13111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C13114yes—
643C2×C22⋊C4D4×C13118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C13112yes—
700C24C2×D4×C13114yes—
701C24C2×D4×C13114yes—
702C24C2×D4×C13112yes—
703C24C2×D4×C13112yes—
704C24C2×D4×C13112yes—
705C24C2×D4×C13112yes—
706C24#41×C13114yes—
707C24#41×C13112yes—
708C24#41×C13112yes—
709C24#41×C13112yes—
710C24C24×C13111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C13112yes—
778C22×C4C2×D4×C13112yes—
779C22×C4C2×D4×C13114yes—
780C22×C4C2×D4×C13114yes—
781C22×C4C2×D4×C13112yes—
782C22×C4C2×D4×C13114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—416no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C13114yes—
880C23#121×C13118yes—
881C23#121×C13114yes—
882C23#121×C13114yes—
883C23#121×C13114yes—
884C23#123×C13114yes—
885C23#123×C13114yes—
886C23#124×C13114yes—
887C23C22×D4×C13111yescharacteristic
888C23C22×D4×C13111yescharacteristic
889C23C22×D4×C13111yescharacteristic
890C23C22×D4×C13112yes—
891C23C22×D4×C13111yescharacteristic
892C23C2×#41×C13111yescharacteristic
893C23C2×#41×C13111yescharacteristic
894C23C2×#41×C13111yescharacteristic
895C23C2×#41×C13112yes—
896C23H(5,𝔽2)×C13112yes—
897C23H(5,𝔽2)×C13112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C13114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C13118yescomplemented
988C22C2×#120×C13111yescharacteristic
989C22C2×#120×C13111yescharacteristic
990C22C2×#121×C13111yescharacteristic
991C22C2×#121×C13111yescharacteristic
992C22C2×#121×C13112yes—
993C22C2×#121×C13111yescharacteristic
994C22C2×#123×C13111yescharacteristic
995C22C2×#123×C13111yescharacteristic
996C22#525×C13111yescharacteristic
997C22#525×C13112yes—
998C22C2×#124×C13111yescharacteristic
999C22#534×C13111yescharacteristic
1000C22#534×C13112yes—
1001C22#535×C13111yescharacteristic
1002C22#538×C13112yes—
1003C22D42×C13112yes—
1004C22D42×C13112yes—
1005C22#546×C13112yes—
1006C22#546×C13112yes—
1007C22#546×C13112yes—
1008C22#546×C13112yes—
1009C22#551×C13112yes—
1010C22#551×C13112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C13111yescharacteristic
1023C2#2408×C13111yescharacteristic
1024C2#2410×C13111yescharacteristic
1025C2#2410×C13112yes—
1026C2#2411×C13111yescharacteristic
1027C2#2412×C13112yes—
1028C2#2418×C13112yes—
1029C2#2472×C13112yes—
1030C2#2534×C13111yescharacteristic
1031C2#2617×C13111yescharacteristic
1032C2#2847×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC22×#120×C131C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C131C2semidirect
3. C2×#394×C131C2semidirect
4. C2×#386×C131C2semidirect
5. C2×#386×C131C2semidirect
6. C2×#380×C131C2semidirect
7. C2×#379×C131C2semidirect
8. #1440×C131C2semidirect
9. #1439×C131C2semidirect
10. #1438×C131C2semidirect
11. C22⋊#95×C131C2semidirect
20. C22×C4⋊C4×C131C22semidirect
31. C22×C22⋊C4×C131C22semidirect
32. C22×C22⋊C4×C131C22semidirect
33. C22×C22⋊C4×C131C22semidirect
39. C2×#95×C131C22semidirect
40. C2×#95×C131C22semidirect
41. C2×#95×C131C22semidirect
42. C2×#95×C131C22semidirect
43. C2×#95×C131C22semidirect
44. C2×#95×C131C22semidirect
82. C23×C4×C131D4semidirect
126. C2×C22⋊C4×C131D4semidirect
432. C2×C4×C131#120semidirect
470. C22×C131#394semidirect
516. #14725C131direct (N × H)
517. C131#14725direct (N × H)
519. C23×C22⋊C4C2×C131semidirect
520. C2×#394C2×C131semidirect
521. C2×#386C2×C131semidirect
522. C2×#386C2×C131semidirect
523. C2×#380C2×C131semidirect
524. C2×#379C2×C131semidirect
525. #1440C2×C131semidirect
526. #1439C2×C131semidirect
527. #1438C2×C131semidirect
528. C22⋊#95C2×C131semidirect
537. C22×C4⋊C4C22×C131semidirect
548. C22×C22⋊C4C22×C131semidirect
549. C22×C22⋊C4C22×C131semidirect
550. C22×C22⋊C4C22×C131semidirect
556. C2×#95C22×C131semidirect
557. C2×#95C22×C131semidirect
558. C2×#95C22×C131semidirect
559. C2×#95C22×C131semidirect
560. C2×#95C22×C131semidirect
561. C2×#95C22×C131semidirect
599. C23×C4D4×C131semidirect
643. C2×C22⋊C4D4×C131semidirect
949. C2×C4#120×C131semidirect
987. C22#394×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1312
C23×C22⋊C4×C1312
C2×#394×C1312
C2×#386×C1312
C2×#380×C1312
C2×#379×C1312
#1440×C1312
#1439×C1312
#1438×C1312
C22⋊#95×C1312
#14725131