Finite Group Databasebeta

← C131×#24257 #45710141

Subgroups — C131×#24257 #45710141

Order 33536.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic, complemented
2C2×#463×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C2×#442×C131C211yesmaximal, characteristic, complemented
6#2537×C131C211yesmaximal, characteristic, complemented
7#2035×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1959×C131C211yesmaximal, characteristic, complemented
12#1955×C131C211yesmaximal, characteristic, complemented
13#1802×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21#546×C131—24no—
22#546×C131—24no—
23C2×#124×C131C2211yescharacteristic
24C2×#123×C131—21no—
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×#121×C131—21no—
27C2×#121×C131—21no—
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic, complemented
31C2×#120×C131—21no—
32C2×C4×D4×C131C2211yescharacteristic
33C2×C4×D4×C131C2211yescharacteristic
34C2×C4×D4×C131C2211yescharacteristic, complemented
35C22×C22⋊C4×C131—21no—
36#463×C131—24no—
37#449×C131—24no—
38#447×C131—24no—
39#442×C131—24no—
40C2×#106×C131C2211yescharacteristic, complemented
41C2×C4⋊C8×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#103×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic
51C2×#102×C131C2211yescharacteristic, complemented
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55C2×C22⋊C8×C131C2211yescharacteristic, complemented
56C2×#97×C131C2211yescharacteristic, complemented
57#394×C131—21no—
58#394×C131—21no—
59#384×C131C2211yescharacteristic, complemented
60#380×C131—21no—
61#380×C131C2211yescharacteristic
62#380×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64#340×C131C2211yescharacteristic, complemented
65C25×C131—21no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131C2311yescharacteristic
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—22no—
76C22×D4×C131—22no—
77C22×D4×C131—22no—
78C22×D4×C131—22no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—41no—
83C22×D4×C131—41no—
84C22×D4×C131D411yescharacteristic
85C22×D4×C131C2311yescharacteristic
86C22×D4×C131C2311yescharacteristic
87C22×D4×C131C2311yescharacteristic
88C23×C4×C131—21no—
89C23×C4×C131—21no—
90C23×C4×C131—21no—
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C2×SD16×C131—22no—
94C2×SD16×C131—22no—
95C2×SD16×C131—41no—
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—41no—
101C2×D8×C131D414yescomplemented
102C22×C8×C131C2311yescharacteristic
103C22×C8×C131C2311yescharacteristic
104C22×C8×C131C2311yescharacteristic
105C22×C8×C131C2311yescharacteristic
106#124×C131—22no—
107#124×C131D414yescomplemented
108#123×C131—28no—
109C22⋊Q8×C131—22no—
110C22⋊Q8×C131—22no—
111#121×C131—28no—
112#121×C131—22no—
113#121×C131—22no—
114#121×C131—22no—
115#121×C131—22no—
116#121×C131—41no—
117#121×C131—41no—
118#121×C131—44no—
119#120×C131—28no—
120C4×D4×C131—22no—
121C4×D4×C131—22no—
122C4×D4×C131—22no—
123C4×D4×C131—22no—
124C4×D4×C131—22no—
125C4×D4×C131D414yescomplemented
126C2×C4⋊C4×C131—21no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—21no—
129C2×C4⋊C4×C131D411yescharacteristic
130C2×C4⋊C4×C131C2311yescharacteristic
131C2×C4⋊C4×C131C2311yescharacteristic
132C2×C4⋊C4×C131C2311yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C22⋊C4×C131—28no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131—21no—
137C2×C22⋊C4×C131—21no—
138C2×C22⋊C4×C131—21no—
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
141C2×C22⋊C4×C131—21no—
142C2×C22⋊C4×C131—21no—
143C2×C22⋊C4×C131—21no—
144C2×C22⋊C4×C131—21no—
145C2×C22⋊C4×C131D411yescharacteristic
146C2×C22⋊C4×C131D411yescharacteristic
147C2×C42×C131C2311yescharacteristic
148#106×C131—22no—
149C4⋊C8×C131—22no—
150#103×C131—22no—
151#103×C131—22no—
152#103×C131—41no—
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—22no—
159#102×C131—41no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131—41no—
163C22⋊C8×C131—41no—
164#97×C131—22no—
165#95×C131—21no—
166#95×C131—21no—
167C24×C131—21no—
168C24×C131—24no—
169C24×C131—21no—
170C24×C131—21no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—42no—
174C24×C131—42no—
175C24×C131—81no—
176C24×C131—81no—
177C24×C131C2×D411yescharacteristic
178C24×C131C2×D411yescharacteristic
179#41×C131—44no—
180#41×C131—44no—
181#41×C131—44no—
182#41×C131—44no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131C2×D412yes—
189C2×D4×C131—24no—
190C2×D4×C131—24no—
191C2×D4×C131—22no—
192C2×D4×C131—24no—
193C2×D4×C131—22no—
194C2×D4×C131—21no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
202C2×D4×C131—21no—
203C2×D4×C131—21no—
204C2×D4×C131—21no—
205C2×D4×C131—21no—
206C2×D4×C131—21no—
207C2×D4×C131—41no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—44no—
211C2×D4×C131—44no—
212C2×D4×C131—44no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—44no—
216C2×D4×C131—42no—
217C2×D4×C131—42no—
218C2×D4×C131—42no—
219C2×D4×C131—42no—
220C2×D4×C131—81no—
221C2×D4×C131—81no—
222C2×D4×C131—81no—
223C2×D4×C131—81no—
224C2×D4×C131C2×D412yes—
225C2×D4×C131C2×D412yes—
226C2×D4×C131C2×D412yes—
227C2×D4×C131C2×D412yes—
228C2×D4×C131#4112yes—
229C22×C4×C131—24no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—24no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—42no—
249C22×C4×C131—42no—
250C22×C4×C131—42no—
251C22×C4×C131—42no—
252C22×C4×C131—42no—
253C22×C4×C131—81no—
254C22×C4×C131—81no—
255C22×C4×C131C2×D411yescharacteristic
256C22×C4×C131C2×D411yescharacteristic
257C22×C4×C131C2×D411yescharacteristic
258C22×C4×C131C2×D411yescharacteristic
259C22×C4×C131C2411yescharacteristic
260SD16×C131—44no—
261D8×C131—28no—
262D8×C131—44no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—21no—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131C2×D412yes—
275C4⋊C4×C131—24no—
276C4⋊C4×C131—22no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—42no—
285C4⋊C4×C131—81no—
286C4⋊C4×C131C2×D412yes—
287C22⋊C4×C131—24no—
288C22⋊C4×C131—24no—
289C22⋊C4×C131—22no—
290C22⋊C4×C131—24no—
291C22⋊C4×C131—24no—
292C22⋊C4×C131—24no—
293C22⋊C4×C131—22no—
294C22⋊C4×C131—42no—
295C22⋊C4×C131—42no—
296C22⋊C4×C131—42no—
297C22⋊C4×C131—42no—
298C22⋊C4×C131—42no—
299C42×C131C2×D412yes—
300C42×C131C2×D412yes—
301C23×C131—21no—
302C23×C131—22no—
303C23×C131—21no—
304C23×C131—22no—
305C23×C131—21no—
306C23×C131—22no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—22no—
311C23×C131—21no—
312C23×C131—22no—
313C23×C131—21no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—48no—
320C23×C131—48no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131—41no—
324C23×C131—41no—
325C23×C131—41no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—41no—
337C23×C131—84no—
338C23×C131—84no—
339C23×C131—84no—
340C23×C131—84no—
341C23×C131—84no—
342C23×C131AGL(1,ℤ/8)12yes—
343C23×C131C22×D411yescharacteristic
344Q8×C131—22no—
345Q8×C131—22no—
346Q8×C131—41no—
347Q8×C131—41no—
348D4×C131—22no—
349D4×C131—22no—
350D4×C131—22no—
351D4×C131—22no—
352D4×C131—22no—
353D4×C131—22no—
354D4×C131—22no—
355D4×C131—44no—
356D4×C131—48no—
357D4×C131—48no—
358D4×C131—41no—
359D4×C131—41no—
360D4×C131—41no—
361D4×C131—41no—
362D4×C131—84no—
363D4×C131—84no—
364D4×C131—84no—
365D4×C131#12114yescomplemented
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
370C2×C4×C131—22no—
371C2×C4×C131—21no—
372C2×C4×C131—22no—
373C2×C4×C131—21no—
374C2×C4×C131—21no—
375C2×C4×C131—21no—
376C2×C4×C131—21no—
377C2×C4×C131—21no—
378C2×C4×C131—48no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—84no—
401C2×C4×C131—84no—
402C2×C4×C131#12012yes—
403C2×C4×C131#12012yes—
404C2×C4×C131C22×D411yescharacteristic
405C2×C4×C131C22×D411yescharacteristic
406C2×C4×C131C22×D411yescharacteristic
407C2×C4×C131C2×#4111yescharacteristic
408C2×C4×C131H(5,𝔽2)11yescharacteristic
409C2×C4×C131H(5,𝔽2)11yescharacteristic
410C8×C131—22no—
411C8×C131—41no—
412C8×C131—41no—
413C8×C131—41no—
414C22×C131—24no—
415C22×C131—22no—
416C22×C131—22no—
417C22×C131—22no—
418C22×C131—41no—
419C22×C131—42no—
420C22×C131—42no—
421C22×C131—41no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—41no—
425C22×C131—42no—
426C22×C131—41no—
427C22×C131—42no—
428C22×C131—41no—
429C22×C131—42no—
430C22×C131—42no—
431C22×C131—41no—
432C22×C131—42no—
433C22×C131—41no—
434C22×C131—42no—
435C22×C131—41no—
436C22×C131—42no—
437C22×C131—41no—
438C22×C131—42no—
439C22×C131—41no—
440C22×C131—41no—
441C22×C131—816no—
442C22×C131—81no—
443C22×C131—81no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131—81no—
448C22×C131—81no—
449C22×C131—81no—
450C22×C131C2×#12011yescharacteristic
451C22×C131D4211yescharacteristic
452C22×C131#54611yescharacteristic
453C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C131#57511yescharacteristic
455C22×C131#57611yescharacteristic
456C22×C131#57711yescharacteristic
457C4×C131—22no—
458C4×C131—22no—
459C4×C131—41no—
460C4×C131—41no—
461C4×C131—42no—
462C4×C131—42no—
463C4×C131—81no—
464C4×C131—81no—
465C4×C131—81no—
466C4×C131C2×#12111yescharacteristic
467C4×C131#53511yescharacteristic
468C4×C131D4211yescharacteristic
469C4×C131#54611yescharacteristic
470C2×C131—42no—
471C2×C131—44no—
472C2×C131—81no—
473C2×C131—82no—
474C2×C131—82no—
475C2×C131#240811yescharacteristic
476C2×C131#300611yescharacteristic
477C2×C131#301211yescharacteristic
478C2×C131#326411yescharacteristic
479C2×C131#326711yescharacteristic
480C2×C131#330611yescharacteristic
481C2×C131#331911yescharacteristic
482#24257C13111yesmaximal, characteristic, direct product factor, Sylow
483C131#2425711yescharacteristic, direct product factor, Sylow
484C2×#546C2×C13111yescharacteristic, complemented
485C2×#463C2×C13111yescharacteristic, complemented
486C2×#449C2×C13111yescharacteristic, complemented
487C2×#447C2×C13111yescharacteristic, complemented
488C2×#442C2×C13111yescharacteristic, complemented
489#2537C2×C13111yescharacteristic, complemented
490#2035C2×C13111yescharacteristic, complemented
491#2034C2×C13111yescharacteristic, complemented
492#2000C2×C13111yescharacteristic, complemented
493#1999C2×C13111yescharacteristic, complemented
494#1959C2×C13111yescharacteristic, complemented
495#1955C2×C13111yescharacteristic, complemented
496#1802C2×C13111yescharacteristic, complemented
497#1788C2×C13111yescharacteristic, complemented
498#1786C2×C13111yescharacteristic, complemented
499C22×#41C22×C13111yescharacteristic
500C23×D4C22×C13111yescharacteristic
501C22×SD16C22×C13111yescharacteristic, complemented
502C22×D8C22×C13111yescharacteristic
503C22×D8C22×C13111yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C13111yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C13111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C13111yescharacteristic
512C2×#121C22×C13111yescharacteristic
513C2×#121C22×C13111yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C13111yescharacteristic
516C2×C4×D4C22×C13111yescharacteristic
517C2×C4×D4C22×C13111yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C13111yescharacteristic, complemented
524C2×C4⋊C8C22×C13111yescharacteristic, complemented
525C2×#103C22×C13111yescharacteristic, complemented
526C2×#103C22×C13111yescharacteristic, complemented
527C2×#103C22×C13111yescharacteristic, complemented
528C2×#102C22×C13111yescharacteristic
529C2×#102C22×C13111yescharacteristic
530C2×#102C22×C13111yescharacteristic
531C2×#102C22×C13111yescharacteristic
532C2×#102C22×C13111yescharacteristic
533C2×#102C22×C13111yescharacteristic
534C2×#102C22×C13111yescharacteristic, complemented
535C2×C22⋊C8C22×C13111yescharacteristic
536C2×C22⋊C8C22×C13111yescharacteristic
537C2×C22⋊C8C22×C13111yescharacteristic, complemented
538C2×C22⋊C8C22×C13111yescharacteristic, complemented
539C2×#97C22×C13111yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C13111yescharacteristic, complemented
543#380—21no—
544#380C22×C13111yescharacteristic
545#380C22×C13111yescharacteristic, complemented
546#340C22×C13111yescharacteristic, complemented
547#340C22×C13111yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C13111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C13111yescharacteristic
568C22×D4C23×C13111yescharacteristic
569C22×D4C23×C13111yescharacteristic
570C22×D4C23×C13111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C13111yescharacteristic
575C23×C4C23×C13111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C13114yescomplemented
585C22×C8C23×C13111yescharacteristic
586C22×C8C23×C13111yescharacteristic
587C22×C8C23×C13111yescharacteristic
588C22×C8C23×C13111yescharacteristic
589#124—22no—
590#124D4×C13114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C13114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C13111yescharacteristic
613C2×C4⋊C4C23×C13111yescharacteristic
614C2×C4⋊C4C23×C13111yescharacteristic
615C2×C4⋊C4C23×C13111yescharacteristic
616C2×C4⋊C4C23×C13111yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C13111yescharacteristic
629C2×C22⋊C4D4×C13111yescharacteristic
630C2×C42C23×C13111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C13111yescharacteristic
661C24C2×D4×C13111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C13112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C13112yes—
708C2×D4C2×D4×C13112yes—
709C2×D4C2×D4×C13112yes—
710C2×D4C2×D4×C13112yes—
711C2×D4#41×C13112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C13111yescharacteristic
739C22×C4C2×D4×C13111yescharacteristic
740C22×C4C2×D4×C13111yescharacteristic
741C22×C4C2×D4×C13111yescharacteristic
742C22×C4C24×C13111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C13112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C13112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C13112yes—
783C42C2×D4×C13112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C13112yes—
826C23C22×D4×C13111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C13114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C13112yes—
886C2×C4#120×C13112yes—
887C2×C4C22×D4×C13111yescharacteristic
888C2×C4C22×D4×C13111yescharacteristic
889C2×C4C22×D4×C13111yescharacteristic
890C2×C4C2×#41×C13111yescharacteristic
891C2×C4H(5,𝔽2)×C13111yescharacteristic
892C2×C4H(5,𝔽2)×C13111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C13111yescharacteristic
934C22D42×C13111yescharacteristic
935C22#546×C13111yescharacteristic
936C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
937C22#575×C13111yescharacteristic
938C22#576×C13111yescharacteristic
939C22#577×C13111yescharacteristic
940C4—22no—
941C4—22no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C13111yescharacteristic
950C4#535×C13111yescharacteristic
951C4D42×C13111yescharacteristic
952C4#546×C13111yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2#2408×C13111yescharacteristic
959C2#3006×C13111yescharacteristic
960C2#3012×C13111yescharacteristic
961C2#3264×C13111yescharacteristic
962C2#3267×C13111yescharacteristic
963C2#3306×C13111yescharacteristic
964C2#3319×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C131C2semidirect
2. C2×#463×C131C2semidirect
3. C2×#449×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C2×#442×C131C2semidirect
6. #2537×C131C2semidirect
7. #2035×C131C2semidirect
8. #2034×C131C2semidirect
9. #2000×C131C2semidirect
10. #1999×C131C2semidirect
11. #1959×C131C2semidirect
12. #1955×C131C2semidirect
13. #1802×C131C2semidirect
14. #1788×C131C2semidirect
15. #1786×C131C2semidirect
18. C22×SD16×C131C22semidirect
30. C2×#121×C131C22semidirect
34. C2×C4×D4×C131C22semidirect
40. C2×#106×C131C22semidirect
41. C2×C4⋊C8×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
44. C2×#103×C131C22semidirect
51. C2×#102×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
55. C2×C22⋊C8×C131C22semidirect
56. C2×#97×C131C22semidirect
59. #384×C131C22semidirect
62. #380×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
101. C2×D8×C131D4semidirect
107. #124×C131D4semidirect
125. C4×D4×C131D4semidirect
365. D4×C131#121semidirect
482. #24257C131direct (N × H)
483. C131#24257direct (N × H)
484. C2×#546C2×C131semidirect
485. C2×#463C2×C131semidirect
486. C2×#449C2×C131semidirect
487. C2×#447C2×C131semidirect
488. C2×#442C2×C131semidirect
489. #2537C2×C131semidirect
490. #2035C2×C131semidirect
491. #2034C2×C131semidirect
492. #2000C2×C131semidirect
493. #1999C2×C131semidirect
494. #1959C2×C131semidirect
495. #1955C2×C131semidirect
496. #1802C2×C131semidirect
497. #1788C2×C131semidirect
498. #1786C2×C131semidirect
501. C22×SD16C22×C131semidirect
513. C2×#121C22×C131semidirect
517. C2×C4×D4C22×C131semidirect
523. C2×#106C22×C131semidirect
524. C2×C4⋊C8C22×C131semidirect
525. C2×#103C22×C131semidirect
526. C2×#103C22×C131semidirect
527. C2×#103C22×C131semidirect
534. C2×#102C22×C131semidirect
537. C2×C22⋊C8C22×C131semidirect
538. C2×C22⋊C8C22×C131semidirect
539. C2×#97C22×C131semidirect
542. #384C22×C131semidirect
545. #380C22×C131semidirect
546. #340C22×C131semidirect
547. #340C22×C131semidirect
584. C2×D8D4×C131semidirect
590. #124D4×C131semidirect
608. C4×D4D4×C131semidirect
848. D4#121×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1312
C2×#463×C1312
C2×#449×C1312
C2×#447×C1312
C2×#442×C1312
#2537×C1312
#2035×C1312
#2034×C1312
#2000×C1312
#1999×C1312
#1959×C1312
#1955×C1312
#1802×C1312
#1788×C1312
#1786×C1312
#24257131