Finite Group Databasebeta

← C131×#29601 #45715485

Subgroups — C131×#29601 #45715485

Order 33536.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic
2C2×#485×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4#2848×C131C211yesmaximal, characteristic, complemented
5#2036×C131C211yesmaximal, characteristic, complemented
6#2035×C131C211yesmaximal, characteristic, complemented
7#2034×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2001×C131C211yesmaximal, characteristic, complemented
10#2001×C131C211yesmaximal, characteristic, complemented
11#2000×C131C211yesmaximal, characteristic, complemented
12#2000×C131C211yesmaximal, characteristic, complemented
13#1825×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1779×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic, complemented
19C22×SD16×C131C2211yescharacteristic, complemented
20#525×C131—24no—
21#525×C131—24no—
22C2×#123×C131—21no—
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×C22⋊Q8×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#120×C131—21no—
31C2×C4×D4×C131—21no—
32C2×C4×D4×C131—21no—
33C2×#117×C131C2211yescharacteristic
34#485×C131—24no—
35#452×C131—24no—
36C2×#107×C131C2211yescharacteristic, complemented
37C2×#106×C131C2211yescharacteristic, complemented
38C2×#103×C131C2211yescharacteristic, complemented
39C2×#103×C131C2211yescharacteristic, complemented
40C2×#103×C131C2211yescharacteristic, complemented
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#102×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic, complemented
46C2×C22⋊C8×C131C2211yescharacteristic
47C2×C22⋊C8×C131C2211yescharacteristic
48C2×C22⋊C8×C131C2211yescharacteristic
49C2×C22⋊C8×C131C2211yescharacteristic
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52#385×C131—21no—
53#385×C131—21no—
54#385×C131—21no—
55#380×C131C2211yescharacteristic
56#380×C131C2211yescharacteristic
57#380×C131C2211yescharacteristic
58#379×C131—21no—
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63C25×C131D411yescharacteristic
64C2×#41×C131—22no—
65C2×#41×C131—41no—
66C2×#41×C131—41no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C2×#41×C131D414yes—
70C22×Q8×C131C2311yescharacteristic
71C22×Q8×C131C2311yescharacteristic
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131C2311yescharacteristic
76C23×C4×C131—21no—
77C23×C4×C131—22no—
78C23×C4×C131—22no—
79C23×C4×C131—41no—
80C23×C4×C131—41no—
81C23×C4×C131—41no—
82C23×C4×C131—41no—
83C23×C4×C131D411yescharacteristic
84C23×C4×C131D411yescharacteristic
85C23×C4×C131D411yescharacteristic
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2311yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C2×Q16×C131—22no—
90C2×Q16×C131—41no—
91C2×Q16×C131—41no—
92C2×SD16×C131—22no—
93C2×SD16×C131—41no—
94C2×SD16×C131—41no—
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99#123×C131—28no—
100C22⋊Q8×C131—22no—
101C22⋊Q8×C131—22no—
102C22⋊Q8×C131—22no—
103C22⋊Q8×C131—22no—
104C22⋊Q8×C131—22no—
105C22⋊Q8×C131—22no—
106C22⋊Q8×C131—41no—
107C22⋊Q8×C131—41no—
108C22⋊Q8×C131—41no—
109C22⋊Q8×C131—41no—
110#121×C131—22no—
111#121×C131—22no—
112#121×C131—22no—
113#121×C131—22no—
114#120×C131—28no—
115C4×D4×C131—28no—
116C4×D4×C131—28no—
117#117×C131—22no—
118#117×C131D414yes—
119C2×C4⋊C4×C131—21no—
120C2×C4⋊C4×C131—21no—
121C2×C4⋊C4×C131—21no—
122C2×C4⋊C4×C131—21no—
123C2×C4⋊C4×C131—21no—
124C2×C4⋊C4×C131C2311yescharacteristic
125C2×C4⋊C4×C131C2311yescharacteristic
126C2×C4⋊C4×C131C2311yescharacteristic
127C2×C4⋊C4×C131C2311yescharacteristic
128C2×C4⋊C4×C131C2311yescharacteristic
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—21no—
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×C42×C131—21no—
141#107×C131—22no—
142#106×C131—22no—
143#103×C131—22no—
144#103×C131—22no—
145#103×C131—22no—
146#103×C131—41no—
147#103×C131—41no—
148#102×C131—22no—
149#102×C131—41no—
150#102×C131—41no—
151C22⋊C8×C131—22no—
152C22⋊C8×C131—22no—
153C22⋊C8×C131—41no—
154C22⋊C8×C131—41no—
155C22⋊C8×C131—41no—
156C22⋊C8×C131—41no—
157#95×C131—21no—
158#95×C131—21no—
159#95×C131—21no—
160C24×C131—22no—
161C24×C131—22no—
162C24×C131—22no—
163C24×C131—21no—
164C24×C131—41no—
165C24×C131—41no—
166C24×C131—41no—
167C24×C131—41no—
168C24×C131C2×D411yescharacteristic
169C24×C131C2×D411yescharacteristic
170C24×C131C2×D411yescharacteristic
171#41×C131—44no—
172#41×C131—44no—
173#41×C131—44no—
174#41×C131—44no—
175C2×Q8×C131—21no—
176C2×Q8×C131—21no—
177C2×Q8×C131—21no—
178C2×Q8×C131—21no—
179C2×Q8×C131—21no—
180C2×Q8×C131—21no—
181C2×Q8×C131—21no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131C2×D412yes—
187C2×D4×C131—24no—
188C2×D4×C131—24no—
189C2×D4×C131—24no—
190C2×D4×C131—21no—
191C2×D4×C131—21no—
192C2×D4×C131—21no—
193C2×D4×C131—21no—
194C2×D4×C131—21no—
195C2×D4×C131—42no—
196C2×D4×C131—42no—
197C2×D4×C131—42no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131C2×D412yes—
202C22×C4×C131—21no—
203C22×C4×C131—21no—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—22no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—22no—
211C22×C4×C131—22no—
212C22×C4×C131—24no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—41no—
230C22×C4×C131—41no—
231C22×C4×C131—41no—
232C22×C4×C131—41no—
233C22×C4×C131—41no—
234C22×C4×C131—41no—
235C22×C4×C131—44no—
236C22×C4×C131—44no—
237C22×C4×C131—44no—
238C22×C4×C131—44no—
239C22×C4×C131—42no—
240C22×C4×C131—42no—
241C22×C4×C131C2×D411yescharacteristic
242C22×C4×C131C2×D411yescharacteristic
243C22×C4×C131C2×D411yescharacteristic
244C22×C4×C131C2×D412yes—
245C22×C4×C131C2×D412yes—
246C22×C4×C131C2411yescharacteristic
247Q16×C131—44no—
248SD16×C131—44no—
249C2×C8×C131—21no—
250C2×C8×C131—21no—
251C2×C8×C131—21no—
252C2×C8×C131—21no—
253C2×C8×C131—21no—
254C2×C8×C131—21no—
255C2×C8×C131—21no—
256C2×C8×C131—21no—
257C2×C8×C131—21no—
258C2×C8×C131—21no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C4⋊C4×C131—24no—
262C4⋊C4×C131—24no—
263C4⋊C4×C131—21no—
264C4⋊C4×C131—21no—
265C4⋊C4×C131—21no—
266C4⋊C4×C131—21no—
267C4⋊C4×C131—21no—
268C4⋊C4×C131—21no—
269C4⋊C4×C131—21no—
270C4⋊C4×C131—21no—
271C4⋊C4×C131—42no—
272C4⋊C4×C131—42no—
273C4⋊C4×C131—42no—
274C4⋊C4×C131C2×D412yes—
275C4⋊C4×C131C2×D412yes—
276C22⋊C4×C131—24no—
277C22⋊C4×C131—24no—
278C22⋊C4×C131—24no—
279C22⋊C4×C131—24no—
280C22⋊C4×C131—24no—
281C22⋊C4×C131—42no—
282C22⋊C4×C131—42no—
283C22⋊C4×C131—42no—
284C22⋊C4×C131—42no—
285C22⋊C4×C131—42no—
286C22⋊C4×C131—42no—
287C42×C131—24no—
288C23×C131—21no—
289C23×C131—21no—
290C23×C131—21no—
291C23×C131—21no—
292C23×C131—21no—
293C23×C131—21no—
294C23×C131—21no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—21no—
300C23×C131—21no—
301C23×C131—21no—
302C23×C131—21no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—22no—
307C23×C131—44no—
308C23×C131—44no—
309C23×C131—44no—
310C23×C131—44no—
311C23×C131—44no—
312C23×C131—44no—
313C23×C131—44no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131#12012yes—
321C23×C131#13512yes—
322C23×C131#13712yes—
323C23×C131C22×D411yescharacteristic
324Q8×C131—22no—
325Q8×C131—22no—
326Q8×C131—41no—
327Q8×C131—41no—
328Q8×C131—41no—
329Q8×C131—41no—
330Q8×C131—41no—
331Q8×C131—41no—
332D4×C131—22no—
333D4×C131—22no—
334D4×C131—48no—
335D4×C131—48no—
336D4×C131—48no—
337D4×C131—41no—
338D4×C131—41no—
339C2×C4×C131—21no—
340C2×C4×C131—21no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—22no—
344C2×C4×C131—22no—
345C2×C4×C131—22no—
346C2×C4×C131—22no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—22no—
350C2×C4×C131—21no—
351C2×C4×C131—21no—
352C2×C4×C131—21no—
353C2×C4×C131—21no—
354C2×C4×C131—44no—
355C2×C4×C131—44no—
356C2×C4×C131—48no—
357C2×C4×C131—44no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131#12012yes—
385C2×C4×C131C22×D411yescharacteristic
386C2×C4×C131C22×D411yescharacteristic
387C2×C4×C131H(5,𝔽2)11yescharacteristic
388C2×C4×C131H(5,𝔽2)11yescharacteristic
389C2×C4×C131H(5,𝔽2)11yescharacteristic
390C2×C4×C131H(5,𝔽2)11yescharacteristic
391C8×C131—41no—
392C8×C131—41no—
393C8×C131—41no—
394C8×C131—41no—
395C22×C131—22no—
396C22×C131—22no—
397C22×C131—22no—
398C22×C131—22no—
399C22×C131—22no—
400C22×C131—22no—
401C22×C131—22no—
402C22×C131—22no—
403C22×C131—22no—
404C22×C131—416no—
405C22×C131—41no—
406C22×C131—41no—
407C22×C131—41no—
408C22×C131—41no—
409C22×C131—41no—
410C22×C131—41no—
411C22×C131—41no—
412C22×C131—41no—
413C22×C131—41no—
414C22×C131—41no—
415C22×C131—41no—
416C22×C131—41no—
417C22×C131—42no—
418C22×C131—42no—
419C22×C131—42no—
420C22×C131—81no—
421C22×C131—81no—
422C22×C131—81no—
423C22×C131—81no—
424C22×C131C2×#12011yescharacteristic
425C22×C131#53411yescharacteristic
426C22×C131#53411yescharacteristic
427C22×C131C2×#13511yescharacteristic
428C22×C131C2×#13711yescharacteristic
429C22×C131#57511yescharacteristic
430C22×C131#57511yescharacteristic
431C4×C131—22no—
432C4×C131—41no—
433C4×C131—41no—
434C4×C131—42no—
435C4×C131—42no—
436C4×C131—42no—
437C4×C131—81no—
438C4×C131—81no—
439C4×C131—81no—
440C4×C131—81no—
441C4×C131#53411yescharacteristic
442C4×C131#53411yescharacteristic
443C4×C131#53511yescharacteristic
444C4×C131#53511yescharacteristic
445C2×C131—42no—
446C2×C131—42no—
447C2×C131—42no—
448C2×C131—82no—
449C2×C131#261311yescharacteristic
450C2×C131#300211yescharacteristic
451C2×C131#300711yescharacteristic
452C2×C131#319011yescharacteristic
453C2×C131#319111yescharacteristic
454C2×C131#319611yescharacteristic
455C2×C131#319711yescharacteristic
456#29601C13111yesmaximal, characteristic, direct product factor, Sylow
457C131#2960111yescharacteristic, direct product factor, Sylow
458C2×#525C2×C13111yescharacteristic
459C2×#485C2×C13111yescharacteristic, complemented
460C2×#452C2×C13111yescharacteristic, complemented
461#2848C2×C13111yescharacteristic, complemented
462#2036C2×C13111yescharacteristic, complemented
463#2035C2×C13111yescharacteristic, complemented
464#2034C2×C13111yescharacteristic, complemented
465#2033C2×C13111yescharacteristic, complemented
466#2001C2×C13111yescharacteristic, complemented
467#2001C2×C13111yescharacteristic, complemented
468#2000C2×C13111yescharacteristic, complemented
469#2000C2×C13111yescharacteristic, complemented
470#1825C2×C13111yescharacteristic, complemented
471#1788C2×C13111yescharacteristic, complemented
472#1779C2×C13111yescharacteristic, complemented
473C22×#41C22×C13111yescharacteristic
474C24×C4C22×C13111yescharacteristic
475C22×Q16C22×C13111yescharacteristic, complemented
476C22×SD16C22×C13111yescharacteristic, complemented
477#525—24no—
478#525—24no—
479C2×#123—21no—
480C2×C22⋊Q8C22×C13111yescharacteristic
481C2×C22⋊Q8C22×C13111yescharacteristic
482C2×C22⋊Q8C22×C13111yescharacteristic
483C2×C22⋊Q8C22×C13111yescharacteristic
484C2×C22⋊Q8C22×C13111yescharacteristic
485C2×#121C22×C13111yescharacteristic
486C2×#121C22×C13111yescharacteristic
487C2×#120—21no—
488C2×C4×D4—21no—
489C2×C4×D4—21no—
490C2×#117C22×C13111yescharacteristic
491#485—24no—
492#452—24no—
493C2×#107C22×C13111yescharacteristic, complemented
494C2×#106C22×C13111yescharacteristic, complemented
495C2×#103C22×C13111yescharacteristic, complemented
496C2×#103C22×C13111yescharacteristic, complemented
497C2×#103C22×C13111yescharacteristic, complemented
498C2×#103C22×C13111yescharacteristic, complemented
499C2×#103C22×C13111yescharacteristic, complemented
500C2×#102C22×C13111yescharacteristic, complemented
501C2×#102C22×C13111yescharacteristic, complemented
502C2×#102C22×C13111yescharacteristic, complemented
503C2×C22⋊C8C22×C13111yescharacteristic
504C2×C22⋊C8C22×C13111yescharacteristic
505C2×C22⋊C8C22×C13111yescharacteristic
506C2×C22⋊C8C22×C13111yescharacteristic
507C2×C22⋊C8C22×C13111yescharacteristic
508C2×C22⋊C8C22×C13111yescharacteristic
509#385—21no—
510#385—21no—
511#385—21no—
512#380C22×C13111yescharacteristic
513#380C22×C13111yescharacteristic
514#380C22×C13111yescharacteristic
515#379—21no—
516#340C22×C13111yescharacteristic, complemented
517#340C22×C13111yescharacteristic, complemented
518#340C22×C13111yescharacteristic, complemented
519#340C22×C13111yescharacteristic, complemented
520C25D4×C13111yescharacteristic
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C13114yes—
527C22×Q8C23×C13111yescharacteristic
528C22×Q8C23×C13111yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C13111yescharacteristic
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4D4×C13111yescharacteristic
541C23×C4D4×C13111yescharacteristic
542C23×C4D4×C13111yescharacteristic
543C23×C4C23×C13111yescharacteristic
544C23×C4C23×C13111yescharacteristic
545C23×C4C23×C13111yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C23×C13111yescharacteristic
553C22×C8C23×C13111yescharacteristic
554C22×C8C23×C13111yescharacteristic
555C22×C8C23×C13111yescharacteristic
556#123—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—28no—
573C4×D4—28no—
574#117—22no—
575#117D4×C13114yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4C23×C13111yescharacteristic
582C2×C4⋊C4C23×C13111yescharacteristic
583C2×C4⋊C4C23×C13111yescharacteristic
584C2×C4⋊C4C23×C13111yescharacteristic
585C2×C4⋊C4C23×C13111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C42—21no—
598#107—22no—
599#106—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—41no—
604#103—41no—
605#102—22no—
606#102—41no—
607#102—41no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24C2×D4×C13111yescharacteristic
626C24C2×D4×C13111yescharacteristic
627C24C2×D4×C13111yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C13112yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4C2×D4×C13112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4C2×D4×C13111yescharacteristic
699C22×C4C2×D4×C13111yescharacteristic
700C22×C4C2×D4×C13111yescharacteristic
701C22×C4C2×D4×C13112yes—
702C22×C4C2×D4×C13112yes—
703C22×C4C24×C13111yescharacteristic
704Q16—44no—
705SD16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4C2×D4×C13112yes—
732C4⋊C4C2×D4×C13112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C42—24no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C13112yes—
778C23#135×C13112yes—
779C23#137×C13112yes—
780C23C22×D4×C13111yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C13112yes—
842C2×C4C22×D4×C13111yescharacteristic
843C2×C4C22×D4×C13111yescharacteristic
844C2×C4H(5,𝔽2)×C13111yescharacteristic
845C2×C4H(5,𝔽2)×C13111yescharacteristic
846C2×C4H(5,𝔽2)×C13111yescharacteristic
847C2×C4H(5,𝔽2)×C13111yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C13111yescharacteristic
882C22#534×C13111yescharacteristic
883C22#534×C13111yescharacteristic
884C22C2×#135×C13111yescharacteristic
885C22C2×#137×C13111yescharacteristic
886C22#575×C13111yescharacteristic
887C22#575×C13111yescharacteristic
888C4—22no—
889C4—42no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4#534×C13111yescharacteristic
899C4#534×C13111yescharacteristic
900C4#535×C13111yescharacteristic
901C4#535×C13111yescharacteristic
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2#2613×C13111yescharacteristic
907C2#3002×C13111yescharacteristic
908C2#3007×C13111yescharacteristic
909C2#3190×C13111yescharacteristic
910C2#3191×C13111yescharacteristic
911C2#3196×C13111yescharacteristic
912C2#3197×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#525×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C131C2semidirect
3. C2×#452×C131C2semidirect
4. #2848×C131C2semidirect
5. #2036×C131C2semidirect
6. #2035×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #2001×C131C2semidirect
10. #2001×C131C2semidirect
11. #2000×C131C2semidirect
12. #2000×C131C2semidirect
13. #1825×C131C2semidirect
14. #1788×C131C2semidirect
15. #1779×C131C2semidirect
18. C22×Q16×C131C22semidirect
19. C22×SD16×C131C22semidirect
36. C2×#107×C131C22semidirect
37. C2×#106×C131C22semidirect
38. C2×#103×C131C22semidirect
39. C2×#103×C131C22semidirect
40. C2×#103×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#102×C131C22semidirect
44. C2×#102×C131C22semidirect
45. C2×#102×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
456. #29601C131direct (N × H)
457. C131#29601direct (N × H)
459. C2×#485C2×C131semidirect
460. C2×#452C2×C131semidirect
461. #2848C2×C131semidirect
462. #2036C2×C131semidirect
463. #2035C2×C131semidirect
464. #2034C2×C131semidirect
465. #2033C2×C131semidirect
466. #2001C2×C131semidirect
467. #2001C2×C131semidirect
468. #2000C2×C131semidirect
469. #2000C2×C131semidirect
470. #1825C2×C131semidirect
471. #1788C2×C131semidirect
472. #1779C2×C131semidirect
475. C22×Q16C22×C131semidirect
476. C22×SD16C22×C131semidirect
493. C2×#107C22×C131semidirect
494. C2×#106C22×C131semidirect
495. C2×#103C22×C131semidirect
496. C2×#103C22×C131semidirect
497. C2×#103C22×C131semidirect
498. C2×#103C22×C131semidirect
499. C2×#103C22×C131semidirect
500. C2×#102C22×C131semidirect
501. C2×#102C22×C131semidirect
502. C2×#102C22×C131semidirect
516. #340C22×C131semidirect
517. #340C22×C131semidirect
518. #340C22×C131semidirect
519. #340C22×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
C2×#485×C1312
C2×#452×C1312
#2848×C1312
#2036×C1312
#2035×C1312
#2034×C1312
#2033×C1312
#2001×C1312
#2000×C1312
#1825×C1312
#1788×C1312
#1779×C1312
#29601131