Finite Group Databasebeta

← C131×#24389 #45710273

Subgroups — C131×#24389 #45710273

Order 33536.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic
2C2×#470×C131C211yesmaximal, characteristic, complemented
3C2×#468×C131C211yesmaximal, characteristic, complemented
4C2×#452×C131C211yesmaximal, characteristic, complemented
5C2×#407×C131C211yesmaximal, characteristic, complemented
6#2848×C131C211yesmaximal, characteristic, complemented
7#2036×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2001×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1895×C131C211yesmaximal, characteristic, complemented
12#1894×C131C211yesmaximal, characteristic, complemented
13#1873×C131C211yesmaximal, characteristic, complemented
14#1854×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic, complemented
19C22×SD16×C131C2211yescharacteristic, complemented
20C22×M16×C131C2211yescharacteristic
21C22×M16×C131C2211yescharacteristic
22#525×C131—24no—
23#525×C131—24no—
24C2×#123×C131—21no—
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×C22⋊Q8×C131C2211yescharacteristic
28C2×C22⋊Q8×C131C2211yescharacteristic
29C2×C22⋊Q8×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic
32C2×#120×C131—21no—
33C2×C4×D4×C131—21no—
34C2×C4×D4×C131—21no—
35C2×#117×C131C2211yescharacteristic
36#470×C131—24no—
37#468×C131—24no—
38#452×C131—24no—
39C2×#107×C131C2211yescharacteristic, complemented
40C2×#106×C131C2211yescharacteristic, complemented
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#103×C131C2211yescharacteristic, complemented
45C2×#103×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×#102×C131C2211yescharacteristic, complemented
48C2×#102×C131C2211yescharacteristic, complemented
49#407×C131—24no—
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54#385×C131—21no—
55#385×C131—21no—
56#385×C131—21no—
57#380×C131C2211yescharacteristic
58#380×C131C2211yescharacteristic
59#380×C131C2211yescharacteristic
60#379×C131—21no—
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64#340×C131C2211yescharacteristic, complemented
65C25×C131D411yescharacteristic
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×Q8×C131C2311yescharacteristic
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131C2311yescharacteristic
78C23×C4×C131—22no—
79C23×C4×C131—21no—
80C23×C4×C131—22no—
81C23×C4×C131—22no—
82C23×C4×C131—22no—
83C23×C4×C131—41no—
84C23×C4×C131—41no—
85C23×C4×C131D411yescharacteristic
86C23×C4×C131D411yescharacteristic
87C23×C4×C131D411yescharacteristic
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C2×Q16×C131—22no—
92C2×Q16×C131—22no—
93C2×Q16×C131—41no—
94C2×SD16×C131—22no—
95C2×SD16×C131—22no—
96C2×SD16×C131—41no—
97C2×M16×C131—22no—
98C2×M16×C131—22no—
99C2×M16×C131—22no—
100C2×M16×C131—22no—
101C2×M16×C131—41no—
102C2×M16×C131—41no—
103C22×C8×C131C2311yescharacteristic
104C22×C8×C131C2311yescharacteristic
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107#123×C131—28no—
108C22⋊Q8×C131—22no—
109C22⋊Q8×C131—22no—
110C22⋊Q8×C131—22no—
111C22⋊Q8×C131—22no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131—22no—
115C22⋊Q8×C131—41no—
116C22⋊Q8×C131—41no—
117C22⋊Q8×C131D414yes—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131D414yes—
122#120×C131—28no—
123C4×D4×C131—28no—
124C4×D4×C131—28no—
125#117×C131—22no—
126#117×C131—22no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—21no—
129C2×C4⋊C4×C131—21no—
130C2×C4⋊C4×C131—21no—
131C2×C4⋊C4×C131—21no—
132C2×C4⋊C4×C131C2311yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C4⋊C4×C131C2311yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
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×C131—21no—
146C2×C22⋊C4×C131—21no—
147C2×C22⋊C4×C131—21no—
148C2×C42×C131—21no—
149#107×C131—22no—
150#106×C131—22no—
151#103×C131—22no—
152#103×C131—22no—
153#103×C131—22no—
154#103×C131—22no—
155#103×C131—41no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—41no—
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131D414yescomplemented
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—22no—
167C24×C131—22no—
168C24×C131—22no—
169C24×C131—21no—
170C24×C131—41no—
171C24×C131—41no—
172C24×C131—41no—
173C24×C131—41no—
174C24×C131C2×D411yescharacteristic
175C24×C131C2×D411yescharacteristic
176C24×C131C2×D411yescharacteristic
177#41×C131—44no—
178#41×C131—44no—
179#41×C131—44no—
180#41×C131—44no—
181C2×Q8×C131—21no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131—21no—
189C2×Q8×C131—21no—
190C2×Q8×C131—21no—
191C2×Q8×C131—21no—
192C2×Q8×C131C2×D412yes—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—24no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—42no—
202C2×D4×C131—42no—
203C2×D4×C131—42no—
204C2×D4×C131—42no—
205C2×D4×C131—42no—
206C2×D4×C131—42no—
207C2×D4×C131C2×D412yes—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—24no—
217C22×C4×C131—22no—
218C22×C4×C131—22no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—22no—
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—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—41no—
237C22×C4×C131—41no—
238C22×C4×C131—41no—
239C22×C4×C131—44no—
240C22×C4×C131—44no—
241C22×C4×C131—44no—
242C22×C4×C131—44no—
243C22×C4×C131—42no—
244C22×C4×C131—42no—
245C22×C4×C131C2×D411yescharacteristic
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2×D412yes—
248C22×C4×C131C2×D412yes—
249C22×C4×C131C2×D411yescharacteristic
250C22×C4×C131C2×D412yes—
251C22×C4×C131#4112yes—
252C22×C4×C131C2411yescharacteristic
253Q16×C131—44no—
254SD16×C131—44no—
255M16×C131—44no—
256M16×C131—44no—
257C2×C8×C131—21no—
258C2×C8×C131—21no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131C2×D412yes—
268C2×C8×C131C2×D412yes—
269C4⋊C4×C131—24no—
270C4⋊C4×C131—24no—
271C4⋊C4×C131—21no—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—42no—
280C4⋊C4×C131—42no—
281C4⋊C4×C131—42no—
282C4⋊C4×C131C2×D412yes—
283C4⋊C4×C131C2×D412yes—
284C22⋊C4×C131—24no—
285C22⋊C4×C131—24no—
286C22⋊C4×C131—24no—
287C22⋊C4×C131—24no—
288C22⋊C4×C131—24no—
289C22⋊C4×C131—42no—
290C22⋊C4×C131—42no—
291C22⋊C4×C131—42no—
292C22⋊C4×C131—42no—
293C22⋊C4×C131—42no—
294C22⋊C4×C131—42no—
295C42×C131—24no—
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—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—21no—
314C23×C131—22no—
315C23×C131—44no—
316C23×C131—44no—
317C23×C131—44no—
318C23×C131—44no—
319C23×C131—44no—
320C23×C131—44no—
321C23×C131—44no—
322C23×C131—41no—
323C23×C131—41no—
324C23×C131—41no—
325C23×C131—41no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131#12012yes—
329C23×C131#12112yes—
330C23×C131#13712yes—
331C23×C131C22×D411yescharacteristic
332Q8×C131—22no—
333Q8×C131—22no—
334Q8×C131—41no—
335Q8×C131—41no—
336Q8×C131—41no—
337Q8×C131—41no—
338Q8×C131—41no—
339Q8×C131—41no—
340D4×C131—22no—
341D4×C131—22no—
342D4×C131—48no—
343D4×C131—48no—
344D4×C131—48no—
345D4×C131—41no—
346D4×C131—41no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—22no—
352C2×C4×C131—22no—
353C2×C4×C131—22no—
354C2×C4×C131—22no—
355C2×C4×C131—22no—
356C2×C4×C131—22no—
357C2×C4×C131—22no—
358C2×C4×C131—22no—
359C2×C4×C131—22no—
360C2×C4×C131—22no—
361C2×C4×C131—21no—
362C2×C4×C131—22no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—44no—
366C2×C4×C131—44no—
367C2×C4×C131—44no—
368C2×C4×C131—48no—
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—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#12012yes—
392C2×C4×C131#12112yes—
393C2×C4×C131C22×D411yescharacteristic
394C2×C4×C131C22×D411yescharacteristic
395C2×C4×C131C22×D411yescharacteristic
396C2×C4×C131C2×#4111yescharacteristic
397C2×C4×C131H(5,𝔽2)11yescharacteristic
398C2×C4×C131H(5,𝔽2)11yescharacteristic
399C8×C131—22no—
400C8×C131—22no—
401C8×C131—41no—
402C8×C131—41no—
403C22×C131—22no—
404C22×C131—22no—
405C22×C131—22no—
406C22×C131—22no—
407C22×C131—22no—
408C22×C131—22no—
409C22×C131—22no—
410C22×C131—22no—
411C22×C131—22no—
412C22×C131—416no—
413C22×C131—41no—
414C22×C131—41no—
415C22×C131—41no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—41no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—41no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—81no—
429C22×C131—81no—
430C22×C131—81no—
431C22×C131—81no—
432C22×C131C2×#12011yescharacteristic
433C22×C131C2×#12111yescharacteristic
434C22×C131#53411yescharacteristic
435C22×C131C2×#13711yescharacteristic
436C22×C131#57511yescharacteristic
437C22×C131#57511yescharacteristic
438C22×C131#57511yescharacteristic
439C4×C131—22no—
440C4×C131—22no—
441C4×C131—41no—
442C4×C131—42no—
443C4×C131—42no—
444C4×C131—42no—
445C4×C131—81no—
446C4×C131—81no—
447C4×C131—81no—
448C4×C131—81no—
449C4×C131D4211yescharacteristic
450C4×C131D4211yescharacteristic
451C4×C131#54611yescharacteristic
452C4×C131#54611yescharacteristic
453C2×C131—42no—
454C2×C131—42no—
455C2×C131—42no—
456C2×C131—82no—
457C2×C131#241011yescharacteristic
458C2×C131#300511yescharacteristic
459C2×C131#300711yescharacteristic
460C2×C131#305411yescharacteristic
461C2×C131#305611yescharacteristic
462C2×C131#319611yescharacteristic
463C2×C131#319711yescharacteristic
464#24389C13111yesmaximal, characteristic, direct product factor, Sylow
465C131#2438911yescharacteristic, direct product factor, Sylow
466C2×#525C2×C13111yescharacteristic
467C2×#470C2×C13111yescharacteristic, complemented
468C2×#468C2×C13111yescharacteristic, complemented
469C2×#452C2×C13111yescharacteristic, complemented
470C2×#407C2×C13111yescharacteristic, complemented
471#2848C2×C13111yescharacteristic, complemented
472#2036C2×C13111yescharacteristic, complemented
473#2034C2×C13111yescharacteristic, complemented
474#2001C2×C13111yescharacteristic, complemented
475#2000C2×C13111yescharacteristic, complemented
476#1895C2×C13111yescharacteristic, complemented
477#1894C2×C13111yescharacteristic, complemented
478#1873C2×C13111yescharacteristic, complemented
479#1854C2×C13111yescharacteristic, complemented
480#1788C2×C13111yescharacteristic, complemented
481C22×#41C22×C13111yescharacteristic
482C24×C4C22×C13111yescharacteristic
483C22×Q16C22×C13111yescharacteristic, complemented
484C22×SD16C22×C13111yescharacteristic, complemented
485C22×M16C22×C13111yescharacteristic
486C22×M16C22×C13111yescharacteristic
487#525—24no—
488#525—24no—
489C2×#123—21no—
490C2×C22⋊Q8C22×C13111yescharacteristic
491C2×C22⋊Q8C22×C13111yescharacteristic
492C2×C22⋊Q8C22×C13111yescharacteristic
493C2×C22⋊Q8C22×C13111yescharacteristic
494C2×C22⋊Q8C22×C13111yescharacteristic
495C2×#121C22×C13111yescharacteristic
496C2×#121C22×C13111yescharacteristic
497C2×#120—21no—
498C2×C4×D4—21no—
499C2×C4×D4—21no—
500C2×#117C22×C13111yescharacteristic
501#470—24no—
502#468—24no—
503#452—24no—
504C2×#107C22×C13111yescharacteristic, complemented
505C2×#106C22×C13111yescharacteristic, complemented
506C2×#103C22×C13111yescharacteristic, complemented
507C2×#103C22×C13111yescharacteristic, complemented
508C2×#103C22×C13111yescharacteristic, complemented
509C2×#103C22×C13111yescharacteristic, complemented
510C2×#103C22×C13111yescharacteristic, complemented
511C2×#102C22×C13111yescharacteristic, complemented
512C2×#102C22×C13111yescharacteristic, complemented
513C2×#102C22×C13111yescharacteristic, complemented
514#407—24no—
515C2×C22⋊C8C22×C13111yescharacteristic
516C2×C22⋊C8C22×C13111yescharacteristic
517C2×C22⋊C8C22×C13111yescharacteristic
518C2×C22⋊C8C22×C13111yescharacteristic
519#385—21no—
520#385—21no—
521#385—21no—
522#380C22×C13111yescharacteristic
523#380C22×C13111yescharacteristic
524#380C22×C13111yescharacteristic
525#379—21no—
526#340C22×C13111yescharacteristic, complemented
527#340C22×C13111yescharacteristic, complemented
528#340C22×C13111yescharacteristic, complemented
529#340C22×C13111yescharacteristic, complemented
530C25D4×C13111yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C13111yescharacteristic
538C22×Q8C23×C13111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C13111yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C13111yescharacteristic
551C23×C4D4×C13111yescharacteristic
552C23×C4D4×C13111yescharacteristic
553C23×C4C23×C13111yescharacteristic
554C23×C4C23×C13111yescharacteristic
555C23×C4C23×C13111yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C13111yescharacteristic
569C22×C8C23×C13111yescharacteristic
570C22×C8C23×C13111yescharacteristic
571C22×C8C23×C13111yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C13114yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C13114yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C13111yescharacteristic
598C2×C4⋊C4C23×C13111yescharacteristic
599C2×C4⋊C4C23×C13111yescharacteristic
600C2×C4⋊C4C23×C13111yescharacteristic
601C2×C4⋊C4C23×C13111yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C13114yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C13111yescharacteristic
640C24C2×D4×C13111yescharacteristic
641C24C2×D4×C13111yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C13112yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C13112yes—
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—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C13111yescharacteristic
711C22×C4C2×D4×C13111yescharacteristic
712C22×C4C2×D4×C13112yes—
713C22×C4C2×D4×C13112yes—
714C22×C4C2×D4×C13111yescharacteristic
715C22×C4C2×D4×C13112yes—
716C22×C4#41×C13112yes—
717C22×C4C24×C13111yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C13112yes—
733C2×C8C2×D4×C13112yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C13112yes—
748C4⋊C4C2×D4×C13112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C13112yes—
794C23#121×C13112yes—
795C23#137×C13112yes—
796C23C22×D4×C13111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C13112yes—
857C2×C4#121×C13112yes—
858C2×C4C22×D4×C13111yescharacteristic
859C2×C4C22×D4×C13111yescharacteristic
860C2×C4C22×D4×C13111yescharacteristic
861C2×C4C2×#41×C13111yescharacteristic
862C2×C4H(5,𝔽2)×C13111yescharacteristic
863C2×C4H(5,𝔽2)×C13111yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C13111yescharacteristic
898C22C2×#121×C13111yescharacteristic
899C22#534×C13111yescharacteristic
900C22C2×#137×C13111yescharacteristic
901C22#575×C13111yescharacteristic
902C22#575×C13111yescharacteristic
903C22#575×C13111yescharacteristic
904C4—22no—
905C4—22no—
906C4—42no—
907C4—42no—
908C4—41no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C13111yescharacteristic
915C4D42×C13111yescharacteristic
916C4#546×C13111yescharacteristic
917C4#546×C13111yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2#2410×C13111yescharacteristic
923C2#3005×C13111yescharacteristic
924C2#3007×C13111yescharacteristic
925C2#3054×C13111yescharacteristic
926C2#3056×C13111yescharacteristic
927C2#3196×C13111yescharacteristic
928C2#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×#470×C131C2semidirect
3. C2×#468×C131C2semidirect
4. C2×#452×C131C2semidirect
5. C2×#407×C131C2semidirect
6. #2848×C131C2semidirect
7. #2036×C131C2semidirect
8. #2034×C131C2semidirect
9. #2001×C131C2semidirect
10. #2000×C131C2semidirect
11. #1895×C131C2semidirect
12. #1894×C131C2semidirect
13. #1873×C131C2semidirect
14. #1854×C131C2semidirect
15. #1788×C131C2semidirect
18. C22×Q16×C131C22semidirect
19. C22×SD16×C131C22semidirect
39. C2×#107×C131C22semidirect
40. C2×#106×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
44. C2×#103×C131C22semidirect
45. C2×#103×C131C22semidirect
46. C2×#102×C131C22semidirect
47. C2×#102×C131C22semidirect
48. C2×#102×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
162. C22⋊C8×C131D4semidirect
464. #24389C131direct (N × H)
465. C131#24389direct (N × H)
467. C2×#470C2×C131semidirect
468. C2×#468C2×C131semidirect
469. C2×#452C2×C131semidirect
470. C2×#407C2×C131semidirect
471. #2848C2×C131semidirect
472. #2036C2×C131semidirect
473. #2034C2×C131semidirect
474. #2001C2×C131semidirect
475. #2000C2×C131semidirect
476. #1895C2×C131semidirect
477. #1894C2×C131semidirect
478. #1873C2×C131semidirect
479. #1854C2×C131semidirect
480. #1788C2×C131semidirect
483. C22×Q16C22×C131semidirect
484. C22×SD16C22×C131semidirect
504. C2×#107C22×C131semidirect
505. C2×#106C22×C131semidirect
506. C2×#103C22×C131semidirect
507. C2×#103C22×C131semidirect
508. C2×#103C22×C131semidirect
509. C2×#103C22×C131semidirect
510. C2×#103C22×C131semidirect
511. C2×#102C22×C131semidirect
512. C2×#102C22×C131semidirect
513. C2×#102C22×C131semidirect
526. #340C22×C131semidirect
527. #340C22×C131semidirect
528. #340C22×C131semidirect
529. #340C22×C131semidirect
627. C22⋊C8D4×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×#470×C1312
C2×#468×C1312
C2×#452×C1312
C2×#407×C1312
#2848×C1312
#2036×C1312
#2034×C1312
#2001×C1312
#2000×C1312
#1895×C1312
#1894×C1312
#1873×C1312
#1854×C1312
#1788×C1312
#24389131