Finite Group Databasebeta

← C131×#22419 #45708303

Subgroups — C131×#22419 #45708303

Order 33536.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic
2C2×#435×C131C211yesmaximal, characteristic, complemented
3C2×#417×C131C211yesmaximal, characteristic, complemented
4C22×#102×C131C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C131C211yesmaximal, characteristic, complemented
6#1983×C131C211yesmaximal, characteristic, complemented
7#1959×C131C211yesmaximal, characteristic, complemented
8#1895×C131C211yesmaximal, characteristic, complemented
9#1892×C131C211yesmaximal, characteristic, complemented
10#1874×C131C211yesmaximal, characteristic, complemented
11#1872×C131C211yesmaximal, characteristic, complemented
12#1802×C131C211yesmaximal, characteristic, complemented
13#1788×C131C211yesmaximal, characteristic, complemented
14#1786×C131C211yesmaximal, characteristic, complemented
15#1762×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic, complemented
19C23×C8×C131C2211yescharacteristic
20#546×C131—24no—
21#546×C131C418yescomplemented
22C2×#124×C131C2211yescharacteristic
23C2×#123×C131—21no—
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×#121×C131—21no—
26C2×#121×C131C2211yescharacteristic
27C2×#120×C131—21no—
28C2×C4×D4×C131—21no—
29C2×C4×D4×C131C2211yescharacteristic
30C2×C4×D4×C131C2211yescharacteristic
31C22×C4⋊C4×C131C2211yescharacteristic
32C22×C4⋊C4×C131C2211yescharacteristic, complemented
33C22×C22⋊C4×C131—21no—
34#435×C131—24no—
35C2×C4⋊C8×C131C2211yescharacteristic, complemented
36#417×C131—24no—
37C2×#103×C131C2211yescharacteristic, complemented
38C2×#103×C131C2211yescharacteristic, complemented
39C2×#103×C131C2211yescharacteristic, complemented
40C2×#103×C131C2211yescharacteristic, complemented
41C2×#102×C131—24no—
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic, complemented
52C2×#97×C131C2211yescharacteristic, complemented
53#389×C131—21no—
54#385×C131—21no—
55#385×C131—21no—
56#384×C131C2211yescharacteristic, complemented
57#380×C131C2211yescharacteristic
58#380×C131C2211yescharacteristic, complemented
59C4×C4⋊C4×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#340×C131C2211yescharacteristic, complemented
64C25×C131—21no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—41no—
69C2×#41×C131—41no—
70C2×#41×C131C2×C414yescomplemented
71C22×Q8×C131C2311yescharacteristic
72C22×D4×C131—22no—
73C22×D4×C131—22no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131—22no—
78C22×D4×C131—41no—
79C22×D4×C131—41no—
80C22×D4×C131C2×C414yescomplemented
81C22×D4×C131D411yescharacteristic
82C22×D4×C131C2311yescharacteristic
83C22×D4×C131C2311yescharacteristic
84C23×C4×C131—21no—
85C23×C4×C131—21no—
86C23×C4×C131—21no—
87C23×C4×C131—21no—
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C2×M16×C131—22no—
91C2×M16×C131—22no—
92C2×M16×C131—41no—
93C22×C8×C131—22no—
94C22×C8×C131—22no—
95C22×C8×C131—41no—
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99C22×C8×C131C2311yescharacteristic
100#124×C131—22no—
101#124×C131C2×C414yescomplemented
102#123×C131—28no—
103C22⋊Q8×C131—22no—
104C22⋊Q8×C131C2×C414yescomplemented
105#121×C131—22no—
106#121×C131—28no—
107#121×C131C2×C414yescomplemented
108#120×C131—28no—
109C4×D4×C131—22no—
110C4×D4×C131—44no—
111C4×D4×C131C2×C414yes—
112C4×D4×C131C2×C414yescomplemented
113C4×D4×C131D414yes—
114C2×C4⋊C4×C131—21no—
115C2×C4⋊C4×C131—22no—
116C2×C4⋊C4×C131—22no—
117C2×C4⋊C4×C131—21no—
118C2×C4⋊C4×C131—21no—
119C2×C4⋊C4×C131—21no—
120C2×C4⋊C4×C131—21no—
121C2×C4⋊C4×C131—41no—
122C2×C4⋊C4×C131—41no—
123C2×C4⋊C4×C131D411yescharacteristic
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—28no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131—21no—
137C2×C22⋊C4×C131D411yescharacteristic
138C2×C22⋊C4×C131D411yescharacteristic
139C2×C42×C131—21no—
140C2×C42×C131C2311yescharacteristic
141C4⋊C8×C131—22no—
142#103×C131—22no—
143#103×C131—22no—
144#103×C131—41no—
145#103×C131—41no—
146#102×C131—22no—
147#102×C131—22no—
148#102×C131—22no—
149#102×C131—22no—
150#102×C131—22no—
151#102×C131—41no—
152#102×C131—41no—
153#102×C131D414yescomplemented
154C22⋊C8×C131—22no—
155C22⋊C8×C131—22no—
156#97×C131—22no—
157#95×C131—21no—
158#95×C131—21no—
159#95×C131—21no—
160C24×C131—21no—
161C24×C131—21no—
162C24×C131—24no—
163C24×C131—42no—
164C24×C131—42no—
165C24×C131—42no—
166C24×C131—42no—
167C24×C131—81no—
168C24×C131—81no—
169C24×C131C2×D411yescharacteristic
170C24×C131C2×D411yescharacteristic
171#41×C131—28no—
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×C131C22×C412yes—
181C2×D4×C131—22no—
182C2×D4×C131—22no—
183C2×D4×C131—28no—
184C2×D4×C131—24no—
185C2×D4×C131—24no—
186C2×D4×C131—24no—
187C2×D4×C131—21no—
188C2×D4×C131—21no—
189C2×D4×C131—21no—
190C2×D4×C131—21no—
191C2×D4×C131—21no—
192C2×D4×C131—21no—
193C2×D4×C131—21no—
194C2×D4×C131—21no—
195C2×D4×C131—44no—
196C2×D4×C131—44no—
197C2×D4×C131—44no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131—42no—
202C2×D4×C131—81no—
203C2×D4×C131—81no—
204C2×D4×C131C22⋊C414yes—
205C2×D4×C131C22×C412yes—
206C2×D4×C131C22×C412yes—
207C2×D4×C131C2×D412yes—
208C2×D4×C131#4112yes—
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—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—24no—
221C22×C4×C131—24no—
222C22×C4×C131—21no—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—42no—
226C22×C4×C131—42no—
227C22×C4×C131—42no—
228C22×C4×C131—42no—
229C22×C4×C131—42no—
230C22×C4×C131—42no—
231C22×C4×C131—81no—
232C22×C4×C131—81no—
233C22×C4×C131—81no—
234C22×C4×C131—81no—
235C22×C4×C131C22×C412yes—
236C22×C4×C131C22×C412yes—
237C22×C4×C131C2×D411yescharacteristic
238C22×C4×C131C2×D411yescharacteristic
239C22×C4×C131C2×D411yescharacteristic
240C22×C4×C131C2×D411yescharacteristic
241C22×C4×C131C2×D412yes—
242C22×C4×C131C2×D412yes—
243C22×C4×C131C2411yescharacteristic
244M16×C131—44no—
245C2×C8×C131—21no—
246C2×C8×C131—21no—
247C2×C8×C131—21no—
248C2×C8×C131—21no—
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—44no—
257C2×C8×C131C2×D412yes—
258C4⋊C4×C131—24no—
259C4⋊C4×C131—21no—
260C4⋊C4×C131—21no—
261C4⋊C4×C131—21no—
262C4⋊C4×C131—21no—
263C4⋊C4×C131—21no—
264C4⋊C4×C131—21no—
265C4⋊C4×C131—21no—
266C4⋊C4×C131—21no—
267C4⋊C4×C131—42no—
268C4⋊C4×C131—42no—
269C4⋊C4×C131—42no—
270C4⋊C4×C131—81no—
271C4⋊C4×C131C22⋊C414yes—
272C4⋊C4×C131C22×C412yes—
273C4⋊C4×C131C2×D412yes—
274C22⋊C4×C131—24no—
275C22⋊C4×C131—24no—
276C22⋊C4×C131—24no—
277C22⋊C4×C131—24no—
278C22⋊C4×C131—24no—
279C22⋊C4×C131—42no—
280C22⋊C4×C131—42no—
281C22⋊C4×C131C22⋊C414yes—
282C22⋊C4×C131C22⋊C414yes—
283C42×C131—42no—
284C42×C131C22×C412yes—
285C42×C131C2×D412yes—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—21no—
289C23×C131—21no—
290C23×C131—22no—
291C23×C131—21no—
292C23×C131—22no—
293C23×C131—21no—
294C23×C131—22no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—22no—
300C23×C131—48no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—41no—
307C23×C131—41no—
308C23×C131—41no—
309C23×C131—41no—
310C23×C131—41no—
311C23×C131—48no—
312C23×C131—84no—
313C23×C131—84no—
314C23×C131—84no—
315C23×C131—84no—
316C23×C131—84no—
317C23×C131C2×C22⋊C412yes—
318C23×C131C2×C22⋊C412yes—
319C23×C131AGL(1,ℤ/8)12yes—
320C23×C131#13712yes—
321C23×C131C22×D411yescharacteristic
322Q8×C131—22no—
323Q8×C131—22no—
324Q8×C131—41no—
325Q8×C131—41no—
326D4×C131—28no—
327D4×C131—22no—
328D4×C131—22no—
329D4×C131—22no—
330D4×C131—22no—
331D4×C131—22no—
332D4×C131—48no—
333D4×C131—48no—
334D4×C131—41no—
335D4×C131—41no—
336D4×C131—84no—
337D4×C131C4×D414yescomplemented
338C2×C4×C131—21no—
339C2×C4×C131—21no—
340C2×C4×C131—21no—
341C2×C4×C131—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—22no—
347C2×C4×C131—22no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—22no—
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—48no—
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—84no—
374C2×C4×C131—84no—
375C2×C4×C131—84no—
376C2×C4×C131C2×C22⋊C412yes—
377C2×C4×C131C2×C22⋊C412yes—
378C2×C4×C131C2×C22⋊C412yes—
379C2×C4×C131C2×C22⋊C412yes—
380C2×C4×C131C23×C411yescharacteristic
381C2×C4×C131C22×D411yescharacteristic
382C2×C4×C131C22×D411yescharacteristic
383C2×C4×C131C2×#4111yescharacteristic
384C2×C4×C131H(5,𝔽2)11yescharacteristic
385C2×C4×C131H(5,𝔽2)11yescharacteristic
386C8×C131—22no—
387C8×C131—41no—
388C8×C131—41no—
389C8×C131—41no—
390C22×C131—22no—
391C22×C131—22no—
392C22×C131—22no—
393C22×C131—22no—
394C22×C131—22no—
395C22×C131—22no—
396C22×C131—22no—
397C22×C131—24no—
398C22×C131—22no—
399C22×C131—22no—
400C22×C131—42no—
401C22×C131—42no—
402C22×C131—41no—
403C22×C131—42no—
404C22×C131—41no—
405C22×C131—42no—
406C22×C131—41no—
407C22×C131—42no—
408C22×C131—41no—
409C22×C131—42no—
410C22×C131—42no—
411C22×C131—42no—
412C22×C131—42no—
413C22×C131—816no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131—81no—
417C22×C131—81no—
418C22×C131#41714yescomplemented
419C22×C131C22×C22⋊C411yescharacteristic
420C22×C131D4211yescharacteristic
421C22×C131#54611yescharacteristic
422C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C131C2×#13711yescharacteristic
424C22×C131#57611yescharacteristic
425C22×C131#57711yescharacteristic
426C4×C131—22no—
427C4×C131—22no—
428C4×C131—22no—
429C4×C131—22no—
430C4×C131—42no—
431C4×C131—42no—
432C4×C131—42no—
433C4×C131—81no—
434C4×C131—81no—
435C4×C131—81no—
436C4×C131C2×C4×D411yescharacteristic
437C4×C131#51811yescharacteristic
438C4×C131D4211yescharacteristic
439C4×C131#54611yescharacteristic
440C2×C131—24no—
441C2×C131—42no—
442C2×C131—44no—
443C2×C131—82no—
444C2×C131D4×C22⋊C411yescharacteristic
445C2×C131C2×#41711yescharacteristic
446C2×C131#289711yescharacteristic
447C2×C131#326411yescharacteristic
448C2×C131#326611yescharacteristic
449C2×C131#330611yescharacteristic
450C2×C131#331411yescharacteristic
451#22419C13111yesmaximal, characteristic, direct product factor, Sylow
452C131#2241911yescharacteristic, direct product factor, Sylow
453C2×#546C2×C13111yescharacteristic
454C2×#435C2×C13111yescharacteristic, complemented
455C2×#417C2×C13111yescharacteristic, complemented
456C22×#102C2×C13111yescharacteristic, complemented
457D4×C4⋊C4C2×C13111yescharacteristic, complemented
458#1983C2×C13111yescharacteristic, complemented
459#1959C2×C13111yescharacteristic, complemented
460#1895C2×C13111yescharacteristic, complemented
461#1892C2×C13111yescharacteristic, complemented
462#1874C2×C13111yescharacteristic, complemented
463#1872C2×C13111yescharacteristic, complemented
464#1802C2×C13111yescharacteristic, complemented
465#1788C2×C13111yescharacteristic, complemented
466#1786C2×C13111yescharacteristic, complemented
467#1762C2×C13111yescharacteristic, complemented
468C22×#41C22×C13111yescharacteristic
469C23×D4C22×C13111yescharacteristic
470C22×M16C22×C13111yescharacteristic, complemented
471C23×C8C22×C13111yescharacteristic
472#546—24no—
473#546C4×C13118yescomplemented
474C2×#124C22×C13111yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C13111yescharacteristic
477C2×#121—21no—
478C2×#121C22×C13111yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C13111yescharacteristic
482C2×C4×D4C22×C13111yescharacteristic
483C22×C4⋊C4C22×C13111yescharacteristic
484C22×C4⋊C4C22×C13111yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C13111yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C13111yescharacteristic, complemented
490C2×#103C22×C13111yescharacteristic, complemented
491C2×#103C22×C13111yescharacteristic, complemented
492C2×#103C22×C13111yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C13111yescharacteristic
495C2×#102C22×C13111yescharacteristic
496C2×#102C22×C13111yescharacteristic
497C2×#102C22×C13111yescharacteristic
498C2×#102C22×C13111yescharacteristic
499C2×#102C22×C13111yescharacteristic
500C2×#102C22×C13111yescharacteristic
501C2×#102C22×C13111yescharacteristic
502C2×C22⋊C8C22×C13111yescharacteristic
503C2×C22⋊C8C22×C13111yescharacteristic, complemented
504C2×#97C22×C13111yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C13111yescharacteristic, complemented
509#380C22×C13111yescharacteristic
510#380C22×C13111yescharacteristic, complemented
511C4×C4⋊C4C22×C13111yescharacteristic, complemented
512#340C22×C13111yescharacteristic, complemented
513#340C22×C13111yescharacteristic, complemented
514#340C22×C13111yescharacteristic, complemented
515#340C22×C13111yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C13114yescomplemented
523C22×Q8C23×C13111yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C13114yescomplemented
533C22×D4D4×C13111yescharacteristic
534C22×D4C23×C13111yescharacteristic
535C22×D4C23×C13111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C13111yescharacteristic
541C23×C4C23×C13111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C13111yescharacteristic
549C22×C8C23×C13111yescharacteristic
550C22×C8C23×C13111yescharacteristic
551C22×C8C23×C13111yescharacteristic
552#124—22no—
553#124C2×C4×C13114yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C13114yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C13114yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C13114yes—
564C4×D4C2×C4×C13114yescomplemented
565C4×D4D4×C13114yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C13111yescharacteristic
576C2×C4⋊C4C23×C13111yescharacteristic
577C2×C4⋊C4C23×C13111yescharacteristic
578C2×C4⋊C4C23×C13111yescharacteristic
579C2×C4⋊C4C23×C13111yescharacteristic
580C2×C4⋊C4C23×C13111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C13111yescharacteristic
590C2×C22⋊C4D4×C13111yescharacteristic
591C2×C42—21no—
592C2×C42C23×C13111yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C13114yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C13111yescharacteristic
622C24C2×D4×C13111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C13112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C13114yes—
657C2×D4C22×C4×C13112yes—
658C2×D4C22×C4×C13112yes—
659C2×D4C2×D4×C13112yes—
660C2×D4#41×C13112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C13112yes—
688C22×C4C22×C4×C13112yes—
689C22×C4C2×D4×C13111yescharacteristic
690C22×C4C2×D4×C13111yescharacteristic
691C22×C4C2×D4×C13111yescharacteristic
692C22×C4C2×D4×C13111yescharacteristic
693C22×C4C2×D4×C13112yes—
694C22×C4C2×D4×C13112yes—
695C22×C4C24×C13111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C13112yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C13114yes—
724C4⋊C4C22×C4×C13112yes—
725C4⋊C4C2×D4×C13112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C13114yes—
734C22⋊C4C22⋊C4×C13114yes—
735C42—42no—
736C42C22×C4×C13112yes—
737C42C2×D4×C13112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C13112yes—
770C23C2×C22⋊C4×C13112yes—
771C23AGL(1,ℤ/8)×C13112yes—
772C23#137×C13112yes—
773C23C22×D4×C13111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C13114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
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—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
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—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C13112yes—
829C2×C4C2×C22⋊C4×C13112yes—
830C2×C4C2×C22⋊C4×C13112yes—
831C2×C4C2×C22⋊C4×C13112yes—
832C2×C4C23×C4×C13111yescharacteristic
833C2×C4C22×D4×C13111yescharacteristic
834C2×C4C22×D4×C13111yescharacteristic
835C2×C4C2×#41×C13111yescharacteristic
836C2×C4H(5,𝔽2)×C13111yescharacteristic
837C2×C4H(5,𝔽2)×C13111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C13114yescomplemented
871C22C22×C22⋊C4×C13111yescharacteristic
872C22D42×C13111yescharacteristic
873C22#546×C13111yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
875C22C2×#137×C13111yescharacteristic
876C22#576×C13111yescharacteristic
877C22#577×C13111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C13111yescharacteristic
889C4#518×C13111yescharacteristic
890C4D42×C13111yescharacteristic
891C4#546×C13111yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C13111yescharacteristic
897C2C2×#417×C13111yescharacteristic
898C2#2897×C13111yescharacteristic
899C2#3264×C13111yescharacteristic
900C2#3266×C13111yescharacteristic
901C2#3306×C13111yescharacteristic
902C2#3314×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC2×#546×C131C2
LCSG ▷ C2×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
2. C2×#435×C131C2semidirect
3. C2×#417×C131C2semidirect
4. C22×#102×C131C2semidirect
5. D4×C4⋊C4×C131C2semidirect
6. #1983×C131C2semidirect
7. #1959×C131C2semidirect
8. #1895×C131C2semidirect
9. #1892×C131C2semidirect
10. #1874×C131C2semidirect
11. #1872×C131C2semidirect
12. #1802×C131C2semidirect
13. #1788×C131C2semidirect
14. #1786×C131C2semidirect
15. #1762×C131C2semidirect
18. C22×M16×C131C22semidirect
21. #546×C131C4semidirect
32. C22×C4⋊C4×C131C22semidirect
35. C2×C4⋊C8×C131C22semidirect
37. C2×#103×C131C22semidirect
38. C2×#103×C131C22semidirect
39. C2×#103×C131C22semidirect
40. C2×#103×C131C22semidirect
51. C2×C22⋊C8×C131C22semidirect
52. C2×#97×C131C22semidirect
56. #384×C131C22semidirect
58. #380×C131C22semidirect
59. C4×C4⋊C4×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #340×C131C22semidirect
70. C2×#41×C131C2×C4semidirect
80. C22×D4×C131C2×C4semidirect
101. #124×C131C2×C4semidirect
104. C22⋊Q8×C131C2×C4semidirect
107. #121×C131C2×C4semidirect
112. C4×D4×C131C2×C4semidirect
153. #102×C131D4semidirect
337. D4×C131C4×D4semidirect
418. C22×C131#417semidirect
451. #22419C131direct (N × H)
452. C131#22419direct (N × H)
454. C2×#435C2×C131semidirect
455. C2×#417C2×C131semidirect
456. C22×#102C2×C131semidirect
457. D4×C4⋊C4C2×C131semidirect
458. #1983C2×C131semidirect
459. #1959C2×C131semidirect
460. #1895C2×C131semidirect
461. #1892C2×C131semidirect
462. #1874C2×C131semidirect
463. #1872C2×C131semidirect
464. #1802C2×C131semidirect
465. #1788C2×C131semidirect
466. #1786C2×C131semidirect
467. #1762C2×C131semidirect
470. C22×M16C22×C131semidirect
473. #546C4×C131semidirect
484. C22×C4⋊C4C22×C131semidirect
487. C2×C4⋊C8C22×C131semidirect
489. C2×#103C22×C131semidirect
490. C2×#103C22×C131semidirect
491. C2×#103C22×C131semidirect
492. C2×#103C22×C131semidirect
503. C2×C22⋊C8C22×C131semidirect
504. C2×#97C22×C131semidirect
508. #384C22×C131semidirect
510. #380C22×C131semidirect
511. C4×C4⋊C4C22×C131semidirect
512. #340C22×C131semidirect
513. #340C22×C131semidirect
514. #340C22×C131semidirect
515. #340C22×C131semidirect
522. C2×#41C2×C4×C131semidirect
532. C22×D4C2×C4×C131semidirect
553. #124C2×C4×C131semidirect
556. C22⋊Q8C2×C4×C131semidirect
559. #121C2×C4×C131semidirect
564. C4×D4C2×C4×C131semidirect
605. #102D4×C131semidirect
789. D4C4×D4×C131semidirect
870. C22#417×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×#435×C1312
C2×#417×C1312
C22×#102×C1312
D4×C4⋊C4×C1312
#1983×C1312
#1959×C1312
#1895×C1312
#1892×C1312
#1874×C1312
#1872×C1312
#1802×C1312
#1788×C1312
#1786×C1312
#1762×C1312
#22419131