Finite Group Databasebeta

← C131×#24247 #45710131

Subgroups — C131×#24247 #45710131

Order 33536.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic
2C2×#464×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#450×C131C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C131C211yesmaximal, characteristic, complemented
6#2536×C131C211yesmaximal, characteristic, complemented
7#2035×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2001×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1958×C131C211yesmaximal, characteristic, complemented
12#1954×C131C211yesmaximal, characteristic, complemented
13#1804×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×Q16×C131C2211yescharacteristic, complemented
19C22×SD16×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic
21#546×C131—24no—
22#546×C131—24no—
23C2×#124×C131C2211yescharacteristic
24C2×#123×C131—21no—
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×C22⋊Q8×C131C2211yescharacteristic, complemented
28C2×#121×C131—21no—
29C2×#121×C131C2211yescharacteristic
30C2×#120×C131—21no—
31C2×C4×Q8×C131C2211yescharacteristic, complemented
32C2×C4×D4×C131C2211yescharacteristic
33C2×C4×D4×C131C2211yescharacteristic
34C22×C22⋊C4×C131—21no—
35#464×C131—24no—
36#452×C131—24no—
37#450×C131—24no—
38C4×SD16×C131—24no—
39C2×#106×C131C2211yescharacteristic, complemented
40C2×C4⋊C8×C131C2211yescharacteristic, complemented
41C2×#103×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×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55C2×C4×C8×C131C2211yescharacteristic, complemented
56#398×C131—21no—
57#394×C131—21no—
58#388×C131—21no—
59#388×C131—21no—
60#382×C131C2211yescharacteristic, complemented
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×Q8×C131C2311yescharacteristic
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—22no—
77C22×D4×C131—22no—
78C22×D4×C131—22no—
79C22×D4×C131—22no—
80C22×D4×C131—21no—
81C22×D4×C131—41no—
82C22×D4×C131—41no—
83C22×D4×C131D411yescharacteristic
84C22×D4×C131C2311yescharacteristic
85C22×D4×C131C2311yescharacteristic
86C23×C4×C131—21no—
87C23×C4×C131—21no—
88C23×C4×C131C2311yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C2×Q16×C131—22no—
91C2×Q16×C131—22no—
92C2×Q16×C131—41no—
93C2×SD16×C131—22no—
94C2×SD16×C131—22no—
95C2×SD16×C131—22no—
96C2×SD16×C131—22no—
97C2×SD16×C131—41no—
98C2×SD16×C131D414yescomplemented
99C22×C8×C131C2311yescharacteristic
100C22×C8×C131C2311yescharacteristic
101C22×C8×C131C2311yescharacteristic
102C22×C8×C131C2311yescharacteristic
103#124×C131—22no—
104#124×C131D414yes—
105#123×C131—28no—
106C22⋊Q8×C131—22no—
107C22⋊Q8×C131—22no—
108C22⋊Q8×C131—22no—
109C22⋊Q8×C131—22no—
110C22⋊Q8×C131—41no—
111C22⋊Q8×C131—41no—
112#121×C131—28no—
113#121×C131—22no—
114#121×C131—22no—
115#120×C131—28no—
116C4×Q8×C131—22no—
117C4×Q8×C131—22no—
118C4×D4×C131—22no—
119C4×D4×C131—22no—
120C4×D4×C131—22no—
121C4×D4×C131D414yes—
122C2×C4⋊C4×C131—21no—
123C2×C4⋊C4×C131—21no—
124C2×C4⋊C4×C131—21no—
125C2×C4⋊C4×C131—21no—
126C2×C4⋊C4×C131D411yescharacteristic
127C2×C4⋊C4×C131C2311yescharacteristic
128C2×C4⋊C4×C131C2311yescharacteristic
129C2×C4⋊C4×C131C2311yescharacteristic
130C2×C4⋊C4×C131C2311yescharacteristic
131C2×C22⋊C4×C131—28no—
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×C22⋊C4×C131—21no—
141C2×C22⋊C4×C131D411yescharacteristic
142C2×C22⋊C4×C131D411yescharacteristic
143C2×C42×C131—21no—
144C2×C42×C131C2311yescharacteristic
145#106×C131—22no—
146C4⋊C8×C131—22no—
147#103×C131—22no—
148#103×C131—22no—
149#103×C131—22no—
150#103×C131—41no—
151#102×C131—22no—
152#102×C131—22no—
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—41no—
157C22⋊C8×C131—22no—
158C22⋊C8×C131—22no—
159C22⋊C8×C131—41no—
160C22⋊C8×C131—41no—
161C4×C8×C131—22no—
162#95×C131—21no—
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—21no—
167C24×C131—24no—
168C24×C131—21no—
169C24×C131—42no—
170C24×C131—42no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—81no—
174C24×C131—81no—
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×C131C2×D412yes—
192C2×Q8×C131C2×D412yes—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—22no—
196C2×D4×C131—24no—
197C2×D4×C131—22no—
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—41no—
207C2×D4×C131—42no—
208C2×D4×C131—42no—
209C2×D4×C131—44no—
210C2×D4×C131—44no—
211C2×D4×C131—44no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—44no—
215C2×D4×C131—81no—
216C2×D4×C131—81no—
217C2×D4×C131C2×D412yes—
218C2×D4×C131C2×D412yes—
219C2×D4×C131C2×D412yes—
220C2×D4×C131#4112yes—
221C22×C4×C131—24no—
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—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—21no—
237C22×C4×C131—24no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—42no—
242C22×C4×C131—42no—
243C22×C4×C131—81no—
244C22×C4×C131—81no—
245C22×C4×C131C2×D411yescharacteristic
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2×D411yescharacteristic
248C22×C4×C131C2×D411yescharacteristic
249C22×C4×C131C2411yescharacteristic
250Q16×C131—44no—
251SD16×C131—28no—
252SD16×C131—44no—
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—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131C2×D412yes—
265C4⋊C4×C131—24no—
266C4⋊C4×C131—22no—
267C4⋊C4×C131—21no—
268C4⋊C4×C131—21no—
269C4⋊C4×C131—21no—
270C4⋊C4×C131—21no—
271C4⋊C4×C131—21no—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—42no—
275C4⋊C4×C131—42no—
276C4⋊C4×C131—42no—
277C4⋊C4×C131C2×D412yes—
278C22⋊C4×C131—24no—
279C22⋊C4×C131—24no—
280C22⋊C4×C131—22no—
281C22⋊C4×C131—24no—
282C22⋊C4×C131—24no—
283C22⋊C4×C131—24no—
284C22⋊C4×C131—22no—
285C22⋊C4×C131—42no—
286C22⋊C4×C131—42no—
287C22⋊C4×C131—42no—
288C22⋊C4×C131—42no—
289C42×C131—42no—
290C42×C131C2×D412yes—
291C42×C131C2×D412yes—
292C23×C131—21no—
293C23×C131—22no—
294C23×C131—21no—
295C23×C131—22no—
296C23×C131—21no—
297C23×C131—22no—
298C23×C131—21no—
299C23×C131—21no—
300C23×C131—21no—
301C23×C131—22no—
302C23×C131—21no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—48no—
310C23×C131—48no—
311C23×C131—41no—
312C23×C131—41no—
313C23×C131—41no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—84no—
322C23×C131—84no—
323C23×C131—84no—
324C23×C131—84no—
325C23×C131—84no—
326C23×C131#13512yes—
327C23×C131C22×D411yescharacteristic
328Q8×C131—22no—
329Q8×C131—22no—
330Q8×C131—22no—
331Q8×C131—22no—
332Q8×C131—41no—
333Q8×C131—41no—
334Q8×C131—41no—
335Q8×C131—41no—
336D4×C131—22no—
337D4×C131—22no—
338D4×C131—22no—
339D4×C131—22no—
340D4×C131—22no—
341D4×C131—44no—
342D4×C131—48no—
343D4×C131—48no—
344D4×C131—41no—
345D4×C131—41no—
346D4×C131—84no—
347D4×C131#12114yes—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—21no—
352C2×C4×C131—22no—
353C2×C4×C131—21no—
354C2×C4×C131—22no—
355C2×C4×C131—21no—
356C2×C4×C131—22no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—21no—
360C2×C4×C131—21no—
361C2×C4×C131—48no—
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—41no—
385C2×C4×C131—84no—
386C2×C4×C131#12012yes—
387C2×C4×C131#12012yes—
388C2×C4×C131C22×D411yescharacteristic
389C2×C4×C131C22×D411yescharacteristic
390C2×C4×C131C22×D411yescharacteristic
391C2×C4×C131C2×#4111yescharacteristic
392C2×C4×C131H(5,𝔽2)11yescharacteristic
393C2×C4×C131H(5,𝔽2)11yescharacteristic
394C8×C131—22no—
395C8×C131—41no—
396C8×C131—41no—
397C8×C131—41no—
398C22×C131—24no—
399C22×C131—22no—
400C22×C131—22no—
401C22×C131—22no—
402C22×C131—41no—
403C22×C131—42no—
404C22×C131—42no—
405C22×C131—41no—
406C22×C131—41no—
407C22×C131—42no—
408C22×C131—42no—
409C22×C131—42no—
410C22×C131—41no—
411C22×C131—42no—
412C22×C131—41no—
413C22×C131—42no—
414C22×C131—41no—
415C22×C131—42no—
416C22×C131—41no—
417C22×C131—42no—
418C22×C131—41no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—41no—
422C22×C131—816no—
423C22×C131—81no—
424C22×C131—81no—
425C22×C131—81no—
426C22×C131—81no—
427C22×C131C2×#12011yescharacteristic
428C22×C131D4211yescharacteristic
429C22×C131#54611yescharacteristic
430C22×C131C2×#13511yescharacteristic
431C22×C131#57511yescharacteristic
432C22×C131#57711yescharacteristic
433C22×C131#57711yescharacteristic
434C4×C131—22no—
435C4×C131—22no—
436C4×C131—41no—
437C4×C131—41no—
438C4×C131—42no—
439C4×C131—42no—
440C4×C131—42no—
441C4×C131—81no—
442C4×C131—81no—
443C4×C131—81no—
444C4×C131C2×#12111yescharacteristic
445C4×C131#53511yescharacteristic
446C4×C131D4211yescharacteristic
447C4×C131#54611yescharacteristic
448C2×C131—42no—
449C2×C131—44no—
450C2×C131—81no—
451C2×C131—82no—
452C2×C131#240811yescharacteristic
453C2×C131#300211yescharacteristic
454C2×C131#300911yescharacteristic
455C2×C131#327511yescharacteristic
456C2×C131#328211yescharacteristic
457C2×C131#329611yescharacteristic
458C2×C131#332311yescharacteristic
459#24247C13111yesmaximal, characteristic, direct product factor, Sylow
460C131#2424711yescharacteristic, direct product factor, Sylow
461C2×#546C2×C13111yescharacteristic
462C2×#464C2×C13111yescharacteristic, complemented
463C2×#452C2×C13111yescharacteristic, complemented
464C2×#450C2×C13111yescharacteristic, complemented
465C2×C4×SD16C2×C13111yescharacteristic, complemented
466#2536C2×C13111yescharacteristic, complemented
467#2035C2×C13111yescharacteristic, complemented
468#2034C2×C13111yescharacteristic, complemented
469#2001C2×C13111yescharacteristic, complemented
470#2000C2×C13111yescharacteristic, complemented
471#1958C2×C13111yescharacteristic, complemented
472#1954C2×C13111yescharacteristic, complemented
473#1804C2×C13111yescharacteristic, complemented
474#1788C2×C13111yescharacteristic, complemented
475#1786C2×C13111yescharacteristic, complemented
476C22×#41C22×C13111yescharacteristic
477C23×D4C22×C13111yescharacteristic
478C22×Q16C22×C13111yescharacteristic, complemented
479C22×SD16C22×C13111yescharacteristic
480C22×SD16C22×C13111yescharacteristic
481#546—24no—
482#546—24no—
483C2×#124C22×C13111yescharacteristic
484C2×#123—21no—
485C2×C22⋊Q8C22×C13111yescharacteristic
486C2×C22⋊Q8C22×C13111yescharacteristic
487C2×C22⋊Q8C22×C13111yescharacteristic, complemented
488C2×#121—21no—
489C2×#121C22×C13111yescharacteristic
490C2×#120—21no—
491C2×C4×Q8C22×C13111yescharacteristic, complemented
492C2×C4×D4C22×C13111yescharacteristic
493C2×C4×D4C22×C13111yescharacteristic
494C22×C22⋊C4—21no—
495#464—24no—
496#452—24no—
497#450—24no—
498C4×SD16—24no—
499C2×#106C22×C13111yescharacteristic, complemented
500C2×C4⋊C8C22×C13111yescharacteristic, complemented
501C2×#103C22×C13111yescharacteristic, complemented
502C2×#103C22×C13111yescharacteristic, complemented
503C2×#103C22×C13111yescharacteristic, complemented
504C2×#103C22×C13111yescharacteristic, complemented
505C2×#102C22×C13111yescharacteristic
506C2×#102C22×C13111yescharacteristic
507C2×#102C22×C13111yescharacteristic
508C2×#102C22×C13111yescharacteristic
509C2×#102C22×C13111yescharacteristic
510C2×#102C22×C13111yescharacteristic
511C2×C22⋊C8C22×C13111yescharacteristic
512C2×C22⋊C8C22×C13111yescharacteristic
513C2×C22⋊C8C22×C13111yescharacteristic, complemented
514C2×C22⋊C8C22×C13111yescharacteristic, complemented
515C2×C4×C8C22×C13111yescharacteristic, complemented
516#398—21no—
517#394—21no—
518#388—21no—
519#388—21no—
520#382C22×C13111yescharacteristic, complemented
521#380C22×C13111yescharacteristic
522#380C22×C13111yescharacteristic, complemented
523#340C22×C13111yescharacteristic, complemented
524#340C22×C13111yescharacteristic, complemented
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C13111yescharacteristic
533C22×Q8C23×C13111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C13111yescharacteristic
544C22×D4C23×C13111yescharacteristic
545C22×D4C23×C13111yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C13111yescharacteristic
549C23×C4C23×C13111yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C13114yescomplemented
559C22×C8C23×C13111yescharacteristic
560C22×C8C23×C13111yescharacteristic
561C22×C8C23×C13111yescharacteristic
562C22×C8C23×C13111yescharacteristic
563#124—22no—
564#124D4×C13114yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C13114yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C13111yescharacteristic
587C2×C4⋊C4C23×C13111yescharacteristic
588C2×C4⋊C4C23×C13111yescharacteristic
589C2×C4⋊C4C23×C13111yescharacteristic
590C2×C4⋊C4C23×C13111yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C13111yescharacteristic
602C2×C22⋊C4D4×C13111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C13111yescharacteristic
605#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C13111yescharacteristic
636C24C2×D4×C13111yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8C2×D4×C13112yes—
652C2×Q8C2×D4×C13112yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C13112yes—
678C2×D4C2×D4×C13112yes—
679C2×D4C2×D4×C13112yes—
680C2×D4#41×C13112yes—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C13111yescharacteristic
706C22×C4C2×D4×C13111yescharacteristic
707C22×C4C2×D4×C13111yescharacteristic
708C22×C4C2×D4×C13111yescharacteristic
709C22×C4C24×C13111yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×D4×C13112yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C13112yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C13112yes—
751C42C2×D4×C13112yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C13112yes—
787C23C22×D4×C13111yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C13114yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
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—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C13112yes—
847C2×C4#120×C13112yes—
848C2×C4C22×D4×C13111yescharacteristic
849C2×C4C22×D4×C13111yescharacteristic
850C2×C4C22×D4×C13111yescharacteristic
851C2×C4C2×#41×C13111yescharacteristic
852C2×C4H(5,𝔽2)×C13111yescharacteristic
853C2×C4H(5,𝔽2)×C13111yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—24no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C13111yescharacteristic
888C22D42×C13111yescharacteristic
889C22#546×C13111yescharacteristic
890C22C2×#135×C13111yescharacteristic
891C22#575×C13111yescharacteristic
892C22#577×C13111yescharacteristic
893C22#577×C13111yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—41no—
898C4—41no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C13111yescharacteristic
905C4#535×C13111yescharacteristic
906C4D42×C13111yescharacteristic
907C4#546×C13111yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2#2408×C13111yescharacteristic
913C2#3002×C13111yescharacteristic
914C2#3009×C13111yescharacteristic
915C2#3275×C13111yescharacteristic
916C2#3282×C13111yescharacteristic
917C2#3296×C13111yescharacteristic
918C2#3323×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#546×C131C2
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
2. C2×#464×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#450×C131C2semidirect
5. C2×C4×SD16×C131C2semidirect
6. #2536×C131C2semidirect
7. #2035×C131C2semidirect
8. #2034×C131C2semidirect
9. #2001×C131C2semidirect
10. #2000×C131C2semidirect
11. #1958×C131C2semidirect
12. #1954×C131C2semidirect
13. #1804×C131C2semidirect
14. #1788×C131C2semidirect
15. #1786×C131C2semidirect
18. C22×Q16×C131C22semidirect
27. C2×C22⋊Q8×C131C22semidirect
31. C2×C4×Q8×C131C22semidirect
39. C2×#106×C131C22semidirect
40. C2×C4⋊C8×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
44. C2×#103×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
55. C2×C4×C8×C131C22semidirect
60. #382×C131C22semidirect
62. #380×C131C22semidirect
63. #340×C131C22semidirect
64. #340×C131C22semidirect
98. C2×SD16×C131D4semidirect
459. #24247C131direct (N × H)
460. C131#24247direct (N × H)
462. C2×#464C2×C131semidirect
463. C2×#452C2×C131semidirect
464. C2×#450C2×C131semidirect
465. C2×C4×SD16C2×C131semidirect
466. #2536C2×C131semidirect
467. #2035C2×C131semidirect
468. #2034C2×C131semidirect
469. #2001C2×C131semidirect
470. #2000C2×C131semidirect
471. #1958C2×C131semidirect
472. #1954C2×C131semidirect
473. #1804C2×C131semidirect
474. #1788C2×C131semidirect
475. #1786C2×C131semidirect
478. C22×Q16C22×C131semidirect
487. C2×C22⋊Q8C22×C131semidirect
491. C2×C4×Q8C22×C131semidirect
499. C2×#106C22×C131semidirect
500. C2×C4⋊C8C22×C131semidirect
501. C2×#103C22×C131semidirect
502. C2×#103C22×C131semidirect
503. C2×#103C22×C131semidirect
504. C2×#103C22×C131semidirect
513. C2×C22⋊C8C22×C131semidirect
514. C2×C22⋊C8C22×C131semidirect
515. C2×C4×C8C22×C131semidirect
520. #382C22×C131semidirect
522. #380C22×C131semidirect
523. #340C22×C131semidirect
524. #340C22×C131semidirect
558. C2×SD16D4×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×#464×C1312
C2×#452×C1312
C2×#450×C1312
C2×C4×SD16×C1312
#2536×C1312
#2035×C1312
#2034×C1312
#2001×C1312
#2000×C1312
#1958×C1312
#1954×C1312
#1804×C1312
#1788×C1312
#1786×C1312
#24247131