Finite Group Databasebeta

← C131×#18282 #45704166

Subgroups — C131×#18282 #45704166

Order 33536.

942 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3564×C131C211yesmaximal, characteristic, complemented
2#3114×C131C211yesmaximal, characteristic, complemented
3#3101×C131C211yesmaximal, characteristic, complemented
4#2603×C131C211yesmaximal, characteristic, complemented
5#1612×C131C211yesmaximal, characteristic, complemented
6#1611×C131C211yesmaximal, characteristic, complemented
7#1609×C131C211yesmaximal, characteristic, complemented
8#1608×C131C211yesmaximal, characteristic, complemented
9#1600×C131C211yesmaximal, characteristic
10#1599×C131C211yesmaximal, characteristic, complemented
11#1597×C131C211yesmaximal, characteristic, complemented
12#1596×C131C211yesmaximal, characteristic, complemented
13#1506×C131C211yesmaximal, characteristic, complemented
14#1500×C131C211yesmaximal, characteristic, complemented
15#1473×C131C211yesmaximal, characteristic, complemented
16#563×C131—21no—
17#563×C131—21no—
18#556×C131—21no—
19#554×C131—21no—
20#552×C131—21no—
21#552×C131—21no—
22#551×C131—21no—
23#551×C131—21no—
24#544×C131C2211yescharacteristic
25#543×C131C2211yescharacteristic
26#542×C131—21no—
27#541×C131—21no—
28#541×C131—21no—
29#539×C131—21no—
30#539×C131C2211yescharacteristic
31#538×C131C2211yescharacteristic
32#533×C131C2211yescharacteristic
33#529×C131C2211yescharacteristic
34C2×#126×C131C2211yescharacteristic
35C2×C4×D4×C131C2211yescharacteristic
36#483×C131C2211yescharacteristic
37#483×C131C2211yescharacteristic
38#483×C131C2211yescharacteristic
39#480×C131C2211yescharacteristic
40#478×C131—21no—
41#476×C131—21no—
42#463×C131—21no—
43#461×C131—21no—
44#450×C131C2211yescharacteristic
45#450×C131C2211yescharacteristic
46#450×C131C2211yescharacteristic
47#447×C131C2211yescharacteristic
48#442×C131—21no—
49#440×C131—21no—
50C4×SD16×C131—21no—
51C4×SD16×C131—21no—
52#432×C131C2211yescharacteristic
53#431×C131C2211yescharacteristic
54#398×C131C2211yescharacteristic
55#397×C131C2211yescharacteristic
56#394×C131C2211yescharacteristic
57#392×C131C2211yescharacteristic
58#390×C131—21no—
59#388×C131—21no—
60#386×C131—21no—
61#385×C131—21no—
62#376×C131C2211yescharacteristic
63#328×C131C2211yescharacteristic
64#328×C131C2211yescharacteristic
65#328×C131C2211yescharacteristic
66#328×C131C2211yescharacteristic
67#328×C131C2211yescharacteristic
68#328×C131C2211yescharacteristic
69#327×C131C2211yescharacteristic
70#327×C131C2211yescharacteristic
71#324×C131C2211yescharacteristic
72#324×C131C2211yescharacteristic
73#323×C131C2211yescharacteristic
74#323×C131C2211yescharacteristic
75C22×D4×C131—21no—
76C22×D4×C131C2311yescharacteristic
77C23×C4×C131—21no—
78C2×SD16×C131—21no—
79C2×SD16×C131—21no—
80C2×SD16×C131—21no—
81C2×D8×C131—21no—
82C4⋊Q8×C131—21no—
83C4⋊Q8×C131—21no—
84C4⋊Q8×C131—21no—
85C4⋊Q8×C131D411yescharacteristic, complemented
86C4⋊Q8×C131D411yescharacteristic, complemented
87#126×C131—21no—
88#126×C131—21no—
89#126×C131—21no—
90#126×C131—21no—
91#126×C131—21no—
92#126×C131—21no—
93#126×C131—21no—
94#126×C131—21no—
95#126×C131—21no—
96#126×C131—21no—
97#126×C131—21no—
98#126×C131—21no—
99#126×C131—21no—
100#125×C131—21no—
101#125×C131—21no—
102#125×C131—21no—
103#125×C131—21no—
104#125×C131—21no—
105#125×C131—21no—
106#125×C131—21no—
107#125×C131—21no—
108#125×C131—21no—
109#125×C131D411yescharacteristic, complemented
110#124×C131—21no—
111#124×C131—21no—
112#124×C131—21no—
113#124×C131D411yescharacteristic, complemented
114#123×C131—21no—
115#123×C131—21no—
116#123×C131—21no—
117#123×C131—21no—
118#123×C131—21no—
119#123×C131—21no—
120#123×C131—21no—
121#123×C131—21no—
122C22⋊Q8×C131—21no—
123C22⋊Q8×C131—21no—
124C22⋊Q8×C131—21no—
125C22⋊Q8×C131—21no—
126C22⋊Q8×C131—21no—
127C22⋊Q8×C131—21no—
128C22⋊Q8×C131—21no—
129C22⋊Q8×C131—21no—
130C22⋊Q8×C131—21no—
131C22⋊Q8×C131—21no—
132C22⋊Q8×C131—21no—
133C22⋊Q8×C131—21no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131—21no—
136C22⋊Q8×C131C2311yescharacteristic
137C22⋊Q8×C131C2311yescharacteristic
138C22⋊Q8×C131C2311yescharacteristic
139#121×C131—21no—
140#121×C131C2311yescharacteristic
141#120×C131—21no—
142C4×Q8×C131—21no—
143C4×Q8×C131—21no—
144C4×Q8×C131—21no—
145C4×Q8×C131D411yescharacteristic, complemented
146C4×Q8×C131D411yescharacteristic, complemented
147C4×Q8×C131D411yescharacteristic, complemented
148C4×D4×C131—21no—
149C4×D4×C131—21no—
150C4×D4×C131—21no—
151C4×D4×C131—21no—
152C4×D4×C131—21no—
153C4×D4×C131—21no—
154C4×D4×C131—21no—
155C4×D4×C131—21no—
156C4×D4×C131—21no—
157C4×D4×C131D411yescharacteristic, complemented
158#117×C131—21no—
159#117×C131—21no—
160#117×C131—21no—
161#117×C131—21no—
162#117×C131—21no—
163#117×C131—21no—
164C2×C4⋊C4×C131—21no—
165C2×C4⋊C4×C131—21no—
166C2×C4⋊C4×C131D411yescharacteristic
167C2×C4⋊C4×C131D411yescharacteristic
168C2×C4⋊C4×C131C2311yescharacteristic
169C2×C4⋊C4×C131C2311yescharacteristic
170C2×C22⋊C4×C131—21no—
171C2×C22⋊C4×C131—21no—
172C2×C22⋊C4×C131—21no—
173C2×C22⋊C4×C131—21no—
174C2×C22⋊C4×C131—21no—
175C2×C22⋊C4×C131—21no—
176C2×C22⋊C4×C131D411yescharacteristic
177C2×C22⋊C4×C131D411yescharacteristic
178C2×C22⋊C4×C131C2311yescharacteristic
179C2×C42×C131—21no—
180C2×C42×C131C2311yescharacteristic
181#107×C131—21no—
182#106×C131—21no—
183#106×C131—21no—
184#106×C131—21no—
185C4⋊C8×C131—21no—
186C4⋊C8×C131—21no—
187#103×C131—21no—
188#103×C131—21no—
189#103×C131—21no—
190#102×C131—21no—
191#102×C131—21no—
192#102×C131—21no—
193#102×C131—21no—
194#102×C131—21no—
195C22⋊C8×C131C2311yescharacteristic
196C22⋊C8×C131C2311yescharacteristic
197C22⋊C8×C131C2311yescharacteristic
198C22⋊C8×C131C2311yescharacteristic
199#97×C131—21no—
200C4×C8×C131—21no—
201#95×C131—21no—
202#95×C131—21no—
203#95×C131—21no—
204#95×C131C2311yescharacteristic
205#95×C131C2311yescharacteristic
206C24×C131—21no—
207C24×C131C2×D411yescharacteristic
208C2×Q8×C131—21no—
209C2×Q8×C131—21no—
210C2×Q8×C131—21no—
211C2×Q8×C131C2×D411yescharacteristic
212C2×Q8×C131C2×D411yescharacteristic
213C2×Q8×C131C2×D411yescharacteristic
214C2×D4×C131—21no—
215C2×D4×C131—21no—
216C2×D4×C131—21no—
217C2×D4×C131—21no—
218C2×D4×C131—21no—
219C2×D4×C131—42no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—81no—
223C2×D4×C131C2×D411yescharacteristic
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—41no—
233C22×C4×C131—41no—
234C22×C4×C131—81no—
235C22×C4×C131—81no—
236C22×C4×C131C2×D411yescharacteristic
237C22×C4×C131C2×D411yescharacteristic
238C22×C4×C131C2×D411yescharacteristic
239C22×C4×C131C2×D411yescharacteristic
240C22×C4×C131C2×D411yescharacteristic
241C22×C4×C131C2411yescharacteristic
242SD16×C131—42no—
243SD16×C131—42no—
244SD16×C131—42no—
245D8×C131—42no—
246C2×C8×C131—21no—
247C2×C8×C131—21no—
248C2×C8×C131—21no—
249C2×C8×C131—21no—
250C4⋊C4×C131—21no—
251C4⋊C4×C131—21no—
252C4⋊C4×C131—21no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—21no—
255C4⋊C4×C131—21no—
256C4⋊C4×C131—21no—
257C4⋊C4×C131—21no—
258C4⋊C4×C131—21no—
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—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—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—81no—
282C4⋊C4×C131C2×D411yescharacteristic
283C4⋊C4×C131C2×D411yescharacteristic
284C4⋊C4×C131C2×D411yescharacteristic
285C4⋊C4×C131C2×D411yescharacteristic
286C22⋊C4×C131—21no—
287C22⋊C4×C131—21no—
288C22⋊C4×C131—21no—
289C22⋊C4×C131—21no—
290C22⋊C4×C131—21no—
291C22⋊C4×C131—21no—
292C22⋊C4×C131—21no—
293C22⋊C4×C131—21no—
294C22⋊C4×C131—21no—
295C22⋊C4×C131—21no—
296C22⋊C4×C131—21no—
297C22⋊C4×C131—21no—
298C22⋊C4×C131—21no—
299C22⋊C4×C131—21no—
300C22⋊C4×C131—21no—
301C22⋊C4×C131—21no—
302C22⋊C4×C131—21no—
303C22⋊C4×C131—21no—
304C22⋊C4×C131—21no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—21no—
307C22⋊C4×C131—42no—
308C22⋊C4×C131—42no—
309C22⋊C4×C131—41no—
310C22⋊C4×C131—41no—
311C22⋊C4×C131—81no—
312C22⋊C4×C131—81no—
313C42×C131—21no—
314C42×C131—21no—
315C42×C131—21no—
316C42×C131—21no—
317C42×C131—21no—
318C42×C131—21no—
319C42×C131—21no—
320C42×C131—42no—
321C42×C131C2×D411yescharacteristic
322C42×C131C2×D411yescharacteristic
323C42×C131C2×D411yescharacteristic
324C42×C131C2×D411yescharacteristic
325C23×C131—22no—
326C23×C131—21no—
327C23×C131—21no—
328C23×C131—21no—
329C23×C131—21no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—41no—
337C23×C131—41no—
338C23×C131C22×D411yescharacteristic
339Q8×C131—41no—
340Q8×C131—41no—
341Q8×C131—41no—
342Q8×C131—81no—
343Q8×C131—81no—
344Q8×C131—81no—
345D4×C131—22no—
346D4×C131—22no—
347D4×C131—41no—
348D4×C131—41no—
349D4×C131—41no—
350D4×C131—41no—
351D4×C131—41no—
352D4×C131—81no—
353D4×C131—81no—
354D4×C131—84no—
355C2×C4×C131—21no—
356C2×C4×C131—21no—
357C2×C4×C131—22no—
358C2×C4×C131—21no—
359C2×C4×C131—21no—
360C2×C4×C131—21no—
361C2×C4×C131—21no—
362C2×C4×C131—21no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
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—81no—
383C2×C4×C131—82no—
384C2×C4×C131—82no—
385C2×C4×C131—81no—
386C2×C4×C131—81no—
387C2×C4×C131—81no—
388C2×C4×C131—81no—
389C2×C4×C131#12011yescharacteristic
390C2×C4×C131#12011yescharacteristic
391C2×C4×C131#12011yescharacteristic
392C2×C4×C131#12011yescharacteristic
393C2×C4×C131C22×D411yescharacteristic
394C2×C4×C131C22×D411yescharacteristic
395C8×C131—41no—
396C8×C131—41no—
397C8×C131—41no—
398C8×C131—41no—
399C22×C131—21no—
400C22×C131—21no—
401C22×C131—42no—
402C22×C131—42no—
403C22×C131—41no—
404C22×C131—41no—
405C22×C131—41no—
406C22×C131—41no—
407C22×C131—41no—
408C22×C131—41no—
409C22×C131—42no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131—81no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131C2×#12011yescharacteristic
417C22×C131#57711yescharacteristic
418C22×C131#57711yescharacteristic
419C4×C131—21no—
420C4×C131—21no—
421C4×C131—21no—
422C4×C131—21no—
423C4×C131—21no—
424C4×C131—21no—
425C4×C131—42no—
426C4×C131—41no—
427C4×C131—41no—
428C4×C131—41no—
429C4×C131—41no—
430C4×C131—41no—
431C4×C131—41no—
432C4×C131—41no—
433C4×C131—41no—
434C4×C131—41no—
435C4×C131—41no—
436C4×C131—81no—
437C4×C131—81no—
438C2×C131—21no—
439C2×C131—21no—
440C2×C131—81no—
441C2×C131—81no—
442C2×C131—82no—
443C2×C131#301011yescharacteristic
444C2×C131#301811yescharacteristic
445C2×C131#302511yescharacteristic
446#18282C13111yesmaximal, characteristic, direct product factor, Sylow
447C131#1828211yescharacteristic, direct product factor, Sylow
448#3564C2×C13111yescharacteristic, complemented
449#3114C2×C13111yescharacteristic, complemented
450#3101C2×C13111yescharacteristic, complemented
451#2603C2×C13111yescharacteristic, complemented
452#1612C2×C13111yescharacteristic, complemented
453#1611C2×C13111yescharacteristic, complemented
454#1609C2×C13111yescharacteristic, complemented
455#1608C2×C13111yescharacteristic, complemented
456#1600C2×C13111yescharacteristic
457#1599C2×C13111yescharacteristic, complemented
458#1597C2×C13111yescharacteristic, complemented
459#1596C2×C13111yescharacteristic, complemented
460#1506C2×C13111yescharacteristic, complemented
461#1500C2×C13111yescharacteristic, complemented
462#1473C2×C13111yescharacteristic, complemented
463#563—21no—
464#563—21no—
465#556—21no—
466#554—21no—
467#552—21no—
468#552—21no—
469#551—21no—
470#551—21no—
471#544C22×C13111yescharacteristic
472#543C22×C13111yescharacteristic
473#542—21no—
474#541—21no—
475#541—21no—
476#539—21no—
477#539C22×C13111yescharacteristic
478#538C22×C13111yescharacteristic
479#533C22×C13111yescharacteristic
480#529C22×C13111yescharacteristic
481C2×#126C22×C13111yescharacteristic
482C2×C4×D4C22×C13111yescharacteristic
483#483C22×C13111yescharacteristic
484#483C22×C13111yescharacteristic
485#483C22×C13111yescharacteristic
486#480C22×C13111yescharacteristic
487#478—21no—
488#476—21no—
489#463—21no—
490#461—21no—
491#450C22×C13111yescharacteristic
492#450C22×C13111yescharacteristic
493#450C22×C13111yescharacteristic
494#447C22×C13111yescharacteristic
495#442—21no—
496#440—21no—
497C4×SD16—21no—
498C4×SD16—21no—
499#432C22×C13111yescharacteristic
500#431C22×C13111yescharacteristic
501#398C22×C13111yescharacteristic
502#397C22×C13111yescharacteristic
503#394C22×C13111yescharacteristic
504#392C22×C13111yescharacteristic
505#390—21no—
506#388—21no—
507#386—21no—
508#385—21no—
509#376C22×C13111yescharacteristic
510#328C22×C13111yescharacteristic
511#328C22×C13111yescharacteristic
512#328C22×C13111yescharacteristic
513#328C22×C13111yescharacteristic
514#328C22×C13111yescharacteristic
515#328C22×C13111yescharacteristic
516#327C22×C13111yescharacteristic
517#327C22×C13111yescharacteristic
518#324C22×C13111yescharacteristic
519#324C22×C13111yescharacteristic
520#323C22×C13111yescharacteristic
521#323C22×C13111yescharacteristic
522C22×D4—21no—
523C22×D4C23×C13111yescharacteristic
524C23×C4—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×D8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—21no—
531C4⋊Q8—21no—
532C4⋊Q8D4×C13111yescharacteristic, complemented
533C4⋊Q8D4×C13111yescharacteristic, complemented
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125—21no—
548#125—21no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#125D4×C13111yescharacteristic, complemented
557#124—21no—
558#124—21no—
559#124—21no—
560#124D4×C13111yescharacteristic, complemented
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8C23×C13111yescharacteristic
584C22⋊Q8C23×C13111yescharacteristic
585C22⋊Q8C23×C13111yescharacteristic
586#121—21no—
587#121C23×C13111yescharacteristic
588#120—21no—
589C4×Q8—21no—
590C4×Q8—21no—
591C4×Q8—21no—
592C4×Q8D4×C13111yescharacteristic, complemented
593C4×Q8D4×C13111yescharacteristic, complemented
594C4×Q8D4×C13111yescharacteristic, complemented
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4D4×C13111yescharacteristic, complemented
605#117—21no—
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4D4×C13111yescharacteristic
614C2×C4⋊C4D4×C13111yescharacteristic
615C2×C4⋊C4C23×C13111yescharacteristic
616C2×C4⋊C4C23×C13111yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4D4×C13111yescharacteristic
624C2×C22⋊C4D4×C13111yescharacteristic
625C2×C22⋊C4C23×C13111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C13111yescharacteristic
628#107—21no—
629#106—21no—
630#106—21no—
631#106—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634#103—21no—
635#103—21no—
636#103—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8C23×C13111yescharacteristic
643C22⋊C8C23×C13111yescharacteristic
644C22⋊C8C23×C13111yescharacteristic
645C22⋊C8C23×C13111yescharacteristic
646#97—21no—
647C4×C8—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95C23×C13111yescharacteristic
652#95C23×C13111yescharacteristic
653C24—21no—
654C24C2×D4×C13111yescharacteristic
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8C2×D4×C13111yescharacteristic
659C2×Q8C2×D4×C13111yescharacteristic
660C2×Q8C2×D4×C13111yescharacteristic
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—81no—
670C2×D4C2×D4×C13111yescharacteristic
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—41no—
680C22×C4—41no—
681C22×C4—81no—
682C22×C4—81no—
683C22×C4C2×D4×C13111yescharacteristic
684C22×C4C2×D4×C13111yescharacteristic
685C22×C4C2×D4×C13111yescharacteristic
686C22×C4C2×D4×C13111yescharacteristic
687C22×C4C2×D4×C13111yescharacteristic
688C22×C4C24×C13111yescharacteristic
689SD16—42no—
690SD16—42no—
691SD16—42no—
692D8—42no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
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—21no—
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—81no—
729C4⋊C4C2×D4×C13111yescharacteristic
730C4⋊C4C2×D4×C13111yescharacteristic
731C4⋊C4C2×D4×C13111yescharacteristic
732C4⋊C4C2×D4×C13111yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—41no—
757C22⋊C4—41no—
758C22⋊C4—81no—
759C22⋊C4—81no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—42no—
768C42C2×D4×C13111yescharacteristic
769C42C2×D4×C13111yescharacteristic
770C42C2×D4×C13111yescharacteristic
771C42C2×D4×C13111yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23C22×D4×C13111yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—81no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—81no—
800D4—81no—
801D4—84no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
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—81no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4#120×C13111yescharacteristic
837C2×C4#120×C13111yescharacteristic
838C2×C4#120×C13111yescharacteristic
839C2×C4#120×C13111yescharacteristic
840C2×C4C22×D4×C13111yescharacteristic
841C2×C4C22×D4×C13111yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22C2×#120×C13111yescharacteristic
864C22#577×C13111yescharacteristic
865C22#577×C13111yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C2—21no—
886C2—21no—
887C2—82no—
888C2—81no—
889C2—81no—
890C2#3010×C13111yescharacteristic
891C2#3018×C13111yescharacteristic
892C2#3025×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#1600×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3564×C131C2semidirect
2. #3114×C131C2semidirect
3. #3101×C131C2semidirect
4. #2603×C131C2semidirect
5. #1612×C131C2semidirect
6. #1611×C131C2semidirect
7. #1609×C131C2semidirect
8. #1608×C131C2semidirect
10. #1599×C131C2semidirect
11. #1597×C131C2semidirect
12. #1596×C131C2semidirect
13. #1506×C131C2semidirect
14. #1500×C131C2semidirect
15. #1473×C131C2semidirect
85. C4⋊Q8×C131D4semidirect
86. C4⋊Q8×C131D4semidirect
109. #125×C131D4semidirect
113. #124×C131D4semidirect
145. C4×Q8×C131D4semidirect
146. C4×Q8×C131D4semidirect
147. C4×Q8×C131D4semidirect
157. C4×D4×C131D4semidirect
446. #18282C131direct (N × H)
447. C131#18282direct (N × H)
448. #3564C2×C131semidirect
449. #3114C2×C131semidirect
450. #3101C2×C131semidirect
451. #2603C2×C131semidirect
452. #1612C2×C131semidirect
453. #1611C2×C131semidirect
454. #1609C2×C131semidirect
455. #1608C2×C131semidirect
457. #1599C2×C131semidirect
458. #1597C2×C131semidirect
459. #1596C2×C131semidirect
460. #1506C2×C131semidirect
461. #1500C2×C131semidirect
462. #1473C2×C131semidirect
532. C4⋊Q8D4×C131semidirect
533. C4⋊Q8D4×C131semidirect
556. #125D4×C131semidirect
560. #124D4×C131semidirect
592. C4×Q8D4×C131semidirect
593. C4×Q8D4×C131semidirect
594. C4×Q8D4×C131semidirect
604. C4×D4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3564×C1312
#3114×C1312
#3101×C1312
#2603×C1312
#1612×C1312
#1611×C1312
#1609×C1312
#1608×C1312
#1600×C1312
#1599×C1312
#1597×C1312
#1596×C1312
#1506×C1312
#1500×C1312
#1473×C1312
#18282131