Finite Group Databasebeta

← C131×#25524 #45711408

Subgroups — C131×#25524 #45711408

Order 33536.

1246 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3494×C131C211yesmaximal, characteristic, complemented
2#3094×C131C211yesmaximal, characteristic, complemented
3#3055×C131C211yesmaximal, characteristic, complemented
4#2856×C131C211yesmaximal, characteristic, complemented
5#2060×C131C211yesmaximal, characteristic, complemented
6#2037×C131C211yesmaximal, characteristic, complemented
7#2027×C131C211yesmaximal, characteristic, complemented
8#2002×C131C211yesmaximal, characteristic, complemented
9#1900×C131C211yesmaximal, characteristic, complemented
10#1896×C131C211yesmaximal, characteristic, complemented
11#1887×C131C211yesmaximal, characteristic, complemented
12#1883×C131C211yesmaximal, characteristic, complemented
13#1859×C131C211yesmaximal, characteristic, complemented
14#1856×C131C211yesmaximal, characteristic, complemented
15C2×#339×C131C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
17C22×M16×C131C2211yescharacteristic
18#555×C131—21no—
19#553×C131—21no—
20#553×C131—21no—
21#551×C131—22no—
22#547×C131—21no—
23#546×C131—22no—
24#544×C131C2211yescharacteristic
25#542×C131—21no—
26#540×C131—21no—
27#535×C131C2211yescharacteristic
28#532×C131—21no—
29C2×#127×C131C2211yescharacteristic
30#529×C131—21no—
31#525×C131C2211yescharacteristic
32C2×#121×C131—22no—
33C2×#121×C131C2211yescharacteristic
34C2×#121×C131C2211yescharacteristic
35#520×C131C2211yescharacteristic
36#518×C131C2211yescharacteristic
37C2×#117×C131C2211yescharacteristic
38C22×C42×C131C2211yescharacteristic
39#482×C131—21no—
40#482×C131—21no—
41#481×C131—21no—
42#480×C131—21no—
43#469×C131—21no—
44#468×C131—21no—
45#466×C131—21no—
46#465×C131—21no—
47#428×C131C2211yescharacteristic
48#428×C131C2211yescharacteristic
49#428×C131C2211yescharacteristic
50C2×#104×C131C2211yescharacteristic
51C2×#104×C131C2211yescharacteristic
52#418×C131C2211yescharacteristic
53#418×C131C2211yescharacteristic
54#418×C131C2211yescharacteristic
55#417×C131C2211yescharacteristic
56C2×#100×C131C2211yescharacteristic
57C2×#100×C131C2211yescharacteristic
58#407×C131C2211yescharacteristic
59#390×C131—22no—
60#390×C131C2211yescharacteristic
61#390×C131C2211yescharacteristic
62#384×C131C2211yescharacteristic
63#343×C131C2211yescharacteristic
64#343×C131C2211yescharacteristic
65#339×C131C2211yescharacteristic
66#339×C131C2211yescharacteristic
67#339×C131C2211yescharacteristic
68#339×C131C2211yescharacteristic
69#339×C131C2211yescharacteristic
70#339×C131C2211yescharacteristic
71C2×#41×C131—22no—
72C2×#41×C131C2311yescharacteristic
73C22×D4×C131—22no—
74C22×D4×C131—21no—
75C22×D4×C131D412yes—
76C22×D4×C131C2311yescharacteristic
77C22×D4×C131C2311yescharacteristic
78C23×C4×C131—21no—
79C23×C4×C131C2311yescharacteristic
80AGL(1,ℤ/8)×C131—22no—
81AGL(1,ℤ/8)×C131—41no—
82C2×SD16×C131—21no—
83C2×D8×C131—21no—
84C2×M16×C131—21no—
85C2×M16×C131—22no—
86C2×M16×C131—41no—
87C2×M16×C131C2311yescharacteristic
88C2×M16×C131C2311yescharacteristic
89C2×M16×C131C2311yescharacteristic
90C2×M16×C131C2311yescharacteristic
91C22×C8×C131—21no—
92C4⋊Q8×C131—21no—
93C4⋊Q8×C131—21no—
94#127×C131—21no—
95#127×C131—22no—
96#127×C131—41no—
97#126×C131—22no—
98#126×C131—22no—
99#125×C131—21no—
100#125×C131—21no—
101#124×C131—22no—
102#124×C131—22no—
103#124×C131—21no—
104#123×C131—22no—
105#123×C131—22no—
106#123×C131—22no—
107#123×C131—22no—
108#123×C131—21no—
109C22⋊Q8×C131—22no—
110C22⋊Q8×C131—22no—
111C22⋊Q8×C131D411yescharacteristic, complemented
112C22⋊Q8×C131D411yescharacteristic, complemented
113#121×C131—22no—
114#121×C131—22no—
115#121×C131—22no—
116#121×C131—21no—
117#121×C131—21no—
118#121×C131—21no—
119#121×C131—21no—
120#121×C131—21no—
121#121×C131—21no—
122#121×C131—21no—
123#121×C131—21no—
124#121×C131—21no—
125#121×C131—21no—
126#121×C131—48no—
127#121×C131D411yescharacteristic, complemented
128#121×C131D411yescharacteristic, complemented
129#120×C131—21no—
130#120×C131—22no—
131C4×Q8×C131—21no—
132C4×D4×C131—22no—
133C4×D4×C131—22no—
134C4×D4×C131—21no—
135C4×D4×C131—22no—
136C4×D4×C131—21no—
137C4×D4×C131—21no—
138C4×D4×C131—21no—
139C4×D4×C131—21no—
140C4×D4×C131—21no—
141C4×D4×C131—21no—
142#117×C131—22no—
143#117×C131—21no—
144#117×C131—21no—
145#117×C131—21no—
146#117×C131D411yescharacteristic, complemented
147#117×C131D411yescharacteristic, complemented
148#117×C131C2311yescharacteristic
149#117×C131C2311yescharacteristic
150#117×C131C2311yescharacteristic
151C2×C4⋊C4×C131—21no—
152C2×C4⋊C4×C131—22no—
153C2×C4⋊C4×C131D411yescharacteristic, complemented
154C2×C4⋊C4×C131D411yescharacteristic, complemented
155C2×C4⋊C4×C131C2311yescharacteristic
156C2×C4⋊C4×C131C2311yescharacteristic
157C2×C22⋊C4×C131—21no—
158C2×C22⋊C4×C131—22no—
159C2×C22⋊C4×C131—22no—
160C2×C22⋊C4×C131—21no—
161C2×C22⋊C4×C131—22no—
162C2×C22⋊C4×C131D412yes—
163C2×C42×C131—21no—
164C2×C42×C131—22no—
165C2×C42×C131—21no—
166C2×C42×C131—41no—
167C2×C42×C131C2311yescharacteristic
168C2×C42×C131C2311yescharacteristic
169#107×C131—21no—
170#107×C131—21no—
171#107×C131—21no—
172#106×C131—21no—
173#106×C131—21no—
174#106×C131—21no—
175#104×C131—22no—
176#104×C131—41no—
177#103×C131—21no—
178#102×C131—21no—
179#102×C131—21no—
180#102×C131—21no—
181#102×C131—21no—
182#102×C131—21no—
183#102×C131—21no—
184#102×C131—21no—
185#100×C131—22no—
186#100×C131—41no—
187C22⋊C8×C131—21no—
188C22⋊C8×C131—21no—
189C24×C131—21no—
190C24×C131C2×D411yescharacteristic
191C24×C131C2×D412yes—
192#41×C131—21no—
193#41×C131—21no—
194#41×C131—21no—
195#41×C131—21no—
196#41×C131—84no—
197C2×Q8×C131—22no—
198C2×Q8×C131C2×D411yescharacteristic
199C2×D4×C131—21no—
200C2×D4×C131—22no—
201C2×D4×C131—21no—
202C2×D4×C131—22no—
203C2×D4×C131—22no—
204C2×D4×C131—21no—
205C2×D4×C131—22no—
206C2×D4×C131—21no—
207C2×D4×C131—21no—
208C2×D4×C131—21no—
209C2×D4×C131—21no—
210C2×D4×C131—21no—
211C2×D4×C131—21no—
212C2×D4×C131—21no—
213C2×D4×C131—21no—
214C2×D4×C131—21no—
215C2×D4×C131—21no—
216C2×D4×C131—21no—
217C2×D4×C131—21no—
218C2×D4×C131—44no—
219C2×D4×C131—44no—
220C2×D4×C131—44no—
221C2×D4×C131—44no—
222C2×D4×C131—44no—
223C2×D4×C131—41no—
224C2×D4×C131—41no—
225C2×D4×C131C2×D411yescharacteristic
226C22×C4×C131—21no—
227C22×C4×C131—21no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—24no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—22no—
235C22×C4×C131—22no—
236C22×C4×C131—22no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—42no—
241C22×C4×C131—42no—
242C22×C4×C131C2×D411yescharacteristic
243C22×C4×C131C2×D411yescharacteristic
244C22×C4×C131C2×D411yescharacteristic
245C22×C4×C131C2×D411yescharacteristic
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2×D412yes—
248C22×C4×C131C2411yescharacteristic
249SD16×C131—42no—
250D8×C131—42no—
251M16×C131—21no—
252M16×C131—21no—
253M16×C131—21no—
254M16×C131—21no—
255M16×C131—21no—
256M16×C131—21no—
257M16×C131—21no—
258M16×C131—42no—
259M16×C131#4112yescomplemented
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—42no—
265C4⋊C4×C131—22no—
266C4⋊C4×C131—22no—
267C4⋊C4×C131—22no—
268C4⋊C4×C131—22no—
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—44no—
278C4⋊C4×C131C2×D411yescharacteristic
279C4⋊C4×C131C2×D411yescharacteristic
280C4⋊C4×C131C2×D411yescharacteristic
281C4⋊C4×C131C2×D411yescharacteristic
282C4⋊C4×C131C2×D411yescharacteristic
283C4⋊C4×C131C2×D411yescharacteristic
284C22⋊C4×C131—22no—
285C22⋊C4×C131—22no—
286C22⋊C4×C131—22no—
287C22⋊C4×C131—22no—
288C22⋊C4×C131—22no—
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—22no—
297C22⋊C4×C131—22no—
298C22⋊C4×C131—21no—
299C22⋊C4×C131—21no—
300C22⋊C4×C131—44no—
301C22⋊C4×C131—44no—
302C22⋊C4×C131—41no—
303C22⋊C4×C131—41no—
304C42×C131—22no—
305C42×C131—21no—
306C42×C131—21no—
307C42×C131—21no—
308C42×C131—21no—
309C42×C131—21no—
310C42×C131—21no—
311C42×C131—21no—
312C42×C131—21no—
313C42×C131—42no—
314C42×C131#4112yescomplemented
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—22no—
318C23×C131—22no—
319C23×C131—21no—
320C23×C131—22no—
321C23×C131—22no—
322C23×C131—41no—
323C23×C131—42no—
324C23×C131—42no—
325C23×C131—42no—
326C23×C131—42no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131#12011yescharacteristic
331C23×C131#12011yescharacteristic
332C23×C131C22×D411yescharacteristic
333Q8×C131—21no—
334Q8×C131—21no—
335Q8×C131—82no—
336D4×C131—21no—
337D4×C131—21no—
338D4×C131—41no—
339D4×C131—41no—
340D4×C131—44no—
341D4×C131—42no—
342D4×C131—41no—
343D4×C131—41no—
344D4×C131—41no—
345D4×C131—41no—
346D4×C131—41no—
347D4×C131—41no—
348D4×C131—41no—
349D4×C131—41no—
350D4×C131—88no—
351D4×C131—81no—
352D4×C131—82no—
353D4×C131—82no—
354D4×C131—82no—
355D4×C131—82no—
356D4×C131—82no—
357C2×C4×C131—22no—
358C2×C4×C131—22no—
359C2×C4×C131—22no—
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—22no—
371C2×C4×C131—21no—
372C2×C4×C131—21no—
373C2×C4×C131—21no—
374C2×C4×C131—21no—
375C2×C4×C131—21no—
376C2×C4×C131—21no—
377C2×C4×C131—21no—
378C2×C4×C131—22no—
379C2×C4×C131—48no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—42no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—42no—
386C2×C4×C131—42no—
387C2×C4×C131—41no—
388C2×C4×C131—81no—
389C2×C4×C131—82no—
390C2×C4×C131—82no—
391C2×C4×C131—82no—
392C2×C4×C131#12011yescharacteristic
393C2×C4×C131#12011yescharacteristic
394C2×C4×C131C22×D411yescharacteristic
395C2×C4×C131C22×D411yescharacteristic
396C2×C4×C131C2×#4111yescharacteristic
397C2×C4×C131C2×#4111yescharacteristic
398C2×C4×C131H(5,𝔽2)11yescharacteristic
399C2×C4×C1312−1+411yescharacteristic
400C8×C131—22no—
401C8×C131—41no—
402C8×C131—41no—
403C8×C131—41no—
404C22×C131—21no—
405C22×C131—21no—
406C22×C131—21no—
407C22×C131—21no—
408C22×C131—21no—
409C22×C131—21no—
410C22×C131—21no—
411C22×C131—42no—
412C22×C131—42no—
413C22×C131—41no—
414C22×C131—42no—
415C22×C131—41no—
416C22×C131—42no—
417C22×C131—42no—
418C22×C131—41no—
419C22×C131—82no—
420C22×C131—82no—
421C22×C131—82no—
422C22×C131—82no—
423C22×C131—81no—
424C22×C131—81no—
425C22×C131—81no—
426C22×C131#45312yes—
427C22×C131C2×#12011yescharacteristic
428C22×C131#54611yescharacteristic
429C22×C131#54711yescharacteristic
430C4×C131—24no—
431C4×C131—21no—
432C4×C131—21no—
433C4×C131—42no—
434C4×C131—41no—
435C4×C131—41no—
436C4×C131—41no—
437C4×C131—42no—
438C4×C131—41no—
439C4×C131—41no—
440C4×C131—41no—
441C4×C131—41no—
442C4×C131—81no—
443C4×C131#53211yescharacteristic
444C4×C131#53711yescharacteristic
445C4×C131#54611yescharacteristic
446C4×C131#54711yescharacteristic
447C2×C131—21no—
448C2×C131—21no—
449C2×C131—22no—
450C2×C131—41no—
451C2×C131—81no—
452C2×C131—82no—
453C2×C131—161no—
454C2×C131#243011yescharacteristic
455C2×C131C2×#45311yescharacteristic
456C2×C131#301811yescharacteristic
457#25524C13111yesmaximal, characteristic, direct product factor, Sylow
458C131#2552411yescharacteristic, direct product factor, Sylow
459#3494C2×C13111yescharacteristic, complemented
460#3094C2×C13111yescharacteristic, complemented
461#3055C2×C13111yescharacteristic, complemented
462#2856C2×C13111yescharacteristic, complemented
463#2060C2×C13111yescharacteristic, complemented
464#2037C2×C13111yescharacteristic, complemented
465#2027C2×C13111yescharacteristic, complemented
466#2002C2×C13111yescharacteristic, complemented
467#1900C2×C13111yescharacteristic, complemented
468#1896C2×C13111yescharacteristic, complemented
469#1887C2×C13111yescharacteristic, complemented
470#1883C2×C13111yescharacteristic, complemented
471#1859C2×C13111yescharacteristic, complemented
472#1856C2×C13111yescharacteristic, complemented
473C2×#339C2×C13111yescharacteristic, complemented
474C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
475C22×M16C22×C13111yescharacteristic
476#555—21no—
477#553—21no—
478#553—21no—
479#551—22no—
480#547—21no—
481#546—22no—
482#544C22×C13111yescharacteristic
483#542—21no—
484#540—21no—
485#535C22×C13111yescharacteristic
486#532—21no—
487C2×#127C22×C13111yescharacteristic
488#529—21no—
489#525C22×C13111yescharacteristic
490C2×#121—22no—
491C2×#121C22×C13111yescharacteristic
492C2×#121C22×C13111yescharacteristic
493#520C22×C13111yescharacteristic
494#518C22×C13111yescharacteristic
495C2×#117C22×C13111yescharacteristic
496C22×C42C22×C13111yescharacteristic
497#482—21no—
498#482—21no—
499#481—21no—
500#480—21no—
501#469—21no—
502#468—21no—
503#466—21no—
504#465—21no—
505#428C22×C13111yescharacteristic
506#428C22×C13111yescharacteristic
507#428C22×C13111yescharacteristic
508C2×#104C22×C13111yescharacteristic
509C2×#104C22×C13111yescharacteristic
510#418C22×C13111yescharacteristic
511#418C22×C13111yescharacteristic
512#418C22×C13111yescharacteristic
513#417C22×C13111yescharacteristic
514C2×#100C22×C13111yescharacteristic
515C2×#100C22×C13111yescharacteristic
516#407C22×C13111yescharacteristic
517#390—22no—
518#390C22×C13111yescharacteristic
519#390C22×C13111yescharacteristic
520#384C22×C13111yescharacteristic
521#343C22×C13111yescharacteristic
522#343C22×C13111yescharacteristic
523#339C22×C13111yescharacteristic
524#339C22×C13111yescharacteristic
525#339C22×C13111yescharacteristic
526#339C22×C13111yescharacteristic
527#339C22×C13111yescharacteristic
528#339C22×C13111yescharacteristic
529C2×#41—22no—
530C2×#41C23×C13111yescharacteristic
531C22×D4—21no—
532C22×D4—22no—
533C22×D4D4×C13112yes—
534C22×D4C23×C13111yescharacteristic
535C22×D4C23×C13111yescharacteristic
536C23×C4—21no—
537C23×C4C23×C13111yescharacteristic
538AGL(1,ℤ/8)—22no—
539AGL(1,ℤ/8)—41no—
540C2×SD16—21no—
541C2×D8—21no—
542C2×M16—21no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16C23×C13111yescharacteristic
546C2×M16C23×C13111yescharacteristic
547C2×M16C23×C13111yescharacteristic
548C2×M16C23×C13111yescharacteristic
549C22×C8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552#127—21no—
553#127—22no—
554#127—41no—
555#126—22no—
556#126—22no—
557#125—21no—
558#125—21no—
559#124—22no—
560#124—22no—
561#124—21no—
562#123—22no—
563#123—22no—
564#123—22no—
565#123—22no—
566#123—21no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8D4×C13111yescharacteristic, complemented
570C22⋊Q8D4×C13111yescharacteristic, complemented
571#121—22no—
572#121—22no—
573#121—22no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—48no—
585#121D4×C13111yescharacteristic, complemented
586#121D4×C13111yescharacteristic, complemented
587#120—21no—
588#120—22no—
589C4×Q8—21no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—21no—
593C4×D4—22no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600#117—22no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117D4×C13111yescharacteristic, complemented
605#117D4×C13111yescharacteristic, complemented
606#117C23×C13111yescharacteristic
607#117C23×C13111yescharacteristic
608#117C23×C13111yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4D4×C13111yescharacteristic, complemented
612C2×C4⋊C4D4×C13111yescharacteristic, complemented
613C2×C4⋊C4C23×C13111yescharacteristic
614C2×C4⋊C4C23×C13111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C13112yes—
621C2×C42—21no—
622C2×C42—22no—
623C2×C42—21no—
624C2×C42—41no—
625C2×C42C23×C13111yescharacteristic
626C2×C42C23×C13111yescharacteristic
627#107—21no—
628#107—21no—
629#107—21no—
630#106—21no—
631#106—21no—
632#106—21no—
633#104—22no—
634#104—41no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643#100—22no—
644#100—41no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24C2×D4×C13111yescharacteristic
649C24C2×D4×C13112yes—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—84no—
655C2×Q8—22no—
656C2×Q8C2×D4×C13111yescharacteristic
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—41no—
683C2×D4C2×D4×C13111yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4C2×D4×C13111yescharacteristic
701C22×C4C2×D4×C13111yescharacteristic
702C22×C4C2×D4×C13111yescharacteristic
703C22×C4C2×D4×C13111yescharacteristic
704C22×C4C2×D4×C13111yescharacteristic
705C22×C4C2×D4×C13112yes—
706C22×C4C24×C13111yescharacteristic
707SD16—42no—
708D8—42no—
709M16—21no—
710M16—21no—
711M16—21no—
712M16—21no—
713M16—21no—
714M16—21no—
715M16—21no—
716M16—42no—
717M16#41×C13112yescomplemented
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—42no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
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—21no—
735C4⋊C4—44no—
736C4⋊C4C2×D4×C13111yescharacteristic
737C4⋊C4C2×D4×C13111yescharacteristic
738C4⋊C4C2×D4×C13111yescharacteristic
739C4⋊C4C2×D4×C13111yescharacteristic
740C4⋊C4C2×D4×C13111yescharacteristic
741C4⋊C4C2×D4×C13111yescharacteristic
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—41no—
761C22⋊C4—41no—
762C42—22no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42—21no—
771C42—42no—
772C42#41×C13112yescomplemented
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23#120×C13111yescharacteristic
789C23#120×C13111yescharacteristic
790C23C22×D4×C13111yescharacteristic
791Q8—21no—
792Q8—21no—
793Q8—82no—
794D4—21no—
795D4—21no—
796D4—44no—
797D4—42no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—88no—
809D4—82no—
810D4—81no—
811D4—82no—
812D4—82no—
813D4—82no—
814D4—82no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—48no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—81no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4#120×C13111yescharacteristic
851C2×C4#120×C13111yescharacteristic
852C2×C4C22×D4×C13111yescharacteristic
853C2×C4C22×D4×C13111yescharacteristic
854C2×C4C2×#41×C13111yescharacteristic
855C2×C4C2×#41×C13111yescharacteristic
856C2×C4H(5,𝔽2)×C13111yescharacteristic
857C2×C42−1+4×C13111yescharacteristic
858C8—22no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—42no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—42no—
874C22—41no—
875C22—41no—
876C22—42no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22#453×C13112yes—
885C22C2×#120×C13111yescharacteristic
886C22#546×C13111yescharacteristic
887C22#547×C13111yescharacteristic
888C4—24no—
889C4—21no—
890C4—21no—
891C4—42no—
892C4—41no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—81no—
901C4#532×C13111yescharacteristic
902C4#537×C13111yescharacteristic
903C4#546×C13111yescharacteristic
904C4#547×C13111yescharacteristic
905C2—21no—
906C2—21no—
907C2—22no—
908C2—41no—
909C2—82no—
910C2—81no—
911C2—161no—
912C2#2430×C13111yescharacteristic
913C2C2×#453×C13111yescharacteristic
914C2#3018×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3494×C131C2semidirect
2. #3094×C131C2semidirect
3. #3055×C131C2semidirect
4. #2856×C131C2semidirect
5. #2060×C131C2semidirect
6. #2037×C131C2semidirect
7. #2027×C131C2semidirect
8. #2002×C131C2semidirect
9. #1900×C131C2semidirect
10. #1896×C131C2semidirect
11. #1887×C131C2semidirect
12. #1883×C131C2semidirect
13. #1859×C131C2semidirect
14. #1856×C131C2semidirect
15. C2×#339×C131C2semidirect
111. C22⋊Q8×C131D4semidirect
112. C22⋊Q8×C131D4semidirect
127. #121×C131D4semidirect
128. #121×C131D4semidirect
146. #117×C131D4semidirect
147. #117×C131D4semidirect
153. C2×C4⋊C4×C131D4semidirect
154. C2×C4⋊C4×C131D4semidirect
259. M16×C131#41semidirect
314. C42×C131#41semidirect
457. #25524C131direct (N × H)
458. C131#25524direct (N × H)
459. #3494C2×C131semidirect
460. #3094C2×C131semidirect
461. #3055C2×C131semidirect
462. #2856C2×C131semidirect
463. #2060C2×C131semidirect
464. #2037C2×C131semidirect
465. #2027C2×C131semidirect
466. #2002C2×C131semidirect
467. #1900C2×C131semidirect
468. #1896C2×C131semidirect
469. #1887C2×C131semidirect
470. #1883C2×C131semidirect
471. #1859C2×C131semidirect
472. #1856C2×C131semidirect
473. C2×#339C2×C131semidirect
569. C22⋊Q8D4×C131semidirect
570. C22⋊Q8D4×C131semidirect
585. #121D4×C131semidirect
586. #121D4×C131semidirect
604. #117D4×C131semidirect
605. #117D4×C131semidirect
611. C2×C4⋊C4D4×C131semidirect
612. C2×C4⋊C4D4×C131semidirect
717. M16#41×C131semidirect
772. C42#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3494×C1312
#3094×C1312
#3055×C1312
#2856×C1312
#2060×C1312
#2037×C1312
#2027×C1312
#2002×C1312
#1900×C1312
#1896×C1312
#1887×C1312
#1883×C1312
#1859×C1312
#1856×C1312
C2×#339×C1312
#25524131