Finite Group Databasebeta

← C131×#33553 #45719437

Subgroups — C131×#33553 #45719437

Order 33536.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C131C211yesmaximal, characteristic, complemented
2#3027×C131C211yesmaximal, characteristic, complemented
3#3025×C131C211yesmaximal, characteristic, complemented
4#3021×C131C211yesmaximal, characteristic, complemented
5#2200×C131C214yesmaximal, complemented
6#2196×C131C214yesmaximal, complemented
7#2128×C131C211yesmaximal, characteristic, complemented
8#2122×C131C211yesmaximal, characteristic, complemented
9#2120×C131C211yesmaximal, characteristic, complemented
10#585×C131C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C131—21no—
12#560×C131—21no—
13#560×C131C2212yescomplemented
14#553×C131—21no—
15#553×C131—21no—
16D42×C131—21no—
17D42×C131—21no—
18D42×C131—21no—
19D42×C131C2212yescomplemented
20#540×C131—21no—
21#538×C131—22no—
22#535×C131—21no—
23#535×C131C2211yescharacteristic
24#535×C131C2211yescharacteristic
25#534×C131—22no—
26#525×C131—21no—
27#525×C131C2211yescharacteristic
28C2×#121×C131—21no—
29#458×C131—21no—
30#458×C131C2212yescomplemented
31B(4,𝔽2)×C131—21no—
32B(4,𝔽2)×C131—22no—
33B(4,𝔽2)×C131C2212yescomplemented
34B(4,𝔽2)×C131C2214yescomplemented
35#454×C131—22no—
36#453×C131C2214yescomplemented
37#421×C131—21no—
38#413×C131C2211yescharacteristic, complemented
39#410×C131—21no—
40#410×C131—21no—
41#410×C131C2211yescharacteristic, complemented
42#410×C131C2211yescharacteristic, complemented
43#353×C131C2214yescomplemented
44#352×C131C2212yescomplemented
45AΣL(1,𝔽16)×C131C2212yescomplemented
46AΣL(1,𝔽16)×C131C2214yescomplemented
472−1+4×C131—21no—
482−1+4×C131—41no—
49H(5,𝔽2)×C131—21no—
50H(5,𝔽2)×C131—21no—
51H(5,𝔽2)×C131—41no—
52H(5,𝔽2)×C131C2312yes—
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C2×#41×C131—21no—
56C2×#41×C131—42no—
57C2×#41×C131C2311yescharacteristic
58C22×D4×C131—21no—
59C22×D4×C131—22no—
60C22×D4×C131—22no—
61C22×D4×C131—22no—
62C22×D4×C131D411yescharacteristic, complemented
63C22×D4×C131D411yescharacteristic, complemented
64C23×C4×C131D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C131—24no—
66AGL(1,ℤ/8)×C131—42no—
67C2×SD16×C131—41no—
68C2×D8×C131—41no—
69C2×M16×C131—21no—
70#127×C131—21no—
71#127×C131—21no—
72#127×C131—41no—
73#127×C131C2312yes—
74#126×C131—22no—
75#126×C131—22no—
76#125×C131—21no—
77#124×C131—21no—
78#124×C131—41no—
79#124×C131D412yescomplemented
80#123×C131—22no—
81#123×C131—22no—
82#123×C131—22no—
83#123×C131—22no—
84#123×C131—22no—
85#123×C131D411yescharacteristic, complemented
86#123×C131C2311yescharacteristic
87C22⋊Q8×C131—21no—
88C22⋊Q8×C131—41no—
89#121×C131—22no—
90#121×C131—21no—
91#121×C131—21no—
92#121×C131—22no—
93#121×C131—22no—
94#121×C131—21no—
95#121×C131—22no—
96#121×C131—21no—
97#121×C131—21no—
98#121×C131—22no—
99#121×C131—21no—
100#121×C131—21no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—22no—
104#121×C131—42no—
105#121×C131—41no—
106#120×C131—22no—
107#120×C131—22no—
108#120×C131—22no—
109#120×C131—21no—
110#120×C131—21no—
111#120×C131—22no—
112#120×C131—22no—
113#120×C131—24no—
114#120×C131D411yescharacteristic, complemented
115#120×C131D412yescomplemented
116#120×C131C2311yescharacteristic
117#120×C131C2312yes—
118C4×D4×C131—22no—
119C4×D4×C131—21no—
120C4×D4×C131—21no—
121C4×D4×C131—21no—
122C4×D4×C131—21no—
123C4×D4×C131—22no—
124C4×D4×C131—42no—
125#117×C131—21no—
126#117×C131—21no—
127#117×C131D411yescharacteristic, complemented
128#117×C131D411yescharacteristic, complemented
129#117×C131D411yescharacteristic, complemented
130C2×C4⋊C4×C131—21no—
131C2×C22⋊C4×C131—22no—
132#104×C131—24no—
133#101×C131—21no—
134#100×C131C2312yes—
135#99×C131—21no—
136#99×C131—21no—
137#99×C131—24no—
138#99×C131—22no—
139#99×C131—22no—
140#99×C131C2312yes—
141#99×C131C2312yes—
142C24×C131—22no—
143C24×C131—21no—
144C24×C131C2×D411yescharacteristic
145C24×C131C2×D412yes—
146#41×C131—22no—
147#41×C131—22no—
148#41×C131—41no—
149#41×C131—41no—
150#41×C131—42no—
151#41×C131—41no—
152#41×C131—41no—
153#41×C131—41no—
154#41×C131—41no—
155#41×C131—41no—
156#41×C131—42no—
157#41×C131—42no—
158#41×C131—42no—
159#41×C131—41no—
160#41×C131—41no—
161#41×C131—41no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—42no—
166C2×Q8×C131C2×D411yescharacteristic
167C2×D4×C131—21no—
168C2×D4×C131—22no—
169C2×D4×C131—22no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—22no—
174C2×D4×C131—22no—
175C2×D4×C131—21no—
176C2×D4×C131—22no—
177C2×D4×C131—22no—
178C2×D4×C131—22no—
179C2×D4×C131—22no—
180C2×D4×C131—22no—
181C2×D4×C131—22no—
182C2×D4×C131—22no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—21no—
186C2×D4×C131—41no—
187C2×D4×C131—41no—
188C2×D4×C131—41no—
189C2×D4×C131—41no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—42no—
193C2×D4×C131—41no—
194C2×D4×C131—42no—
195C2×D4×C131—44no—
196C2×D4×C131—81no—
197C2×D4×C131—81no—
198C2×D4×C131—84no—
199C2×D4×C131—84no—
200C2×D4×C131—84no—
201C2×D4×C131C2×D411yescharacteristic
202C2×D4×C131C2×D411yescharacteristic
203C2×D4×C131C2×D412yes—
204C2×D4×C131C2411yescharacteristic
205C22×C4×C131—22no—
206C22×C4×C131—22no—
207C22×C4×C131—22no—
208C22×C4×C131—22no—
209C22×C4×C131—22no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—41no—
213C22×C4×C131—41no—
214C22×C4×C131—41no—
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C22×C4×C131C2×D411yescharacteristic
218C22×C4×C131C2×D411yescharacteristic
219SD16×C131—44no—
220D8×C131—44no—
221M16×C131—22no—
222M16×C131—41no—
223C2×C8×C131—41no—
224C4⋊C4×C131—22no—
225C4⋊C4×C131—22no—
226C4⋊C4×C131—22no—
227C4⋊C4×C131—21no—
228C4⋊C4×C131—21no—
229C4⋊C4×C131—21no—
230C4⋊C4×C131—21no—
231C4⋊C4×C131—21no—
232C4⋊C4×C131—41no—
233C4⋊C4×C131—41no—
234C4⋊C4×C131—42no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—22no—
239C22⋊C4×C131—21no—
240C22⋊C4×C131—21no—
241C22⋊C4×C131—21no—
242C22⋊C4×C131—22no—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—21no—
245C22⋊C4×C131—22no—
246C22⋊C4×C131—21no—
247C22⋊C4×C131—22no—
248C22⋊C4×C131—22no—
249C22⋊C4×C131—22no—
250C22⋊C4×C131—42no—
251C22⋊C4×C131—44no—
252C22⋊C4×C131—42no—
253C22⋊C4×C131C2×D412yes—
254C22⋊C4×C131C2×D411yescharacteristic
255C22⋊C4×C131C2×D411yescharacteristic
256C42×C131—21no—
257C42×C131—21no—
258C42×C131—41no—
259C42×C131—41no—
260C42×C131C2×D412yes—
261C23×C131—21no—
262C23×C131—22no—
263C23×C131—22no—
264C23×C131—22no—
265C23×C131—22no—
266C23×C131—41no—
267C23×C131—42no—
268C23×C131—41no—
269C23×C131—44no—
270C23×C131—42no—
271C23×C131—81no—
272C23×C131—82no—
273C23×C131—82no—
274C23×C131—82no—
275C23×C131—82no—
276C23×C131#12011yescharacteristic
277C23×C131C22×D411yescharacteristic
278C23×C131C22×D411yescharacteristic
279Q8×C131—22no—
280Q8×C131—41no—
281Q8×C131—41no—
282Q8×C131—41no—
283Q8×C131—41no—
284D4×C131—22no—
285D4×C131—41no—
286D4×C131—41no—
287D4×C131—41no—
288D4×C131—42no—
289D4×C131—41no—
290D4×C131—41no—
291D4×C131—42no—
292D4×C131—42no—
293D4×C131—42no—
294D4×C131—42no—
295D4×C131—44no—
296D4×C131—44no—
297D4×C131—42no—
298D4×C131—42no—
299D4×C131—41no—
300D4×C131—41no—
301D4×C131—41no—
302D4×C131—41no—
303D4×C131—41no—
304D4×C131—81no—
305D4×C131—82no—
306D4×C131—82no—
307D4×C131—82no—
308D4×C131—82no—
309D4×C131—82no—
310D4×C131—82no—
311D4×C131—82no—
312D4×C131—84no—
313D4×C131—164no—
314C2×C4×C131—21no—
315C2×C4×C131—21no—
316C2×C4×C131—21no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—21no—
320C2×C4×C131—22no—
321C2×C4×C131—22no—
322C2×C4×C131—22no—
323C2×C4×C131—21no—
324C2×C4×C131—21no—
325C2×C4×C131—22no—
326C2×C4×C131—21no—
327C2×C4×C131—42no—
328C2×C4×C131—42no—
329C2×C4×C131—42no—
330C2×C4×C131—41no—
331C2×C4×C131—42no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—41no—
335C2×C4×C131—42no—
336C2×C4×C131—42no—
337C2×C4×C131—81no—
338C2×C4×C131—82no—
339C2×C4×C131—82no—
340C2×C4×C131—82no—
341C2×C4×C131#12011yescharacteristic
342C2×C4×C131#12011yescharacteristic
343C2×C4×C131#12011yescharacteristic
344C2×C4×C131C22×D411yescharacteristic
345C8×C131—42no—
346C22×C131—22no—
347C22×C131—21no—
348C22×C131—21no—
349C22×C131—21no—
350C22×C131—41no—
351C22×C131—41no—
352C22×C131—41no—
353C22×C131—41no—
354C22×C131—42no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—42no—
358C22×C131—42no—
359C22×C131—41no—
360C22×C131—42no—
361C22×C131—42no—
362C22×C131—42no—
363C22×C131—81no—
364C22×C131—82no—
365C22×C131—82no—
366C22×C131—84no—
367C22×C131—161no—
368C22×C131—164no—
369C22×C131—162no—
370C22×C131C2×#12011yescharacteristic
371C4×C131—21no—
372C4×C131—21no—
373C4×C131—21no—
374C4×C131—42no—
375C4×C131—41no—
376C4×C131—41no—
377C4×C131—42no—
378C4×C131—42no—
379C4×C131—41no—
380C4×C131—82no—
381C4×C131—82no—
382C4×C131B(4,𝔽2)11yescharacteristic
383C4×C131B(4,𝔽2)11yescharacteristic
384C2×C131—21no—
385C2×C131—41no—
386C2×C131—41no—
387C2×C131—42no—
388C2×C131—41no—
389C2×C131—82no—
390C2×C131—82no—
391C2×C131—82no—
392C2×C131C2×B(4,𝔽2)11yescharacteristic
393#33553C13111yesmaximal, characteristic, direct product factor, Sylow
394C131#3355311yescharacteristic, direct product factor, Sylow
395#3537C2×C13111yescharacteristic, complemented
396#3027C2×C13111yescharacteristic, complemented
397#3025C2×C13111yescharacteristic, complemented
398#3021C2×C13111yescharacteristic, complemented
399#2200C2×C13114yescomplemented
400#2196C2×C13114yescomplemented
401#2128C2×C13111yescharacteristic, complemented
402#2122C2×C13111yescharacteristic, complemented
403#2120C2×C13111yescharacteristic, complemented
404#585C22×C13111yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—21no—
406#560—21no—
407#560C22×C13112yescomplemented
408#553—21no—
409#553—21no—
410D42—21no—
411D42—21no—
412D42—21no—
413D42C22×C13112yescomplemented
414#540—21no—
415#538—22no—
416#535—21no—
417#535C22×C13111yescharacteristic
418#535C22×C13111yescharacteristic
419#534—22no—
420#525—21no—
421#525C22×C13111yescharacteristic
422C2×#121—21no—
423#458—21no—
424#458C22×C13112yescomplemented
425B(4,𝔽2)—21no—
426B(4,𝔽2)—22no—
427B(4,𝔽2)C22×C13112yescomplemented
428B(4,𝔽2)C22×C13114yescomplemented
429#454—22no—
430#453C22×C13114yescomplemented
431#421—21no—
432#413C22×C13111yescharacteristic, complemented
433#410—21no—
434#410—21no—
435#410C22×C13111yescharacteristic, complemented
436#410C22×C13111yescharacteristic, complemented
437#353C22×C13114yescomplemented
438#352C22×C13112yescomplemented
439AΣL(1,𝔽16)C22×C13112yescomplemented
440AΣL(1,𝔽16)C22×C13114yescomplemented
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C13112yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C13111yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C13111yescharacteristic, complemented
457C22×D4D4×C13111yescharacteristic, complemented
458C23×C4D4×C13111yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C13112yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C13112yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C13111yescharacteristic, complemented
480#123C23×C13111yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C13111yescharacteristic, complemented
509#120D4×C13112yescomplemented
510#120C23×C13111yescharacteristic
511#120C23×C13112yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C13111yescharacteristic, complemented
522#117D4×C13111yescharacteristic, complemented
523#117D4×C13111yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C13112yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C13112yes—
535#99C23×C13112yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C13111yescharacteristic
539C24C2×D4×C13112yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C13111yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C13111yescharacteristic
596C2×D4C2×D4×C13111yescharacteristic
597C2×D4C2×D4×C13112yes—
598C2×D4C24×C13111yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C13111yescharacteristic
610C22×C4C2×D4×C13111yescharacteristic
611C22×C4C2×D4×C13111yescharacteristic
612C22×C4C2×D4×C13111yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C13112yes—
648C22⋊C4C2×D4×C13111yescharacteristic
649C22⋊C4C2×D4×C13111yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C13112yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C13111yescharacteristic
671C23C22×D4×C13111yescharacteristic
672C23C22×D4×C13111yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C13111yescharacteristic
736C2×C4#120×C13111yescharacteristic
737C2×C4#120×C13111yescharacteristic
738C2×C4C22×D4×C13111yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C13111yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4B(4,𝔽2)×C13111yescharacteristic
777C4B(4,𝔽2)×C13111yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×B(4,𝔽2)×C13111yescharacteristic
subgroupG/H
center, socleC2×C131C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C131
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3537×C131C2semidirect
2. #3027×C131C2semidirect
3. #3025×C131C2semidirect
4. #3021×C131C2semidirect
5. #2200×C131C2semidirect
6. #2196×C131C2semidirect
7. #2128×C131C2semidirect
8. #2122×C131C2semidirect
9. #2120×C131C2semidirect
10. #585×C131C22semidirect
13. #560×C131C22semidirect
19. D42×C131C22semidirect
30. #458×C131C22semidirect
33. B(4,𝔽2)×C131C22semidirect
34. B(4,𝔽2)×C131C22semidirect
36. #453×C131C22semidirect
38. #413×C131C22semidirect
41. #410×C131C22semidirect
42. #410×C131C22semidirect
43. #353×C131C22semidirect
44. #352×C131C22semidirect
45. AΣL(1,𝔽16)×C131C22semidirect
46. AΣL(1,𝔽16)×C131C22semidirect
62. C22×D4×C131D4semidirect
63. C22×D4×C131D4semidirect
64. C23×C4×C131D4semidirect
79. #124×C131D4semidirect
85. #123×C131D4semidirect
114. #120×C131D4semidirect
115. #120×C131D4semidirect
127. #117×C131D4semidirect
128. #117×C131D4semidirect
129. #117×C131D4semidirect
393. #33553C131direct (N × H)
394. C131#33553direct (N × H)
395. #3537C2×C131semidirect
396. #3027C2×C131semidirect
397. #3025C2×C131semidirect
398. #3021C2×C131semidirect
399. #2200C2×C131semidirect
400. #2196C2×C131semidirect
401. #2128C2×C131semidirect
402. #2122C2×C131semidirect
403. #2120C2×C131semidirect
404. #585C22×C131semidirect
407. #560C22×C131semidirect
413. D42C22×C131semidirect
424. #458C22×C131semidirect
427. B(4,𝔽2)C22×C131semidirect
428. B(4,𝔽2)C22×C131semidirect
430. #453C22×C131semidirect
432. #413C22×C131semidirect
435. #410C22×C131semidirect
436. #410C22×C131semidirect
437. #353C22×C131semidirect
438. #352C22×C131semidirect
439. AΣL(1,𝔽16)C22×C131semidirect
440. AΣL(1,𝔽16)C22×C131semidirect
456. C22×D4D4×C131semidirect
457. C22×D4D4×C131semidirect
458. C23×C4D4×C131semidirect
473. #124D4×C131semidirect
479. #123D4×C131semidirect
508. #120D4×C131semidirect
509. #120D4×C131semidirect
521. #117D4×C131semidirect
522. #117D4×C131semidirect
523. #117D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3537×C1312
#3027×C1312
#3025×C1312
#3021×C1312
#2200×C1312
#2196×C1312
#2128×C1312
#2122×C1312
#2120×C1312
#33553131