Finite Group Databasebeta

← C131×#25144 #45711028

Subgroups — C131×#25144 #45711028

Order 33536.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C131C211yesmaximal, characteristic, complemented
2#3056×C131C211yesmaximal, characteristic, complemented
3#3003×C131C211yesmaximal, characteristic
4C2×#450×C131C211yesmaximal, characteristic, complemented
5#2933×C131C211yesmaximal, characteristic, complemented
6C22×#100×C131C211yesmaximal, characteristic, complemented
7#2063×C131C211yesmaximal, characteristic, complemented
8#2051×C131C211yesmaximal, characteristic, complemented
9#2046×C131C211yesmaximal, characteristic, complemented
10#2019×C131C211yesmaximal, characteristic, complemented
11#1977×C131C211yesmaximal, characteristic, complemented
12#1931×C131C211yesmaximal, characteristic, complemented
13#1907×C131C211yesmaximal, characteristic, complemented
14#1901×C131C211yesmaximal, characteristic, complemented
15#1855×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C2×#137×C131C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic
21C22×SD16×C131C2211yescharacteristic
22C2×#131×C131C2211yescharacteristic, complemented
23C22×M16×C131C2211yescharacteristic
24C22×M16×C131C2211yescharacteristic
25#525×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27#471×C131—24no—
28#470×C131—21no—
29#468×C131—21no—
30#467×C131—21no—
31#465×C131—21no—
32#450×C131—21no—
33#450×C131—21no—
34#450×C131—21no—
35#450×C131—21no—
36#450×C131—21no—
37#450×C131—21no—
38#447×C131—21no—
39#447×C131—21no—
40#436×C131—21no—
41#435×C131—21no—
42#435×C131—21no—
43C8×D4×C131—21no—
44C2×#108×C131C2211yescharacteristic, complemented
45C2×#108×C131C2211yescharacteristic, complemented
46#428×C131C2211yescharacteristic, complemented
47#424×C131C2211yescharacteristic, complemented
48#419×C131C2211yescharacteristic, complemented
49#418×C131C2211yescharacteristic
50#418×C131C2211yescharacteristic
51#417×C131C2211yescharacteristic, complemented
52C2×#102×C131C2211yescharacteristic
53C2×#102×C131C2211yescharacteristic
54C2×#101×C131C2211yescharacteristic, complemented
55C2×#101×C131C2211yescharacteristic, complemented
56C2×#100×C131—24no—
57C2×#100×C131C2211yescharacteristic
58C2×#100×C131C2211yescharacteristic
59C2×#100×C131C2211yescharacteristic
60C2×#100×C131C2211yescharacteristic
61#408×C131C2211yescharacteristic, complemented
62#407×C131C2211yescharacteristic
63C2×C22⋊C8×C131C2211yescharacteristic
64#405×C131C2211yescharacteristic, complemented
65#343×C131C2211yescharacteristic, complemented
66#343×C131C2211yescharacteristic, complemented
67#341×C131C2211yescharacteristic, complemented
68#341×C131C2211yescharacteristic, complemented
69C25×C131—21no—
70C2×#41×C131C2311yescharacteristic
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—21no—
78C22×D4×C131—21no—
79C22×D4×C131—41no—
80C22×D4×C131—41no—
81C22×D4×C131C2311yescharacteristic
82C22×D4×C131C2311yescharacteristic
83C23×C4×C131C2311yescharacteristic
84#137×C131—22no—
85#137×C131—41no—
86AGL(1,ℤ/8)×C131—22no—
87AGL(1,ℤ/8)×C131—22no—
88AGL(1,ℤ/8)×C131—41no—
89AGL(1,ℤ/8)×C131—41no—
90C2×Q16×C131—21no—
91C2×SD16×C131—21no—
92C2×SD16×C131—21no—
93C2×SD16×C131—21no—
94C2×SD16×C131—22no—
95C2×SD16×C131—22no—
96C2×SD16×C131—21no—
97C2×SD16×C131—21no—
98C2×SD16×C131—21no—
99C2×SD16×C131—21no—
100C2×SD16×C131—41no—
101C2×SD16×C131—41no—
102C2×D8×C131—21no—
103C2×D8×C131—21no—
104#131×C131—22no—
105#131×C131—41no—
106C2×M16×C131—21no—
107C2×M16×C131—21no—
108C2×M16×C131—21no—
109C2×M16×C131—22no—
110C2×M16×C131—22no—
111C2×M16×C131—41no—
112C2×M16×C131—41no—
113C2×M16×C131C2311yescharacteristic
114C2×M16×C131C2311yescharacteristic
115C2×M16×C131C2311yescharacteristic
116C2×M16×C131C2311yescharacteristic
117C2×M16×C131C2311yescharacteristic
118C2×M16×C131C2311yescharacteristic
119C22×C8×C131—21no—
120C22×C8×C131—21no—
121C22×C8×C131—21no—
122C22×C8×C131C2311yescharacteristic
123C22×C8×C131C2311yescharacteristic
124#123×C131—21no—
125C22⋊Q8×C131—21no—
126C22⋊Q8×C131—21no—
127C22⋊Q8×C131—21no—
128C22⋊Q8×C131—21no—
129C22⋊Q8×C131D411yescharacteristic
130C22⋊Q8×C131D411yescharacteristic
131#121×C131D411yescharacteristic
132#121×C131D411yescharacteristic
133#120×C131—21no—
134C4×D4×C131—21no—
135C4×D4×C131—21no—
136#117×C131C2311yescharacteristic
137C2×C4⋊C4×C131—21no—
138C2×C4⋊C4×C131C2311yescharacteristic
139C2×C22⋊C4×C131—21no—
140#108×C131—22no—
141#108×C131—41no—
142#107×C131—21no—
143#106×C131—21no—
144C4⋊C8×C131—21no—
145C4⋊C8×C131—21no—
146#103×C131—21no—
147#103×C131—21no—
148#103×C131—21no—
149#102×C131—21no—
150#102×C131—21no—
151#102×C131—21no—
152#102×C131—21no—
153#102×C131—21no—
154#102×C131—21no—
155#102×C131—21no—
156#102×C131—21no—
157#102×C131—21no—
158#101×C131—22no—
159#101×C131—41no—
160#100×C131—22no—
161#100×C131—22no—
162#100×C131—22no—
163#100×C131D414yescomplemented
164C22⋊C8×C131—21no—
165C22⋊C8×C131—21no—
166C22⋊C8×C131—21no—
167C22⋊C8×C131—21no—
168C22⋊C8×C131D411yescharacteristic
169C22⋊C8×C131D411yescharacteristic
170C22⋊C8×C131D411yescharacteristic
171C22⋊C8×C131D411yescharacteristic
172#97×C131—21no—
173C4×C8×C131—21no—
174C24×C131—24no—
175C24×C131—21no—
176C24×C131—21no—
177C24×C131—42no—
178C24×C131—41no—
179C24×C131—41no—
180C24×C131—82no—
181C24×C131—82no—
182C24×C131#4111yescharacteristic
183#41×C131—21no—
184#41×C131—21no—
185#41×C131—21no—
186#41×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131—21no—
189C2×Q8×C131—21no—
190C2×Q8×C131—21no—
191C2×Q8×C131—21no—
192C2×Q8×C131—21no—
193C2×Q8×C131C2×D411yescharacteristic
194C2×D4×C131—24no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
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—21no—
207C2×D4×C131—21no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—42no—
216C2×D4×C131—42no—
217C2×D4×C131—41no—
218C2×D4×C131—41no—
219C2×D4×C131C2×D412yes—
220C2×D4×C131C2×D411yescharacteristic
221C2×D4×C131#4112yes—
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×C131C2×D411yescharacteristic
230C22×C4×C131C2×D411yescharacteristic
231C22×C4×C131C2×D411yescharacteristic
232C22×C4×C131C2×D411yescharacteristic
233C22×C4×C131#4111yescharacteristic
234C22×C4×C131C2411yescharacteristic
235Q16×C131—42no—
236SD16×C131—42no—
237SD16×C131—42no—
238SD16×C131—42no—
239SD16×C131—42no—
240SD16×C131—42no—
241SD16×C131—42no—
242SD16×C131—42no—
243D8×C131—42no—
244D8×C131—42no—
245M16×C131—21no—
246M16×C131—21no—
247M16×C131—21no—
248M16×C131—21no—
249M16×C131—21no—
250M16×C131—21no—
251M16×C131—21no—
252M16×C131—21no—
253M16×C131—21no—
254M16×C131—21no—
255M16×C131—42no—
256M16×C131—42no—
257M16×C131—42no—
258M16×C131C2×D412yes—
259M16×C131C2×D412yes—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—42no—
271C2×C8×C131—42no—
272C2×C8×C131—42no—
273C2×C8×C131C2×D411yescharacteristic
274C2×C8×C131C2×D411yescharacteristic
275C2×C8×C131C2×D411yescharacteristic
276C2×C8×C131C2×D411yescharacteristic
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—41no—
282C4⋊C4×C131—41no—
283C4⋊C4×C131C2×D411yescharacteristic
284C4⋊C4×C131C2×D411yescharacteristic
285C22⋊C4×C131—21no—
286C22⋊C4×C131—21no—
287C22⋊C4×C131—21no—
288C22⋊C4×C131—21no—
289C22⋊C4×C131—21no—
290C22⋊C4×C131—41no—
291C22⋊C4×C131—41no—
292C42×C131—21no—
293C23×C131—21no—
294C23×C131—21no—
295C23×C131—22no—
296C23×C131—21no—
297C23×C131—22no—
298C23×C131—22no—
299C23×C131—41no—
300C23×C131—44no—
301C23×C131—44no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—81no—
307C23×C131—81no—
308C23×C131—81no—
309C23×C131—81no—
310C23×C131—82no—
311C23×C131—82no—
312C23×C131—82no—
313C23×C131—88no—
314C23×C131—88no—
315C23×C131—82no—
316C23×C131#12111yescharacteristic
317C23×C131#12111yescharacteristic
318C23×C131C2×#4111yescharacteristic
319Q8×C131—21no—
320Q8×C131—21no—
321Q8×C131—41no—
322Q8×C131—41no—
323Q8×C131—41no—
324Q8×C131—41no—
325D4×C131—21no—
326D4×C131—22no—
327D4×C131—22no—
328D4×C131—21no—
329D4×C131—22no—
330D4×C131—22no—
331D4×C131—44no—
332D4×C131—44no—
333D4×C131—41no—
334D4×C131—41no—
335D4×C131—42no—
336D4×C131—41no—
337D4×C131—41no—
338D4×C131—41no—
339D4×C131—41no—
340D4×C131—81no—
341C2×C4×C131—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—21no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—21no—
352C2×C4×C131—21no—
353C2×C4×C131—21no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—81no—
361C2×C4×C131#12111yescharacteristic
362C2×C4×C131#12111yescharacteristic
363C2×C4×C131C22×D411yescharacteristic
364C2×C4×C131C22×D411yescharacteristic
365C2×C4×C131C22×D411yescharacteristic
366C2×C4×C131C2×#4111yescharacteristic
367C2×C4×C131H(5,𝔽2)11yescharacteristic
368C2×C4×C131H(5,𝔽2)11yescharacteristic
369C8×C131—21no—
370C8×C131—21no—
371C8×C131—22no—
372C8×C131—22no—
373C8×C131—21no—
374C8×C131—21no—
375C8×C131—41no—
376C8×C131—41no—
377C8×C131—41no—
378C8×C131—41no—
379C22×C131—21no—
380C22×C131—21no—
381C22×C131—21no—
382C22×C131—21no—
383C22×C131—21no—
384C22×C131—21no—
385C22×C131—21no—
386C22×C131—42no—
387C22×C131—42no—
388C22×C131—41no—
389C22×C131—42no—
390C22×C131—42no—
391C22×C131—41no—
392C22×C131—41no—
393C22×C131—82no—
394C22×C131—82no—
395C22×C131—88no—
396C22×C131—82no—
397C22×C131—82no—
398C22×C131—88no—
399C22×C131—81no—
400C22×C131—81no—
401C22×C131—81no—
402C22×C131—81no—
403C22×C131#47112yescomplemented
404C22×C131C2×#12111yescharacteristic
405C22×C131#52511yescharacteristic
406C22×C131#53811yescharacteristic
407C4×C131—21no—
408C4×C131—21no—
409C4×C131—41no—
410C4×C131—41no—
411C4×C131—41no—
412C4×C131—81no—
413C4×C131—81no—
414C4×C131D4211yescharacteristic
415C4×C131D4211yescharacteristic
416C4×C131#54611yescharacteristic
417C4×C131#54611yescharacteristic
418C2×C131—21no—
419C2×C131—21no—
420C2×C131—22no—
421C2×C131—41no—
422C2×C131—81no—
423C2×C131—82no—
424C2×C131—82no—
425C2×C131#242411yescharacteristic
426C2×C131C2×#47111yescharacteristic
427C2×C131#306811yescharacteristic
428#25144C13111yesmaximal, characteristic, direct product factor, Sylow
429C131#2514411yescharacteristic, direct product factor, Sylow
430C2×#471C2×C13111yescharacteristic, complemented
431#3056C2×C13111yescharacteristic, complemented
432#3003C2×C13111yescharacteristic
433C2×#450C2×C13111yescharacteristic, complemented
434#2933C2×C13111yescharacteristic, complemented
435C22×#100C2×C13111yescharacteristic, complemented
436#2063C2×C13111yescharacteristic, complemented
437#2051C2×C13111yescharacteristic, complemented
438#2046C2×C13111yescharacteristic, complemented
439#2019C2×C13111yescharacteristic, complemented
440#1977C2×C13111yescharacteristic, complemented
441#1931C2×C13111yescharacteristic, complemented
442#1907C2×C13111yescharacteristic, complemented
443#1901C2×C13111yescharacteristic, complemented
444#1855C2×C13111yescharacteristic, complemented
445C23×D4C22×C13111yescharacteristic
446C2×#137C22×C13111yescharacteristic, complemented
447C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
448C2×AGL(1,ℤ/8)C22×C13111yescharacteristic
449C22×SD16C22×C13111yescharacteristic
450C22×SD16C22×C13111yescharacteristic
451C2×#131C22×C13111yescharacteristic, complemented
452C22×M16C22×C13111yescharacteristic
453C22×M16C22×C13111yescharacteristic
454#525C22×C13111yescharacteristic
455C2×C22⋊Q8C22×C13111yescharacteristic
456#471—24no—
457#470—21no—
458#468—21no—
459#467—21no—
460#465—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#450—21no—
467#447—21no—
468#447—21no—
469#436—21no—
470#435—21no—
471#435—21no—
472C8×D4—21no—
473C2×#108C22×C13111yescharacteristic, complemented
474C2×#108C22×C13111yescharacteristic, complemented
475#428C22×C13111yescharacteristic, complemented
476#424C22×C13111yescharacteristic, complemented
477#419C22×C13111yescharacteristic, complemented
478#418C22×C13111yescharacteristic
479#418C22×C13111yescharacteristic
480#417C22×C13111yescharacteristic, complemented
481C2×#102C22×C13111yescharacteristic
482C2×#102C22×C13111yescharacteristic
483C2×#101C22×C13111yescharacteristic, complemented
484C2×#101C22×C13111yescharacteristic, complemented
485C2×#100—24no—
486C2×#100C22×C13111yescharacteristic
487C2×#100C22×C13111yescharacteristic
488C2×#100C22×C13111yescharacteristic
489C2×#100C22×C13111yescharacteristic
490#408C22×C13111yescharacteristic, complemented
491#407C22×C13111yescharacteristic
492C2×C22⋊C8C22×C13111yescharacteristic
493#405C22×C13111yescharacteristic, complemented
494#343C22×C13111yescharacteristic, complemented
495#343C22×C13111yescharacteristic, complemented
496#341C22×C13111yescharacteristic, complemented
497#341C22×C13111yescharacteristic, complemented
498C25—21no—
499C2×#41C23×C13111yescharacteristic
500C22×Q8C23×C13111yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C13111yescharacteristic
511C22×D4C23×C13111yescharacteristic
512C23×C4C23×C13111yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C13111yescharacteristic
543C2×M16C23×C13111yescharacteristic
544C2×M16C23×C13111yescharacteristic
545C2×M16C23×C13111yescharacteristic
546C2×M16C23×C13111yescharacteristic
547C2×M16C23×C13111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C13111yescharacteristic
552C22×C8C23×C13111yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C13111yescharacteristic
559C22⋊Q8D4×C13111yescharacteristic
560#121D4×C13111yescharacteristic
561#121D4×C13111yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C13111yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C13111yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C13114yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C13111yescharacteristic
598C22⋊C8D4×C13111yescharacteristic
599C22⋊C8D4×C13111yescharacteristic
600C22⋊C8D4×C13111yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C13111yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C13111yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C13112yes—
649C2×D4C2×D4×C13111yescharacteristic
650C2×D4#41×C13112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C13111yescharacteristic
659C22×C4C2×D4×C13111yescharacteristic
660C22×C4C2×D4×C13111yescharacteristic
661C22×C4C2×D4×C13111yescharacteristic
662C22×C4#41×C13111yescharacteristic
663C22×C4C24×C13111yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C13112yes—
688M16C2×D4×C13112yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C13111yescharacteristic
703C2×C8C2×D4×C13111yescharacteristic
704C2×C8C2×D4×C13111yescharacteristic
705C2×C8C2×D4×C13111yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C13111yescharacteristic
713C4⋊C4C2×D4×C13111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C13111yescharacteristic
746C23#121×C13111yescharacteristic
747C23C2×#41×C13111yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C13111yescharacteristic
791C2×C4#121×C13111yescharacteristic
792C2×C4C22×D4×C13111yescharacteristic
793C2×C4C22×D4×C13111yescharacteristic
794C2×C4C22×D4×C13111yescharacteristic
795C2×C4C2×#41×C13111yescharacteristic
796C2×C4H(5,𝔽2)×C13111yescharacteristic
797C2×C4H(5,𝔽2)×C13111yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22#471×C13112yescomplemented
833C22C2×#121×C13111yescharacteristic
834C22#525×C13111yescharacteristic
835C22#538×C13111yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C13111yescharacteristic
844C4D42×C13111yescharacteristic
845C4#546×C13111yescharacteristic
846C4#546×C13111yescharacteristic
847C2—22no—
848C2—21no—
849C2—21no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2#2424×C13111yescharacteristic
855C2C2×#471×C13111yescharacteristic
856C2#3068×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3003×C131C2
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. C2×#471×C131C2semidirect
2. #3056×C131C2semidirect
4. C2×#450×C131C2semidirect
5. #2933×C131C2semidirect
6. C22×#100×C131C2semidirect
7. #2063×C131C2semidirect
8. #2051×C131C2semidirect
9. #2046×C131C2semidirect
10. #2019×C131C2semidirect
11. #1977×C131C2semidirect
12. #1931×C131C2semidirect
13. #1907×C131C2semidirect
14. #1901×C131C2semidirect
15. #1855×C131C2semidirect
17. C2×#137×C131C22semidirect
22. C2×#131×C131C22semidirect
44. C2×#108×C131C22semidirect
45. C2×#108×C131C22semidirect
46. #428×C131C22semidirect
47. #424×C131C22semidirect
48. #419×C131C22semidirect
51. #417×C131C22semidirect
54. C2×#101×C131C22semidirect
55. C2×#101×C131C22semidirect
61. #408×C131C22semidirect
64. #405×C131C22semidirect
65. #343×C131C22semidirect
66. #343×C131C22semidirect
67. #341×C131C22semidirect
68. #341×C131C22semidirect
163. #100×C131D4semidirect
403. C22×C131#471semidirect
428. #25144C131direct (N × H)
429. C131#25144direct (N × H)
430. C2×#471C2×C131semidirect
431. #3056C2×C131semidirect
433. C2×#450C2×C131semidirect
434. #2933C2×C131semidirect
435. C22×#100C2×C131semidirect
436. #2063C2×C131semidirect
437. #2051C2×C131semidirect
438. #2046C2×C131semidirect
439. #2019C2×C131semidirect
440. #1977C2×C131semidirect
441. #1931C2×C131semidirect
442. #1907C2×C131semidirect
443. #1901C2×C131semidirect
444. #1855C2×C131semidirect
446. C2×#137C22×C131semidirect
451. C2×#131C22×C131semidirect
473. C2×#108C22×C131semidirect
474. C2×#108C22×C131semidirect
475. #428C22×C131semidirect
476. #424C22×C131semidirect
477. #419C22×C131semidirect
480. #417C22×C131semidirect
483. C2×#101C22×C131semidirect
484. C2×#101C22×C131semidirect
490. #408C22×C131semidirect
493. #405C22×C131semidirect
494. #343C22×C131semidirect
495. #343C22×C131semidirect
496. #341C22×C131semidirect
497. #341C22×C131semidirect
592. #100D4×C131semidirect
832. C22#471×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C1312
#3056×C1312
#3003×C1312
C2×#450×C1312
#2933×C1312
C22×#100×C1312
#2063×C1312
#2051×C1312
#2046×C1312
#2019×C1312
#1977×C1312
#1931×C1312
#1907×C1312
#1901×C1312
#1855×C1312
#25144131