Finite Group Databasebeta

← C2×#2009×C131 #45709295

Subgroups — C2×#2009×C131 #45709295

Order 33536.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C131C211yesmaximal, characteristic
2C22×#137×C131C211yesmaximal, characteristic, complemented
3C2×#536×C131C211yesmaximal, characteristic, complemented
4C2×#421×C131C211yesmaximal, characteristic, complemented
5C2×#419×C131C211yesmaximal, characteristic, complemented
6C2×#410×C131C211yesmaximal, characteristic, complemented
7#2009×C131C218yesmaximal, direct product factor
8C2×#344×C131C211yesmaximal, characteristic, complemented
9C22×#41×C131C2211yescharacteristic
10C22×#41×C131C2211yescharacteristic
11C23×Q8×C131C2211yescharacteristic
12#575×C131—22no—
13#575×C131—22no—
14#575×C131—22no—
15#575×C131C2214yes—
16C2×#137×C131—22no—
17C2×#137×C131—22no—
18C2×#137×C131—22no—
19C2×#137×C131—21no—
20C2×#137×C131—21no—
21C2×#137×C131—22no—
22C2×#137×C131—22no—
23C2×#137×C131C2214yescomplemented
24C2×AGL(1,ℤ/8)×C131—21no—
25C2×AGL(1,ℤ/8)×C131—21no—
26C2×#135×C131—22no—
27C22×Q16×C131—21no—
28C22×SD16×C131—21no—
29C22×M16×C131C2211yescharacteristic
30C22×M16×C131C2211yescharacteristic
31#536×C131—22no—
32#536×C131—22no—
33#536×C131—22no—
34#536×C131C2214yescomplemented
35C2×C4⋊Q8×C131—21no—
36C2×#124×C131—21no—
37C2×#123×C131—22no—
38C2×C22⋊Q8×C131—22no—
39C2×#117×C131C2211yescharacteristic
40C2×#117×C131C2211yescharacteristic
41#421×C131—22no—
42#421×C131C2214yescomplemented
43C2×#104×C131—22no—
44#419×C131—22no—
45#419×C131C2214yescomplemented
46C2×#103×C131—22no—
47#410×C131—22no—
48#410×C131C2214yescomplemented
49C2×#99×C131—22no—
50#344×C131C2214yescomplemented
51C2×#41×C131—21no—
52C2×#41×C131—21no—
53C2×#41×C131—21no—
54C2×#41×C131—21no—
55C2×#41×C131—21no—
56C2×#41×C131—21no—
57C2×#41×C131—21no—
58C2×#41×C131—21no—
59C2×#41×C131—21no—
60C2×#41×C131—21no—
61C2×#41×C131—21no—
62C2×#41×C131—21no—
63C2×#41×C131—21no—
64C2×#41×C131—21no—
65C2×#41×C131—21no—
66C2×#41×C131—21no—
67C2×#41×C131—21no—
68C2×#41×C131—21no—
69C2×#41×C131—21no—
70C2×#41×C131—21no—
71C2×#41×C131D412yes—
72C2×#41×C131D412yes—
73C2×#41×C131C2312yes—
74C2×#41×C131C2312yes—
75C22×Q8×C131—21no—
76C22×Q8×C131—21no—
77C22×Q8×C131—21no—
78C22×Q8×C131—21no—
79C22×Q8×C131—21no—
80C22×Q8×C131—21no—
81C22×Q8×C131—21no—
82C22×Q8×C131—21no—
83C22×Q8×C131—21no—
84C22×Q8×C131—21no—
85C22×Q8×C131—21no—
86C22×Q8×C131D412yes—
87C22×Q8×C131D411yescharacteristic
88C22×Q8×C131D412yes—
89C22×Q8×C131D411yescharacteristic
90C22×Q8×C131C2312yes—
91C22×D4×C131—21no—
92C22×D4×C131—21no—
93C22×D4×C131D411yescharacteristic
94C22×D4×C131D411yescharacteristic
95C23×C4×C131—21no—
96C23×C4×C131—21no—
97C23×C4×C131—21no—
98C23×C4×C131C2311yescharacteristic
99#137×C131—28no—
100#137×C131—28no—
101#137×C131—24no—
102#137×C131—24no—
103#137×C131—28no—
104#137×C131—24no—
105#137×C131—24no—
106#137×C131—28no—
107AGL(1,ℤ/8)×C131—24no—
108AGL(1,ℤ/8)×C131—24no—
109AGL(1,ℤ/8)×C131—24no—
110AGL(1,ℤ/8)×C131—24no—
111#135×C131—28no—
112#135×C131—28no—
113C2×Q16×C131—24no—
114C2×Q16×C131—24no—
115C2×Q16×C131—22no—
116C2×Q16×C131—24no—
117C2×SD16×C131—24no—
118C2×SD16×C131—24no—
119C2×SD16×C131—22no—
120C2×SD16×C131—22no—
121C2×SD16×C131—24no—
122C2×D8×C131—22no—
123C2×M16×C131—21no—
124C2×M16×C131—21no—
125C2×M16×C131—21no—
126C2×M16×C131—21no—
127C2×M16×C131—21no—
128C2×M16×C131—21no—
129C2×M16×C131—21no—
130C2×M16×C131D412yes—
131C2×M16×C131D412yes—
132C2×M16×C131D412yes—
133C2×M16×C131C2312yes—
134C2×M16×C131C2312yes—
135C22×C8×C131—21no—
136C22×C8×C131D412yes—
137C4⋊Q8×C131—24no—
138C4⋊Q8×C131—24no—
139#124×C131—24no—
140#124×C131—24no—
141#123×C131—28no—
142#123×C131—28no—
143C22⋊Q8×C131—28no—
144C22⋊Q8×C131—28no—
145#117×C131—21no—
146#117×C131—21no—
147#117×C131—21no—
148#117×C131—21no—
149#117×C131—21no—
150#117×C131D412yes—
151#117×C131C2312yes—
152#117×C131C2312yes—
153C2×C4⋊C4×C131—24no—
154C2×C4⋊C4×C131—21no—
155C2×C4⋊C4×C131—21no—
156C2×C22⋊C4×C131—24no—
157C2×C22⋊C4×C131—21no—
158C2×C22⋊C4×C131D412yes—
159C2×C42×C131—21no—
160C2×C42×C131—21no—
161#104×C131—28no—
162#103×C131—28no—
163#99×C131—28no—
164C24×C131—21no—
165C24×C131—21no—
166C24×C131C2×D411yescharacteristic
167#41×C131—22no—
168#41×C131—22no—
169#41×C131—22no—
170#41×C131—22no—
171#41×C131—22no—
172#41×C131—22no—
173#41×C131—22no—
174#41×C131—22no—
175#41×C131—22no—
176#41×C131—22no—
177#41×C131—22no—
178#41×C131—22no—
179#41×C131—22no—
180#41×C131—22no—
181#41×C131—22no—
182#41×C131—22no—
183#41×C131—41no—
184#41×C131—41no—
185#41×C131—41no—
186#41×C131—41no—
187#41×C131—41no—
188#41×C131—41no—
189#41×C131—41no—
190#41×C131—41no—
191#41×C131—41no—
192#41×C131—41no—
193#41×C131—41no—
194#41×C131—41no—
195#41×C131—41no—
196#41×C131—41no—
197#41×C131—41no—
198#41×C131—41no—
199C2×Q8×C131—22no—
200C2×Q8×C131—22no—
201C2×Q8×C131—21no—
202C2×Q8×C131—21no—
203C2×Q8×C131—22no—
204C2×Q8×C131—22no—
205C2×Q8×C131—22no—
206C2×Q8×C131—21no—
207C2×Q8×C131—21no—
208C2×Q8×C131—21no—
209C2×Q8×C131—21no—
210C2×Q8×C131—22no—
211C2×Q8×C131—22no—
212C2×Q8×C131—21no—
213C2×Q8×C131—21no—
214C2×Q8×C131—22no—
215C2×Q8×C131—22no—
216C2×Q8×C131—22no—
217C2×Q8×C131—22no—
218C2×Q8×C131—21no—
219C2×Q8×C131—21no—
220C2×Q8×C131—22no—
221C2×Q8×C131—22no—
222C2×Q8×C131—22no—
223C2×Q8×C131—22no—
224C2×Q8×C131—41no—
225C2×Q8×C131—41no—
226C2×Q8×C131—41no—
227C2×Q8×C131—41no—
228C2×Q8×C131—41no—
229C2×Q8×C131—41no—
230C2×Q8×C131—41no—
231C2×Q8×C131—41no—
232C2×Q8×C131—41no—
233C2×Q8×C131—41no—
234C2×Q8×C131—41no—
235C2×Q8×C131—41no—
236C2×Q8×C131C2×D414yes—
237C2×Q8×C131C2×D412yes—
238C2×Q8×C131C2×D412yes—
239C2×D4×C131—22no—
240C2×D4×C131—22no—
241C2×D4×C131—22no—
242C2×D4×C131—22no—
243C2×D4×C131—21no—
244C2×D4×C131—21no—
245C2×D4×C131—21no—
246C2×D4×C131—21no—
247C2×D4×C131—21no—
248C2×D4×C131—21no—
249C2×D4×C131—21no—
250C2×D4×C131—21no—
251C2×D4×C131—21no—
252C2×D4×C131—21no—
253C2×D4×C131—41no—
254C2×D4×C131—41no—
255C2×D4×C131—41no—
256C2×D4×C131—41no—
257C2×D4×C131—41no—
258C2×D4×C131—41no—
259C2×D4×C131—41no—
260C2×D4×C131—41no—
261C2×D4×C131C2×D412yes—
262C2×D4×C131C2×D412yes—
263C22×C4×C131—22no—
264C22×C4×C131—22no—
265C22×C4×C131—21no—
266C22×C4×C131—22no—
267C22×C4×C131—21no—
268C22×C4×C131—22no—
269C22×C4×C131—22no—
270C22×C4×C131—22no—
271C22×C4×C131—22no—
272C22×C4×C131—22no—
273C22×C4×C131—41no—
274C22×C4×C131—41no—
275C22×C4×C131—41no—
276C22×C4×C131—41no—
277C22×C4×C131—41no—
278C22×C4×C131—41no—
279C22×C4×C131—41no—
280C22×C4×C131—41no—
281C22×C4×C131—41no—
282C22×C4×C131—41no—
283C22×C4×C131—41no—
284C22×C4×C131—41no—
285C22×C4×C131—41no—
286C22×C4×C131C2×D411yescharacteristic
287C22×C4×C131C2×D411yescharacteristic
288C22×C4×C131C2×D411yescharacteristic
289C22×C4×C131C2×D411yescharacteristic
290C22×C4×C131C2×D411yescharacteristic
291C22×C4×C131C2×D411yescharacteristic
292C22×C4×C131C2×D411yescharacteristic
293C22×C4×C131C2×D411yescharacteristic
294C22×C4×C131C2×D411yescharacteristic
295C22×C4×C131C2×D411yescharacteristic
296C22×C4×C131C2×D411yescharacteristic
297C22×C4×C131#4111yescharacteristic
298C22×C4×C131#4111yescharacteristic
299C22×C4×C131C2411yescharacteristic
300Q16×C131—216no—
301Q16×C131—28no—
302SD16×C131—216no—
303SD16×C131—28no—
304SD16×C131—28no—
305D8×C131—28no—
306M16×C131—22no—
307M16×C131—22no—
308M16×C131—22no—
309M16×C131—22no—
310M16×C131—22no—
311M16×C131—22no—
312M16×C131—22no—
313M16×C131C2×D414yes—
314C2×C8×C131—22no—
315C2×C8×C131—22no—
316C2×C8×C131—22no—
317C2×C8×C131—22no—
318C2×C8×C131—22no—
319C2×C8×C131C2×D414yes—
320C4⋊C4×C131—216no—
321C4⋊C4×C131—22no—
322C4⋊C4×C131—22no—
323C4⋊C4×C131—22no—
324C4⋊C4×C131—41no—
325C22⋊C4×C131—216no—
326C22⋊C4×C131—22no—
327C22⋊C4×C131—22no—
328C22⋊C4×C131—41no—
329C22⋊C4×C131C2×D414yes—
330C42×C131—22no—
331C42×C131—22no—
332C42×C131—22no—
333C42×C131—41no—
334C23×C131—22no—
335C23×C131—22no—
336C23×C131—42no—
337C23×C131—44no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—41no—
342C23×C131—82no—
343C23×C131#12011yescharacteristic
344C23×C131#12011yescharacteristic
345C23×C131#12111yescharacteristic
346C23×C131#12111yescharacteristic
347C23×C131#12711yescharacteristic
348C23×C131#12711yescharacteristic
349C23×C131C22×D411yescharacteristic
350Q8×C131—24no—
351Q8×C131—22no—
352Q8×C131—22no—
353Q8×C131—22no—
354Q8×C131—24no—
355Q8×C131—22no—
356Q8×C131—42no—
357Q8×C131—42no—
358Q8×C131—42no—
359Q8×C131—42no—
360Q8×C131—42no—
361Q8×C131—42no—
362Q8×C131—41no—
363Q8×C131—41no—
364Q8×C131—41no—
365Q8×C131—41no—
366D4×C131—22no—
367D4×C131—22no—
368D4×C131—22no—
369D4×C131—22no—
370D4×C131—42no—
371D4×C131—42no—
372D4×C131—42no—
373D4×C131—42no—
374D4×C131—42no—
375D4×C131—42no—
376D4×C131—42no—
377D4×C131—42no—
378D4×C131—41no—
379D4×C131—41no—
380D4×C131—41no—
381D4×C131—41no—
382C2×C4×C131—24no—
383C2×C4×C131—24no—
384C2×C4×C131—22no—
385C2×C4×C131—22no—
386C2×C4×C131—44no—
387C2×C4×C131—42no—
388C2×C4×C131—42no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—42no—
392C2×C4×C131—42no—
393C2×C4×C131—42no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—42no—
397C2×C4×C131—42no—
398C2×C4×C131—42no—
399C2×C4×C131—42no—
400C2×C4×C131—42no—
401C2×C4×C131—42no—
402C2×C4×C131—42no—
403C2×C4×C131—42no—
404C2×C4×C131—42no—
405C2×C4×C131—42no—
406C2×C4×C131—82no—
407C2×C4×C131#12011yescharacteristic
408C2×C4×C131#12011yescharacteristic
409C2×C4×C131#12011yescharacteristic
410C2×C4×C131#12011yescharacteristic
411C2×C4×C131#12011yescharacteristic
412C2×C4×C131#12011yescharacteristic
413C2×C4×C131#12011yescharacteristic
414C2×C4×C131#12011yescharacteristic
415C2×C4×C131#12011yescharacteristic
416C2×C4×C131#12011yescharacteristic
417C2×C4×C131#12111yescharacteristic
418C2×C4×C131#12111yescharacteristic
419C2×C4×C131#12111yescharacteristic
420C2×C4×C131#12111yescharacteristic
421C2×C4×C131#12111yescharacteristic
422C2×C4×C131#12111yescharacteristic
423C2×C4×C131#12111yescharacteristic
424C2×C4×C131#12111yescharacteristic
425C2×C4×C131#12111yescharacteristic
426C2×C4×C131#12111yescharacteristic
427C2×C4×C131#12711yescharacteristic
428C2×C4×C131#12711yescharacteristic
429C2×C4×C131C22×D411yescharacteristic
430C2×C4×C131C22×D411yescharacteristic
431C2×C4×C131C22×D411yescharacteristic
432C2×C4×C131C22×D411yescharacteristic
433C2×C4×C131C22×D411yescharacteristic
434C2×C4×C131C2×#4111yescharacteristic
435C8×C131—24no—
436C8×C131—24no—
437C22×C131—22no—
438C22×C131—22no—
439C22×C131—22no—
440C22×C131—41no—
441C22×C131—41no—
442C22×C131—41no—
443C22×C131—41no—
444C22×C131—44no—
445C22×C131—42no—
446C22×C131—42no—
447C22×C131—82no—
448C22×C131—82no—
449C22×C131—82no—
450C22×C131—82no—
451C22×C131—82no—
452C22×C131#39211yescharacteristic
453C22×C131#39211yescharacteristic
454C22×C131#39211yescharacteristic
455C22×C131#39211yescharacteristic
456C22×C131C2×#12011yescharacteristic
457C22×C131C2×#12111yescharacteristic
458C22×C131C2×#12711yescharacteristic
459C4×C131—44no—
460C4×C131—42no—
461C4×C131—42no—
462C4×C131—44no—
463C4×C131—82no—
464C4×C131#39211yescharacteristic
465C4×C131#39211yescharacteristic
466C4×C131#39211yescharacteristic
467C4×C131#39211yescharacteristic
468C4×C131C2×#12011yescharacteristic
469C4×C131C2×#12011yescharacteristic
470C4×C131C2×#12111yescharacteristic
471C4×C131C2×#12111yescharacteristic
472C2×C131—21no—
473C2×C131—21no—
474C2×C131—21no—
475C2×C131—21no—
476C2×C131—21no—
477C2×C131—21no—
478C2×C131—82no—
479C2×C131—82no—
480C2×C131#200912yesdirect product factor
481C2×C131C2×#39211yescharacteristic
482C2×#2009C13111yesmaximal, characteristic, direct product factor, Sylow
483C131C2×#200911yescharacteristic, direct product factor, Sylow
484C2×#575C2×C13111yescharacteristic
485C22×#137C2×C13111yescharacteristic, complemented
486C2×#536C2×C13111yescharacteristic, complemented
487C2×#421C2×C13111yescharacteristic, complemented
488C2×#419C2×C13111yescharacteristic, complemented
489C2×#410C2×C13111yescharacteristic, complemented
490#2009C2×C13118yesdirect product factor
491C2×#344C2×C13111yescharacteristic, complemented
492C22×#41C22×C13111yescharacteristic
493C22×#41C22×C13111yescharacteristic
494C23×Q8C22×C13111yescharacteristic
495#575—22no—
496#575—22no—
497#575—22no—
498#575C22×C13114yes—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—22no—
502C2×#137—21no—
503C2×#137—21no—
504C2×#137—22no—
505C2×#137—22no—
506C2×#137C22×C13114yescomplemented
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)—21no—
509C2×#135—22no—
510C22×Q16—21no—
511C22×SD16—21no—
512C22×M16C22×C13111yescharacteristic
513C22×M16C22×C13111yescharacteristic
514#536—22no—
515#536—22no—
516#536—22no—
517#536C22×C13114yescomplemented
518C2×C4⋊Q8—21no—
519C2×#124—21no—
520C2×#123—22no—
521C2×C22⋊Q8—22no—
522C2×#117C22×C13111yescharacteristic
523C2×#117C22×C13111yescharacteristic
524#421—22no—
525#421C22×C13114yescomplemented
526C2×#104—22no—
527#419—22no—
528#419C22×C13114yescomplemented
529C2×#103—22no—
530#410—22no—
531#410C22×C13114yescomplemented
532C2×#99—22no—
533#344C22×C13114yescomplemented
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41D4×C13112yes—
555C2×#41D4×C13112yes—
556C2×#41C23×C13112yes—
557C2×#41C23×C13112yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8D4×C13112yes—
570C22×Q8D4×C13111yescharacteristic
571C22×Q8D4×C13112yes—
572C22×Q8D4×C13111yescharacteristic
573C22×Q8C23×C13112yes—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4D4×C13111yescharacteristic
577C22×D4D4×C13111yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C13111yescharacteristic
582#137—28no—
583#137—28no—
584#137—24no—
585#137—24no—
586#137—28no—
587#137—24no—
588#137—24no—
589#137—28no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—22no—
599C2×Q16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—24no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—21no—
613C2×M16D4×C13112yes—
614C2×M16D4×C13112yes—
615C2×M16D4×C13112yes—
616C2×M16C23×C13112yes—
617C2×M16C23×C13112yes—
618C22×C8—21no—
619C22×C8D4×C13112yes—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622#124—24no—
623#124—24no—
624#123—28no—
625#123—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117D4×C13112yes—
634#117C23×C13112yes—
635#117C23×C13112yes—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C13112yes—
642C2×C42—21no—
643C2×C42—21no—
644#104—28no—
645#103—28no—
646#99—28no—
647C24—21no—
648C24—21no—
649C24C2×D4×C13111yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C13114yes—
720C2×Q8C2×D4×C13112yes—
721C2×Q8C2×D4×C13112yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C13112yes—
745C2×D4C2×D4×C13112yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C13111yescharacteristic
770C22×C4C2×D4×C13111yescharacteristic
771C22×C4C2×D4×C13111yescharacteristic
772C22×C4C2×D4×C13111yescharacteristic
773C22×C4C2×D4×C13111yescharacteristic
774C22×C4C2×D4×C13111yescharacteristic
775C22×C4C2×D4×C13111yescharacteristic
776C22×C4C2×D4×C13111yescharacteristic
777C22×C4C2×D4×C13111yescharacteristic
778C22×C4C2×D4×C13111yescharacteristic
779C22×C4C2×D4×C13111yescharacteristic
780C22×C4#41×C13111yescharacteristic
781C22×C4#41×C13111yescharacteristic
782C22×C4C24×C13111yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C13114yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C13114yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C13114yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#120×C13111yescharacteristic
827C23#120×C13111yescharacteristic
828C23#121×C13111yescharacteristic
829C23#121×C13111yescharacteristic
830C23#127×C13111yescharacteristic
831C23#127×C13111yescharacteristic
832C23C22×D4×C13111yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8—42no—
848Q8—42no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4#120×C13111yescharacteristic
891C2×C4#120×C13111yescharacteristic
892C2×C4#120×C13111yescharacteristic
893C2×C4#120×C13111yescharacteristic
894C2×C4#120×C13111yescharacteristic
895C2×C4#120×C13111yescharacteristic
896C2×C4#120×C13111yescharacteristic
897C2×C4#120×C13111yescharacteristic
898C2×C4#120×C13111yescharacteristic
899C2×C4#120×C13111yescharacteristic
900C2×C4#121×C13111yescharacteristic
901C2×C4#121×C13111yescharacteristic
902C2×C4#121×C13111yescharacteristic
903C2×C4#121×C13111yescharacteristic
904C2×C4#121×C13111yescharacteristic
905C2×C4#121×C13111yescharacteristic
906C2×C4#121×C13111yescharacteristic
907C2×C4#121×C13111yescharacteristic
908C2×C4#121×C13111yescharacteristic
909C2×C4#121×C13111yescharacteristic
910C2×C4#127×C13111yescharacteristic
911C2×C4#127×C13111yescharacteristic
912C2×C4C22×D4×C13111yescharacteristic
913C2×C4C22×D4×C13111yescharacteristic
914C2×C4C22×D4×C13111yescharacteristic
915C2×C4C22×D4×C13111yescharacteristic
916C2×C4C22×D4×C13111yescharacteristic
917C2×C4C2×#41×C13111yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22#392×C13111yescharacteristic
936C22#392×C13111yescharacteristic
937C22#392×C13111yescharacteristic
938C22#392×C13111yescharacteristic
939C22C2×#120×C13111yescharacteristic
940C22C2×#121×C13111yescharacteristic
941C22C2×#127×C13111yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4#392×C13111yescharacteristic
948C4#392×C13111yescharacteristic
949C4#392×C13111yescharacteristic
950C4#392×C13111yescharacteristic
951C4C2×#120×C13111yescharacteristic
952C4C2×#120×C13111yescharacteristic
953C4C2×#121×C13111yescharacteristic
954C4C2×#121×C13111yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2#2009×C13112yesdirect product factor
964C2C2×#392×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#575×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
2. C22×#137×C131C2semidirect
3. C2×#536×C131C2semidirect
4. C2×#421×C131C2semidirect
5. C2×#419×C131C2semidirect
6. C2×#410×C131C2semidirect
7. #2009×C131C2direct (N × H)
8. C2×#344×C131C2semidirect
23. C2×#137×C131C22semidirect
34. #536×C131C22semidirect
42. #421×C131C22semidirect
45. #419×C131C22semidirect
48. #410×C131C22semidirect
50. #344×C131C22semidirect
480. C2×C131#2009direct (N × H)
482. C2×#2009C131direct (N × H)
483. C131C2×#2009direct (N × H)
485. C22×#137C2×C131semidirect
486. C2×#536C2×C131semidirect
487. C2×#421C2×C131semidirect
488. C2×#419C2×C131semidirect
489. C2×#410C2×C131semidirect
490. #2009C2×C131direct (N × H)
491. C2×#344C2×C131semidirect
506. C2×#137C22×C131semidirect
517. #536C22×C131semidirect
525. #421C22×C131semidirect
528. #419C22×C131semidirect
531. #410C22×C131semidirect
533. #344C22×C131semidirect
963. C2#2009×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#575×C1312
C22×#137×C1312
C2×#536×C1312
C2×#421×C1312
C2×#419×C1312
C2×#410×C1312
#2009×C1312
C2×#344×C1312
C2×#2009131