Finite Group Databasebeta

← C131×#32965 #45718849

Subgroups — C131×#32965 #45718849

Order 33536.

1282 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C131C211yesmaximal, characteristic
2C2×#475×C131C211yesmaximal, characteristic, complemented
3C2×#476×C131C211yesmaximal, characteristic, complemented
4#2628×C131C211yesmaximal, characteristic, complemented
5#1865×C131C212yesmaximal, complemented
6#1864×C131C212yesmaximal, complemented
7#1853×C131C212yesmaximal, complemented
8#1805×C131C211yesmaximal, characteristic, complemented
9#1804×C131C211yesmaximal, characteristic, complemented
10#1798×C131C211yesmaximal, characteristic, complemented
11#1788×C131C212yesmaximal
12C22×#41×C131C2211yescharacteristic
13C2×C4⋊Q8×C131C2211yescharacteristic
14#520×C131—24no—
15#520×C131—24no—
16C2×C4×Q8×C131C2211yescharacteristic
17C2×C4×Q8×C131C2211yescharacteristic
18C2×C4×D4×C131—21no—
19C2×C4×D4×C131—21no—
20C2×C4×D4×C131C2211yescharacteristic
21C2×C4×D4×C131C2211yescharacteristic
22C2×#117×C131—21no—
23C2×#117×C131C2211yescharacteristic
24C22×C4⋊C4×C131—21no—
25C22×C4⋊C4×C131C2211yescharacteristic
26#476×C131—24no—
27#475×C131—24no—
28C2×#106×C131C2212yes—
29C2×#106×C131C2212yes—
30C2×C4⋊C8×C131C2211yescharacteristic
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×#103×C131C2212yes—
33C2×#103×C131C2212yes—
34C2×#102×C131C2212yes—
35C2×#102×C131C2212yes—
36C2×C22⋊C8×C131C2212yes—
37#400×C131—21no—
38#399×C131—21no—
39#395×C131—21no—
40#393×C131—21no—
41#389×C131C2212yes—
42#382×C131C2211yescharacteristic
43#380×C131C2212yes—
44#340×C131C2212yes—
45#340×C131C2212yes—
46#336×C131C2212yes—
47C2×#41×C131—22no—
48C2×#41×C131—22no—
49C2×#41×C131—22no—
50C2×#41×C131—22no—
51C2×#41×C131—22no—
52C2×#41×C131Q814yescomplemented
53C22×Q8×C131—21no—
54C22×Q8×C131C2311yescharacteristic
55C22×D4×C131—21no—
56C22×D4×C131C2311yescharacteristic
57C23×C4×C131—21no—
58C23×C4×C131—21no—
59C23×C4×C131—21no—
60C23×C4×C131—21no—
61C23×C4×C131C2311yescharacteristic
62C22×C8×C131C2312yes—
63C22×C8×C131C2312yes—
64C4⋊Q8×C131—22no—
65C4⋊Q8×C131—22no—
66C4×Q8×C131—22no—
67C4×Q8×C131—22no—
68C4×Q8×C131—22no—
69C4×Q8×C131D414yes—
70C4×D4×C131—28no—
71C4×D4×C131—28no—
72C4×D4×C131—22no—
73C4×D4×C131—22no—
74C4×D4×C131—22no—
75C4×D4×C131D414yes—
76#117×C131—28no—
77#117×C131—22no—
78#117×C131—22no—
79C2×C4⋊C4×C131—28no—
80C2×C4⋊C4×C131—21no—
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131—21no—
83C2×C4⋊C4×C131—22no—
84C2×C4⋊C4×C131—22no—
85C2×C4⋊C4×C131—21no—
86C2×C4⋊C4×C131—22no—
87C2×C4⋊C4×C131D411yescharacteristic
88C2×C4⋊C4×C131D411yescharacteristic
89C2×C4⋊C4×C131C2312yes—
90C2×C4⋊C4×C131C2312yes—
91C2×C4⋊C4×C131C2311yescharacteristic
92C2×C4⋊C4×C131C2311yescharacteristic
93C2×C22⋊C4×C131—21no—
94C2×C22⋊C4×C131—21no—
95C2×C22⋊C4×C131—22no—
96C2×C22⋊C4×C131D411yescharacteristic
97C2×C22⋊C4×C131D411yescharacteristic
98C2×C42×C131—21no—
99C2×C42×C131—21no—
100C2×C42×C131C2311yescharacteristic
101C2×C42×C131C2311yescharacteristic
102#106×C131—24no—
103#106×C131—24no—
104C4⋊C8×C131—22no—
105C4⋊C8×C131—22no—
106#103×C131—24no—
107#103×C131—24no—
108#102×C131—24no—
109#102×C131—24no—
110C22⋊C8×C131—24no—
111#95×C131—22no—
112#95×C131—21no—
113#95×C131—22no—
114#95×C131—21no—
115C24×C131—21no—
116C24×C131C2×D411yescharacteristic
117#41×C131—28no—
118#41×C131—28no—
119#41×C131—28no—
120#41×C131—28no—
121C2×Q8×C131—21no—
122C2×Q8×C131—21no—
123C2×Q8×C131—21no—
124C2×Q8×C131—42no—
125C2×Q8×C131—82no—
126C2×Q8×C131C2×D412yes—
127C2×Q8×C131C2×Q812yes—
128C2×Q8×C131#4112yes—
129C2×D4×C131—24no—
130C2×D4×C131—24no—
131C2×D4×C131—24no—
132C2×D4×C131—21no—
133C2×D4×C131—21no—
134C2×D4×C131—21no—
135C2×D4×C131C2×D412yes—
136C2×D4×C131C2×Q812yes—
137C2×D4×C131#4112yes—
138C22×C4×C131—24no—
139C22×C4×C131—24no—
140C22×C4×C131—21no—
141C22×C4×C131—24no—
142C22×C4×C131—21no—
143C22×C4×C131—21no—
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—21no—
147C22×C4×C131—21no—
148C22×C4×C131—24no—
149C22×C4×C131—24no—
150C22×C4×C131—24no—
151C22×C4×C131—22no—
152C22×C4×C131—22no—
153C22×C4×C131—82no—
154C22×C4×C131—82no—
155C22×C4×C131—82no—
156C22×C4×C131C2×D411yescharacteristic
157C22×C4×C131C2×D411yescharacteristic
158C22×C4×C131C2×D411yescharacteristic
159C22×C4×C131C2×D411yescharacteristic
160C22×C4×C131C2×D411yescharacteristic
161C22×C4×C131C2×Q812yes—
162C22×C4×C131#4112yes—
163C22×C4×C131C2411yescharacteristic
164C2×C8×C131—22no—
165C2×C8×C131—22no—
166C2×C8×C131—22no—
167C2×C8×C131—22no—
168C2×C8×C131—22no—
169C2×C8×C131—22no—
170C4⋊C4×C131—24no—
171C4⋊C4×C131—24no—
172C4⋊C4×C131—22no—
173C4⋊C4×C131—24no—
174C4⋊C4×C131—22no—
175C4⋊C4×C131—21no—
176C4⋊C4×C131—21no—
177C4⋊C4×C131—22no—
178C4⋊C4×C131—22no—
179C4⋊C4×C131—22no—
180C4⋊C4×C131—22no—
181C4⋊C4×C131—42no—
182C4⋊C4×C131—82no—
183C4⋊C4×C131C2×D412yes—
184C4⋊C4×C131C2×D412yes—
185C22⋊C4×C131—24no—
186C22⋊C4×C131—24no—
187C22⋊C4×C131—22no—
188C22⋊C4×C131—22no—
189C22⋊C4×C131—82no—
190C42×C131—24no—
191C42×C131—24no—
192C42×C131—21no—
193C42×C131—21no—
194C42×C131C2×D412yes—
195C42×C131C2×D412yes—
196C23×C131—21no—
197C23×C131—22no—
198C23×C131—22no—
199C23×C131—21no—
200C23×C131—22no—
201C23×C131—22no—
202C23×C131—22no—
203C23×C131—42no—
204C23×C131—42no—
205C23×C131C22⋊Q812yes—
206C23×C131C22×D411yescharacteristic
207Q8×C131—22no—
208Q8×C131—22no—
209Q8×C131—22no—
210Q8×C131—84no—
211Q8×C131C22⋊Q814yes—
212D4×C131—216no—
213D4×C131—22no—
214D4×C131—22no—
215D4×C131—22no—
216D4×C131C22⋊Q814yes—
217C2×C4×C131—216no—
218C2×C4×C131—22no—
219C2×C4×C131—21no—
220C2×C4×C131—22no—
221C2×C4×C131—21no—
222C2×C4×C131—22no—
223C2×C4×C131—22no—
224C2×C4×C131—22no—
225C2×C4×C131—22no—
226C2×C4×C131—22no—
227C2×C4×C131—22no—
228C2×C4×C131—22no—
229C2×C4×C131—21no—
230C2×C4×C131—21no—
231C2×C4×C131—22no—
232C2×C4×C131—22no—
233C2×C4×C131—22no—
234C2×C4×C131—22no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—42no—
239C2×C4×C131—42no—
240C2×C4×C131—42no—
241C2×C4×C131—42no—
242C2×C4×C131—42no—
243C2×C4×C131—84no—
244C2×C4×C131—84no—
245C2×C4×C131—84no—
246C2×C4×C131#12012yes—
247C2×C4×C131#12012yes—
248C2×C4×C131C22⋊Q812yes—
249C2×C4×C131C22×D411yescharacteristic
250C2×C4×C131C22×D411yescharacteristic
251C2×C4×C131C22×Q811yescharacteristic
252C2×C4×C131C2×#4111yescharacteristic
253C2×C4×C131C2×#4111yescharacteristic
254C2×C4×C131C2×#4111yescharacteristic
255C8×C131—42no—
256C8×C131—42no—
257C22×C131—24no—
258C22×C131—22no—
259C22×C131—24no—
260C22×C131—44no—
261C22×C131—42no—
262C22×C131—44no—
263C22×C131—41no—
264C22×C131—42no—
265C22×C131—41no—
266C22×C131—42no—
267C22×C131C2×#12011yescharacteristic
268C22×C131C2×C22⋊Q811yescharacteristic
269C22×C131#52511yescharacteristic
270C22×C131#57712yes—
271C22×C131#57712yes—
272C4×C131—22no—
273C4×C131—24no—
274C4×C131—22no—
275C4×C131—22no—
276C4×C131—41no—
277C4×C131—42no—
278C4×C131—42no—
279C4×C131—41no—
280C4×C131—82no—
281C4×C131—82no—
282C4×C131C2×C22⋊Q811yescharacteristic
283C4×C131C2×C22⋊Q811yescharacteristic
284C4×C131#52511yescharacteristic
285C4×C131#52511yescharacteristic
286C2×C131—42no—
287C2×C131—44no—
288C2×C131#284811yescharacteristic
289C2×C131#300911yescharacteristic
290C2×C131#301011yescharacteristic
291C2×C131#308412yes—
292C2×C131#312512yes—
293#32965C13111yesmaximal, characteristic, direct product factor, Sylow
294C131#3296511yescharacteristic, direct product factor, Sylow
295C2×#520C2×C13111yescharacteristic
296C2×#475C2×C13111yescharacteristic, complemented
297C2×#476C2×C13111yescharacteristic, complemented
298#2628C2×C13111yescharacteristic, complemented
299#1865C2×C13112yescomplemented
300#1864C2×C13112yescomplemented
301#1853C2×C13112yescomplemented
302#1805C2×C13111yescharacteristic, complemented
303#1804C2×C13111yescharacteristic, complemented
304#1798C2×C13111yescharacteristic, complemented
305#1788C2×C13112yes—
306C22×#41C22×C13111yescharacteristic
307C2×C4⋊Q8C22×C13111yescharacteristic
308#520—24no—
309#520—24no—
310C2×C4×Q8C22×C13111yescharacteristic
311C2×C4×Q8C22×C13111yescharacteristic
312C2×C4×D4—21no—
313C2×C4×D4—21no—
314C2×C4×D4C22×C13111yescharacteristic
315C2×C4×D4C22×C13111yescharacteristic
316C2×#117—21no—
317C2×#117C22×C13111yescharacteristic
318C22×C4⋊C4—21no—
319C22×C4⋊C4C22×C13111yescharacteristic
320#476—24no—
321#475—24no—
322C2×#106C22×C13112yes—
323C2×#106C22×C13112yes—
324C2×C4⋊C8C22×C13111yescharacteristic
325C2×C4⋊C8C22×C13111yescharacteristic
326C2×#103C22×C13112yes—
327C2×#103C22×C13112yes—
328C2×#102C22×C13112yes—
329C2×#102C22×C13112yes—
330C2×C22⋊C8C22×C13112yes—
331#400—21no—
332#399—21no—
333#395—21no—
334#393—21no—
335#389C22×C13112yes—
336#382C22×C13111yescharacteristic
337#380C22×C13112yes—
338#340C22×C13112yes—
339#340C22×C13112yes—
340#336C22×C13112yes—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41Q8×C13114yescomplemented
347C22×Q8—21no—
348C22×Q8C23×C13111yescharacteristic
349C22×D4—21no—
350C22×D4C23×C13111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C23×C13111yescharacteristic
356C22×C8C23×C13112yes—
357C22×C8C23×C13112yes—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8D4×C13114yes—
364C4×D4—28no—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4D4×C13114yes—
370#117—28no—
371#117—22no—
372#117—22no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4D4×C13111yescharacteristic
382C2×C4⋊C4D4×C13111yescharacteristic
383C2×C4⋊C4C23×C13112yes—
384C2×C4⋊C4C23×C13112yes—
385C2×C4⋊C4C23×C13111yescharacteristic
386C2×C4⋊C4C23×C13111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4D4×C13111yescharacteristic
391C2×C22⋊C4D4×C13111yescharacteristic
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C23×C13111yescharacteristic
395C2×C42C23×C13111yescharacteristic
396#106—24no—
397#106—24no—
398C4⋊C8—22no—
399C4⋊C8—22no—
400#103—24no—
401#103—24no—
402#102—24no—
403#102—24no—
404C22⋊C8—24no—
405#95—22no—
406#95—21no—
407#95—21no—
408#95—22no—
409C24—21no—
410C24C2×D4×C13111yescharacteristic
411#41—28no—
412#41—28no—
413#41—28no—
414#41—28no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—42no—
419C2×Q8—82no—
420C2×Q8C2×D4×C13112yes—
421C2×Q8C2×Q8×C13112yes—
422C2×Q8#41×C13112yes—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4C2×D4×C13112yes—
430C2×D4C2×Q8×C13112yes—
431C2×D4#41×C13112yes—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—82no—
448C22×C4—82no—
449C22×C4—82no—
450C22×C4C2×D4×C13111yescharacteristic
451C22×C4C2×D4×C13111yescharacteristic
452C22×C4C2×D4×C13111yescharacteristic
453C22×C4C2×D4×C13111yescharacteristic
454C22×C4C2×D4×C13111yescharacteristic
455C22×C4C2×Q8×C13112yes—
456C22×C4#41×C13112yes—
457C22×C4C24×C13111yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—42no—
476C4⋊C4—82no—
477C4⋊C4C2×D4×C13112yes—
478C4⋊C4C2×D4×C13112yes—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—82no—
484C42—24no—
485C42—24no—
486C42—21no—
487C42—21no—
488C42C2×D4×C13112yes—
489C42C2×D4×C13112yes—
490C23—21no—
491C23—22no—
492C23—22no—
493C23—21no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23C22⋊Q8×C13112yes—
500C23C22×D4×C13111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—22no—
504Q8—84no—
505Q8C22⋊Q8×C13114yes—
506D4—216no—
507D4—22no—
508D4—22no—
509D4—22no—
510D4C22⋊Q8×C13114yes—
511C2×C4—216no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4#120×C13112yes—
541C2×C4#120×C13112yes—
542C2×C4C22⋊Q8×C13112yes—
543C2×C4C22×D4×C13111yescharacteristic
544C2×C4C22×D4×C13111yescharacteristic
545C2×C4C22×Q8×C13111yescharacteristic
546C2×C4C2×#41×C13111yescharacteristic
547C2×C4C2×#41×C13111yescharacteristic
548C2×C4C2×#41×C13111yescharacteristic
549C8—42no—
550C8—42no—
551C22—24no—
552C22—22no—
553C22—24no—
554C22—41no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—44no—
561C22C2×#120×C13111yescharacteristic
562C22C2×C22⋊Q8×C13111yescharacteristic
563C22#525×C13111yescharacteristic
564C22#577×C13112yes—
565C22#577×C13112yes—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—24no—
570C4—41no—
571C4—42no—
572C4—42no—
573C4—41no—
574C4—82no—
575C4—82no—
576C4C2×C22⋊Q8×C13111yescharacteristic
577C4C2×C22⋊Q8×C13111yescharacteristic
578C4#525×C13111yescharacteristic
579C4#525×C13111yescharacteristic
580C2—42no—
581C2—44no—
582C2#2848×C13111yescharacteristic
583C2#3009×C13111yescharacteristic
584C2#3010×C13111yescharacteristic
585C2#3084×C13112yes—
586C2#3125×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×#41×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#475×C131C2semidirect
3. C2×#476×C131C2semidirect
4. #2628×C131C2semidirect
5. #1865×C131C2semidirect
6. #1864×C131C2semidirect
7. #1853×C131C2semidirect
8. #1805×C131C2semidirect
9. #1804×C131C2semidirect
10. #1798×C131C2semidirect
52. C2×#41×C131Q8semidirect
293. #32965C131direct (N × H)
294. C131#32965direct (N × H)
296. C2×#475C2×C131semidirect
297. C2×#476C2×C131semidirect
298. #2628C2×C131semidirect
299. #1865C2×C131semidirect
300. #1864C2×C131semidirect
301. #1853C2×C131semidirect
302. #1805C2×C131semidirect
303. #1804C2×C131semidirect
304. #1798C2×C131semidirect
346. C2×#41Q8×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1312
C2×#475×C1312
C2×#476×C1312
#2628×C1312
#1865×C1312
#1864×C1312
#1853×C1312
#1805×C1312
#1804×C1312
#1798×C1312
#1788×C1312
#32965131