Finite Group Databasebeta

← C131×#29698 #45715582

Subgroups — C131×#29698 #45715582

Order 33536.

1076 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C131C211yesmaximal, characteristic
2C2×#476×C131C211yesmaximal, characteristic, complemented
3C2×#474×C131C211yesmaximal, characteristic, complemented
4#2628×C131C211yesmaximal, characteristic, complemented
5#2059×C131C212yesmaximal, complemented
6#2041×C131C212yesmaximal, complemented
7#2034×C131C212yesmaximal, complemented
8#2033×C131C212yesmaximal, complemented
9#1804×C131C211yesmaximal, characteristic, complemented
10#1804×C131C211yesmaximal, characteristic, complemented
11#1798×C131C211yesmaximal, characteristic, complemented
12#540×C131—24no—
13#540×C131—24no—
14C2×C4⋊Q8×C131C2211yescharacteristic
15C2×#127×C131C2211yescharacteristic
16C2×#125×C131C2211yescharacteristic
17C2×#123×C131—21no—
18C2×#123×C131—21no—
19C2×#121×C131—21no—
20C2×#121×C131—21no—
21C2×#121×C131C2211yescharacteristic
22C2×#121×C131C2211yescharacteristic
23C2×C4×D4×C131C2211yescharacteristic
24C2×C4×D4×C131C2211yescharacteristic
25C2×#117×C131C2211yescharacteristic
26#476×C131—24no—
27#474×C131—24no—
28C2×#107×C131C2212yes—
29C2×#106×C131C2212yes—
30C2×C4⋊C8×C131C2211yescharacteristic
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×#102×C131C2212yes—
33C2×#102×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—
47C22×Q8×C131—21no—
48C22×D4×C131—21no—
49C22×D4×C131—21no—
50C22×D4×C131—21no—
51C22×D4×C131—21no—
52C22×D4×C131C2311yescharacteristic
53C22×D4×C131C2311yescharacteristic
54C23×C4×C131—21no—
55C23×C4×C131—21no—
56C23×C4×C131C2311yescharacteristic
57C22×C8×C131C2312yes—
58C22×C8×C131C2312yes—
59C4⋊Q8×C131—22no—
60C4⋊Q8×C131—22no—
61#127×C131—22no—
62#127×C131—22no—
63#125×C131—22no—
64#125×C131—22no—
65#123×C131—28no—
66#123×C131—28no—
67#121×C131—28no—
68#121×C131—28no—
69#121×C131—22no—
70#121×C131—22no—
71#121×C131—22no—
72#121×C131—22no—
73C4×D4×C131—22no—
74C4×D4×C131—22no—
75C4×D4×C131D414yes—
76C4×D4×C131D414yes—
77#117×C131—22no—
78#117×C131—22no—
79C2×C4⋊C4×C131—21no—
80C2×C4⋊C4×C131—21no—
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131D411yescharacteristic
84C2×C4⋊C4×C131D411yescharacteristic
85C2×C4⋊C4×C131C2312yes—
86C2×C4⋊C4×C131C2312yes—
87C2×C4⋊C4×C131C2311yescharacteristic
88C2×C4⋊C4×C131C2311yescharacteristic
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—21no—
91C2×C22⋊C4×C131—21no—
92C2×C22⋊C4×C131—21no—
93C2×C22⋊C4×C131—22no—
94C2×C22⋊C4×C131D411yescharacteristic
95C2×C22⋊C4×C131D411yescharacteristic
96C2×C42×C131C2311yescharacteristic
97C2×C42×C131C2311yescharacteristic
98#107×C131—24no—
99#106×C131—24no—
100C4⋊C8×C131—22no—
101C4⋊C8×C131—22no—
102#102×C131—24no—
103#102×C131—24no—
104#102×C131—42no—
105#102×C131—42no—
106C22⋊C8×C131—42no—
107#95×C131—22no—
108#95×C131—21no—
109#95×C131—22no—
110#95×C131—21no—
111C24×C131—21no—
112C24×C131—21no—
113C24×C131C2×D411yescharacteristic
114C2×Q8×C131—42no—
115C2×Q8×C131—82no—
116C2×D4×C131—24no—
117C2×D4×C131—24no—
118C2×D4×C131—24no—
119C2×D4×C131—24no—
120C2×D4×C131—21no—
121C2×D4×C131—21no—
122C2×D4×C131—21no—
123C2×D4×C131—21no—
124C2×D4×C131—21no—
125C2×D4×C131—21no—
126C2×D4×C131—21no—
127C2×D4×C131—21no—
128C2×D4×C131—21no—
129C2×D4×C131—21no—
130C2×D4×C131—82no—
131C2×D4×C131—82no—
132C2×D4×C131—82no—
133C2×D4×C131—82no—
134C2×D4×C131C2×D412yes—
135C2×D4×C131C2×D412yes—
136C22×C4×C131—21no—
137C22×C4×C131—21no—
138C22×C4×C131—21no—
139C22×C4×C131—21no—
140C22×C4×C131—21no—
141C22×C4×C131—21no—
142C22×C4×C131—21no—
143C22×C4×C131—21no—
144C22×C4×C131—24no—
145C22×C4×C131—24no—
146C22×C4×C131—22no—
147C22×C4×C131—22no—
148C22×C4×C131—82no—
149C22×C4×C131—82no—
150C22×C4×C131C2×D411yescharacteristic
151C22×C4×C131C2×D411yescharacteristic
152C22×C4×C131C2×D411yescharacteristic
153C22×C4×C131C2×D411yescharacteristic
154C22×C4×C131C2×D411yescharacteristic
155C22×C4×C131C2411yescharacteristic
156C2×C8×C131—22no—
157C2×C8×C131—22no—
158C2×C8×C131—22no—
159C2×C8×C131—22no—
160C2×C8×C131—22no—
161C2×C8×C131—22no—
162C4⋊C4×C131—24no—
163C4⋊C4×C131—24no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131—22no—
166C4⋊C4×C131—21no—
167C4⋊C4×C131—21no—
168C4⋊C4×C131—22no—
169C4⋊C4×C131—22no—
170C4⋊C4×C131—22no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—42no—
173C4⋊C4×C131—82no—
174C4⋊C4×C131C2×D412yes—
175C4⋊C4×C131C2×D412yes—
176C22⋊C4×C131—24no—
177C22⋊C4×C131—24no—
178C22⋊C4×C131—24no—
179C22⋊C4×C131—24no—
180C22⋊C4×C131—22no—
181C22⋊C4×C131—22no—
182C22⋊C4×C131—82no—
183C42×C131—21no—
184C42×C131—21no—
185C42×C131C2×D412yes—
186C42×C131C2×D412yes—
187C23×C131—21no—
188C23×C131—22no—
189C23×C131—22no—
190C23×C131—21no—
191C23×C131—21no—
192C23×C131—22no—
193C23×C131—22no—
194C23×C131—41no—
195C23×C131—41no—
196C23×C131—41no—
197C23×C131—41no—
198C23×C131—42no—
199C23×C131—42no—
200C23×C131—42no—
201C23×C131—42no—
202C23×C131C22×D411yescharacteristic
203Q8×C131—84no—
204D4×C131—22no—
205D4×C131—22no—
206D4×C131—22no—
207D4×C131—22no—
208D4×C131—41no—
209D4×C131—41no—
210D4×C131—41no—
211D4×C131—41no—
212D4×C131—84no—
213D4×C131—84no—
214D4×C131—84no—
215D4×C131—84no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—21no—
219C2×C4×C131—21no—
220C2×C4×C131—21no—
221C2×C4×C131—22no—
222C2×C4×C131—22no—
223C2×C4×C131—21no—
224C2×C4×C131—21no—
225C2×C4×C131—22no—
226C2×C4×C131—22no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—41no—
230C2×C4×C131—41no—
231C2×C4×C131—41no—
232C2×C4×C131—41no—
233C2×C4×C131—42no—
234C2×C4×C131—42no—
235C2×C4×C131—42no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—42no—
239C2×C4×C131—84no—
240C2×C4×C131—84no—
241C2×C4×C131#12012yes—
242C2×C4×C131#12012yes—
243C2×C4×C131C22×D411yescharacteristic
244C2×C4×C131C22×D411yescharacteristic
245C2×C4×C131H(5,𝔽2)11yescharacteristic
246C2×C4×C1312−1+411yescharacteristic
247C2×C4×C1312−1+411yescharacteristic
248C2×C4×C1312−1+411yescharacteristic
249C8×C131—42no—
250C8×C131—42no—
251C22×C131—41no—
252C22×C131—42no—
253C22×C131—42no—
254C22×C131—42no—
255C22×C131—42no—
256C22×C131—42no—
257C22×C131—41no—
258C22×C131—42no—
259C22×C131—42no—
260C22×C131—41no—
261C22×C131—42no—
262C22×C131—82no—
263C22×C131—82no—
264C22×C131—82no—
265C22×C131—82no—
266C22×C131C2×#12011yescharacteristic
267C22×C131#53611yescharacteristic
268C22×C131#53711yescharacteristic
269C22×C131#57612yes—
270C22×C131#57712yes—
271C4×C131—22no—
272C4×C131—22no—
273C4×C131—41no—
274C4×C131—41no—
275C4×C131—42no—
276C4×C131—41no—
277C4×C131—42no—
278C4×C131—82no—
279C4×C131—82no—
280C4×C131#53611yescharacteristic
281C4×C131#53611yescharacteristic
282C4×C131#53711yescharacteristic
283C4×C131#53711yescharacteristic
284C2×C131—81no—
285C2×C131—82no—
286C2×C131—82no—
287C2×C131#261611yescharacteristic
288C2×C131#300811yescharacteristic
289C2×C131#300911yescharacteristic
290C2×C131#324112yes—
291C2×C131#325712yes—
292#29698C13111yesmaximal, characteristic, direct product factor, Sylow
293C131#2969811yescharacteristic, direct product factor, Sylow
294C2×#540C2×C13111yescharacteristic
295C2×#476C2×C13111yescharacteristic, complemented
296C2×#474C2×C13111yescharacteristic, complemented
297#2628C2×C13111yescharacteristic, complemented
298#2059C2×C13112yescomplemented
299#2041C2×C13112yescomplemented
300#2034C2×C13112yescomplemented
301#2033C2×C13112yescomplemented
302#1804C2×C13111yescharacteristic, complemented
303#1804C2×C13111yescharacteristic, complemented
304#1798C2×C13111yescharacteristic, complemented
305#540—24no—
306#540—24no—
307C2×C4⋊Q8C22×C13111yescharacteristic
308C2×#127C22×C13111yescharacteristic
309C2×#125C22×C13111yescharacteristic
310C2×#123—21no—
311C2×#123—21no—
312C2×#121—21no—
313C2×#121—21no—
314C2×#121C22×C13111yescharacteristic
315C2×#121C22×C13111yescharacteristic
316C2×C4×D4C22×C13111yescharacteristic
317C2×C4×D4C22×C13111yescharacteristic
318C2×#117C22×C13111yescharacteristic
319#476—24no—
320#474—24no—
321C2×#107C22×C13112yes—
322C2×#106C22×C13112yes—
323C2×C4⋊C8C22×C13111yescharacteristic
324C2×C4⋊C8C22×C13111yescharacteristic
325C2×#102C22×C13112yes—
326C2×#102C22×C13112yes—
327C2×#102C22×C13112yes—
328C2×#102C22×C13112yes—
329C2×C22⋊C8C22×C13112yes—
330#400—21no—
331#399—21no—
332#395—21no—
333#393—21no—
334#389C22×C13112yes—
335#382C22×C13111yescharacteristic
336#380C22×C13112yes—
337#340C22×C13112yes—
338#340C22×C13112yes—
339#336C22×C13112yes—
340C22×Q8—21no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4C23×C13111yescharacteristic
346C22×D4C23×C13111yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4C23×C13111yescharacteristic
350C22×C8C23×C13112yes—
351C22×C8C23×C13112yes—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354#127—22no—
355#127—22no—
356#125—22no—
357#125—22no—
358#123—28no—
359#123—28no—
360#121—28no—
361#121—28no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4D4×C13114yes—
369C4×D4D4×C13114yes—
370#117—22no—
371#117—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4D4×C13111yescharacteristic
377C2×C4⋊C4D4×C13111yescharacteristic
378C2×C4⋊C4C23×C13112yes—
379C2×C4⋊C4C23×C13112yes—
380C2×C4⋊C4C23×C13111yescharacteristic
381C2×C4⋊C4C23×C13111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4D4×C13111yescharacteristic
388C2×C22⋊C4D4×C13111yescharacteristic
389C2×C42C23×C13111yescharacteristic
390C2×C42C23×C13111yescharacteristic
391#107—24no—
392#106—24no—
393C4⋊C8—22no—
394C4⋊C8—22no—
395#102—24no—
396#102—24no—
397#102—42no—
398#102—42no—
399C22⋊C8—42no—
400#95—22no—
401#95—21no—
402#95—21no—
403#95—22no—
404C24—21no—
405C24—21no—
406C24C2×D4×C13111yescharacteristic
407C2×Q8—42no—
408C2×Q8—82no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4—82no—
427C2×D4C2×D4×C13112yes—
428C2×D4C2×D4×C13112yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—82no—
442C22×C4—82no—
443C22×C4C2×D4×C13111yescharacteristic
444C22×C4C2×D4×C13111yescharacteristic
445C22×C4C2×D4×C13111yescharacteristic
446C22×C4C2×D4×C13111yescharacteristic
447C22×C4C2×D4×C13111yescharacteristic
448C22×C4C24×C13111yescharacteristic
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—42no—
466C4⋊C4—82no—
467C4⋊C4C2×D4×C13112yes—
468C4⋊C4C2×D4×C13112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—82no—
476C42—21no—
477C42—21no—
478C42C2×D4×C13112yes—
479C42C2×D4×C13112yes—
480C23—21no—
481C23—22no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—22no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23C22×D4×C13111yescharacteristic
496Q8—84no—
497D4—22no—
498D4—22no—
499D4—22no—
500D4—22no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—84no—
506D4—84no—
507D4—84no—
508D4—84no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—84no—
533C2×C4—84no—
534C2×C4#120×C13112yes—
535C2×C4#120×C13112yes—
536C2×C4C22×D4×C13111yescharacteristic
537C2×C4C22×D4×C13111yescharacteristic
538C2×C4H(5,𝔽2)×C13111yescharacteristic
539C2×C42−1+4×C13111yescharacteristic
540C2×C42−1+4×C13111yescharacteristic
541C2×C42−1+4×C13111yescharacteristic
542C8—42no—
543C8—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22C2×#120×C13111yescharacteristic
560C22#536×C13111yescharacteristic
561C22#537×C13111yescharacteristic
562C22#576×C13112yes—
563C22#577×C13112yes—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—82no—
572C4—82no—
573C4#536×C13111yescharacteristic
574C4#536×C13111yescharacteristic
575C4#537×C13111yescharacteristic
576C4#537×C13111yescharacteristic
577C2—81no—
578C2—82no—
579C2—82no—
580C2#2616×C13111yescharacteristic
581C2#3008×C13111yescharacteristic
582C2#3009×C13111yescharacteristic
583C2#3241×C13112yes—
584C2#3257×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#540×C131C2
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×#476×C131C2semidirect
3. C2×#474×C131C2semidirect
4. #2628×C131C2semidirect
5. #2059×C131C2semidirect
6. #2041×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #1804×C131C2semidirect
10. #1804×C131C2semidirect
11. #1798×C131C2semidirect
292. #29698C131direct (N × H)
293. C131#29698direct (N × H)
295. C2×#476C2×C131semidirect
296. C2×#474C2×C131semidirect
297. #2628C2×C131semidirect
298. #2059C2×C131semidirect
299. #2041C2×C131semidirect
300. #2034C2×C131semidirect
301. #2033C2×C131semidirect
302. #1804C2×C131semidirect
303. #1804C2×C131semidirect
304. #1798C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1312
C2×#476×C1312
C2×#474×C1312
#2628×C1312
#2059×C1312
#2041×C1312
#2034×C1312
#2033×C1312
#1804×C1312
#1798×C1312
#29698131