Finite Group Databasebeta

← C131×#18591 #45704475

Subgroups — C131×#18591 #45704475

Order 33536.

894 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C131C211yesmaximal, characteristic
2#3255×C131C211yesmaximal, characteristic, complemented
3#3165×C131C211yesmaximal, characteristic, complemented
4#3107×C131C211yesmaximal, characteristic
5#1653×C131C212yesmaximal, complemented
6#1651×C131C212yesmaximal, complemented
7#1649×C131C212yesmaximal, complemented
8#1648×C131C212yesmaximal, complemented
9#1546×C131C211yesmaximal, characteristic, complemented
10#1489×C131C211yesmaximal, characteristic
11#1485×C131C211yesmaximal, characteristic, complemented
12Q82×C131—21no—
13#557×C131C2212yes—
14#554×C131—21no—
15#554×C131—22no—
16D4×Q8×C131—22no—
17D4×Q8×C131C2212yes—
18#544×C131—22no—
19#544×C131—21no—
20#533×C131—21no—
21#533×C131C2211yescharacteristic
22#533×C131C2211yescharacteristic
23C2×C4⋊Q8×C131—21no—
24C2×C4⋊Q8×C131C2211yescharacteristic
25#520×C131—21no—
26C4×#41×C131C2211yescharacteristic
27#501×C131—22no—
28#500×C131C2212yes—
29#498×C131C2212yes—
30#485×C131—21no—
31#475×C131—21no—
32#475×C131C2212yes—
33#475×C131C2211yescharacteristic
34#474×C131C2211yescharacteristic
35#470×C131—22no—
36#462×C131—21no—
37#462×C131C2212yes—
38#462×C131C2211yescharacteristic
39#461×C131C2211yescharacteristic
40#452×C131—21no—
41C4×Q16×C131—21no—
42C4×SD16×C131—21no—
43#431×C131C2211yescharacteristic
44#428×C131—22no—
45#423×C131C2211yescharacteristic
46C4×M16×C131C2211yescharacteristic
47#332×C131C2212yes—
48#332×C131C2212yes—
49Q8⋊C8×C131C2212yes—
50Q8⋊C8×C131C2212yes—
51Q8⋊C8×C131C2212yes—
52D4⋊C8×C131C2212yes—
53C2×#41×C131D411yescharacteristic
54C22×Q8×C131—22no—
55C22×Q8×C131—21no—
56C2×Q16×C131—21no—
57C2×Q16×C131—22no—
58C2×SD16×C131—21no—
59C2×M16×C131—21no—
60C2×M16×C131—21no—
61C4⋊Q8×C131—22no—
62C4⋊Q8×C131—22no—
63C4⋊Q8×C131—24no—
64C4⋊Q8×C131—22no—
65C4⋊Q8×C131—22no—
66C4⋊Q8×C131—21no—
67C4⋊Q8×C131—21no—
68C4⋊Q8×C131D411yescharacteristic
69C4⋊Q8×C131D411yescharacteristic
70C4⋊Q8×C131D412yes—
71C4⋊Q8×C131C2311yescharacteristic
72C4⋊Q8×C131C2311yescharacteristic
73C4⋊Q8×C131C2312yes—
74#125×C131—22no—
75#125×C131—24no—
76#125×C131—22no—
77#125×C131—21no—
78#125×C131—21no—
79C22⋊Q8×C131—22no—
80C22⋊Q8×C131—24no—
81C22⋊Q8×C131—24no—
82C22⋊Q8×C131—21no—
83C22⋊Q8×C131—22no—
84C22⋊Q8×C131—24no—
85C22⋊Q8×C131—21no—
86C22⋊Q8×C131—21no—
87C22⋊Q8×C131D412yes—
88C4×Q8×C131—22no—
89C4×Q8×C131—22no—
90C4×Q8×C131—22no—
91C4×Q8×C131—21no—
92C4×Q8×C131—21no—
93C4×Q8×C131—21no—
94C4×Q8×C131D411yescharacteristic
95C4×Q8×C131C2311yescharacteristic
96C4×Q8×C131C2312yes—
97C4×D4×C131—24no—
98C4×D4×C131—22no—
99C4×D4×C131—21no—
100C4×D4×C131—21no—
101C4×D4×C131D411yescharacteristic
102C4×D4×C131C2311yescharacteristic
103#117×C131—22no—
104#117×C131—21no—
105#117×C131—21no—
106#117×C131—21no—
107#117×C131D411yescharacteristic
108C2×C4⋊C4×C131—22no—
109C2×C4⋊C4×C131—22no—
110C2×C4⋊C4×C131—21no—
111C2×C4⋊C4×C131D412yes—
112C2×C42×C131—21no—
113C2×C42×C131C2311yescharacteristic
114#107×C131—24no—
115#107×C131—21no—
116#106×C131—24no—
117#106×C131—21no—
118#106×C131—22no—
119C4⋊C8×C131—21no—
120C4⋊C8×C131C2312yes—
121C4⋊C8×C131C2311yescharacteristic
122C4⋊C8×C131C2311yescharacteristic
123#103×C131—21no—
124#103×C131—22no—
125#103×C131—21no—
126#103×C131—21no—
127#103×C131—22no—
128#102×C131—21no—
129C22⋊C8×C131—21no—
130#97×C131—21no—
131C4×C8×C131—21no—
132C4×C8×C131C2312yes—
133#41×C131—22no—
134#41×C131—22no—
135C2×Q8×C131—24no—
136C2×Q8×C131—21no—
137C2×Q8×C131—22no—
138C2×Q8×C131—22no—
139C2×Q8×C131—21no—
140C2×Q8×C131—21no—
141C2×Q8×C131—81no—
142C2×Q8×C131—81no—
143C2×Q8×C131—82no—
144C2×Q8×C131—82no—
145C2×Q8×C131C2×D412yes—
146C2×Q8×C131C2×D411yescharacteristic
147C2×D4×C131—21no—
148C2×D4×C131C2×D411yescharacteristic
149C22×C4×C131—21no—
150C22×C4×C131—24no—
151C22×C4×C131—22no—
152C22×C4×C131—21no—
153C22×C4×C131—21no—
154C22×C4×C131C2×D411yescharacteristic
155C22×C4×C131C2×D411yescharacteristic
156C22×C4×C131C2×D411yescharacteristic
157Q16×C131—42no—
158Q16×C131—82no—
159SD16×C131—42no—
160M16×C131—24no—
161M16×C131—81no—
162C2×C8×C131—22no—
163C2×C8×C131—21no—
164C2×C8×C131—21no—
165C2×C8×C131—22no—
166C4⋊C4×C131—24no—
167C4⋊C4×C131—24no—
168C4⋊C4×C131—24no—
169C4⋊C4×C131—24no—
170C4⋊C4×C131—21no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—21no—
173C4⋊C4×C131—22no—
174C4⋊C4×C131—21no—
175C4⋊C4×C131—21no—
176C4⋊C4×C131—22no—
177C4⋊C4×C131—22no—
178C4⋊C4×C131—21no—
179C4⋊C4×C131—22no—
180C4⋊C4×C131—21no—
181C4⋊C4×C131—21no—
182C4⋊C4×C131—21no—
183C4⋊C4×C131—21no—
184C4⋊C4×C131—41no—
185C4⋊C4×C131—41no—
186C4⋊C4×C131C2×D411yescharacteristic
187C4⋊C4×C131C2×D412yes—
188C4⋊C4×C131C2×D411yescharacteristic
189C4⋊C4×C131C2×D414yes—
190C22⋊C4×C131—24no—
191C22⋊C4×C131—22no—
192C22⋊C4×C131—21no—
193C22⋊C4×C131—21no—
194C22⋊C4×C131—21no—
195C22⋊C4×C131—41no—
196C42×C131—24no—
197C42×C131—21no—
198C42×C131—21no—
199C42×C131—21no—
200C42×C131—22no—
201C42×C131—41no—
202C42×C131C2×D411yescharacteristic
203C42×C131C2×D411yescharacteristic
204C42×C131C2×D411yescharacteristic
205C42×C131C2411yescharacteristic
206C23×C131—21no—
207C23×C131#12011yescharacteristic
208Q8×C131—21no—
209Q8×C131—22no—
210Q8×C131—22no—
211Q8×C131—42no—
212Q8×C131—42no—
213Q8×C131—42no—
214Q8×C131—41no—
215Q8×C131—41no—
216Q8×C131—41no—
217Q8×C131—41no—
218Q8×C131—82no—
219Q8×C131—84no—
220Q8×C131#13712yes—
221D4×C131—24no—
222D4×C131—21no—
223D4×C131#13712yes—
224C2×C4×C131—24no—
225C2×C4×C131—21no—
226C2×C4×C131—21no—
227C2×C4×C131—21no—
228C2×C4×C131—21no—
229C2×C4×C131—21no—
230C2×C4×C131—22no—
231C2×C4×C131—22no—
232C2×C4×C131—21no—
233C2×C4×C131—21no—
234C2×C4×C131—22no—
235C2×C4×C131—24no—
236C2×C4×C131—41no—
237C2×C4×C131—41no—
238C2×C4×C131—42no—
239C2×C4×C131—41no—
240C2×C4×C131—41no—
241C2×C4×C131—82no—
242C2×C4×C131—84no—
243C2×C4×C131#12011yescharacteristic
244C2×C4×C131#12011yescharacteristic
245C2×C4×C131#12011yescharacteristic
246C2×C4×C131C22×D411yescharacteristic
247C2×C4×C131C22×D411yescharacteristic
248C2×C4×C131C22×D411yescharacteristic
249C8×C131—24no—
250C8×C131—41no—
251C8×C131—41no—
252C8×C131—42no—
253C22×C131—21no—
254C22×C131—22no—
255C22×C131—21no—
256C22×C131—21no—
257C22×C131—41no—
258C22×C131—41no—
259C22×C131C2×#12011yescharacteristic
260C4×C131—21no—
261C4×C131—22no—
262C4×C131—21no—
263C4×C131—21no—
264C4×C131—41no—
265C4×C131—42no—
266C4×C131—44no—
267C4×C131—41no—
268C4×C131—42no—
269C4×C131—81no—
270C4×C131—81no—
271C4×C131#45612yes—
272C4×C131C2×#13711yescharacteristic
273C4×C131C2×#13711yescharacteristic
274C4×C131#57611yescharacteristic
275C4×C131#57711yescharacteristic
276C2×C131—41no—
277C2×C131—42no—
278C2×C131#300411yescharacteristic
279C2×C131#301211yescharacteristic
280C2×C131C2×#45611yescharacteristic
281#18591C13111yesmaximal, characteristic, direct product factor, Sylow
282C131#1859111yescharacteristic, direct product factor, Sylow
283#3503C2×C13111yescharacteristic
284#3255C2×C13111yescharacteristic, complemented
285#3165C2×C13111yescharacteristic, complemented
286#3107C2×C13111yescharacteristic
287#1653C2×C13112yescomplemented
288#1651C2×C13112yescomplemented
289#1649C2×C13112yescomplemented
290#1648C2×C13112yescomplemented
291#1546C2×C13111yescharacteristic, complemented
292#1489C2×C13111yescharacteristic
293#1485C2×C13111yescharacteristic, complemented
294Q82—21no—
295#557C22×C13112yes—
296#554—21no—
297#554—22no—
298D4×Q8—22no—
299D4×Q8C22×C13112yes—
300#544—22no—
301#544—21no—
302#533—21no—
303#533C22×C13111yescharacteristic
304#533C22×C13111yescharacteristic
305C2×C4⋊Q8—21no—
306C2×C4⋊Q8C22×C13111yescharacteristic
307#520—21no—
308C4×#41C22×C13111yescharacteristic
309#501—22no—
310#500C22×C13112yes—
311#498C22×C13112yes—
312#485—21no—
313#475—21no—
314#475C22×C13111yescharacteristic
315#475C22×C13112yes—
316#474C22×C13111yescharacteristic
317#470—22no—
318#462—21no—
319#462C22×C13111yescharacteristic
320#462C22×C13112yes—
321#461C22×C13111yescharacteristic
322#452—21no—
323C4×Q16—21no—
324C4×SD16—21no—
325#431C22×C13111yescharacteristic
326#428—22no—
327#423C22×C13111yescharacteristic
328C4×M16C22×C13111yescharacteristic
329#332C22×C13112yes—
330#332C22×C13112yes—
331Q8⋊C8C22×C13112yes—
332Q8⋊C8C22×C13112yes—
333Q8⋊C8C22×C13112yes—
334D4⋊C8C22×C13112yes—
335C2×#41D4×C13111yescharacteristic
336C22×Q8—22no—
337C22×Q8—21no—
338C2×Q16—21no—
339C2×Q16—22no—
340C2×SD16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—24no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8D4×C13111yescharacteristic
351C4⋊Q8D4×C13112yes—
352C4⋊Q8D4×C13111yescharacteristic
353C4⋊Q8C23×C13111yescharacteristic
354C4⋊Q8C23×C13111yescharacteristic
355C4⋊Q8C23×C13112yes—
356#125—22no—
357#125—24no—
358#125—22no—
359#125—21no—
360#125—21no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364C22⋊Q8—21no—
365C22⋊Q8—22no—
366C22⋊Q8—24no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8D4×C13112yes—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8D4×C13111yescharacteristic
377C4×Q8C23×C13111yescharacteristic
378C4×Q8C23×C13112yes—
379C4×D4—24no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4D4×C13111yescharacteristic
384C4×D4C23×C13111yescharacteristic
385#117—22no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117D4×C13111yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4D4×C13112yes—
394C2×C42—21no—
395C2×C42C23×C13111yescharacteristic
396#107—24no—
397#107—21no—
398#106—24no—
399#106—21no—
400#106—22no—
401C4⋊C8—21no—
402C4⋊C8C23×C13112yes—
403C4⋊C8C23×C13111yescharacteristic
404C4⋊C8C23×C13111yescharacteristic
405#103—21no—
406#103—22no—
407#103—21no—
408#103—21no—
409#103—22no—
410#102—21no—
411C22⋊C8—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8C23×C13112yes—
415#41—22no—
416#41—22no—
417C2×Q8—24no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—81no—
424C2×Q8—81no—
425C2×Q8—82no—
426C2×Q8—82no—
427C2×Q8C2×D4×C13112yes—
428C2×Q8C2×D4×C13111yescharacteristic
429C2×D4—21no—
430C2×D4C2×D4×C13111yescharacteristic
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D4×C13111yescharacteristic
437C22×C4C2×D4×C13111yescharacteristic
438C22×C4C2×D4×C13111yescharacteristic
439Q16—42no—
440Q16—82no—
441SD16—42no—
442M16—24no—
443M16—81no—
444C2×C8—22no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—22no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C13111yescharacteristic
469C4⋊C4C2×D4×C13112yes—
470C4⋊C4C2×D4×C13111yescharacteristic
471C4⋊C4C2×D4×C13114yes—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C42—24no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—22no—
483C42—41no—
484C42C2×D4×C13111yescharacteristic
485C42C2×D4×C13111yescharacteristic
486C42C2×D4×C13111yescharacteristic
487C42C24×C13111yescharacteristic
488C23—21no—
489C23#120×C13111yescharacteristic
490Q8—21no—
491Q8—22no—
492Q8—22no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—82no—
501Q8—84no—
502Q8#137×C13112yes—
503D4—24no—
504D4—21no—
505D4#137×C13112yes—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—84no—
525C2×C4#120×C13111yescharacteristic
526C2×C4#120×C13111yescharacteristic
527C2×C4#120×C13111yescharacteristic
528C2×C4C22×D4×C13111yescharacteristic
529C2×C4C22×D4×C13111yescharacteristic
530C2×C4C22×D4×C13111yescharacteristic
531C8—24no—
532C8—41no—
533C8—41no—
534C8—42no—
535C22—21no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22C2×#120×C13111yescharacteristic
542C4—21no—
543C4—22no—
544C4—21no—
545C4—21no—
546C4—41no—
547C4—42no—
548C4—44no—
549C4—41no—
550C4—42no—
551C4—81no—
552C4—81no—
553C4#456×C13112yes—
554C4C2×#137×C13111yescharacteristic
555C4C2×#137×C13111yescharacteristic
556C4#576×C13111yescharacteristic
557C4#577×C13111yescharacteristic
558C2—41no—
559C2—42no—
560C2#3004×C13111yescharacteristic
561C2#3012×C13111yescharacteristic
562C2C2×#456×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC42C24×C131
prime radicalC2×#41×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3255×C131C2semidirect
3. #3165×C131C2semidirect
5. #1653×C131C2semidirect
6. #1651×C131C2semidirect
7. #1649×C131C2semidirect
8. #1648×C131C2semidirect
9. #1546×C131C2semidirect
11. #1485×C131C2semidirect
281. #18591C131direct (N × H)
282. C131#18591direct (N × H)
284. #3255C2×C131semidirect
285. #3165C2×C131semidirect
287. #1653C2×C131semidirect
288. #1651C2×C131semidirect
289. #1649C2×C131semidirect
290. #1648C2×C131semidirect
291. #1546C2×C131semidirect
293. #1485C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3503×C1312
#3255×C1312
#3165×C1312
#3107×C1312
#1653×C1312
#1651×C1312
#1649×C1312
#1648×C1312
#1546×C1312
#1489×C1312
#1485×C1312
#18591131