Finite Group Databasebeta

← C137×#20265 #46869651

Subgroups — C137×#20265 #46869651

Order 35072.

608 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3400×C137C211yesmaximal, characteristic, complemented
2#3399×C137C211yesmaximal, characteristic
3#3381×C137C211yesmaximal, characteristic, complemented
4#3333×C137C211yesmaximal, characteristic, complemented
5#1715×C137C211yesmaximal, characteristic, complemented
6#1698×C137C211yesmaximal, characteristic, complemented
7#1692×C137C211yesmaximal, characteristic, complemented
8#1685×C137C211yesmaximal, characteristic, complemented
9#1668×C137C211yesmaximal, characteristic, complemented
10#1641×C137C211yesmaximal, characteristic, complemented
11#1630×C137C211yesmaximal, characteristic, complemented
12#1626×C137C211yesmaximal, characteristic, complemented
13#1622×C137C211yesmaximal, characteristic, complemented
14#1592×C137C211yesmaximal, characteristic, complemented
15#1584×C137C211yesmaximal, characteristic, complemented
16#559×C137C2211yescharacteristic
17#557×C137C2211yescharacteristic
18#554×C137C2211yescharacteristic
19#550×C137C2211yescharacteristic
20#499×C137—21no—
21#498×C137C2211yescharacteristic
22#497×C137—21no—
23#496×C137—21no—
24#493×C137C2211yescharacteristic
25#492×C137C2211yescharacteristic
26#492×C137C2211yescharacteristic
27#486×C137C2211yescharacteristic
28#486×C137C2211yescharacteristic
29#480×C137—21no—
30#479×C137—21no—
31#478×C137—21no—
32#477×C137C2211yescharacteristic
33#477×C137C2211yescharacteristic
34#474×C137C2211yescharacteristic
35#468×C137—21no—
36#464×C137—21no—
37#463×C137—21no—
38#462×C137C2211yescharacteristic
39#461×C137—21no—
40#460×C137C2211yescharacteristic
41#460×C137C2211yescharacteristic
42#460×C137C2211yescharacteristic
43#459×C137—21no—
44#459×C137C2211yescharacteristic
45#452×C137—21no—
46#446×C137C2211yescharacteristic
47#446×C137C2211yescharacteristic
48C8×Q8×C137C2211yescharacteristic
49#442×C137—21no—
50#440×C137—21no—
51C4×Q16×C137C2211yescharacteristic
52C4×SD16×C137—21no—
53C4×SD16×C137C2211yescharacteristic
54#436×C137C2211yescharacteristic
55#417×C137—21no—
56#335×C137C2211yescharacteristic
57#335×C137C2211yescharacteristic
58#333×C137C2211yescharacteristic
59#332×C137C2211yescharacteristic
60#331×C137C2211yescharacteristic
61#331×C137C2211yescharacteristic
62Q8⋊C8×C137C2211yescharacteristic
63Q8⋊C8×C137C2211yescharacteristic
64Q8⋊C8×C137C2211yescharacteristic
65D4⋊C8×C137C2211yescharacteristic
66#322×C137C2211yescharacteristic
67C2×#41×C137—21no—
68C2×Q16×C137—21no—
69C2×Q16×C137D411yescharacteristic
70C2×SD16×C137—21no—
71C2×SD16×C137—21no—
72C2×SD16×C137—21no—
73C2×SD16×C137—21no—
74C2×SD16×C137—21no—
75C2×SD16×C137—41no—
76C2×SD16×C137D411yescharacteristic
77C2×D8×C137—21no—
78C2×D8×C137—21no—
79C2×D8×C137—21no—
80C2×M16×C137—21no—
81C4⋊Q8×C137—21no—
82C4⋊Q8×C137C2311yescharacteristic
83C4⋊Q8×C137C2311yescharacteristic
84#127×C137—21no—
85#127×C137C2311yescharacteristic
86#127×C137C2311yescharacteristic
87#125×C137—21no—
88#125×C137—21no—
89#125×C137—41no—
90#124×C137—21no—
91#124×C137—21no—
92#123×C137—41no—
93C22⋊Q8×C137—21no—
94C22⋊Q8×C137—41no—
95#121×C137—21no—
96#121×C137—41no—
97C4×Q8×C137—21no—
98C4×Q8×C137—21no—
99C4×Q8×C137C2311yescharacteristic
100C4×Q8×C137C2311yescharacteristic
101C4×Q8×C137C2311yescharacteristic
102C4×D4×C137—21no—
103C4×D4×C137—21no—
104C4×D4×C137—21no—
105C4×D4×C137—21no—
106C4×D4×C137C2311yescharacteristic
107C2×C4⋊C4×C137—21no—
108#107×C137—21no—
109#107×C137—21no—
110#107×C137—21no—
111#107×C137D411yescharacteristic
112#106×C137—21no—
113#106×C137—21no—
114#106×C137D411yescharacteristic
115C4⋊C8×C137—21no—
116C4⋊C8×C137—21no—
117C4⋊C8×C137—21no—
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120C4⋊C8×C137C2311yescharacteristic
121C4⋊C8×C137C2311yescharacteristic
122#103×C137—21no—
123#103×C137—21no—
124#103×C137—21no—
125#103×C137D411yescharacteristic
126#103×C137D411yescharacteristic
127#103×C137D411yescharacteristic
128#102×C137—21no—
129#102×C137—21no—
130#102×C137—21no—
131#102×C137—21no—
132#102×C137—21no—
133#102×C137—21no—
134#102×C137—21no—
135#102×C137—41no—
136#102×C137D411yescharacteristic
137C22⋊C8×C137—21no—
138#97×C137—21no—
139#97×C137—21no—
140C4×C8×C137—21no—
141C4×C8×C137C2311yescharacteristic
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144#41×C137—42no—
145#41×C137—81no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137C2×D411yescharacteristic
149C2×Q8×C137C2×D411yescharacteristic
150C2×Q8×C137C2×D411yescharacteristic
151C2×D4×C137—21no—
152C2×D4×C137—21no—
153C2×D4×C137—21no—
154C2×D4×C137—21no—
155C2×D4×C137—21no—
156C2×D4×C137—21no—
157C2×D4×C137—41no—
158C2×D4×C137—41no—
159C2×D4×C137C2×D411yescharacteristic
160C22×C4×C137—21no—
161C22×C4×C137—41no—
162C22×C4×C137—41no—
163C22×C4×C137—41no—
164Q16×C137—41no—
165Q16×C137—81no—
166SD16×C137—22no—
167SD16×C137—42no—
168SD16×C137—81no—
169SD16×C137—81no—
170SD16×C137—81no—
171SD16×C137—81no—
172SD16×C137—82no—
173D8×C137—42no—
174D8×C137—81no—
175D8×C137—81no—
176M16×C137—81no—
177C2×C8×C137—21no—
178C2×C8×C137—21no—
179C2×C8×C137—21no—
180C2×C8×C137—21no—
181C2×C8×C137—21no—
182C2×C8×C137C2×D411yescharacteristic
183C2×C8×C137C2×D411yescharacteristic
184C2×C8×C137C2×D411yescharacteristic
185C2×C8×C137C2×D411yescharacteristic
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—21no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—41no—
194C4⋊C4×C137—41no—
195C4⋊C4×C137—41no—
196C4⋊C4×C137—41no—
197C4⋊C4×C137—41no—
198C4⋊C4×C137C2×D411yescharacteristic
199C4⋊C4×C137C2×D411yescharacteristic
200C4⋊C4×C137C2×D411yescharacteristic
201C4⋊C4×C137C2×D411yescharacteristic
202C22⋊C4×C137—21no—
203C22⋊C4×C137—41no—
204C22⋊C4×C137—41no—
205C22⋊C4×C137—41no—
206C22⋊C4×C137—41no—
207C22⋊C4×C137—41no—
208C42×C137—21no—
209C42×C137—21no—
210C42×C137—21no—
211C42×C137—41no—
212C42×C137C2411yescharacteristic
213C23×C137—21no—
214C23×C137—41no—
215C23×C137—41no—
216Q8×C137—21no—
217Q8×C137—21no—
218Q8×C137—21no—
219Q8×C137—21no—
220Q8×C137—21no—
221Q8×C137—21no—
222Q8×C137—41no—
223Q8×C137—41no—
224Q8×C137—81no—
225D4×C137—21no—
226D4×C137—21no—
227D4×C137—41no—
228D4×C137—41no—
229D4×C137—41no—
230D4×C137—41no—
231D4×C137—41no—
232D4×C137—41no—
233D4×C137—41no—
234D4×C137—41no—
235D4×C137—81no—
236D4×C137—81no—
237D4×C137—82no—
238D4×C137—161no—
239C2×C4×C137—21no—
240C2×C4×C137—21no—
241C2×C4×C137—21no—
242C2×C4×C137—21no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—41no—
247C2×C4×C137—41no—
248C2×C4×C137—41no—
249C2×C4×C137—41no—
250C2×C4×C137—82no—
251C2×C4×C137—161no—
252C2×C4×C137—161no—
253C2×C4×C137C22×D411yescharacteristic
254C2×C4×C137C22×D411yescharacteristic
255C2×C4×C137H(5,𝔽2)11yescharacteristic
256C8×C137—21no—
257C8×C137—21no—
258C8×C137—21no—
259C8×C137—41no—
260C8×C137—41no—
261C8×C137—41no—
262C8×C137—41no—
263C8×C137—41no—
264C8×C137#13712yes—
265C22×C137—41no—
266C22×C137—41no—
267C22×C137—41no—
268C22×C137—81no—
269C22×C137—81no—
270C22×C137—81no—
271C22×C137—81no—
272C22×C137—81no—
273C22×C137—81no—
274C22×C137D4211yescharacteristic
275C4×C137—21no—
276C4×C137—41no—
277C4×C137—41no—
278C4×C137—41no—
279C4×C137—41no—
280C4×C137—41no—
281C4×C137—41no—
282C4×C137—41no—
283C4×C137—81no—
284C4×C137—81no—
285C4×C137C2×#13711yescharacteristic
286C4×C137#57511yescharacteristic
287C4×C137#57611yescharacteristic
288C4×C137#57711yescharacteristic
289C2×C137—81no—
290C2×C137—161no—
291C2×C137—161no—
292C2×C137#326811yescharacteristic
293C2×C137#327811yescharacteristic
294C2×C137#328811yescharacteristic
295#20265C13711yesmaximal, characteristic, direct product factor, Sylow
296C137#2026511yescharacteristic, direct product factor, Sylow
297#3400C2×C13711yescharacteristic, complemented
298#3399C2×C13711yescharacteristic
299#3381C2×C13711yescharacteristic, complemented
300#3333C2×C13711yescharacteristic, complemented
301#1715C2×C13711yescharacteristic, complemented
302#1698C2×C13711yescharacteristic, complemented
303#1692C2×C13711yescharacteristic, complemented
304#1685C2×C13711yescharacteristic, complemented
305#1668C2×C13711yescharacteristic, complemented
306#1641C2×C13711yescharacteristic, complemented
307#1630C2×C13711yescharacteristic, complemented
308#1626C2×C13711yescharacteristic, complemented
309#1622C2×C13711yescharacteristic, complemented
310#1592C2×C13711yescharacteristic, complemented
311#1584C2×C13711yescharacteristic, complemented
312#559C22×C13711yescharacteristic
313#557C22×C13711yescharacteristic
314#554C22×C13711yescharacteristic
315#550C22×C13711yescharacteristic
316#499—21no—
317#498C22×C13711yescharacteristic
318#497—21no—
319#496—21no—
320#493C22×C13711yescharacteristic
321#492C22×C13711yescharacteristic
322#492C22×C13711yescharacteristic
323#486C22×C13711yescharacteristic
324#486C22×C13711yescharacteristic
325#480—21no—
326#479—21no—
327#478—21no—
328#477C22×C13711yescharacteristic
329#477C22×C13711yescharacteristic
330#474C22×C13711yescharacteristic
331#468—21no—
332#464—21no—
333#463—21no—
334#462C22×C13711yescharacteristic
335#461—21no—
336#460C22×C13711yescharacteristic
337#460C22×C13711yescharacteristic
338#460C22×C13711yescharacteristic
339#459—21no—
340#459C22×C13711yescharacteristic
341#452—21no—
342#446C22×C13711yescharacteristic
343#446C22×C13711yescharacteristic
344C8×Q8C22×C13711yescharacteristic
345#442—21no—
346#440—21no—
347C4×Q16C22×C13711yescharacteristic
348C4×SD16—21no—
349C4×SD16C22×C13711yescharacteristic
350#436C22×C13711yescharacteristic
351#417—21no—
352#335C22×C13711yescharacteristic
353#335C22×C13711yescharacteristic
354#333C22×C13711yescharacteristic
355#332C22×C13711yescharacteristic
356#331C22×C13711yescharacteristic
357#331C22×C13711yescharacteristic
358Q8⋊C8C22×C13711yescharacteristic
359Q8⋊C8C22×C13711yescharacteristic
360Q8⋊C8C22×C13711yescharacteristic
361D4⋊C8C22×C13711yescharacteristic
362#322C22×C13711yescharacteristic
363C2×#41—21no—
364C2×Q16—21no—
365C2×Q16D4×C13711yescharacteristic
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—41no—
372C2×SD16D4×C13711yescharacteristic
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C13711yescharacteristic
379C4⋊Q8C23×C13711yescharacteristic
380#127—21no—
381#127C23×C13711yescharacteristic
382#127C23×C13711yescharacteristic
383#125—21no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—21no—
388#123—41no—
389C22⋊Q8—21no—
390C22⋊Q8—41no—
391#121—21no—
392#121—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C13711yescharacteristic
396C4×Q8C23×C13711yescharacteristic
397C4×Q8C23×C13711yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C13711yescharacteristic
403C2×C4⋊C4—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107D4×C13711yescharacteristic
408#106—21no—
409#106—21no—
410#106D4×C13711yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C13711yescharacteristic
415C4⋊C8C23×C13711yescharacteristic
416C4⋊C8C23×C13711yescharacteristic
417C4⋊C8C23×C13711yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103D4×C13711yescharacteristic
422#103D4×C13711yescharacteristic
423#103D4×C13711yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—41no—
432#102D4×C13711yescharacteristic
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C13711yescharacteristic
438C4×C8C23×C13711yescharacteristic
439C4×C8C23×C13711yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C13711yescharacteristic
445C2×Q8C2×D4×C13711yescharacteristic
446C2×Q8C2×D4×C13711yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C13711yescharacteristic
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—41no—
461Q16—81no—
462SD16—22no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468SD16—82no—
469D8—42no—
470D8—81no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8C2×D4×C13711yescharacteristic
479C2×C8C2×D4×C13711yescharacteristic
480C2×C8C2×D4×C13711yescharacteristic
481C2×C8C2×D4×C13711yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C13711yescharacteristic
495C4⋊C4C2×D4×C13711yescharacteristic
496C4⋊C4C2×D4×C13711yescharacteristic
497C4⋊C4C2×D4×C13711yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C13711yescharacteristic
509C23—21no—
510C23—41no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—81no—
533D4—82no—
534D4—161no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—161no—
548C2×C4—161no—
549C2×C4C22×D4×C13711yescharacteristic
550C2×C4C22×D4×C13711yescharacteristic
551C2×C4H(5,𝔽2)×C13711yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8#137×C13712yes—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C13711yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4C2×#137×C13711yescharacteristic
582C4#575×C13711yescharacteristic
583C4#576×C13711yescharacteristic
584C4#577×C13711yescharacteristic
585C2—81no—
586C2—161no—
587C2—161no—
588C2#3268×C13711yescharacteristic
589C2#3278×C13711yescharacteristic
590C2#3288×C13711yescharacteristic
subgroupG/H
center, socleC22×C137D42
commutator, Frattini, cosocleC42C24×C137
prime radical#3399×C137C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3400×C137C2semidirect
3. #3381×C137C2semidirect
4. #3333×C137C2semidirect
5. #1715×C137C2semidirect
6. #1698×C137C2semidirect
7. #1692×C137C2semidirect
8. #1685×C137C2semidirect
9. #1668×C137C2semidirect
10. #1641×C137C2semidirect
11. #1630×C137C2semidirect
12. #1626×C137C2semidirect
13. #1622×C137C2semidirect
14. #1592×C137C2semidirect
15. #1584×C137C2semidirect
295. #20265C137direct (N × H)
296. C137#20265direct (N × H)
297. #3400C2×C137semidirect
299. #3381C2×C137semidirect
300. #3333C2×C137semidirect
301. #1715C2×C137semidirect
302. #1698C2×C137semidirect
303. #1692C2×C137semidirect
304. #1685C2×C137semidirect
305. #1668C2×C137semidirect
306. #1641C2×C137semidirect
307. #1630C2×C137semidirect
308. #1626C2×C137semidirect
309. #1622C2×C137semidirect
310. #1592C2×C137semidirect
311. #1584C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3400×C1372
#3399×C1372
#3381×C1372
#3333×C1372
#1715×C1372
#1698×C1372
#1692×C1372
#1685×C1372
#1668×C1372
#1641×C1372
#1630×C1372
#1626×C1372
#1622×C1372
#1592×C1372
#1584×C1372
#20265137