Finite Group Databasebeta

← C137×#18832 #46868218

Subgroups — C137×#18832 #46868218

Order 35072.

928 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
1#3511×C137C211yesmaximal, characteristic, complemented
2#3226×C137C211yesmaximal, characteristic, complemented
3#3214×C137C211yesmaximal, characteristic, complemented
4#3115×C137C211yesmaximal, characteristic, complemented
5#1650×C137C212yesmaximal, complemented
6#1647×C137C212yesmaximal, complemented
7#1628×C137C212yesmaximal, complemented
8#1625×C137C212yesmaximal, complemented
9#1556×C137C211yesmaximal, characteristic, complemented
10#1496×C137C211yesmaximal, characteristic, complemented
11#1488×C137C211yesmaximal, characteristic, complemented
12#556×C137C2212yes—
13#555×C137—21no—
14#554×C137—21no—
15#553×C137—22no—
16#548×C137—22no—
17#547×C137C2212yes—
18#542×C137—22no—
19#537×C137—21no—
20#533×C137—21no—
21#532×C137—21no—
22#532×C137C2211yescharacteristic
23#532×C137C2211yescharacteristic
24C2×C4⋊Q8×C137C2211yescharacteristic
25#520×C137—21no—
26C4×#41×C137C2211yescharacteristic
27#500×C137C2212yes—
28#496×C137—21no—
29#489×C137—21no—
30#486×C137C2212yes—
31#482×C137—21no—
32#480×C137—22no—
33#475×C137C2211yescharacteristic
34#474×C137—22no—
35#474×C137C2211yescharacteristic
36#461×C137C2212yes—
37#460×C137C2211yescharacteristic
38#459×C137C2211yescharacteristic
39#459×C137C2212yes—
40#449×C137—21no—
41#449×C137—22no—
42#442×C137—21no—
43#440×C137—21no—
44#432×C137C2211yescharacteristic
45#432×C137C2211yescharacteristic
46#431×C137C2211yescharacteristic
47#332×C137C2212yes—
48#332×C137C2212yes—
49Q8⋊C8×C137C2212yes—
50D4⋊C8×C137C2212yes—
51D4⋊C8×C137C2212yes—
52D4⋊C8×C137C2212yes—
53C2×#41×C137—22no—
54C2×#41×C137—21no—
55C2×#41×C137—21no—
56C2×#41×C137D411yescharacteristic
57C22×Q8×C137—21no—
58C2×SD16×C137—21no—
59C2×SD16×C137—22no—
60C2×D8×C137—21no—
61C2×D8×C137—22no—
62C4⋊Q8×C137—21no—
63C4⋊Q8×C137—21no—
64C4⋊Q8×C137D412yes—
65C4⋊Q8×C137D411yescharacteristic
66C4⋊Q8×C137C2311yescharacteristic
67C4⋊Q8×C137C2312yes—
68#127×C137D411yescharacteristic
69#127×C137C2311yescharacteristic
70#126×C137—24no—
71#125×C137—22no—
72#124×C137—24no—
73#124×C137—22no—
74#124×C137—21no—
75#124×C137—21no—
76#123×C137—24no—
77C22⋊Q8×C137—22no—
78C22⋊Q8×C137—24no—
79C22⋊Q8×C137—22no—
80C22⋊Q8×C137—22no—
81#121×C137—22no—
82#121×C137—22no—
83#121×C137—24no—
84#121×C137—22no—
85#121×C137—21no—
86#121×C137—21no—
87#121×C137—21no—
88#121×C137D412yes—
89C4×Q8×C137—22no—
90C4×Q8×C137—22no—
91C4×Q8×C137D411yescharacteristic
92C4×Q8×C137C2311yescharacteristic
93C4×D4×C137—22no—
94C4×D4×C137—24no—
95C4×D4×C137—22no—
96C4×D4×C137—21no—
97C4×D4×C137—21no—
98C4×D4×C137—21no—
99C4×D4×C137—21no—
100C4×D4×C137—21no—
101C4×D4×C137D411yescharacteristic
102C4×D4×C137C2312yes—
103C4×D4×C137C2311yescharacteristic
104#117×C137—22no—
105#117×C137—22no—
106#117×C137—21no—
107#117×C137D411yescharacteristic
108C2×C4⋊C4×C137—21no—
109C2×C4⋊C4×C137—22no—
110C2×C4⋊C4×C137D412yes—
111C2×C42×C137—21no—
112C2×C42×C137C2311yescharacteristic
113#107×C137—21no—
114#107×C137—24no—
115#106×C137—21no—
116C4⋊C8×C137—21no—
117C4⋊C8×C137C2312yes—
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120#103×C137—21no—
121#103×C137—22no—
122#102×C137—21no—
123#102×C137—21no—
124#102×C137—21no—
125#102×C137—22no—
126#102×C137—24no—
127C22⋊C8×C137—21no—
128C22⋊C8×C137—21no—
129C22⋊C8×C137—21no—
130#97×C137—21no—
131#97×C137—21no—
132C4×C8×C137C2312yes—
133#41×C137—41no—
134#41×C137—41no—
135#41×C137—42no—
136#41×C137—42no—
137#41×C137—82no—
138#41×C137—82no—
139#41×C137—82no—
140C2×Q8×C137—21no—
141C2×Q8×C137—22no—
142C2×Q8×C137—22no—
143C2×Q8×C137—21no—
144C2×Q8×C137—82no—
145C2×Q8×C137C2×D411yescharacteristic
146C2×D4×C137—21no—
147C2×D4×C137—22no—
148C2×D4×C137—24no—
149C2×D4×C137—21no—
150C2×D4×C137—21no—
151C2×D4×C137—21no—
152C2×D4×C137—21no—
153C2×D4×C137—21no—
154C2×D4×C137—41no—
155C2×D4×C137C2×D411yescharacteristic
156C2×D4×C137C2×D412yes—
157C22×C4×C137—24no—
158C22×C4×C137—22no—
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—21no—
162C22×C4×C137—22no—
163C22×C4×C137—41no—
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2×D411yescharacteristic
166C22×C4×C137C2×D411yescharacteristic
167SD16×C137—42no—
168SD16×C137—82no—
169D8×C137—42no—
170D8×C137—82no—
171C2×C8×C137—22no—
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—22no—
175C4⋊C4×C137—24no—
176C4⋊C4×C137—24no—
177C4⋊C4×C137—22no—
178C4⋊C4×C137—22no—
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—22no—
182C4⋊C4×C137—21no—
183C4⋊C4×C137—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137C2×D412yes—
186C4⋊C4×C137C2×D411yescharacteristic
187C4⋊C4×C137C2×D411yescharacteristic
188C4⋊C4×C137C2×D414yes—
189C22⋊C4×C137—24no—
190C22⋊C4×C137—24no—
191C22⋊C4×C137—24no—
192C22⋊C4×C137—21no—
193C22⋊C4×C137—21no—
194C22⋊C4×C137—22no—
195C22⋊C4×C137—21no—
196C22⋊C4×C137—22no—
197C22⋊C4×C137—41no—
198C22⋊C4×C137—41no—
199C42×C137—24no—
200C42×C137—21no—
201C42×C137—21no—
202C42×C137—21no—
203C42×C137C2×D411yescharacteristic
204C42×C137C2×D411yescharacteristic
205C42×C137C2×D411yescharacteristic
206C42×C137C2411yescharacteristic
207C23×C137—21no—
208C23×C137—22no—
209C23×C137—41no—
210C23×C137#12011yescharacteristic
211Q8×C137—21no—
212Q8×C137—21no—
213Q8×C137—42no—
214Q8×C137—42no—
215Q8×C137—42no—
216Q8×C137—42no—
217Q8×C137—82no—
218D4×C137—21no—
219D4×C137—21no—
220D4×C137—22no—
221D4×C137—22no—
222D4×C137—42no—
223D4×C137—42no—
224D4×C137—42no—
225D4×C137—42no—
226D4×C137—44no—
227D4×C137—41no—
228D4×C137—41no—
229D4×C137—42no—
230D4×C137—84no—
231D4×C137—82no—
232C2×C4×C137—21no—
233C2×C4×C137—21no—
234C2×C4×C137—22no—
235C2×C4×C137—21no—
236C2×C4×C137—21no—
237C2×C4×C137—22no—
238C2×C4×C137—21no—
239C2×C4×C137—24no—
240C2×C4×C137—41no—
241C2×C4×C137—42no—
242C2×C4×C137—42no—
243C2×C4×C137—42no—
244C2×C4×C137—42no—
245C2×C4×C137—42no—
246C2×C4×C137—41no—
247C2×C4×C137—82no—
248C2×C4×C137—82no—
249C2×C4×C137—84no—
250C2×C4×C137#12011yescharacteristic
251C2×C4×C137#12011yescharacteristic
252C2×C4×C137#12011yescharacteristic
253C2×C4×C137C22×D411yescharacteristic
254C2×C4×C137C22×D411yescharacteristic
255C2×C4×C137C22×D411yescharacteristic
256C8×C137—42no—
257C8×C137—41no—
258C8×C137—41no—
259C8×C137—42no—
260C22×C137—21no—
261C22×C137—21no—
262C22×C137—21no—
263C22×C137—41no—
264C22×C137—42no—
265C22×C137—41no—
266C22×C137—42no—
267C22×C137—41no—
268C22×C137—42no—
269C22×C137—81no—
270C22×C137—81no—
271C22×C137—81no—
272C22×C137C2×#12011yescharacteristic
273C4×C137—21no—
274C4×C137—21no—
275C4×C137—21no—
276C4×C137—21no—
277C4×C137—41no—
278C4×C137—42no—
279C4×C137—41no—
280C4×C137—44no—
281C4×C137—41no—
282C4×C137—81no—
283C4×C137#57511yescharacteristic
284C4×C137#57511yescharacteristic
285C4×C137#57612yes—
286C2×C137—41no—
287C2×C137—81no—
288C2×C137—82no—
289C2×C137—161no—
290C2×C137#300511yescharacteristic
291C2×C137#300811yescharacteristic
292C2×C137#302011yescharacteristic
293#18832C13711yesmaximal, characteristic, direct product factor, Sylow
294C137#1883211yescharacteristic, direct product factor, Sylow
295#3511C2×C13711yescharacteristic, complemented
296#3226C2×C13711yescharacteristic, complemented
297#3214C2×C13711yescharacteristic, complemented
298#3115C2×C13711yescharacteristic, complemented
299#1650C2×C13712yescomplemented
300#1647C2×C13712yescomplemented
301#1628C2×C13712yescomplemented
302#1625C2×C13712yescomplemented
303#1556C2×C13711yescharacteristic, complemented
304#1496C2×C13711yescharacteristic, complemented
305#1488C2×C13711yescharacteristic, complemented
306#556C22×C13712yes—
307#555—21no—
308#554—21no—
309#553—22no—
310#548—22no—
311#547C22×C13712yes—
312#542—22no—
313#537—21no—
314#533—21no—
315#532—21no—
316#532C22×C13711yescharacteristic
317#532C22×C13711yescharacteristic
318C2×C4⋊Q8C22×C13711yescharacteristic
319#520—21no—
320C4×#41C22×C13711yescharacteristic
321#500C22×C13712yes—
322#496—21no—
323#489—21no—
324#486C22×C13712yes—
325#482—21no—
326#480—22no—
327#475C22×C13711yescharacteristic
328#474—22no—
329#474C22×C13711yescharacteristic
330#461C22×C13712yes—
331#460C22×C13711yescharacteristic
332#459C22×C13711yescharacteristic
333#459C22×C13712yes—
334#449—21no—
335#449—22no—
336#442—21no—
337#440—21no—
338#432C22×C13711yescharacteristic
339#432C22×C13711yescharacteristic
340#431C22×C13711yescharacteristic
341#332C22×C13712yes—
342#332C22×C13712yes—
343Q8⋊C8C22×C13712yes—
344D4⋊C8C22×C13712yes—
345D4⋊C8C22×C13712yes—
346D4⋊C8C22×C13712yes—
347C2×#41—22no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41D4×C13711yescharacteristic
351C22×Q8—21no—
352C2×SD16—21no—
353C2×SD16—22no—
354C2×D8—21no—
355C2×D8—22no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8D4×C13712yes—
359C4⋊Q8D4×C13711yescharacteristic
360C4⋊Q8C23×C13711yescharacteristic
361C4⋊Q8C23×C13712yes—
362#127D4×C13711yescharacteristic
363#127C23×C13711yescharacteristic
364#126—24no—
365#125—22no—
366#124—24no—
367#124—22no—
368#124—21no—
369#124—21no—
370#123—24no—
371C22⋊Q8—22no—
372C22⋊Q8—24no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375#121—22no—
376#121—22no—
377#121—24no—
378#121—22no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121D4×C13712yes—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8D4×C13711yescharacteristic
386C4×Q8C23×C13711yescharacteristic
387C4×D4—22no—
388C4×D4—24no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4D4×C13711yescharacteristic
396C4×D4C23×C13711yescharacteristic
397C4×D4C23×C13712yes—
398#117—22no—
399#117—22no—
400#117—21no—
401#117D4×C13711yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4D4×C13712yes—
405C2×C42—21no—
406C2×C42C23×C13711yescharacteristic
407#107—21no—
408#107—24no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C13711yescharacteristic
412C4⋊C8C23×C13711yescharacteristic
413C4⋊C8C23×C13712yes—
414#103—21no—
415#103—22no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—22no—
420#102—24no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426C4×C8C23×C13712yes—
427#41—41no—
428#41—41no—
429#41—42no—
430#41—42no—
431#41—82no—
432#41—82no—
433#41—82no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—82no—
439C2×Q8C2×D4×C13711yescharacteristic
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×D4×C13711yescharacteristic
450C2×D4C2×D4×C13712yes—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4C2×D4×C13711yescharacteristic
459C22×C4C2×D4×C13711yescharacteristic
460C22×C4C2×D4×C13711yescharacteristic
461SD16—42no—
462SD16—82no—
463D8—42no—
464D8—82no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—22no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C2×D4×C13712yes—
480C4⋊C4C2×D4×C13711yescharacteristic
481C4⋊C4C2×D4×C13711yescharacteristic
482C4⋊C4C2×D4×C13714yes—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—24no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42C2×D4×C13711yescharacteristic
498C42C2×D4×C13711yescharacteristic
499C42C2×D4×C13711yescharacteristic
500C42C24×C13711yescharacteristic
501C23—21no—
502C23—22no—
503C23—41no—
504C23#120×C13711yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—42no—
511Q8—82no—
512D4—21no—
513D4—21no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—44no—
521D4—41no—
522D4—41no—
523D4—42no—
524D4—84no—
525D4—82no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—84no—
544C2×C4#120×C13711yescharacteristic
545C2×C4#120×C13711yescharacteristic
546C2×C4#120×C13711yescharacteristic
547C2×C4C22×D4×C13711yescharacteristic
548C2×C4C22×D4×C13711yescharacteristic
549C2×C4C22×D4×C13711yescharacteristic
550C8—42no—
551C8—41no—
552C8—41no—
553C8—42no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C2×#120×C13711yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—44no—
575C4—41no—
576C4—81no—
577C4#575×C13711yescharacteristic
578C4#575×C13711yescharacteristic
579C4#576×C13712yes—
580C2—41no—
581C2—81no—
582C2—82no—
583C2—161no—
584C2#3005×C13711yescharacteristic
585C2#3008×C13711yescharacteristic
586C2#3020×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3511×C137C2semidirect
2. #3226×C137C2semidirect
3. #3214×C137C2semidirect
4. #3115×C137C2semidirect
5. #1650×C137C2semidirect
6. #1647×C137C2semidirect
7. #1628×C137C2semidirect
8. #1625×C137C2semidirect
9. #1556×C137C2semidirect
10. #1496×C137C2semidirect
11. #1488×C137C2semidirect
293. #18832C137direct (N × H)
294. C137#18832direct (N × H)
295. #3511C2×C137semidirect
296. #3226C2×C137semidirect
297. #3214C2×C137semidirect
298. #3115C2×C137semidirect
299. #1650C2×C137semidirect
300. #1647C2×C137semidirect
301. #1628C2×C137semidirect
302. #1625C2×C137semidirect
303. #1556C2×C137semidirect
304. #1496C2×C137semidirect
305. #1488C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3511×C1372
#3226×C1372
#3214×C1372
#3115×C1372
#1650×C1372
#1647×C1372
#1628×C1372
#1625×C1372
#1556×C1372
#1496×C1372
#1488×C1372
#18832137