Finite Group Databasebeta

← C137×#18820 #46868206

Subgroups — C137×#18820 #46868206

Order 35072.

940 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
1#3511×C137C211yesmaximal, characteristic, complemented
2#3214×C137C211yesmaximal, characteristic, complemented
3#3206×C137C211yesmaximal, characteristic, complemented
4#3115×C137C211yesmaximal, characteristic, complemented
5#1646×C137C212yesmaximal, complemented
6#1643×C137C212yesmaximal, complemented
7#1624×C137C212yesmaximal, complemented
8#1622×C137C212yesmaximal, complemented
9#1558×C137C211yesmaximal, characteristic, complemented
10#1496×C137C211yesmaximal, characteristic, complemented
11#1488×C137C211yesmaximal, characteristic, complemented
12#556×C137—21no—
13#555×C137C2212yes—
14#554×C137C2212yes—
15#553×C137—22no—
16#548×C137—22no—
17#547×C137—21no—
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#496×C137—21no—
28#492×C137C2212yes—
29#489×C137—21no—
30#487×C137C2212yes—
31#482×C137—21no—
32#475×C137C2211yescharacteristic
33#474×C137C2211yescharacteristic
34#461×C137—22no—
35#461×C137C2212yes—
36#460×C137C2211yescharacteristic
37#459×C137C2211yescharacteristic
38#459×C137C2212yes—
39#449×C137—21no—
40#449×C137—22no—
41#448×C137—22no—
42#442×C137—21no—
43#440×C137—21no—
44#432×C137C2211yescharacteristic
45#432×C137C2211yescharacteristic
46#431×C137C2211yescharacteristic
47#333×C137C2212yes—
48#333×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×C137D412yes—
58C2×SD16×C137—21no—
59C2×SD16×C137—24no—
60C2×SD16×C137—22no—
61C2×D8×C137—21no—
62C2×D8×C137—22no—
63C4⋊Q8×C137—21no—
64C4⋊Q8×C137—21no—
65C4⋊Q8×C137D412yes—
66C4⋊Q8×C137D411yescharacteristic
67C4⋊Q8×C137C2311yescharacteristic
68C4⋊Q8×C137C2312yes—
69#127×C137D411yescharacteristic
70#127×C137C2311yescharacteristic
71#126×C137—24no—
72#125×C137—22no—
73#124×C137—22no—
74#124×C137—24no—
75#124×C137—21no—
76#124×C137—21no—
77#123×C137—24no—
78C22⋊Q8×C137—22no—
79C22⋊Q8×C137—22no—
80C22⋊Q8×C137—22no—
81C22⋊Q8×C137—24no—
82#121×C137—22no—
83#121×C137—24no—
84#121×C137—22no—
85#121×C137—22no—
86#121×C137—21no—
87#121×C137—21no—
88#121×C137—21no—
89#121×C137D412yes—
90C4×Q8×C137—22no—
91C4×Q8×C137—22no—
92C4×Q8×C137D411yescharacteristic
93C4×Q8×C137C2311yescharacteristic
94C4×D4×C137—22no—
95C4×D4×C137—24no—
96C4×D4×C137—22no—
97C4×D4×C137—21no—
98C4×D4×C137—21no—
99C4×D4×C137—21no—
100C4×D4×C137—21no—
101C4×D4×C137—21no—
102C4×D4×C137D411yescharacteristic
103C4×D4×C137C2312yes—
104C4×D4×C137C2311yescharacteristic
105#117×C137—22no—
106#117×C137—22no—
107#117×C137—21no—
108#117×C137D411yescharacteristic
109C2×C4⋊C4×C137—21no—
110C2×C4⋊C4×C137—21no—
111C2×C4⋊C4×C137—22no—
112C2×C42×C137—21no—
113C2×C42×C137C2311yescharacteristic
114#107×C137—21no—
115#106×C137—21no—
116C4⋊C8×C137—21no—
117C4⋊C8×C137C2312yes—
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120#103×C137—21no—
121#103×C137—24no—
122#103×C137—22no—
123#102×C137—21no—
124#102×C137—21no—
125#102×C137—21no—
126#102×C137—22no—
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—84no—
139C2×Q8×C137—21no—
140C2×Q8×C137—22no—
141C2×Q8×C137—21no—
142C2×Q8×C137—82no—
143C2×Q8×C137C2×D411yescharacteristic
144C2×Q8×C137C2×D414yes—
145C2×D4×C137—21no—
146C2×D4×C137—22no—
147C2×D4×C137—24no—
148C2×D4×C137—21no—
149C2×D4×C137—21no—
150C2×D4×C137—21no—
151C2×D4×C137—21no—
152C2×D4×C137—21no—
153C2×D4×C137—41no—
154C2×D4×C137C2×D411yescharacteristic
155C2×D4×C137C2×D412yes—
156C22×C4×C137—24no—
157C22×C4×C137—22no—
158C22×C4×C137—21no—
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—22no—
162C22×C4×C137—41no—
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2×D411yescharacteristic
166SD16×C137—42no—
167SD16×C137—82no—
168SD16×C137—84no—
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—22no—
183C4⋊C4×C137—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137—21no—
186C4⋊C4×C137C2×D412yes—
187C4⋊C4×C137C2×D411yescharacteristic
188C4⋊C4×C137C2×D411yescharacteristic
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—44no—
214Q8×C137—44no—
215Q8×C137—42no—
216Q8×C137—42no—
217D4×C137—21no—
218D4×C137—21no—
219D4×C137—22no—
220D4×C137—22no—
221D4×C137—42no—
222D4×C137—42no—
223D4×C137—42no—
224D4×C137—42no—
225D4×C137—44no—
226D4×C137—41no—
227D4×C137—41no—
228D4×C137—42no—
229D4×C137—84no—
230D4×C137—82no—
231C2×C4×C137—21no—
232C2×C4×C137—21no—
233C2×C4×C137—22no—
234C2×C4×C137—21no—
235C2×C4×C137—21no—
236C2×C4×C137—22no—
237C2×C4×C137—21no—
238C2×C4×C137—24no—
239C2×C4×C137—41no—
240C2×C4×C137—42no—
241C2×C4×C137—42no—
242C2×C4×C137—42no—
243C2×C4×C137—42no—
244C2×C4×C137—42no—
245C2×C4×C137—41no—
246C2×C4×C137—82no—
247C2×C4×C137—82no—
248C2×C4×C137—84no—
249C2×C4×C137#12011yescharacteristic
250C2×C4×C137#12011yescharacteristic
251C2×C4×C137#12011yescharacteristic
252C2×C4×C137C22×D411yescharacteristic
253C2×C4×C137C22×D411yescharacteristic
254C2×C4×C137C22×D411yescharacteristic
255C8×C137—42no—
256C8×C137—41no—
257C8×C137—41no—
258C8×C137—42no—
259C22×C137—21no—
260C22×C137—21no—
261C22×C137—21no—
262C22×C137—41no—
263C22×C137—42no—
264C22×C137—41no—
265C22×C137—42no—
266C22×C137—41no—
267C22×C137—42no—
268C22×C137—81no—
269C22×C137—81no—
270C22×C137—81no—
271C22×C137C2×#12011yescharacteristic
272C4×C137—21no—
273C4×C137—21no—
274C4×C137—21no—
275C4×C137—21no—
276C4×C137—41no—
277C4×C137—42no—
278C4×C137—41no—
279C4×C137—41no—
280C4×C137—44no—
281C4×C137—81no—
282C4×C137#57511yescharacteristic
283C4×C137#57511yescharacteristic
284C4×C137#57712yes—
285C2×C137—41no—
286C2×C137—81no—
287C2×C137—82no—
288C2×C137—161no—
289C2×C137#300511yescharacteristic
290C2×C137#301011yescharacteristic
291C2×C137#301911yescharacteristic
292#18820C13711yesmaximal, characteristic, direct product factor, Sylow
293C137#1882011yescharacteristic, direct product factor, Sylow
294#3511C2×C13711yescharacteristic, complemented
295#3214C2×C13711yescharacteristic, complemented
296#3206C2×C13711yescharacteristic, complemented
297#3115C2×C13711yescharacteristic, complemented
298#1646C2×C13712yescomplemented
299#1643C2×C13712yescomplemented
300#1624C2×C13712yescomplemented
301#1622C2×C13712yescomplemented
302#1558C2×C13711yescharacteristic, complemented
303#1496C2×C13711yescharacteristic, complemented
304#1488C2×C13711yescharacteristic, complemented
305#556—21no—
306#555C22×C13712yes—
307#554C22×C13712yes—
308#553—22no—
309#548—22no—
310#547—21no—
311#542—22no—
312#537—21no—
313#533—21no—
314#532—21no—
315#532C22×C13711yescharacteristic
316#532C22×C13711yescharacteristic
317C2×C4⋊Q8C22×C13711yescharacteristic
318#520—21no—
319C4×#41C22×C13711yescharacteristic
320#496—21no—
321#492C22×C13712yes—
322#489—21no—
323#487C22×C13712yes—
324#482—21no—
325#475C22×C13711yescharacteristic
326#474C22×C13711yescharacteristic
327#461—22no—
328#461C22×C13712yes—
329#460C22×C13711yescharacteristic
330#459C22×C13711yescharacteristic
331#459C22×C13712yes—
332#449—21no—
333#449—22no—
334#448—22no—
335#442—21no—
336#440—21no—
337#432C22×C13711yescharacteristic
338#432C22×C13711yescharacteristic
339#431C22×C13711yescharacteristic
340#333C22×C13712yes—
341#333C22×C13712yes—
342Q8⋊C8C22×C13712yes—
343D4⋊C8C22×C13712yes—
344D4⋊C8C22×C13712yes—
345D4⋊C8C22×C13712yes—
346C2×#41—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41D4×C13711yescharacteristic
350C22×Q8D4×C13712yes—
351C2×SD16—21no—
352C2×SD16—24no—
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—22no—
367#124—24no—
368#124—21no—
369#124—21no—
370#123—24no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375#121—22no—
376#121—24no—
377#121—22no—
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—21no—
404C2×C4⋊C4—22no—
405C2×C42—21no—
406C2×C42C23×C13711yescharacteristic
407#107—21no—
408#106—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C13711yescharacteristic
411C4⋊C8C23×C13711yescharacteristic
412C4⋊C8C23×C13712yes—
413#103—21no—
414#103—24no—
415#103—22no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—22no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423#97—21no—
424#97—21no—
425C4×C8C23×C13712yes—
426#41—41no—
427#41—41no—
428#41—42no—
429#41—42no—
430#41—82no—
431#41—84no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—82no—
436C2×Q8C2×D4×C13711yescharacteristic
437C2×Q8C2×D4×C13714yes—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4C2×D4×C13711yescharacteristic
448C2×D4C2×D4×C13712yes—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4C2×D4×C13711yescharacteristic
457C22×C4C2×D4×C13711yescharacteristic
458C22×C4C2×D4×C13711yescharacteristic
459SD16—42no—
460SD16—82no—
461SD16—84no—
462D8—42no—
463D8—82no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—22no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4C2×D4×C13712yes—
480C4⋊C4C2×D4×C13711yescharacteristic
481C4⋊C4C2×D4×C13711yescharacteristic
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—24no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42C2×D4×C13711yescharacteristic
497C42C2×D4×C13711yescharacteristic
498C42C2×D4×C13711yescharacteristic
499C42C24×C13711yescharacteristic
500C23—21no—
501C23—22no—
502C23—41no—
503C23#120×C13711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—44no—
507Q8—44no—
508Q8—42no—
509Q8—42no—
510D4—21no—
511D4—21no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—44no—
519D4—41no—
520D4—41no—
521D4—42no—
522D4—84no—
523D4—82no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—84no—
542C2×C4#120×C13711yescharacteristic
543C2×C4#120×C13711yescharacteristic
544C2×C4#120×C13711yescharacteristic
545C2×C4C22×D4×C13711yescharacteristic
546C2×C4C22×D4×C13711yescharacteristic
547C2×C4C22×D4×C13711yescharacteristic
548C8—42no—
549C8—41no—
550C8—41no—
551C8—42no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#120×C13711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—44no—
574C4—81no—
575C4#575×C13711yescharacteristic
576C4#575×C13711yescharacteristic
577C4#577×C13712yes—
578C2—41no—
579C2—81no—
580C2—82no—
581C2—161no—
582C2#3005×C13711yescharacteristic
583C2#3010×C13711yescharacteristic
584C2#3019×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. #3214×C137C2semidirect
3. #3206×C137C2semidirect
4. #3115×C137C2semidirect
5. #1646×C137C2semidirect
6. #1643×C137C2semidirect
7. #1624×C137C2semidirect
8. #1622×C137C2semidirect
9. #1558×C137C2semidirect
10. #1496×C137C2semidirect
11. #1488×C137C2semidirect
292. #18820C137direct (N × H)
293. C137#18820direct (N × H)
294. #3511C2×C137semidirect
295. #3214C2×C137semidirect
296. #3206C2×C137semidirect
297. #3115C2×C137semidirect
298. #1646C2×C137semidirect
299. #1643C2×C137semidirect
300. #1624C2×C137semidirect
301. #1622C2×C137semidirect
302. #1558C2×C137semidirect
303. #1496C2×C137semidirect
304. #1488C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3511×C1372
#3214×C1372
#3206×C1372
#3115×C1372
#1646×C1372
#1643×C1372
#1624×C1372
#1622×C1372
#1558×C1372
#1496×C1372
#1488×C1372
#18820137