Finite Group Databasebeta

← C137×#19863 #46869249

Subgroups — C137×#19863 #46869249

Order 35072.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3393×C137C211yesmaximal, characteristic, complemented
2#3353×C137C211yesmaximal, characteristic, complemented
3#3340×C137C211yesmaximal, characteristic, complemented
4#3303×C137C211yesmaximal, characteristic
5#1723×C137C211yesmaximal, characteristic, complemented
6#1691×C137C211yesmaximal, characteristic, complemented
7#1684×C137C211yesmaximal, characteristic, complemented
8#1673×C137C211yesmaximal, characteristic, complemented
9#1669×C137C211yesmaximal, characteristic, complemented
10#1650×C137C211yesmaximal, characteristic, complemented
11#1647×C137C211yesmaximal, characteristic, complemented
12#1646×C137C211yesmaximal, characteristic, complemented
13#1638×C137C211yesmaximal, characteristic, complemented
14#1581×C137C211yesmaximal, characteristic, complemented
15SD16⋊C8×C137C211yesmaximal, characteristic, complemented
16#556×C137C2211yescharacteristic
17#556×C137C2211yescharacteristic
18#555×C137C2211yescharacteristic
19#547×C137C2211yescharacteristic
20#500×C137C2211yescharacteristic
21#500×C137C2211yescharacteristic
22#498×C137C2211yescharacteristic
23#495×C137—21no—
24#494×C137C2211yescharacteristic
25#487×C137C2211yescharacteristic
26#487×C137C2211yescharacteristic
27#485×C137—21no—
28#485×C137—21no—
29#484×C137—21no—
30#482×C137—21no—
31#482×C137—21no—
32#477×C137C2211yescharacteristic
33#476×C137C2211yescharacteristic
34#475×C137C2211yescharacteristic
35#474×C137C2211yescharacteristic
36#474×C137C2211yescharacteristic
37#468×C137—21no—
38#465×C137—21no—
39#465×C137—21no—
40#464×C137—21no—
41#464×C137—21no—
42#461×C137C2211yescharacteristic
43#461×C137C2211yescharacteristic
44#461×C137C2211yescharacteristic
45#449×C137—21no—
46C8×Q8×C137C2211yescharacteristic
47C4×Q16×C137—21no—
48C4×SD16×C137C2211yescharacteristic
49C4×D8×C137C2211yescharacteristic
50#436×C137C2211yescharacteristic
51C8×D4×C137C2211yescharacteristic
52C8×D4×C137C2211yescharacteristic
53#428×C137—21no—
54#427×C137—21no—
55#416×C137—21no—
56#335×C137C2211yescharacteristic
57#335×C137C2211yescharacteristic
58#333×C137C2211yescharacteristic
59#332×C137C2211yescharacteristic
60#332×C137C2211yescharacteristic
61#332×C137C2211yescharacteristic
62Q8⋊C8×C137C2211yescharacteristic
63D4⋊C8×C137C2211yescharacteristic
64D4⋊C8×C137C2211yescharacteristic
65D4⋊C8×C137C2211yescharacteristic
66#322×C137C2211yescharacteristic
67C2×#41×C137—21no—
68C2×Q16×C137—21no—
69C2×Q16×C137—21no—
70C2×SD16×C137—21no—
71C2×SD16×C137—21no—
72C2×SD16×C137—21no—
73C2×SD16×C137D411yescharacteristic
74C2×D8×C137D411yescharacteristic
75C2×M16×C137—21no—
76C22×C8×C137—21no—
77C22×C8×C137—21no—
78C4⋊Q8×C137C2311yescharacteristic
79C4⋊Q8×C137C2311yescharacteristic
80C4⋊Q8×C137C2311yescharacteristic
81C4⋊Q8×C137C2311yescharacteristic
82#126×C137—41no—
83#126×C137—41no—
84#124×C137—21no—
85#124×C137—21no—
86#124×C137—41no—
87#123×C137—41no—
88C22⋊Q8×C137—21no—
89C22⋊Q8×C137—21no—
90C22⋊Q8×C137—21no—
91#121×C137—21no—
92#121×C137—21no—
93#121×C137—21no—
94C4×Q8×C137—21no—
95C4×Q8×C137—21no—
96C4×Q8×C137C2311yescharacteristic
97C4×D4×C137C2311yescharacteristic
98C4×D4×C137C2311yescharacteristic
99C4×D4×C137C2311yescharacteristic
100#117×C137—21no—
101#117×C137—21no—
102#117×C137—21no—
103#117×C137—21no—
104C2×C4⋊C4×C137—21no—
105#107×C137—21no—
106#107×C137—21no—
107#107×C137—21no—
108#107×C137—21no—
109#107×C137—21no—
110#107×C137—41no—
111#107×C137D411yescharacteristic
112#106×C137—21no—
113#106×C137—21no—
114#106×C137—21no—
115#106×C137—21no—
116#106×C137D411yescharacteristic
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×C137—21no—
126#103×C137—21no—
127#103×C137—21no—
128#103×C137—21no—
129#103×C137—41no—
130#103×C137D411yescharacteristic
131#102×C137—21no—
132#102×C137—21no—
133#102×C137—21no—
134#102×C137D411yescharacteristic
135#102×C137D411yescharacteristic
136#102×C137D411yescharacteristic
137C22⋊C8×C137—21no—
138C22⋊C8×C137—21no—
139C22⋊C8×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×C137—21no—
149C2×Q8×C137—21no—
150C2×Q8×C137C2×D411yescharacteristic
151C2×D4×C137—41no—
152C2×D4×C137—41no—
153C2×D4×C137C2×D411yescharacteristic
154C2×D4×C137C2×D411yescharacteristic
155C2×D4×C137C2×D411yescharacteristic
156C22×C4×C137—21no—
157C22×C4×C137—21no—
158C22×C4×C137—21no—
159C22×C4×C137—41no—
160Q16×C137—42no—
161Q16×C137—81no—
162SD16×C137—22no—
163SD16×C137—81no—
164SD16×C137—81no—
165SD16×C137—81no—
166D8×C137—41no—
167M16×C137—42no—
168C2×C8×C137—21no—
169C2×C8×C137—21no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—21no—
173C2×C8×C137—42no—
174C2×C8×C137—81no—
175C2×C8×C137C2×D411yescharacteristic
176C2×C8×C137C2×D411yescharacteristic
177C2×C8×C137C2×D411yescharacteristic
178C2×C8×C137C2×D411yescharacteristic
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—21no—
183C4⋊C4×C137—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137—21no—
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—41no—
189C4⋊C4×C137—41no—
190C4⋊C4×C137—41no—
191C4⋊C4×C137C2×D411yescharacteristic
192C4⋊C4×C137C2×D411yescharacteristic
193C4⋊C4×C137C2×D411yescharacteristic
194C4⋊C4×C137C2×D411yescharacteristic
195C22⋊C4×C137—21no—
196C22⋊C4×C137—21no—
197C22⋊C4×C137—21no—
198C22⋊C4×C137—41no—
199C22⋊C4×C137—41no—
200C22⋊C4×C137—41no—
201C22⋊C4×C137—41no—
202C22⋊C4×C137—41no—
203C22⋊C4×C137—41no—
204C22⋊C4×C137—41no—
205C42×C137—21no—
206C42×C137—41no—
207C42×C137—41no—
208C42×C137—41no—
209C42×C137C2411yescharacteristic
210C23×C137—21no—
211C23×C137—21no—
212C23×C137—21no—
213Q8×C137—21no—
214Q8×C137—21no—
215Q8×C137—41no—
216Q8×C137—41no—
217Q8×C137—41no—
218Q8×C137—41no—
219Q8×C137—41no—
220Q8×C137—41no—
221Q8×C137—81no—
222D4×C137—21no—
223D4×C137—21no—
224D4×C137—21no—
225D4×C137—21no—
226D4×C137—21no—
227D4×C137—21no—
228D4×C137—82no—
229D4×C137—161no—
230C2×C4×C137—21no—
231C2×C4×C137—21no—
232C2×C4×C137—21no—
233C2×C4×C137—21no—
234C2×C4×C137—21no—
235C2×C4×C137—41no—
236C2×C4×C137—41no—
237C2×C4×C137—41no—
238C2×C4×C137—41no—
239C2×C4×C137—41no—
240C2×C4×C137—41no—
241C2×C4×C137—41no—
242C2×C4×C137—41no—
243C2×C4×C137—41no—
244C2×C4×C137—41no—
245C2×C4×C137—82no—
246C2×C4×C137C22×D411yescharacteristic
247C2×C4×C137C22×D411yescharacteristic
248C2×C4×C137H(5,𝔽2)11yescharacteristic
249C8×C137—21no—
250C8×C137—21no—
251C8×C137—21no—
252C8×C137—41no—
253C8×C137—41no—
254C8×C137—41no—
255C8×C137—41no—
256C8×C137—41no—
257C8×C137#13512yes—
258C22×C137—41no—
259C22×C137—41no—
260C22×C137—41no—
261C22×C137—41no—
262C22×C137—41no—
263C22×C137—41no—
264C22×C137—41no—
265C22×C137—41no—
266C22×C137—41no—
267C22×C137D4211yescharacteristic
268C4×C137—21no—
269C4×C137—41no—
270C4×C137—41no—
271C4×C137—41no—
272C4×C137—41no—
273C4×C137—41no—
274C4×C137—81no—
275C4×C137—81no—
276C4×C137—81no—
277C4×C137—81no—
278C4×C137C2×#13511yescharacteristic
279C4×C137#57511yescharacteristic
280C4×C137#57611yescharacteristic
281C4×C137#57811yescharacteristic
282C2×C137—81no—
283C2×C137—81no—
284C2×C137—81no—
285C2×C137#326811yescharacteristic
286C2×C137#328311yescharacteristic
287C2×C137#328911yescharacteristic
288#19863C13711yesmaximal, characteristic, direct product factor, Sylow
289C137#1986311yescharacteristic, direct product factor, Sylow
290#3393C2×C13711yescharacteristic, complemented
291#3353C2×C13711yescharacteristic, complemented
292#3340C2×C13711yescharacteristic, complemented
293#3303C2×C13711yescharacteristic
294#1723C2×C13711yescharacteristic, complemented
295#1691C2×C13711yescharacteristic, complemented
296#1684C2×C13711yescharacteristic, complemented
297#1673C2×C13711yescharacteristic, complemented
298#1669C2×C13711yescharacteristic, complemented
299#1650C2×C13711yescharacteristic, complemented
300#1647C2×C13711yescharacteristic, complemented
301#1646C2×C13711yescharacteristic, complemented
302#1638C2×C13711yescharacteristic, complemented
303#1581C2×C13711yescharacteristic, complemented
304SD16⋊C8C2×C13711yescharacteristic, complemented
305#556C22×C13711yescharacteristic
306#556C22×C13711yescharacteristic
307#555C22×C13711yescharacteristic
308#547C22×C13711yescharacteristic
309#500C22×C13711yescharacteristic
310#500C22×C13711yescharacteristic
311#498C22×C13711yescharacteristic
312#495—21no—
313#494C22×C13711yescharacteristic
314#487C22×C13711yescharacteristic
315#487C22×C13711yescharacteristic
316#485—21no—
317#485—21no—
318#484—21no—
319#482—21no—
320#482—21no—
321#477C22×C13711yescharacteristic
322#476C22×C13711yescharacteristic
323#475C22×C13711yescharacteristic
324#474C22×C13711yescharacteristic
325#474C22×C13711yescharacteristic
326#468—21no—
327#465—21no—
328#465—21no—
329#464—21no—
330#464—21no—
331#461C22×C13711yescharacteristic
332#461C22×C13711yescharacteristic
333#461C22×C13711yescharacteristic
334#449—21no—
335C8×Q8C22×C13711yescharacteristic
336C4×Q16—21no—
337C4×SD16C22×C13711yescharacteristic
338C4×D8C22×C13711yescharacteristic
339#436C22×C13711yescharacteristic
340C8×D4C22×C13711yescharacteristic
341C8×D4C22×C13711yescharacteristic
342#428—21no—
343#427—21no—
344#416—21no—
345#335C22×C13711yescharacteristic
346#335C22×C13711yescharacteristic
347#333C22×C13711yescharacteristic
348#332C22×C13711yescharacteristic
349#332C22×C13711yescharacteristic
350#332C22×C13711yescharacteristic
351Q8⋊C8C22×C13711yescharacteristic
352D4⋊C8C22×C13711yescharacteristic
353D4⋊C8C22×C13711yescharacteristic
354D4⋊C8C22×C13711yescharacteristic
355#322C22×C13711yescharacteristic
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C13711yescharacteristic
363C2×D8D4×C13711yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8C23×C13711yescharacteristic
368C4⋊Q8C23×C13711yescharacteristic
369C4⋊Q8C23×C13711yescharacteristic
370C4⋊Q8C23×C13711yescharacteristic
371#126—41no—
372#126—41no—
373#124—21no—
374#124—21no—
375#124—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C13711yescharacteristic
386C4×D4C23×C13711yescharacteristic
387C4×D4C23×C13711yescharacteristic
388C4×D4C23×C13711yescharacteristic
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—41no—
400#107D4×C13711yescharacteristic
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C13711yescharacteristic
406C4⋊C8—21no—
407C4⋊C8C23×C13711yescharacteristic
408C4⋊C8C23×C13711yescharacteristic
409C4⋊C8C23×C13711yescharacteristic
410C4⋊C8C23×C13711yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—41no—
419#103D4×C13711yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C13711yescharacteristic
424#102D4×C13711yescharacteristic
425#102D4×C13711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C4×C8—21no—
430C4×C8C23×C13711yescharacteristic
431C4×C8C23×C13711yescharacteristic
432C4×C8C23×C13711yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×D4×C13711yescharacteristic
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C13711yescharacteristic
443C2×D4C2×D4×C13711yescharacteristic
444C2×D4C2×D4×C13711yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449Q16—42no—
450Q16—81no—
451SD16—22no—
452SD16—81no—
453SD16—81no—
454SD16—81no—
455D8—41no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—81no—
464C2×C8C2×D4×C13711yescharacteristic
465C2×C8C2×D4×C13711yescharacteristic
466C2×C8C2×D4×C13711yescharacteristic
467C2×C8C2×D4×C13711yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C13711yescharacteristic
481C4⋊C4C2×D4×C13711yescharacteristic
482C4⋊C4C2×D4×C13711yescharacteristic
483C4⋊C4C2×D4×C13711yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42C24×C13711yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4C22×D4×C13711yescharacteristic
536C2×C4C22×D4×C13711yescharacteristic
537C2×C4H(5,𝔽2)×C13711yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8#135×C13712yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22D42×C13711yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C13711yescharacteristic
568C4#575×C13711yescharacteristic
569C4#576×C13711yescharacteristic
570C4#578×C13711yescharacteristic
571C2—81no—
572C2—81no—
573C2—81no—
574C2#3268×C13711yescharacteristic
575C2#3283×C13711yescharacteristic
576C2#3289×C13711yescharacteristic
subgroupG/H
center, socleC22×C137D42
commutator, Frattini, cosocleC42C24×C137
prime radical#3303×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. #3393×C137C2semidirect
2. #3353×C137C2semidirect
3. #3340×C137C2semidirect
5. #1723×C137C2semidirect
6. #1691×C137C2semidirect
7. #1684×C137C2semidirect
8. #1673×C137C2semidirect
9. #1669×C137C2semidirect
10. #1650×C137C2semidirect
11. #1647×C137C2semidirect
12. #1646×C137C2semidirect
13. #1638×C137C2semidirect
14. #1581×C137C2semidirect
15. SD16⋊C8×C137C2semidirect
288. #19863C137direct (N × H)
289. C137#19863direct (N × H)
290. #3393C2×C137semidirect
291. #3353C2×C137semidirect
292. #3340C2×C137semidirect
294. #1723C2×C137semidirect
295. #1691C2×C137semidirect
296. #1684C2×C137semidirect
297. #1673C2×C137semidirect
298. #1669C2×C137semidirect
299. #1650C2×C137semidirect
300. #1647C2×C137semidirect
301. #1646C2×C137semidirect
302. #1638C2×C137semidirect
303. #1581C2×C137semidirect
304. SD16⋊C8C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3393×C1372
#3353×C1372
#3340×C1372
#3303×C1372
#1723×C1372
#1691×C1372
#1684×C1372
#1673×C1372
#1669×C1372
#1650×C1372
#1647×C1372
#1646×C1372
#1638×C1372
#1581×C1372
SD16⋊C8×C1372
#19863137