Finite Group Databasebeta

← C137×#20305 #46869691

Subgroups — C137×#20305 #46869691

Order 35072.

604 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3384×C137C211yesmaximal, characteristic, complemented
2#3354×C137C211yesmaximal, characteristic
3#3331×C137C211yesmaximal, characteristic, complemented
4#3329×C137C211yesmaximal, characteristic, complemented
5#1707×C137C211yesmaximal, characteristic, complemented
6#1703×C137C211yesmaximal, characteristic, complemented
7#1703×C137C211yesmaximal, characteristic, complemented
8#1692×C137C211yesmaximal, characteristic, complemented
9#1691×C137C211yesmaximal, characteristic, complemented
10#1649×C137C211yesmaximal, characteristic, complemented
11#1647×C137C211yesmaximal, characteristic, complemented
12#1634×C137C211yesmaximal, characteristic, complemented
13#1632×C137C211yesmaximal, characteristic, complemented
14#1590×C137C211yesmaximal, characteristic, complemented
15#1589×C137C211yesmaximal, characteristic, complemented
16#555×C137C2211yescharacteristic
17#554×C137C2211yescharacteristic
18D4×Q8×C137C2211yescharacteristic
19#547×C137C2211yescharacteristic
20#501×C137—21no—
21#500×C137C2211yescharacteristic
22#498×C137C2211yescharacteristic
23#498×C137C2211yescharacteristic
24#494×C137C2211yescharacteristic
25#487×C137C2211yescharacteristic
26#487×C137C2211yescharacteristic
27#485×C137—21no—
28#483×C137—21no—
29#482×C137—21no—
30#481×C137—21no—
31#478×C137—21no—
32#477×C137C2211yescharacteristic
33#476×C137—21no—
34#476×C137C2211yescharacteristic
35#476×C137C2211yescharacteristic
36#476×C137C2211yescharacteristic
37#474×C137C2211yescharacteristic
38#474×C137C2211yescharacteristic
39#470×C137—21no—
40#469×C137—21no—
41#468×C137—21no—
42#462×C137C2211yescharacteristic
43#461×C137C2211yescharacteristic
44#452×C137—21no—
45#448×C137—21no—
46#446×C137C2211yescharacteristic
47#442×C137—21no—
48C4×SD16×C137C2211yescharacteristic
49C4×D8×C137C2211yescharacteristic
50#436×C137C2211yescharacteristic
51#436×C137C2211yescharacteristic
52#436×C137C2211yescharacteristic
53#428×C137—21no—
54#419×C137—21no—
55#417×C137—21no—
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#333×C137C2211yescharacteristic
59#333×C137C2211yescharacteristic
60#332×C137C2211yescharacteristic
61#332×C137C2211yescharacteristic
62Q8⋊C8×C137C2211yescharacteristic
63D4⋊C8×C137C2211yescharacteristic
64D4⋊C8×C137C2211yescharacteristic
65D4⋊C8×C137C2211yescharacteristic
66C82×C137C2211yescharacteristic
67C2×#41×C137—21no—
68C22×Q8×C137—21no—
69C2×Q16×C137—21no—
70C2×Q16×C137—41no—
71C2×SD16×C137—21no—
72C2×SD16×C137D411yescharacteristic
73C2×D8×C137D411yescharacteristic
74C2×M16×C137—21no—
75C2×M16×C137—21no—
76C2×M16×C137—21no—
77C4⋊Q8×C137—21no—
78C4⋊Q8×C137C2311yescharacteristic
79C4⋊Q8×C137C2311yescharacteristic
80C4⋊Q8×C137C2311yescharacteristic
81C4⋊Q8×C137C2311yescharacteristic
82#125×C137—21no—
83#124×C137—41no—
84#123×C137—41no—
85C22⋊Q8×C137—21no—
86C22⋊Q8×C137—21no—
87C22⋊Q8×C137—21no—
88C22⋊Q8×C137—41no—
89C22⋊Q8×C137—41no—
90#121×C137—21no—
91#121×C137—21no—
92#121×C137—21no—
93C4×Q8×C137C2311yescharacteristic
94C4×D4×C137—21no—
95C4×D4×C137—21no—
96C4×D4×C137C2311yescharacteristic
97C4×D4×C137C2311yescharacteristic
98C4×D4×C137C2311yescharacteristic
99#117×C137—21no—
100#117×C137—21no—
101C2×C4⋊C4×C137—21no—
102C2×C4⋊C4×C137—21no—
103#107×C137—21no—
104#107×C137—21no—
105#107×C137—21no—
106#107×C137—41no—
107#107×C137D411yescharacteristic
108#106×C137—21no—
109#106×C137—21no—
110#106×C137—21no—
111#106×C137—21no—
112#106×C137—21no—
113#106×C137—21no—
114#106×C137—21no—
115#106×C137D411yescharacteristic
116C4⋊C8×C137—21no—
117C4⋊C8×C137C2311yescharacteristic
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120C4⋊C8×C137C2311yescharacteristic
121#103×C137—21no—
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×C137D411yescharacteristic
129#102×C137—21no—
130#102×C137—21no—
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—
140#97×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×C137—41no—
151C2×Q8×C137—42no—
152C2×Q8×C137—81no—
153C2×Q8×C137C2×D411yescharacteristic
154C2×D4×C137—41no—
155C2×D4×C137—41no—
156C2×D4×C137C2×D411yescharacteristic
157C2×D4×C137C2×D411yescharacteristic
158C2×D4×C137C2×D411yescharacteristic
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—21no—
162C22×C4×C137—41no—
163C22×C4×C137—41no—
164C22×C4×C137—41no—
165Q16×C137—82no—
166Q16×C137—81no—
167SD16×C137—41no—
168SD16×C137—81no—
169D8×C137—22no—
170M16×C137—42no—
171M16×C137—81no—
172M16×C137—81no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137C2×D411yescharacteristic
179C2×C8×C137C2×D411yescharacteristic
180C2×C8×C137C2×D411yescharacteristic
181C2×C8×C137C2×D411yescharacteristic
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—21no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—41no—
192C4⋊C4×C137—41no—
193C4⋊C4×C137—41no—
194C4⋊C4×C137—41no—
195C4⋊C4×C137C2×D411yescharacteristic
196C4⋊C4×C137C2×D411yescharacteristic
197C4⋊C4×C137C2×D411yescharacteristic
198C4⋊C4×C137C2×D411yescharacteristic
199C22⋊C4×C137—21no—
200C22⋊C4×C137—21no—
201C22⋊C4×C137—21no—
202C22⋊C4×C137—41no—
203C22⋊C4×C137—41no—
204C22⋊C4×C137—41no—
205C22⋊C4×C137—41no—
206C22⋊C4×C137—41no—
207C42×C137—21no—
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—81no—
220Q8×C137—81no—
221Q8×C137—82no—
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×C137—82no—
247C2×C4×C137—161no—
248C2×C4×C137C22×D411yescharacteristic
249C2×C4×C137C22×D411yescharacteristic
250C2×C4×C137H(5,𝔽2)11yescharacteristic
251C8×C137—22no—
252C8×C137—21no—
253C8×C137—21no—
254C8×C137—21no—
255C8×C137—41no—
256C8×C137—41no—
257C8×C137—41no—
258C8×C137—41no—
259C8×C137#13712yes—
260C22×C137—41no—
261C22×C137—41no—
262C22×C137—41no—
263C22×C137—41no—
264C22×C137—41no—
265C22×C137—41no—
266C22×C137—41no—
267C22×C137—41no—
268C22×C137—41no—
269C22×C137D4211yescharacteristic
270C4×C137—21no—
271C4×C137—41no—
272C4×C137—41no—
273C4×C137—41no—
274C4×C137—41no—
275C4×C137—41no—
276C4×C137—81no—
277C4×C137—81no—
278C4×C137—81no—
279C4×C137—81no—
280C4×C137C2×#13711yescharacteristic
281C4×C137#57511yescharacteristic
282C4×C137#57611yescharacteristic
283C4×C137#57811yescharacteristic
284C2×C137—81no—
285C2×C137—81no—
286C2×C137—81no—
287C2×C137#327311yescharacteristic
288C2×C137#327611yescharacteristic
289C2×C137#329111yescharacteristic
290#20305C13711yesmaximal, characteristic, direct product factor, Sylow
291C137#2030511yescharacteristic, direct product factor, Sylow
292#3384C2×C13711yescharacteristic, complemented
293#3354C2×C13711yescharacteristic
294#3331C2×C13711yescharacteristic, complemented
295#3329C2×C13711yescharacteristic, complemented
296#1707C2×C13711yescharacteristic, complemented
297#1703C2×C13711yescharacteristic, complemented
298#1703C2×C13711yescharacteristic, complemented
299#1692C2×C13711yescharacteristic, complemented
300#1691C2×C13711yescharacteristic, complemented
301#1649C2×C13711yescharacteristic, complemented
302#1647C2×C13711yescharacteristic, complemented
303#1634C2×C13711yescharacteristic, complemented
304#1632C2×C13711yescharacteristic, complemented
305#1590C2×C13711yescharacteristic, complemented
306#1589C2×C13711yescharacteristic, complemented
307#555C22×C13711yescharacteristic
308#554C22×C13711yescharacteristic
309D4×Q8C22×C13711yescharacteristic
310#547C22×C13711yescharacteristic
311#501—21no—
312#500C22×C13711yescharacteristic
313#498C22×C13711yescharacteristic
314#498C22×C13711yescharacteristic
315#494C22×C13711yescharacteristic
316#487C22×C13711yescharacteristic
317#487C22×C13711yescharacteristic
318#485—21no—
319#483—21no—
320#482—21no—
321#481—21no—
322#478—21no—
323#477C22×C13711yescharacteristic
324#476—21no—
325#476C22×C13711yescharacteristic
326#476C22×C13711yescharacteristic
327#476C22×C13711yescharacteristic
328#474C22×C13711yescharacteristic
329#474C22×C13711yescharacteristic
330#470—21no—
331#469—21no—
332#468—21no—
333#462C22×C13711yescharacteristic
334#461C22×C13711yescharacteristic
335#452—21no—
336#448—21no—
337#446C22×C13711yescharacteristic
338#442—21no—
339C4×SD16C22×C13711yescharacteristic
340C4×D8C22×C13711yescharacteristic
341#436C22×C13711yescharacteristic
342#436C22×C13711yescharacteristic
343#436C22×C13711yescharacteristic
344#428—21no—
345#419—21no—
346#417—21no—
347#335C22×C13711yescharacteristic
348#334C22×C13711yescharacteristic
349#333C22×C13711yescharacteristic
350#333C22×C13711yescharacteristic
351#332C22×C13711yescharacteristic
352#332C22×C13711yescharacteristic
353Q8⋊C8C22×C13711yescharacteristic
354D4⋊C8C22×C13711yescharacteristic
355D4⋊C8C22×C13711yescharacteristic
356D4⋊C8C22×C13711yescharacteristic
357C82C22×C13711yescharacteristic
358C2×#41—21no—
359C22×Q8—21no—
360C2×Q16—21no—
361C2×Q16—41no—
362C2×SD16—21no—
363C2×SD16D4×C13711yescharacteristic
364C2×D8D4×C13711yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C13711yescharacteristic
370C4⋊Q8C23×C13711yescharacteristic
371C4⋊Q8C23×C13711yescharacteristic
372C4⋊Q8C23×C13711yescharacteristic
373#125—21no—
374#124—41no—
375#123—41no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—41no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×Q8C23×C13711yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C13711yescharacteristic
388C4×D4C23×C13711yescharacteristic
389C4×D4C23×C13711yescharacteristic
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#107D4×C13711yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106D4×C13711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8C23×C13711yescharacteristic
409C4⋊C8C23×C13711yescharacteristic
410C4⋊C8C23×C13711yescharacteristic
411C4⋊C8C23×C13711yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C13711yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C13711yescharacteristic
426#102D4×C13711yescharacteristic
427#102D4×C13711yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432C4×C8C23×C13711yescharacteristic
433C4×C8C23×C13711yescharacteristic
434C4×C8C23×C13711yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C13711yescharacteristic
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C2×D4×C13711yescharacteristic
448C2×D4C2×D4×C13711yescharacteristic
449C2×D4C2×D4×C13711yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—82no—
457Q16—81no—
458SD16—41no—
459SD16—81no—
460D8—22no—
461M16—42no—
462M16—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×D4×C13711yescharacteristic
470C2×C8C2×D4×C13711yescharacteristic
471C2×C8C2×D4×C13711yescharacteristic
472C2×C8C2×D4×C13711yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C13711yescharacteristic
487C4⋊C4C2×D4×C13711yescharacteristic
488C4⋊C4C2×D4×C13711yescharacteristic
489C4⋊C4C2×D4×C13711yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—41no—
500C42C24×C13711yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511Q8—81no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—82no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
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—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—161no—
539C2×C4C22×D4×C13711yescharacteristic
540C2×C4C22×D4×C13711yescharacteristic
541C2×C4H(5,𝔽2)×C13711yescharacteristic
542C8—22no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8#137×C13712yes—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D42×C13711yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#137×C13711yescharacteristic
572C4#575×C13711yescharacteristic
573C4#576×C13711yescharacteristic
574C4#578×C13711yescharacteristic
575C2—81no—
576C2—81no—
577C2—81no—
578C2#3273×C13711yescharacteristic
579C2#3276×C13711yescharacteristic
580C2#3291×C13711yescharacteristic
subgroupG/H
center, socleC22×C137D42
commutator, Frattini, cosocleC42C24×C137
prime radical#3354×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. #3384×C137C2semidirect
3. #3331×C137C2semidirect
4. #3329×C137C2semidirect
5. #1707×C137C2semidirect
6. #1703×C137C2semidirect
7. #1703×C137C2semidirect
8. #1692×C137C2semidirect
9. #1691×C137C2semidirect
10. #1649×C137C2semidirect
11. #1647×C137C2semidirect
12. #1634×C137C2semidirect
13. #1632×C137C2semidirect
14. #1590×C137C2semidirect
15. #1589×C137C2semidirect
290. #20305C137direct (N × H)
291. C137#20305direct (N × H)
292. #3384C2×C137semidirect
294. #3331C2×C137semidirect
295. #3329C2×C137semidirect
296. #1707C2×C137semidirect
297. #1703C2×C137semidirect
298. #1703C2×C137semidirect
299. #1692C2×C137semidirect
300. #1691C2×C137semidirect
301. #1649C2×C137semidirect
302. #1647C2×C137semidirect
303. #1634C2×C137semidirect
304. #1632C2×C137semidirect
305. #1590C2×C137semidirect
306. #1589C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3384×C1372
#3354×C1372
#3331×C1372
#3329×C1372
#1707×C1372
#1703×C1372
#1692×C1372
#1691×C1372
#1649×C1372
#1647×C1372
#1634×C1372
#1632×C1372
#1590×C1372
#1589×C1372
#20305137