Finite Group Databasebeta

← C137×#19587 #46868973

Subgroups — C137×#19587 #46868973

Order 35072.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3252×C137C211yesmaximal, characteristic
2#3233×C137C211yesmaximal, characteristic
3#3231×C137C211yesmaximal, characteristic, complemented
4#2994×C137C211yesmaximal, characteristic
5#1703×C137C211yesmaximal, characteristic, complemented
6#1700×C137C211yesmaximal, characteristic, complemented
7#1696×C137C211yesmaximal, characteristic, complemented
8#1691×C137C211yesmaximal, characteristic, complemented
9#1684×C137C211yesmaximal, characteristic, complemented
10#1679×C137C211yesmaximal, characteristic, complemented
11#1675×C137C211yesmaximal, characteristic, complemented
12#1672×C137C211yesmaximal, characteristic, complemented
13#1574×C137C211yesmaximal, characteristic, complemented
14#1550×C137C211yesmaximal, characteristic, complemented
15#1542×C137C211yesmaximal, characteristic, complemented
16#533×C137C2211yescharacteristic
17#533×C137C2211yescharacteristic
18#529×C137C2211yescharacteristic
19#500×C137C2211yescharacteristic
20#499×C137—21no—
21#498×C137C2211yescharacteristic
22#488×C137—21no—
23#487×C137C2211yescharacteristic
24#487×C137C2211yescharacteristic
25#485×C137—21no—
26#485×C137—21no—
27#485×C137—21no—
28#482×C137—21no—
29#479×C137—21no—
30#479×C137—21no—
31#479×C137—21no—
32#477×C137C2211yescharacteristic
33#477×C137C2211yescharacteristic
34#476×C137C2211yescharacteristic
35#476×C137C2211yescharacteristic
36#475×C137C2211yescharacteristic
37#474×C137C2211yescharacteristic
38#470×C137—21no—
39#468×C137—21no—
40#464×C137—21no—
41#462×C137C2211yescharacteristic
42#461×C137C2211yescharacteristic
43#446×C137C2211yescharacteristic
44C8×Q8×C137C2211yescharacteristic
45#436×C137C2211yescharacteristic
46#435×C137—21no—
47C8×D4×C137—21no—
48C8×D4×C137C2211yescharacteristic
49#433×C137—21no—
50#431×C137C2211yescharacteristic
51#431×C137C2211yescharacteristic
52#424×C137—21no—
53#423×C137C2211yescharacteristic
54C2×C4⋊C8×C137C2211yescharacteristic
55#335×C137C2211yescharacteristic
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#334×C137C2211yescharacteristic
59#333×C137C2211yescharacteristic
60#333×C137C2211yescharacteristic
61#333×C137C2211yescharacteristic
62#333×C137C2211yescharacteristic
63#332×C137C2211yescharacteristic
64#332×C137C2211yescharacteristic
65#332×C137C2211yescharacteristic
66#332×C137C2211yescharacteristic
67C2×Q16×C137—21no—
68C2×SD16×C137—21no—
69C2×M16×C137—21no—
70C2×M16×C137—21no—
71C22×C8×C137—21no—
72C22×C8×C137—21no—
73C4⋊Q8×C137C2311yescharacteristic
74C4⋊Q8×C137C2311yescharacteristic
75C4⋊Q8×C137C2311yescharacteristic
76C4⋊Q8×C137C2311yescharacteristic
77#126×C137—21no—
78#125×C137—21no—
79#125×C137—21no—
80#125×C137D411yescharacteristic
81#124×C137D411yescharacteristic
82#123×C137—21no—
83C22⋊Q8×C137—21no—
84C22⋊Q8×C137—21no—
85C22⋊Q8×C137—21no—
86C22⋊Q8×C137—21no—
87C22⋊Q8×C137D411yescharacteristic
88#121×C137D411yescharacteristic
89C4×Q8×C137—21no—
90C4×Q8×C137—21no—
91C4×Q8×C137—21no—
92C4×Q8×C137—21no—
93C4×Q8×C137C2311yescharacteristic
94C4×D4×C137—21no—
95C4×D4×C137C2311yescharacteristic
96#117×C137—21no—
97#117×C137—21no—
98#117×C137—21no—
99C2×C42×C137C2311yescharacteristic
100#107×C137—21no—
101#107×C137—21no—
102#107×C137—21no—
103#107×C137—21no—
104#107×C137—21no—
105#106×C137—21no—
106#106×C137—21no—
107#106×C137—21no—
108#106×C137—21no—
109#106×C137—21no—
110C4⋊C8×C137—21no—
111C4⋊C8×C137—21no—
112C4⋊C8×C137—21no—
113C4⋊C8×C137—21no—
114C4⋊C8×C137D411yescharacteristic
115C4⋊C8×C137D411yescharacteristic
116C4⋊C8×C137C2311yescharacteristic
117C4⋊C8×C137C2311yescharacteristic
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—21no—
130#103×C137—21no—
131#102×C137—21no—
132#102×C137—21no—
133#102×C137—21no—
134C22⋊C8×C137—21no—
135C22⋊C8×C137—21no—
136C22⋊C8×C137—21no—
137C22⋊C8×C137D411yescharacteristic
138C22⋊C8×C137D411yescharacteristic
139#97×C137—21no—
140C4×C8×C137—21no—
141C4×C8×C137—21no—
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144C2×Q8×C137—21no—
145C2×Q8×C137—21no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137C2×D411yescharacteristic
149C2×D4×C137—21no—
150C2×D4×C137C2×D411yescharacteristic
151C22×C4×C137—21no—
152C22×C4×C137C2×D411yescharacteristic
153C22×C4×C137C2×D411yescharacteristic
154C22×C4×C137#4111yescharacteristic
155Q16×C137—81no—
156SD16×C137—81no—
157M16×C137—81no—
158M16×C137—81no—
159C2×C8×C137—21no—
160C2×C8×C137—21no—
161C2×C8×C137—21no—
162C2×C8×C137—21no—
163C2×C8×C137—21no—
164C2×C8×C137—21no—
165C2×C8×C137—81no—
166C2×C8×C137—81no—
167C2×C8×C137C2×D411yescharacteristic
168C2×C8×C137C2×D411yescharacteristic
169C2×C8×C137C2×D411yescharacteristic
170C2×C8×C137C2×D411yescharacteristic
171C4⋊C4×C137—21no—
172C4⋊C4×C137—21no—
173C4⋊C4×C137—21no—
174C4⋊C4×C137—21no—
175C4⋊C4×C137—21no—
176C4⋊C4×C137—21no—
177C4⋊C4×C137—21no—
178C4⋊C4×C137—21no—
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—21no—
183C4⋊C4×C137—41no—
184C4⋊C4×C137—41no—
185C4⋊C4×C137—41no—
186C4⋊C4×C137—41no—
187C4⋊C4×C137C2×D411yescharacteristic
188C4⋊C4×C137C2×D411yescharacteristic
189C22⋊C4×C137—21no—
190C22⋊C4×C137—21no—
191C22⋊C4×C137—21no—
192C22⋊C4×C137—21no—
193C22⋊C4×C137—21no—
194C22⋊C4×C137—41no—
195C22⋊C4×C137—41no—
196C42×C137—21no—
197C42×C137—41no—
198C42×C137—41no—
199C42×C137C2×D411yescharacteristic
200C42×C137C2×D411yescharacteristic
201C42×C137#4111yescharacteristic
202C42×C137C2411yescharacteristic
203C23×C137—21no—
204C23×C137#12111yescharacteristic
205Q8×C137—21no—
206Q8×C137—21no—
207Q8×C137—41no—
208Q8×C137—41no—
209Q8×C137—41no—
210Q8×C137—41no—
211Q8×C137—81no—
212Q8×C137—81no—
213D4×C137—21no—
214D4×C137—21no—
215D4×C137—42no—
216C2×C4×C137—21no—
217C2×C4×C137—21no—
218C2×C4×C137—21no—
219C2×C4×C137—21no—
220C2×C4×C137—21no—
221C2×C4×C137—21no—
222C2×C4×C137—21no—
223C2×C4×C137—41no—
224C2×C4×C137—41no—
225C2×C4×C137—41no—
226C2×C4×C137—41no—
227C2×C4×C137—41no—
228C2×C4×C137—41no—
229C2×C4×C137—41no—
230C2×C4×C137#12111yescharacteristic
231C2×C4×C137#12111yescharacteristic
232C2×C4×C137#12111yescharacteristic
233C2×C4×C137C22×D411yescharacteristic
234C2×C4×C137C22×D411yescharacteristic
235C2×C4×C137C2×#4111yescharacteristic
236C8×C137—21no—
237C8×C137—21no—
238C8×C137—21no—
239C8×C137—21no—
240C8×C137—41no—
241C8×C137—41no—
242C8×C137—41no—
243C8×C137—41no—
244C8×C137—41no—
245C8×C137—41no—
246C22×C137—21no—
247C22×C137—21no—
248C22×C137—21no—
249C22×C137—41no—
250C22×C137—41no—
251C22×C137—41no—
252C22×C137C2×#12111yescharacteristic
253C4×C137—21no—
254C4×C137—21no—
255C4×C137—21no—
256C4×C137—21no—
257C4×C137—41no—
258C4×C137—41no—
259C4×C137—41no—
260C4×C137—81no—
261C4×C137—81no—
262C4×C137—81no—
263C4×C137—81no—
264C4×C137#57711yescharacteristic
265C4×C137#57711yescharacteristic
266C4×C137#57811yescharacteristic
267C4×C137#57811yescharacteristic
268C2×C137—41no—
269C2×C137—81no—
270C2×C137#304611yescharacteristic
271C2×C137#306311yescharacteristic
272C2×C137#306711yescharacteristic
273#19587C13711yesmaximal, characteristic, direct product factor, Sylow
274C137#1958711yescharacteristic, direct product factor, Sylow
275#3252C2×C13711yescharacteristic
276#3233C2×C13711yescharacteristic
277#3231C2×C13711yescharacteristic, complemented
278#2994C2×C13711yescharacteristic
279#1703C2×C13711yescharacteristic, complemented
280#1700C2×C13711yescharacteristic, complemented
281#1696C2×C13711yescharacteristic, complemented
282#1691C2×C13711yescharacteristic, complemented
283#1684C2×C13711yescharacteristic, complemented
284#1679C2×C13711yescharacteristic, complemented
285#1675C2×C13711yescharacteristic, complemented
286#1672C2×C13711yescharacteristic, complemented
287#1574C2×C13711yescharacteristic, complemented
288#1550C2×C13711yescharacteristic, complemented
289#1542C2×C13711yescharacteristic, complemented
290#533C22×C13711yescharacteristic
291#533C22×C13711yescharacteristic
292#529C22×C13711yescharacteristic
293#500C22×C13711yescharacteristic
294#499—21no—
295#498C22×C13711yescharacteristic
296#488—21no—
297#487C22×C13711yescharacteristic
298#487C22×C13711yescharacteristic
299#485—21no—
300#485—21no—
301#485—21no—
302#482—21no—
303#479—21no—
304#479—21no—
305#479—21no—
306#477C22×C13711yescharacteristic
307#477C22×C13711yescharacteristic
308#476C22×C13711yescharacteristic
309#476C22×C13711yescharacteristic
310#475C22×C13711yescharacteristic
311#474C22×C13711yescharacteristic
312#470—21no—
313#468—21no—
314#464—21no—
315#462C22×C13711yescharacteristic
316#461C22×C13711yescharacteristic
317#446C22×C13711yescharacteristic
318C8×Q8C22×C13711yescharacteristic
319#436C22×C13711yescharacteristic
320#435—21no—
321C8×D4—21no—
322C8×D4C22×C13711yescharacteristic
323#433—21no—
324#431C22×C13711yescharacteristic
325#431C22×C13711yescharacteristic
326#424—21no—
327#423C22×C13711yescharacteristic
328C2×C4⋊C8C22×C13711yescharacteristic
329#335C22×C13711yescharacteristic
330#335C22×C13711yescharacteristic
331#334C22×C13711yescharacteristic
332#334C22×C13711yescharacteristic
333#333C22×C13711yescharacteristic
334#333C22×C13711yescharacteristic
335#333C22×C13711yescharacteristic
336#333C22×C13711yescharacteristic
337#332C22×C13711yescharacteristic
338#332C22×C13711yescharacteristic
339#332C22×C13711yescharacteristic
340#332C22×C13711yescharacteristic
341C2×Q16—21no—
342C2×SD16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C22×C8—21no—
346C22×C8—21no—
347C4⋊Q8C23×C13711yescharacteristic
348C4⋊Q8C23×C13711yescharacteristic
349C4⋊Q8C23×C13711yescharacteristic
350C4⋊Q8C23×C13711yescharacteristic
351#126—21no—
352#125—21no—
353#125—21no—
354#125D4×C13711yescharacteristic
355#124D4×C13711yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8D4×C13711yescharacteristic
362#121D4×C13711yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C13711yescharacteristic
368C4×D4—21no—
369C4×D4C23×C13711yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373C2×C42C23×C13711yescharacteristic
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8D4×C13711yescharacteristic
389C4⋊C8D4×C13711yescharacteristic
390C4⋊C8C23×C13711yescharacteristic
391C4⋊C8C23×C13711yescharacteristic
392C4⋊C8C23×C13711yescharacteristic
393C4⋊C8C23×C13711yescharacteristic
394C4⋊C8C23×C13711yescharacteristic
395C4⋊C8C23×C13711yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C13711yescharacteristic
412C22⋊C8D4×C13711yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C13711yescharacteristic
417C4×C8C23×C13711yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C13711yescharacteristic
423C2×D4—21no—
424C2×D4C2×D4×C13711yescharacteristic
425C22×C4—21no—
426C22×C4C2×D4×C13711yescharacteristic
427C22×C4C2×D4×C13711yescharacteristic
428C22×C4#41×C13711yescharacteristic
429Q16—81no—
430SD16—81no—
431M16—81no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8—81no—
441C2×C8C2×D4×C13711yescharacteristic
442C2×C8C2×D4×C13711yescharacteristic
443C2×C8C2×D4×C13711yescharacteristic
444C2×C8C2×D4×C13711yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C13711yescharacteristic
462C4⋊C4C2×D4×C13711yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42C2×D4×C13711yescharacteristic
474C42C2×D4×C13711yescharacteristic
475C42#41×C13711yescharacteristic
476C42C24×C13711yescharacteristic
477C23—21no—
478C23#121×C13711yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—81no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4#121×C13711yescharacteristic
505C2×C4#121×C13711yescharacteristic
506C2×C4#121×C13711yescharacteristic
507C2×C4C22×D4×C13711yescharacteristic
508C2×C4C22×D4×C13711yescharacteristic
509C2×C4C2×#41×C13711yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#121×C13711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4#577×C13711yescharacteristic
539C4#577×C13711yescharacteristic
540C4#578×C13711yescharacteristic
541C4#578×C13711yescharacteristic
542C2—41no—
543C2—81no—
544C2#3046×C13711yescharacteristic
545C2#3063×C13711yescharacteristic
546C2#3067×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#121×C137D4
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
3. #3231×C137C2semidirect
5. #1703×C137C2semidirect
6. #1700×C137C2semidirect
7. #1696×C137C2semidirect
8. #1691×C137C2semidirect
9. #1684×C137C2semidirect
10. #1679×C137C2semidirect
11. #1675×C137C2semidirect
12. #1672×C137C2semidirect
13. #1574×C137C2semidirect
14. #1550×C137C2semidirect
15. #1542×C137C2semidirect
273. #19587C137direct (N × H)
274. C137#19587direct (N × H)
277. #3231C2×C137semidirect
279. #1703C2×C137semidirect
280. #1700C2×C137semidirect
281. #1696C2×C137semidirect
282. #1691C2×C137semidirect
283. #1684C2×C137semidirect
284. #1679C2×C137semidirect
285. #1675C2×C137semidirect
286. #1672C2×C137semidirect
287. #1574C2×C137semidirect
288. #1550C2×C137semidirect
289. #1542C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3252×C1372
#3233×C1372
#3231×C1372
#2994×C1372
#1703×C1372
#1700×C1372
#1696×C1372
#1691×C1372
#1684×C1372
#1679×C1372
#1675×C1372
#1672×C1372
#1574×C1372
#1550×C1372
#1542×C1372
#19587137