Finite Group Databasebeta

← C137×#20296 #46869682

Subgroups — C137×#20296 #46869682

Order 35072.

578 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3375×C137C211yesmaximal, characteristic, complemented
2#3373×C137C211yesmaximal, characteristic
3#3369×C137C211yesmaximal, characteristic, complemented
4#3328×C137C211yesmaximal, characteristic, complemented
5#1711×C137C211yesmaximal, characteristic, complemented
6#1704×C137C211yesmaximal, characteristic, complemented
7#1702×C137C211yesmaximal, characteristic, complemented
8#1700×C137C211yesmaximal, characteristic, complemented
9#1697×C137C211yesmaximal, characteristic
10#1645×C137C211yesmaximal, characteristic, complemented
11#1640×C137C211yesmaximal, characteristic, complemented
12#1637×C137C211yesmaximal, characteristic, complemented
13#1628×C137C211yesmaximal, characteristic
14#1591×C137C211yesmaximal, characteristic, complemented
15#1590×C137C211yesmaximal, characteristic, complemented
16#559×C137C2211yescharacteristic
17Q82×C137C2211yescharacteristic
18#556×C137C2211yescharacteristic
19D4×Q8×C137C2211yescharacteristic
20#489×C137—21no—
21#489×C137—21no—
22#489×C137—21no—
23#487×C137C2211yescharacteristic
24#487×C137C2211yescharacteristic
25#487×C137C2211yescharacteristic
26#486×C137C2211yescharacteristic
27#486×C137C2211yescharacteristic
28#486×C137C2211yescharacteristic
29#485×C137—21no—
30#477×C137C2211yescharacteristic
31#476×C137—21no—
32#476×C137C2211yescharacteristic
33#475×C137—21no—
34#475×C137C2211yescharacteristic
35#475×C137C2211yescharacteristic
36#474×C137—21no—
37#470×C137—21no—
38#464×C137—21no—
39#464×C137—21no—
40#463×C137—21no—
41#462×C137C2211yescharacteristic
42#462×C137C2211yescharacteristic
43#460×C137C2211yescharacteristic
44#459×C137C2211yescharacteristic
45#451×C137—21no—
46#446×C137C2211yescharacteristic
47#446×C137C2211yescharacteristic
48#446×C137C2211yescharacteristic
49#442×C137—21no—
50#441×C137—21no—
51#440×C137—21no—
52C4×Q16×C137C2211yescharacteristic
53C4×SD16×C137C2211yescharacteristic
54#436×C137C2211yescharacteristic
55#419×C137—21no—
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#333×C137C2211yescharacteristic
59#332×C137C2211yescharacteristic
60#332×C137C2211yescharacteristic
61#331×C137C2211yescharacteristic
62Q8⋊C8×C137C2211yescharacteristic
63Q8⋊C8×C137C2211yescharacteristic
64Q8⋊C8×C137C2211yescharacteristic
65D4⋊C8×C137C2211yescharacteristic
66C82×C137C2211yescharacteristic
67C22×Q8×C137—21no—
68C2×Q16×C137—21no—
69C2×Q16×C137—21no—
70C2×Q16×C137D411yescharacteristic
71C2×SD16×C137—21no—
72C2×SD16×C137D411yescharacteristic
73C2×D8×C137—21no—
74C2×M16×C137—21no—
75C4⋊Q8×C137—21no—
76C4⋊Q8×C137—21no—
77C4⋊Q8×C137—21no—
78C4⋊Q8×C137—41no—
79C4⋊Q8×C137C2311yescharacteristic
80C4⋊Q8×C137C2311yescharacteristic
81C4⋊Q8×C137C2311yescharacteristic
82#127×C137C2311yescharacteristic
83#126×C137—41no—
84#124×C137—21no—
85#124×C137—21no—
86#124×C137—21no—
87#123×C137—41no—
88C22⋊Q8×C137—21no—
89C22⋊Q8×C137—21no—
90C22⋊Q8×C137—41no—
91C4×Q8×C137—21no—
92C4×Q8×C137—21no—
93C4×Q8×C137—21no—
94C4×Q8×C137C2311yescharacteristic
95C4×Q8×C137C2311yescharacteristic
96C4×Q8×C137C2311yescharacteristic
97C4×D4×C137—21no—
98C4×D4×C137—21no—
99C4×D4×C137—21no—
100C4×D4×C137C2311yescharacteristic
101#117×C137—21no—
102#107×C137—21no—
103#107×C137D411yescharacteristic
104#106×C137—21no—
105#106×C137—21no—
106#106×C137—21no—
107#106×C137D411yescharacteristic
108C4⋊C8×C137—21no—
109C4⋊C8×C137—21no—
110C4⋊C8×C137—21no—
111C4⋊C8×C137C2311yescharacteristic
112C4⋊C8×C137C2311yescharacteristic
113C4⋊C8×C137C2311yescharacteristic
114C4⋊C8×C137C2311yescharacteristic
115#103×C137—21no—
116#103×C137—21no—
117#103×C137—21no—
118#103×C137—21no—
119#103×C137—21no—
120#103×C137—21no—
121#103×C137—21no—
122#103×C137—21no—
123#103×C137—21no—
124#103×C137—41no—
125#103×C137D411yescharacteristic
126#103×C137D411yescharacteristic
127#103×C137D411yescharacteristic
128#102×C137—21no—
129#102×C137—21no—
130#102×C137—21no—
131#102×C137—21no—
132#102×C137—21no—
133#102×C137—21no—
134#102×C137—21no—
135#102×C137—41no—
136#102×C137D411yescharacteristic
137C22⋊C8×C137—21no—
138#97×C137—21no—
139#97×C137—21no—
140#97×C137—21no—
141C4×C8×C137C2311yescharacteristic
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144C2×Q8×C137—21no—
145C2×Q8×C137—21no—
146C2×Q8×C137—21no—
147C2×Q8×C137—41no—
148C2×Q8×C137—41no—
149C2×Q8×C137—42no—
150C2×Q8×C137—81no—
151C2×Q8×C137C2×D411yescharacteristic
152C2×Q8×C137C2×D411yescharacteristic
153C2×Q8×C137C2×D411yescharacteristic
154C2×D4×C137—21no—
155C2×D4×C137—21no—
156C2×D4×C137—21no—
157C2×D4×C137C2×D411yescharacteristic
158C22×C4×C137—21no—
159C22×C4×C137—41no—
160C22×C4×C137—41no—
161Q16×C137—41no—
162Q16×C137—42no—
163Q16×C137—81no—
164SD16×C137—41no—
165SD16×C137—42no—
166D8×C137—42no—
167M16×C137—81no—
168C2×C8×C137—21no—
169C2×C8×C137—21no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—21no—
173C2×C8×C137C2×D411yescharacteristic
174C2×C8×C137C2×D411yescharacteristic
175C2×C8×C137C2×D411yescharacteristic
176C2×C8×C137C2×D411yescharacteristic
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—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137—21no—
186C4⋊C4×C137—41no—
187C4⋊C4×C137—41no—
188C4⋊C4×C137—41no—
189C4⋊C4×C137—41no—
190C4⋊C4×C137C2×D411yescharacteristic
191C4⋊C4×C137C2×D411yescharacteristic
192C4⋊C4×C137C2×D411yescharacteristic
193C4⋊C4×C137C2×D411yescharacteristic
194C22⋊C4×C137—21no—
195C22⋊C4×C137—41no—
196C22⋊C4×C137—41no—
197C22⋊C4×C137—41no—
198C22⋊C4×C137—41no—
199C22⋊C4×C137—41no—
200C22⋊C4×C137—41no—
201C42×C137—21no—
202C42×C137—21no—
203C42×C137—21no—
204C42×C137—41no—
205C42×C137—41no—
206C42×C137C2411yescharacteristic
207C23×C137—21no—
208C23×C137—41no—
209Q8×C137—21no—
210Q8×C137—21no—
211Q8×C137—21no—
212Q8×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—82no—
221Q8×C137—161no—
222D4×C137—21no—
223D4×C137—21no—
224D4×C137—41no—
225D4×C137—41no—
226D4×C137—41no—
227D4×C137—41no—
228D4×C137—81no—
229C2×C4×C137—21no—
230C2×C4×C137—21no—
231C2×C4×C137—21no—
232C2×C4×C137—21no—
233C2×C4×C137—21no—
234C2×C4×C137—21no—
235C2×C4×C137—21no—
236C2×C4×C137—41no—
237C2×C4×C137—41no—
238C2×C4×C137—41no—
239C2×C4×C137—41no—
240C2×C4×C137—41no—
241C2×C4×C137—82no—
242C2×C4×C137—161no—
243C2×C4×C137C22×D411yescharacteristic
244C2×C4×C137C22×D411yescharacteristic
245C2×C4×C137H(5,𝔽2)11yescharacteristic
246C8×C137—21no—
247C8×C137—21no—
248C8×C137—21no—
249C8×C137—21no—
250C8×C137—41no—
251C8×C137—41no—
252C8×C137—41no—
253C8×C137—41no—
254C8×C137—41no—
255C22×C137—41no—
256C22×C137—41no—
257C22×C137—41no—
258C22×C137—81no—
259C22×C137—81no—
260C22×C137—81no—
261C22×C137D4211yescharacteristic
262C4×C137—21no—
263C4×C137—41no—
264C4×C137—41no—
265C4×C137—41no—
266C4×C137—41no—
267C4×C137—41no—
268C4×C137—41no—
269C4×C137—41no—
270C4×C137—81no—
271C4×C137—81no—
272C4×C137—81no—
273C4×C137#57511yescharacteristic
274C4×C137#57511yescharacteristic
275C4×C137#57711yescharacteristic
276C4×C137#57811yescharacteristic
277C2×C137—81no—
278C2×C137—161no—
279C2×C137#327511yescharacteristic
280C2×C137#327711yescharacteristic
281C2×C137#329011yescharacteristic
282#20296C13711yesmaximal, characteristic, direct product factor, Sylow
283C137#2029611yescharacteristic, direct product factor, Sylow
284#3375C2×C13711yescharacteristic, complemented
285#3373C2×C13711yescharacteristic
286#3369C2×C13711yescharacteristic, complemented
287#3328C2×C13711yescharacteristic, complemented
288#1711C2×C13711yescharacteristic, complemented
289#1704C2×C13711yescharacteristic, complemented
290#1702C2×C13711yescharacteristic, complemented
291#1700C2×C13711yescharacteristic, complemented
292#1697C2×C13711yescharacteristic
293#1645C2×C13711yescharacteristic, complemented
294#1640C2×C13711yescharacteristic, complemented
295#1637C2×C13711yescharacteristic, complemented
296#1628C2×C13711yescharacteristic
297#1591C2×C13711yescharacteristic, complemented
298#1590C2×C13711yescharacteristic, complemented
299#559C22×C13711yescharacteristic
300Q82C22×C13711yescharacteristic
301#556C22×C13711yescharacteristic
302D4×Q8C22×C13711yescharacteristic
303#489—21no—
304#489—21no—
305#489—21no—
306#487C22×C13711yescharacteristic
307#487C22×C13711yescharacteristic
308#487C22×C13711yescharacteristic
309#486C22×C13711yescharacteristic
310#486C22×C13711yescharacteristic
311#486C22×C13711yescharacteristic
312#485—21no—
313#477C22×C13711yescharacteristic
314#476—21no—
315#476C22×C13711yescharacteristic
316#475—21no—
317#475C22×C13711yescharacteristic
318#475C22×C13711yescharacteristic
319#474—21no—
320#470—21no—
321#464—21no—
322#464—21no—
323#463—21no—
324#462C22×C13711yescharacteristic
325#462C22×C13711yescharacteristic
326#460C22×C13711yescharacteristic
327#459C22×C13711yescharacteristic
328#451—21no—
329#446C22×C13711yescharacteristic
330#446C22×C13711yescharacteristic
331#446C22×C13711yescharacteristic
332#442—21no—
333#441—21no—
334#440—21no—
335C4×Q16C22×C13711yescharacteristic
336C4×SD16C22×C13711yescharacteristic
337#436C22×C13711yescharacteristic
338#419—21no—
339#335C22×C13711yescharacteristic
340#334C22×C13711yescharacteristic
341#333C22×C13711yescharacteristic
342#332C22×C13711yescharacteristic
343#332C22×C13711yescharacteristic
344#331C22×C13711yescharacteristic
345Q8⋊C8C22×C13711yescharacteristic
346Q8⋊C8C22×C13711yescharacteristic
347Q8⋊C8C22×C13711yescharacteristic
348D4⋊C8C22×C13711yescharacteristic
349C82C22×C13711yescharacteristic
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16D4×C13711yescharacteristic
354C2×SD16—21no—
355C2×SD16D4×C13711yescharacteristic
356C2×D8—21no—
357C2×M16—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8C23×C13711yescharacteristic
363C4⋊Q8C23×C13711yescharacteristic
364C4⋊Q8C23×C13711yescharacteristic
365#127C23×C13711yescharacteristic
366#126—41no—
367#124—21no—
368#124—21no—
369#124—21no—
370#123—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8C23×C13711yescharacteristic
378C4×Q8C23×C13711yescharacteristic
379C4×Q8C23×C13711yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C13711yescharacteristic
384#117—21no—
385#107—21no—
386#107D4×C13711yescharacteristic
387#106—21no—
388#106—21no—
389#106—21no—
390#106D4×C13711yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C13711yescharacteristic
395C4⋊C8C23×C13711yescharacteristic
396C4⋊C8C23×C13711yescharacteristic
397C4⋊C8C23×C13711yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C13711yescharacteristic
409#103D4×C13711yescharacteristic
410#103D4×C13711yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—41no—
419#102D4×C13711yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422#97—21no—
423#97—21no—
424C4×C8C23×C13711yescharacteristic
425C4×C8C23×C13711yescharacteristic
426C4×C8C23×C13711yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C13711yescharacteristic
435C2×Q8C2×D4×C13711yescharacteristic
436C2×Q8C2×D4×C13711yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C13711yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444Q16—41no—
445Q16—42no—
446Q16—81no—
447SD16—41no—
448SD16—42no—
449D8—42no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8C2×D4×C13711yescharacteristic
457C2×C8C2×D4×C13711yescharacteristic
458C2×C8C2×D4×C13711yescharacteristic
459C2×C8C2×D4×C13711yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C13711yescharacteristic
474C4⋊C4C2×D4×C13711yescharacteristic
475C4⋊C4C2×D4×C13711yescharacteristic
476C4⋊C4C2×D4×C13711yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42—41no—
489C42C24×C13711yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—82no—
504Q8—161no—
505D4—21no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—161no—
526C2×C4C22×D4×C13711yescharacteristic
527C2×C4C22×D4×C13711yescharacteristic
528C2×C4H(5,𝔽2)×C13711yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C13711yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4#575×C13711yescharacteristic
557C4#575×C13711yescharacteristic
558C4#577×C13711yescharacteristic
559C4#578×C13711yescharacteristic
560C2—81no—
561C2—161no—
562C2#3275×C13711yescharacteristic
563C2#3277×C13711yescharacteristic
564C2#3290×C13711yescharacteristic
subgroupG/H
center, socleC22×C137D42
commutator, Frattini, cosocleC42C24×C137
prime radical#459×C137C22
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. #3375×C137C2semidirect
3. #3369×C137C2semidirect
4. #3328×C137C2semidirect
5. #1711×C137C2semidirect
6. #1704×C137C2semidirect
7. #1702×C137C2semidirect
8. #1700×C137C2semidirect
10. #1645×C137C2semidirect
11. #1640×C137C2semidirect
12. #1637×C137C2semidirect
14. #1591×C137C2semidirect
15. #1590×C137C2semidirect
282. #20296C137direct (N × H)
283. C137#20296direct (N × H)
284. #3375C2×C137semidirect
286. #3369C2×C137semidirect
287. #3328C2×C137semidirect
288. #1711C2×C137semidirect
289. #1704C2×C137semidirect
290. #1702C2×C137semidirect
291. #1700C2×C137semidirect
293. #1645C2×C137semidirect
294. #1640C2×C137semidirect
295. #1637C2×C137semidirect
297. #1591C2×C137semidirect
298. #1590C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3375×C1372
#3373×C1372
#3369×C1372
#3328×C1372
#1711×C1372
#1704×C1372
#1702×C1372
#1700×C1372
#1697×C1372
#1645×C1372
#1640×C1372
#1637×C1372
#1628×C1372
#1591×C1372
#1590×C1372
#20296137