Finite Group Databasebeta

← C137×#19481 #46868867

Subgroups — C137×#19481 #46868867

Order 35072.

610 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#3210×C137C211yesmaximal, characteristic, complemented
2#3115×C137C211yesmaximal, characteristic
3#3076×C137C211yesmaximal, characteristic, complemented
4#2990×C137C211yesmaximal, characteristic, complemented
5#1704×C137C211yesmaximal, characteristic, complemented
6#1698×C137C211yesmaximal, characteristic, complemented
7#1690×C137C211yesmaximal, characteristic, complemented
8#1686×C137C211yesmaximal, characteristic, complemented
9#1683×C137C211yesmaximal, characteristic, complemented
10#1677×C137C211yesmaximal, characteristic, complemented
11#1669×C137C211yesmaximal, characteristic, complemented
12#1665×C137C211yesmaximal, characteristic, complemented
13#1573×C137C211yesmaximal, characteristic, complemented
14#1559×C137C211yesmaximal, characteristic, complemented
15#1547×C137C211yesmaximal, characteristic, complemented
16#533×C137C2211yescharacteristic
17#532×C137C2211yescharacteristic
18C4×#41×C137C2211yescharacteristic
19#494×C137C2211yescharacteristic
20#492×C137C2211yescharacteristic
21#487×C137C2211yescharacteristic
22#486×C137C2211yescharacteristic
23#482×C137—21no—
24#479×C137—21no—
25#478×C137—21no—
26#477×C137C2211yescharacteristic
27#476×C137C2211yescharacteristic
28#475×C137C2211yescharacteristic
29#475×C137C2211yescharacteristic
30#474×C137C2211yescharacteristic
31#474×C137C2211yescharacteristic
32#464×C137—21no—
33#464×C137—21no—
34#460×C137C2211yescharacteristic
35#459×C137C2211yescharacteristic
36#452×C137—21no—
37#452×C137—21no—
38#449×C137—21no—
39#446×C137C2211yescharacteristic
40#446×C137C2211yescharacteristic
41#442×C137—21no—
42#440×C137—21no—
43#435×C137—21no—
44#435×C137—21no—
45C8×D4×C137C2211yescharacteristic
46C8×D4×C137C2211yescharacteristic
47#432×C137—21no—
48#432×C137C2211yescharacteristic
49#431×C137C2211yescharacteristic
50#427×C137—21no—
51#423×C137C2211yescharacteristic
52C2×C4⋊C8×C137—21no—
53C2×C4⋊C8×C137C2211yescharacteristic
54#416×C137—21no—
55#335×C137C2211yescharacteristic
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#334×C137C2211yescharacteristic
59#333×C137C2211yescharacteristic
60#333×C137C2211yescharacteristic
61#332×C137C2211yescharacteristic
62#332×C137C2211yescharacteristic
63#332×C137C2211yescharacteristic
64#332×C137C2211yescharacteristic
65#331×C137C2211yescharacteristic
66#331×C137C2211yescharacteristic
67C2×#41×C137—21no—
68C2×#41×C137D411yescharacteristic
69C2×Q16×C137—21no—
70C2×Q16×C137—21no—
71C2×SD16×C137—21no—
72C2×SD16×C137—21no—
73C2×SD16×C137—21no—
74C2×D8×C137—21no—
75C2×M16×C137—21no—
76C22×C8×C137—21no—
77C22×C8×C137—21no—
78C22×C8×C137—21no—
79C4⋊Q8×C137C2311yescharacteristic
80C4⋊Q8×C137C2311yescharacteristic
81C4⋊Q8×C137C2311yescharacteristic
82#127×C137C2311yescharacteristic
83#125×C137—21no—
84#124×C137—21no—
85C22⋊Q8×C137—21no—
86C22⋊Q8×C137—21no—
87#121×C137—21no—
88#121×C137—21no—
89C4×Q8×C137—21no—
90C4×Q8×C137—21no—
91C4×Q8×C137D411yescharacteristic
92C4×Q8×C137C2311yescharacteristic
93C4×D4×C137—21no—
94C4×D4×C137—21no—
95C4×D4×C137—21no—
96C4×D4×C137—21no—
97C4×D4×C137D411yescharacteristic
98C4×D4×C137C2311yescharacteristic
99#117×C137—21no—
100#117×C137—21no—
101#117×C137D411yescharacteristic
102C2×C42×C137—21no—
103C2×C42×C137C2311yescharacteristic
104#107×C137—21no—
105#107×C137—21no—
106#107×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#102×C137—21no—
128#102×C137—21no—
129#102×C137—21no—
130#102×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—
140#97×C137—21no—
141#97×C137—21no—
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144#41×C137—22no—
145#41×C137—41no—
146#41×C137—81no—
147#41×C137—81no—
148C2×Q8×C137—21no—
149C2×Q8×C137—21no—
150C2×Q8×C137—21no—
151C2×Q8×C137C2×D411yescharacteristic
152C2×D4×C137—21no—
153C2×D4×C137—21no—
154C2×D4×C137—21no—
155C2×D4×C137—21no—
156C2×D4×C137—41no—
157C2×D4×C137C2×D411yescharacteristic
158C22×C4×C137—21no—
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—41no—
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137#4111yescharacteristic
165Q16×C137—81no—
166Q16×C137—81no—
167SD16×C137—42no—
168SD16×C137—81no—
169SD16×C137—81no—
170D8×C137—42no—
171M16×C137—81no—
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137—42no—
179C2×C8×C137—81no—
180C2×C8×C137—81no—
181C2×C8×C137C2×D411yescharacteristic
182C2×C8×C137C2×D411yescharacteristic
183C2×C8×C137C2×D411yescharacteristic
184C2×C8×C137C2×D411yescharacteristic
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—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—41no—
194C4⋊C4×C137—41no—
195C4⋊C4×C137C2×D411yescharacteristic
196C4⋊C4×C137C2×D411yescharacteristic
197C22⋊C4×C137—21no—
198C22⋊C4×C137—21no—
199C22⋊C4×C137—21no—
200C22⋊C4×C137—41no—
201C22⋊C4×C137—41no—
202C22⋊C4×C137—41no—
203C42×C137—21no—
204C42×C137—21no—
205C42×C137—21no—
206C42×C137—41no—
207C42×C137C2×D411yescharacteristic
208C42×C137C2×D411yescharacteristic
209C42×C137#4111yescharacteristic
210C42×C137C2411yescharacteristic
211C23×C137—21no—
212C23×C137—41no—
213C23×C137#12111yescharacteristic
214Q8×C137—21no—
215Q8×C137—21no—
216Q8×C137—41no—
217Q8×C137—41no—
218Q8×C137—41no—
219Q8×C137—41no—
220Q8×C137—81no—
221D4×C137—21no—
222D4×C137—42no—
223D4×C137—41no—
224D4×C137—41no—
225D4×C137—41no—
226D4×C137—41no—
227D4×C137—81no—
228D4×C137—82no—
229D4×C137#13712yes—
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—21no—
237C2×C4×C137—41no—
238C2×C4×C137—42no—
239C2×C4×C137—42no—
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#12111yescharacteristic
247C2×C4×C137#12111yescharacteristic
248C2×C4×C137#12111yescharacteristic
249C2×C4×C137C22×D411yescharacteristic
250C2×C4×C137C22×D411yescharacteristic
251C2×C4×C137C2×#4111yescharacteristic
252C8×C137—21no—
253C8×C137—21no—
254C8×C137—21no—
255C8×C137—21no—
256C8×C137—41no—
257C8×C137—41no—
258C8×C137—41no—
259C8×C137—41no—
260C8×C137—41no—
261C8×C137—41no—
262C22×C137—21no—
263C22×C137—21no—
264C22×C137—22no—
265C22×C137—21no—
266C22×C137—41no—
267C22×C137—41no—
268C22×C137—81no—
269C22×C137—81no—
270C22×C137—81no—
271C22×C137C2×#12111yescharacteristic
272C4×C137—21no—
273C4×C137—21no—
274C4×C137—21no—
275C4×C137—21no—
276C4×C137—41no—
277C4×C137—41no—
278C4×C137—41no—
279C4×C137—81no—
280C4×C137—81no—
281C4×C137—81no—
282C4×C137C2×#13711yescharacteristic
283C4×C137#57511yescharacteristic
284C4×C137#57611yescharacteristic
285C4×C137#57711yescharacteristic
286C2×C137—41no—
287C2×C137—42no—
288C2×C137—161no—
289C2×C137#304511yescharacteristic
290C2×C137#305611yescharacteristic
291C2×C137#306711yescharacteristic
292#19481C13711yesmaximal, characteristic, direct product factor, Sylow
293C137#1948111yescharacteristic, direct product factor, Sylow
294#3210C2×C13711yescharacteristic, complemented
295#3115C2×C13711yescharacteristic
296#3076C2×C13711yescharacteristic, complemented
297#2990C2×C13711yescharacteristic, complemented
298#1704C2×C13711yescharacteristic, complemented
299#1698C2×C13711yescharacteristic, complemented
300#1690C2×C13711yescharacteristic, complemented
301#1686C2×C13711yescharacteristic, complemented
302#1683C2×C13711yescharacteristic, complemented
303#1677C2×C13711yescharacteristic, complemented
304#1669C2×C13711yescharacteristic, complemented
305#1665C2×C13711yescharacteristic, complemented
306#1573C2×C13711yescharacteristic, complemented
307#1559C2×C13711yescharacteristic, complemented
308#1547C2×C13711yescharacteristic, complemented
309#533C22×C13711yescharacteristic
310#532C22×C13711yescharacteristic
311C4×#41C22×C13711yescharacteristic
312#494C22×C13711yescharacteristic
313#492C22×C13711yescharacteristic
314#487C22×C13711yescharacteristic
315#486C22×C13711yescharacteristic
316#482—21no—
317#479—21no—
318#478—21no—
319#477C22×C13711yescharacteristic
320#476C22×C13711yescharacteristic
321#475C22×C13711yescharacteristic
322#475C22×C13711yescharacteristic
323#474C22×C13711yescharacteristic
324#474C22×C13711yescharacteristic
325#464—21no—
326#464—21no—
327#460C22×C13711yescharacteristic
328#459C22×C13711yescharacteristic
329#452—21no—
330#452—21no—
331#449—21no—
332#446C22×C13711yescharacteristic
333#446C22×C13711yescharacteristic
334#442—21no—
335#440—21no—
336#435—21no—
337#435—21no—
338C8×D4C22×C13711yescharacteristic
339C8×D4C22×C13711yescharacteristic
340#432—21no—
341#432C22×C13711yescharacteristic
342#431C22×C13711yescharacteristic
343#427—21no—
344#423C22×C13711yescharacteristic
345C2×C4⋊C8—21no—
346C2×C4⋊C8C22×C13711yescharacteristic
347#416—21no—
348#335C22×C13711yescharacteristic
349#335C22×C13711yescharacteristic
350#334C22×C13711yescharacteristic
351#334C22×C13711yescharacteristic
352#333C22×C13711yescharacteristic
353#333C22×C13711yescharacteristic
354#332C22×C13711yescharacteristic
355#332C22×C13711yescharacteristic
356#332C22×C13711yescharacteristic
357#332C22×C13711yescharacteristic
358#331C22×C13711yescharacteristic
359#331C22×C13711yescharacteristic
360C2×#41—21no—
361C2×#41D4×C13711yescharacteristic
362C2×Q16—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×D8—21no—
368C2×M16—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C4⋊Q8C23×C13711yescharacteristic
373C4⋊Q8C23×C13711yescharacteristic
374C4⋊Q8C23×C13711yescharacteristic
375#127C23×C13711yescharacteristic
376#125—21no—
377#124—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8D4×C13711yescharacteristic
385C4×Q8C23×C13711yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4D4×C13711yescharacteristic
391C4×D4C23×C13711yescharacteristic
392#117—21no—
393#117—21no—
394#117D4×C13711yescharacteristic
395C2×C42—21no—
396C2×C42C23×C13711yescharacteristic
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C13711yescharacteristic
408C4⋊C8D4×C13711yescharacteristic
409C4⋊C8C23×C13711yescharacteristic
410C4⋊C8C23×C13711yescharacteristic
411C4⋊C8C23×C13711yescharacteristic
412C4⋊C8C23×C13711yescharacteristic
413C4⋊C8C23×C13711yescharacteristic
414C4⋊C8C23×C13711yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8D4×C13711yescharacteristic
431C22⋊C8D4×C13711yescharacteristic
432#97—21no—
433#97—21no—
434#97—21no—
435C4×C8C23×C13711yescharacteristic
436C4×C8C23×C13711yescharacteristic
437#41—22no—
438#41—41no—
439#41—81no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C13711yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4C2×D4×C13711yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C13711yescharacteristic
456C22×C4C2×D4×C13711yescharacteristic
457C22×C4#41×C13711yescharacteristic
458Q16—81no—
459Q16—81no—
460SD16—42no—
461SD16—81no—
462SD16—81no—
463D8—42no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8—81no—
474C2×C8C2×D4×C13711yescharacteristic
475C2×C8C2×D4×C13711yescharacteristic
476C2×C8C2×D4×C13711yescharacteristic
477C2×C8C2×D4×C13711yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
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—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42C2×D4×C13711yescharacteristic
501C42C2×D4×C13711yescharacteristic
502C42#41×C13711yescharacteristic
503C42C24×C13711yescharacteristic
504C23—21no—
505C23—41no—
506C23#121×C13711yescharacteristic
507Q8—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—81no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522D4#137×C13712yes—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C13711yescharacteristic
540C2×C4#121×C13711yescharacteristic
541C2×C4#121×C13711yescharacteristic
542C2×C4C22×D4×C13711yescharacteristic
543C2×C4C22×D4×C13711yescharacteristic
544C2×C4C2×#41×C13711yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—21no—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C13711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#137×C13711yescharacteristic
576C4#575×C13711yescharacteristic
577C4#576×C13711yescharacteristic
578C4#577×C13711yescharacteristic
579C2—41no—
580C2—42no—
581C2—161no—
582C2#3045×C13711yescharacteristic
583C2#3056×C13711yescharacteristic
584C2#3067×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3115×C137C2
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. #3210×C137C2semidirect
3. #3076×C137C2semidirect
4. #2990×C137C2semidirect
5. #1704×C137C2semidirect
6. #1698×C137C2semidirect
7. #1690×C137C2semidirect
8. #1686×C137C2semidirect
9. #1683×C137C2semidirect
10. #1677×C137C2semidirect
11. #1669×C137C2semidirect
12. #1665×C137C2semidirect
13. #1573×C137C2semidirect
14. #1559×C137C2semidirect
15. #1547×C137C2semidirect
292. #19481C137direct (N × H)
293. C137#19481direct (N × H)
294. #3210C2×C137semidirect
296. #3076C2×C137semidirect
297. #2990C2×C137semidirect
298. #1704C2×C137semidirect
299. #1698C2×C137semidirect
300. #1690C2×C137semidirect
301. #1686C2×C137semidirect
302. #1683C2×C137semidirect
303. #1677C2×C137semidirect
304. #1669C2×C137semidirect
305. #1665C2×C137semidirect
306. #1573C2×C137semidirect
307. #1559C2×C137semidirect
308. #1547C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3210×C1372
#3115×C1372
#3076×C1372
#2990×C1372
#1704×C1372
#1698×C1372
#1690×C1372
#1686×C1372
#1683×C1372
#1677×C1372
#1669×C1372
#1665×C1372
#1573×C1372
#1559×C1372
#1547×C1372
#19481137