Finite Group Databasebeta

← C137×#19418 #46868804

Subgroups — C137×#19418 #46868804

Order 35072.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3231×C137C211yesmaximal, characteristic, complemented
2#3116×C137C211yesmaximal, characteristic
3#3107×C137C211yesmaximal, characteristic
4#2988×C137C211yesmaximal, characteristic
5#1684×C137C211yesmaximal, characteristic, complemented
6#1683×C137C211yesmaximal, characteristic, complemented
7#1680×C137C211yesmaximal, characteristic, complemented
8#1679×C137C211yesmaximal, characteristic, complemented
9#1674×C137C211yesmaximal, characteristic, complemented
10#1673×C137C211yesmaximal, characteristic, complemented
11#1672×C137C211yesmaximal, characteristic, complemented
12#1671×C137C211yesmaximal, characteristic, complemented
13#1572×C137C211yesmaximal, characteristic, complemented
14#1552×C137C211yesmaximal, characteristic, complemented
15#1542×C137C211yesmaximal, characteristic, complemented
16#533×C137C2211yescharacteristic
17#533×C137C2211yescharacteristic
18C4×#41×C137C2211yescharacteristic
19#500×C137C2211yescharacteristic
20#498×C137C2211yescharacteristic
21#487×C137C2211yescharacteristic
22#487×C137C2211yescharacteristic
23#485×C137—21no—
24#485×C137—21no—
25#485×C137—21no—
26#485×C137—21no—
27#479×C137—21no—
28#479×C137—21no—
29#477×C137C2211yescharacteristic
30#476×C137C2211yescharacteristic
31#475×C137C2211yescharacteristic
32#474×C137C2211yescharacteristic
33#462×C137C2211yescharacteristic
34#462×C137C2211yescharacteristic
35#461×C137C2211yescharacteristic
36#461×C137C2211yescharacteristic
37#452×C137—21no—
38#452×C137—21no—
39C8×Q8×C137C2211yescharacteristic
40C8×Q8×C137C2211yescharacteristic
41#441×C137—21no—
42#440×C137—21no—
43C4×Q16×C137—21no—
44C4×SD16×C137—21no—
45C8×D4×C137—21no—
46C8×D4×C137—21no—
47C8×D4×C137C2211yescharacteristic
48C8×D4×C137C2211yescharacteristic
49#432×C137C2211yescharacteristic
50#431×C137—21no—
51#431×C137C2211yescharacteristic
52#431×C137C2211yescharacteristic
53C2×C4⋊C8×C137—21no—
54C2×C4⋊C8×C137C2211yescharacteristic
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#332×C137C2211yescharacteristic
66#332×C137C2211yescharacteristic
67C2×#41×C137D411yescharacteristic
68C2×Q16×C137—21no—
69C2×Q16×C137—21no—
70C2×SD16×C137—21no—
71C2×SD16×C137—21no—
72C22×C8×C137—21no—
73C22×C8×C137—21no—
74C22×C8×C137—21no—
75C4⋊Q8×C137C2311yescharacteristic
76C4⋊Q8×C137C2311yescharacteristic
77C4⋊Q8×C137C2311yescharacteristic
78C4⋊Q8×C137C2311yescharacteristic
79#125×C137—21no—
80#125×C137—21no—
81C22⋊Q8×C137—21no—
82C22⋊Q8×C137—21no—
83C22⋊Q8×C137—21no—
84C22⋊Q8×C137—21no—
85C4×Q8×C137—21no—
86C4×Q8×C137—21no—
87C4×Q8×C137—21no—
88C4×Q8×C137—21no—
89C4×Q8×C137D411yescharacteristic
90C4×Q8×C137C2311yescharacteristic
91C4×D4×C137—21no—
92C4×D4×C137—21no—
93C4×D4×C137D411yescharacteristic
94C4×D4×C137C2311yescharacteristic
95#117×C137—21no—
96#117×C137—21no—
97#117×C137—21no—
98#117×C137D411yescharacteristic
99C2×C42×C137—21no—
100C2×C42×C137C2311yescharacteristic
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—
109C4⋊C8×C137—21no—
110C4⋊C8×C137—21no—
111C4⋊C8×C137—21no—
112C4⋊C8×C137D411yescharacteristic
113C4⋊C8×C137D411yescharacteristic
114C4⋊C8×C137C2311yescharacteristic
115C4⋊C8×C137C2311yescharacteristic
116C4⋊C8×C137C2311yescharacteristic
117C4⋊C8×C137C2311yescharacteristic
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120#103×C137—21no—
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×C137—21no—
129#103×C137—21no—
130#102×C137—21no—
131#102×C137—21no—
132C22⋊C8×C137—21no—
133C22⋊C8×C137—21no—
134C22⋊C8×C137—21no—
135C22⋊C8×C137—21no—
136C22⋊C8×C137D411yescharacteristic
137C22⋊C8×C137D411yescharacteristic
138#97×C137—21no—
139C4×C8×C137—21no—
140C4×C8×C137—21no—
141C4×C8×C137—21no—
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144#41×C137—22no—
145#41×C137—22no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137—21no—
149C2×Q8×C137—21no—
150C2×Q8×C137C2×D411yescharacteristic
151C2×D4×C137—21no—
152C2×D4×C137C2×D411yescharacteristic
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137C2×D411yescharacteristic
157C22×C4×C137C2×D411yescharacteristic
158C22×C4×C137#4111yescharacteristic
159Q16×C137—42no—
160Q16×C137—42no—
161SD16×C137—42no—
162SD16×C137—42no—
163C2×C8×C137—21no—
164C2×C8×C137—21no—
165C2×C8×C137—21no—
166C2×C8×C137—21no—
167C2×C8×C137—21no—
168C2×C8×C137—21no—
169C2×C8×C137—81no—
170C2×C8×C137—81no—
171C2×C8×C137—81no—
172C2×C8×C137C2×D411yescharacteristic
173C2×C8×C137C2×D411yescharacteristic
174C2×C8×C137C2×D411yescharacteristic
175C2×C8×C137C2×D411yescharacteristic
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—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
192C22⋊C4×C137—21no—
193C22⋊C4×C137—21no—
194C22⋊C4×C137—21no—
195C22⋊C4×C137—41no—
196C22⋊C4×C137—41no—
197C42×C137—21no—
198C42×C137—21no—
199C42×C137—21no—
200C42×C137—41no—
201C42×C137—41no—
202C42×C137C2×D411yescharacteristic
203C42×C137C2×D411yescharacteristic
204C42×C137#4111yescharacteristic
205C42×C137C2411yescharacteristic
206C23×C137—21no—
207C23×C137#12111yescharacteristic
208Q8×C137—21no—
209Q8×C137—41no—
210Q8×C137—41no—
211Q8×C137—41no—
212Q8×C137—41no—
213Q8×C137—41no—
214Q8×C137—41no—
215Q8×C137—81no—
216Q8×C137#13512yes—
217D4×C137—24no—
218D4×C137—21no—
219D4×C137#13512yes—
220C2×C4×C137—24no—
221C2×C4×C137—21no—
222C2×C4×C137—21no—
223C2×C4×C137—21no—
224C2×C4×C137—21no—
225C2×C4×C137—21no—
226C2×C4×C137—21no—
227C2×C4×C137—21no—
228C2×C4×C137—41no—
229C2×C4×C137—41no—
230C2×C4×C137—41no—
231C2×C4×C137—41no—
232C2×C4×C137—41no—
233C2×C4×C137—41no—
234C2×C4×C137—41no—
235C2×C4×C137—81no—
236C2×C4×C137#12111yescharacteristic
237C2×C4×C137#12111yescharacteristic
238C2×C4×C137#12111yescharacteristic
239C2×C4×C137C22×D411yescharacteristic
240C2×C4×C137C22×D411yescharacteristic
241C2×C4×C137C2×#4111yescharacteristic
242C8×C137—21no—
243C8×C137—21no—
244C8×C137—21no—
245C8×C137—21no—
246C8×C137—41no—
247C8×C137—41no—
248C8×C137—41no—
249C8×C137—41no—
250C8×C137—41no—
251C8×C137—41no—
252C22×C137—21no—
253C22×C137—21no—
254C22×C137—22no—
255C22×C137—21no—
256C22×C137—41no—
257C22×C137—41no—
258C22×C137C2×#12111yescharacteristic
259C4×C137—21no—
260C4×C137—21no—
261C4×C137—22no—
262C4×C137—21no—
263C4×C137—21no—
264C4×C137—41no—
265C4×C137—41no—
266C4×C137—81no—
267C4×C137—81no—
268C4×C137—81no—
269C4×C137—81no—
270C4×C137C2×#13511yescharacteristic
271C4×C137C2×#13511yescharacteristic
272C4×C137#57711yescharacteristic
273C4×C137#57811yescharacteristic
274C2×C137—41no—
275C2×C137—42no—
276C2×C137#304611yescharacteristic
277C2×C137#305011yescharacteristic
278C2×C137#306911yescharacteristic
279#19418C13711yesmaximal, characteristic, direct product factor, Sylow
280C137#1941811yescharacteristic, direct product factor, Sylow
281#3231C2×C13711yescharacteristic, complemented
282#3116C2×C13711yescharacteristic
283#3107C2×C13711yescharacteristic
284#2988C2×C13711yescharacteristic
285#1684C2×C13711yescharacteristic, complemented
286#1683C2×C13711yescharacteristic, complemented
287#1680C2×C13711yescharacteristic, complemented
288#1679C2×C13711yescharacteristic, complemented
289#1674C2×C13711yescharacteristic, complemented
290#1673C2×C13711yescharacteristic, complemented
291#1672C2×C13711yescharacteristic, complemented
292#1671C2×C13711yescharacteristic, complemented
293#1572C2×C13711yescharacteristic, complemented
294#1552C2×C13711yescharacteristic, complemented
295#1542C2×C13711yescharacteristic, complemented
296#533C22×C13711yescharacteristic
297#533C22×C13711yescharacteristic
298C4×#41C22×C13711yescharacteristic
299#500C22×C13711yescharacteristic
300#498C22×C13711yescharacteristic
301#487C22×C13711yescharacteristic
302#487C22×C13711yescharacteristic
303#485—21no—
304#485—21no—
305#485—21no—
306#485—21no—
307#479—21no—
308#479—21no—
309#477C22×C13711yescharacteristic
310#476C22×C13711yescharacteristic
311#475C22×C13711yescharacteristic
312#474C22×C13711yescharacteristic
313#462C22×C13711yescharacteristic
314#462C22×C13711yescharacteristic
315#461C22×C13711yescharacteristic
316#461C22×C13711yescharacteristic
317#452—21no—
318#452—21no—
319C8×Q8C22×C13711yescharacteristic
320C8×Q8C22×C13711yescharacteristic
321#441—21no—
322#440—21no—
323C4×Q16—21no—
324C4×SD16—21no—
325C8×D4—21no—
326C8×D4—21no—
327C8×D4C22×C13711yescharacteristic
328C8×D4C22×C13711yescharacteristic
329#432C22×C13711yescharacteristic
330#431—21no—
331#431C22×C13711yescharacteristic
332#431C22×C13711yescharacteristic
333C2×C4⋊C8—21no—
334C2×C4⋊C8C22×C13711yescharacteristic
335#335C22×C13711yescharacteristic
336#335C22×C13711yescharacteristic
337#334C22×C13711yescharacteristic
338#334C22×C13711yescharacteristic
339#333C22×C13711yescharacteristic
340#333C22×C13711yescharacteristic
341#332C22×C13711yescharacteristic
342#332C22×C13711yescharacteristic
343#332C22×C13711yescharacteristic
344#332C22×C13711yescharacteristic
345#332C22×C13711yescharacteristic
346#332C22×C13711yescharacteristic
347C2×#41D4×C13711yescharacteristic
348C2×Q16—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8C23×C13711yescharacteristic
356C4⋊Q8C23×C13711yescharacteristic
357C4⋊Q8C23×C13711yescharacteristic
358C4⋊Q8C23×C13711yescharacteristic
359#125—21no—
360#125—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C13711yescharacteristic
370C4×Q8C23×C13711yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4D4×C13711yescharacteristic
374C4×D4C23×C13711yescharacteristic
375#117—21no—
376#117—21no—
377#117—21no—
378#117D4×C13711yescharacteristic
379C2×C42—21no—
380C2×C42C23×C13711yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C13711yescharacteristic
393C4⋊C8D4×C13711yescharacteristic
394C4⋊C8C23×C13711yescharacteristic
395C4⋊C8C23×C13711yescharacteristic
396C4⋊C8C23×C13711yescharacteristic
397C4⋊C8C23×C13711yescharacteristic
398C4⋊C8C23×C13711yescharacteristic
399C4⋊C8C23×C13711yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C13711yescharacteristic
417C22⋊C8D4×C13711yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C13711yescharacteristic
423C4×C8C23×C13711yescharacteristic
424#41—22no—
425#41—22no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8C2×D4×C13711yescharacteristic
431C2×D4—21no—
432C2×D4C2×D4×C13711yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D4×C13711yescharacteristic
437C22×C4C2×D4×C13711yescharacteristic
438C22×C4#41×C13711yescharacteristic
439Q16—42no—
440Q16—42no—
441SD16—42no—
442SD16—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—81no—
450C2×C8—81no—
451C2×C8—81no—
452C2×C8C2×D4×C13711yescharacteristic
453C2×C8C2×D4×C13711yescharacteristic
454C2×C8C2×D4×C13711yescharacteristic
455C2×C8C2×D4×C13711yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4C2×D4×C13711yescharacteristic
471C4⋊C4C2×D4×C13711yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42C2×D4×C13711yescharacteristic
483C42C2×D4×C13711yescharacteristic
484C42#41×C13711yescharacteristic
485C42C24×C13711yescharacteristic
486C23—21no—
487C23#121×C13711yescharacteristic
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8#135×C13712yes—
497D4—24no—
498D4—21no—
499D4#135×C13712yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4#121×C13711yescharacteristic
517C2×C4#121×C13711yescharacteristic
518C2×C4#121×C13711yescharacteristic
519C2×C4C22×D4×C13711yescharacteristic
520C2×C4C22×D4×C13711yescharacteristic
521C2×C4C2×#41×C13711yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22C2×#121×C13711yescharacteristic
539C4—21no—
540C4—21no—
541C4—22no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C2×#135×C13711yescharacteristic
551C4C2×#135×C13711yescharacteristic
552C4#577×C13711yescharacteristic
553C4#578×C13711yescharacteristic
554C2—41no—
555C2—42no—
556C2#3046×C13711yescharacteristic
557C2#3050×C13711yescharacteristic
558C2#3069×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radicalC2×#41×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
1. #3231×C137C2semidirect
5. #1684×C137C2semidirect
6. #1683×C137C2semidirect
7. #1680×C137C2semidirect
8. #1679×C137C2semidirect
9. #1674×C137C2semidirect
10. #1673×C137C2semidirect
11. #1672×C137C2semidirect
12. #1671×C137C2semidirect
13. #1572×C137C2semidirect
14. #1552×C137C2semidirect
15. #1542×C137C2semidirect
279. #19418C137direct (N × H)
280. C137#19418direct (N × H)
281. #3231C2×C137semidirect
285. #1684C2×C137semidirect
286. #1683C2×C137semidirect
287. #1680C2×C137semidirect
288. #1679C2×C137semidirect
289. #1674C2×C137semidirect
290. #1673C2×C137semidirect
291. #1672C2×C137semidirect
292. #1671C2×C137semidirect
293. #1572C2×C137semidirect
294. #1552C2×C137semidirect
295. #1542C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3231×C1372
#3116×C1372
#3107×C1372
#2988×C1372
#1684×C1372
#1683×C1372
#1680×C1372
#1679×C1372
#1674×C1372
#1673×C1372
#1672×C1372
#1671×C1372
#1572×C1372
#1552×C1372
#1542×C1372
#19418137