Finite Group Databasebeta

← C137×#19045 #46868431

Subgroups — C137×#19045 #46868431

Order 35072.

870 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559×C137C211yesmaximal, characteristic
2#3236×C137C211yesmaximal, characteristic, complemented
3#3181×C137C211yesmaximal, characteristic, complemented
4#3135×C137C211yesmaximal, characteristic, complemented
5#1664×C137C212yesmaximal, complemented
6#1664×C137C212yesmaximal, complemented
7#1662×C137C212yesmaximal, complemented
8#1661×C137C212yesmaximal, complemented
9#1532×C137C211yesmaximal, characteristic, complemented
10#1530×C137C211yesmaximal, characteristic, complemented
11C2×#330×C137C211yesmaximal, characteristic, complemented
12#563×C137C2212yes—
13#562×C137C2212yes—
14#554×C137—21no—
15#553×C137—21no—
16#553×C137—21no—
17#547×C137—22no—
18#547×C137—21no—
19#544×C137—21no—
20#540×C137—21no—
21#539×C137—22no—
22#539×C137—21no—
23#537×C137—21no—
24#533×C137C2211yescharacteristic
25#532×C137C2211yescharacteristic
26#529×C137C2211yescharacteristic
27C2×#125×C137C2211yescharacteristic
28#501×C137C2211yescharacteristic
29#501×C137C2212yes—
30#497×C137C2211yescharacteristic
31#491×C137—21no—
32#491×C137C2211yescharacteristic
33#491×C137C2212yes—
34#490×C137—21no—
35#489×C137C2212yes—
36#489×C137C2212yes—
37#489×C137C2211yescharacteristic
38#484×C137—21no—
39#483×C137—21no—
40#479×C137—22no—
41#467×C137—21no—
42#465×C137—21no—
43#441×C137—21no—
44#440×C137—21no—
45#432×C137C2211yescharacteristic
46#416×C137—22no—
47C2×#97×C137C2211yescharacteristic
48C2×#97×C137C2211yescharacteristic
49#330×C137C2212yes—
50#330×C137C2212yes—
51#330×C137C2212yes—
52#329×C137C2212yes—
53#329×C137C2212yes—
54#329×C137C2212yes—
55C2×#41×C137—22no—
56C2×#41×C137D412yes—
57C2×Q16×C137—21no—
58C2×SD16×C137—21no—
59C22×C8×C137—21no—
60C22×C8×C137—21no—
61C4⋊Q8×C137—21no—
62C4⋊Q8×C137—22no—
63C4⋊Q8×C137D411yescharacteristic
64C4⋊Q8×C137C2311yescharacteristic
65C4⋊Q8×C137C2311yescharacteristic
66#127×C137D411yescharacteristic
67#126×C137—22no—
68#126×C137—22no—
69#126×C137—21no—
70#125×C137—22no—
71#125×C137—21no—
72#125×C137—21no—
73#125×C137—21no—
74#125×C137—21no—
75#125×C137D412yes—
76#125×C137C2312yes—
77#125×C137C2311yescharacteristic
78#124×C137C2312yes—
79#124×C137C2311yescharacteristic
80#123×C137—22no—
81#123×C137—22no—
82#123×C137—22no—
83#123×C137—22no—
84#123×C137—21no—
85#123×C137—22no—
86#123×C137—22no—
87C22⋊Q8×C137—22no—
88C22⋊Q8×C137—22no—
89C22⋊Q8×C137—22no—
90C22⋊Q8×C137—22no—
91C22⋊Q8×C137—22no—
92C22⋊Q8×C137—22no—
93C22⋊Q8×C137—21no—
94C22⋊Q8×C137—21no—
95C22⋊Q8×C137D411yescharacteristic
96#121×C137—22no—
97#121×C137—22no—
98#121×C137—21no—
99#121×C137—21no—
100#121×C137—22no—
101#121×C137—22no—
102#121×C137—21no—
103#121×C137—21no—
104#121×C137D411yescharacteristic
105C4×Q8×C137—21no—
106C4×Q8×C137—21no—
107C4×Q8×C137D411yescharacteristic
108C4×D4×C137—22no—
109C4×D4×C137—22no—
110C4×D4×C137—21no—
111C4×D4×C137—21no—
112C4×D4×C137—21no—
113C4×D4×C137—21no—
114C4×D4×C137—21no—
115C4×D4×C137D411yescharacteristic
116#117×C137—21no—
117#117×C137—21no—
118#117×C137—21no—
119C2×C4⋊C4×C137—22no—
120C2×C4⋊C4×C137—21no—
121C2×C4⋊C4×C137—21no—
122C2×C4⋊C4×C137—21no—
123C2×C4⋊C4×C137D411yescharacteristic
124C2×C4⋊C4×C137D411yescharacteristic
125C2×C42×C137C2311yescharacteristic
126#107×C137—21no—
127#107×C137—22no—
128#106×C137—21no—
129#106×C137—22no—
130C4⋊C8×C137—21no—
131#103×C137—22no—
132#103×C137—22no—
133#103×C137—21no—
134#103×C137—21no—
135#103×C137—21no—
136#103×C137—22no—
137#103×C137—22no—
138#102×C137—22no—
139#102×C137—22no—
140#102×C137—21no—
141C22⋊C8×C137—21no—
142#97×C137—21no—
143#97×C137—21no—
144#97×C137C2312yes—
145#97×C137C2311yescharacteristic
146#97×C137C2311yescharacteristic
147#97×C137C2312yes—
148#41×C137—44no—
149#41×C137—84no—
150C2×Q8×C137—22no—
151C2×Q8×C137—21no—
152C2×Q8×C137—21no—
153C2×Q8×C137C2×D412yes—
154C2×Q8×C137C2×D411yescharacteristic
155C2×D4×C137—22no—
156C2×D4×C137—21no—
157C2×D4×C137—22no—
158C2×D4×C137—22no—
159C2×D4×C137—21no—
160C2×D4×C137—21no—
161C2×D4×C137C2×D412yes—
162C2×D4×C137C2×D411yescharacteristic
163C22×C4×C137—21no—
164C22×C4×C137—22no—
165C22×C4×C137—22no—
166C22×C4×C137—22no—
167C22×C4×C137—21no—
168C22×C4×C137—21no—
169C22×C4×C137—22no—
170C22×C4×C137C2×D411yescharacteristic
171C22×C4×C137C2×D411yescharacteristic
172C22×C4×C137C2×D411yescharacteristic
173Q16×C137—42no—
174SD16×C137—42no—
175C2×C8×C137—21no—
176C2×C8×C137—22no—
177C2×C8×C137—21no—
178C2×C8×C137—22no—
179C2×C8×C137—42no—
180C2×C8×C137—42no—
181C4⋊C4×C137—22no—
182C4⋊C4×C137—22no—
183C4⋊C4×C137—22no—
184C4⋊C4×C137—22no—
185C4⋊C4×C137—22no—
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—21no—
189C4⋊C4×C137—22no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—22no—
194C4⋊C4×C137—22no—
195C4⋊C4×C137—21no—
196C4⋊C4×C137—21no—
197C4⋊C4×C137—21no—
198C4⋊C4×C137—21no—
199C4⋊C4×C137—21no—
200C4⋊C4×C137—21no—
201C4⋊C4×C137—41no—
202C4⋊C4×C137—41no—
203C4⋊C4×C137C2×D412yes—
204C4⋊C4×C137C2×D411yescharacteristic
205C4⋊C4×C137C2×D412yes—
206C4⋊C4×C137C2×D411yescharacteristic
207C22⋊C4×C137—22no—
208C22⋊C4×C137—22no—
209C22⋊C4×C137—22no—
210C22⋊C4×C137—22no—
211C22⋊C4×C137—22no—
212C22⋊C4×C137—21no—
213C22⋊C4×C137—21no—
214C22⋊C4×C137—21no—
215C22⋊C4×C137—21no—
216C22⋊C4×C137—22no—
217C22⋊C4×C137—22no—
218C22⋊C4×C137—21no—
219C22⋊C4×C137—41no—
220C42×C137—22no—
221C42×C137—21no—
222C42×C137—41no—
223C42×C137C2×D411yescharacteristic
224C42×C137C2×D411yescharacteristic
225C42×C137C2×D411yescharacteristic
226C42×C137C2411yescharacteristic
227C23×C137—22no—
228C23×C137—21no—
229C23×C137#12011yescharacteristic
230Q8×C137—41no—
231Q8×C137—42no—
232Q8×C137—41no—
233Q8×C137—41no—
234Q8×C137—42no—
235Q8×C137—82no—
236D4×C137—41no—
237D4×C137—42no—
238D4×C137—42no—
239D4×C137—44no—
240D4×C137—42no—
241D4×C137—81no—
242D4×C137—82no—
243D4×C137—82no—
244C2×C4×C137—22no—
245C2×C4×C137—21no—
246C2×C4×C137—21no—
247C2×C4×C137—22no—
248C2×C4×C137—22no—
249C2×C4×C137—21no—
250C2×C4×C137—22no—
251C2×C4×C137—41no—
252C2×C4×C137—41no—
253C2×C4×C137—42no—
254C2×C4×C137—42no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—82no—
258C2×C4×C137—81no—
259C2×C4×C137—82no—
260C2×C4×C137—82no—
261C2×C4×C137—82no—
262C2×C4×C137#12011yescharacteristic
263C2×C4×C137#12011yescharacteristic
264C2×C4×C137#12011yescharacteristic
265C2×C4×C137C22×D411yescharacteristic
266C2×C4×C137C22×D411yescharacteristic
267C2×C4×C137C22×D411yescharacteristic
268C8×C137—22no—
269C8×C137—42no—
270C8×C137—42no—
271C8×C137—41no—
272C22×C137—21no—
273C22×C137—21no—
274C22×C137—42no—
275C22×C137—41no—
276C22×C137—42no—
277C22×C137—41no—
278C22×C137—41no—
279C22×C137—42no—
280C22×C137#45512yes—
281C22×C137C2×#12011yescharacteristic
282C4×C137—21no—
283C4×C137—21no—
284C4×C137—21no—
285C4×C137—21no—
286C4×C137—21no—
287C4×C137—21no—
288C4×C137—42no—
289C4×C137—42no—
290C4×C137—41no—
291C4×C137—42no—
292C4×C137—41no—
293C4×C137—41no—
294C4×C137—81no—
295C4×C137—81no—
296C2×C137—22no—
297C2×C137—82no—
298C2×C137—81no—
299C2×C137C2×#45511yescharacteristic
300C2×C137#301811yescharacteristic
301C2×C137#302011yescharacteristic
302#19045C13711yesmaximal, characteristic, direct product factor, Sylow
303C137#1904511yescharacteristic, direct product factor, Sylow
304#3559C2×C13711yescharacteristic
305#3236C2×C13711yescharacteristic, complemented
306#3181C2×C13711yescharacteristic, complemented
307#3135C2×C13711yescharacteristic, complemented
308#1664C2×C13712yescomplemented
309#1664C2×C13712yescomplemented
310#1662C2×C13712yescomplemented
311#1661C2×C13712yescomplemented
312#1532C2×C13711yescharacteristic, complemented
313#1530C2×C13711yescharacteristic, complemented
314C2×#330C2×C13711yescharacteristic, complemented
315#563C22×C13712yes—
316#562C22×C13712yes—
317#554—21no—
318#553—21no—
319#553—21no—
320#547—22no—
321#547—21no—
322#544—21no—
323#540—21no—
324#539—22no—
325#539—21no—
326#537—21no—
327#533C22×C13711yescharacteristic
328#532C22×C13711yescharacteristic
329#529C22×C13711yescharacteristic
330C2×#125C22×C13711yescharacteristic
331#501C22×C13711yescharacteristic
332#501C22×C13712yes—
333#497C22×C13711yescharacteristic
334#491—21no—
335#491C22×C13711yescharacteristic
336#491C22×C13712yes—
337#490—21no—
338#489C22×C13712yes—
339#489C22×C13712yes—
340#489C22×C13711yescharacteristic
341#484—21no—
342#483—21no—
343#479—22no—
344#467—21no—
345#465—21no—
346#441—21no—
347#440—21no—
348#432C22×C13711yescharacteristic
349#416—22no—
350C2×#97C22×C13711yescharacteristic
351C2×#97C22×C13711yescharacteristic
352#330C22×C13712yes—
353#330C22×C13712yes—
354#330C22×C13712yes—
355#329C22×C13712yes—
356#329C22×C13712yes—
357#329C22×C13712yes—
358C2×#41—22no—
359C2×#41D4×C13712yes—
360C2×Q16—21no—
361C2×SD16—21no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—22no—
366C4⋊Q8D4×C13711yescharacteristic
367C4⋊Q8C23×C13711yescharacteristic
368C4⋊Q8C23×C13711yescharacteristic
369#127D4×C13711yescharacteristic
370#126—22no—
371#126—22no—
372#126—21no—
373#125—22no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125D4×C13712yes—
379#125C23×C13712yes—
380#125C23×C13711yescharacteristic
381#124C23×C13711yescharacteristic
382#124C23×C13712yes—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—21no—
388#123—22no—
389#123—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8D4×C13711yescharacteristic
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—22no—
404#121—22no—
405#121—21no—
406#121—21no—
407#121D4×C13711yescharacteristic
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8D4×C13711yescharacteristic
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4D4×C13711yescharacteristic
419#117—21no—
420#117—21no—
421#117—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4D4×C13711yescharacteristic
427C2×C4⋊C4D4×C13711yescharacteristic
428C2×C42C23×C13711yescharacteristic
429#107—21no—
430#107—22no—
431#106—21no—
432#106—22no—
433C4⋊C8—21no—
434#103—22no—
435#103—22no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—22no—
440#103—22no—
441#102—22no—
442#102—22no—
443#102—21no—
444C22⋊C8—21no—
445#97—21no—
446#97—21no—
447#97C23×C13712yes—
448#97C23×C13711yescharacteristic
449#97C23×C13711yescharacteristic
450#97C23×C13712yes—
451#41—44no—
452#41—84no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C13712yes—
457C2×Q8C2×D4×C13711yescharacteristic
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4C2×D4×C13712yes—
465C2×D4C2×D4×C13711yescharacteristic
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4C2×D4×C13711yescharacteristic
474C22×C4C2×D4×C13711yescharacteristic
475C22×C4C2×D4×C13711yescharacteristic
476Q16—42no—
477SD16—42no—
478C2×C8—21no—
479C2×C8—22no—
480C2×C8—21no—
481C2×C8—22no—
482C2×C8—42no—
483C2×C8—42no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C13712yes—
507C4⋊C4C2×D4×C13711yescharacteristic
508C4⋊C4C2×D4×C13712yes—
509C4⋊C4C2×D4×C13711yescharacteristic
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C42—22no—
524C42—21no—
525C42—41no—
526C42C2×D4×C13711yescharacteristic
527C42C2×D4×C13711yescharacteristic
528C42C2×D4×C13711yescharacteristic
529C42C24×C13711yescharacteristic
530C23—22no—
531C23—21no—
532C23#120×C13711yescharacteristic
533Q8—41no—
534Q8—42no—
535Q8—41no—
536Q8—41no—
537Q8—42no—
538Q8—82no—
539D4—41no—
540D4—42no—
541D4—42no—
542D4—44no—
543D4—42no—
544D4—81no—
545D4—82no—
546D4—82no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4#120×C13711yescharacteristic
566C2×C4#120×C13711yescharacteristic
567C2×C4#120×C13711yescharacteristic
568C2×C4C22×D4×C13711yescharacteristic
569C2×C4C22×D4×C13711yescharacteristic
570C2×C4C22×D4×C13711yescharacteristic
571C8—22no—
572C8—42no—
573C8—41no—
574C8—42no—
575C22—21no—
576C22—21no—
577C22—42no—
578C22—41no—
579C22—42no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22#455×C13712yes—
584C22C2×#120×C13711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—42no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—82no—
601C2—81no—
602C2C2×#455×C13711yescharacteristic
603C2#3018×C13711yescharacteristic
604C2#3020×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radical#3559×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
2. #3236×C137C2semidirect
3. #3181×C137C2semidirect
4. #3135×C137C2semidirect
5. #1664×C137C2semidirect
6. #1664×C137C2semidirect
7. #1662×C137C2semidirect
8. #1661×C137C2semidirect
9. #1532×C137C2semidirect
10. #1530×C137C2semidirect
11. C2×#330×C137C2semidirect
302. #19045C137direct (N × H)
303. C137#19045direct (N × H)
305. #3236C2×C137semidirect
306. #3181C2×C137semidirect
307. #3135C2×C137semidirect
308. #1664C2×C137semidirect
309. #1664C2×C137semidirect
310. #1662C2×C137semidirect
311. #1661C2×C137semidirect
312. #1532C2×C137semidirect
313. #1530C2×C137semidirect
314. C2×#330C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3559×C1372
#3236×C1372
#3181×C1372
#3135×C1372
#1664×C1372
#1662×C1372
#1661×C1372
#1532×C1372
#1530×C1372
C2×#330×C1372
#19045137