Finite Group Databasebeta

← C137×#18962 #46868348

Subgroups — C137×#18962 #46868348

Order 35072.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C137C211yesmaximal, characteristic, complemented
2#3253×C137C211yesmaximal, characteristic, complemented
3#3247×C137C211yesmaximal, characteristic, complemented
4#3207×C137C211yesmaximal, characteristic, complemented
5#1638×C137C211yesmaximal, characteristic, complemented
6#1635×C137C211yesmaximal, characteristic, complemented
7#1631×C137C211yesmaximal, characteristic, complemented
8#1629×C137C211yesmaximal, characteristic, complemented
9#1628×C137C211yesmaximal, characteristic, complemented
10#1625×C137C211yesmaximal, characteristic, complemented
11#1621×C137C211yesmaximal, characteristic, complemented
12#1619×C137C211yesmaximal, characteristic, complemented
13#1547×C137C211yesmaximal, characteristic, complemented
14#1495×C137C211yesmaximal, characteristic, complemented
15#1480×C137C211yesmaximal, characteristic, complemented
16#560×C137—22no—
17#556×C137C2211yescharacteristic
18#553×C137—21no—
19#550×C137—21no—
20#550×C137C2211yescharacteristic
21#547×C137C2211yescharacteristic
22#546×C137—21no—
23#546×C137—21no—
24D42×C137C2211yescharacteristic
25#542×C137—21no—
26#538×C137—22no—
27#537×C137—21no—
28#535×C137—21no—
29#535×C137—21no—
30#532×C137C2211yescharacteristic
31#532×C137C2211yescharacteristic
32#532×C137C2211yescharacteristic, complemented
33#529×C137C2211yescharacteristic
34#493×C137C2211yescharacteristic
35#492×C137C2211yescharacteristic
36#487×C137C2211yescharacteristic, complemented
37#486×C137C2211yescharacteristic, complemented
38#478×C137—21no—
39#477×C137C2211yescharacteristic, complemented
40#476×C137—21no—
41#476×C137C2211yescharacteristic
42#476×C137C2211yescharacteristic
43#476×C137C2211yescharacteristic, complemented
44#469×C137—21no—
45#469×C137—21no—
46#466×C137—21no—
47#465×C137—21no—
48#463×C137—21no—
49#463×C137—22no—
50#460×C137C2211yescharacteristic, complemented
51#459×C137—21no—
52#459×C137C2211yescharacteristic
53#459×C137C2211yescharacteristic
54#459×C137C2211yescharacteristic, complemented
55#449×C137—22no—
56#431×C137C2211yescharacteristic, complemented
57#423×C137C2211yescharacteristic, complemented
58C2×C4⋊C8×C137C2211yescharacteristic, complemented
59#332×C137C2211yescharacteristic, complemented
60#332×C137C2211yescharacteristic, complemented
61#331×C137C2211yescharacteristic
62#331×C137C2211yescharacteristic
63Q8⋊C8×C137C2211yescharacteristic, complemented
64Q8⋊C8×C137C2211yescharacteristic, complemented
65D4⋊C8×C137C2211yescharacteristic
66D4⋊C8×C137C2211yescharacteristic
67D4⋊C8×C137C2211yescharacteristic
68D4⋊C8×C137C2211yescharacteristic
69D4⋊C8×C137C2211yescharacteristic, complemented
70D4⋊C8×C137C2211yescharacteristic, complemented
71C2×#41×C137—21no—
72C2×#41×C137—21no—
73C2×#41×C137—21no—
74C2×#41×C137—21no—
75C2×#41×C137—21no—
76C22×D4×C137—21no—
77C22×D4×C137—21no—
78C2×SD16×C137—21no—
79C2×SD16×C137—22no—
80C2×D8×C137—22no—
81C2×D8×C137—21no—
82C2×D8×C137—21no—
83C2×D8×C137—21no—
84C2×M16×C137—21no—
85C22×C8×C137—21no—
86C4⋊Q8×C137D411yescharacteristic
87C4⋊Q8×C137C2311yescharacteristic
88C4⋊Q8×C137C2311yescharacteristic
89#127×C137—22no—
90#127×C137—21no—
91#127×C137D411yescharacteristic
92#127×C137C2311yescharacteristic
93#127×C137C2311yescharacteristic
94#126×C137—22no—
95#126×C137—22no—
96#126×C137—21no—
97#125×C137D411yescharacteristic
98#124×C137—22no—
99#124×C137—21no—
100#124×C137—21no—
101#124×C137—21no—
102#124×C137—21no—
103#124×C137D411yescharacteristic
104#123×C137—22no—
105#123×C137—22no—
106#123×C137—21no—
107#123×C137—22no—
108C22⋊Q8×C137—22no—
109C22⋊Q8×C137—21no—
110C22⋊Q8×C137—21no—
111C22⋊Q8×C137D411yescharacteristic
112#121×C137—22no—
113#121×C137—22no—
114#121×C137—22no—
115#121×C137—22no—
116#121×C137—22no—
117#121×C137—21no—
118#121×C137—22no—
119#121×C137—21no—
120#121×C137—21no—
121#121×C137—21no—
122#121×C137—21no—
123#121×C137—21no—
124#121×C137—21no—
125#121×C137—21no—
126#121×C137D412yes—
127#121×C137D411yescharacteristic
128#121×C137D411yescharacteristic
129#121×C137D411yescharacteristic
130#120×C137—22no—
131#120×C137—22no—
132#120×C137—22no—
133#120×C137—22no—
134C4×Q8×C137—21no—
135C4×Q8×C137C2311yescharacteristic
136C4×D4×C137—22no—
137C4×D4×C137—21no—
138C4×D4×C137—21no—
139C4×D4×C137—21no—
140C4×D4×C137—21no—
141C4×D4×C137—21no—
142C4×D4×C137—21no—
143C4×D4×C137D412yes—
144C4×D4×C137C2311yescharacteristic
145C4×D4×C137C2311yescharacteristic
146C4×D4×C137C2311yescharacteristic
147#117×C137—21no—
148#117×C137—21no—
149C2×C4⋊C4×C137—21no—
150C2×C22⋊C4×C137—22no—
151C2×C42×C137C2311yescharacteristic
152#107×C137—21no—
153#106×C137—21no—
154#106×C137—21no—
155#106×C137—21no—
156C4⋊C8×C137—21no—
157C4⋊C8×C137—21no—
158C4⋊C8×C137—21no—
159C4⋊C8×C137C2311yescharacteristic
160C4⋊C8×C137C2311yescharacteristic
161C4⋊C8×C137C2311yescharacteristic
162C4⋊C8×C137C2311yescharacteristic
163#103×C137—21no—
164#103×C137—22no—
165#102×C137—21no—
166#102×C137—21no—
167#102×C137—21no—
168#102×C137—22no—
169#102×C137—21no—
170#102×C137—21no—
171#102×C137—21no—
172#102×C137—21no—
173C22⋊C8×C137—21no—
174C4×C8×C137C2311yescharacteristic
175C4×C8×C137C2311yescharacteristic
176C24×C137—22no—
177#41×C137—81no—
178#41×C137—81no—
179#41×C137—81no—
180#41×C137—81no—
181#41×C137—81no—
182#41×C137—81no—
183#41×C137—81no—
184#41×C137—81no—
185#41×C137—82no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137C2×D411yescharacteristic
190C2×D4×C137—22no—
191C2×D4×C137—22no—
192C2×D4×C137—22no—
193C2×D4×C137—22no—
194C2×D4×C137—22no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—22no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
203C2×D4×C137—21no—
204C2×D4×C137—21no—
205C2×D4×C137—21no—
206C2×D4×C137—41no—
207C2×D4×C137—81no—
208C2×D4×C137—81no—
209C2×D4×C137—81no—
210C2×D4×C137—81no—
211C2×D4×C137C2×D411yescharacteristic
212C2×D4×C137C2×D411yescharacteristic
213C2×D4×C137C2×D411yescharacteristic
214C2×D4×C137C2×D412yes—
215C22×C4×C137—22no—
216C22×C4×C137—22no—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—22no—
221C22×C4×C137—41no—
222C22×C4×C137C2×D411yescharacteristic
223C22×C4×C137C2×D411yescharacteristic
224C22×C4×C137C2×D411yescharacteristic
225SD16×C137—81no—
226SD16×C137—82no—
227D8×C137—81no—
228D8×C137—81no—
229D8×C137—81no—
230D8×C137—82no—
231M16×C137—81no—
232C2×C8×C137—21no—
233C2×C8×C137—21no—
234C2×C8×C137—21no—
235C2×C8×C137—21no—
236C2×C8×C137—21no—
237C2×C8×C137—21no—
238C2×C8×C137—81no—
239C4⋊C4×C137—22no—
240C4⋊C4×C137—22no—
241C4⋊C4×C137—21no—
242C4⋊C4×C137—21no—
243C4⋊C4×C137—21no—
244C4⋊C4×C137—21no—
245C4⋊C4×C137—21no—
246C4⋊C4×C137—21no—
247C4⋊C4×C137—21no—
248C4⋊C4×C137—21no—
249C4⋊C4×C137C2×D412yes—
250C4⋊C4×C137C2×D411yescharacteristic
251C4⋊C4×C137C2×D411yescharacteristic
252C4⋊C4×C137C2×D411yescharacteristic
253C4⋊C4×C137C2×D411yescharacteristic
254C22⋊C4×C137—22no—
255C22⋊C4×C137—22no—
256C22⋊C4×C137—22no—
257C22⋊C4×C137—22no—
258C22⋊C4×C137—22no—
259C22⋊C4×C137—21no—
260C22⋊C4×C137—21no—
261C22⋊C4×C137—21no—
262C22⋊C4×C137—21no—
263C22⋊C4×C137—21no—
264C22⋊C4×C137—21no—
265C22⋊C4×C137—22no—
266C22⋊C4×C137—22no—
267C22⋊C4×C137—21no—
268C22⋊C4×C137—21no—
269C22⋊C4×C137—21no—
270C22⋊C4×C137—41no—
271C22⋊C4×C137—41no—
272C42×C137—22no—
273C42×C137—21no—
274C42×C137C2×D411yescharacteristic
275C42×C137C2×D411yescharacteristic
276C42×C137C2×D411yescharacteristic
277C42×C137C2411yescharacteristic
278C23×C137—21no—
279C23×C137—21no—
280C23×C137—22no—
281C23×C137—21no—
282C23×C137—41no—
283C23×C137—82no—
284C23×C137—82no—
285C23×C137—82no—
286C23×C137#12011yescharacteristic
287Q8×C137—21no—
288Q8×C137—21no—
289Q8×C137—42no—
290Q8×C137—41no—
291Q8×C137—41no—
292Q8×C137—81no—
293D4×C137—21no—
294D4×C137—21no—
295D4×C137—21no—
296D4×C137—21no—
297D4×C137—21no—
298D4×C137—21no—
299D4×C137—42no—
300D4×C137—42no—
301D4×C137—41no—
302D4×C137—41no—
303D4×C137—41no—
304D4×C137—41no—
305D4×C137—41no—
306D4×C137—41no—
307D4×C137—41no—
308D4×C137—41no—
309D4×C137—81no—
310D4×C137—81no—
311D4×C137—81no—
312D4×C137—81no—
313D4×C137—81no—
314D4×C137—82no—
315D4×C137—82no—
316D4×C137—82no—
317D4×C137—82no—
318D4×C137—82no—
319D4×C137—82no—
320D4×C137—82no—
321C2×C4×C137—21no—
322C2×C4×C137—21no—
323C2×C4×C137—21no—
324C2×C4×C137—21no—
325C2×C4×C137—21no—
326C2×C4×C137—21no—
327C2×C4×C137—21no—
328C2×C4×C137—22no—
329C2×C4×C137—21no—
330C2×C4×C137—21no—
331C2×C4×C137—41no—
332C2×C4×C137—41no—
333C2×C4×C137—41no—
334C2×C4×C137—41no—
335C2×C4×C137—41no—
336C2×C4×C137—41no—
337C2×C4×C137—41no—
338C2×C4×C137—41no—
339C2×C4×C137—82no—
340C2×C4×C137—82no—
341C2×C4×C137—82no—
342C2×C4×C137—82no—
343C2×C4×C137#12011yescharacteristic
344C2×C4×C137#12011yescharacteristic
345C2×C4×C137#12011yescharacteristic
346C2×C4×C137C22×D411yescharacteristic
347C2×C4×C137C22×D411yescharacteristic
348C2×C4×C137C22×D411yescharacteristic
349C8×C137—41no—
350C8×C137—41no—
351C8×C137—41no—
352C8×C137—41no—
353C8×C137—41no—
354C8×C137—41no—
355C22×C137—21no—
356C22×C137—21no—
357C22×C137—21no—
358C22×C137—41no—
359C22×C137—41no—
360C22×C137—41no—
361C22×C137—41no—
362C22×C137—42no—
363C22×C137—42no—
364C22×C137—41no—
365C22×C137—41no—
366C22×C137—42no—
367C22×C137—41no—
368C22×C137—41no—
369C22×C137—41no—
370C22×C137—81no—
371C22×C137—81no—
372C22×C137—81no—
373C22×C137—164no—
374C22×C137C2×#12011yescharacteristic
375C4×C137—21no—
376C4×C137—21no—
377C4×C137—21no—
378C4×C137—21no—
379C4×C137—41no—
380C4×C137—41no—
381C4×C137—41no—
382C4×C137—41no—
383C4×C137—42no—
384C4×C137—41no—
385C4×C137—81no—
386C4×C137#57611yescharacteristic
387C4×C137#57611yescharacteristic
388C4×C137#57711yescharacteristic
389C4×C137#57711yescharacteristic
390C2×C137—41no—
391C2×C137—81no—
392C2×C137—82no—
393C2×C137—81no—
394C2×C137—81no—
395C2×C137—161no—
396C2×C137#301211yescharacteristic
397C2×C137#301211yescharacteristic
398C2×C137#302111yescharacteristic
399#18962C13711yesmaximal, characteristic, direct product factor, Sylow
400C137#1896211yescharacteristic, direct product factor, Sylow
401#3546C2×C13711yescharacteristic, complemented
402#3253C2×C13711yescharacteristic, complemented
403#3247C2×C13711yescharacteristic, complemented
404#3207C2×C13711yescharacteristic, complemented
405#1638C2×C13711yescharacteristic, complemented
406#1635C2×C13711yescharacteristic, complemented
407#1631C2×C13711yescharacteristic, complemented
408#1629C2×C13711yescharacteristic, complemented
409#1628C2×C13711yescharacteristic, complemented
410#1625C2×C13711yescharacteristic, complemented
411#1621C2×C13711yescharacteristic, complemented
412#1619C2×C13711yescharacteristic, complemented
413#1547C2×C13711yescharacteristic, complemented
414#1495C2×C13711yescharacteristic, complemented
415#1480C2×C13711yescharacteristic, complemented
416#560—22no—
417#556C22×C13711yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C13711yescharacteristic
421#547C22×C13711yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C13711yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C13711yescharacteristic
431#532C22×C13711yescharacteristic
432#532C22×C13711yescharacteristic, complemented
433#529C22×C13711yescharacteristic
434#493C22×C13711yescharacteristic
435#492C22×C13711yescharacteristic
436#487C22×C13711yescharacteristic, complemented
437#486C22×C13711yescharacteristic, complemented
438#478—21no—
439#477C22×C13711yescharacteristic, complemented
440#476—21no—
441#476C22×C13711yescharacteristic
442#476C22×C13711yescharacteristic
443#476C22×C13711yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C13711yescharacteristic, complemented
451#459—21no—
452#459C22×C13711yescharacteristic
453#459C22×C13711yescharacteristic
454#459C22×C13711yescharacteristic, complemented
455#449—22no—
456#431C22×C13711yescharacteristic, complemented
457#423C22×C13711yescharacteristic, complemented
458C2×C4⋊C8C22×C13711yescharacteristic, complemented
459#332C22×C13711yescharacteristic, complemented
460#332C22×C13711yescharacteristic, complemented
461#331C22×C13711yescharacteristic
462#331C22×C13711yescharacteristic
463Q8⋊C8C22×C13711yescharacteristic, complemented
464Q8⋊C8C22×C13711yescharacteristic, complemented
465D4⋊C8C22×C13711yescharacteristic
466D4⋊C8C22×C13711yescharacteristic
467D4⋊C8C22×C13711yescharacteristic
468D4⋊C8C22×C13711yescharacteristic
469D4⋊C8C22×C13711yescharacteristic, complemented
470D4⋊C8C22×C13711yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C13711yescharacteristic
487C4⋊Q8C23×C13711yescharacteristic
488C4⋊Q8C23×C13711yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C13711yescharacteristic
492#127C23×C13711yescharacteristic
493#127C23×C13711yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C13711yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C13711yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C13711yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C13711yescharacteristic
527#121D4×C13711yescharacteristic
528#121D4×C13711yescharacteristic
529#121D4×C13712yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C13711yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C13712yes—
544C4×D4C23×C13711yescharacteristic
545C4×D4C23×C13711yescharacteristic
546C4×D4C23×C13711yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C13711yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C13711yescharacteristic
560C4⋊C8C23×C13711yescharacteristic
561C4⋊C8C23×C13711yescharacteristic
562C4⋊C8C23×C13711yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C13711yescharacteristic
575C4×C8C23×C13711yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C13711yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C13711yescharacteristic
612C2×D4C2×D4×C13711yescharacteristic
613C2×D4C2×D4×C13711yescharacteristic
614C2×D4C2×D4×C13712yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C13711yescharacteristic
623C22×C4C2×D4×C13711yescharacteristic
624C22×C4C2×D4×C13711yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C13712yes—
650C4⋊C4C2×D4×C13711yescharacteristic
651C4⋊C4C2×D4×C13711yescharacteristic
652C4⋊C4C2×D4×C13711yescharacteristic
653C4⋊C4C2×D4×C13711yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C13711yescharacteristic
675C42C2×D4×C13711yescharacteristic
676C42C2×D4×C13711yescharacteristic
677C42C24×C13711yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C13711yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C13711yescharacteristic
744C2×C4#120×C13711yescharacteristic
745C2×C4#120×C13711yescharacteristic
746C2×C4C22×D4×C13711yescharacteristic
747C2×C4C22×D4×C13711yescharacteristic
748C2×C4C22×D4×C13711yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C13711yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C13711yescharacteristic
787C4#576×C13711yescharacteristic
788C4#577×C13711yescharacteristic
789C4#577×C13711yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2#3012×C13711yescharacteristic
797C2#3012×C13711yescharacteristic
798C2#3021×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
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. #3546×C137C2semidirect
2. #3253×C137C2semidirect
3. #3247×C137C2semidirect
4. #3207×C137C2semidirect
5. #1638×C137C2semidirect
6. #1635×C137C2semidirect
7. #1631×C137C2semidirect
8. #1629×C137C2semidirect
9. #1628×C137C2semidirect
10. #1625×C137C2semidirect
11. #1621×C137C2semidirect
12. #1619×C137C2semidirect
13. #1547×C137C2semidirect
14. #1495×C137C2semidirect
15. #1480×C137C2semidirect
32. #532×C137C22semidirect
36. #487×C137C22semidirect
37. #486×C137C22semidirect
39. #477×C137C22semidirect
43. #476×C137C22semidirect
50. #460×C137C22semidirect
54. #459×C137C22semidirect
56. #431×C137C22semidirect
57. #423×C137C22semidirect
58. C2×C4⋊C8×C137C22semidirect
59. #332×C137C22semidirect
60. #332×C137C22semidirect
63. Q8⋊C8×C137C22semidirect
64. Q8⋊C8×C137C22semidirect
69. D4⋊C8×C137C22semidirect
70. D4⋊C8×C137C22semidirect
399. #18962C137direct (N × H)
400. C137#18962direct (N × H)
401. #3546C2×C137semidirect
402. #3253C2×C137semidirect
403. #3247C2×C137semidirect
404. #3207C2×C137semidirect
405. #1638C2×C137semidirect
406. #1635C2×C137semidirect
407. #1631C2×C137semidirect
408. #1629C2×C137semidirect
409. #1628C2×C137semidirect
410. #1625C2×C137semidirect
411. #1621C2×C137semidirect
412. #1619C2×C137semidirect
413. #1547C2×C137semidirect
414. #1495C2×C137semidirect
415. #1480C2×C137semidirect
432. #532C22×C137semidirect
436. #487C22×C137semidirect
437. #486C22×C137semidirect
439. #477C22×C137semidirect
443. #476C22×C137semidirect
450. #460C22×C137semidirect
454. #459C22×C137semidirect
456. #431C22×C137semidirect
457. #423C22×C137semidirect
458. C2×C4⋊C8C22×C137semidirect
459. #332C22×C137semidirect
460. #332C22×C137semidirect
463. Q8⋊C8C22×C137semidirect
464. Q8⋊C8C22×C137semidirect
469. D4⋊C8C22×C137semidirect
470. D4⋊C8C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3546×C1372
#3253×C1372
#3247×C1372
#3207×C1372
#1638×C1372
#1635×C1372
#1631×C1372
#1629×C1372
#1628×C1372
#1625×C1372
#1621×C1372
#1619×C1372
#1547×C1372
#1495×C1372
#1480×C1372
#18962137