Finite Group Databasebeta

← C137×#18974 #46868360

Subgroups — C137×#18974 #46868360

Order 35072.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C137C211yesmaximal, characteristic
2#3254×C137C211yesmaximal, characteristic, complemented
3#3248×C137C211yesmaximal, characteristic, complemented
4#3228×C137C211yesmaximal, characteristic, complemented
5#1654×C137C211yesmaximal, characteristic, complemented
6#1652×C137C211yesmaximal, characteristic, complemented
7#1650×C137C211yesmaximal, characteristic, complemented
8#1647×C137C211yesmaximal, characteristic, complemented
9#1642×C137C211yesmaximal, characteristic, complemented
10#1641×C137C211yesmaximal, characteristic, complemented
11#1639×C137C211yesmaximal, characteristic, complemented
12#1639×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#533×C137C2211yescharacteristic, complemented
31#532×C137C2211yescharacteristic
32#532×C137C2211yescharacteristic
33#529×C137C2211yescharacteristic
34#500×C137C2211yescharacteristic, complemented
35#498×C137C2211yescharacteristic, complemented
36#486×C137C2211yescharacteristic
37#486×C137C2211yescharacteristic
38#482×C137—22no—
39#479×C137—21no—
40#478×C137—22no—
41#477×C137—21no—
42#475×C137C2211yescharacteristic, complemented
43#474×C137C2211yescharacteristic
44#474×C137C2211yescharacteristic
45#474×C137C2211yescharacteristic, complemented
46#468×C137—21no—
47#468×C137—21no—
48#467×C137—21no—
49#465×C137—21no—
50#464×C137—21no—
51#462×C137C2211yescharacteristic, complemented
52#461×C137C2211yescharacteristic
53#461×C137C2211yescharacteristic
54#461×C137C2211yescharacteristic, complemented
55#460×C137—21no—
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—
75C22×D4×C137—21no—
76C22×D4×C137—21no—
77C2×Q16×C137—21no—
78C2×SD16×C137—21no—
79C2×SD16×C137—21no—
80C2×SD16×C137—21no—
81C2×M16×C137—21no—
82C22×C8×C137—21no—
83C4⋊Q8×C137D411yescharacteristic
84C4⋊Q8×C137C2311yescharacteristic
85C4⋊Q8×C137C2311yescharacteristic
86C4⋊Q8×C137C2311yescharacteristic
87#127×C137—22no—
88#127×C137—21no—
89#127×C137D411yescharacteristic
90#127×C137C2311yescharacteristic
91#126×C137—22no—
92#126×C137—22no—
93#126×C137—21no—
94#125×C137—21no—
95#125×C137D411yescharacteristic
96#124×C137—22no—
97#124×C137—21no—
98#124×C137—21no—
99#124×C137—21no—
100#124×C137D411yescharacteristic
101#123×C137—22no—
102#123×C137—22no—
103#123×C137—21no—
104#123×C137—22no—
105C22⋊Q8×C137—22no—
106C22⋊Q8×C137—21no—
107C22⋊Q8×C137—21no—
108C22⋊Q8×C137—21no—
109C22⋊Q8×C137—21no—
110C22⋊Q8×C137D411yescharacteristic
111#121×C137—22no—
112#121×C137—22no—
113#121×C137—22no—
114#121×C137—22no—
115#121×C137—22no—
116#121×C137—21no—
117#121×C137—22no—
118#121×C137—21no—
119#121×C137—21no—
120#121×C137—21no—
121#121×C137—21no—
122#121×C137—21no—
123#121×C137D411yescharacteristic
124#121×C137D411yescharacteristic
125#121×C137D411yescharacteristic
126#121×C137D412yes—
127#120×C137—22no—
128#120×C137—22no—
129#120×C137—22no—
130#120×C137—22no—
131C4×Q8×C137—21no—
132C4×Q8×C137—21no—
133C4×Q8×C137—21no—
134C4×Q8×C137C2311yescharacteristic
135C4×D4×C137—22no—
136C4×D4×C137—21no—
137C4×D4×C137—21no—
138C4×D4×C137—21no—
139C4×D4×C137—21no—
140C4×D4×C137D412yes—
141C4×D4×C137C2311yescharacteristic
142C4×D4×C137C2311yescharacteristic
143C4×D4×C137C2311yescharacteristic
144#117×C137—21no—
145#117×C137—21no—
146#117×C137—21no—
147C2×C4⋊C4×C137—21no—
148C2×C22⋊C4×C137—22no—
149C2×C42×C137C2311yescharacteristic
150#107×C137—21no—
151#107×C137—21no—
152#107×C137—21no—
153#107×C137—22no—
154#106×C137—21no—
155#106×C137—22no—
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—21no—
165#103×C137—21no—
166#103×C137—21no—
167#103×C137—21no—
168#102×C137—21no—
169#102×C137—21no—
170#102×C137—21no—
171#102×C137—22no—
172#102×C137—22no—
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—
185C2×Q8×C137—21no—
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—81no—
204C2×D4×C137—81no—
205C2×D4×C137—81no—
206C2×D4×C137—81no—
207C2×D4×C137C2×D411yescharacteristic
208C2×D4×C137C2×D411yescharacteristic
209C2×D4×C137C2×D411yescharacteristic
210C2×D4×C137C2×D412yes—
211C22×C4×C137—22no—
212C22×C4×C137—22no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—22no—
217C22×C4×C137C2×D411yescharacteristic
218C22×C4×C137C2×D411yescharacteristic
219C22×C4×C137C2×D411yescharacteristic
220Q16×C137—81no—
221SD16×C137—81no—
222SD16×C137—81no—
223SD16×C137—81no—
224M16×C137—81no—
225C2×C8×C137—21no—
226C2×C8×C137—21no—
227C2×C8×C137—21no—
228C2×C8×C137—21no—
229C2×C8×C137—21no—
230C2×C8×C137—21no—
231C2×C8×C137—81no—
232C4⋊C4×C137—22no—
233C4⋊C4×C137—22no—
234C4⋊C4×C137—21no—
235C4⋊C4×C137—21no—
236C4⋊C4×C137—21no—
237C4⋊C4×C137—21no—
238C4⋊C4×C137—21no—
239C4⋊C4×C137—21no—
240C4⋊C4×C137—21no—
241C4⋊C4×C137—21no—
242C4⋊C4×C137—21no—
243C4⋊C4×C137—21no—
244C4⋊C4×C137—41no—
245C4⋊C4×C137—41no—
246C4⋊C4×C137C2×D411yescharacteristic
247C4⋊C4×C137C2×D411yescharacteristic
248C4⋊C4×C137C2×D411yescharacteristic
249C4⋊C4×C137C2×D411yescharacteristic
250C4⋊C4×C137C2×D412yes—
251C22⋊C4×C137—22no—
252C22⋊C4×C137—22no—
253C22⋊C4×C137—22no—
254C22⋊C4×C137—22no—
255C22⋊C4×C137—22no—
256C22⋊C4×C137—21no—
257C22⋊C4×C137—21no—
258C22⋊C4×C137—21no—
259C22⋊C4×C137—21no—
260C22⋊C4×C137—21no—
261C22⋊C4×C137—21no—
262C22⋊C4×C137—22no—
263C22⋊C4×C137—22no—
264C22⋊C4×C137—21no—
265C22⋊C4×C137—21no—
266C22⋊C4×C137—21no—
267C22⋊C4×C137—41no—
268C42×C137—22no—
269C42×C137—21no—
270C42×C137—41no—
271C42×C137C2×D411yescharacteristic
272C42×C137C2×D411yescharacteristic
273C42×C137C2×D411yescharacteristic
274C42×C137C2411yescharacteristic
275C23×C137—21no—
276C23×C137—21no—
277C23×C137—22no—
278C23×C137—21no—
279C23×C137—82no—
280C23×C137—82no—
281C23×C137—82no—
282C23×C137#12011yescharacteristic
283Q8×C137—21no—
284Q8×C137—21no—
285Q8×C137—41no—
286Q8×C137—41no—
287Q8×C137—41no—
288Q8×C137—41no—
289Q8×C137—41no—
290Q8×C137—41no—
291Q8×C137—81no—
292D4×C137—21no—
293D4×C137—21no—
294D4×C137—21no—
295D4×C137—21no—
296D4×C137—21no—
297D4×C137—21no—
298D4×C137—42no—
299D4×C137—41no—
300D4×C137—41no—
301D4×C137—41no—
302D4×C137—41no—
303D4×C137—81no—
304D4×C137—81no—
305D4×C137—81no—
306D4×C137—81no—
307D4×C137—81no—
308D4×C137—82no—
309D4×C137—82no—
310D4×C137—82no—
311D4×C137—82no—
312D4×C137—82no—
313D4×C137—82no—
314C2×C4×C137—21no—
315C2×C4×C137—21no—
316C2×C4×C137—21no—
317C2×C4×C137—21no—
318C2×C4×C137—21no—
319C2×C4×C137—21no—
320C2×C4×C137—21no—
321C2×C4×C137—22no—
322C2×C4×C137—21no—
323C2×C4×C137—21no—
324C2×C4×C137—41no—
325C2×C4×C137—41no—
326C2×C4×C137—41no—
327C2×C4×C137—41no—
328C2×C4×C137—41no—
329C2×C4×C137—41no—
330C2×C4×C137—41no—
331C2×C4×C137—41no—
332C2×C4×C137—41no—
333C2×C4×C137—82no—
334C2×C4×C137—82no—
335C2×C4×C137—82no—
336C2×C4×C137#12011yescharacteristic
337C2×C4×C137#12011yescharacteristic
338C2×C4×C137#12011yescharacteristic
339C2×C4×C137C22×D411yescharacteristic
340C2×C4×C137C22×D411yescharacteristic
341C2×C4×C137C22×D411yescharacteristic
342C8×C137—41no—
343C8×C137—41no—
344C8×C137—41no—
345C8×C137—41no—
346C8×C137—41no—
347C8×C137—41no—
348C22×C137—21no—
349C22×C137—21no—
350C22×C137—21no—
351C22×C137—41no—
352C22×C137—41no—
353C22×C137—41no—
354C22×C137—41no—
355C22×C137—42no—
356C22×C137—42no—
357C22×C137—41no—
358C22×C137—41no—
359C22×C137—42no—
360C22×C137—41no—
361C22×C137—41no—
362C22×C137—41no—
363C22×C137—164no—
364C22×C137C2×#12011yescharacteristic
365C4×C137—21no—
366C4×C137—21no—
367C4×C137—21no—
368C4×C137—21no—
369C4×C137—41no—
370C4×C137—41no—
371C4×C137—41no—
372C4×C137—41no—
373C4×C137—42no—
374C4×C137—41no—
375C4×C137—81no—
376C4×C137—81no—
377C4×C137#57611yescharacteristic
378C4×C137#57611yescharacteristic
379C4×C137#57711yescharacteristic
380C4×C137#57711yescharacteristic
381C2×C137—41no—
382C2×C137—81no—
383C2×C137—82no—
384C2×C137—81no—
385C2×C137—81no—
386C2×C137#301211yescharacteristic
387C2×C137#301211yescharacteristic
388C2×C137#302211yescharacteristic
389#18974C13711yesmaximal, characteristic, direct product factor, Sylow
390C137#1897411yescharacteristic, direct product factor, Sylow
391#3546C2×C13711yescharacteristic
392#3254C2×C13711yescharacteristic, complemented
393#3248C2×C13711yescharacteristic, complemented
394#3228C2×C13711yescharacteristic, complemented
395#1654C2×C13711yescharacteristic, complemented
396#1652C2×C13711yescharacteristic, complemented
397#1650C2×C13711yescharacteristic, complemented
398#1647C2×C13711yescharacteristic, complemented
399#1642C2×C13711yescharacteristic, complemented
400#1641C2×C13711yescharacteristic, complemented
401#1639C2×C13711yescharacteristic, complemented
402#1639C2×C13711yescharacteristic, complemented
403#1547C2×C13711yescharacteristic, complemented
404#1495C2×C13711yescharacteristic, complemented
405#1480C2×C13711yescharacteristic, complemented
406#560—22no—
407#556C22×C13711yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C13711yescharacteristic
411#547C22×C13711yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C13711yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C13711yescharacteristic, complemented
421#532C22×C13711yescharacteristic
422#532C22×C13711yescharacteristic
423#529C22×C13711yescharacteristic
424#500C22×C13711yescharacteristic, complemented
425#498C22×C13711yescharacteristic, complemented
426#486C22×C13711yescharacteristic
427#486C22×C13711yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C13711yescharacteristic, complemented
433#474C22×C13711yescharacteristic
434#474C22×C13711yescharacteristic
435#474C22×C13711yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C13711yescharacteristic, complemented
442#461C22×C13711yescharacteristic
443#461C22×C13711yescharacteristic
444#461C22×C13711yescharacteristic, complemented
445#460—21no—
446#431C22×C13711yescharacteristic, complemented
447#423C22×C13711yescharacteristic, complemented
448C2×C4⋊C8C22×C13711yescharacteristic, complemented
449#332C22×C13711yescharacteristic, complemented
450#332C22×C13711yescharacteristic, complemented
451#331C22×C13711yescharacteristic
452#331C22×C13711yescharacteristic
453Q8⋊C8C22×C13711yescharacteristic, complemented
454Q8⋊C8C22×C13711yescharacteristic, complemented
455D4⋊C8C22×C13711yescharacteristic
456D4⋊C8C22×C13711yescharacteristic
457D4⋊C8C22×C13711yescharacteristic
458D4⋊C8C22×C13711yescharacteristic
459D4⋊C8C22×C13711yescharacteristic, complemented
460D4⋊C8C22×C13711yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C13711yescharacteristic
474C4⋊Q8C23×C13711yescharacteristic
475C4⋊Q8C23×C13711yescharacteristic
476C4⋊Q8C23×C13711yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C13711yescharacteristic
480#127C23×C13711yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C13711yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C13711yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C13711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C13711yescharacteristic
514#121D4×C13711yescharacteristic
515#121D4×C13711yescharacteristic
516#121D4×C13712yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C13711yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C13712yes—
531C4×D4C23×C13711yescharacteristic
532C4×D4C23×C13711yescharacteristic
533C4×D4C23×C13711yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C13711yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C13711yescharacteristic
550C4⋊C8C23×C13711yescharacteristic
551C4⋊C8C23×C13711yescharacteristic
552C4⋊C8C23×C13711yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C13711yescharacteristic
565C4×C8C23×C13711yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C13711yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C13711yescharacteristic
598C2×D4C2×D4×C13711yescharacteristic
599C2×D4C2×D4×C13711yescharacteristic
600C2×D4C2×D4×C13712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C13711yescharacteristic
608C22×C4C2×D4×C13711yescharacteristic
609C22×C4C2×D4×C13711yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C13711yescharacteristic
637C4⋊C4C2×D4×C13711yescharacteristic
638C4⋊C4C2×D4×C13711yescharacteristic
639C4⋊C4C2×D4×C13711yescharacteristic
640C4⋊C4C2×D4×C13712yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C13711yescharacteristic
662C42C2×D4×C13711yescharacteristic
663C42C2×D4×C13711yescharacteristic
664C42C24×C13711yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C13711yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C13711yescharacteristic
727C2×C4#120×C13711yescharacteristic
728C2×C4#120×C13711yescharacteristic
729C2×C4C22×D4×C13711yescharacteristic
730C2×C4C22×D4×C13711yescharacteristic
731C2×C4C22×D4×C13711yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C13711yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C13711yescharacteristic
768C4#576×C13711yescharacteristic
769C4#577×C13711yescharacteristic
770C4#577×C13711yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2#3012×C13711yescharacteristic
777C2#3012×C13711yescharacteristic
778C2#3022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radical#3546×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. #3254×C137C2semidirect
3. #3248×C137C2semidirect
4. #3228×C137C2semidirect
5. #1654×C137C2semidirect
6. #1652×C137C2semidirect
7. #1650×C137C2semidirect
8. #1647×C137C2semidirect
9. #1642×C137C2semidirect
10. #1641×C137C2semidirect
11. #1639×C137C2semidirect
12. #1639×C137C2semidirect
13. #1547×C137C2semidirect
14. #1495×C137C2semidirect
15. #1480×C137C2semidirect
30. #533×C137C22semidirect
34. #500×C137C22semidirect
35. #498×C137C22semidirect
42. #475×C137C22semidirect
45. #474×C137C22semidirect
51. #462×C137C22semidirect
54. #461×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
389. #18974C137direct (N × H)
390. C137#18974direct (N × H)
392. #3254C2×C137semidirect
393. #3248C2×C137semidirect
394. #3228C2×C137semidirect
395. #1654C2×C137semidirect
396. #1652C2×C137semidirect
397. #1650C2×C137semidirect
398. #1647C2×C137semidirect
399. #1642C2×C137semidirect
400. #1641C2×C137semidirect
401. #1639C2×C137semidirect
402. #1639C2×C137semidirect
403. #1547C2×C137semidirect
404. #1495C2×C137semidirect
405. #1480C2×C137semidirect
420. #533C22×C137semidirect
424. #500C22×C137semidirect
425. #498C22×C137semidirect
432. #475C22×C137semidirect
435. #474C22×C137semidirect
441. #462C22×C137semidirect
444. #461C22×C137semidirect
446. #431C22×C137semidirect
447. #423C22×C137semidirect
448. C2×C4⋊C8C22×C137semidirect
449. #332C22×C137semidirect
450. #332C22×C137semidirect
453. Q8⋊C8C22×C137semidirect
454. Q8⋊C8C22×C137semidirect
459. D4⋊C8C22×C137semidirect
460. 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
#3254×C1372
#3248×C1372
#3228×C1372
#1654×C1372
#1652×C1372
#1650×C1372
#1647×C1372
#1642×C1372
#1641×C1372
#1639×C1372
#1547×C1372
#1495×C1372
#1480×C1372
#18974137