Finite Group Databasebeta

← C137×#18564 #46867950

Subgroups — C137×#18564 #46867950

Order 35072.

1082 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3522×C137C211yesmaximal, characteristic, complemented
2#3217×C137C211yesmaximal, characteristic, complemented
3#3151×C137C211yesmaximal, characteristic, complemented
4C2×#460×C137C211yesmaximal, characteristic, complemented
5#1623×C137C212yesmaximal, complemented
6#1622×C137C212yesmaximal, complemented
7#1621×C137C212yesmaximal, complemented
8#1620×C137C212yesmaximal, complemented
9#1551×C137C211yesmaximal, characteristic, complemented
10#1491×C137C211yesmaximal, characteristic, complemented
11#1483×C137C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C137—22no—
13C22×SD16×C137—21no—
14#559×C137—21no—
15#559×C137C2211yescharacteristic, complemented
16Q82×C137C2211yescharacteristic, complemented
17#554×C137—21no—
18#554×C137C2211yescharacteristic, complemented
19#550×C137C2211yescharacteristic, complemented
20#548×C137—21no—
21#547×C137—22no—
22#547×C137—21no—
23#542×C137—22no—
24#542×C137—21no—
25#532×C137—21no—
26#532×C137C2211yescharacteristic
27C2×#127×C137C2211yescharacteristic
28#529×C137—21no—
29#529×C137C2211yescharacteristic
30#520×C137—21no—
31C2×C4×Q8×C137C2211yescharacteristic
32#496×C137—22no—
33#496×C137—21no—
34#493×C137C2212yes—
35#492×C137C2212yes—
36#490×C137—21no—
37#460×C137—21no—
38#460×C137—21no—
39#460×C137C2212yes—
40#460×C137C2212yes—
41#460×C137C2212yes—
42#459×C137C2212yes—
43#450×C137—21no—
44#447×C137—21no—
45#432×C137C2211yescharacteristic
46C2×C4⋊C8×C137C2211yescharacteristic
47C2×#102×C137—21no—
48C4×M16×C137C2211yescharacteristic
49#333×C137C2212yescomplemented
50#331×C137C2212yescomplemented
51Q8⋊C8×C137C2212yescomplemented
52Q8⋊C8×C137C2212yescomplemented
53Q8⋊C8×C137C2212yescomplemented
54D4⋊C8×C137C2212yescomplemented
55C2×#41×C137—22no—
56C2×#41×C137—21no—
57C2×#41×C137D412yes—
58C22×Q8×C137D411yescharacteristic
59C22×D4×C137—21no—
60C22×D4×C137—21no—
61C22×D4×C137—21no—
62AGL(1,ℤ/8)×C137—48no—
63C2×SD16×C137—22no—
64C2×SD16×C137—22no—
65C2×SD16×C137—24no—
66C2×SD16×C137—22no—
67C2×SD16×C137—44no—
68C2×D8×C137—24no—
69C2×D8×C137—22no—
70C2×M16×C137—21no—
71C22×C8×C137—21no—
72C4⋊Q8×C137—22no—
73C4⋊Q8×C137—21no—
74C4⋊Q8×C137—21no—
75C4⋊Q8×C137C2311yescharacteristic
76#127×C137—21no—
77#127×C137—21no—
78#127×C137—21no—
79#127×C137—21no—
80#127×C137C2312yes—
81#127×C137C2311yescharacteristic
82#126×C137—22no—
83#126×C137—21no—
84#125×C137—21no—
85#125×C137D411yescharacteristic
86#124×C137—22no—
87#124×C137—22no—
88#124×C137—21no—
89#124×C137—21no—
90#124×C137D411yescharacteristic
91#124×C137D412yes—
92#123×C137—22no—
93#123×C137—22no—
94#123×C137—22no—
95#123×C137—22no—
96#123×C137—21no—
97C22⋊Q8×C137—22no—
98C22⋊Q8×C137—22no—
99C22⋊Q8×C137—22no—
100C22⋊Q8×C137—22no—
101C22⋊Q8×C137—21no—
102C22⋊Q8×C137D411yescharacteristic
103#121×C137—22no—
104#121×C137—22no—
105#121×C137—21no—
106#121×C137—21no—
107#121×C137—21no—
108#121×C137D411yescharacteristic
109C4×Q8×C137—21no—
110C4×Q8×C137—21no—
111C4×Q8×C137—21no—
112C4×Q8×C137—21no—
113C4×Q8×C137D411yescharacteristic
114C4×Q8×C137D411yescharacteristic
115C4×Q8×C137C2311yescharacteristic
116C4×Q8×C137C2311yescharacteristic
117C4×Q8×C137C2311yescharacteristic
118C4×D4×C137—22no—
119C4×D4×C137—22no—
120C4×D4×C137—22no—
121C4×D4×C137—21no—
122C4×D4×C137—21no—
123C4×D4×C137—21no—
124C4×D4×C137—21no—
125C4×D4×C137—21no—
126C4×D4×C137—21no—
127C4×D4×C137—21no—
128C4×D4×C137C2311yescharacteristic
129#117×C137—22no—
130#117×C137—21no—
131C2×C4⋊C4×C137—22no—
132C2×C4⋊C4×C137—21no—
133C2×C4⋊C4×C137—21no—
134C2×C4⋊C4×C137D411yescharacteristic
135C2×C42×C137—21no—
136C2×C42×C137C2311yescharacteristic
137C4⋊C8×C137—21no—
138C4⋊C8×C137C2312yes—
139C4⋊C8×C137C2312yes—
140#102×C137—22no—
141#102×C137—22no—
142#102×C137—22no—
143#102×C137—22no—
144C22⋊C8×C137—21no—
145#97×C137—21no—
146#97×C137—21no—
147C4×C8×C137C2312yes—
148C24×C137—41no—
149#41×C137—44no—
150#41×C137—42no—
151#41×C137—42no—
152#41×C137—84no—
153C2×Q8×C137—22no—
154C2×Q8×C137—21no—
155C2×Q8×C137—22no—
156C2×Q8×C137—41no—
157C2×Q8×C137C2×D411yescharacteristic
158C2×Q8×C137C2×D411yescharacteristic
159C2×Q8×C137C2×D411yescharacteristic
160C2×Q8×C137C2×D412yes—
161C2×D4×C137—22no—
162C2×D4×C137—22no—
163C2×D4×C137—21no—
164C2×D4×C137—22no—
165C2×D4×C137—21no—
166C2×D4×C137—21no—
167C2×D4×C137—22no—
168C2×D4×C137—22no—
169C2×D4×C137—22no—
170C2×D4×C137—42no—
171C2×D4×C137—44no—
172C2×D4×C137—42no—
173C2×D4×C137—41no—
174C2×D4×C137—41no—
175C2×D4×C137—41no—
176C2×D4×C137—82no—
177C2×D4×C137C2×D411yescharacteristic
178C2×D4×C137C2×D412yes—
179C22×C4×C137—22no—
180C22×C4×C137—21no—
181C22×C4×C137—21no—
182C22×C4×C137—22no—
183C22×C4×C137—22no—
184C22×C4×C137—21no—
185C22×C4×C137—22no—
186C22×C4×C137C2×D411yescharacteristic
187C22×C4×C137C2×D411yescharacteristic
188C22×C4×C137C2×D411yescharacteristic
189SD16×C137—48no—
190SD16×C137—44no—
191SD16×C137—44no—
192SD16×C137—82no—
193D8×C137—48no—
194D8×C137—82no—
195M16×C137—24no—
196C2×C8×C137—22no—
197C2×C8×C137—22no—
198C2×C8×C137—22no—
199C2×C8×C137—42no—
200C4⋊C4×C137—22no—
201C4⋊C4×C137—22no—
202C4⋊C4×C137—22no—
203C4⋊C4×C137—22no—
204C4⋊C4×C137—21no—
205C4⋊C4×C137—21no—
206C4⋊C4×C137—21no—
207C4⋊C4×C137—21no—
208C4⋊C4×C137—21no—
209C4⋊C4×C137—21no—
210C4⋊C4×C137—21no—
211C4⋊C4×C137—21no—
212C4⋊C4×C137—21no—
213C4⋊C4×C137—21no—
214C4⋊C4×C137—21no—
215C4⋊C4×C137C2×D411yescharacteristic
216C4⋊C4×C137C2×D411yescharacteristic
217C4⋊C4×C137C2×D411yescharacteristic
218C4⋊C4×C137C2×D411yescharacteristic
219C22⋊C4×C137—22no—
220C22⋊C4×C137—22no—
221C22⋊C4×C137—22no—
222C22⋊C4×C137—22no—
223C22⋊C4×C137—22no—
224C22⋊C4×C137—21no—
225C22⋊C4×C137—22no—
226C22⋊C4×C137—21no—
227C22⋊C4×C137—21no—
228C22⋊C4×C137—22no—
229C22⋊C4×C137—21no—
230C22⋊C4×C137—21no—
231C42×C137—22no—
232C42×C137—21no—
233C42×C137—21no—
234C42×C137—21no—
235C42×C137—21no—
236C42×C137—21no—
237C42×C137C2×D411yescharacteristic
238C42×C137C2×D411yescharacteristic
239C42×C137C2×D411yescharacteristic
240C42×C137C2411yescharacteristic
241C23×C137—21no—
242C23×C137—22no—
243C23×C137—42no—
244C23×C137—82no—
245C23×C137—82no—
246C23×C137—82no—
247C23×C137#12011yescharacteristic
248Q8×C137—21no—
249Q8×C137—21no—
250Q8×C137—21no—
251Q8×C137—22no—
252Q8×C137—42no—
253Q8×C137—42no—
254Q8×C137—82no—
255Q8×C137AGL(1,ℤ/8)12yescomplemented
256D4×C137—22no—
257D4×C137—42no—
258D4×C137—44no—
259D4×C137—44no—
260D4×C137—44no—
261D4×C137—42no—
262D4×C137—41no—
263D4×C137—42no—
264D4×C137—41no—
265D4×C137—42no—
266D4×C137—42no—
267D4×C137—42no—
268D4×C137—42no—
269D4×C137—82no—
270D4×C137—82no—
271D4×C137—82no—
272D4×C137—82no—
273C2×C4×C137—21no—
274C2×C4×C137—22no—
275C2×C4×C137—21no—
276C2×C4×C137—21no—
277C2×C4×C137—22no—
278C2×C4×C137—21no—
279C2×C4×C137—21no—
280C2×C4×C137—21no—
281C2×C4×C137—21no—
282C2×C4×C137—22no—
283C2×C4×C137—21no—
284C2×C4×C137—21no—
285C2×C4×C137—42no—
286C2×C4×C137—44no—
287C2×C4×C137—42no—
288C2×C4×C137—41no—
289C2×C4×C137—41no—
290C2×C4×C137—82no—
291C2×C4×C137—82no—
292C2×C4×C137—82no—
293C2×C4×C137#12011yescharacteristic
294C2×C4×C137#12011yescharacteristic
295C2×C4×C137#12011yescharacteristic
296C2×C4×C137C22×D411yescharacteristic
297C2×C4×C137C22×D411yescharacteristic
298C2×C4×C137C22×D411yescharacteristic
299C8×C137—24no—
300C8×C137—42no—
301C8×C137—42no—
302C22×C137—21no—
303C22×C137—21no—
304C22×C137—42no—
305C22×C137—41no—
306C22×C137—41no—
307C22×C137—42no—
308C22×C137—42no—
309C22×C137—41no—
310C22×C137—82no—
311C22×C137—82no—
312C22×C137—82no—
313C22×C137—164no—
314C22×C137#45312yes—
315C22×C137C2×#12011yescharacteristic
316C4×C137—21no—
317C4×C137—22no—
318C4×C137—21no—
319C4×C137—21no—
320C4×C137—21no—
321C4×C137—41no—
322C4×C137—41no—
323C4×C137—41no—
324C4×C137—41no—
325C4×C137—41no—
326C4×C137—42no—
327C4×C137—41no—
328C4×C137C2×AGL(1,ℤ/8)11yescharacteristic
329C4×C137#57511yescharacteristic
330C4×C137#57712yes—
331C2×C137—22no—
332C2×C137—81no—
333C2×C137—82no—
334C2×C137—162no—
335C2×C137#300611yescharacteristic
336C2×C137#301011yescharacteristic
337C2×C137C2×#45311yescharacteristic
338#18564C13711yesmaximal, characteristic, direct product factor, Sylow
339C137#1856411yescharacteristic, direct product factor, Sylow
340#3522C2×C13711yescharacteristic, complemented
341#3217C2×C13711yescharacteristic, complemented
342#3151C2×C13711yescharacteristic, complemented
343C2×#460C2×C13711yescharacteristic, complemented
344#1623C2×C13712yescomplemented
345#1622C2×C13712yescomplemented
346#1621C2×C13712yescomplemented
347#1620C2×C13712yescomplemented
348#1551C2×C13711yescharacteristic, complemented
349#1491C2×C13711yescharacteristic, complemented
350#1483C2×C13711yescharacteristic, complemented
351C2×AGL(1,ℤ/8)—22no—
352C22×SD16—21no—
353#559—21no—
354#559C22×C13711yescharacteristic, complemented
355Q82C22×C13711yescharacteristic, complemented
356#554—21no—
357#554C22×C13711yescharacteristic, complemented
358#550C22×C13711yescharacteristic, complemented
359#548—21no—
360#547—22no—
361#547—21no—
362#542—22no—
363#542—21no—
364#532—21no—
365#532C22×C13711yescharacteristic
366C2×#127C22×C13711yescharacteristic
367#529—21no—
368#529C22×C13711yescharacteristic
369#520—21no—
370C2×C4×Q8C22×C13711yescharacteristic
371#496—22no—
372#496—21no—
373#493C22×C13712yes—
374#492C22×C13712yes—
375#490—21no—
376#460—21no—
377#460—21no—
378#460C22×C13712yes—
379#460C22×C13712yes—
380#460C22×C13712yes—
381#459C22×C13712yes—
382#450—21no—
383#447—21no—
384#432C22×C13711yescharacteristic
385C2×C4⋊C8C22×C13711yescharacteristic
386C2×#102—21no—
387C4×M16C22×C13711yescharacteristic
388#333C22×C13712yescomplemented
389#331C22×C13712yescomplemented
390Q8⋊C8C22×C13712yescomplemented
391Q8⋊C8C22×C13712yescomplemented
392Q8⋊C8C22×C13712yescomplemented
393D4⋊C8C22×C13712yescomplemented
394C2×#41—22no—
395C2×#41—21no—
396C2×#41D4×C13712yes—
397C22×Q8D4×C13711yescharacteristic
398C22×D4—21no—
399C22×D4—21no—
400C22×D4—21no—
401AGL(1,ℤ/8)—48no—
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16—24no—
405C2×SD16—22no—
406C2×SD16—44no—
407C2×D8—24no—
408C2×D8—22no—
409C2×M16—21no—
410C22×C8—21no—
411C4⋊Q8—22no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8C23×C13711yescharacteristic
415#127—21no—
416#127—21no—
417#127—21no—
418#127—21no—
419#127C23×C13712yes—
420#127C23×C13711yescharacteristic
421#126—22no—
422#126—21no—
423#125—21no—
424#125D4×C13711yescharacteristic
425#124—22no—
426#124—22no—
427#124—21no—
428#124—21no—
429#124D4×C13711yescharacteristic
430#124D4×C13712yes—
431#123—22no—
432#123—22no—
433#123—22no—
434#123—22no—
435#123—21no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—21no—
441C22⋊Q8D4×C13711yescharacteristic
442#121—22no—
443#121—22no—
444#121—21no—
445#121—21no—
446#121—21no—
447#121D4×C13711yescharacteristic
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8—21no—
452C4×Q8D4×C13711yescharacteristic
453C4×Q8D4×C13711yescharacteristic
454C4×Q8C23×C13711yescharacteristic
455C4×Q8C23×C13711yescharacteristic
456C4×Q8C23×C13711yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4C23×C13711yescharacteristic
468#117—22no—
469#117—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4D4×C13711yescharacteristic
474C2×C42—21no—
475C2×C42C23×C13711yescharacteristic
476C4⋊C8—21no—
477C4⋊C8C23×C13712yes—
478C4⋊C8C23×C13712yes—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483C22⋊C8—21no—
484#97—21no—
485#97—21no—
486C4×C8C23×C13712yes—
487C24—41no—
488#41—44no—
489#41—42no—
490#41—42no—
491#41—84no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—22no—
495C2×Q8—41no—
496C2×Q8C2×D4×C13711yescharacteristic
497C2×Q8C2×D4×C13711yescharacteristic
498C2×Q8C2×D4×C13711yescharacteristic
499C2×Q8C2×D4×C13712yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—42no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—82no—
516C2×D4C2×D4×C13711yescharacteristic
517C2×D4C2×D4×C13712yes—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4C2×D4×C13711yescharacteristic
526C22×C4C2×D4×C13711yescharacteristic
527C22×C4C2×D4×C13711yescharacteristic
528SD16—48no—
529SD16—44no—
530SD16—44no—
531SD16—82no—
532D8—48no—
533D8—82no—
534M16—24no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—42no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4C2×D4×C13711yescharacteristic
555C4⋊C4C2×D4×C13711yescharacteristic
556C4⋊C4C2×D4×C13711yescharacteristic
557C4⋊C4C2×D4×C13711yescharacteristic
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C42—22no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42C2×D4×C13711yescharacteristic
577C42C2×D4×C13711yescharacteristic
578C42C2×D4×C13711yescharacteristic
579C42C24×C13711yescharacteristic
580C23—21no—
581C23—22no—
582C23—42no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23#120×C13711yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—21no—
590Q8—22no—
591Q8—42no—
592Q8—42no—
593Q8—82no—
594Q8AGL(1,ℤ/8)×C13712yescomplemented
595D4—22no—
596D4—42no—
597D4—44no—
598D4—44no—
599D4—44no—
600D4—42no—
601D4—41no—
602D4—42no—
603D4—41no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—82no—
609D4—82no—
610D4—82no—
611D4—82no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—42no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—82no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4#120×C13711yescharacteristic
633C2×C4#120×C13711yescharacteristic
634C2×C4#120×C13711yescharacteristic
635C2×C4C22×D4×C13711yescharacteristic
636C2×C4C22×D4×C13711yescharacteristic
637C2×C4C22×D4×C13711yescharacteristic
638C8—24no—
639C8—42no—
640C8—42no—
641C22—21no—
642C22—21no—
643C22—42no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—41no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—164no—
653C22#453×C13712yes—
654C22C2×#120×C13711yescharacteristic
655C4—21no—
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4C2×AGL(1,ℤ/8)×C13711yescharacteristic
668C4#575×C13711yescharacteristic
669C4#577×C13712yes—
670C2—22no—
671C2—81no—
672C2—82no—
673C2—162no—
674C2#3006×C13711yescharacteristic
675C2#3010×C13711yescharacteristic
676C2C2×#453×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. #3522×C137C2semidirect
2. #3217×C137C2semidirect
3. #3151×C137C2semidirect
4. C2×#460×C137C2semidirect
5. #1623×C137C2semidirect
6. #1622×C137C2semidirect
7. #1621×C137C2semidirect
8. #1620×C137C2semidirect
9. #1551×C137C2semidirect
10. #1491×C137C2semidirect
11. #1483×C137C2semidirect
15. #559×C137C22semidirect
16. Q82×C137C22semidirect
18. #554×C137C22semidirect
19. #550×C137C22semidirect
49. #333×C137C22semidirect
50. #331×C137C22semidirect
51. Q8⋊C8×C137C22semidirect
52. Q8⋊C8×C137C22semidirect
53. Q8⋊C8×C137C22semidirect
54. D4⋊C8×C137C22semidirect
255. Q8×C137AGL(1,ℤ/8)semidirect
338. #18564C137direct (N × H)
339. C137#18564direct (N × H)
340. #3522C2×C137semidirect
341. #3217C2×C137semidirect
342. #3151C2×C137semidirect
343. C2×#460C2×C137semidirect
344. #1623C2×C137semidirect
345. #1622C2×C137semidirect
346. #1621C2×C137semidirect
347. #1620C2×C137semidirect
348. #1551C2×C137semidirect
349. #1491C2×C137semidirect
350. #1483C2×C137semidirect
354. #559C22×C137semidirect
355. Q82C22×C137semidirect
357. #554C22×C137semidirect
358. #550C22×C137semidirect
388. #333C22×C137semidirect
389. #331C22×C137semidirect
390. Q8⋊C8C22×C137semidirect
391. Q8⋊C8C22×C137semidirect
392. Q8⋊C8C22×C137semidirect
393. D4⋊C8C22×C137semidirect
594. Q8AGL(1,ℤ/8)×C137semidirect

Maximal subgroups

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

subgroupindex
#3522×C1372
#3217×C1372
#3151×C1372
C2×#460×C1372
#1623×C1372
#1622×C1372
#1621×C1372
#1620×C1372
#1551×C1372
#1491×C1372
#1483×C1372
#18564137