Finite Group Databasebeta

← C137×#18418 #46867804

Subgroups — C137×#18418 #46867804

Order 35072.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C137C211yesmaximal, characteristic, complemented
2#3192×C137C211yesmaximal, characteristic, complemented
3#3188×C137C211yesmaximal, characteristic, complemented
4#2656×C137C211yesmaximal, characteristic, complemented
5#1618×C137C212yesmaximal, complemented
6#1613×C137C212yesmaximal, complemented
7#1600×C137C212yesmaximal, complemented
8#1595×C137C212yesmaximal, complemented
9#1504×C137C211yesmaximal, characteristic, complemented
10C2×#327×C137C211yesmaximal, characteristic, complemented
11#1471×C137C211yesmaximal, characteristic, complemented
12#560×C137—22no—
13#553×C137—21no—
14#553×C137—21no—
15D42×C137—22no—
16D42×C137—21no—
17D42×C137—21no—
18#540×C137—21no—
19#538×C137—21no—
20#538×C137C2212yes—
21#535×C137—21no—
22#534×C137—21no—
23#534×C137C2212yes—
24#525×C137C2211yescharacteristic
25C2×#121×C137—22no—
26C2×#121×C137C2211yescharacteristic
27C2×#121×C137C2211yescharacteristic
28C2×#121×C137C2211yescharacteristic, complemented
29#484×C137C2211yescharacteristic, complemented
30#482×C137—21no—
31#481×C137—21no—
32#481×C137C2211yescharacteristic, complemented
33#481×C137C2212yescomplemented
34#469×C137—22no—
35#466×C137—21no—
36#465×C137—21no—
37#450×C137C2211yescharacteristic, complemented
38#449×C137—21no—
39#447×C137—21no—
40#447×C137C2211yescharacteristic, complemented
41#447×C137C2212yescomplemented
42#407×C137C2211yescharacteristic, complemented
43C2×C22⋊C8×C137C2211yescharacteristic, complemented
44#399×C137—21no—
45#399×C137C2212yescomplemented
46#392×C137—21no—
47#392×C137C2212yescomplemented
48C2×#95×C137C2211yescharacteristic, complemented
49#328×C137C2212yescomplemented
50#327×C137C2212yescomplemented
51#327×C137C2212yescomplemented
52#327×C137C2212yescomplemented
53#323×C137C2212yescomplemented
54#323×C137C2212yescomplemented
55C2×#41×C137D411yescharacteristic, complemented
56C22×D4×C137—22no—
57C22×D4×C137—21no—
58C22×D4×C137—21no—
59C22×D4×C137—22no—
60C22×D4×C137—21no—
61C22×D4×C137—22no—
62C22×D4×C137D412yes—
63C22×D4×C137D411yescharacteristic
64C22×D4×C137D411yescharacteristic, complemented
65C22×D4×C137C2311yescharacteristic
66C23×C4×C137—21no—
67C23×C4×C137C2311yescharacteristic
68C2×SD16×C137—21no—
69C2×D8×C137—22no—
70C2×D8×C137—21no—
71C2×M16×C137—21no—
72C22×C8×C137—21no—
73#127×C137—22no—
74#127×C137—21no—
75#126×C137—22no—
76#126×C137—22no—
77#125×C137—21no—
78#124×C137—22no—
79#123×C137—22no—
80#123×C137—21no—
81#123×C137—22no—
82#123×C137—22no—
83#123×C137—22no—
84C22⋊Q8×C137D411yescharacteristic, complemented
85C22⋊Q8×C137C2311yescharacteristic
86#121×C137—22no—
87#121×C137—21no—
88#121×C137—21no—
89#121×C137—22no—
90#121×C137—22no—
91#121×C137—22no—
92#121×C137—22no—
93#121×C137—21no—
94#121×C137—21no—
95#121×C137—21no—
96#121×C137—21no—
97#121×C137—21no—
98#121×C137—21no—
99#121×C137—22no—
100#121×C137—21no—
101#121×C137—21no—
102#121×C137—21no—
103#121×C137—21no—
104#121×C137—48no—
105#121×C137D411yescharacteristic, complemented
106#121×C137D412yescomplemented
107#121×C137C2312yes—
108#121×C137C2311yescharacteristic
109#120×C137—22no—
110#120×C137—22no—
111#120×C137—22no—
112#120×C137—21no—
113#120×C137—22no—
114#120×C137—22no—
115#120×C137—22no—
116C4×D4×C137—22no—
117C4×D4×C137—21no—
118C4×D4×C137—21no—
119C4×D4×C137—21no—
120C4×D4×C137—21no—
121C4×D4×C137—22no—
122#117×C137—21no—
123#117×C137D411yescharacteristic, complemented
124C2×C4⋊C4×C137—22no—
125C2×C4⋊C4×C137D411yescharacteristic
126C2×C4⋊C4×C137D411yescharacteristic, complemented
127C2×C4⋊C4×C137C2311yescharacteristic
128C2×C22⋊C4×C137—21no—
129C2×C22⋊C4×C137—22no—
130C2×C22⋊C4×C137—21no—
131C2×C22⋊C4×C137—22no—
132C2×C22⋊C4×C137C2312yes—
133#107×C137—21no—
134#106×C137—21no—
135#106×C137—22no—
136#103×C137—21no—
137#102×C137—22no—
138#102×C137—21no—
139#102×C137—21no—
140#102×C137—22no—
141#102×C137—21no—
142C22⋊C8×C137—21no—
143C22⋊C8×C137—21no—
144C22⋊C8×C137C2311yescharacteristic
145C22⋊C8×C137C2311yescharacteristic
146C22⋊C8×C137C2312yes—
147#95×C137—21no—
148#95×C137C2312yes—
149C24×C137—22no—
150C24×C137—21no—
151C24×C137—21no—
152C24×C137C2×D411yescharacteristic
153C24×C137C2×D412yes—
154#41×C137—81no—
155C2×Q8×C137C2×D411yescharacteristic
156C2×D4×C137—22no—
157C2×D4×C137—21no—
158C2×D4×C137—21no—
159C2×D4×C137—22no—
160C2×D4×C137—22no—
161C2×D4×C137—22no—
162C2×D4×C137—22no—
163C2×D4×C137—22no—
164C2×D4×C137—22no—
165C2×D4×C137—21no—
166C2×D4×C137—22no—
167C2×D4×C137—22no—
168C2×D4×C137—21no—
169C2×D4×C137—21no—
170C2×D4×C137—21no—
171C2×D4×C137—21no—
172C2×D4×C137—21no—
173C2×D4×C137—44no—
174C2×D4×C137—44no—
175C2×D4×C137—44no—
176C2×D4×C137—41no—
177C2×D4×C137—41no—
178C2×D4×C137—81no—
179C2×D4×C137—81no—
180C2×D4×C137—82no—
181C2×D4×C137—81no—
182C2×D4×C137—82no—
183C2×D4×C137—82no—
184C2×D4×C137—81no—
185C2×D4×C137—81no—
186C2×D4×C137—82no—
187C2×D4×C137—82no—
188C2×D4×C137—84no—
189C2×D4×C137C2×D411yescharacteristic
190C2×D4×C137C2×D412yes—
191C22×C4×C137—22no—
192C22×C4×C137—22no—
193C22×C4×C137—22no—
194C22×C4×C137—24no—
195C22×C4×C137—21no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—81no—
199C22×C4×C137—81no—
200C22×C4×C137—81no—
201C22×C4×C137C2×D412yes—
202C22×C4×C137C2×D411yescharacteristic
203C22×C4×C137C2×D411yescharacteristic
204C22×C4×C137C2×D411yescharacteristic
205C22×C4×C137C2×D411yescharacteristic
206C22×C4×C137C2×D411yescharacteristic
207C22×C4×C137C2411yescharacteristic
208SD16×C137—81no—
209D8×C137—81no—
210D8×C137—82no—
211M16×C137—81no—
212C2×C8×C137—21no—
213C2×C8×C137—22no—
214C2×C8×C137—21no—
215C2×C8×C137—81no—
216C4⋊C4×C137—22no—
217C4⋊C4×C137—22no—
218C4⋊C4×C137—21no—
219C4⋊C4×C137—21no—
220C4⋊C4×C137—21no—
221C4⋊C4×C137—21no—
222C4⋊C4×C137—21no—
223C4⋊C4×C137—21no—
224C4⋊C4×C137—21no—
225C4⋊C4×C137—44no—
226C4⋊C4×C137C2×D412yes—
227C4⋊C4×C137C2×D411yescharacteristic
228C4⋊C4×C137C2×D411yescharacteristic
229C22⋊C4×C137—22no—
230C22⋊C4×C137—22no—
231C22⋊C4×C137—22no—
232C22⋊C4×C137—22no—
233C22⋊C4×C137—22no—
234C22⋊C4×C137—21no—
235C22⋊C4×C137—21no—
236C22⋊C4×C137—21no—
237C22⋊C4×C137—22no—
238C22⋊C4×C137—21no—
239C22⋊C4×C137—22no—
240C22⋊C4×C137—22no—
241C22⋊C4×C137—22no—
242C22⋊C4×C137—21no—
243C22⋊C4×C137—44no—
244C22⋊C4×C137—44no—
245C22⋊C4×C137—41no—
246C22⋊C4×C137—41no—
247C42×C137—22no—
248C42×C137—21no—
249C23×C137—21no—
250C23×C137—21no—
251C23×C137—22no—
252C23×C137—22no—
253C23×C137—22no—
254C23×C137—21no—
255C23×C137—22no—
256C23×C137—22no—
257C23×C137—41no—
258C23×C137—42no—
259C23×C137—42no—
260C23×C137—42no—
261C23×C137—42no—
262C23×C137—42no—
263C23×C137—41no—
264C23×C137—41no—
265C23×C137—41no—
266C23×C137—81no—
267C23×C137—81no—
268C23×C137—82no—
269C23×C137—82no—
270C23×C137—82no—
271C23×C137#12011yescharacteristic
272C23×C137#12011yescharacteristic
273C23×C137C22×D411yescharacteristic
274Q8×C137—41no—
275D4×C137—42no—
276D4×C137—41no—
277D4×C137—42no—
278D4×C137—42no—
279D4×C137—42no—
280D4×C137—41no—
281D4×C137—41no—
282D4×C137—42no—
283D4×C137—41no—
284D4×C137—42no—
285D4×C137—41no—
286D4×C137—44no—
287D4×C137—42no—
288D4×C137—81no—
289D4×C137—82no—
290D4×C137—82no—
291D4×C137—81no—
292D4×C137—82no—
293D4×C137—82no—
294D4×C137—82no—
295D4×C137—82no—
296D4×C137—82no—
297D4×C137—88no—
298D4×C137—82no—
299D4×C137—82no—
300C2×C4×C137—24no—
301C2×C4×C137—21no—
302C2×C4×C137—22no—
303C2×C4×C137—22no—
304C2×C4×C137—21no—
305C2×C4×C137—21no—
306C2×C4×C137—41no—
307C2×C4×C137—41no—
308C2×C4×C137—41no—
309C2×C4×C137—41no—
310C2×C4×C137—41no—
311C2×C4×C137—41no—
312C2×C4×C137—42no—
313C2×C4×C137—42no—
314C2×C4×C137—42no—
315C2×C4×C137—42no—
316C2×C4×C137—42no—
317C2×C4×C137—41no—
318C2×C4×C137—81no—
319C2×C4×C137—84no—
320C2×C4×C137—82no—
321C2×C4×C137—82no—
322C2×C4×C137#12011yescharacteristic
323C2×C4×C137#12011yescharacteristic
324C2×C4×C137C22×D411yescharacteristic
325C2×C4×C137C22×D411yescharacteristic
326C8×C137—41no—
327C8×C137—41no—
328C8×C137—42no—
329C22×C137—21no—
330C22×C137—21no—
331C22×C137—21no—
332C22×C137—21no—
333C22×C137—21no—
334C22×C137—21no—
335C22×C137—21no—
336C22×C137—42no—
337C22×C137—42no—
338C22×C137—42no—
339C22×C137—42no—
340C22×C137—41no—
341C22×C137—42no—
342C22×C137—42no—
343C22×C137—41no—
344C22×C137—41no—
345C22×C137—42no—
346C22×C137—42no—
347C22×C137—82no—
348C22×C137—82no—
349C22×C137—82no—
350C22×C137—82no—
351C22×C137—81no—
352C22×C137—81no—
353C22×C137—81no—
354C22×C137—162no—
355C22×C137—164no—
356C22×C137#45312yes—
357C22×C137C2×#12011yescharacteristic
358C22×C137#57611yescharacteristic
359C22×C137#57711yescharacteristic
360C4×C137—21no—
361C4×C137—21no—
362C4×C137—21no—
363C4×C137—21no—
364C4×C137—44no—
365C4×C137—42no—
366C4×C137—41no—
367C4×C137—42no—
368C4×C137—41no—
369C4×C137—41no—
370C4×C137—81no—
371C2×C137—21no—
372C2×C137—21no—
373C2×C137—22no—
374C2×C137—41no—
375C2×C137—82no—
376C2×C137—82no—
377C2×C137—81no—
378C2×C137—161no—
379C2×C137#301211yescharacteristic
380C2×C137C2×#45311yescharacteristic
381C2×C137#302611yescharacteristic
382#18418C13711yesmaximal, characteristic, direct product factor, Sylow
383C137#1841811yescharacteristic, direct product factor, Sylow
384#3537C2×C13711yescharacteristic, complemented
385#3192C2×C13711yescharacteristic, complemented
386#3188C2×C13711yescharacteristic, complemented
387#2656C2×C13711yescharacteristic, complemented
388#1618C2×C13712yescomplemented
389#1613C2×C13712yescomplemented
390#1600C2×C13712yescomplemented
391#1595C2×C13712yescomplemented
392#1504C2×C13711yescharacteristic, complemented
393C2×#327C2×C13711yescharacteristic, complemented
394#1471C2×C13711yescharacteristic, complemented
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C13712yes—
404#535—21no—
405#534—21no—
406#534C22×C13712yes—
407#525C22×C13711yescharacteristic
408C2×#121—22no—
409C2×#121C22×C13711yescharacteristic
410C2×#121C22×C13711yescharacteristic
411C2×#121C22×C13711yescharacteristic, complemented
412#484C22×C13711yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C13711yescharacteristic, complemented
416#481C22×C13712yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C13711yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C13711yescharacteristic, complemented
424#447C22×C13712yescomplemented
425#407C22×C13711yescharacteristic, complemented
426C2×C22⋊C8C22×C13711yescharacteristic, complemented
427#399—21no—
428#399C22×C13712yescomplemented
429#392—21no—
430#392C22×C13712yescomplemented
431C2×#95C22×C13711yescharacteristic, complemented
432#328C22×C13712yescomplemented
433#327C22×C13712yescomplemented
434#327C22×C13712yescomplemented
435#327C22×C13712yescomplemented
436#323C22×C13712yescomplemented
437#323C22×C13712yescomplemented
438C2×#41D4×C13711yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C13712yes—
446C22×D4D4×C13711yescharacteristic
447C22×D4D4×C13711yescharacteristic, complemented
448C22×D4C23×C13711yescharacteristic
449C23×C4—21no—
450C23×C4C23×C13711yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C13711yescharacteristic, complemented
468C22⋊Q8C23×C13711yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C13712yescomplemented
489#121D4×C13711yescharacteristic, complemented
490#121C23×C13712yes—
491#121C23×C13711yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C13711yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C13711yescharacteristic
509C2×C4⋊C4D4×C13711yescharacteristic, complemented
510C2×C4⋊C4C23×C13711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C13712yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C13711yescharacteristic
528C22⋊C8C23×C13711yescharacteristic
529C22⋊C8C23×C13712yes—
530#95—21no—
531#95C23×C13712yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C13711yescharacteristic
536C24C2×D4×C13712yes—
537#41—81no—
538C2×Q8C2×D4×C13711yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C13711yescharacteristic
573C2×D4C2×D4×C13712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C13712yes—
585C22×C4C2×D4×C13711yescharacteristic
586C22×C4C2×D4×C13711yescharacteristic
587C22×C4C2×D4×C13711yescharacteristic
588C22×C4C2×D4×C13711yescharacteristic
589C22×C4C2×D4×C13711yescharacteristic
590C22×C4C24×C13711yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C13712yes—
610C4⋊C4C2×D4×C13711yescharacteristic
611C4⋊C4C2×D4×C13711yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C13711yescharacteristic
655C23#120×C13711yescharacteristic
656C23C22×D4×C13711yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C13711yescharacteristic
706C2×C4#120×C13711yescharacteristic
707C2×C4C22×D4×C13711yescharacteristic
708C2×C4C22×D4×C13711yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C13712yes—
740C22C2×#120×C13711yescharacteristic
741C22#576×C13711yescharacteristic
742C22#577×C13711yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2#3012×C13711yescharacteristic
763C2C2×#453×C13711yescharacteristic
764C2#3026×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3537×C137C2semidirect
2. #3192×C137C2semidirect
3. #3188×C137C2semidirect
4. #2656×C137C2semidirect
5. #1618×C137C2semidirect
6. #1613×C137C2semidirect
7. #1600×C137C2semidirect
8. #1595×C137C2semidirect
9. #1504×C137C2semidirect
10. C2×#327×C137C2semidirect
11. #1471×C137C2semidirect
28. C2×#121×C137C22semidirect
29. #484×C137C22semidirect
32. #481×C137C22semidirect
33. #481×C137C22semidirect
37. #450×C137C22semidirect
40. #447×C137C22semidirect
41. #447×C137C22semidirect
42. #407×C137C22semidirect
43. C2×C22⋊C8×C137C22semidirect
45. #399×C137C22semidirect
47. #392×C137C22semidirect
48. C2×#95×C137C22semidirect
49. #328×C137C22semidirect
50. #327×C137C22semidirect
51. #327×C137C22semidirect
52. #327×C137C22semidirect
53. #323×C137C22semidirect
54. #323×C137C22semidirect
55. C2×#41×C137D4semidirect
64. C22×D4×C137D4semidirect
84. C22⋊Q8×C137D4semidirect
105. #121×C137D4semidirect
106. #121×C137D4semidirect
123. #117×C137D4semidirect
126. C2×C4⋊C4×C137D4semidirect
382. #18418C137direct (N × H)
383. C137#18418direct (N × H)
384. #3537C2×C137semidirect
385. #3192C2×C137semidirect
386. #3188C2×C137semidirect
387. #2656C2×C137semidirect
388. #1618C2×C137semidirect
389. #1613C2×C137semidirect
390. #1600C2×C137semidirect
391. #1595C2×C137semidirect
392. #1504C2×C137semidirect
393. C2×#327C2×C137semidirect
394. #1471C2×C137semidirect
411. C2×#121C22×C137semidirect
412. #484C22×C137semidirect
415. #481C22×C137semidirect
416. #481C22×C137semidirect
420. #450C22×C137semidirect
423. #447C22×C137semidirect
424. #447C22×C137semidirect
425. #407C22×C137semidirect
426. C2×C22⋊C8C22×C137semidirect
428. #399C22×C137semidirect
430. #392C22×C137semidirect
431. C2×#95C22×C137semidirect
432. #328C22×C137semidirect
433. #327C22×C137semidirect
434. #327C22×C137semidirect
435. #327C22×C137semidirect
436. #323C22×C137semidirect
437. #323C22×C137semidirect
438. C2×#41D4×C137semidirect
447. C22×D4D4×C137semidirect
467. C22⋊Q8D4×C137semidirect
488. #121D4×C137semidirect
489. #121D4×C137semidirect
506. #117D4×C137semidirect
509. C2×C4⋊C4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3537×C1372
#3192×C1372
#3188×C1372
#2656×C1372
#1618×C1372
#1613×C1372
#1600×C1372
#1595×C1372
#1504×C1372
C2×#327×C1372
#1471×C1372
#18418137