Finite Group Databasebeta

← C137×#18272 #46867658

Subgroups — C137×#18272 #46867658

Order 35072.

1122 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C137C211yesmaximal, characteristic, complemented
2#3109×C137C211yesmaximal, characteristic, complemented
3#3105×C137C211yesmaximal, characteristic, complemented
4#2540×C137C211yesmaximal, characteristic, complemented
5#1618×C137C212yesmaximal, complemented
6#1613×C137C212yesmaximal, complemented
7#1600×C137C212yesmaximal, complemented
8#1595×C137C212yesmaximal, complemented
9#1509×C137C211yesmaximal, characteristic, complemented
10#1502×C137C211yesmaximal, characteristic, complemented
11#1469×C137C211yesmaximal, characteristic, complemented
12#562×C137—21no—
13H(3,𝔽4)×C137—21no—
14#559×C137—21no—
15#548×C137—21no—
16#546×C137—21no—
17#546×C137—22no—
18D42×C137—21no—
19#542×C137—21no—
20#538×C137—22no—
21#538×C137C2212yes—
22#535×C137—21no—
23#534×C137C2212yes—
24#532×C137C2211yescharacteristic
25#529×C137C2211yescharacteristic
26C2×#124×C137C2211yescharacteristic
27C2×C22⋊Q8×C137—21no—
28C2×#121×C137—21no—
29C2×C4×D4×C137C2211yescharacteristic, complemented
30#484×C137C2211yescharacteristic, complemented
31#481×C137C2211yescharacteristic
32#481×C137C2212yescomplemented
33#478×C137—21no—
34#476×C137—21no—
35#463×C137—21no—
36#459×C137—21no—
37#450×C137C2211yescharacteristic, complemented
38#447×C137C2211yescharacteristic
39#447×C137C2212yescomplemented
40#442×C137—22no—
41C4×SD16×C137—21no—
42C4×D8×C137—21no—
43#432×C137C2211yescharacteristic, complemented
44#431×C137C2211yescharacteristic, complemented
45#399×C137C2212yescomplemented
46#392×C137C2212yescomplemented
47#390×C137—22no—
48C4×C4⋊C4×C137C2211yescharacteristic, complemented
49#328×C137C2212yescomplemented
50#327×C137C2212yes—
51#327×C137C2212yescomplemented
52#327×C137C2212yescomplemented
53#323×C137C2212yescomplemented
54#323×C137C2212yescomplemented
55C2×#41×C137—21no—
56C2×#41×C137—21no—
57C22×Q8×C137D411yescharacteristic
58C22×D4×C137—21no—
59C22×D4×C137—22no—
60C22×D4×C137—22no—
61C22×D4×C137D411yescharacteristic
62C22×D4×C137C2311yescharacteristic
63C23×C4×C137—21no—
64C2×SD16×C137—21no—
65C2×D8×C137—21no—
66C2×D8×C137—22no—
67C4⋊Q8×C137D411yescharacteristic, complemented
68#127×C137—21no—
69#127×C137D411yescharacteristic, complemented
70#126×C137—22no—
71#126×C137—21no—
72#125×C137D411yescharacteristic, complemented
73#124×C137—21no—
74#124×C137—22no—
75#124×C137—22no—
76#124×C137—22no—
77#124×C137—21no—
78#124×C137—21no—
79#124×C137—21no—
80#124×C137—21no—
81#124×C137—21no—
82#124×C137D411yescharacteristic, complemented
83#123×C137—22no—
84#123×C137—21no—
85#123×C137—22no—
86#123×C137—22no—
87#123×C137—22no—
88C22⋊Q8×C137—22no—
89C22⋊Q8×C137—21no—
90C22⋊Q8×C137—22no—
91C22⋊Q8×C137—44no—
92C22⋊Q8×C137C2311yescharacteristic
93#121×C137—22no—
94#121×C137—22no—
95#121×C137—22no—
96#121×C137—21no—
97#121×C137—22no—
98#121×C137—21no—
99#121×C137—22no—
100#121×C137—44no—
101#121×C137C2311yescharacteristic
102#121×C137C2312yes—
103#120×C137—22no—
104#120×C137—22no—
105#120×C137—22no—
106#120×C137—22no—
107#120×C137—22no—
108C4×Q8×C137—21no—
109C4×Q8×C137D411yescharacteristic, complemented
110C4×D4×C137—22no—
111C4×D4×C137—21no—
112C4×D4×C137—21no—
113C4×D4×C137—22no—
114C4×D4×C137—21no—
115C4×D4×C137—21no—
116C4×D4×C137—21no—
117C4×D4×C137—21no—
118C4×D4×C137—21no—
119C4×D4×C137D411yescharacteristic, complemented
120C4×D4×C137D412yescomplemented
121#117×C137—21no—
122C2×C4⋊C4×C137—21no—
123C2×C4⋊C4×C137—22no—
124C2×C4⋊C4×C137C2311yescharacteristic
125C2×C22⋊C4×C137—22no—
126C2×C22⋊C4×C137—22no—
127C2×C22⋊C4×C137—21no—
128C2×C22⋊C4×C137—22no—
129C2×C22⋊C4×C137D412yes—
130C2×C22⋊C4×C137C2312yes—
131C2×C42×C137—21no—
132C2×C42×C137C2311yescharacteristic
133#107×C137—21no—
134#106×C137—21no—
135#106×C137—22no—
136C4⋊C8×C137—21no—
137C4⋊C8×C137—21no—
138#103×C137—21no—
139#102×C137—21no—
140#102×C137—22no—
141#102×C137—21no—
142#102×C137—21no—
143#102×C137—22no—
144C22⋊C8×C137C2311yescharacteristic
145C22⋊C8×C137C2311yescharacteristic
146C22⋊C8×C137C2312yes—
147#97×C137—21no—
148C4×C8×C137—21no—
149#95×C137C2312yes—
150C24×C137—22no—
151C24×C137—21no—
152C24×C137C2×D412yes—
153#41×C137—81no—
154#41×C137—81no—
155#41×C137—82no—
156C2×Q8×C137—21no—
157C2×Q8×C137—21no—
158C2×Q8×C137—21no—
159C2×Q8×C137—42no—
160C2×Q8×C137C2×D411yescharacteristic
161C2×D4×C137—22no—
162C2×D4×C137—21no—
163C2×D4×C137—22no—
164C2×D4×C137—22no—
165C2×D4×C137—22no—
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—21no—
174C2×D4×C137—42no—
175C2×D4×C137—44no—
176C2×D4×C137—42no—
177C2×D4×C137—44no—
178C2×D4×C137—82no—
179C2×D4×C137—82no—
180C2×D4×C137—82no—
181C2×D4×C137—82no—
182C2×D4×C137C2×D411yescharacteristic
183C2×D4×C137C2×D412yes—
184C22×C4×C137—22no—
185C22×C4×C137—22no—
186C22×C4×C137—22no—
187C22×C4×C137—21no—
188C22×C4×C137—22no—
189C22×C4×C137—21no—
190C22×C4×C137—42no—
191C22×C4×C137—42no—
192C22×C4×C137—41no—
193C22×C4×C137—41no—
194C22×C4×C137C2×D411yescharacteristic
195C22×C4×C137C2×D411yescharacteristic
196C22×C4×C137C2×D412yes—
197C22×C4×C137C2411yescharacteristic
198SD16×C137—42no—
199D8×C137—44no—
200D8×C137—42no—
201C2×C8×C137—21no—
202C2×C8×C137—21no—
203C2×C8×C137—22no—
204C4⋊C4×C137—24no—
205C4⋊C4×C137—22no—
206C4⋊C4×C137—22no—
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—44no—
215C4⋊C4×C137C2×D412yes—
216C4⋊C4×C137C2×D411yescharacteristic
217C4⋊C4×C137C2×D411yescharacteristic
218C22⋊C4×C137—22no—
219C22⋊C4×C137—22no—
220C22⋊C4×C137—22no—
221C22⋊C4×C137—22no—
222C22⋊C4×C137—22no—
223C22⋊C4×C137—21no—
224C22⋊C4×C137—21no—
225C22⋊C4×C137—22no—
226C22⋊C4×C137—22no—
227C22⋊C4×C137—21no—
228C22⋊C4×C137—21no—
229C22⋊C4×C137—22no—
230C22⋊C4×C137—22no—
231C22⋊C4×C137—22no—
232C22⋊C4×C137—21no—
233C22⋊C4×C137—22no—
234C22⋊C4×C137—44no—
235C22⋊C4×C137—44no—
236C22⋊C4×C137—41no—
237C22⋊C4×C137—41no—
238C42×C137—22no—
239C42×C137—21no—
240C42×C137—81no—
241C42×C137C2×D411yescharacteristic
242C42×C137C2×D411yescharacteristic
243C42×C137C2×D411yescharacteristic
244C42×C137C2×D411yescharacteristic
245C23×C137—22no—
246C23×C137—22no—
247C23×C137—21no—
248C23×C137—22no—
249C23×C137—22no—
250C23×C137—22no—
251C23×C137—41no—
252C23×C137—41no—
253C23×C137—41no—
254C23×C137—42no—
255C23×C137—42no—
256C23×C137—41no—
257C23×C137—41no—
258C23×C137—41no—
259C23×C137—82no—
260C23×C137—82no—
261C23×C137—82no—
262C23×C137C22×D411yescharacteristic
263Q8×C137—41no—
264Q8×C137—42no—
265Q8×C137—81no—
266Q8×C137—81no—
267D4×C137—22no—
268D4×C137—22no—
269D4×C137—42no—
270D4×C137—41no—
271D4×C137—41no—
272D4×C137—41no—
273D4×C137—41no—
274D4×C137—42no—
275D4×C137—41no—
276D4×C137—42no—
277D4×C137—42no—
278D4×C137—42no—
279D4×C137—81no—
280D4×C137—81no—
281D4×C137—82no—
282D4×C137—82no—
283D4×C137—82no—
284D4×C137—82no—
285D4×C137—82no—
286D4×C137—88no—
287C2×C4×C137—21no—
288C2×C4×C137—21no—
289C2×C4×C137—22no—
290C2×C4×C137—24no—
291C2×C4×C137—21no—
292C2×C4×C137—22no—
293C2×C4×C137—22no—
294C2×C4×C137—21no—
295C2×C4×C137—21no—
296C2×C4×C137—41no—
297C2×C4×C137—42no—
298C2×C4×C137—42no—
299C2×C4×C137—42no—
300C2×C4×C137—42no—
301C2×C4×C137—41no—
302C2×C4×C137—41no—
303C2×C4×C137—41no—
304C2×C4×C137—82no—
305C2×C4×C137—82no—
306C2×C4×C137—82no—
307C2×C4×C137—82no—
308C2×C4×C137—82no—
309C2×C4×C137#12011yescharacteristic
310C2×C4×C137#12011yescharacteristic
311C2×C4×C137#12011yescharacteristic
312C2×C4×C137#12011yescharacteristic
313C2×C4×C137C22×D411yescharacteristic
314C2×C4×C137C22×D411yescharacteristic
315C8×C137—42no—
316C8×C137—41no—
317C8×C137—41no—
318C22×C137—21no—
319C22×C137—21no—
320C22×C137—42no—
321C22×C137—42no—
322C22×C137—42no—
323C22×C137—42no—
324C22×C137—41no—
325C22×C137—41no—
326C22×C137—42no—
327C22×C137—42no—
328C22×C137—42no—
329C22×C137—42no—
330C22×C137—41no—
331C22×C137—42no—
332C22×C137—82no—
333C22×C137—82no—
334C22×C137—81no—
335C22×C137—81no—
336C22×C137—81no—
337C22×C137—81no—
338C22×C137—164no—
339C22×C137C2×#12011yescharacteristic
340C22×C137#57611yescharacteristic
341C22×C137#57711yescharacteristic
342C4×C137—21no—
343C4×C137—21no—
344C4×C137—21no—
345C4×C137—21no—
346C4×C137—21no—
347C4×C137—44no—
348C4×C137—41no—
349C4×C137—42no—
350C4×C137—41no—
351C4×C137—42no—
352C4×C137—41no—
353C4×C137—81no—
354C4×C137#45312yes—
355C2×C137—21no—
356C2×C137—21no—
357C2×C137—82no—
358C2×C137—82no—
359C2×C137—82no—
360C2×C137—81no—
361C2×C137#301211yescharacteristic
362C2×C137C2×#45311yescharacteristic
363C2×C137#302511yescharacteristic
364#18272C13711yesmaximal, characteristic, direct product factor, Sylow
365C137#1827211yescharacteristic, direct product factor, Sylow
366#3558C2×C13711yescharacteristic, complemented
367#3109C2×C13711yescharacteristic, complemented
368#3105C2×C13711yescharacteristic, complemented
369#2540C2×C13711yescharacteristic, complemented
370#1618C2×C13712yescomplemented
371#1613C2×C13712yescomplemented
372#1600C2×C13712yescomplemented
373#1595C2×C13712yescomplemented
374#1509C2×C13711yescharacteristic, complemented
375#1502C2×C13711yescharacteristic, complemented
376#1469C2×C13711yescharacteristic, complemented
377#562—21no—
378H(3,𝔽4)—21no—
379#559—21no—
380#548—21no—
381#546—21no—
382#546—22no—
383D42—21no—
384#542—21no—
385#538—22no—
386#538C22×C13712yes—
387#535—21no—
388#534C22×C13712yes—
389#532C22×C13711yescharacteristic
390#529C22×C13711yescharacteristic
391C2×#124C22×C13711yescharacteristic
392C2×C22⋊Q8—21no—
393C2×#121—21no—
394C2×C4×D4C22×C13711yescharacteristic, complemented
395#484C22×C13711yescharacteristic, complemented
396#481C22×C13711yescharacteristic
397#481C22×C13712yescomplemented
398#478—21no—
399#476—21no—
400#463—21no—
401#459—21no—
402#450C22×C13711yescharacteristic, complemented
403#447C22×C13711yescharacteristic
404#447C22×C13712yescomplemented
405#442—22no—
406C4×SD16—21no—
407C4×D8—21no—
408#432C22×C13711yescharacteristic, complemented
409#431C22×C13711yescharacteristic, complemented
410#399C22×C13712yescomplemented
411#392C22×C13712yescomplemented
412#390—22no—
413C4×C4⋊C4C22×C13711yescharacteristic, complemented
414#328C22×C13712yescomplemented
415#327C22×C13712yes—
416#327C22×C13712yescomplemented
417#327C22×C13712yescomplemented
418#323C22×C13712yescomplemented
419#323C22×C13712yescomplemented
420C2×#41—21no—
421C2×#41—21no—
422C22×Q8D4×C13711yescharacteristic
423C22×D4—21no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4D4×C13711yescharacteristic
427C22×D4C23×C13711yescharacteristic
428C23×C4—21no—
429C2×SD16—21no—
430C2×D8—21no—
431C2×D8—22no—
432C4⋊Q8D4×C13711yescharacteristic, complemented
433#127—21no—
434#127D4×C13711yescharacteristic, complemented
435#126—22no—
436#126—21no—
437#125D4×C13711yescharacteristic, complemented
438#124—21no—
439#124—22no—
440#124—22no—
441#124—22no—
442#124—21no—
443#124—21no—
444#124—21no—
445#124—21no—
446#124—21no—
447#124D4×C13711yescharacteristic, complemented
448#123—22no—
449#123—21no—
450#123—22no—
451#123—22no—
452#123—22no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455C22⋊Q8—22no—
456C22⋊Q8—44no—
457C22⋊Q8C23×C13711yescharacteristic
458#121—22no—
459#121—22no—
460#121—22no—
461#121—21no—
462#121—22no—
463#121—21no—
464#121—22no—
465#121—44no—
466#121C23×C13711yescharacteristic
467#121C23×C13712yes—
468#120—22no—
469#120—22no—
470#120—22no—
471#120—22no—
472#120—22no—
473C4×Q8—21no—
474C4×Q8D4×C13711yescharacteristic, complemented
475C4×D4—22no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—22no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4D4×C13711yescharacteristic, complemented
485C4×D4D4×C13712yescomplemented
486#117—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4C23×C13711yescharacteristic
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4D4×C13712yes—
495C2×C22⋊C4C23×C13712yes—
496C2×C42—21no—
497C2×C42C23×C13711yescharacteristic
498#107—21no—
499#106—21no—
500#106—22no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—21no—
504#102—21no—
505#102—22no—
506#102—21no—
507#102—21no—
508#102—22no—
509C22⋊C8C23×C13712yes—
510C22⋊C8C23×C13711yescharacteristic
511C22⋊C8C23×C13711yescharacteristic
512#97—21no—
513C4×C8—21no—
514#95C23×C13712yes—
515C24—22no—
516C24—21no—
517C24C2×D4×C13712yes—
518#41—81no—
519#41—81no—
520#41—82no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—42no—
525C2×Q8C2×D4×C13711yescharacteristic
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—44no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C2×D4—82no—
547C2×D4C2×D4×C13711yescharacteristic
548C2×D4C2×D4×C13712yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C2×D4×C13711yescharacteristic
560C22×C4C2×D4×C13711yescharacteristic
561C22×C4C2×D4×C13712yes—
562C22×C4C24×C13711yescharacteristic
563SD16—42no—
564D8—44no—
565D8—42no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—22no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—44no—
580C4⋊C4C2×D4×C13712yes—
581C4⋊C4C2×D4×C13711yescharacteristic
582C4⋊C4C2×D4×C13711yescharacteristic
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—21no—
589C22⋊C4—21no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—21no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—21no—
598C22⋊C4—22no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C42—22no—
604C42—21no—
605C42—81no—
606C42C2×D4×C13711yescharacteristic
607C42C2×D4×C13711yescharacteristic
608C42C2×D4×C13711yescharacteristic
609C42C2×D4×C13711yescharacteristic
610C23—22no—
611C23—22no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23C22×D4×C13711yescharacteristic
628Q8—41no—
629Q8—42no—
630Q8—81no—
631Q8—81no—
632D4—22no—
633D4—22no—
634D4—42no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—42no—
640D4—41no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—81no—
645D4—81no—
646D4—82no—
647D4—82no—
648D4—82no—
649D4—82no—
650D4—82no—
651D4—88no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4#120×C13711yescharacteristic
675C2×C4#120×C13711yescharacteristic
676C2×C4#120×C13711yescharacteristic
677C2×C4#120×C13711yescharacteristic
678C2×C4C22×D4×C13711yescharacteristic
679C2×C4C22×D4×C13711yescharacteristic
680C8—42no—
681C8—41no—
682C8—41no—
683C22—21no—
684C22—21no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—82no—
698C22—82no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—164no—
704C22C2×#120×C13711yescharacteristic
705C22#576×C13711yescharacteristic
706C22#577×C13711yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—44no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—81no—
719C4#453×C13712yes—
720C2—21no—
721C2—21no—
722C2—82no—
723C2—82no—
724C2—81no—
725C2—82no—
726C2#3012×C13711yescharacteristic
727C2C2×#453×C13711yescharacteristic
728C2#3025×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3558×C137C2semidirect
2. #3109×C137C2semidirect
3. #3105×C137C2semidirect
4. #2540×C137C2semidirect
5. #1618×C137C2semidirect
6. #1613×C137C2semidirect
7. #1600×C137C2semidirect
8. #1595×C137C2semidirect
9. #1509×C137C2semidirect
10. #1502×C137C2semidirect
11. #1469×C137C2semidirect
29. C2×C4×D4×C137C22semidirect
30. #484×C137C22semidirect
32. #481×C137C22semidirect
37. #450×C137C22semidirect
39. #447×C137C22semidirect
43. #432×C137C22semidirect
44. #431×C137C22semidirect
45. #399×C137C22semidirect
46. #392×C137C22semidirect
48. C4×C4⋊C4×C137C22semidirect
49. #328×C137C22semidirect
51. #327×C137C22semidirect
52. #327×C137C22semidirect
53. #323×C137C22semidirect
54. #323×C137C22semidirect
67. C4⋊Q8×C137D4semidirect
69. #127×C137D4semidirect
72. #125×C137D4semidirect
82. #124×C137D4semidirect
109. C4×Q8×C137D4semidirect
119. C4×D4×C137D4semidirect
120. C4×D4×C137D4semidirect
364. #18272C137direct (N × H)
365. C137#18272direct (N × H)
366. #3558C2×C137semidirect
367. #3109C2×C137semidirect
368. #3105C2×C137semidirect
369. #2540C2×C137semidirect
370. #1618C2×C137semidirect
371. #1613C2×C137semidirect
372. #1600C2×C137semidirect
373. #1595C2×C137semidirect
374. #1509C2×C137semidirect
375. #1502C2×C137semidirect
376. #1469C2×C137semidirect
394. C2×C4×D4C22×C137semidirect
395. #484C22×C137semidirect
397. #481C22×C137semidirect
402. #450C22×C137semidirect
404. #447C22×C137semidirect
408. #432C22×C137semidirect
409. #431C22×C137semidirect
410. #399C22×C137semidirect
411. #392C22×C137semidirect
413. C4×C4⋊C4C22×C137semidirect
414. #328C22×C137semidirect
416. #327C22×C137semidirect
417. #327C22×C137semidirect
418. #323C22×C137semidirect
419. #323C22×C137semidirect
432. C4⋊Q8D4×C137semidirect
434. #127D4×C137semidirect
437. #125D4×C137semidirect
447. #124D4×C137semidirect
474. C4×Q8D4×C137semidirect
484. C4×D4D4×C137semidirect
485. C4×D4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3558×C1372
#3109×C1372
#3105×C1372
#2540×C1372
#1618×C1372
#1613×C1372
#1600×C1372
#1595×C1372
#1509×C1372
#1502×C1372
#1469×C1372
#18272137