Finite Group Databasebeta

← C137×#18787 #46868173

Subgroups — C137×#18787 #46868173

Order 35072.

1206 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
1D4×#41×C137C211yesmaximal, characteristic
2#3206×C137C211yesmaximal, characteristic, complemented
3#3079×C137C211yesmaximal, characteristic, complemented
4C2×#476×C137C211yesmaximal, characteristic, complemented
5#1637×C137C212yesmaximal, complemented
6#1635×C137C212yesmaximal, complemented
7#1631×C137C212yesmaximal, complemented
8#1629×C137C212yesmaximal, complemented
9#1547×C137C211yesmaximal, characteristic, complemented
10#1486×C137C211yesmaximal, characteristic, complemented
11#1477×C137C211yesmaximal, characteristic, complemented
12C22×#41×C137—21no—
13#550×C137C2211yescharacteristic
14D4×Q8×C137C2211yescharacteristic
15#548×C137—21no—
16#547×C137—21no—
17#547×C137C2211yescharacteristic
18#546×C137—22no—
19#546×C137—21no—
20D42×C137—21no—
21D42×C137C2211yescharacteristic
22#532×C137—21no—
23#532×C137C2211yescharacteristic
24C2×C4⋊Q8×C137C2211yescharacteristic, complemented
25#525×C137—22no—
26#525×C137—21no—
27C4×#41×C137C2211yescharacteristic
28C2×C4×D4×C137—21no—
29C2×C4×D4×C137C2211yescharacteristic
30#492×C137C2212yescomplemented
31#487×C137C2212yescomplemented
32#477×C137C2212yescomplemented
33#476×C137—21no—
34#476×C137—21no—
35#476×C137C2212yes—
36#476×C137C2212yescomplemented
37#476×C137C2212yescomplemented
38#475×C137—21no—
39#474×C137—21no—
40#461×C137—22no—
41#448×C137—22no—
42#431×C137C2211yescharacteristic, complemented
43#428×C137—21no—
44C2×#106×C137—21no—
45#423×C137C2211yescharacteristic, complemented
46C2×C4⋊C8×C137C2211yescharacteristic, complemented
47#417×C137—21no—
48C2×#102×C137—21no—
49#332×C137C2212yescomplemented
50#331×C137C2212yescomplemented
51Q8⋊C8×C137C2212yescomplemented
52D4⋊C8×C137C2212yes—
53D4⋊C8×C137C2212yescomplemented
54D4⋊C8×C137C2212yescomplemented
55C2×#41×C137—22no—
56C2×#41×C137—22no—
57C2×#41×C137—21no—
58C2×#41×C137—21no—
59C2×#41×C137—21no—
60C2×#41×C137—44no—
61C2×#41×C137—44no—
62C2×#41×C137D411yescharacteristic
63C22×Q8×C137—21no—
64C22×Q8×C137—21no—
65C22×D4×C137—22no—
66C22×D4×C137—21no—
67C22×D4×C137—21no—
68C22×D4×C137D411yescharacteristic
69C23×C4×C137—22no—
70C23×C4×C137—21no—
71C2×SD16×C137—24no—
72C2×M16×C137—21no—
73C22×C8×C137—21no—
74C4⋊Q8×C137—21no—
75C4⋊Q8×C137—21no—
76C4⋊Q8×C137—21no—
77C4⋊Q8×C137—21no—
78C4⋊Q8×C137C2312yes—
79C4⋊Q8×C137C2311yescharacteristic
80#127×C137—21no—
81#127×C137C2311yescharacteristic
82#124×C137—22no—
83#124×C137—21no—
84#123×C137—22no—
85#123×C137—22no—
86#123×C137—22no—
87C22⋊Q8×C137—22no—
88C22⋊Q8×C137—21no—
89C22⋊Q8×C137—22no—
90C22⋊Q8×C137—21no—
91#121×C137—22no—
92#121×C137—22no—
93#121×C137—22no—
94#121×C137—21no—
95#121×C137—21no—
96#121×C137—21no—
97#121×C137—21no—
98#121×C137—21no—
99#121×C137D412yes—
100#120×C137—22no—
101#120×C137—22no—
102#120×C137—22no—
103C4×Q8×C137D411yescharacteristic
104C4×Q8×C137C2311yescharacteristic
105C4×D4×C137—22no—
106C4×D4×C137—22no—
107C4×D4×C137—22no—
108C4×D4×C137—21no—
109C4×D4×C137—21no—
110C4×D4×C137—21no—
111C4×D4×C137—21no—
112C4×D4×C137—21no—
113C4×D4×C137—21no—
114C4×D4×C137—21no—
115C4×D4×C137D412yes—
116C4×D4×C137D411yescharacteristic
117C4×D4×C137D411yescharacteristic
118C4×D4×C137D411yescharacteristic
119C4×D4×C137C2311yescharacteristic
120C4×D4×C137C2311yescharacteristic
121C4×D4×C137C2311yescharacteristic
122#117×C137—21no—
123#117×C137D411yescharacteristic
124C2×C4⋊C4×C137—21no—
125C2×C4⋊C4×C137—21no—
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137D411yescharacteristic
128C2×C22⋊C4×C137—22no—
129C2×C22⋊C4×C137—21no—
130C2×C42×C137—21no—
131C2×C42×C137C2311yescharacteristic
132#107×C137—22no—
133#106×C137—22no—
134#106×C137—22no—
135#106×C137—22no—
136C4⋊C8×C137—21no—
137C4⋊C8×C137—21no—
138C4⋊C8×C137—21no—
139C4⋊C8×C137C2312yes—
140C4⋊C8×C137C2312yes—
141#103×C137—22no—
142#103×C137—24no—
143#102×C137—22no—
144#102×C137—22no—
145#102×C137—22no—
146C22⋊C8×C137—21no—
147C4×C8×C137C2312yes—
148C24×C137—22no—
149C24×C137—21no—
150#41×C137—22no—
151#41×C137—48no—
152#41×C137—48no—
153#41×C137—42no—
154#41×C137—42no—
155#41×C137—42no—
156#41×C137—42no—
157#41×C137—42no—
158#41×C137—42no—
159#41×C137SD1614yescomplemented
160C2×Q8×C137—22no—
161C2×Q8×C137—21no—
162C2×Q8×C137—22no—
163C2×Q8×C137—42no—
164C2×Q8×C137—42no—
165C2×Q8×C137—41no—
166C2×Q8×C137—82no—
167C2×Q8×C137C2×D411yescharacteristic
168C2×D4×C137—21no—
169C2×D4×C137—22no—
170C2×D4×C137—22no—
171C2×D4×C137—22no—
172C2×D4×C137—22no—
173C2×D4×C137—22no—
174C2×D4×C137—22no—
175C2×D4×C137—22no—
176C2×D4×C137—21no—
177C2×D4×C137—21no—
178C2×D4×C137—21no—
179C2×D4×C137—41no—
180C2×D4×C137—42no—
181C2×D4×C137—48no—
182C2×D4×C137—42no—
183C2×D4×C137—42no—
184C2×D4×C137—42no—
185C2×D4×C137C2×D411yescharacteristic
186C2×D4×C137C2×D411yescharacteristic
187C2×D4×C137C2×D411yescharacteristic
188C2×D4×C137C2×D412yes—
189C22×C4×C137—21no—
190C22×C4×C137—22no—
191C22×C4×C137—22no—
192C22×C4×C137—22no—
193C22×C4×C137—21no—
194C22×C4×C137—21no—
195C22×C4×C137—22no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—21no—
199C22×C4×C137—21no—
200C22×C4×C137—21no—
201C22×C4×C137—48no—
202C22×C4×C137—42no—
203C22×C4×C137—42no—
204C22×C4×C137—41no—
205C22×C4×C137C2×D411yescharacteristic
206C22×C4×C137C2×D411yescharacteristic
207C22×C4×C137C2×D411yescharacteristic
208SD16×C137—84no—
209M16×C137—42no—
210C2×C8×C137—22no—
211C2×C8×C137—22no—
212C2×C8×C137—22no—
213C2×C8×C137—42no—
214C4⋊C4×C137—22no—
215C4⋊C4×C137—22no—
216C4⋊C4×C137—21no—
217C4⋊C4×C137—21no—
218C4⋊C4×C137—21no—
219C4⋊C4×C137—21no—
220C4⋊C4×C137—22no—
221C4⋊C4×C137—22no—
222C4⋊C4×C137—41no—
223C4⋊C4×C137—41no—
224C4⋊C4×C137C2×D412yes—
225C4⋊C4×C137C2×D411yescharacteristic
226C4⋊C4×C137C2×D411yescharacteristic
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—21no—
234C22⋊C4×C137—21no—
235C22⋊C4×C137—22no—
236C22⋊C4×C137—21no—
237C22⋊C4×C137—21no—
238C22⋊C4×C137—22no—
239C22⋊C4×C137—21no—
240C22⋊C4×C137—21no—
241C22⋊C4×C137—21no—
242C42×C137—21no—
243C42×C137—21no—
244C42×C137—21no—
245C42×C137C2×D411yescharacteristic
246C42×C137C2×D411yescharacteristic
247C42×C137C2×D411yescharacteristic
248C42×C137C2411yescharacteristic
249C23×C137—21no—
250C23×C137—21no—
251C23×C137—21no—
252C23×C137—22no—
253C23×C137—42no—
254C23×C137—44no—
255C23×C137—44no—
256C23×C137—42no—
257C23×C137—81no—
258C23×C137—82no—
259C23×C137#12011yescharacteristic
260Q8×C137—21no—
261Q8×C137—44no—
262Q8×C137—44no—
263Q8×C137—41no—
264Q8×C137—41no—
265Q8×C137—82no—
266Q8×C137C2×SD1612yes—
267D4×C137—24no—
268D4×C137—21no—
269D4×C137—21no—
270D4×C137—21no—
271D4×C137—21no—
272D4×C137—42no—
273D4×C137—42no—
274D4×C137—44no—
275D4×C137—44no—
276D4×C137—44no—
277D4×C137—44no—
278D4×C137—44no—
279D4×C137—41no—
280D4×C137—41no—
281D4×C137—41no—
282D4×C137—41no—
283D4×C137—82no—
284D4×C137C2×SD1612yes—
285D4×C137#13712yes—
286C2×C4×C137—21no—
287C2×C4×C137—21no—
288C2×C4×C137—21no—
289C2×C4×C137—24no—
290C2×C4×C137—21no—
291C2×C4×C137—21no—
292C2×C4×C137—21no—
293C2×C4×C137—22no—
294C2×C4×C137—21no—
295C2×C4×C137—41no—
296C2×C4×C137—44no—
297C2×C4×C137—44no—
298C2×C4×C137—44no—
299C2×C4×C137—42no—
300C2×C4×C137—41no—
301C2×C4×C137—41no—
302C2×C4×C137—41no—
303C2×C4×C137—41no—
304C2×C4×C137—41no—
305C2×C4×C137—41no—
306C2×C4×C137—42no—
307C2×C4×C137—44no—
308C2×C4×C137—42no—
309C2×C4×C137—42no—
310C2×C4×C137—81no—
311C2×C4×C137—82no—
312C2×C4×C137#12011yescharacteristic
313C2×C4×C137#12011yescharacteristic
314C2×C4×C137#12011yescharacteristic
315C2×C4×C137C2×SD1612yes—
316C2×C4×C137AGL(1,ℤ/8)12yes—
317C2×C4×C137C22×D411yescharacteristic
318C2×C4×C137C22×D411yescharacteristic
319C2×C4×C137C22×D411yescharacteristic
320C8×C137—42no—
321C8×C137—42no—
322C8×C137—42no—
323C22×C137—21no—
324C22×C137—21no—
325C22×C137—22no—
326C22×C137—22no—
327C22×C137—41no—
328C22×C137—41no—
329C22×C137—41no—
330C22×C137—41no—
331C22×C137—42no—
332C22×C137—41no—
333C22×C137—41no—
334C22×C137—42no—
335C22×C137—42no—
336C22×C137—41no—
337C22×C137—84no—
338C22×C137—88no—
339C22×C137#45012yes—
340C22×C137C2×#12011yescharacteristic
341C4×C137—22no—
342C4×C137—21no—
343C4×C137—21no—
344C4×C137—21no—
345C4×C137—41no—
346C4×C137—42no—
347C4×C137—41no—
348C4×C137—41no—
349C4×C137—41no—
350C4×C137—82no—
351C4×C137#45012yes—
352C4×C137C22×SD1611yescharacteristic
353C4×C137C2×AGL(1,ℤ/8)11yescharacteristic
354C4×C137C2×#13711yescharacteristic
355C4×C137#57511yescharacteristic
356C2×C137—22no—
357C2×C137—42no—
358C2×C137—42no—
359C2×C137—81no—
360C2×C137—82no—
361C2×C137C2×#45011yescharacteristic
362C2×C137#300711yescharacteristic
363C2×C137#302111yescharacteristic
364#18787C13711yesmaximal, characteristic, direct product factor, Sylow
365C137#1878711yescharacteristic, direct product factor, Sylow
366D4×#41C2×C13711yescharacteristic
367#3206C2×C13711yescharacteristic, complemented
368#3079C2×C13711yescharacteristic, complemented
369C2×#476C2×C13711yescharacteristic, complemented
370#1637C2×C13712yescomplemented
371#1635C2×C13712yescomplemented
372#1631C2×C13712yescomplemented
373#1629C2×C13712yescomplemented
374#1547C2×C13711yescharacteristic, complemented
375#1486C2×C13711yescharacteristic, complemented
376#1477C2×C13711yescharacteristic, complemented
377C22×#41—21no—
378#550C22×C13711yescharacteristic
379D4×Q8C22×C13711yescharacteristic
380#548—21no—
381#547—21no—
382#547C22×C13711yescharacteristic
383#546—22no—
384#546—21no—
385D42—21no—
386D42C22×C13711yescharacteristic
387#532—21no—
388#532C22×C13711yescharacteristic
389C2×C4⋊Q8C22×C13711yescharacteristic, complemented
390#525—22no—
391#525—21no—
392C4×#41C22×C13711yescharacteristic
393C2×C4×D4—21no—
394C2×C4×D4C22×C13711yescharacteristic
395#492C22×C13712yescomplemented
396#487C22×C13712yescomplemented
397#477C22×C13712yescomplemented
398#476—21no—
399#476—21no—
400#476C22×C13712yes—
401#476C22×C13712yescomplemented
402#476C22×C13712yescomplemented
403#475—21no—
404#474—21no—
405#461—22no—
406#448—22no—
407#431C22×C13711yescharacteristic, complemented
408#428—21no—
409C2×#106—21no—
410#423C22×C13711yescharacteristic, complemented
411C2×C4⋊C8C22×C13711yescharacteristic, complemented
412#417—21no—
413C2×#102—21no—
414#332C22×C13712yescomplemented
415#331C22×C13712yescomplemented
416Q8⋊C8C22×C13712yescomplemented
417D4⋊C8C22×C13712yes—
418D4⋊C8C22×C13712yescomplemented
419D4⋊C8C22×C13712yescomplemented
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—44no—
426C2×#41—44no—
427C2×#41D4×C13711yescharacteristic
428C22×Q8—21no—
429C22×Q8—21no—
430C22×D4—22no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4D4×C13711yescharacteristic
434C23×C4—22no—
435C23×C4—21no—
436C2×SD16—24no—
437C2×M16—21no—
438C22×C8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8—21no—
442C4⋊Q8—21no—
443C4⋊Q8C23×C13712yes—
444C4⋊Q8C23×C13711yescharacteristic
445#127—21no—
446#127C23×C13711yescharacteristic
447#124—22no—
448#124—21no—
449#123—22no—
450#123—22no—
451#123—22no—
452C22⋊Q8—22no—
453C22⋊Q8—21no—
454C22⋊Q8—22no—
455C22⋊Q8—21no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121D4×C13712yes—
465#120—22no—
466#120—22no—
467#120—22no—
468C4×Q8D4×C13711yescharacteristic
469C4×Q8C23×C13711yescharacteristic
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4D4×C13711yescharacteristic
481C4×D4D4×C13711yescharacteristic
482C4×D4D4×C13711yescharacteristic
483C4×D4D4×C13712yes—
484C4×D4C23×C13711yescharacteristic
485C4×D4C23×C13711yescharacteristic
486C4×D4C23×C13711yescharacteristic
487#117—21no—
488#117D4×C13711yescharacteristic
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C13711yescharacteristic
493C2×C22⋊C4—22no—
494C2×C22⋊C4—21no—
495C2×C42—21no—
496C2×C42C23×C13711yescharacteristic
497#107—22no—
498#106—22no—
499#106—22no—
500#106—22no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503C4⋊C8—21no—
504C4⋊C8C23×C13712yes—
505C4⋊C8C23×C13712yes—
506#103—22no—
507#103—24no—
508#102—22no—
509#102—22no—
510#102—22no—
511C22⋊C8—21no—
512C4×C8C23×C13712yes—
513C24—22no—
514C24—21no—
515#41—22no—
516#41—48no—
517#41—48no—
518#41—42no—
519#41—42no—
520#41—42no—
521#41—42no—
522#41—42no—
523#41—42no—
524#41SD16×C13714yescomplemented
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—41no—
531C2×Q8—82no—
532C2×Q8C2×D4×C13711yescharacteristic
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—48no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C2×D4×C13711yescharacteristic
551C2×D4C2×D4×C13711yescharacteristic
552C2×D4C2×D4×C13711yescharacteristic
553C2×D4C2×D4×C13712yes—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—48no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4C2×D4×C13711yescharacteristic
571C22×C4C2×D4×C13711yescharacteristic
572C22×C4C2×D4×C13711yescharacteristic
573SD16—84no—
574M16—42no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—42no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4C2×D4×C13712yes—
590C4⋊C4C2×D4×C13711yescharacteristic
591C4⋊C4C2×D4×C13711yescharacteristic
592C4⋊C4C2×D4×C13711yescharacteristic
593C4⋊C4C2×D4×C13711yescharacteristic
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42C2×D4×C13711yescharacteristic
611C42C2×D4×C13711yescharacteristic
612C42C2×D4×C13711yescharacteristic
613C42C24×C13711yescharacteristic
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—42no—
619C23—44no—
620C23—44no—
621C23—42no—
622C23—81no—
623C23—82no—
624C23#120×C13711yescharacteristic
625Q8—21no—
626Q8—44no—
627Q8—44no—
628Q8—41no—
629Q8—41no—
630Q8—82no—
631Q8C2×SD16×C13712yes—
632D4—24no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—42no—
638D4—42no—
639D4—44no—
640D4—44no—
641D4—44no—
642D4—44no—
643D4—44no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—82no—
649D4C2×SD16×C13712yes—
650D4#137×C13712yes—
651C2×C4—21no—
652C2×C4—24no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—44no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—82no—
677C2×C4#120×C13711yescharacteristic
678C2×C4#120×C13711yescharacteristic
679C2×C4#120×C13711yescharacteristic
680C2×C4C2×SD16×C13712yes—
681C2×C4AGL(1,ℤ/8)×C13712yes—
682C2×C4C22×D4×C13711yescharacteristic
683C2×C4C22×D4×C13711yescharacteristic
684C2×C4C22×D4×C13711yescharacteristic
685C8—42no—
686C8—42no—
687C8—42no—
688C22—21no—
689C22—21no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—84no—
703C22—88no—
704C22#450×C13712yes—
705C22C2×#120×C13711yescharacteristic
706C4—22no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—82no—
716C4#450×C13712yes—
717C4C22×SD16×C13711yescharacteristic
718C4C2×AGL(1,ℤ/8)×C13711yescharacteristic
719C4C2×#137×C13711yescharacteristic
720C4#575×C13711yescharacteristic
721C2—22no—
722C2—42no—
723C2—42no—
724C2—81no—
725C2—82no—
726C2C2×#450×C13711yescharacteristic
727C2#3007×C13711yescharacteristic
728C2#3021×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radicalD4×#41×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. #3206×C137C2semidirect
3. #3079×C137C2semidirect
4. C2×#476×C137C2semidirect
5. #1637×C137C2semidirect
6. #1635×C137C2semidirect
7. #1631×C137C2semidirect
8. #1629×C137C2semidirect
9. #1547×C137C2semidirect
10. #1486×C137C2semidirect
11. #1477×C137C2semidirect
24. C2×C4⋊Q8×C137C22semidirect
30. #492×C137C22semidirect
31. #487×C137C22semidirect
32. #477×C137C22semidirect
36. #476×C137C22semidirect
37. #476×C137C22semidirect
42. #431×C137C22semidirect
45. #423×C137C22semidirect
46. C2×C4⋊C8×C137C22semidirect
49. #332×C137C22semidirect
50. #331×C137C22semidirect
51. Q8⋊C8×C137C22semidirect
53. D4⋊C8×C137C22semidirect
54. D4⋊C8×C137C22semidirect
159. #41×C137SD16semidirect
364. #18787C137direct (N × H)
365. C137#18787direct (N × H)
367. #3206C2×C137semidirect
368. #3079C2×C137semidirect
369. C2×#476C2×C137semidirect
370. #1637C2×C137semidirect
371. #1635C2×C137semidirect
372. #1631C2×C137semidirect
373. #1629C2×C137semidirect
374. #1547C2×C137semidirect
375. #1486C2×C137semidirect
376. #1477C2×C137semidirect
389. C2×C4⋊Q8C22×C137semidirect
395. #492C22×C137semidirect
396. #487C22×C137semidirect
397. #477C22×C137semidirect
401. #476C22×C137semidirect
402. #476C22×C137semidirect
407. #431C22×C137semidirect
410. #423C22×C137semidirect
411. C2×C4⋊C8C22×C137semidirect
414. #332C22×C137semidirect
415. #331C22×C137semidirect
416. Q8⋊C8C22×C137semidirect
418. D4⋊C8C22×C137semidirect
419. D4⋊C8C22×C137semidirect
524. #41SD16×C137semidirect

Maximal subgroups

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

subgroupindex
D4×#41×C1372
#3206×C1372
#3079×C1372
C2×#476×C1372
#1637×C1372
#1635×C1372
#1631×C1372
#1629×C1372
#1547×C1372
#1486×C1372
#1477×C1372
#18787137