Finite Group Databasebeta

← C137×#24056 #46873442

Subgroups — C137×#24056 #46873442

Order 35072.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C137C211yesmaximal, characteristic
2#2849×C137C212yesmaximal, complemented
3C2×#386×C137C211yesmaximal, characteristic, complemented
4#2044×C137C214yesmaximal, complemented
5#1898×C137C212yesmaximal, complemented
6#1867×C137C212yesmaximal, complemented
7#1790×C137C212yesmaximal, complemented
8#1781×C137C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C137C2211yescharacteristic
10C23×D4×C137C2211yescharacteristic
11C24×C4×C137C2211yescharacteristic, complemented
12#546×C137—22no—
13#546×C137—22no—
14D42×C137—22no—
15D42×C137—22no—
16#535×C137—21no—
17#534×C137—21no—
18#534×C137C2212yes—
19#525×C137—21no—
20C2×#123×C137—22no—
21C2×#120×C137—21no—
22C2×#120×C137C2212yes—
23#518×C137C2211yescharacteristic
24C22×C22⋊C4×C137—21no—
25C22×C22⋊C4×C137C2211yescharacteristic, complemented
26C2×#99×C137C2212yes—
27C2×#99×C137C2212yescomplemented
28C2×#99×C137C2214yescomplemented
29#386×C137—21no—
30#386×C137—21no—
31#386×C137—22no—
32#386×C137C2212yes—
33#386×C137C2212yescomplemented
34#386×C137C2214yescomplemented
35#385×C137—22no—
36#385×C137C2214yescomplemented
37#381×C137—22no—
38#379×C137C2212yescomplemented
39C2×#95×C137—21no—
40#342×C137C2214yescomplemented
41C25×C137D411yescharacteristic
42C25×C137C2311yescharacteristic
43H(5,𝔽2)×C137—24no—
44H(5,𝔽2)×C137—42no—
45C2×#41×C137—21no—
46C2×#41×C137—22no—
47C22×D4×C137—21no—
48C22×D4×C137—22no—
49C22×D4×C137—22no—
50C22×D4×C137—22no—
51C22×D4×C137—21no—
52C22×D4×C137—21no—
53C22×D4×C137—24no—
54C22×D4×C137—42no—
55C22×D4×C137D411yescharacteristic
56C22×D4×C137D411yescharacteristic
57C22×D4×C137D412yes—
58C22×D4×C137D412yes—
59C22×D4×C137C2312yes—
60C22×D4×C137C2311yescharacteristic
61C22×D4×C137C2311yescharacteristic
62C23×C4×C137—21no—
63C23×C4×C137—22no—
64C23×C4×C137—21no—
65C23×C4×C137—22no—
66C23×C4×C137—21no—
67C23×C4×C137—44no—
68C23×C4×C137D411yescharacteristic
69C23×C4×C137C2312yes—
70#127×C137—22no—
71#124×C137—22no—
72#123×C137—22no—
73#123×C137—22no—
74#123×C137—22no—
75#123×C137—48no—
76C22⋊Q8×C137—21no—
77C22⋊Q8×C137—21no—
78#121×C137—21no—
79#121×C137—21no—
80#121×C137—22no—
81#121×C137—22no—
82#121×C137—22no—
83#121×C137—22no—
84#121×C137—22no—
85#121×C137—22no—
86#120×C137—22no—
87#120×C137—22no—
88#120×C137—22no—
89#120×C137—22no—
90#120×C137—22no—
91#120×C137—22no—
92#120×C137—22no—
93#120×C137—22no—
94#120×C137—22no—
95C4×D4×C137—22no—
96C4×D4×C137—22no—
97C4×D4×C137—22no—
98C4×D4×C137—22no—
99#117×C137—21no—
100C2×C4⋊C4×C137—24no—
101C2×C22⋊C4×C137—21no—
102C2×C22⋊C4×C137—21no—
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137—22no—
105C2×C22⋊C4×C137—22no—
106C2×C22⋊C4×C137—21no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—22no—
109C2×C22⋊C4×C137—24no—
110C2×C22⋊C4×C137—42no—
111C2×C22⋊C4×C137—44no—
112C2×C22⋊C4×C137D412yes—
113C2×C22⋊C4×C137D412yes—
114C2×C22⋊C4×C137C2314yes—
115C2×C22⋊C4×C137C2312yes—
116C2×C22⋊C4×C137C2312yes—
117#99×C137—24no—
118#99×C137—42no—
119#99×C137—44no—
120#95×C137—22no—
121#95×C137—22no—
122#95×C137—24no—
123#95×C137—24no—
124C24×C137—22no—
125C24×C137—22no—
126C24×C137—21no—
127C24×C137—22no—
128C24×C137—21no—
129C24×C137—21no—
130C24×C137—42no—
131C24×C137—42no—
132C24×C137—41no—
133C24×C137—42no—
134C24×C137—42no—
135C24×C137C2×D411yescharacteristic
136C24×C137C2×D412yes—
137C24×C137C2×D412yes—
138C24×C137C2×D411yescharacteristic
139C24×C137C2×D412yes—
140C24×C137C2×D411yescharacteristic
141C24×C137C2×D411yescharacteristic
142C24×C137C2411yescharacteristic
143#41×C137—48no—
144#41×C137—42no—
145#41×C137—42no—
146C2×Q8×C137—21no—
147C2×D4×C137—22no—
148C2×D4×C137—22no—
149C2×D4×C137—22no—
150C2×D4×C137—21no—
151C2×D4×C137—22no—
152C2×D4×C137—22no—
153C2×D4×C137—22no—
154C2×D4×C137—22no—
155C2×D4×C137—22no—
156C2×D4×C137—22no—
157C2×D4×C137—22no—
158C2×D4×C137—22no—
159C2×D4×C137—22no—
160C2×D4×C137—24no—
161C2×D4×C137—22no—
162C2×D4×C137—24no—
163C2×D4×C137—22no—
164C2×D4×C137—22no—
165C2×D4×C137—22no—
166C2×D4×C137—22no—
167C2×D4×C137—22no—
168C2×D4×C137—41no—
169C2×D4×C137—41no—
170C2×D4×C137—48no—
171C2×D4×C137—48no—
172C2×D4×C137—48no—
173C2×D4×C137—42no—
174C2×D4×C137—42no—
175C2×D4×C137—44no—
176C2×D4×C137—44no—
177C2×D4×C137—82no—
178C2×D4×C137—82no—
179C2×D4×C137#4114yes—
180C22×C4×C137—21no—
181C22×C4×C137—24no—
182C22×C4×C137—22no—
183C22×C4×C137—28no—
184C22×C4×C137—21no—
185C22×C4×C137—21no—
186C22×C4×C137—22no—
187C22×C4×C137—24no—
188C22×C4×C137—21no—
189C22×C4×C137—21no—
190C22×C4×C137—22no—
191C22×C4×C137—24no—
192C22×C4×C137—22no—
193C22×C4×C137—44no—
194C22×C4×C137—41no—
195C22×C4×C137—44no—
196C22×C4×C137—48no—
197C22×C4×C137—42no—
198C22×C4×C137—44no—
199C22×C4×C137—42no—
200C22×C4×C137—41no—
201C22×C4×C137—41no—
202C22×C4×C137—42no—
203C22×C4×C137—42no—
204C22×C4×C137—42no—
205C22×C4×C137C2×D412yes—
206C22×C4×C137C2×D411yescharacteristic
207C22×C4×C137C2×D411yescharacteristic
208C22×C4×C137C2×D412yes—
209C22×C4×C137C2×D412yes—
210C4⋊C4×C137—21no—
211C4⋊C4×C137—21no—
212C4⋊C4×C137—22no—
213C4⋊C4×C137—22no—
214C4⋊C4×C137—48no—
215C22⋊C4×C137—22no—
216C22⋊C4×C137—22no—
217C22⋊C4×C137—22no—
218C22⋊C4×C137—22no—
219C22⋊C4×C137—22no—
220C22⋊C4×C137—22no—
221C22⋊C4×C137—22no—
222C22⋊C4×C137—22no—
223C22⋊C4×C137—22no—
224C22⋊C4×C137—22no—
225C22⋊C4×C137—22no—
226C22⋊C4×C137—24no—
227C22⋊C4×C137—24no—
228C22⋊C4×C137—24no—
229C22⋊C4×C137—44no—
230C22⋊C4×C137—44no—
231C22⋊C4×C137—48no—
232C22⋊C4×C137—44no—
233C22⋊C4×C137—42no—
234C22⋊C4×C137—44no—
235C42×C137—22no—
236C23×C137—21no—
237C23×C137—21no—
238C23×C137—22no—
239C23×C137—22no—
240C23×C137—21no—
241C23×C137—21no—
242C23×C137—21no—
243C23×C137—24no—
244C23×C137—24no—
245C23×C137—24no—
246C23×C137—24no—
247C23×C137—21no—
248C23×C137—21no—
249C23×C137—22no—
250C23×C137—21no—
251C23×C137—21no—
252C23×C137—24no—
253C23×C137—42no—
254C23×C137—41no—
255C23×C137—41no—
256C23×C137—42no—
257C23×C137—41no—
258C23×C137—41no—
259C23×C137—42no—
260C23×C137—42no—
261C23×C137—48no—
262C23×C137—48no—
263C23×C137—41no—
264C23×C137—41no—
265C23×C137—41no—
266C23×C137—41no—
267C23×C137—48no—
268C23×C137—42no—
269C23×C137—42no—
270C23×C137—42no—
271C23×C137—42no—
272C23×C137—42no—
273C23×C137—81no—
274C23×C137—81no—
275C23×C137—84no—
276C23×C137—81no—
277C23×C137—81no—
278C23×C137#12012yes—
279C23×C137#12011yescharacteristic
280C23×C137#12011yescharacteristic
281C23×C137#12312yescomplemented
282C23×C137C22×D411yescharacteristic
283C23×C137C22×D412yes—
284C23×C137C2×#4112yes—
285C23×C137H(5,𝔽2)12yes—
286Q8×C137—42no—
287D4×C137—28no—
288D4×C137—44no—
289D4×C137—42no—
290D4×C137—44no—
291D4×C137—44no—
292D4×C137—42no—
293D4×C137—42no—
294D4×C137—44no—
295D4×C137—44no—
296D4×C137—44no—
297D4×C137—44no—
298D4×C137—82no—
299D4×C137—82no—
300D4×C137—82no—
301D4×C137—82no—
302C2×C4×C137—21no—
303C2×C4×C137—21no—
304C2×C4×C137—24no—
305C2×C4×C137—28no—
306C2×C4×C137—22no—
307C2×C4×C137—22no—
308C2×C4×C137—22no—
309C2×C4×C137—21no—
310C2×C4×C137—21no—
311C2×C4×C137—21no—
312C2×C4×C137—24no—
313C2×C4×C137—42no—
314C2×C4×C137—42no—
315C2×C4×C137—44no—
316C2×C4×C137—44no—
317C2×C4×C137—42no—
318C2×C4×C137—44no—
319C2×C4×C137—48no—
320C2×C4×C137—42no—
321C2×C4×C137—42no—
322C2×C4×C137—44no—
323C2×C4×C137—42no—
324C2×C4×C137—42no—
325C2×C4×C137—44no—
326C2×C4×C137—42no—
327C2×C4×C137—44no—
328C2×C4×C137—42no—
329C2×C4×C137—42no—
330C2×C4×C137—44no—
331C2×C4×C137—81no—
332C2×C4×C137—81no—
333C2×C4×C137—84no—
334C2×C4×C137#12312yescomplemented
335C22×C137—24no—
336C22×C137—24no—
337C22×C137—21no—
338C22×C137—21no—
339C22×C137—22no—
340C22×C137—21no—
341C22×C137—21no—
342C22×C137—22no—
343C22×C137—21no—
344C22×C137—21no—
345C22×C137—22no—
346C22×C137—22no—
347C22×C137—22no—
348C22×C137—22no—
349C22×C137—42no—
350C22×C137—42no—
351C22×C137—48no—
352C22×C137—48no—
353C22×C137—42no—
354C22×C137—42no—
355C22×C137—42no—
356C22×C137—42no—
357C22×C137—41no—
358C22×C137—41no—
359C22×C137—42no—
360C22×C137—41no—
361C22×C137—42no—
362C22×C137—41no—
363C22×C137—42no—
364C22×C137—41no—
365C22×C137—81no—
366C22×C137—84no—
367C22×C137—84no—
368C22×C137—84no—
369C22×C137—81no—
370C22×C137—162no—
371C22×C137B(4,𝔽2)12yes—
372C22×C137#45812yes—
373C22×C137C2×#12011yescharacteristic
374C22×C137C2×#12311yescharacteristic
375C22×C137#53411yescharacteristic
376C22×C137#54614yes—
377C4×C137—22no—
378C4×C137—41no—
379C4×C137—42no—
380C4×C137—44no—
381C4×C137—42no—
382C4×C137—42no—
383C4×C137—84no—
384C4×C137—82no—
385C2×C137—21no—
386C2×C137—24no—
387C2×C137—21no—
388C2×C137—22no—
389C2×C137—22no—
390C2×C137—42no—
391C2×C137—42no—
392C2×C137—81no—
393C2×C137—82no—
394C2×C137#240511yescharacteristic
395C2×C137C2×B(4,𝔽2)11yescharacteristic
396C2×C137C2×#45811yescharacteristic
397#24056C13711yesmaximal, characteristic, direct product factor, Sylow
398C137#2405611yescharacteristic, direct product factor, Sylow
399#3484C2×C13711yescharacteristic
400#2849C2×C13712yescomplemented
401C2×#386C2×C13711yescharacteristic, complemented
402#2044C2×C13714yescomplemented
403#1898C2×C13712yescomplemented
404#1867C2×C13712yescomplemented
405#1790C2×C13712yescomplemented
406#1781C2×C13711yescharacteristic, complemented
407C2×H(5,𝔽2)C22×C13711yescharacteristic
408C23×D4C22×C13711yescharacteristic
409C24×C4C22×C13711yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C13712yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C13712yes—
421#518C22×C13711yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C13711yescharacteristic, complemented
424C2×#99C22×C13712yes—
425C2×#99C22×C13714yescomplemented
426C2×#99C22×C13712yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C13712yes—
431#386C22×C13714yescomplemented
432#386C22×C13712yescomplemented
433#385—22no—
434#385C22×C13714yescomplemented
435#381—22no—
436#379C22×C13712yescomplemented
437C2×#95—21no—
438#342C22×C13714yescomplemented
439C25D4×C13711yescharacteristic
440C25C23×C13711yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C13711yescharacteristic
454C22×D4D4×C13711yescharacteristic
455C22×D4D4×C13712yes—
456C22×D4D4×C13712yes—
457C22×D4C23×C13712yes—
458C22×D4C23×C13711yescharacteristic
459C22×D4C23×C13711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C13711yescharacteristic
467C23×C4C23×C13712yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C13712yes—
511C2×C22⋊C4D4×C13712yes—
512C2×C22⋊C4C23×C13712yes—
513C2×C22⋊C4C23×C13714yes—
514C2×C22⋊C4C23×C13712yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C13711yescharacteristic
534C24C2×D4×C13712yes—
535C24C2×D4×C13712yes—
536C24C2×D4×C13711yescharacteristic
537C24C2×D4×C13712yes—
538C24C2×D4×C13711yescharacteristic
539C24C2×D4×C13711yescharacteristic
540C24C24×C13711yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C13714yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C13712yes—
604C22×C4C2×D4×C13711yescharacteristic
605C22×C4C2×D4×C13711yescharacteristic
606C22×C4C2×D4×C13712yes—
607C22×C4C2×D4×C13712yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C13712yes—
677C23#120×C13711yescharacteristic
678C23#120×C13711yescharacteristic
679C23#123×C13712yescomplemented
680C23C22×D4×C13711yescharacteristic
681C23C22×D4×C13712yes—
682C23C2×#41×C13712yes—
683C23H(5,𝔽2)×C13712yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C13712yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22B(4,𝔽2)×C13712yes—
770C22#458×C13712yes—
771C22C2×#120×C13711yescharacteristic
772C22C2×#123×C13711yescharacteristic
773C22#534×C13711yescharacteristic
774C22#546×C13714yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2#2405×C13711yescharacteristic
793C2C2×B(4,𝔽2)×C13711yescharacteristic
794C2C2×#458×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
prime radical#3484×C137C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C25×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2849×C137C2semidirect
3. C2×#386×C137C2semidirect
4. #2044×C137C2semidirect
5. #1898×C137C2semidirect
6. #1867×C137C2semidirect
7. #1790×C137C2semidirect
8. #1781×C137C2semidirect
11. C24×C4×C137C22semidirect
25. C22×C22⋊C4×C137C22semidirect
27. C2×#99×C137C22semidirect
28. C2×#99×C137C22semidirect
33. #386×C137C22semidirect
34. #386×C137C22semidirect
36. #385×C137C22semidirect
38. #379×C137C22semidirect
40. #342×C137C22semidirect
281. C23×C137#123semidirect
334. C2×C4×C137#123semidirect
397. #24056C137direct (N × H)
398. C137#24056direct (N × H)
400. #2849C2×C137semidirect
401. C2×#386C2×C137semidirect
402. #2044C2×C137semidirect
403. #1898C2×C137semidirect
404. #1867C2×C137semidirect
405. #1790C2×C137semidirect
406. #1781C2×C137semidirect
409. C24×C4C22×C137semidirect
423. C22×C22⋊C4C22×C137semidirect
425. C2×#99C22×C137semidirect
426. C2×#99C22×C137semidirect
431. #386C22×C137semidirect
432. #386C22×C137semidirect
434. #385C22×C137semidirect
436. #379C22×C137semidirect
438. #342C22×C137semidirect
679. C23#123×C137semidirect
732. C2×C4#123×C137semidirect

Maximal subgroups

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

subgroupindex
#3484×C1372
#2849×C1372
C2×#386×C1372
#2044×C1372
#1898×C1372
#1867×C1372
#1790×C1372
#1781×C1372
#24056137