Finite Group Databasebeta

← C137×#24140 #46873526

Subgroups — C137×#24140 #46873526

Order 35072.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C137C211yesmaximal, characteristic, complemented
2#2848×C137C211yesmaximal, characteristic, complemented
3#2847×C137C211yesmaximal, characteristic, complemented
4C4×#120×C137C211yesmaximal, characteristic, complemented
5#2044×C137C212yesmaximal, complemented
6#2021×C137C212yesmaximal, complemented
7#1996×C137C211yesmaximal, characteristic, complemented
8#1964×C137C211yesmaximal, characteristic, complemented
9#1889×C137C212yesmaximal, complemented
10#1867×C137C212yesmaximal, complemented
11#1799×C137C211yesmaximal, characteristic, complemented
12C24×C4×C137C2211yescharacteristic
13#553×C137—21no—
14#553×C137—22no—
15#552×C137—21no—
16#551×C137—22no—
17#548×C137—21no—
18#546×C137—21no—
19#539×C137—21no—
20#538×C137—21no—
21#534×C137C2212yes—
22#529×C137—21no—
23#525×C137—21no—
24C2×C22⋊Q8×C137—21no—
25C2×C22⋊Q8×C137C2211yescharacteristic
26C2×#121×C137—21no—
27C2×#121×C137C2211yescharacteristic
28C2×#120×C137C2211yescharacteristic
29C2×#120×C137C2212yes—
30#518×C137C2212yes—
31C2×C4×D4×C137—21no—
32C2×C4×D4×C137C2211yescharacteristic
33C2×#99×C137C2212yes—
34C2×#99×C137C2212yes—
35C2×#99×C137C2212yes—
36#386×C137—21no—
37#386×C137—22no—
38#386×C137C2211yescharacteristic
39#386×C137C2212yes—
40#385×C137—21no—
41#385×C137—22no—
42#385×C137C2211yescharacteristic
43#385×C137C2212yes—
44#380×C137—21no—
45#380×C137—21no—
46#380×C137C2211yescharacteristic
47#380×C137C2211yescharacteristic
48#379×C137C2212yes—
49#379×C137C2211yescharacteristic
50C4×C22⋊C4×C137—21no—
51C4×C22⋊C4×C137C2211yescharacteristic
52#342×C137C2212yes—
53#342×C137C2212yes—
54#342×C137C2212yes—
55C25×C137C2311yescharacteristic
56C2×#41×C137—21no—
57C22×Q8×C137D411yescharacteristic, complemented
58C22×D4×C137—21no—
59C22×D4×C137—22no—
60C22×D4×C137D411yescharacteristic, complemented
61C22×D4×C137C2311yescharacteristic
62C22×D4×C137C2312yes—
63C23×C4×C137—21no—
64C23×C4×C137—21no—
65C23×C4×C137—21no—
66C23×C4×C137—21no—
67C23×C4×C137—21no—
68C23×C4×C137—21no—
69C23×C4×C137—44no—
70C23×C4×C137D411yescharacteristic, complemented
71C23×C4×C137C2311yescharacteristic
72C23×C4×C137C2311yescharacteristic
73#126×C137—22no—
74#126×C137—22no—
75#126×C137—22no—
76#125×C137—21no—
77#125×C137—22no—
78#124×C137—21no—
79#124×C137—22no—
80#123×C137—22no—
81#123×C137—22no—
82#123×C137—22no—
83#123×C137—22no—
84#123×C137—22no—
85C22⋊Q8×C137—21no—
86C22⋊Q8×C137—22no—
87C22⋊Q8×C137—21no—
88C22⋊Q8×C137—21no—
89C22⋊Q8×C137—21no—
90C22⋊Q8×C137—21no—
91C22⋊Q8×C137—44no—
92#121×C137—21no—
93#121×C137—22no—
94#121×C137—21no—
95#121×C137—21no—
96#121×C137—21no—
97#121×C137—21no—
98#121×C137—22no—
99#121×C137—22no—
100#121×C137—44no—
101#120×C137—22no—
102#120×C137—22no—
103#120×C137—22no—
104#120×C137—22no—
105#120×C137—24no—
106#120×C137—42no—
107C4×Q8×C137—21no—
108C4×D4×C137—22no—
109C4×D4×C137—21no—
110C4×D4×C137—21no—
111C4×D4×C137—21no—
112C4×D4×C137—21no—
113C4×D4×C137—21no—
114C4×D4×C137—22no—
115C4×D4×C137—22no—
116C4×D4×C137—22no—
117C4×D4×C137—22no—
118C4×D4×C137—44no—
119#117×C137—21no—
120#117×C137—22no—
121#117×C137—22no—
122C2×C4⋊C4×C137—21no—
123C2×C4⋊C4×C137—21no—
124C2×C4⋊C4×C137—21no—
125C2×C4⋊C4×C137—22no—
126C2×C4⋊C4×C137D411yescharacteristic, complemented
127C2×C4⋊C4×C137D411yescharacteristic, complemented
128C2×C4⋊C4×C137D411yescharacteristic, complemented
129C2×C4⋊C4×C137D412yescomplemented
130C2×C22⋊C4×C137—22no—
131C2×C22⋊C4×C137—21no—
132C2×C22⋊C4×C137—21no—
133C2×C22⋊C4×C137—22no—
134C2×C22⋊C4×C137—21no—
135C2×C22⋊C4×C137—22no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—22no—
138C2×C22⋊C4×C137—22no—
139C2×C22⋊C4×C137D411yescharacteristic, complemented
140C2×C22⋊C4×C137D412yescomplemented
141C2×C22⋊C4×C137C2311yescharacteristic
142C2×C22⋊C4×C137C2312yes—
143C2×C22⋊C4×C137C2312yes—
144C2×C22⋊C4×C137C2311yescharacteristic
145C2×C22⋊C4×C137C2312yes—
146C2×C22⋊C4×C137C2311yescharacteristic
147C2×C42×C137—21no—
148C2×C42×C137D411yescharacteristic, complemented
149#99×C137—24no—
150#99×C137—42no—
151#99×C137—42no—
152#95×C137—21no—
153#95×C137—21no—
154#95×C137—21no—
155#95×C137—22no—
156#95×C137—22no—
157#95×C137—21no—
158#95×C137—21no—
159C24×C137—21no—
160C24×C137—21no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—21no—
164C24×C137—21no—
165C24×C137—42no—
166C24×C137—42no—
167C24×C137C2×D412yes—
168C24×C137C2×D411yescharacteristic
169C24×C137#4112yescomplemented
170C24×C137C2411yescharacteristic
171#41×C137—82no—
172C2×Q8×C137—21no—
173C2×Q8×C137—21no—
174C2×Q8×C137—42no—
175C2×D4×C137—24no—
176C2×D4×C137—21no—
177C2×D4×C137—22no—
178C2×D4×C137—21no—
179C2×D4×C137—22no—
180C2×D4×C137—22no—
181C2×D4×C137—21no—
182C2×D4×C137—21no—
183C2×D4×C137—22no—
184C2×D4×C137—21no—
185C2×D4×C137—22no—
186C2×D4×C137—21no—
187C2×D4×C137—22no—
188C2×D4×C137—22no—
189C2×D4×C137—22no—
190C2×D4×C137—21no—
191C2×D4×C137—21no—
192C2×D4×C137—42no—
193C2×D4×C137—42no—
194C2×D4×C137—42no—
195C2×D4×C137—44no—
196C2×D4×C137—44no—
197C2×D4×C137—44no—
198C22×C4×C137—24no—
199C22×C4×C137—24no—
200C22×C4×C137—24no—
201C22×C4×C137—21no—
202C22×C4×C137—21no—
203C22×C4×C137—21no—
204C22×C4×C137—21no—
205C22×C4×C137—22no—
206C22×C4×C137—22no—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—22no—
211C22×C4×C137—22no—
212C22×C4×C137—42no—
213C22×C4×C137—42no—
214C22×C4×C137—42no—
215C22×C4×C137—42no—
216C22×C4×C137—42no—
217C22×C4×C137—42no—
218C22×C4×C137—42no—
219C22×C4×C137—42no—
220C22×C4×C137—42no—
221C22×C4×C137—42no—
222C22×C4×C137—42no—
223C22×C4×C137—42no—
224C22×C4×C137—41no—
225C22×C4×C137—41no—
226C22×C4×C137—41no—
227C22×C4×C137—41no—
228C22×C4×C137C2×D411yescharacteristic
229C22×C4×C137C2×D412yes—
230C22×C4×C137C2×D411yescharacteristic
231C22×C4×C137C2×D411yescharacteristic
232C22×C4×C137C2×D411yescharacteristic
233C22×C4×C137C2×D411yescharacteristic
234C22×C4×C137C2×D412yes—
235C22×C4×C137C2×D411yescharacteristic
236C22×C4×C137C2×D412yes—
237C22×C4×C137C2×D411yescharacteristic
238C22×C4×C137C2×D411yescharacteristic
239C22×C4×C137C2×D411yescharacteristic
240C4⋊C4×C137—22no—
241C4⋊C4×C137—22no—
242C4⋊C4×C137—22no—
243C4⋊C4×C137—22no—
244C4⋊C4×C137—21no—
245C4⋊C4×C137—22no—
246C4⋊C4×C137—21no—
247C4⋊C4×C137—21no—
248C4⋊C4×C137—21no—
249C4⋊C4×C137—21no—
250C4⋊C4×C137—22no—
251C4⋊C4×C137—21no—
252C4⋊C4×C137—42no—
253C4⋊C4×C137—42no—
254C4⋊C4×C137—42no—
255C4⋊C4×C137—44no—
256C22⋊C4×C137—22no—
257C22⋊C4×C137—22no—
258C22⋊C4×C137—24no—
259C22⋊C4×C137—22no—
260C22⋊C4×C137—22no—
261C22⋊C4×C137—22no—
262C22⋊C4×C137—22no—
263C22⋊C4×C137—21no—
264C22⋊C4×C137—22no—
265C22⋊C4×C137—21no—
266C22⋊C4×C137—22no—
267C22⋊C4×C137—21no—
268C22⋊C4×C137—22no—
269C22⋊C4×C137—21no—
270C22⋊C4×C137—21no—
271C22⋊C4×C137—22no—
272C22⋊C4×C137—22no—
273C22⋊C4×C137—22no—
274C22⋊C4×C137—21no—
275C22⋊C4×C137—22no—
276C22⋊C4×C137—22no—
277C22⋊C4×C137—21no—
278C22⋊C4×C137—44no—
279C22⋊C4×C137—42no—
280C22⋊C4×C137—44no—
281C22⋊C4×C137—44no—
282C22⋊C4×C137—42no—
283C22⋊C4×C137—42no—
284C22⋊C4×C137—44no—
285C22⋊C4×C137#4112yescomplemented
286C42×C137—22no—
287C42×C137—22no—
288C42×C137—21no—
289C42×C137—21no—
290C42×C137—42no—
291C23×C137—22no—
292C23×C137—22no—
293C23×C137—22no—
294C23×C137—22no—
295C23×C137—22no—
296C23×C137—22no—
297C23×C137—22no—
298C23×C137—22no—
299C23×C137—22no—
300C23×C137—21no—
301C23×C137—22no—
302C23×C137—21no—
303C23×C137—21no—
304C23×C137—22no—
305C23×C137—22no—
306C23×C137—41no—
307C23×C137—44no—
308C23×C137—41no—
309C23×C137—41no—
310C23×C137—41no—
311C23×C137—41no—
312C23×C137—41no—
313C23×C137—41no—
314C23×C137—41no—
315C23×C137—44no—
316C23×C137—44no—
317C23×C137—44no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—42no—
321C23×C137—42no—
322C23×C137—41no—
323C23×C137—41no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137C22×D411yescharacteristic
327C23×C137C22×D411yescharacteristic
328C23×C137C22×D411yescharacteristic
329C23×C137C2×#4111yescharacteristic
330C23×C137C2×#4111yescharacteristic
331C23×C137H(5,𝔽2)11yescharacteristic
332C23×C1372−1+411yescharacteristic
333Q8×C137—42no—
334Q8×C137—81no—
335D4×C137—48no—
336D4×C137—42no—
337D4×C137—42no—
338D4×C137—41no—
339D4×C137—41no—
340D4×C137—41no—
341D4×C137—42no—
342D4×C137—42no—
343D4×C137—41no—
344D4×C137—42no—
345D4×C137—81no—
346D4×C137—82no—
347D4×C137—82no—
348D4×C137—88no—
349C2×C4×C137—22no—
350C2×C4×C137—22no—
351C2×C4×C137—22no—
352C2×C4×C137—22no—
353C2×C4×C137—22no—
354C2×C4×C137—22no—
355C2×C4×C137—21no—
356C2×C4×C137—22no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—22no—
360C2×C4×C137—22no—
361C2×C4×C137—21no—
362C2×C4×C137—22no—
363C2×C4×C137—21no—
364C2×C4×C137—22no—
365C2×C4×C137—22no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—44no—
370C2×C4×C137—44no—
371C2×C4×C137—44no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—44no—
379C2×C4×C137—42no—
380C2×C4×C137—41no—
381C2×C4×C137—42no—
382C2×C4×C137—41no—
383C2×C4×C137—42no—
384C2×C4×C137—41no—
385C2×C4×C137—42no—
386C2×C4×C137—42no—
387C2×C4×C137—42no—
388C2×C4×C137—41no—
389C2×C4×C137—42no—
390C2×C4×C137—41no—
391C2×C4×C137—42no—
392C2×C4×C137—42no—
393C2×C4×C137—81no—
394C2×C4×C137—82no—
395C2×C4×C137—82no—
396C2×C4×C137#12011yescharacteristic
397C2×C4×C137#12011yescharacteristic
398C2×C4×C137#12011yescharacteristic
399C2×C4×C137#12011yescharacteristic
400C22×C137—21no—
401C22×C137—21no—
402C22×C137—21no—
403C22×C137—21no—
404C22×C137—21no—
405C22×C137—21no—
406C22×C137—24no—
407C22×C137—24no—
408C22×C137—24no—
409C22×C137—41no—
410C22×C137—41no—
411C22×C137—41no—
412C22×C137—41no—
413C22×C137—42no—
414C22×C137—42no—
415C22×C137—42no—
416C22×C137—42no—
417C22×C137—42no—
418C22×C137—42no—
419C22×C137—42no—
420C22×C137—42no—
421C22×C137—42no—
422C22×C137—42no—
423C22×C137—42no—
424C22×C137—42no—
425C22×C137—42no—
426C22×C137—41no—
427C22×C137—42no—
428C22×C137—41no—
429C22×C137—42no—
430C22×C137—42no—
431C22×C137—41no—
432C22×C137—82no—
433C22×C137—81no—
434C22×C137—82no—
435C22×C137C2×#12011yescharacteristic
436C22×C137#52511yescharacteristic
437C22×C137#53711yescharacteristic
438C22×C137#54611yescharacteristic
439C22×C137#54711yescharacteristic
440C22×C137#54811yescharacteristic
441C22×C137#55011yescharacteristic
442C4×C137—21no—
443C4×C137—21no—
444C4×C137—21no—
445C4×C137—42no—
446C4×C137—41no—
447C4×C137—42no—
448C4×C137—42no—
449C4×C137—41no—
450C4×C137—42no—
451C4×C137—41no—
452C4×C137—42no—
453C4×C137—82no—
454C4×C137—81no—
455C4×C137—82no—
456C4×C137B(4,𝔽2)12yes—
457C2×C137—21no—
458C2×C137—21no—
459C2×C137—21no—
460C2×C137—21no—
461C2×C137—21no—
462C2×C137—21no—
463C2×C137—44no—
464C2×C137—81no—
465C2×C137—82no—
466C2×C137#240711yescharacteristic
467C2×C137C2×B(4,𝔽2)11yescharacteristic
468C2×C137#302511yescharacteristic
469#24140C13711yesmaximal, characteristic, direct product factor, Sylow
470C137#2414011yescharacteristic, direct product factor, Sylow
471#3505C2×C13711yescharacteristic, complemented
472#2848C2×C13711yescharacteristic, complemented
473#2847C2×C13711yescharacteristic, complemented
474C4×#120C2×C13711yescharacteristic, complemented
475#2044C2×C13712yescomplemented
476#2021C2×C13712yescomplemented
477#1996C2×C13711yescharacteristic, complemented
478#1964C2×C13711yescharacteristic, complemented
479#1889C2×C13712yescomplemented
480#1867C2×C13712yescomplemented
481#1799C2×C13711yescharacteristic, complemented
482C24×C4C22×C13711yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C13712yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C13711yescharacteristic
496C2×#121—21no—
497C2×#121C22×C13711yescharacteristic
498C2×#120C22×C13711yescharacteristic
499C2×#120C22×C13712yes—
500#518C22×C13712yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C13711yescharacteristic
503C2×#99C22×C13712yes—
504C2×#99C22×C13712yes—
505C2×#99C22×C13712yes—
506#386—22no—
507#386—21no—
508#386C22×C13712yes—
509#386C22×C13711yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C13712yes—
513#385C22×C13711yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C13711yescharacteristic
517#380C22×C13711yescharacteristic
518#379C22×C13712yes—
519#379C22×C13711yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C13711yescharacteristic
522#342C22×C13712yes—
523#342C22×C13712yes—
524#342C22×C13712yes—
525C25C23×C13711yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C13711yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C13711yescharacteristic, complemented
531C22×D4C23×C13711yescharacteristic
532C22×D4C23×C13712yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C13711yescharacteristic, complemented
541C23×C4C23×C13711yescharacteristic
542C23×C4C23×C13711yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C13711yescharacteristic, complemented
597C2×C4⋊C4D4×C13711yescharacteristic, complemented
598C2×C4⋊C4D4×C13711yescharacteristic, complemented
599C2×C4⋊C4D4×C13712yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C13711yescharacteristic, complemented
610C2×C22⋊C4D4×C13712yescomplemented
611C2×C22⋊C4C23×C13712yes—
612C2×C22⋊C4C23×C13711yescharacteristic
613C2×C22⋊C4C23×C13712yes—
614C2×C22⋊C4C23×C13711yescharacteristic
615C2×C22⋊C4C23×C13712yes—
616C2×C22⋊C4C23×C13711yescharacteristic
617C2×C42—21no—
618C2×C42D4×C13711yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C13712yes—
638C24C2×D4×C13711yescharacteristic
639C24#41×C13712yescomplemented
640C24C24×C13711yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C13711yescharacteristic
699C22×C4C2×D4×C13712yes—
700C22×C4C2×D4×C13711yescharacteristic
701C22×C4C2×D4×C13711yescharacteristic
702C22×C4C2×D4×C13711yescharacteristic
703C22×C4C2×D4×C13711yescharacteristic
704C22×C4C2×D4×C13712yes—
705C22×C4C2×D4×C13711yescharacteristic
706C22×C4C2×D4×C13712yes—
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13711yescharacteristic
709C22×C4C2×D4×C13711yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C13712yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C13711yescharacteristic
797C23C22×D4×C13711yescharacteristic
798C23C22×D4×C13711yescharacteristic
799C23C2×#41×C13711yescharacteristic
800C23C2×#41×C13711yescharacteristic
801C23H(5,𝔽2)×C13711yescharacteristic
802C232−1+4×C13711yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C13711yescharacteristic
867C2×C4#120×C13711yescharacteristic
868C2×C4#120×C13711yescharacteristic
869C2×C4#120×C13711yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C13711yescharacteristic
906C22#525×C13711yescharacteristic
907C22#537×C13711yescharacteristic
908C22#546×C13711yescharacteristic
909C22#547×C13711yescharacteristic
910C22#548×C13711yescharacteristic
911C22#550×C13711yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C13712yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2#2407×C13711yescharacteristic
937C2C2×B(4,𝔽2)×C13711yescharacteristic
938C2#3025×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C137C2semidirect
2. #2848×C137C2semidirect
3. #2847×C137C2semidirect
4. C4×#120×C137C2semidirect
5. #2044×C137C2semidirect
6. #2021×C137C2semidirect
7. #1996×C137C2semidirect
8. #1964×C137C2semidirect
9. #1889×C137C2semidirect
10. #1867×C137C2semidirect
11. #1799×C137C2semidirect
57. C22×Q8×C137D4semidirect
60. C22×D4×C137D4semidirect
70. C23×C4×C137D4semidirect
126. C2×C4⋊C4×C137D4semidirect
127. C2×C4⋊C4×C137D4semidirect
128. C2×C4⋊C4×C137D4semidirect
129. C2×C4⋊C4×C137D4semidirect
139. C2×C22⋊C4×C137D4semidirect
140. C2×C22⋊C4×C137D4semidirect
148. C2×C42×C137D4semidirect
169. C24×C137#41semidirect
285. C22⋊C4×C137#41semidirect
469. #24140C137direct (N × H)
470. C137#24140direct (N × H)
471. #3505C2×C137semidirect
472. #2848C2×C137semidirect
473. #2847C2×C137semidirect
474. C4×#120C2×C137semidirect
475. #2044C2×C137semidirect
476. #2021C2×C137semidirect
477. #1996C2×C137semidirect
478. #1964C2×C137semidirect
479. #1889C2×C137semidirect
480. #1867C2×C137semidirect
481. #1799C2×C137semidirect
527. C22×Q8D4×C137semidirect
530. C22×D4D4×C137semidirect
540. C23×C4D4×C137semidirect
596. C2×C4⋊C4D4×C137semidirect
597. C2×C4⋊C4D4×C137semidirect
598. C2×C4⋊C4D4×C137semidirect
599. C2×C4⋊C4D4×C137semidirect
609. C2×C22⋊C4D4×C137semidirect
610. C2×C22⋊C4D4×C137semidirect
618. C2×C42D4×C137semidirect
639. C24#41×C137semidirect
755. C22⋊C4#41×C137semidirect

Maximal subgroups

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

subgroupindex
#3505×C1372
#2848×C1372
#2847×C1372
C4×#120×C1372
#2044×C1372
#2021×C1372
#1996×C1372
#1964×C1372
#1889×C1372
#1867×C1372
#1799×C1372
#24140137