Finite Group Databasebeta

← C2×#20253018 #27083436

Subgroups — C2×#20253018 #27083436

Order 12032.

2898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094057C211yesmaximal, characteristic, complemented
2C2×#15689634C211yesmaximal, characteristic
3C22×#13094003C211yesmaximal, characteristic, complemented
4#20253018C2116yesmaximal, direct product factor
5C2×#15689381C212yesmaximal, complemented
6C2×#15689369C212yesmaximal, complemented
7C2×#15689364C212yesmaximal, complemented
8C2×#15689352C212yesmaximal, complemented
9C2×#15689165C211yesmaximal, characteristic, complemented
10C2×#15689125C211yesmaximal, characteristic, complemented
11C2×#15689133C211yesmaximal, characteristic, complemented
12C23×M16×C47C211yesmaximal, characteristic, complemented
13C22×#10625350C2211yescharacteristic
14C23×Dic94C2211yescharacteristic
15C2×#13094057—28no—
16C2×#13094057C2218yescomplemented
17C22×Dic188C2212yescomplemented
18C22×#10625325C2212yescomplemented
19#15689634—24no—
20#15689634C2218yes—
21C2×#13094007—21no—
22C2×#13094003—21no—
23C2×#13094003—21no—
24C2×#13094003—24no—
25C2×#13094003C2212yes—
26C2×#13094003C2211yescharacteristic
27C2×#13094003C2212yes—
28C2×#13094003C2211yescharacteristic
29C2×#13094003C2218yescomplemented
30C2×#13093998C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32C2×#13093993—21no—
33C2×C4×C22⋊D47—21no—
34C2×C4×C22⋊D47—21no—
35C2×#13093983C2211yescharacteristic
36C22×C4⋊Dic47C2211yescharacteristic
37C22×Dic47⋊C4—21no—
38C22×C22⋊Dic47—21no—
39#15689381C22116yescomplemented
40#15689369C22116yescomplemented
41#15689364C22116yescomplemented
42#15689352C22116yescomplemented
43#15689165C2218yescomplemented
44C2×#13093958C2212yescomplemented
45C2×#13093956C2212yescomplemented
46#15689133C2218yescomplemented
47#15689125C2218yescomplemented
48C2×#13093949C2212yescomplemented
49C2×#13093949C2212yescomplemented
50C2×#13093949C2212yescomplemented
51C2×#13093946C2212yescomplemented
52C24×C4×C47C2211yescharacteristic
53C22×M16×C47—28no—
54C22×M16×C47C2212yes—
55C22×M16×C47C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C22×M16×C47C2218yescomplemented
58C23×C8×C47C2212yes—
59C2×#10625350—22no—
60C2×#10625350—24no—
61C2×#10625350—24no—
62C2×#10625350C2314yes—
63C22×Dic94—24no—
64C22×Dic94—24no—
65C22×Dic94—21no—
66C22×Dic94—22no—
67C22×Dic94C2312yes—
68C22×Dic94C2311yescharacteristic
69C22×Dic94C2314yes—
70C22×D188C2311yescharacteristic
71C22×C22⋊D47—21no—
72C22×C22⋊D47—21no—
73C22×C22⋊D47—21no—
74C23×Dic47—21no—
75C23×Dic47—21no—
76C22×C4×D47—21no—
77#13094057—232no—
78C2×Dic188—28no—
79C2×Dic188C2318yescomplemented
80C2×#10625325—28no—
81C2×#10625325C2318yescomplemented
82#13094007—28no—
83#13094003—24no—
84#13094003—24no—
85#13094003—28no—
86#13094003—28no—
87#13094003—22no—
88#13094003—22no—
89#13094003C2318yes—
90#13094003C2314yes—
91#13094003C2318yes—
92#13094003C2314yes—
93#13093998—22no—
94#13093998—22no—
95#13093998C2314yes—
96#13093998C2314yes—
97#13093993—28no—
98C4×C22⋊D47—28no—
99C4×C22⋊D47—28no—
100#13093983—22no—
101#13093983C2314yes—
102C2×C4⋊Dic47—21no—
103C2×C4⋊Dic47—22no—
104C2×C4⋊Dic47C2312yes—
105C2×C4⋊Dic47C2314yes—
106C2×C4⋊Dic47C2311yescharacteristic
107C2×C4⋊Dic47C2311yescharacteristic
108C2×Dic47⋊C4—22no—
109C2×Dic47⋊C4—22no—
110C2×Dic47⋊C4—28no—
111C2×Dic47⋊C4—21no—
112C2×Dic47⋊C4—21no—
113C2×C22⋊Dic47—22no—
114C2×C22⋊Dic47—22no—
115C2×C22⋊Dic47—28no—
116C2×C22⋊Dic47—21no—
117C2×C22⋊Dic47—21no—
118C2×C22⋊Dic47—21no—
119C2×(C2×D47)⋊C4—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×C4×Dic47—21no—
122#13093958C2318yescomplemented
123#13093956C2318yescomplemented
124#13093949C2318yescomplemented
125#13093949C2318yescomplemented
126#13093949C2318yescomplemented
127#13093946C2318yescomplemented
128C25×C47D411yescharacteristic
129C23×C4×C47—24no—
130C23×C4×C47—24no—
131C23×C4×C47D411yescharacteristic
132C23×C4×C47D411yescharacteristic
133C23×C4×C47D411yescharacteristic
134C23×C4×C47D414yes—
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2314yes—
138C23×C4×C47C2311yescharacteristic
139C2×M16×C47—24no—
140C2×M16×C47—232no—
141C2×M16×C47—28no—
142C2×M16×C47D418yescomplemented
143C2×M16×C47C2318yes—
144C2×M16×C47C2314yes—
145C2×M16×C47C2314yes—
146C22×C8×C47—28no—
147C22×C8×C47C2312yes—
148C22×C8×C47C2318yes—
149C22×C8×C47C2312yes—
150C24×C47—24no—
151C24×C47—24no—
152C24×C47—42no—
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D414yes—
155C24×C47C2×D411yescharacteristic
156C24×C47C2×D411yescharacteristic
157C23×D47—21no—
158C22×C4×C47—24no—
159C22×C4×C47—24no—
160C22×C4×C47—24no—
161C22×C4×C47—216no—
162C22×C4×C47—22no—
163C22×C4×C47—28no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—28no—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D414yes—
171C22×C4×C47C2×D414yes—
172C22×C4×C47C2×D414yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D412yes—
177C22×C4×C47C2×D414yes—
178C22×C4×C47#4114yes—
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2411yescharacteristic
182C22×C4×C47C2412yes—
183C2×C22⋊D47—24no—
184C2×C22⋊D47—24no—
185C2×C22⋊D47—24no—
186C2×C22⋊D47—44no—
187C2×C22⋊D47—44no—
188C2×C22⋊D47—44no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—24no—
192C22×Dic47—22no—
193C22×Dic47—21no—
194C22×Dic47—24no—
195C22×Dic47—22no—
196C22×Dic47—44no—
197C22×Dic47—44no—
198#10625350—28no—
199#10625350—28no—
200#10625350—48no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—21no—
204C2×D188C2412yes—
205C2×C4×D47—24no—
206C2×C4×D47—44no—
207C2×Dic94—24no—
208C2×Dic94—22no—
209C2×Dic94—28no—
210C2×Dic94—24no—
211C2×Dic94—28no—
212C2×Dic94—22no—
213C2×Dic94—24no—
214C2×Dic94—22no—
215C2×Dic94—21no—
216C2×Dic94—44no—
217C2×Dic94—48no—
218C2×Dic94C2414yes—
219C2×Dic94C2412yes—
220M16×C47—28no—
221M16×C47—216no—
222M16×C47C2×D4116yescomplemented
223C2×C8×C47—24no—
224C2×C8×C47—216no—
225C2×C8×C47C2×D418yes—
226C2×C8×C47C2414yes—
227C2×C8×C47C2414yes—
228C22⋊Dic47—28no—
229C22⋊Dic47—28no—
230C22⋊Dic47—24no—
231C22⋊Dic47—24no—
232C22⋊Dic47—24no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235C4⋊Dic47—24no—
236C4⋊Dic47—22no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47C2414yes—
240C4⋊Dic47C2412yes—
241C4⋊Dic47C2412yes—
242Dic47⋊C4—28no—
243Dic47⋊C4—28no—
244Dic47⋊C4—24no—
245Dic47⋊C4—24no—
246C4×Dic47—24no—
247Dic188—216no—
248#10625325—216no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—28no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—28no—
257C23×C47—22no—
258C23×C47—44no—
259C23×C47—416no—
260C23×C47#12114yes—
261C23×C47#13714yescomplemented
262C23×C47C22×D412yes—
263C23×C47C22×D412yes—
264C23×C47C22×D412yes—
265C23×C47C22×D411yescharacteristic
266C22×D47—22no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C2×C4×C47—28no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—24no—
274C2×C4×C47—24no—
275C2×C4×C47—28no—
276C2×C4×C47—28no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47#12114yes—
282C2×C4×C47#12118yes—
283C2×C4×C47C22×D412yes—
284C2×C4×C47C22×D414yes—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4112yes—
290C2×C4×C47C2×#4114yes—
291C2×C4×C47C2511yescharacteristic
292C22⋊D47—48no—
293C22⋊D47—48no—
294C22⋊D47—48no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—22no—
300C2×Dic47—48no—
301C2×Dic47—48no—
302C2×Dic47—44no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—44no—
306C2×Dic47—42no—
307D188—22no—
308D188—22no—
309D188—42no—
310C4×D47—48no—
311Dic94—24no—
312Dic94—22no—
313Dic94—24no—
314Dic94—22no—
315Dic94—44no—
316Dic94—48no—
317Dic94—42no—
318C8×C47—24no—
319C8×C47C22×D418yes—
320C2×#3056—471nomaximal, Sylow
321C22×C47—22no—
322C22×C47—28no—
323C22×C47—28no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—416no—
331C22×C47—44no—
332C22×C47C2×#12114yes—
333C22×C47C2×#12112yes—
334C22×C47C2×#13712yes—
335C22×C47C2×#13714yescomplemented
336C22×C47#57512yes—
337C22×C47C23×D411yescharacteristic
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—42no—
341C2×D47—84no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47C2×#12112yes—
345C4×C47C2×#12114yes—
346C4×C47C23×D411yescharacteristic
347C4×C47C22×#4111yescharacteristic
348Dic47—44no—
349Dic47—42no—
350Dic47—42no—
351Dic47—44no—
352Dic47—42no—
353C22×#137—471no—
354C23×M16D4711yescharacteristic, complemented
355C2×#525—471no—
356C22×C22⋊Q8—471no—
357#3056—4716no—
358C2×#470—472no—
359C2×#468—472no—
360C2×#467—472no—
361C2×#465—472no—
362C2×#428—471no—
363C2×#417—471no—
364C2×#419—471no—
365C2×C47—24no—
366C2×C47—24no—
367C2×C47—42no—
368C2×C47#305614yescomplemented
369C2×C47C22×#12111yescharacteristic
370C2×C47C22×#13711yescharacteristic
371C2×C47C2×#57511yescharacteristic
372D47—82no—
373C22×#41—471no—
374C23×Q8—471no—
375C24×C4C2×D4711yescharacteristic
376C2×#137—478no—
377C2×#137—948no—
378C22×Q16—472no—
379C22×SD16—472no—
380C22×M16—28no—
381C22×M16C2×D4711yescharacteristic
382C22×M16C2×D4712yes—
383C22×M16C2×D4711yescharacteristic
384C22×M16C2×D4718yescomplemented
385C23×C8C2×D4712yes—
386#525—478no—
387#525—944no—
388C2×#123—941no—
389C2×C22⋊Q8—472no—
390C2×C22⋊Q8—472no—
391C2×C22⋊Q8—478no—
392C2×C22⋊Q8—471no—
393C2×C22⋊Q8—471no—
394C2×C22⋊Q8—941no—
395C2×C22⋊Q8—941no—
396C2×C22⋊Q8—944no—
397C2×#121—471no—
398C2×#121—471no—
399C2×#120—941no—
400C2×C4×D4—941no—
401C2×C4×D4—941no—
402C2×#117—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—941no—
405C22×C22⋊C4—941no—
406#470—4716no—
407#468—4716no—
408#467—4716no—
409#465—4716no—
410#428—478no—
411C2×#107—472no—
412C2×#106—472no—
413#419—478no—
414#417—478no—
415C2×#103—472no—
416C2×#103—472no—
417C2×#103—472no—
418C2×#102—472no—
419C47C2×#305611yescharacteristic, complemented, Sylow
420C25D18811yescharacteristic
421C2×#41—474no—
422C2×#41—942no—
423C2×#41—944no—
424C2×#41—944no—
425C22×Q8—472no—
426C22×Q8—471no—
427C22×Q8—474no—
428C22×Q8—942no—
429C22×Q8—941no—
430C22×Q8—944no—
431C22×Q8—944no—
432C22×D4—471no—
433C22×D4—941no—
434C22×D4—941no—
435C22×D4—941no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—941no—
439C23×C4—941no—
440C23×C4—941no—
441C23×C4D18811yescharacteristic
442C23×C4D18811yescharacteristic
443C23×C4D18811yescharacteristic
444C23×C4D18814yes—
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4714yes—
448C23×C4C22×D4711yescharacteristic
449#137—9432no—
450C2×Q16—478no—
451C2×Q16—948no—
452C2×SD16—478no—
453C2×SD16—948no—
454C2×M16—24no—
455C2×M16—232no—
456C2×M16—28no—
457C2×M16C22⋊D4718yescomplemented
458C2×M16C22×D4714yes—
459C2×M16C22×D4718yes—
460C2×M16C22×D4714yes—
461C22×C8—28no—
462C22×C8C22×D4712yes—
463C22×C8C22×D4718yes—
464C22×C8C22×D4712yes—
465#123—948no—
466C22⋊Q8—478no—
467C22⋊Q8—478no—
468C22⋊Q8—474no—
469C22⋊Q8—474no—
470C22⋊Q8—948no—
471C22⋊Q8—948no—
472C22⋊Q8—944no—
473C22⋊Q8—944no—
474C22⋊Q8—942no—
475C22⋊Q8—942no—
476#121—474no—
477#121—474no—
478#121—942no—
479#121—942no—
480#120—948no—
481C4×D4—948no—
482C4×D4—948no—
483#117—474no—
484#117—942no—
485C2×C4⋊C4—472no—
486C2×C4⋊C4—474no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—942no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—948no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C22⋊C4—948no—
497C2×C22⋊C4—942no—
498C2×C22⋊C4—942no—
499C2×C22⋊C4—941no—
500C2×C22⋊C4—941no—
501C2×C22⋊C4—941no—
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C42—941no—
505#107—478no—
506#106—478no—
507#103—478no—
508#103—478no—
509#103—478no—
510#102—478no—
511C24—24no—
512C24—24no—
513C24—42no—
514C24—941no—
515C24C2×D18811yescharacteristic
516C24C2×D18814yes—
517C24C2×D18811yescharacteristic
518C24C2×D18811yescharacteristic
519#41—948no—
520#41—948no—
521#41—1888no—
522C2×Q8—474no—
523C2×Q8—472no—
524C2×Q8—944no—
525C2×Q8—942no—
526C2×Q8—941no—
527C2×Q8—944no—
528C2×Q8—942no—
529C2×Q8—948no—
530C2×Q8—944no—
531C2×Q8—948no—
532C2×Q8—942no—
533C2×Q8—1884no—
534C2×Q8—1888no—
535C2×D4—472no—
536C2×D4—944no—
537C2×D4—944no—
538C2×D4—944no—
539C2×D4—942no—
540C2×D4—941no—
541C2×D4—942no—
542C2×D4—1884no—
543C2×D4—1884no—
544C2×D4—1884no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—216no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—944no—
556C22×C4—944no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—942no—
560C22×C4—941no—
561C22×C4—942no—
562C22×C4—944no—
563C22×C4—1884no—
564C22×C4—1884no—
565C22×C4—1884no—
566C22×C4C2×D18814yes—
567C22×C4C2×D18814yes—
568C22×C4C2×D18814yes—
569C22×C4C2×D18812yes—
570C22×C4C2×D18812yes—
571C22×C4C2×D18811yescharacteristic
572C22×C4C2×D18811yescharacteristic
573C22×C4C2×D18812yes—
574C22×C4C2×D18811yescharacteristic
575C22×C4#1062535014yes—
576C22×C4C2×C22⋊D4714yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4712yes—
580C22×C4C23×D4711yescharacteristic
581Q16—9416no—
582SD16—9416no—
583M16—28no—
584M16—216no—
585M16C2×C22⋊D47116yescomplemented
586C2×C8—24no—
587C2×C8—216no—
588C2×C8C2×C22⋊D4718yes—
589C2×C8C23×D4714yes—
590C2×C8C23×D4714yes—
591C4⋊C4—474no—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—948no—
595C4⋊C4—948no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—942no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C22⋊C4—948no—
603C22⋊C4—948no—
604C22⋊C4—944no—
605C22⋊C4—944no—
606C22⋊C4—944no—
607C22⋊C4—944no—
608C22⋊C4—944no—
609C42—944no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—28no—
615C23—22no—
616C23—22no—
617C23—28no—
618C23—22no—
619C23—44no—
620C23—416no—
621C23—942no—
622C23—1882no—
623C23—1882no—
624C23—1882no—
625C23#1309399814yes—
626C23#1309405714yescomplemented
627C23C22×D18812yes—
628C23C22×D18812yes—
629C23C22×D18812yes—
630C23C22×D18811yescharacteristic
631Q8—944no—
632Q8—942no—
633Q8—944no—
634Q8—942no—
635Q8—1888no—
636Q8—1884no—
637Q8—1882no—
638D4—942no—
639D4—942no—
640D4—1888no—
641D4—1888no—
642D4—1888no—
643D4—1882no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—944no—
658C2×C4—942no—
659C2×C4—944no—
660C2×C4—1888no—
661C2×C4—1882no—
662C2×C4—1888no—
663C2×C4—1884no—
664C2×C4—1882no—
665C2×C4—1884no—
666C2×C4—1882no—
667C2×C4—1888no—
668C2×C4#1309399814yes—
669C2×C4#1309399818yes—
670C2×C4C22×C22⋊D4712yes—
671C2×C4C22×C22⋊D4714yes—
672C2×C4C22×D18812yes—
673C2×C4C22×D18812yes—
674C2×C4C22×D18812yes—
675C2×C4C22×D18811yescharacteristic
676C2×C4C2×#1062535012yes—
677C2×C4C2×#1062535014yes—
678C2×C4C24×D4711yescharacteristic
679C8—24no—
680C8C22×C22⋊D4718yes—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—28no—
685C22—28no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—416no—
691C22—44no—
692C22—3764no—
693C22—1882no—
694C22—1882no—
695C22—1882no—
696C22C2×#1309399814yes—
697C22C2×#1309399812yes—
698C22C2×#1309405712yes—
699C22C2×#1309405714yescomplemented
700C22#1568992312yes—
701C22C23×D18811yescharacteristic
702C4—22no—
703C4—22no—
704C4—1882no—
705C4—1884no—
706C4—1882no—
707C4—1882no—
708C4—1884no—
709C4C2×#1309399814yes—
710C4C2×#1309399812yes—
711C4C23×C22⋊D4711yescharacteristic
712C4C22×#1062535011yescharacteristic
713C2—24no—
714C2—24no—
715C2—42no—
716C2—3762no—
717C2#2025301814yesdirect product factor
718C2C22×#1309399811yescharacteristic
719C2C22×#1309405711yescharacteristic
720C2C2×#1568992311yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC23×M16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689634C2
hypercenterC23×M16D47
hypocenterC47C2×#3056
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
1. C22×#13094057C2semidirect
3. C22×#13094003C2semidirect
4. #20253018C2direct (N × H)
5. C2×#15689381C2semidirect
6. C2×#15689369C2semidirect
7. C2×#15689364C2semidirect
8. C2×#15689352C2semidirect
9. C2×#15689165C2semidirect
10. C2×#15689125C2semidirect
11. C2×#15689133C2semidirect
12. C23×M16×C47C2semidirect
16. C2×#13094057C22semidirect
17. C22×Dic188C22semidirect
18. C22×#10625325C22semidirect
29. C2×#13094003C22semidirect
39. #15689381C22semidirect
40. #15689369C22semidirect
41. #15689364C22semidirect
42. #15689352C22semidirect
43. #15689165C22semidirect
44. C2×#13093958C22semidirect
45. C2×#13093956C22semidirect
46. #15689133C22semidirect
47. #15689125C22semidirect
48. C2×#13093949C22semidirect
49. C2×#13093949C22semidirect
50. C2×#13093949C22semidirect
51. C2×#13093946C22semidirect
57. C22×M16×C47C22semidirect
79. C2×Dic188C23semidirect
81. C2×#10625325C23semidirect
122. #13093958C23semidirect
123. #13093956C23semidirect
124. #13093949C23semidirect
125. #13093949C23semidirect
126. #13093949C23semidirect
127. #13093946C23semidirect
142. C2×M16×C47D4semidirect
222. M16×C47C2×D4semidirect
261. C23×C47#137semidirect
335. C22×C47C2×#137semidirect
354. C23×M16D47semidirect
368. C2×C47#3056semidirect
384. C22×M16C2×D47semidirect
419. C47C2×#3056semidirect
457. C2×M16C22⋊D47semidirect
585. M16C2×C22⋊D47semidirect
626. C23#13094057semidirect
699. C22C2×#13094057semidirect
717. C2#20253018direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940572
C2×#156896342
C22×#130940032
#202530182
C2×#156893812
C2×#156893692
C2×#156893642
C2×#156893522
C2×#156891652
C2×#156891252
C2×#156891332
C23×M16×C472
C2×#305647