Finite Group Databasebeta

← #27124855

Subgroups — #27124855

Order 12032.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257307C214yesmaximal, complemented
2#20257289C214yesmaximal, complemented
3#20257283C212yesmaximal, complemented
4#20257279C212yesmaximal, complemented
5#20257275C211yesmaximal, characteristic, complemented
6#20257274C211yesmaximal, characteristic, complemented
7#20257262C211yesmaximal, characteristic, complemented
8#20257245C214yesmaximal, complemented
9#20257232C214yesmaximal, complemented
10#20257215C218yesmaximal, complemented
11#20256987C214yesmaximal, complemented
12#20256984C214yesmaximal, complemented
13#20256939C218yesmaximal, complemented
14#20256772C214yesmaximal, complemented
15#20256719C212yesmaximal, complemented
16#20256683C214yesmaximal, complemented
17#533×D47C211yesmaximal, characteristic, complemented
18C2×#15689671C211yesmaximal, characteristic, complemented
19#20256586C212yesmaximal, complemented
20C4×#41×D47C211yesmaximal, characteristic, complemented
21C47×#3508C211yesmaximal, characteristic, complemented
22C22×#10625352C2212yes—
23C2×#41×D47C2211yescharacteristic
24#15689859C2218yescomplemented
25#15689859C2214yescomplemented
26#15689856C2218yescomplemented
27#15689852C2214yescomplemented
28#15689851C2214yescomplemented
29#15689846C2214yescomplemented
30#15689843C2214yescomplemented
31#15689843C2218yescomplemented
32#15689842C2218yescomplemented
33#15689842C2218yescomplemented
34#15689837C2218yescomplemented
35#15689832C2218yescomplemented
36#15689823C2218yescomplemented
37#15689820C2218yescomplemented
38#15689820C22116yescomplemented
39#15689818C22116yescomplemented
40#15689816C22116yescomplemented
41#15689815C2218yescomplemented
42#15689813C2218yescomplemented
43#15689810C22116yescomplemented
44#15689804C22116yescomplemented
45#15689799C22116yescomplemented
46#15689793C2214yescomplemented
47#15689781C2218yescomplemented
48#15689780C2218yescomplemented
49#15689772C2218yescomplemented
50#15689767C2218yescomplemented
51#15689740C2218yescomplemented
52#15689738C2218yescomplemented
53#15689736C2214yescomplemented
54#15689735C2214yescomplemented
55#15689727C2214yescomplemented
56#15689716C22116yescomplemented
57#15689705C22116yescomplemented
58#15689702C2218yescomplemented
59#15689699C2212yes—
60#15689694C2212yes—
61#15689693C2214yescomplemented
62#15689690C2212yes—
63#15689686C2214yescomplemented
64#15689683C2218yes—
65#15689680C2214yescomplemented
66#15689680C2211yescharacteristic, complemented
67#15689679C2212yescomplemented
68#15689678C2214yescomplemented
69#15689678C2212yescomplemented
70#15689677C2214yescomplemented
71#15689676C2212yescomplemented
72#15689675C2214yescomplemented
73#15689672C2214yescomplemented
74#15689671C2212yes—
75#15689671C2212yes—
76#15689671C2214yes—
77#15689671C2212yescomplemented
78#15689671C2214yescomplemented
79#15689671C2212yescomplemented
80#15689671C2214yescomplemented
81#15689671C2214yescomplemented
82C2×#13094024C2211yescharacteristic, complemented
83C4⋊Q8×D47C2212yescomplemented
84#15689655C2218yescomplemented
85#15689655C2218yescomplemented
86#15689654C2218yescomplemented
87#15689654C22116yescomplemented
88#15689654C2218yescomplemented
89#15689652C2218yescomplemented
90#15689652C2218yescomplemented
91#15689650C22116yescomplemented
92#125×D47C2212yescomplemented
93C2×#13094011C2212yescomplemented
94#15689633C2218yescomplemented
95#15689633C2218yescomplemented
96#15689630C2218yescomplemented
97#15689629C2218yes—
98C22⋊Q8×D47C2214yes—
99C2×#13093995C2214yes—
100#15689602C2218yescomplemented
101#15689602C2218yescomplemented
102#15689600C2212yescomplemented
103#15689600C2212yescomplemented
104#15689598C2212yescomplemented
105#15689596C2218yes—
106#41×Dic47C2211yescharacteristic
107#41×Dic47C2218yescomplemented
108C4×#10625354C2212yescomplemented
109C4×#10625350C2211yescharacteristic
110C4×#10625350C2212yescomplemented
111#15689591C2211yescharacteristic
112#15689591C2212yescomplemented
113C4×#10625352C2214yes—
114C4×#10625352C2218yescomplemented
115C4×#10625352C2212yescomplemented
116C4×#10625352C2218yescomplemented
117C4×#10625352C2218yescomplemented
118C4×Q8×D47C2212yescomplemented
119C4×Q8×D47C2214yescomplemented
120C2×D4×Dic47C2214yescomplemented
121C4×D4×D47C2214yes—
122C4×D4×D47C2212yescomplemented
123C2×#13093980C2218yescomplemented
124#117×D47C2211yescharacteristic
125#117×D47C2212yes—
126#117×D47C2212yescomplemented
127C2×C42×D47C2211yescharacteristic
128C2×C42×D47C2212yescomplemented
129C47×#559C2214yescomplemented
130C47×#550C2214yescomplemented
131C47×#546C2218yescomplemented
132C47×#540C2214yescomplemented
133C47×#535C2212yes—
134C47×#533C2211yescharacteristic, complemented
135C47×#532C2214yescomplemented
136C2×#127×C47C2211yescharacteristic, complemented
137C47×#518C2212yescomplemented
138C4×#41×C47C2211yescharacteristic
139C2×#10625354C2311yescharacteristic
140C2×#10625350C2311yescharacteristic
141C2×#10625350C2312yes—
142C2×#10625352—216no—
143C2×#10625352C2312yes—
144C2×#10625352C2314yes—
145C2×#10625352C2311yescharacteristic
146C2×#10625352C2314yes—
147C2×#10625352C2314yes—
148C2×#10625352C2314yes—
149C2×#10625352C2318yes—
150#41×D47—28no—
151C22×Dic94C2312yes—
152C2×Q8×D47C2311yescharacteristic
153C2×Q8×D47C2314yes—
154C22×C22⋊D47C2314yes—
155C2×D4×D47C2312yes—
156C2×D4×D47C2311yescharacteristic
157C23×Dic47C2314yes—
158C22×C4×D47C2312yes—
159C22×C4×D47C2312yes—
160C22×C4×D47C2314yes—
161C22×C4×D47C2311yescharacteristic
162#13094024C2312yes—
163#13094024C2314yes—
164#13094024C2314yes—
165#13094024C2312yes—
166#13094024C2312yes—
167#13094023C2314yes—
168#13094023C2314yes—
169#13094022C2314yes—
170#13094022C2314yes—
171#13094020C2314yes—
172#13094019C23116yes—
173#13094017C23116yes—
174#13094017C23116yes—
175#13094017C23116yes—
176#13094017C23116yes—
177#13094017C23116yes—
178#13094016C2312yes—
179#13094016C2318yes—
180#13094015C23116yes—
181#13094015C2318yes—
182#13094015C2314yes—
183#13094014C23116yes—
184#13094014C2318yes—
185#13094012C2314yes—
186#13094011C2314yes—
187#13094011C23116yes—
188#13094011C2318yes—
189#13094011C2318yes—
190#13094011C2314yes—
191#13094011C2314yes—
192#13094011C2314yes—
193#13094010C23116yes—
194#13094008C2318yes—
195#13094007C23116yes—
196#13094006C23116yes—
197#13094006C23116yes—
198#13094005C23116yes—
199#13094005C23116yes—
200#13094005C2318yes—
201#13094005C23116yes—
202#13094004C2318yes—
203#13094004C2314yes—
204#13094003C2318yes—
205#13094003C23116yes—
206#13094003C2314yes—
207#13094003C2318yes—
208#13094002C2318yes—
209#13094001C23116yes—
210#13094001C2318yes—
211#13094001C23116yes—
212#13094000C2318yes—
213#13094000C2314yes—
214#13093997C23116yes—
215#13093996C23116yes—
216#13093996C23116yes—
217#13093995C2318yes—
218#13093995C2318yes—
219#13093995C2318yes—
220#13093995C23116yes—
221#13093995C2318yes—
222#13093995C2318yes—
223#13093995C2318yes—
224#13093993C2318yes—
225#13093992C23116yes—
226Q8×Dic47C2318yes—
227Q8×Dic47C2312yes—
228Q8×Dic47C2314yes—
229C4×Dic94C2318yes—
230C4×Dic94C2318yes—
231C4×Dic94C2314yes—
232C4×Dic94C2314yes—
233C4×Dic94C2318yes—
234C4×Dic94C2312yes—
235C4×Dic94C2318yes—
236#13093989C2318yes—
237#13093989C2314yes—
238#13093989C2312yes—
239#13093989C2314yes—
240#13093989C2318yes—
241#13093989C2318yes—
242C4×D188C2314yes—
243C4×D188C2312yes—
244D4×Dic47C2318yes—
245D4×Dic47C2318yes—
246D4×Dic47C2318yes—
247D4×Dic47C2318yes—
248D4×Dic47C2314yes—
249D4×Dic47C23116yes—
250D4×Dic47C2318yes—
251D4×Dic47C2312yes—
252D4×Dic47C2318yes—
253D4×Dic47C2318yes—
254D4×Dic47C23116yes—
255#13093986C2314yes—
256#13093986C2312yes—
257C4×C22⋊D47C2314yes—
258C4×C22⋊D47C2314yes—
259C4×C22⋊D47C2314yes—
260C4×C22⋊D47C23116yes—
261C4×C22⋊D47C23116yes—
262C4×C22⋊D47C23116yes—
263(C22⋊D47)⋊C4C23116yes—
264(C22⋊D47)⋊C4C2314yes—
265(C22⋊D47)⋊C4C2314yes—
266(C22⋊D47)⋊C4C2314yes—
267(C22⋊D47)⋊C4C23116yes—
268(C22⋊D47)⋊C4C23116yes—
269#13093983C2312yes—
270#13093983C23116yes—
271#13093983C2318yes—
272#13093983C2311yescharacteristic
273#13093983C2312yes—
274#13093982C2318yes—
275#13093982C2312yes—
276#13093982C2314yes—
277#13093982C2314yes—
278#13093981C2312yes—
279#13093981C2312yes—
280#13093981C2312yes—
281#13093981C2314yes—
282#13093980C2318yes—
283#13093980C2318yes—
284#13093980C23116yes—
285#13093980C23116yes—
286#13093980C2312yes—
287#13093980C2314yes—
288#13093980C2314yes—
289#13093980C23116yes—
290C2×C4⋊Dic47C2314yes—
291C2×Dic47⋊C4C23116yes—
292C4⋊C4×D47C2318yes—
293C4⋊C4×D47C2314yes—
294C4⋊C4×D47C2312yes—
295C4⋊C4×D47C2314yes—
296C4⋊C4×D47C2314yes—
297C2×C22⋊Dic47C2318yes—
298C2×C22⋊Dic47C2318yes—
299C22⋊C4×D47C2312yes—
300C22⋊C4×D47C2314yes—
301C22⋊C4×D47C2314yes—
302C2×C4×Dic47C2312yes—
303C2×C4×Dic47C2311yescharacteristic
304C2×C4×Dic47C2314yes—
305C2×C4×Dic47C2312yes—
306C2×C4×Dic47C23116yes—
307C42×D47C2311yescharacteristic
308C42×D47C2311yescharacteristic
309C42×D47C2312yes—
310C42×D47C2312yes—
311C42×D47C2311yescharacteristic
312C42×D47C2311yescharacteristic
313C42×D47C2312yes—
314C42×D47C2314yes—
315C42×D47C2314yes—
316C42×D47C2312yes—
317C42×D47C2312yes—
318C42×D47C2314yes—
319C2×#41×C47C2311yescharacteristic
320C2×#41×C47C2318yes—
321C22×D4×C47C2312yes—
322C22×D4×C47C2314yes—
323C4⋊Q8×C47C2312yes—
324#127×C47C2314yes—
325#127×C47C2312yes—
326#127×C47C2312yes—
327#127×C47C2314yes—
328#125×C47C2312yes—
329#124×C47C2318yes—
330#124×C47C2314yes—
331#123×C47C23116yes—
332C22⋊Q8×C47C2314yes—
333#121×C47C2318yes—
334#121×C47C2318yes—
335#121×C47C23116yes—
336#120×C47C2318yes—
337C4×Q8×C47C2312yes—
338C4×Q8×C47C2314yes—
339C4×D4×C47C2318yes—
340C4×D4×C47C2314yes—
341C4×D4×C47C2312yes—
342C4×D4×C47C2318yes—
343C4×D4×C47C2318yes—
344#117×C47C2312yes—
345#117×C47C2311yescharacteristic
346#117×C47C2312yes—
347C2×C22⋊C4×C47C2318yes—
348C2×C42×C47C2311yescharacteristic
349C2×C42×C47C2312yes—
350C24×C47C2414yes—
351C23×D47C2412yes—
352C23×D47C2411yescharacteristic
353#41×C47—24no—
354#41×C47—416no—
355C2×Q8×C47C2411yescharacteristic
356C2×Q8×C47C2414yes—
357C2×D4×C47—28no—
358C2×D4×C47—48no—
359C2×D4×C47C2412yes—
360C2×D4×C47C2414yes—
361C2×D4×C47C2414yes—
362C2×D4×C47C2411yescharacteristic
363C2×D4×C47C2418yes—
364C2×D4×C47C24116yes—
365C2×D4×C47C2418yes—
366C22×C4×C47C2412yes—
367C22×C4×C47C2414yes—
368C22×C4×C47C2412yes—
369C22×C4×C47C24116yes—
370C22×C4×C47C2411yescharacteristic
371C2×C22⋊D47—216no—
372C2×C22⋊D47C2418yes—
373C2×C22⋊D47C2412yes—
374C2×C22⋊D47C2412yes—
375C2×C22⋊D47C2418yes—
376C2×C22⋊D47C2412yes—
377C2×C22⋊D47C24116yes—
378C22×Dic47—216no—
379C22×Dic47C2418yes—
380C22×Dic47C2412yes—
381C22×Dic47C2414yes—
382C22×Dic47C2418yes—
383C22×Dic47C2412yes—
384C22×Dic47C2414yes—
385C22×Dic47C24116yes—
386C22×Dic47C2411yescharacteristic
387#10625354—24no—
388Q8×D47—24no—
389Q8×D47—48no—
390#10625352—28no—
391#10625352—24no—
392#10625352—216no—
393#10625352—216no—
394#10625352—216no—
395#10625352—216no—
396#10625352—416no—
397D4×D47—28no—
398D4×D47—24no—
399#10625350—24no—
400#10625350—28no—
401C2×D188C2412yes—
402C2×D188C2411yescharacteristic
403C2×C4×D47—28no—
404C2×C4×D47—48no—
405C2×C4×D47—44no—
406C2×C4×D47#4118yescomplemented
407C2×C4×D47C2412yes—
408C2×C4×D47C2412yes—
409C2×C4×D47C2412yes—
410C2×C4×D47C2412yes—
411C2×C4×D47C2412yes—
412C2×C4×D47C2414yes—
413C2×C4×D47C2414yes—
414C2×C4×D47C2412yes—
415C2×C4×D47C2412yes—
416C2×C4×D47C2414yes—
417C2×C4×D47C2418yes—
418C2×C4×D47C2411yescharacteristic
419C2×C4×D47C2411yescharacteristic
420C2×C4×D47C2411yescharacteristic
421C2×C4×D47C2411yescharacteristic
422C2×Dic94—28no—
423C2×Dic94C2412yes—
424C2×Dic94C2414yes—
425C2×Dic94C2411yescharacteristic
426C2×Dic94C2414yes—
427C2×Dic94C2414yes—
428C2×Dic94C2418yes—
429C4⋊C4×C47C2412yes—
430C4⋊C4×C47C2414yes—
431C4⋊C4×C47C2414yes—
432C4⋊C4×C47C2414yes—
433C4⋊C4×C47C2418yes—
434C22⋊C4×C47C2412yes—
435C22⋊C4×C47C2414yes—
436C22⋊C4×C47C24116yes—
437C22⋊C4×C47C2414yes—
438C22⋊C4×C47C24116yes—
439C42×C47C2411yescharacteristic
440C42×C47C2412yes—
441C42×C47C2411yescharacteristic
442C42×C47C2414yes—
443C42×C47C2412yes—
444C42×C47C2414yes—
445C22⋊Dic47C2412yes—
446C22⋊Dic47C2414yes—
447C22⋊Dic47C2414yes—
448C22⋊Dic47C24116yes—
449C22⋊Dic47C24116yes—
450C22⋊Dic47C24116yes—
451C22⋊Dic47C24116yes—
452C22⋊Dic47C24116yes—
453(C2×D47)⋊C4C2414yes—
454(C2×D47)⋊C4C2418yes—
455(C2×D47)⋊C4C2414yes—
456(C2×D47)⋊C4C2414yes—
457(C2×D47)⋊C4C24116yes—
458C4⋊Dic47C2412yes—
459C4⋊Dic47C2414yes—
460C4⋊Dic47C2414yes—
461C4⋊Dic47C2414yes—
462C4⋊Dic47C2418yes—
463C4⋊Dic47C2418yes—
464C4⋊Dic47C2418yes—
465C4⋊Dic47C24116yes—
466Dic47⋊C4C2414yes—
467Dic47⋊C4C2418yes—
468Dic47⋊C4C2418yes—
469Dic47⋊C4C2414yes—
470Dic47⋊C4C2414yes—
471Dic47⋊C4C2418yes—
472Dic47⋊C4C2418yes—
473Dic47⋊C4C24116yes—
474Dic47⋊C4C24116yes—
475Dic47⋊C4C24116yes—
476C4×Dic47C2412yes—
477C4×Dic47C2411yescharacteristic
478C4×Dic47C2414yes—
479C4×Dic47C2414yes—
480C4×Dic47C2412yes—
481C4×Dic47C2412yes—
482C4×Dic47C2411yescharacteristic
483C4×Dic47C2414yes—
484C4×Dic47C2412yes—
485C4×Dic47C2412yes—
486C4×Dic47C2414yes—
487C4×Dic47C2412yes—
488C4×Dic47C2418yes—
489C4×Dic47C2414yes—
490C4×Dic47C24116yes—
491C4×Dic47C24116yes—
492C23×C47—28no—
493C23×C47—48no—
494C23×C47C2512yes—
495C23×C47C2518yes—
496C23×C47C2511yescharacteristic
497C22×D47—24no—
498C22×D47—42no—
499C22×D47—44no—
500C22×D47C2×#4114yes—
501C22×D47C2512yes—
502C22×D47C2511yescharacteristic
503C22×D47C2511yescharacteristic
504Q8×C47—22no—
505Q8×C47—28no—
506D4×C47—24no—
507D4×C47—22no—
508D4×C47—28no—
509D4×C47—28no—
510D4×C47—216no—
511D4×C47—48no—
512D4×C47—416no—
513C2×C4×C47—24no—
514C2×C4×C47—24no—
515C2×C4×C47—28no—
516C2×C4×C47—416no—
517C2×C4×C47C2×#4114yes—
518C2×C4×C47C2514yes—
519C2×C4×C47C2518yes—
520C2×C4×C47C2512yes—
521C2×C4×C47C2512yes—
522C2×C4×C47C2511yescharacteristic
523C2×C4×C47C2511yescharacteristic
524C2×C4×C47C2512yes—
525C22⋊D47—24no—
526C22⋊D47—24no—
527C22⋊D47—216no—
528C22⋊D47—216no—
529C22⋊D47—24no—
530C22⋊D47—416no—
531C2×Dic47—28no—
532C2×Dic47—24no—
533C2×Dic47—216no—
534C2×Dic47—216no—
535C2×Dic47—42no—
536C2×Dic47—44no—
537C2×Dic47—416no—
538C2×Dic47C2×#4114yes—
539C2×Dic47C2514yes—
540C2×Dic47C2512yes—
541C2×Dic47C2518yes—
542C2×Dic47C2518yes—
543C2×Dic47C2512yes—
544C2×Dic47C2512yes—
545C2×Dic47C2511yescharacteristic
546C2×Dic47C2511yescharacteristic
547D188—24no—
548D188—22no—
549C4×D47—24no—
550C4×D47—24no—
551C4×D47—24no—
552C4×D47—28no—
553C4×D47—24no—
554C4×D47—24no—
555C4×D47—42no—
556C4×D47—44no—
557C4×D47—42no—
558C4×D47—44no—
559C4×D47—48no—
560C4×D47C2×#4114yes—
561C4×D47C2×#4114yes—
562C4×D47C2×#4114yes—
563C4×D47C2×#4114yes—
564Dic94—28no—
565Dic94—28no—
566Dic94—22no—
567Dic94—28no—
568Dic94—24no—
569Dic94—48no—
570#62815—471nomaximal, Sylow
571C22×C47—22no—
572C22×C47—28no—
573C22×C47—22no—
574C22×C47—216no—
575C22×C47—24no—
576C22×C47—88no—
577C22×C47C22×#4112yes—
578C22×C47C2611yescharacteristic
579C2×D47—22no—
580C2×D47—22no—
581C2×D47—22no—
582C2×D47—24no—
583C2×D47—44no—
584C2×D47—48no—
585C2×D47C22×#4112yes—
586C2×D47C22×#4112yes—
587C4×C47—22no—
588C4×C47—28no—
589C4×C47—24no—
590C4×C47—22no—
591C4×C47C22×#4112yes—
592C4×C47C22×#4112yes—
593C4×C47#58514yes—
594Dic47—22no—
595Dic47—28no—
596Dic47—28no—
597Dic47—22no—
598Dic47—22no—
599Dic47—24no—
600Dic47C22×#4112yes—
601Dic47C22×#4112yes—
602#3512—474no—
603#3511—474no—
604#3510—472no—
605#3510—472no—
606#3509—471no—
607#3509—471no—
608#3508—471no—
609#3508D4711yescharacteristic, complemented
610#3507—474no—
611#3506—474no—
612#3505—478no—
613#3480—474no—
614#3480—474no—
615#3475—478no—
616#3455—474no—
617#3449—472no—
618#3444—474no—
619C2×#533—471no—
620C2×#532—471no—
621#3428—472no—
622C2×C4×#41—471no—
623C2×C47—22no—
624C2×C47—42no—
625C2×C47—48no—
626C2×C47C23×#4111yescharacteristic
627C2×C47C2×#58512yes—
628D47—22no—
629D47—22no—
630D47—42no—
631C22×#41—471no—
632C22×#41—472no—
633#559—478no—
634#559—474no—
635#559—478no—
636#559C2×D4714yescomplemented
637#557—474no—
638#557—474no—
639#556—478no—
640#556—478no—
641#556—474no—
642#556—474no—
643#556—478no—
644#555—478no—
645#554—478no—
646#553—4716no—
647#553—4716no—
648#553—478no—
649#553—4716no—
650#553—478no—
651#552—4716no—
652#552—478no—
653#552—478no—
654#551—4716no—
655#551—4716no—
656#550—474no—
657#550C2×D4714yescomplemented
658#548—478no—
659#548—478no—
660#547—478no—
661#546—478no—
662#546C2×D4718yescomplemented
663#542—478no—
664#542—478no—
665#541—474no—
666#541—474no—
667#540—474no—
668#540C2×D4714yescomplemented
669#539—4716no—
670#538—4716no—
671#537—478no—
672#536—472no—
673#536—474no—
674#536—472no—
675#535—472no—
676#535—474no—
677#535C2×D4712yes—
678#534—478no—
679#533—472no—
680#533—474no—
681#533—472no—
682#533—474no—
683#533—474no—
684#533—472no—
685#533—471no—
686#533—474no—
687#533C2×D4711yescharacteristic, complemented
688#532—472no—
689#532—472no—
690#532—474no—
691#532—474no—
692#532—472no—
693#532—472no—
694#532—474no—
695#532—474no—
696#532—474no—
697#532C2×D4714yescomplemented
698C2×C4⋊Q8—472no—
699C2×C4⋊Q8—471no—
700C2×#127C2×D4711yescharacteristic, complemented
701#529—478no—
702#529—478no—
703#529—4716no—
704#529—478no—
705#529—478no—
706#529—4716no—
707#529—478no—
708#529—478no—
709C2×#125—472no—
710C2×#124—472no—
711#525—478no—
712#525—478no—
713#525—478no—
714#525—478no—
715C2×C22⋊Q8—474no—
716C2×#121—474no—
717#520—478no—
718#520—478no—
719#519—472no—
720#519—472no—
721#518—472no—
722#518—478no—
723#518C2×D4712yescomplemented
724C4×#41—471no—
725C4×#41—478no—
726C4×#41—472no—
727C4×#41—474no—
728C4×#41—472no—
729C4×#41—478no—
730C4×#41—478no—
731C4×#41—478no—
732C4×#41—471no—
733C4×#41—472no—
734C4×#41—471no—
735C4×#41—472no—
736C4×#41C2×D4711yescharacteristic
737C2×C4×Q8—472no—
738C2×C4×Q8—474no—
739C2×C4×D4—474no—
740C2×C4×D4—474no—
741C2×C4×D4—472no—
742C2×#117—471no—
743C2×#117—472no—
744C2×#117—472no—
745C2×#117—478no—
746C22×C42—471no—
747C22×C42—472no—
748C47#6281511yescharacteristic, complemented, Sylow
749C2×#41—471no—
750C2×#41—472no—
751C2×#41—474no—
752C2×#41—471no—
753C2×#41—474no—
754C2×#41—474no—
755C2×#41—474no—
756C2×#41—478no—
757C2×#41—471no—
758C2×#41—472no—
759C2×#41—9416no—
760C2×#41—948no—
761C2×#41C22×D4711yescharacteristic
762C2×#41C22×D4718yes—
763C22×Q8—471no—
764C22×Q8—474no—
765C22×Q8—472no—
766C22×D4—474no—
767C22×D4—472no—
768C22×D4—471no—
769C22×D4C22×D4712yes—
770C22×D4C22×D4714yes—
771C23×C4—471no—
772C23×C4—474no—
773C23×C4—472no—
774C23×C4—472no—
775C23×C4—474no—
776C4⋊Q8—474no—
777C4⋊Q8—474no—
778C4⋊Q8—474no—
779C4⋊Q8—474no—
780C4⋊Q8—472no—
781C4⋊Q8—472no—
782C4⋊Q8—472no—
783C4⋊Q8—474no—
784C4⋊Q8—474no—
785C4⋊Q8C22×D4712yes—
786#127—474no—
787#127C22×D4712yes—
788#127C22×D4712yes—
789#127C22×D4714yes—
790#127C22×D4714yes—
791#126—4716no—
792#126—4716no—
793#126—4716no—
794#126—4716no—
795#126—4716no—
796#126—4716no—
797#125—474no—
798#125—478no—
799#125—478no—
800#125—4716no—
801#125—4716no—
802#125—472no—
803#125—478no—
804#125C22×D4712yes—
805#124—474no—
806#124—474no—
807#124—478no—
808#124—478no—
809#124—4716no—
810#124—474no—
811#124—474no—
812#124—4716no—
813#124—474no—
814#124C22×D4718yes—
815#124C22×D4714yes—
816#123—4716no—
817#123—478no—
818#123—4716no—
819#123—4716no—
820#123—4716no—
821#123—4716no—
822#123—4716no—
823#123—478no—
824#123C22×D47116yes—
825C22⋊Q8—474no—
826C22⋊Q8—478no—
827C22⋊Q8—474no—
828C22⋊Q8—478no—
829C22⋊Q8—478no—
830C22⋊Q8—4716no—
831C22⋊Q8—474no—
832C22⋊Q8—478no—
833C22⋊Q8—478no—
834C22⋊Q8—478no—
835C22⋊Q8—4716no—
836C22⋊Q8—4716no—
837C22⋊Q8C22×D4714yes—
838#121—478no—
839#121—478no—
840#121—478no—
841#121—478no—
842#121—478no—
843#121—478no—
844#121—4716no—
845#121—4716no—
846#121—4716no—
847#121—4716no—
848#121C22×D4718yes—
849#121C22×D4718yes—
850#121C22×D47116yes—
851#120—478no—
852#120—4716no—
853#120C22×D4718yes—
854C4×Q8—474no—
855C4×Q8—472no—
856C4×Q8—478no—
857C4×Q8—474no—
858C4×Q8—474no—
859C4×Q8—472no—
860C4×Q8—478no—
861C4×Q8—478no—
862C4×Q8—478no—
863C4×Q8—474no—
864C4×Q8—472no—
865C4×Q8—474no—
866C4×Q8—478no—
867C4×Q8—478no—
868C4×Q8—478no—
869C4×Q8—478no—
870C4×Q8C22×D4712yes—
871C4×Q8C22×D4714yes—
872C4×D4—478no—
873C4×D4—474no—
874C4×D4—472no—
875C4×D4—478no—
876C4×D4—478no—
877C4×D4—478no—
878C4×D4—478no—
879C4×D4—478no—
880C4×D4—4716no—
881C4×D4—4716no—
882C4×D4—478no—
883C4×D4—474no—
884C4×D4—474no—
885C4×D4—474no—
886C4×D4—4716no—
887C4×D4—4716no—
888C4×D4—4716no—
889C4×D4—474no—
890C4×D4—472no—
891C4×D4—474no—
892C4×D4—474no—
893C4×D4—474no—
894C4×D4—4716no—
895C4×D4—4716no—
896C4×D4—4716no—
897C4×D4—474no—
898C4×D4—472no—
899C4×D4C22×D4714yes—
900C4×D4C22×D4712yes—
901C4×D4C22×D4718yes—
902C4×D4C22×D4718yes—
903C4×D4C22×D4718yes—
904#117—471no—
905#117—472no—
906#117—472no—
907#117—478no—
908#117—4716no—
909#117—472no—
910#117—474no—
911#117—474no—
912#117—478no—
913#117—472no—
914#117—474no—
915#117—4716no—
916#117—474no—
917#117—478no—
918#117—478no—
919#117—4716no—
920#117—4716no—
921#117—472no—
922#117—472no—
923#117—472no—
924#117—474no—
925#117C22×D4711yescharacteristic
926#117C22×D4712yes—
927#117C22×D4712yes—
928C2×C4⋊C4—4716no—
929C2×C4⋊C4—474no—
930C2×C4⋊C4—472no—
931C2×C4⋊C4—474no—
932C2×C4⋊C4—474no—
933C2×C4⋊C4—478no—
934C2×C4⋊C4—474no—
935C2×C22⋊C4—478no—
936C2×C22⋊C4—478no—
937C2×C22⋊C4—472no—
938C2×C22⋊C4—474no—
939C2×C22⋊C4—474no—
940C2×C22⋊C4C22×D4718yes—
941C2×C42—4716no—
942C2×C42—472no—
943C2×C42—474no—
944C2×C42—471no—
945C2×C42—472no—
946C2×C42—472no—
947C2×C42—471no—
948C2×C42—474no—
949C2×C42—474no—
950C2×C42—472no—
951C2×C42—472no—
952C2×C42—474no—
953C2×C42—471no—
954C2×C42—472no—
955C2×C42—471no—
956C2×C42—472no—
957C2×C42—471no—
958C2×C42C22×D4711yescharacteristic
959C2×C42C22×D4712yes—
960C24—471no—
961C24—472no—
962C24C23×D4714yes—
963#41—24no—
964#41—416no—
965#41—948no—
966#41—948no—
967#41—9416no—
968#41—9416no—
969#41—9416no—
970#41—9416no—
971#41—944no—
972#41—944no—
973#41—944no—
974#41—18816no—
975C2×Q8—472no—
976C2×Q8—474no—
977C2×Q8—474no—
978C2×Q8—471no—
979C2×Q8—474no—
980C2×Q8—478no—
981C2×Q8—944no—
982C2×Q8—948no—
983C2×Q8—1888no—
984C2×Q8C23×D4714yes—
985C2×Q8C23×D4711yescharacteristic
986C2×D4—28no—
987C2×D4—48no—
988C2×D4—472no—
989C2×D4—478no—
990C2×D4—472no—
991C2×D4—472no—
992C2×D4—478no—
993C2×D4—4716no—
994C2×D4—472no—
995C2×D4—471no—
996C2×D4—944no—
997C2×D4—948no—
998C2×D4—9416no—
999C2×D4C23×D4718yes—
1000C2×D4C23×D4712yes—
1001C2×D4C23×D4714yes—
1002C2×D4C23×D4711yescharacteristic
1003C2×D4C23×D4714yes—
1004C2×D4C23×D47116yes—
1005C2×D4C23×D4718yes—
1006C22×C4—471no—
1007C22×C4—478no—
1008C22×C4—471no—
1009C22×C4—471no—
1010C22×C4—471no—
1011C22×C4—471no—
1012C22×C4—472no—
1013C22×C4—478no—
1014C22×C4—474no—
1015C22×C4—478no—
1016C22×C4—472no—
1017C22×C4—474no—
1018C22×C4—4716no—
1019C22×C4—472no—
1020C22×C4—472no—
1021C22×C4—472no—
1022C22×C4—472no—
1023C22×C4—474no—
1024C22×C4—472no—
1025C22×C4—474no—
1026C22×C4—472no—
1027C22×C4—472no—
1028C22×C4—474no—
1029C22×C4—478no—
1030C22×C4—948no—
1031C22×C4—9416no—
1032C22×C4—1884no—
1033C22×C4—1888no—
1034C22×C4C23×D4712yes—
1035C22×C4C23×D4714yes—
1036C22×C4C23×D4712yes—
1037C22×C4C23×D47116yes—
1038C22×C4C23×D4711yescharacteristic
1039C4⋊C4—474no—
1040C4⋊C4—478no—
1041C4⋊C4—474no—
1042C4⋊C4—478no—
1043C4⋊C4—4716no—
1044C4⋊C4—4716no—
1045C4⋊C4—474no—
1046C4⋊C4—478no—
1047C4⋊C4—478no—
1048C4⋊C4—4716no—
1049C4⋊C4—472no—
1050C4⋊C4—474no—
1051C4⋊C4—474no—
1052C4⋊C4—478no—
1053C4⋊C4—474no—
1054C4⋊C4—478no—
1055C4⋊C4—478no—
1056C4⋊C4—4716no—
1057C4⋊C4C23×D4714yes—
1058C4⋊C4C23×D4712yes—
1059C4⋊C4C23×D4714yes—
1060C4⋊C4C23×D4714yes—
1061C4⋊C4C23×D4718yes—
1062C22⋊C4—472no—
1063C22⋊C4—474no—
1064C22⋊C4—4716no—
1065C22⋊C4—4716no—
1066C22⋊C4—474no—
1067C22⋊C4—4716no—
1068C22⋊C4—4716no—
1069C22⋊C4—4716no—
1070C22⋊C4—474no—
1071C22⋊C4—478no—
1072C22⋊C4—474no—
1073C22⋊C4—474no—
1074C22⋊C4—4716no—
1075C22⋊C4C23×D4712yes—
1076C22⋊C4C23×D4714yes—
1077C22⋊C4C23×D4714yes—
1078C22⋊C4C23×D47116yes—
1079C22⋊C4C23×D47116yes—
1080C42—474no—
1081C42—472no—
1082C42—471no—
1083C42—472no—
1084C42—478no—
1085C42—472no—
1086C42—474no—
1087C42—474no—
1088C42—471no—
1089C42—472no—
1090C42—472no—
1091C42—474no—
1092C42—472no—
1093C42—4716no—
1094C42—4716no—
1095C42—474no—
1096C42C23×D4711yescharacteristic
1097C42C23×D4712yes—
1098C42C23×D4711yescharacteristic
1099C42C23×D4714yes—
1100C42C23×D4712yes—
1101C42C23×D4714yes—
1102C23—28no—
1103C23—48no—
1104C23—471no—
1105C23—471no—
1106C23—474no—
1107C23—472no—
1108C23—944no—
1109C23—1882no—
1110C23—1884no—
1111C23C24×D4712yes—
1112C23C24×D4718yes—
1113C23C24×D4711yescharacteristic
1114Q8—22no—
1115Q8—28no—
1116Q8—944no—
1117Q8—948no—
1118Q8—948no—
1119Q8—942no—
1120Q8—948no—
1121Q8—1888no—
1122D4—24no—
1123D4—28no—
1124D4—28no—
1125D4—22no—
1126D4—216no—
1127D4—48no—
1128D4—416no—
1129D4—944no—
1130D4—944no—
1131D4—944no—
1132D4—9416no—
1133D4—9416no—
1134D4—944no—
1135D4—942no—
1136D4—18816no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—416no—
1141C2×C4—474no—
1142C2×C4—471no—
1143C2×C4—471no—
1144C2×C4—474no—
1145C2×C4—474no—
1146C2×C4—474no—
1147C2×C4—474no—
1148C2×C4—474no—
1149C2×C4—472no—
1150C2×C4—472no—
1151C2×C4—478no—
1152C2×C4—472no—
1153C2×C4—478no—
1154C2×C4—944no—
1155C2×C4—944no—
1156C2×C4—944no—
1157C2×C4—9416no—
1158C2×C4—9416no—
1159C2×C4—948no—
1160C2×C4—944no—
1161C2×C4—944no—
1162C2×C4—944no—
1163C2×C4—948no—
1164C2×C4—1884no—
1165C2×C4—1884no—
1166C2×C4—1882no—
1167C2×C4—1882no—
1168C2×C4—1888no—
1169C2×C4—1884no—
1170C2×C4—1882no—
1171C2×C4—18816no—
1172C2×C4#41×D4714yes—
1173C2×C4C24×D4714yes—
1174C2×C4C24×D4718yes—
1175C2×C4C24×D4712yes—
1176C2×C4C24×D4712yes—
1177C2×C4C24×D4711yescharacteristic
1178C2×C4C24×D4711yescharacteristic
1179C2×C4C24×D4712yes—
1180C22—22no—
1181C22—22no—
1182C22—28no—
1183C22—24no—
1184C22—216no—
1185C22—88no—
1186C22—472no—
1187C22—472no—
1188C22—942no—
1189C22—942no—
1190C22—942no—
1191C22—944no—
1192C22—1884no—
1193C22—1888no—
1194C22C2×#41×D4712yes—
1195C22C25×D4711yescharacteristic
1196C4—22no—
1197C4—24no—
1198C4—22no—
1199C4—28no—
1200C4—472no—
1201C4—472no—
1202C4—942no—
1203C4—948no—
1204C4—942no—
1205C4—944no—
1206C4—942no—
1207C4—948no—
1208C4C2×#41×D4712yes—
1209C4C2×#41×D4712yes—
1210C4#1568995814yes—
1211C2—22no—
1212C2—48no—
1213C2—42no—
1214C2—942no—
1215C2—942no—
1216C2—1882no—
1217C2C22×#41×D4711yescharacteristic
1218C2C2×#1568995812yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3508C2
hypercenter#3508D47
hypocenterC47#62815
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #20257307C2semidirect
2. #20257289C2semidirect
3. #20257283C2semidirect
4. #20257279C2semidirect
5. #20257275C2semidirect
6. #20257274C2semidirect
7. #20257262C2semidirect
8. #20257245C2semidirect
9. #20257232C2semidirect
10. #20257215C2semidirect
11. #20256987C2semidirect
12. #20256984C2semidirect
13. #20256939C2semidirect
14. #20256772C2semidirect
15. #20256719C2semidirect
16. #20256683C2semidirect
17. #533×D47C2semidirect
18. C2×#15689671C2semidirect
19. #20256586C2semidirect
20. C4×#41×D47C2semidirect
21. C47×#3508C2semidirect
24. #15689859C22semidirect
25. #15689859C22semidirect
26. #15689856C22semidirect
27. #15689852C22semidirect
28. #15689851C22semidirect
29. #15689846C22semidirect
30. #15689843C22semidirect
31. #15689843C22semidirect
32. #15689842C22semidirect
33. #15689842C22semidirect
34. #15689837C22semidirect
35. #15689832C22semidirect
36. #15689823C22semidirect
37. #15689820C22semidirect
38. #15689820C22semidirect
39. #15689818C22semidirect
40. #15689816C22semidirect
41. #15689815C22semidirect
42. #15689813C22semidirect
43. #15689810C22semidirect
44. #15689804C22semidirect
45. #15689799C22semidirect
46. #15689793C22semidirect
47. #15689781C22semidirect
48. #15689780C22semidirect
49. #15689772C22semidirect
50. #15689767C22semidirect
51. #15689740C22semidirect
52. #15689738C22semidirect
53. #15689736C22semidirect
54. #15689735C22semidirect
55. #15689727C22semidirect
56. #15689716C22semidirect
57. #15689705C22semidirect
58. #15689702C22semidirect
61. #15689693C22semidirect
63. #15689686C22semidirect
65. #15689680C22semidirect
66. #15689680C22semidirect
67. #15689679C22semidirect
68. #15689678C22semidirect
69. #15689678C22semidirect
70. #15689677C22semidirect
71. #15689676C22semidirect
72. #15689675C22semidirect
73. #15689672C22semidirect
77. #15689671C22semidirect
78. #15689671C22semidirect
79. #15689671C22semidirect
80. #15689671C22semidirect
81. #15689671C22semidirect
82. C2×#13094024C22semidirect
83. C4⋊Q8×D47C22semidirect
84. #15689655C22semidirect
85. #15689655C22semidirect
86. #15689654C22semidirect
87. #15689654C22semidirect
88. #15689654C22semidirect
89. #15689652C22semidirect
90. #15689652C22semidirect
91. #15689650C22semidirect
92. #125×D47C22semidirect
93. C2×#13094011C22semidirect
94. #15689633C22semidirect
95. #15689633C22semidirect
96. #15689630C22semidirect
100. #15689602C22semidirect
101. #15689602C22semidirect
102. #15689600C22semidirect
103. #15689600C22semidirect
104. #15689598C22semidirect
107. #41×Dic47C22semidirect
108. C4×#10625354C22semidirect
110. C4×#10625350C22semidirect
112. #15689591C22semidirect
114. C4×#10625352C22semidirect
115. C4×#10625352C22semidirect
116. C4×#10625352C22semidirect
117. C4×#10625352C22semidirect
118. C4×Q8×D47C22semidirect
119. C4×Q8×D47C22semidirect
120. C2×D4×Dic47C22semidirect
122. C4×D4×D47C22semidirect
123. C2×#13093980C22semidirect
126. #117×D47C22semidirect
128. C2×C42×D47C22semidirect
129. C47×#559C22semidirect
130. C47×#550C22semidirect
131. C47×#546C22semidirect
132. C47×#540C22semidirect
134. C47×#533C22semidirect
135. C47×#532C22semidirect
136. C2×#127×C47C22semidirect
137. C47×#518C22semidirect
406. C2×C4×D47#41semidirect
609. #3508D47semidirect
636. #559C2×D47semidirect
657. #550C2×D47semidirect
662. #546C2×D47semidirect
668. #540C2×D47semidirect
687. #533C2×D47semidirect
697. #532C2×D47semidirect
700. C2×#127C2×D47semidirect
723. #518C2×D47semidirect
748. C47#62815semidirect

Maximal subgroups

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

subgroupindex
#202573072
#202572892
#202572832
#202572792
#202572752
#202572742
#202572622
#202572452
#202572322
#202572152
#202569872
#202569842
#202569392
#202567722
#202567192
#202566832
#533×D472
C2×#156896712
#202565862
C4×#41×D472
C47×#35082
#6281547