Finite Group Databasebeta

← #27124504

Subgroups — #27124504

Order 12032.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257485C211yesmaximal, characteristic, complemented
2#20257483C213yesmaximal, complemented
3#20257470C213yesmaximal, complemented
4#20257468C211yesmaximal, characteristic, complemented
5#20257372C216yesmaximal, complemented
6#20257370C212yesmaximal, complemented
7#20257245C213yesmaximal, complemented
8#20257243C213yesmaximal, complemented
9#20257192C211yesmaximal, characteristic, complemented
10#20257153C211yesmaximal, characteristic, complemented
11#20257092C216yesmaximal, complemented
12#20257034C212yesmaximal, complemented
13#20257010C212yesmaximal, complemented
14#20257001C216yesmaximal, complemented
15#20256985C213yesmaximal, complemented
16Q8×#10625350C211yesmaximal, characteristic, complemented
17#41×Dic94C213yesmaximal, complemented
18#20256813C216yesmaximal, complemented
19#20256683C213yesmaximal, complemented
20#20256681C213yesmaximal, complemented
21C4×#13094071C212yesmaximal, complemented
22C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
23C47×#3480C211yesmaximal, characteristic, complemented
24C2×#13094071C2212yes—
25C22×Q8×D47C2211yescharacteristic
26#15689859C2213yescomplemented
27#15689855C2216yescomplemented
28Q8×Dic94C2211yescharacteristic, complemented
29Q8×Dic94C2213yescomplemented
30#15689852C2212yescomplemented
31#15689852C2213yescomplemented
32#15689851C2213yescomplemented
33#15689850C2216yescomplemented
34#15689849C2216yescomplemented
35#15689848C2213yescomplemented
36#15689847C2213yescomplemented
37#15689843C2216yescomplemented
38#15689842C2216yescomplemented
39#15689842C2216yescomplemented
40#15689840C22112yescomplemented
41#15689833C2213yescomplemented
42#15689832C22112yes—
43#15689832C2216yescomplemented
44#15689830C2216yes—
45#15689830C2213yescomplemented
46#15689828C2216yes—
47#15689825C2216yes—
48#15689816C22112yes—
49#15689815C2216yescomplemented
50#15689812C2216yes—
51#15689812C2216yescomplemented
52#15689811C2216yes—
53#15689810C22112yescomplemented
54#15689809C22112yes—
55#15689793C2213yescomplemented
56Q8×D188C2212yes—
57Q8×D188C2211yescharacteristic, complemented
58D4×Dic94C2216yes—
59D4×Dic94C2213yescomplemented
60Q8×C22⋊D47C2212yes—
61#15689786C2216yes—
62#15689781C2216yes—
63#15689780C2212yes—
64#15689780C2212yescomplemented
65#15689779C2216yes—
66#15689779C2216yescomplemented
67#15689778C2216yes—
68#15689773C2216yes—
69#15689771C22112yes—
70#15689753C2216yes—
71#15689742C2216yescomplemented
72#15689741C22112yescomplemented
73#15689740C2216yescomplemented
74#15689736C2216yescomplemented
75#15689733C2216yescomplemented
76#15689730C22112yescomplemented
77#15689716C22112yes—
78#15689714C22112yes—
79#15689702C2216yes—
80#15689696C2216yes—
81#15689693C2216yes—
82#15689680C2213yes—
83#15689680C2216yescomplemented
84#15689678C2213yes—
85#15689678C2213yes—
86#15689677C2213yes—
87#15689677C2213yes—
88#15689677C2216yescomplemented
89#15689676C2213yes—
90#15689676C22112yescomplemented
91#15689671C2213yes—
92#15689671C2213yes—
93#15689670C2213yes—
94#15689670C2213yes—
95#15689669C2213yes—
96#15689660C2213yes—
97#15689660C2213yes—
98#15689655C2216yes—
99#15689655C2213yes—
100#15689655C2213yes—
101#15689655C2216yes—
102#15689655C2216yescomplemented
103#15689654C2216yes—
104#15689654C2216yes—
105#15689653C2216yes—
106#15689653C2216yes—
107#15689653C22112yescomplemented
108#15689652C2216yes—
109#15689652C2216yes—
110#15689651C2216yes—
111#15689651C2216yes—
112#15689635C2211yescharacteristic
113#15689633C2216yes—
114#15689633C2216yes—
115#15689632C2216yes—
116#15689632C2216yes—
117#15689630C2213yes—
118#15689606C2212yescomplemented
119#15689603C2216yes—
120#15689602C2216yes—
121#15689602C2216yescomplemented
122#15689600C2216yescomplemented
123#15689599C2212yes—
124#15689599C2212yescomplemented
125#41×Dic47C2216yes—
126C4×#10625350C2216yes—
127C4×#10625350C2213yes—
128C4×#10625350C2216yes—
129C4×#10625352C2216yes—
130C4×#10625352C2216yes—
131C4×#10625352C2216yescomplemented
132C2×Q8×Dic47C2211yescharacteristic
133C2×C4×Dic94C2213yes—
134C2×C4×Dic94C2216yescomplemented
135C2×#13093989C2213yes—
136C4×Q8×D47C2213yes—
137C4×Q8×D47C2211yescharacteristic
138C4×Q8×D47C2211yescharacteristic
139C4×Q8×D47C2211yescharacteristic
140C4×Q8×D47C2213yes—
141C4×Q8×D47C2213yes—
142C4×Q8×D47C2213yes—
143C4×Q8×D47C2211yescharacteristic
144C4×Q8×D47C2212yescomplemented
145C2×C4⋊C4×D47C2213yes—
146C2×C42×D47C2213yes—
147C47×#559C2213yescomplemented
148C47×#557C2211yescharacteristic, complemented
149C47×#556C2213yescomplemented
150C47×#553C2216yes—
151C47×#550C2211yescharacteristic, complemented
152C47×#548C2212yes—
153C47×#532C2213yes—
154C47×#529C2216yescomplemented
155C4×#41×C47C2213yes—
156C4×#41×C47C2212yescomplemented
157C2×C4×Q8×C47C2211yescharacteristic
158#13094071—216no—
159C2×#10625350C2311yescharacteristic
160C2×#10625350C2316yes—
161C2×#10625350C2316yes—
162C2×#10625352C2316yes—
163C2×#10625352C2316yes—
164C2×#10625352C2316yes—
165C22×Dic94C2313yes—
166C22×Dic94C2316yes—
167C2×Q8×D47—28no—
168C2×Q8×D47C2311yescharacteristic
169C2×Q8×D47C2312yes—
170C2×Q8×D47C2313yes—
171C2×Q8×D47C2313yes—
172C2×Q8×D47C2311yescharacteristic
173C22×C4×D47C2311yescharacteristic
174C22×C4×D47C2313yes—
175C22×C4×D47C2313yes—
176#13094024C2316yes—
177#13094024C2316yes—
178#13094024C2313yes—
179#13094024C2313yes—
180#13094023C23112yes—
181#13094023C2316yes—
182#13094023C23112yes—
183#13094023C2313yes—
184#13094023C2313yes—
185#13094022C2316yes—
186#13094022C2313yes—
187#13094020C2313yes—
188#13094019C2316yes—
189#13094019C23112yes—
190#13094019C2316yes—
191#13094017C2316yes—
192#13094017C23112yes—
193#13094017C23112yes—
194#13094017C23112yes—
195#13094017C2316yes—
196#13094017C23112yes—
197#13094016C23112yes—
198#13094016C2316yes—
199#13094015C2316yes—
200#13094015C2316yes—
201#13094015C23112yes—
202#13094015C23112yes—
203#13094015C2316yes—
204#13094015C2313yes—
205#13094015C2313yes—
206#13094014C2316yes—
207#13094014C23112yes—
208#13094014C23112yes—
209#13094014C2316yes—
210#13094013C2313yes—
211#13094011C2316yes—
212#13094011C2316yes—
213#13094011C2316yes—
214#13094011C2313yes—
215#13094010C2316yes—
216#13094010C23112yes—
217#13094010C2316yes—
218#13094009C2316yes—
219#13094009C2316yes—
220#13094008C23112yes—
221#13094008C2312yes—
222#13094006C23112yes—
223#13094006C23112yes—
224#13094006C2316yes—
225#13094006C2316yes—
226#13094006C23112yes—
227#13094005C23112yes—
228#13094005C2316yes—
229#13094004C2316yes—
230#13094004C2316yes—
231#13094004C2316yes—
232#13094004C2316yes—
233#13094004C2311yescharacteristic
234#13094004C2311yescharacteristic
235#13094003C2316yes—
236#13094003C2316yes—
237#13094003C23112yes—
238#13094003C2316yes—
239#13094003C2316yes—
240#13094002C23112yes—
241#13094002C2316yes—
242#13094002C2316yes—
243#13094001C23112yes—
244#13094001C23112yes—
245#13094001C23112yes—
246#13094001C23112yes—
247#13094001C23112yes—
248#13094001C2316yes—
249#13094001C2316yes—
250#13094000C2316yes—
251#13094000C2313yes—
252#13094000C2313yes—
253#13093999C2311yescharacteristic
254#13093999C2311yescharacteristic
255#13093997C2316yes—
256#13093997C2316yes—
257#13093996C23112yes—
258#13093996C2316yes—
259#13093996C2316yes—
260#13093995C2316yes—
261#13093995C2316yes—
262#13093995C2313yes—
263#13093995C2313yes—
264#13093995C2316yes—
265#13093994C2312yes—
266#13093992C2316yes—
267Q8×Dic47C2313yes—
268Q8×Dic47C2312yes—
269Q8×Dic47C2311yescharacteristic
270Q8×Dic47C2313yes—
271Q8×Dic47C2311yescharacteristic
272Q8×Dic47C2316yes—
273Q8×Dic47C2316yes—
274C4×Dic94C2316yes—
275C4×Dic94C2316yes—
276C4×Dic94C2313yes—
277C4×Dic94C23112yes—
278C4×Dic94C2316yes—
279C4×Dic94C2313yes—
280C4×Dic94C2316yes—
281C4×Dic94C2313yes—
282C4×Dic94C2316yes—
283C4×Dic94C2313yes—
284C4×Dic94C2316yes—
285C4×Dic94C2313yes—
286C4×Dic94C2316yes—
287C4×Dic94C2316yes—
288C4×Dic94C2316yes—
289C4×Dic94C2313yes—
290C4×Dic94C2316yes—
291#13093989C2316yes—
292#13093989C2316yes—
293#13093989C2313yes—
294#13093989C2316yes—
295#13093989C2313yes—
296#13093989C2316yes—
297#13093989C2316yes—
298#13093989C2313yes—
299#13093989C2316yes—
300#13093989C2313yes—
301C4×D188C2316yes—
302C4×D188C2313yes—
303C4×D188C2313yes—
304C4×D188C2312yes—
305C4×D188C2312yes—
306C4×D188C2316yes—
307D4×Dic47C2316yes—
308D4×Dic47C2316yes—
309D4×Dic47C23112yes—
310D4×Dic47C2316yes—
311D4×Dic47C2316yes—
312D4×Dic47C23112yes—
313D4×Dic47C2316yes—
314C4×C22⋊D47C2316yes—
315C4×C22⋊D47C2316yes—
316C4×C22⋊D47C2316yes—
317C4×C22⋊D47C2316yes—
318C4×C22⋊D47C2316yes—
319C4×C22⋊D47C2316yes—
320C4×C22⋊D47C2316yes—
321C4×C22⋊D47C2316yes—
322C4×C22⋊D47C2316yes—
323C4×C22⋊D47C2316yes—
324(C22⋊D47)⋊C4C23112yes—
325(C22⋊D47)⋊C4C23112yes—
326(C22⋊D47)⋊C4C23112yes—
327#13093983C2316yes—
328#13093983C2316yes—
329#13093983C2313yes—
330#13093983C23112yes—
331#13093982C2316yes—
332#13093982C2316yes—
333#13093982C2316yes—
334#13093981C2316yes—
335#13093981C2316yes—
336#13093981C2316yes—
337#13093981C2316yes—
338#13093981C2316yes—
339#13093980C23112yes—
340#13093980C23112yes—
341#13093980C23112yes—
342C2×C4⋊Dic47C2316yes—
343C2×C4⋊Dic47C2313yes—
344C2×Dic47⋊C4C23112yes—
345C2×Dic47⋊C4C2316yes—
346C4⋊C4×D47C2313yes—
347C4⋊C4×D47C2316yes—
348C4⋊C4×D47C2313yes—
349C4⋊C4×D47C2313yes—
350C4⋊C4×D47C2316yes—
351C4⋊C4×D47C2313yes—
352C4⋊C4×D47C2316yes—
353C2×C4×Dic47C2313yes—
354C2×C4×Dic47C2313yes—
355C2×C4×Dic47C2313yes—
356C2×C4×Dic47C23112yes—
357C42×D47C2313yes—
358C42×D47C2313yes—
359C42×D47C2313yes—
360C42×D47C2313yes—
361C42×D47C2313yes—
362C42×D47C2313yes—
363C42×D47C2313yes—
364C42×D47C2313yes—
365C42×D47C2316yes—
366C2×#41×C47C2312yes—
367C2×#41×C47C2313yes—
368C22×Q8×C47C2311yescharacteristic
369C4⋊Q8×C47C2313yes—
370#127×C47C2313yes—
371#126×C47C23112yes—
372#125×C47C2316yes—
373#124×C47C2316yes—
374#124×C47C2316yes—
375#123×C47C23112yes—
376C22⋊Q8×C47C2316yes—
377#121×C47C2316yes—
378#121×C47C2316yes—
379#121×C47C2316yes—
380C4×Q8×C47C2312yes—
381C4×Q8×C47C2311yescharacteristic
382C4×Q8×C47C2311yescharacteristic
383C4×Q8×C47C2313yes—
384C4×Q8×C47C2313yes—
385C4×Q8×C47C2313yes—
386C4×Q8×C47C2313yes—
387C4×D4×C47C2316yes—
388C4×D4×C47C2316yes—
389C4×D4×C47C2313yes—
390C4×D4×C47C2316yes—
391C4×D4×C47C2313yes—
392C4×D4×C47C2316yes—
393C4×D4×C47C2316yes—
394#117×C47C2311yescharacteristic
395#117×C47C2316yes—
396#117×C47C2316yes—
397C2×C4⋊C4×C47C2313yes—
398C2×C42×C47C2313yes—
399C2×C42×C47C2316yes—
400C23×D47C2411yescharacteristic
401#41×C47—28no—
402#41×C47—212no—
403C2×Q8×C47—24no—
404C2×Q8×C47C2413yes—
405C2×Q8×C47C2413yes—
406C2×Q8×C47C2411yescharacteristic
407C2×D4×C47C2416yes—
408C2×D4×C47C2416yes—
409C2×D4×C47C2413yes—
410C2×D4×C47C2416yes—
411C22×C4×C47C2413yes—
412C22×C4×C47C2416yes—
413C22×C4×C47C2416yes—
414C22×C4×C47C2413yes—
415C22×C4×C47C2416yes—
416C22×C4×C47C2411yescharacteristic
417C2×C22⋊D47C2416yes—
418C2×C22⋊D47C2416yes—
419C2×C22⋊D47C2416yes—
420C2×C22⋊D47C2412yes—
421C2×C22⋊D47C2416yes—
422C22×Dic47C2411yescharacteristic
423C22×Dic47C2413yes—
424C22×Dic47C24112yes—
425C22×Dic47C2413yes—
426C22×Dic47C24112yes—
427Q8×D47—24no—
428Q8×D47—28no—
429Q8×D47—212no—
430Q8×D47—212no—
431Q8×D47#4118yescomplemented
432#10625352—224no—
433#10625352—224no—
434#10625352—412no—
435#10625350—24no—
436#10625350—224no—
437#10625350—412no—
438C2×D188C2411yescharacteristic
439C2×D188C2412yes—
440C2×D188C2412yes—
441C2×C4×D47—24no—
442C2×C4×D47—212no—
443C2×C4×D47—46no—
444C2×C4×D47C2411yescharacteristic
445C2×C4×D47C2411yescharacteristic
446C2×C4×D47C2411yescharacteristic
447C2×C4×D47C2411yescharacteristic
448C2×C4×D47C2412yes—
449C2×C4×D47C2413yes—
450C2×C4×D47C2413yes—
451C2×C4×D47C2413yes—
452C2×C4×D47C2413yes—
453C2×C4×D47C2413yes—
454C2×C4×D47C2416yes—
455C2×C4×D47C2413yes—
456C2×C4×D47C2413yes—
457C2×C4×D47C2416yes—
458C2×C4×D47C2413yes—
459C2×Dic94—212no—
460C2×Dic94—224no—
461C2×Dic94C2416yes—
462C2×Dic94C2413yes—
463C2×Dic94C2416yes—
464C2×Dic94C2411yescharacteristic
465C2×Dic94C2416yes—
466C2×Dic94C2416yes—
467C2×Dic94C2416yes—
468C2×Dic94C2413yes—
469C4⋊C4×C47C2413yes—
470C4⋊C4×C47C2413yes—
471C4⋊C4×C47C2416yes—
472C4⋊C4×C47C2411yescharacteristic
473C4⋊C4×C47C2411yescharacteristic
474C4⋊C4×C47C2416yes—
475C4⋊C4×C47C2416yes—
476C4⋊C4×C47C2416yes—
477C4⋊C4×C47C2416yes—
478C22⋊C4×C47C2412yes—
479C22⋊C4×C47C2416yes—
480C22⋊C4×C47C24112yes—
481C22⋊C4×C47C2416yes—
482C22⋊C4×C47C24112yes—
483C42×C47C2412yes—
484C42×C47C2413yes—
485C42×C47C2413yes—
486C42×C47C2416yes—
487C42×C47C2416yes—
488C42×C47C2413yes—
489C42×C47C2413yes—
490C22⋊Dic47C2416yes—
491C22⋊Dic47C2416yes—
492C22⋊Dic47C2416yes—
493C22⋊Dic47C2416yes—
494C22⋊Dic47C2416yes—
495C22⋊Dic47C24112yes—
496C22⋊Dic47C24112yes—
497(C2×D47)⋊C4C2412yes—
498(C2×D47)⋊C4C2412yes—
499(C2×D47)⋊C4C2412yes—
500(C2×D47)⋊C4C2412yes—
501(C2×D47)⋊C4C2416yes—
502(C2×D47)⋊C4C2416yes—
503(C2×D47)⋊C4C2416yes—
504(C2×D47)⋊C4C2416yes—
505(C2×D47)⋊C4C2416yes—
506(C2×D47)⋊C4C2416yes—
507C4⋊Dic47C2413yes—
508C4⋊Dic47C2413yes—
509C4⋊Dic47C2416yes—
510C4⋊Dic47C2416yes—
511C4⋊Dic47C2416yes—
512C4⋊Dic47C2416yes—
513C4⋊Dic47C2412yes—
514C4⋊Dic47C2412yes—
515C4⋊Dic47C2413yes—
516C4⋊Dic47C2413yes—
517C4⋊Dic47C24112yes—
518C4⋊Dic47C24112yes—
519C4⋊Dic47C2416yes—
520Dic47⋊C4C2416yes—
521Dic47⋊C4C2416yes—
522Dic47⋊C4C2416yes—
523Dic47⋊C4C2416yes—
524Dic47⋊C4C24112yes—
525Dic47⋊C4C2416yes—
526Dic47⋊C4C2416yes—
527Dic47⋊C4C2416yes—
528Dic47⋊C4C2416yes—
529Dic47⋊C4C2416yes—
530Dic47⋊C4C24112yes—
531Dic47⋊C4C2416yes—
532Dic47⋊C4C2416yes—
533Dic47⋊C4C2416yes—
534Dic47⋊C4C2416yes—
535Dic47⋊C4C2416yes—
536C4×Dic47C2413yes—
537C4×Dic47C2413yes—
538C4×Dic47C2413yes—
539C4×Dic47C2413yes—
540C4×Dic47C2413yes—
541C4×Dic47C2413yes—
542C4×Dic47C2413yes—
543C4×Dic47C2413yes—
544C4×Dic47C2413yes—
545C4×Dic47C2413yes—
546C4×Dic47C2413yes—
547C4×Dic47C2413yes—
548C4×Dic47C2416yes—
549C4×Dic47C2416yes—
550C4×Dic47C2416yes—
551C4×Dic47C24112yes—
552C4×Dic47C24112yes—
553C23×C47C2516yes—
554C23×C47C2511yescharacteristic
555C22×D47—22no—
556C22×D47—22no—
557C22×D47—22no—
558C22×D47C2512yes—
559C22×D47C2511yescharacteristic
560C22×D47C2511yescharacteristic
561Q8×C47—26no—
562Q8×C47—26no—
563Q8×C47C2×#4114yes—
564D4×C47—212no—
565D4×C47—212no—
566D4×C47—26no—
567D4×C47—46no—
568C2×C4×C47—26no—
569C2×C4×C47—212no—
570C2×C4×C47—212no—
571C2×C4×C47—43no—
572C2×C4×C47—46no—
573C2×C4×C472−1+414yescomplemented
574C2×C4×C47C2513yes—
575C2×C4×C47C2516yes—
576C2×C4×C47C2513yes—
577C2×C4×C47C2513yes—
578C2×C4×C47C2512yes—
579C2×C4×C47C2512yes—
580C2×C4×C47C2513yes—
581C2×C4×C47C2511yescharacteristic
582C2×C4×C47C2511yescharacteristic
583C22⋊D47—24no—
584C22⋊D47—212no—
585C22⋊D47—212no—
586C22⋊D47—212no—
587C22⋊D47—46no—
588C2×Dic47—22no—
589C2×Dic47—26no—
590C2×Dic47—224no—
591C2×Dic47—43no—
592C2×Dic47—412no—
593C2×Dic47C2511yescharacteristic
594C2×Dic47C2511yescharacteristic
595C2×Dic47C2513yes—
596C2×Dic47C2512yes—
597C2×Dic47C2513yes—
598C2×Dic47C2516yes—
599C2×Dic47C2516yes—
600C2×Dic47C2513yes—
601C2×Dic47C2513yes—
602D188—24no—
603D188—24no—
604D188—22no—
605C4×D47—26no—
606C4×D47—26no—
607C4×D47—26no—
608C4×D47—26no—
609C4×D47—212no—
610C4×D47—22no—
611C4×D47—22no—
612C4×D47—22no—
613C4×D47—22no—
614C4×D47—24no—
615C4×D47—26no—
616C4×D47—43no—
617C4×D47—43no—
618C4×D47—46no—
619C4×D47C2×#41112yes—
620Dic94—212no—
621Dic94—26no—
622Dic94—22no—
623Dic94—212no—
624Dic94—212no—
625Dic94—46no—
626Dic94—46no—
627Dic94C2×#41112yes—
628#62788—471nomaximal, Sylow
629C22×C47—21no—
630C22×C47—21no—
631C22×C47—26no—
632C22×C47—26no—
633C22×C47—26no—
634C22×C47C2×2−1+412yes—
635C22×C47C2611yescharacteristic
636C2×D47—28no—
637C2×D47—21no—
638C2×D47—21no—
639C2×D47—21no—
640C2×D47—21no—
641C2×D47—22no—
642C2×D47—22no—
643C2×D47—22no—
644C2×D47C22×#4112yes—
645C2×D47#58512yes—
646C4×C47—22no—
647C4×C47—23no—
648C4×C47—26no—
649C4×C47—22no—
650C4×C47—23no—
651C4×C47—23no—
652C4×C47C22×#4116yes—
653C4×C47C2×2−1+412yes—
654C4×C47C2×2−1+412yes—
655Dic47—23no—
656Dic47—26no—
657Dic47—22no—
658Dic47—21no—
659Dic47—21no—
660Dic47—26no—
661Dic47—23no—
662Dic47—23no—
663Dic47C22×#4116yes—
664#3523—471no—
665#3523—473no—
666#3522—473no—
667#3522—471no—
668#3516—476no—
669#3516—472no—
670#3507—473no—
671#3507—473no—
672#3502—471no—
673#3497—471no—
674#3492—476no—
675#3486—472no—
676#3482—476no—
677#3482—472no—
678#3480—473no—
679#3480D4711yescharacteristic, complemented
680Q8×#41—473no—
681Q8×#41—471no—
682#3461—476no—
683#3444—473no—
684#3444—473no—
685C4×2−1+4—472no—
686C22×C4×Q8—471no—
687C2×C47—22no—
688C2×C47—46no—
689C2×C47C23×#4111yescharacteristic
690C2×C47C22×2−1+411yescharacteristic
691C2×C47C2×#58511yescharacteristic
692D47—22no—
693D47—22no—
694D47—42no—
695C2×2−1+4—472no—
696C23×Q8—471no—
697#559—473no—
698#559—476no—
699#559C2×D4713yescomplemented
700Q82—471no—
701Q82—473no—
702#557—473no—
703#557—476no—
704#557—476no—
705#557—473no—
706#557—473no—
707#557—472no—
708#557C2×D4711yescharacteristic, complemented
709#556—473no—
710#556—4712no—
711#556—476no—
712#556—476no—
713#556—476no—
714#556C2×D4713yescomplemented
715#554—473no—
716#554—476no—
717#554—473no—
718#554—4712no—
719#554—476no—
720#554—476no—
721#553—4712no—
722#553—476no—
723#553C2×D4716yes—
724#552—4712no—
725#552—476no—
726#552—4712no—
727#552—476no—
728#552—476no—
729#552—476no—
730#550—473no—
731#550C2×D4711yescharacteristic, complemented
732D4×Q8—472no—
733D4×Q8—476no—
734D4×Q8—472no—
735D4×Q8—471no—
736D4×Q8—476no—
737D4×Q8—473no—
738#548—472no—
739#548—472no—
740#548—476no—
741#548—476no—
742#548—476no—
743#548C2×D4712yes—
744#547—4712no—
745#547—476no—
746#547—476no—
747#544—476no—
748#542—476no—
749#542—4712no—
750#542—476no—
751#541—4712no—
752#541—476no—
753#541—476no—
754#539—4712no—
755#539—4712no—
756#537—476no—
757#536—476no—
758#536—476no—
759#533—473no—
760#533—473no—
761#533—473no—
762#533—473no—
763#533—476no—
764#533—473no—
765#533—4712no—
766#533—473no—
767#533—476no—
768#532—473no—
769#532—473no—
770#532—473no—
771#532—473no—
772#532—473no—
773#532C2×D4713yes—
774#529—476no—
775#529—476no—
776#529—476no—
777#529—476no—
778#529—473no—
779#529—473no—
780#529—476no—
781#529—476no—
782#529—473no—
783#529—476no—
784#529—476no—
785#529—473no—
786#529—4712no—
787#529—476no—
788#529—476no—
789#529—476no—
790#529C2×D4716yescomplemented
791#525—473no—
792#525—476no—
793#525—476no—
794#525—476no—
795#525—476no—
796#525—471no—
797#520—472no—
798#520—476no—
799#520—476no—
800#520—476no—
801#519—472no—
802#519—472no—
803#519—476no—
804C4×#41—476no—
805C4×#41—476no—
806C4×#41—476no—
807C4×#41—476no—
808C4×#41—476no—
809C4×#41—473no—
810C4×#41—476no—
811C4×#41C2×D4713yes—
812C4×#41C2×D4712yescomplemented
813C2×C4×Q8—471no—
814C2×C4×Q8—471no—
815C2×C4×Q8—473no—
816C2×C4×Q8—471no—
817C2×C4×Q8—473no—
818C2×C4×Q8—471no—
819C2×C4×Q8—473no—
820C2×C4×Q8—471no—
821C2×C4×Q8—473no—
822C2×C4×Q8—472no—
823C2×C4×Q8—473no—
824C2×C4×Q8—473no—
825C2×C4×Q8—476no—
826C2×C4×Q8C2×D4711yescharacteristic
827C22×C4⋊C4—473no—
828C22×C42—473no—
829C47#6278811yescharacteristic, complemented, Sylow
8302−1+4—9416no—
831C2×#41—476no—
832C2×#41—476no—
833C2×#41—476no—
834C2×#41—471no—
835C2×#41—476no—
836C2×#41—476no—
837C2×#41C22×D4713yes—
838C2×#41C22×D4712yes—
839C22×Q8—471no—
840C22×Q8—473no—
841C22×Q8—473no—
842C22×Q8—471no—
843C22×Q8—472no—
844C22×Q8—473no—
845C22×Q8—476no—
846C22×Q8—948no—
847C22×Q8C22×D4711yescharacteristic
848C23×C4—473no—
849C23×C4—471no—
850C23×C4—473no—
851C4⋊Q8—473no—
852C4⋊Q8—476no—
853C4⋊Q8—473no—
854C4⋊Q8—473no—
855C4⋊Q8—4712no—
856C4⋊Q8—4712no—
857C4⋊Q8—476no—
858C4⋊Q8—473no—
859C4⋊Q8—473no—
860C4⋊Q8—476no—
861C4⋊Q8—476no—
862C4⋊Q8C22×D4713yes—
863#127—473no—
864#127C22×D4713yes—
865#126—476no—
866#126—476no—
867#126—4712no—
868#126—4712no—
869#126—476no—
870#126—476no—
871#126—4712no—
872#126—4712no—
873#126—4712no—
874#126C22×D47112yes—
875#125—476no—
876#125—476no—
877#125—476no—
878#125—476no—
879#125—473no—
880#125—473no—
881#125—4712no—
882#125—476no—
883#125—4712no—
884#125—4712no—
885#125—4712no—
886#125—476no—
887#125—4712no—
888#125C22×D4716yes—
889#124—473no—
890#124—476no—
891#124—476no—
892#124—473no—
893#124—476no—
894#124—476no—
895#124—476no—
896#124—4712no—
897#124C22×D4716yes—
898#124C22×D4716yes—
899#123—476no—
900#123—4712no—
901#123—476no—
902#123—476no—
903#123—472no—
904#123—4712no—
905#123—476no—
906#123—476no—
907#123—4712no—
908#123—4712no—
909#123—4712no—
910#123C22×D47112yes—
911C22⋊Q8—473no—
912C22⋊Q8—473no—
913C22⋊Q8—476no—
914C22⋊Q8—476no—
915C22⋊Q8—476no—
916C22⋊Q8—476no—
917C22⋊Q8—476no—
918C22⋊Q8—4712no—
919C22⋊Q8—471no—
920C22⋊Q8—471no—
921C22⋊Q8—476no—
922C22⋊Q8—476no—
923C22⋊Q8—476no—
924C22⋊Q8—476no—
925C22⋊Q8—476no—
926C22⋊Q8—476no—
927C22⋊Q8—4712no—
928C22⋊Q8—476no—
929C22⋊Q8—476no—
930C22⋊Q8—4712no—
931C22⋊Q8—4712no—
932C22⋊Q8—4712no—
933C22⋊Q8—4712no—
934C22⋊Q8—4712no—
935C22⋊Q8C22×D4716yes—
936#121—473no—
937#121—473no—
938#121—476no—
939#121—476no—
940#121—476no—
941#121—476no—
942#121—476no—
943#121—4712no—
944#121—471no—
945#121—471no—
946#121—476no—
947#121—476no—
948#121C22×D4716yes—
949#121C22×D4716yes—
950#121C22×D4716yes—
951#120—476no—
952#120—472no—
953C4×Q8—471no—
954C4×Q8—473no—
955C4×Q8—471no—
956C4×Q8—473no—
957C4×Q8—472no—
958C4×Q8—476no—
959C4×Q8—476no—
960C4×Q8—473no—
961C4×Q8—476no—
962C4×Q8—473no—
963C4×Q8—473no—
964C4×Q8—476no—
965C4×Q8—473no—
966C4×Q8—476no—
967C4×Q8—476no—
968C4×Q8—476no—
969C4×Q8—476no—
970C4×Q8—473no—
971C4×Q8—476no—
972C4×Q8—473no—
973C4×Q8—473no—
974C4×Q8—473no—
975C4×Q8—476no—
976C4×Q8—476no—
977C4×Q8—476no—
978C4×Q8—476no—
979C4×Q8—476no—
980C4×Q8—4712no—
981C4×Q8—476no—
982C4×Q8—476no—
983C4×Q8—476no—
984C4×Q8—476no—
985C4×Q8—473no—
986C4×Q8—473no—
987C4×Q8C22×D4711yescharacteristic
988C4×Q8C22×D4713yes—
989C4×Q8C22×D4711yescharacteristic
990C4×Q8C22×D4713yes—
991C4×Q8C22×D4713yes—
992C4×Q8C22×D4713yes—
993C4×Q8C22×D4712yes—
994C4×D4—476no—
995C4×D4—476no—
996C4×D4—4712no—
997C4×D4—4712no—
998C4×D4—476no—
999C4×D4—476no—
1000C4×D4—476no—
1001C4×D4—476no—
1002C4×D4—476no—
1003C4×D4—476no—
1004C4×D4—476no—
1005C4×D4—476no—
1006C4×D4—476no—
1007C4×D4—476no—
1008C4×D4—476no—
1009C4×D4—476no—
1010C4×D4—476no—
1011C4×D4—4712no—
1012C4×D4—4712no—
1013C4×D4—4712no—
1014C4×D4—472no—
1015C4×D4—472no—
1016C4×D4—476no—
1017C4×D4—476no—
1018C4×D4—473no—
1019C4×D4—473no—
1020C4×D4C22×D4716yes—
1021C4×D4C22×D4716yes—
1022C4×D4C22×D4716yes—
1023C4×D4C22×D4716yes—
1024C4×D4C22×D4713yes—
1025C4×D4C22×D4713yes—
1026C4×D4C22×D4716yes—
1027#117—473no—
1028#117—476no—
1029#117—4712no—
1030#117—476no—
1031#117—476no—
1032#117—476no—
1033#117—476no—
1034#117—4712no—
1035#117—4712no—
1036#117—4712no—
1037#117—476no—
1038#117—476no—
1039#117—476no—
1040#117—476no—
1041#117—476no—
1042#117C22×D4711yescharacteristic
1043#117C22×D4716yes—
1044#117C22×D4716yes—
1045C2×C4⋊C4—476no—
1046C2×C4⋊C4—473no—
1047C2×C4⋊C4—4712no—
1048C2×C4⋊C4—476no—
1049C2×C4⋊C4—473no—
1050C2×C4⋊C4—473no—
1051C2×C4⋊C4—476no—
1052C2×C4⋊C4—476no—
1053C2×C4⋊C4—473no—
1054C2×C4⋊C4—473no—
1055C2×C4⋊C4—476no—
1056C2×C4⋊C4C22×D4713yes—
1057C2×C42—473no—
1058C2×C42—473no—
1059C2×C42—473no—
1060C2×C42—4712no—
1061C2×C42—473no—
1062C2×C42—473no—
1063C2×C42—473no—
1064C2×C42—473no—
1065C2×C42—473no—
1066C2×C42—473no—
1067C2×C42—473no—
1068C2×C42—473no—
1069C2×C42—476no—
1070C2×C42C22×D4713yes—
1071C2×C42C22×D4716yes—
1072C24—471no—
1073#41—28no—
1074#41—212no—
1075#41—9424no—
1076#41—9424no—
1077#41—9424no—
1078#41—944no—
1079#41—18812no—
1080#41—18812no—
1081C2×Q8—24no—
1082C2×Q8—478no—
1083C2×Q8—473no—
1084C2×Q8—471no—
1085C2×Q8—476no—
1086C2×Q8—473no—
1087C2×Q8—476no—
1088C2×Q8—476no—
1089C2×Q8—476no—
1090C2×Q8—476no—
1091C2×Q8—9412no—
1092C2×Q8—9424no—
1093C2×Q8—9412no—
1094C2×Q8—9412no—
1095C2×Q8—944no—
1096C2×Q8—948no—
1097C2×Q8C23×D4713yes—
1098C2×Q8C23×D4713yes—
1099C2×Q8C23×D4711yescharacteristic
1100C2×D4—472no—
1101C2×D4—476no—
1102C2×D4—476no—
1103C2×D4—476no—
1104C2×D4—476no—
1105C2×D4—471no—
1106C2×D4—472no—
1107C2×D4—472no—
1108C2×D4C23×D4716yes—
1109C2×D4C23×D4713yes—
1110C2×D4C23×D4716yes—
1111C2×D4C23×D4716yes—
1112C22×C4—473no—
1113C22×C4—471no—
1114C22×C4—473no—
1115C22×C4—4712no—
1116C22×C4—473no—
1117C22×C4—4712no—
1118C22×C4—471no—
1119C22×C4—471no—
1120C22×C4—473no—
1121C22×C4—473no—
1122C22×C4—473no—
1123C22×C4—473no—
1124C22×C4—473no—
1125C22×C4—476no—
1126C22×C4—471no—
1127C22×C4—471no—
1128C22×C4—472no—
1129C22×C4—473no—
1130C22×C4—473no—
1131C22×C4—476no—
1132C22×C4—9412no—
1133C22×C4—944no—
1134C22×C4—1886no—
1135C22×C4C23×D4713yes—
1136C22×C4C23×D4716yes—
1137C22×C4C23×D4716yes—
1138C22×C4C23×D4713yes—
1139C22×C4C23×D4716yes—
1140C22×C4C23×D4711yescharacteristic
1141C4⋊C4—476no—
1142C4⋊C4—476no—
1143C4⋊C4—476no—
1144C4⋊C4—476no—
1145C4⋊C4—476no—
1146C4⋊C4—476no—
1147C4⋊C4—4712no—
1148C4⋊C4—476no—
1149C4⋊C4—476no—
1150C4⋊C4—476no—
1151C4⋊C4—476no—
1152C4⋊C4—476no—
1153C4⋊C4—476no—
1154C4⋊C4—4712no—
1155C4⋊C4—476no—
1156C4⋊C4—476no—
1157C4⋊C4—473no—
1158C4⋊C4—473no—
1159C4⋊C4—476no—
1160C4⋊C4—476no—
1161C4⋊C4—476no—
1162C4⋊C4—472no—
1163C4⋊C4—472no—
1164C4⋊C4—473no—
1165C4⋊C4—473no—
1166C4⋊C4—476no—
1167C4⋊C4—476no—
1168C4⋊C4—4712no—
1169C4⋊C4—4712no—
1170C4⋊C4C23×D4713yes—
1171C4⋊C4C23×D4713yes—
1172C4⋊C4C23×D4716yes—
1173C4⋊C4C23×D4716yes—
1174C4⋊C4C23×D4716yes—
1175C4⋊C4C23×D4711yescharacteristic
1176C4⋊C4C23×D4711yescharacteristic
1177C4⋊C4C23×D4716yes—
1178C4⋊C4C23×D4716yes—
1179C22⋊C4—476no—
1180C22⋊C4—476no—
1181C22⋊C4—476no—
1182C22⋊C4—476no—
1183C22⋊C4—4712no—
1184C22⋊C4—4712no—
1185C22⋊C4—476no—
1186C22⋊C4—472no—
1187C22⋊C4—472no—
1188C22⋊C4—476no—
1189C22⋊C4—476no—
1190C22⋊C4—476no—
1191C22⋊C4—472no—
1192C22⋊C4—472no—
1193C22⋊C4—476no—
1194C22⋊C4—476no—
1195C22⋊C4—476no—
1196C22⋊C4C23×D47112yes—
1197C22⋊C4C23×D47112yes—
1198C22⋊C4C23×D4712yes—
1199C22⋊C4C23×D4716yes—
1200C22⋊C4C23×D4716yes—
1201C42—473no—
1202C42—473no—
1203C42—473no—
1204C42—473no—
1205C42—473no—
1206C42—473no—
1207C42—473no—
1208C42—473no—
1209C42—473no—
1210C42—473no—
1211C42—4712no—
1212C42—476no—
1213C42—4712no—
1214C42—476no—
1215C42—473no—
1216C42—473no—
1217C42—476no—
1218C42C23×D4713yes—
1219C42C23×D4713yes—
1220C42C23×D4716yes—
1221C42C23×D4716yes—
1222C42C23×D4713yes—
1223C42C23×D4713yes—
1224C42C23×D4712yes—
1225C23—471no—
1226C23—471no—
1227C23—472no—
1228C23—942no—
1229C23—942no—
1230C23—942no—
1231C23C24×D4716yes—
1232C23C24×D4711yescharacteristic
1233Q8—26no—
1234Q8—26no—
1235Q8—4712no—
1236Q8—9412no—
1237Q8—9412no—
1238Q8—946no—
1239Q8—9412no—
1240Q8—942no—
1241Q8—1886no—
1242Q8—1886no—
1243Q8#41×D4714yes—
1244D4—212no—
1245D4—212no—
1246D4—26no—
1247D4—46no—
1248D4—944no—
1249D4—944no—
1250D4—9412no—
1251D4—9412no—
1252D4—9412no—
1253D4—944no—
1254D4—942no—
1255D4—1886no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—473no—
1262C2×C4—4712no—
1263C2×C4—471no—
1264C2×C4—471no—
1265C2×C4—473no—
1266C2×C4—472no—
1267C2×C4—473no—
1268C2×C4—476no—
1269C2×C4—476no—
1270C2×C4—473no—
1271C2×C4—946no—
1272C2×C4—946no—
1273C2×C4—946no—
1274C2×C4—946no—
1275C2×C4—946no—
1276C2×C4—9424no—
1277C2×C4—942no—
1278C2×C4—946no—
1279C2×C4—9412no—
1280C2×C4—942no—
1281C2×C4—942no—
1282C2×C4—942no—
1283C2×C4—942no—
1284C2×C4—944no—
1285C2×C4—1883no—
1286C2×C4—1883no—
1287C2×C4—1886no—
1288C2×C4—1883no—
1289C2×C4—18812no—
1290C2×C4#1309407114yescomplemented
1291C2×C4C24×D4713yes—
1292C2×C4C24×D4716yes—
1293C2×C4C24×D4713yes—
1294C2×C4C24×D4713yes—
1295C2×C4C24×D4712yes—
1296C2×C4C24×D4712yes—
1297C2×C4C24×D4713yes—
1298C2×C4C24×D4711yescharacteristic
1299C2×C4C24×D4711yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—26no—
1303C22—26no—
1304C22—26no—
1305C22—472no—
1306C22—472no—
1307C22—948no—
1308C22—941no—
1309C22—941no—
1310C22—941no—
1311C22—941no—
1312C22—942no—
1313C22—942no—
1314C22—942no—
1315C22C2×#1309407112yes—
1316C22C25×D4711yescharacteristic
1317C4—22no—
1318C4—23no—
1319C4—26no—
1320C4—23no—
1321C4—22no—
1322C4—23no—
1323C4—476no—
1324C4—946no—
1325C4—943no—
1326C4—941no—
1327C4—941no—
1328C4—942no—
1329C4—943no—
1330C4—943no—
1331C4—946no—
1332C4C2×#41×D4716yes—
1333C4C2×#1309407112yes—
1334C4C2×#1309407112yes—
1335C2—22no—
1336C2—46no—
1337C2—942no—
1338C2—942no—
1339C2—1882no—
1340C2C22×#41×D4711yescharacteristic
1341C2C22×#1309407111yescharacteristic
1342C2#585×D4711yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC47×#3480C2
hypercenter#3480D47
hypocenterC47#62788
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #20257485C2semidirect
2. #20257483C2semidirect
3. #20257470C2semidirect
4. #20257468C2semidirect
5. #20257372C2semidirect
6. #20257370C2semidirect
7. #20257245C2semidirect
8. #20257243C2semidirect
9. #20257192C2semidirect
10. #20257153C2semidirect
11. #20257092C2semidirect
12. #20257034C2semidirect
13. #20257010C2semidirect
14. #20257001C2semidirect
15. #20256985C2semidirect
16. Q8×#10625350C2semidirect
17. #41×Dic94C2semidirect
18. #20256813C2semidirect
19. #20256683C2semidirect
20. #20256681C2semidirect
21. C4×#13094071C2semidirect
22. C2×C4×Q8×D47C2semidirect
23. C47×#3480C2semidirect
26. #15689859C22semidirect
27. #15689855C22semidirect
28. Q8×Dic94C22semidirect
29. Q8×Dic94C22semidirect
30. #15689852C22semidirect
31. #15689852C22semidirect
32. #15689851C22semidirect
33. #15689850C22semidirect
34. #15689849C22semidirect
35. #15689848C22semidirect
36. #15689847C22semidirect
37. #15689843C22semidirect
38. #15689842C22semidirect
39. #15689842C22semidirect
40. #15689840C22semidirect
41. #15689833C22semidirect
43. #15689832C22semidirect
45. #15689830C22semidirect
49. #15689815C22semidirect
51. #15689812C22semidirect
53. #15689810C22semidirect
55. #15689793C22semidirect
57. Q8×D188C22semidirect
59. D4×Dic94C22semidirect
64. #15689780C22semidirect
66. #15689779C22semidirect
71. #15689742C22semidirect
72. #15689741C22semidirect
73. #15689740C22semidirect
74. #15689736C22semidirect
75. #15689733C22semidirect
76. #15689730C22semidirect
83. #15689680C22semidirect
88. #15689677C22semidirect
90. #15689676C22semidirect
102. #15689655C22semidirect
107. #15689653C22semidirect
118. #15689606C22semidirect
121. #15689602C22semidirect
122. #15689600C22semidirect
124. #15689599C22semidirect
131. C4×#10625352C22semidirect
134. C2×C4×Dic94C22semidirect
144. C4×Q8×D47C22semidirect
147. C47×#559C22semidirect
148. C47×#557C22semidirect
149. C47×#556C22semidirect
151. C47×#550C22semidirect
154. C47×#529C22semidirect
156. C4×#41×C47C22semidirect
431. Q8×D47#41semidirect
573. C2×C4×C472−1+4semidirect
679. #3480D47semidirect
699. #559C2×D47semidirect
708. #557C2×D47semidirect
714. #556C2×D47semidirect
731. #550C2×D47semidirect
790. #529C2×D47semidirect
812. C4×#41C2×D47semidirect
829. C47#62788semidirect
1290. C2×C4#13094071semidirect

Maximal subgroups

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

subgroupindex
#202574852
#202574832
#202574702
#202574682
#202573722
#202573702
#202572452
#202572432
#202571922
#202571532
#202570922
#202570342
#202570102
#202570012
#202569852
Q8×#106253502
#41×Dic942
#202568132
#202566832
#202566812
C4×#130940712
C2×C4×Q8×D472
C47×#34802
#6278847