Finite Group Databasebeta

← D47×#3567 #27123712

Subgroups — D47×#3567 #27123712

Order 12032.

6662 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20258078C211yesmaximal, characteristic, complemented
2#20258077C216yesmaximal, complemented
3#20258076C213yesmaximal, complemented
4#20258075C213yesmaximal, complemented
5#20258074C216yesmaximal, complemented
6#20258073C216yesmaximal, complemented
7#20258072C216yesmaximal, complemented
8#564×D47C211yesmaximal, characteristic, complemented
9#562×D47C213yesmaximal, complemented
10#553×D47C216yesmaximal, complemented
11#552×D47C216yesmaximal, complemented
12#540×D47C216yesmaximal, complemented
13#539×D47C216yesmaximal, complemented
14#529×D47C213yesmaximal, complemented
15C47×#3567C211yesmaximal, characteristic, complemented
16C47⋊#564C2216yescomplemented
17C47⋊#564C2216yescomplemented
18C47⋊#564C2213yescomplemented
19#15689871C2213yescomplemented
20#15689870C2216yescomplemented
21#15689870C2216yescomplemented
22#15689869C2216yescomplemented
23#15689869C2216yescomplemented
24#15689868C2216yescomplemented
25#15689868C2216yescomplemented
26#15689867C2213yescomplemented
27#15689867C2213yescomplemented
28#15689826C2216yescomplemented
29#15689825C2216yescomplemented
30#15689824C2216yescomplemented
31#15689824C2216yescomplemented
32#15689823C2216yescomplemented
33#15689822C2216yescomplemented
34#15689822C2216yescomplemented
35#15689821C2216yescomplemented
36#15689820C2216yescomplemented
37#15689819C2216yescomplemented
38#15689818C2216yescomplemented
39#15689818C2216yescomplemented
40#15689817C2216yescomplemented
41#15689816C2216yescomplemented
42#15689816C2216yescomplemented
43#15689815C2216yescomplemented
44#15689814C2216yescomplemented
45#15689813C2216yescomplemented
46#15689812C2216yescomplemented
47#15689811C2216yescomplemented
48#15689810C2216yescomplemented
49#15689810C2216yescomplemented
50#15689809C2216yescomplemented
51#15689809C2216yescomplemented
52#15689808C2216yescomplemented
53#15689807C2216yescomplemented
54#15689806C2216yescomplemented
55#15689806C2216yescomplemented
56#15689805C2216yescomplemented
57#15689805C2216yescomplemented
58#15689729C2216yescomplemented
59#15689728C2216yescomplemented
60#15689727C2216yescomplemented
61#15689726C2216yescomplemented
62#15689726C2216yescomplemented
63#15689725C2216yescomplemented
64#15689725C2216yescomplemented
65#15689725C2216yescomplemented
66#15689725C2216yescomplemented
67#15689724C2216yescomplemented
68#15689724C2216yescomplemented
69#15689723C2216yescomplemented
70#15689723C2216yescomplemented
71#15689723C2216yescomplemented
72#15689723C2216yescomplemented
73#15689722C2216yescomplemented
74#15689721C2216yescomplemented
75#15689721C2216yescomplemented
76#15689720C2216yescomplemented
77#15689719C2216yescomplemented
78#15689719C2216yescomplemented
79#15689718C2216yescomplemented
80#15689717C2216yescomplemented
81#15689717C2216yescomplemented
82#15689716C2216yescomplemented
83#15689716C2216yescomplemented
84#15689715C2216yescomplemented
85#15689715C2216yescomplemented
86#15689714C2216yescomplemented
87#15689714C2216yescomplemented
88#127×D47C2212yes—
89#15689660C2213yescomplemented
90#15689659C2213yescomplemented
91#15689658C2213yescomplemented
92#15689657C2213yescomplemented
93#15689656C2216yescomplemented
94#15689655C2213yescomplemented
95#15689654C2213yescomplemented
96#15689653C2216yescomplemented
97#15689652C2213yescomplemented
98#15689651C2216yescomplemented
99#15689650C2216yescomplemented
100#126×D47C2216yes—
101#126×D47C2216yes—
102#126×D47C2212yes—
103#125×D47C2216yes—
104#125×D47C2216yes—
105#125×D47C2213yes—
106#125×D47C2216yes—
107#124×D47C2213yes—
108#123×D47C2216yes—
109#123×D47C2216yes—
110#123×D47C2216yes—
111#123×D47C2216yes—
112#123×D47C2216yes—
113C22⋊Q8×D47C2216yes—
114C22⋊Q8×D47C2216yes—
115C22⋊Q8×D47C2213yes—
116#121×D47C2213yes—
117#121×D47C2216yes—
118#121×D47C2216yes—
119#121×D47C2216yes—
120#121×D47C2216yes—
121C4×Q8×D47C2213yes—
122C4×D4×D47C2216yes—
123C4×D4×D47C2213yes—
124C4×D4×D47C2216yes—
125C4×D4×D47C2216yes—
126#117×D47C2216yes—
127#117×D47C2216yes—
128C2×C4⋊C4×D47C2216yes—
129C2×C42×D47C2211yescharacteristic
130C47×#564C2211yescharacteristic, complemented
131C47×#562C2213yescomplemented
132C47×#553C2216yescomplemented
133C47×#552C2216yescomplemented
134C47×#540C2216yescomplemented
135C47×#539C2216yescomplemented
136C47×#529C2213yescomplemented
137C2×Q8×D47C2313yes—
138C2×D4×D47C2316yes—
139C2×D4×D47C2313yes—
140C2×D4×D47C2316yes—
141C2×D4×D47C2316yes—
142C22×C4×D47C2313yes—
143C22×C4×D47C2316yes—
144C22×C4×D47C2316yes—
145C22×C4×D47C2316yes—
146#13094021C2312yes—
147#13094020C2316yes—
148#13094020C2316yes—
149#13094019C2316yes—
150#13094019C2316yes—
151#13094019C2316yes—
152#13094019C2316yes—
153#13094019C2316yes—
154#13094019C2316yes—
155#13094019C2316yes—
156#13094018C2316yes—
157#13094018C2316yes—
158#13094018C2312yes—
159#13094017C2316yes—
160#13094017C2316yes—
161#13094017C2316yes—
162#13094017C2316yes—
163#13094017C2316yes—
164#13094017C2316yes—
165#13094017C2316yes—
166#13094016C2316yes—
167#13094016C2316yes—
168#13094016C2316yes—
169#13094016C2313yes—
170#13094015C2316yes—
171#13094015C2316yes—
172#13094015C2316yes—
173#13094015C2316yes—
174#13094015C2316yes—
175#13094015C2316yes—
176#13094015C2313yes—
177#13094015C2313yes—
178#13094014C2316yes—
179#13094014C2316yes—
180#13094014C2316yes—
181#13094014C2316yes—
182#13094014C2316yes—
183#13094014C2316yes—
184#13094014C2316yes—
185#13094014C2316yes—
186#13094014C2316yes—
187#13094014C2316yes—
188#13094014C2316yes—
189#13094014C2316yes—
190#13094014C2316yes—
191#13094014C2316yes—
192#13094013C2313yes—
193#13094012C2313yes—
194#13094011C2313yes—
195#13094010C2316yes—
196#13094010C2316yes—
197#13094009C2316yes—
198#13094009C2316yes—
199#13094009C2316yes—
200#13094009C2316yes—
201#13094009C2316yes—
202#13094009C2316yes—
203#13094009C2316yes—
204#13094009C2316yes—
205#13094009C2316yes—
206#13094009C2316yes—
207#13094008C2316yes—
208#13094008C2316yes—
209#13094008C2316yes—
210#13094008C2316yes—
211#13094008C2316yes—
212#13094007C2316yes—
213#13094007C2316yes—
214#13094007C2316yes—
215#13094007C2316yes—
216#13094007C2316yes—
217#13094006C2316yes—
218#13094006C2316yes—
219#13094006C2316yes—
220#13094006C2316yes—
221#13094006C2316yes—
222#13094006C2316yes—
223#13094006C2316yes—
224#13094006C2316yes—
225#13094006C2316yes—
226#13094006C2316yes—
227#13094005C2316yes—
228#13094005C2316yes—
229#13094005C2316yes—
230#13094005C2316yes—
231#13094005C2316yes—
232#13094004C2316yes—
233#13094004C2316yes—
234#13094004C2313yes—
235#13094003C2316yes—
236#13094003C2316yes—
237#13094003C2313yes—
238#13094002C2316yes—
239#13094002C2316yes—
240#13094002C2316yes—
241#13094002C2316yes—
242#13094002C2316yes—
243#13094001C2316yes—
244#13094001C2316yes—
245#13094001C2316yes—
246#13094001C2316yes—
247#13094001C2316yes—
248#13094000C2316yes—
249#13094000C2316yes—
250#13094000C2313yes—
251#13093999C2313yes—
252#13093999C2316yes—
253#13093999C2316yes—
254#13093999C2316yes—
255#13093999C2316yes—
256#13093998C2316yes—
257#13093998C2316yes—
258#13093998C2316yes—
259#13093998C2316yes—
260#13093998C2313yes—
261#13093997C2316yes—
262#13093997C2316yes—
263#13093997C2316yes—
264#13093997C2316yes—
265#13093997C2316yes—
266#13093997C2316yes—
267#13093997C2316yes—
268#13093997C2316yes—
269#13093997C2316yes—
270#13093996C2316yes—
271#13093996C2316yes—
272#13093996C2316yes—
273#13093996C2316yes—
274#13093996C2316yes—
275#13093996C2316yes—
276#13093996C2316yes—
277#13093996C2316yes—
278#13093996C2316yes—
279#13093995C2316yes—
280#13093995C2316yes—
281#13093995C2316yes—
282#13093995C2313yes—
283#13093995C2316yes—
284Q8×Dic47C2313yes—
285C4×Dic94C2313yes—
286C4×Dic94C2316yes—
287#13093989C2313yes—
288#13093989C2316yes—
289C4×D188C2316yes—
290C4×D188C2316yes—
291C4×D188C2313yes—
292C4×D188C2316yes—
293D4×Dic47C2316yes—
294D4×Dic47C2316yes—
295D4×Dic47C2313yes—
296D4×Dic47C2316yes—
297#13093986C2316yes—
298#13093986C2316yes—
299#13093986C2316yes—
300#13093986C2313yes—
301C4×C22⋊D47C2316yes—
302C4×C22⋊D47C2316yes—
303C4×C22⋊D47C2316yes—
304C4×C22⋊D47C2316yes—
305C4×C22⋊D47C2316yes—
306C4×C22⋊D47C2316yes—
307C4×C22⋊D47C2316yes—
308(C22⋊D47)⋊C4C2316yes—
309(C22⋊D47)⋊C4C2316yes—
310(C22⋊D47)⋊C4C2316yes—
311(C22⋊D47)⋊C4C2316yes—
312(C22⋊D47)⋊C4C2316yes—
313(C22⋊D47)⋊C4C2316yes—
314(C22⋊D47)⋊C4C2316yes—
315#13093983C2316yes—
316#13093983C2316yes—
317#13093982C2316yes—
318#13093982C2316yes—
319#13093982C2316yes—
320#13093982C2316yes—
321#13093981C2316yes—
322#13093981C2316yes—
323#13093981C2316yes—
324#13093981C2316yes—
325#13093980C2316yes—
326#13093980C2316yes—
327#13093980C2316yes—
328#13093980C2316yes—
329C2×C4⋊Dic47C2316yes—
330C2×Dic47⋊C4C2316yes—
331C2×Dic47⋊C4C2316yes—
332C4⋊C4×D47C2316yes—
333C4⋊C4×D47C2316yes—
334C4⋊C4×D47C2316yes—
335C4⋊C4×D47C2316yes—
336C4⋊C4×D47C2316yes—
337C4⋊C4×D47C2316yes—
338C4⋊C4×D47C2316yes—
339C4⋊C4×D47C2316yes—
340C4⋊C4×D47C2316yes—
341C4⋊C4×D47C2316yes—
342C4⋊C4×D47C2316yes—
343C4⋊C4×D47C2316yes—
344C4⋊C4×D47C2313yes—
345C4⋊C4×D47C2313yes—
346C22⋊C4×D47C2316yes—
347C22⋊C4×D47C2316yes—
348C22⋊C4×D47C2316yes—
349C22⋊C4×D47C2316yes—
350C22⋊C4×D47C2316yes—
351C22⋊C4×D47C2316yes—
352C22⋊C4×D47C2316yes—
353C2×C4×Dic47C2313yes—
354C42×D47C2313yes—
355C42×D47C2311yescharacteristic
356C42×D47C2313yes—
357C42×D47C2311yescharacteristic
358C42×D47C2312yes—
359C42×D47C2316yes—
360C42×D47C2312yes—
361#127×C47C2312yes—
362#126×C47C2316yes—
363#126×C47C2316yes—
364#126×C47C2312yes—
365#125×C47C2316yes—
366#125×C47C2316yes—
367#125×C47C2313yes—
368#125×C47C2316yes—
369#124×C47C2313yes—
370#123×C47C2316yes—
371#123×C47C2316yes—
372#123×C47C2316yes—
373#123×C47C2316yes—
374#123×C47C2316yes—
375C22⋊Q8×C47C2316yes—
376C22⋊Q8×C47C2313yes—
377C22⋊Q8×C47C2316yes—
378#121×C47C2313yes—
379#121×C47C2316yes—
380#121×C47C2316yes—
381#121×C47C2316yes—
382#121×C47C2316yes—
383C4×Q8×C47C2313yes—
384C4×D4×C47C2316yes—
385C4×D4×C47C2313yes—
386C4×D4×C47C2316yes—
387C4×D4×C47C2316yes—
388#117×C47C2316yes—
389#117×C47C2316yes—
390C2×C4⋊C4×C47C2316yes—
391C2×C42×C47C2311yescharacteristic
392C23×D47C2416yes—
393C23×D47C2411yescharacteristic
394C2×Q8×C47C2413yes—
395C2×D4×C47C2416yes—
396C2×D4×C47C2413yes—
397C2×D4×C47C2416yes—
398C2×D4×C47C2416yes—
399C22×C4×C47C2413yes—
400C22×C4×C47C2416yes—
401C22×C4×C47C2416yes—
402C22×C4×C47C2416yes—
403C2×C22⋊D47C2416yes—
404C2×C22⋊D47C2416yes—
405C2×C22⋊D47C2416yes—
406C2×C22⋊D47C2416yes—
407C2×C22⋊D47C2416yes—
408C2×C22⋊D47C2416yes—
409C2×C22⋊D47C2416yes—
410C22×Dic47C2413yes—
411C22×Dic47C2416yes—
412C22×Dic47C2416yes—
413C22×Dic47C2416yes—
414Q8×D47—46no—
415D4×D47—412no—
416D4×D47—412no—
417D4×D47—412no—
418D4×D47—46no—
419C2×D188C2413yes—
420C2×D188C2416yes—
421C2×D188C2416yes—
422C2×D188C2416yes—
423C2×C4×D47—412no—
424C2×C4×D47—46no—
425C2×C4×D47—412no—
426C2×C4×D47—412no—
427C2×C4×D47C2413yes—
428C2×C4×D47C2413yes—
429C2×C4×D47C2416yes—
430C2×C4×D47C2416yes—
431C2×C4×D47C2416yes—
432C2×C4×D47C2413yes—
433C2×C4×D47C2413yes—
434C2×C4×D47C2416yes—
435C2×C4×D47C2416yes—
436C2×C4×D47C2416yes—
437C2×C4×D47C2416yes—
438C2×C4×D47C2416yes—
439C2×C4×D47C2416yes—
440C2×Dic94C2413yes—
441C2×Dic94C2416yes—
442C4⋊C4×C47C2416yes—
443C4⋊C4×C47C2416yes—
444C4⋊C4×C47C2416yes—
445C4⋊C4×C47C2416yes—
446C4⋊C4×C47C2416yes—
447C4⋊C4×C47C2416yes—
448C4⋊C4×C47C2416yes—
449C4⋊C4×C47C2416yes—
450C4⋊C4×C47C2413yes—
451C4⋊C4×C47C2413yes—
452C22⋊C4×C47C2416yes—
453C22⋊C4×C47C2416yes—
454C22⋊C4×C47C2416yes—
455C22⋊C4×C47C2416yes—
456C22⋊C4×C47C2416yes—
457C22⋊C4×C47C2416yes—
458C22⋊C4×C47C2416yes—
459C42×C47C2413yes—
460C42×C47C2411yescharacteristic
461C42×C47C2412yes—
462C42×C47C2416yes—
463C42×C47C2412yes—
464C22⋊Dic47C2416yes—
465C22⋊Dic47C2416yes—
466C22⋊Dic47C2416yes—
467C22⋊Dic47C2416yes—
468C22⋊Dic47C2416yes—
469C22⋊Dic47C2416yes—
470C22⋊Dic47C2416yes—
471(C2×D47)⋊C4C2416yes—
472(C2×D47)⋊C4C2416yes—
473(C2×D47)⋊C4C2416yes—
474(C2×D47)⋊C4C2416yes—
475(C2×D47)⋊C4C2416yes—
476(C2×D47)⋊C4C2416yes—
477(C2×D47)⋊C4C2416yes—
478(C2×D47)⋊C4C2416yes—
479(C2×D47)⋊C4C2416yes—
480(C2×D47)⋊C4C2416yes—
481(C2×D47)⋊C4C2416yes—
482(C2×D47)⋊C4C2416yes—
483(C2×D47)⋊C4C2416yes—
484(C2×D47)⋊C4C2416yes—
485C4⋊Dic47C2416yes—
486C4⋊Dic47C2416yes—
487C4⋊Dic47C2416yes—
488C4⋊Dic47C2416yes—
489C4⋊Dic47C2416yes—
490C4⋊Dic47C2416yes—
491C4⋊Dic47C2416yes—
492C4⋊Dic47C2416yes—
493C4⋊Dic47C2413yes—
494C4⋊Dic47C2413yes—
495Dic47⋊C4C2416yes—
496Dic47⋊C4C2416yes—
497Dic47⋊C4C2416yes—
498Dic47⋊C4C2416yes—
499Dic47⋊C4C2416yes—
500Dic47⋊C4C2416yes—
501Dic47⋊C4C2416yes—
502Dic47⋊C4C2416yes—
503Dic47⋊C4C2416yes—
504Dic47⋊C4C2416yes—
505Dic47⋊C4C2416yes—
506Dic47⋊C4C2416yes—
507Dic47⋊C4C2416yes—
508Dic47⋊C4C2416yes—
509Dic47⋊C4C2416yes—
510Dic47⋊C4C2416yes—
511Dic47⋊C4C2416yes—
512Dic47⋊C4C2416yes—
513C4×Dic47C2413yes—
514C4×Dic47C2413yes—
515C4×Dic47C2413yes—
516C4×Dic47C2413yes—
517C4×Dic47C2416yes—
518C4×Dic47C2416yes—
519C4×Dic47C2416yes—
520C4×Dic47C2416yes—
521C4×Dic47C2416yes—
522C23×C47C2516yes—
523C23×C47C2511yescharacteristic
524C22×D47—212no—
525C22×D47—212no—
526C22×D47—26no—
527C22×D47—212no—
528C22×D47C2516yes—
529C22×D47C2511yescharacteristic
530C22×D47C2511yescharacteristic
531Q8×C47—43no—
532D4×C47—43no—
533D4×C47—46no—
534D4×C47—46no—
535D4×C47—46no—
536C2×C4×C47—46no—
537C2×C4×C47—46no—
538C2×C4×C47—43no—
539C2×C4×C47—46no—
540C2×C4×C47C2513yes—
541C2×C4×C47C2516yes—
542C2×C4×C47C2513yes—
543C2×C4×C47C2516yes—
544C2×C4×C47C2516yes—
545C22⋊D47—46no—
546C22⋊D47—46no—
547C22⋊D47—46no—
548C22⋊D47—46no—
549C22⋊D47—46no—
550C22⋊D47—46no—
551C22⋊D47—46no—
552C2×Dic47—46no—
553C2×Dic47—46no—
554C2×Dic47—43no—
555C2×Dic47—46no—
556C2×Dic47C2513yes—
557C2×Dic47C2516yes—
558C2×Dic47C2513yes—
559C2×Dic47C2516yes—
560C2×Dic47C2516yes—
561D188—43no—
562D188—46no—
563D188—46no—
564D188—46no—
565C4×D47—26no—
566C4×D47—212no—
567C4×D47—212no—
568C4×D47—212no—
569C4×D47—26no—
570C4×D47—46no—
571C4×D47—46no—
572C4×D47—43no—
573C4×D47—43no—
574C4×D47—46no—
575C4×D47—46no—
576C4×D47—46no—
577C4×D47—46no—
578Dic94—43no—
579Dic94—46no—
580C2×#3567—471nomaximal, Sylow
581C22×C47—26no—
582C22×C47—26no—
583C22×C47—23no—
584C22×C47—26no—
585C22×C47C2611yescharacteristic
586C2×D47—26no—
587C2×D47—26no—
588C2×D47—23no—
589C2×D47—26no—
590C2×D47—424no—
591C2×D47—44no—
592C2×D47#58516yes—
593C4×C47—26no—
594C4×C47—23no—
595C4×C47—23no—
596C4×C47—26no—
597C4×C47—26no—
598Dic47—26no—
599Dic47—23no—
600Dic47—23no—
601Dic47—26no—
602Dic47—26no—
603#3567—471no—
604#3567—473no—
605#3567—476no—
606#3567—476no—
607#3567—476no—
608#3567—476no—
609#3567—473no—
610#3567D4711yescharacteristic, direct product factor
611C2×#564—471no—
612C2×#562—473no—
613C2×#553—476no—
614C2×#552—476no—
615C2×#540—476no—
616C2×#539—476no—
617C2×#529—473no—
618C2×C47—46no—
619C2×C47—41no—
620C2×C47C2×#58513yes—
621D47—46no—
622D47—41no—
623D47#356714yesdirect product factor
624#564—476no—
625#564—476no—
626#564—473no—
627#564C2×D4711yescharacteristic, complemented
628#562—473no—
629#562—473no—
630#562—473no—
631#562—476no—
632#562—476no—
633#562—476no—
634#562—476no—
635#562—476no—
636#562—476no—
637#562C2×D4713yescomplemented
638#553—476no—
639#553—476no—
640#553—476no—
641#553—476no—
642#553—476no—
643#553—476no—
644#553—476no—
645#553—476no—
646#553—476no—
647#553—476no—
648#553—476no—
649#553—476no—
650#553—476no—
651#553—476no—
652#553—476no—
653#553C2×D4716yescomplemented
654#552—476no—
655#552—476no—
656#552—476no—
657#552—476no—
658#552—476no—
659#552—476no—
660#552—476no—
661#552—476no—
662#552—476no—
663#552—476no—
664#552—476no—
665#552—476no—
666#552—476no—
667#552—476no—
668#552—476no—
669#552C2×D4716yescomplemented
670#540—476no—
671#540—476no—
672#540—476no—
673#540—476no—
674#540—476no—
675#540—476no—
676#540—476no—
677#540—476no—
678#540—476no—
679#540—476no—
680#540—476no—
681#540—476no—
682#540—476no—
683#540—476no—
684#540—476no—
685#540C2×D4716yescomplemented
686#539—476no—
687#539—476no—
688#539—476no—
689#539—476no—
690#539—476no—
691#539—476no—
692#539—476no—
693#539—476no—
694#539—476no—
695#539—476no—
696#539—476no—
697#539—476no—
698#539—476no—
699#539—476no—
700#539—476no—
701#539C2×D4716yescomplemented
702C2×#127—472no—
703#529—476no—
704#529—473no—
705#529—473no—
706#529—476no—
707#529—473no—
708#529—473no—
709#529—473no—
710#529—476no—
711#529—473no—
712#529—476no—
713#529—473no—
714#529C2×D4713yescomplemented
715C2×#126—476no—
716C2×#126—472no—
717C2×#126—476no—
718C2×#125—473no—
719C2×#125—476no—
720C2×#125—476no—
721C2×#125—476no—
722C2×#124—473no—
723C2×#123—476no—
724C2×#123—476no—
725C2×#123—476no—
726C2×#123—476no—
727C2×#123—476no—
728C2×C22⋊Q8—473no—
729C2×C22⋊Q8—476no—
730C2×C22⋊Q8—476no—
731C2×#121—473no—
732C2×#121—476no—
733C2×#121—476no—
734C2×#121—476no—
735C2×#121—476no—
736C2×C4×Q8—473no—
737C2×C4×D4—476no—
738C2×C4×D4—473no—
739C2×C4×D4—476no—
740C2×C4×D4—476no—
741C2×#117—476no—
742C2×#117—476no—
743C22×C4⋊C4—476no—
744C22×C42—471no—
745C47C2×#356711yescharacteristic, complemented, Sylow
746C22×Q8—473no—
747C22×D4—476no—
748C22×D4—473no—
749C22×D4—476no—
750C22×D4—476no—
751C23×C4—476no—
752C23×C4—476no—
753C23×C4—476no—
754C23×C4—473no—
755#127—476no—
756#127—476no—
757#127—472no—
758#127C22×D4712yes—
759#126—476no—
760#126—476no—
761#126—476no—
762#126—476no—
763#126—476no—
764#126—476no—
765#126—476no—
766#126—476no—
767#126—476no—
768#126—476no—
769#126—476no—
770#126—476no—
771#126—476no—
772#126—476no—
773#126—476no—
774#126—472no—
775#126—476no—
776#126C22×D4716yes—
777#126C22×D4712yes—
778#126C22×D4716yes—
779#125—476no—
780#125—476no—
781#125—473no—
782#125—473no—
783#125—476no—
784#125—476no—
785#125—476no—
786#125—476no—
787#125—476no—
788#125—476no—
789#125—476no—
790#125—476no—
791#125—476no—
792#125—476no—
793#125—476no—
794#125—476no—
795#125—476no—
796#125—476no—
797#125—476no—
798#125—476no—
799#125—476no—
800#125—476no—
801#125—473no—
802#125—476no—
803#125—476no—
804#125—476no—
805#125C22×D4713yes—
806#125C22×D4716yes—
807#125C22×D4716yes—
808#125C22×D4716yes—
809#124—473no—
810#124—473no—
811#124—476no—
812#124—476no—
813#124—473no—
814#124C22×D4713yes—
815#123—476no—
816#123—476no—
817#123—476no—
818#123—476no—
819#123—476no—
820#123—476no—
821#123—476no—
822#123—476no—
823#123—476no—
824#123—476no—
825#123—476no—
826#123—476no—
827#123—476no—
828#123—476no—
829#123—476no—
830#123—476no—
831#123—476no—
832#123—476no—
833#123—476no—
834#123—476no—
835#123—476no—
836#123—476no—
837#123—476no—
838#123—476no—
839#123—476no—
840#123—476no—
841#123—476no—
842#123—476no—
843#123—476no—
844#123—476no—
845#123—476no—
846#123—476no—
847#123—476no—
848#123—476no—
849#123—476no—
850#123C22×D4716yes—
851#123C22×D4716yes—
852#123C22×D4716yes—
853#123C22×D4716yes—
854#123C22×D4716yes—
855C22⋊Q8—473no—
856C22⋊Q8—476no—
857C22⋊Q8—476no—
858C22⋊Q8—473no—
859C22⋊Q8—476no—
860C22⋊Q8—476no—
861C22⋊Q8—476no—
862C22⋊Q8—473no—
863C22⋊Q8—476no—
864C22⋊Q8—476no—
865C22⋊Q8—476no—
866C22⋊Q8—476no—
867C22⋊Q8—476no—
868C22⋊Q8—476no—
869C22⋊Q8—476no—
870C22⋊Q8—476no—
871C22⋊Q8—476no—
872C22⋊Q8—476no—
873C22⋊Q8—476no—
874C22⋊Q8C22×D4713yes—
875C22⋊Q8C22×D4716yes—
876C22⋊Q8C22×D4716yes—
877#121—473no—
878#121—476no—
879#121—476no—
880#121—476no—
881#121—476no—
882#121—476no—
883#121—476no—
884#121—476no—
885#121—476no—
886#121—476no—
887#121—476no—
888#121—476no—
889#121—476no—
890#121—476no—
891#121—473no—
892#121—476no—
893#121—476no—
894#121—476no—
895#121—476no—
896#121—473no—
897#121—476no—
898#121—476no—
899#121—476no—
900#121—476no—
901#121—476no—
902#121—476no—
903#121—476no—
904#121—476no—
905#121—476no—
906#121—476no—
907#121—476no—
908#121—476no—
909#121—476no—
910#121C22×D4713yes—
911#121C22×D4716yes—
912#121C22×D4716yes—
913#121C22×D4716yes—
914#121C22×D4716yes—
915C4×Q8—473no—
916C4×Q8—473no—
917C4×Q8—476no—
918C4×Q8—476no—
919C4×Q8—473no—
920C4×Q8C22×D4713yes—
921C4×D4—476no—
922C4×D4—473no—
923C4×D4—476no—
924C4×D4—476no—
925C4×D4—476no—
926C4×D4—476no—
927C4×D4—476no—
928C4×D4—476no—
929C4×D4—476no—
930C4×D4—476no—
931C4×D4—476no—
932C4×D4—476no—
933C4×D4—473no—
934C4×D4—476no—
935C4×D4—476no—
936C4×D4—476no—
937C4×D4—476no—
938C4×D4—476no—
939C4×D4—476no—
940C4×D4—476no—
941C4×D4—476no—
942C4×D4—476no—
943C4×D4—476no—
944C4×D4—473no—
945C4×D4—476no—
946C4×D4—476no—
947C4×D4C22×D4716yes—
948C4×D4C22×D4713yes—
949C4×D4C22×D4716yes—
950C4×D4C22×D4716yes—
951#117—476no—
952#117—476no—
953#117—476no—
954#117—476no—
955#117—476no—
956#117—476no—
957#117—476no—
958#117—476no—
959#117—476no—
960#117—476no—
961#117—476no—
962#117—476no—
963#117—476no—
964#117—476no—
965#117C22×D4716yes—
966#117C22×D4716yes—
967C2×C4⋊C4—476no—
968C2×C4⋊C4—476no—
969C2×C4⋊C4—476no—
970C2×C4⋊C4—476no—
971C2×C4⋊C4—476no—
972C2×C4⋊C4—476no—
973C2×C4⋊C4—476no—
974C2×C4⋊C4—476no—
975C2×C4⋊C4—476no—
976C2×C4⋊C4—476no—
977C2×C4⋊C4—476no—
978C2×C4⋊C4—476no—
979C2×C4⋊C4—476no—
980C2×C4⋊C4—476no—
981C2×C4⋊C4—476no—
982C2×C4⋊C4—473no—
983C2×C4⋊C4—473no—
984C2×C4⋊C4C22×D4716yes—
985C2×C22⋊C4—476no—
986C2×C22⋊C4—476no—
987C2×C22⋊C4—476no—
988C2×C22⋊C4—476no—
989C2×C22⋊C4—476no—
990C2×C22⋊C4—476no—
991C2×C22⋊C4—476no—
992C2×C42—473no—
993C2×C42—472no—
994C2×C42—476no—
995C2×C42—473no—
996C2×C42—472no—
997C2×C42—471no—
998C2×C42—471no—
999C2×C42—473no—
1000C2×C42C22×D4711yescharacteristic
1001C24—476no—
1002C24—471no—
1003C2×Q8—476no—
1004C2×Q8—473no—
1005C2×Q8—1886no—
1006C2×Q8C23×D4713yes—
1007C2×D4—476no—
1008C2×D4—476no—
1009C2×D4—476no—
1010C2×D4—476no—
1011C2×D4—476no—
1012C2×D4—476no—
1013C2×D4—476no—
1014C2×D4—476no—
1015C2×D4—473no—
1016C2×D4—476no—
1017C2×D4—476no—
1018C2×D4—18812no—
1019C2×D4—18812no—
1020C2×D4—18812no—
1021C2×D4—1886no—
1022C2×D4C23×D4716yes—
1023C2×D4C23×D4713yes—
1024C2×D4C23×D4716yes—
1025C2×D4C23×D4716yes—
1026C22×C4—473no—
1027C22×C4—476no—
1028C22×C4—476no—
1029C22×C4—476no—
1030C22×C4—473no—
1031C22×C4—473no—
1032C22×C4—476no—
1033C22×C4—476no—
1034C22×C4—476no—
1035C22×C4—473no—
1036C22×C4—473no—
1037C22×C4—476no—
1038C22×C4—476no—
1039C22×C4—476no—
1040C22×C4—476no—
1041C22×C4—476no—
1042C22×C4—476no—
1043C22×C4—18812no—
1044C22×C4—1886no—
1045C22×C4—18812no—
1046C22×C4—18812no—
1047C22×C4C23×D4713yes—
1048C22×C4C23×D4716yes—
1049C22×C4C23×D4716yes—
1050C22×C4C23×D4716yes—
1051C4⋊C4—476no—
1052C4⋊C4—476no—
1053C4⋊C4—476no—
1054C4⋊C4—476no—
1055C4⋊C4—476no—
1056C4⋊C4—476no—
1057C4⋊C4—476no—
1058C4⋊C4—476no—
1059C4⋊C4—476no—
1060C4⋊C4—476no—
1061C4⋊C4—476no—
1062C4⋊C4—476no—
1063C4⋊C4—476no—
1064C4⋊C4—476no—
1065C4⋊C4—476no—
1066C4⋊C4—476no—
1067C4⋊C4—476no—
1068C4⋊C4—476no—
1069C4⋊C4—476no—
1070C4⋊C4—476no—
1071C4⋊C4—476no—
1072C4⋊C4—476no—
1073C4⋊C4—476no—
1074C4⋊C4—476no—
1075C4⋊C4—476no—
1076C4⋊C4—476no—
1077C4⋊C4—473no—
1078C4⋊C4—473no—
1079C4⋊C4C23×D4716yes—
1080C4⋊C4C23×D4716yes—
1081C4⋊C4C23×D4716yes—
1082C4⋊C4C23×D4716yes—
1083C4⋊C4C23×D4716yes—
1084C4⋊C4C23×D4716yes—
1085C4⋊C4C23×D4716yes—
1086C4⋊C4C23×D4716yes—
1087C4⋊C4C23×D4713yes—
1088C4⋊C4C23×D4713yes—
1089C22⋊C4—476no—
1090C22⋊C4—476no—
1091C22⋊C4—476no—
1092C22⋊C4—476no—
1093C22⋊C4—476no—
1094C22⋊C4—476no—
1095C22⋊C4—476no—
1096C22⋊C4—476no—
1097C22⋊C4—476no—
1098C22⋊C4—476no—
1099C22⋊C4—476no—
1100C22⋊C4—476no—
1101C22⋊C4—476no—
1102C22⋊C4—476no—
1103C22⋊C4—476no—
1104C22⋊C4—476no—
1105C22⋊C4—476no—
1106C22⋊C4—476no—
1107C22⋊C4—476no—
1108C22⋊C4—476no—
1109C22⋊C4—476no—
1110C22⋊C4C23×D4716yes—
1111C22⋊C4C23×D4716yes—
1112C22⋊C4C23×D4716yes—
1113C22⋊C4C23×D4716yes—
1114C22⋊C4C23×D4716yes—
1115C22⋊C4C23×D4716yes—
1116C22⋊C4C23×D4716yes—
1117C42—473no—
1118C42—473no—
1119C42—473no—
1120C42—473no—
1121C42—476no—
1122C42—476no—
1123C42—476no—
1124C42—476no—
1125C42—476no—
1126C42C23×D4713yes—
1127C42C23×D4711yescharacteristic
1128C42C23×D4712yes—
1129C42C23×D4716yes—
1130C42C23×D4712yes—
1131C23—471no—
1132C23—476no—
1133C23—471no—
1134C23—9412no—
1135C23—9412no—
1136C23—946no—
1137C23—9412no—
1138C23C24×D4716yes—
1139C23C24×D4711yescharacteristic
1140Q8—43no—
1141Q8—1886no—
1142Q8—1883no—
1143D4—46no—
1144D4—46no—
1145D4—46no—
1146D4—43no—
1147D4—1886no—
1148D4—1886no—
1149D4—1886no—
1150D4—1883no—
1151D4—1886no—
1152D4—1886no—
1153D4—1886no—
1154D4—1886no—
1155D4—1886no—
1156D4—1886no—
1157D4—1886no—
1158C2×C4—46no—
1159C2×C4—43no—
1160C2×C4—46no—
1161C2×C4—46no—
1162C2×C4—473no—
1163C2×C4—473no—
1164C2×C4—476no—
1165C2×C4—476no—
1166C2×C4—476no—
1167C2×C4—946no—
1168C2×C4—9412no—
1169C2×C4—9412no—
1170C2×C4—9412no—
1171C2×C4—946no—
1172C2×C4—1886no—
1173C2×C4—1883no—
1174C2×C4—1886no—
1175C2×C4—1886no—
1176C2×C4—1886no—
1177C2×C4—1886no—
1178C2×C4—1886no—
1179C2×C4—1883no—
1180C2×C4—1886no—
1181C2×C4—1883no—
1182C2×C4—1886no—
1183C2×C4—1886no—
1184C2×C4C24×D4713yes—
1185C2×C4C24×D4713yes—
1186C2×C4C24×D4716yes—
1187C2×C4C24×D4716yes—
1188C2×C4C24×D4716yes—
1189C22—26no—
1190C22—26no—
1191C22—23no—
1192C22—26no—
1193C22—476no—
1194C22—946no—
1195C22—946no—
1196C22—943no—
1197C22—946no—
1198C22—18824no—
1199C22—1884no—
1200C22C25×D4711yescharacteristic
1201C4—23no—
1202C4—26no—
1203C4—26no—
1204C4—26no—
1205C4—23no—
1206C4—943no—
1207C4—946no—
1208C4—946no—
1209C4—946no—
1210C4—943no—
1211C2—46no—
1212C2—41no—
1213C2—474no—
1214C2—1886no—
1215C2—1881no—
1216C2#585×D4713yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3567C2
hypercenter#3567D47
hypocenterC47C2×#3567
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3567

Complements

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

NH ≅ G/Ntype
1. #20258078C2semidirect
2. #20258077C2semidirect
3. #20258076C2semidirect
4. #20258075C2semidirect
5. #20258074C2semidirect
6. #20258073C2semidirect
7. #20258072C2semidirect
8. #564×D47C2semidirect
9. #562×D47C2semidirect
10. #553×D47C2semidirect
11. #552×D47C2semidirect
12. #540×D47C2semidirect
13. #539×D47C2semidirect
14. #529×D47C2semidirect
15. C47×#3567C2semidirect
16. C47⋊#564C22semidirect
17. C47⋊#564C22semidirect
18. C47⋊#564C22semidirect
19. #15689871C22semidirect
20. #15689870C22semidirect
21. #15689870C22semidirect
22. #15689869C22semidirect
23. #15689869C22semidirect
24. #15689868C22semidirect
25. #15689868C22semidirect
26. #15689867C22semidirect
27. #15689867C22semidirect
28. #15689826C22semidirect
29. #15689825C22semidirect
30. #15689824C22semidirect
31. #15689824C22semidirect
32. #15689823C22semidirect
33. #15689822C22semidirect
34. #15689822C22semidirect
35. #15689821C22semidirect
36. #15689820C22semidirect
37. #15689819C22semidirect
38. #15689818C22semidirect
39. #15689818C22semidirect
40. #15689817C22semidirect
41. #15689816C22semidirect
42. #15689816C22semidirect
43. #15689815C22semidirect
44. #15689814C22semidirect
45. #15689813C22semidirect
46. #15689812C22semidirect
47. #15689811C22semidirect
48. #15689810C22semidirect
49. #15689810C22semidirect
50. #15689809C22semidirect
51. #15689809C22semidirect
52. #15689808C22semidirect
53. #15689807C22semidirect
54. #15689806C22semidirect
55. #15689806C22semidirect
56. #15689805C22semidirect
57. #15689805C22semidirect
58. #15689729C22semidirect
59. #15689728C22semidirect
60. #15689727C22semidirect
61. #15689726C22semidirect
62. #15689726C22semidirect
63. #15689725C22semidirect
64. #15689725C22semidirect
65. #15689725C22semidirect
66. #15689725C22semidirect
67. #15689724C22semidirect
68. #15689724C22semidirect
69. #15689723C22semidirect
70. #15689723C22semidirect
71. #15689723C22semidirect
72. #15689723C22semidirect
73. #15689722C22semidirect
74. #15689721C22semidirect
75. #15689721C22semidirect
76. #15689720C22semidirect
77. #15689719C22semidirect
78. #15689719C22semidirect
79. #15689718C22semidirect
80. #15689717C22semidirect
81. #15689717C22semidirect
82. #15689716C22semidirect
83. #15689716C22semidirect
84. #15689715C22semidirect
85. #15689715C22semidirect
86. #15689714C22semidirect
87. #15689714C22semidirect
89. #15689660C22semidirect
90. #15689659C22semidirect
91. #15689658C22semidirect
92. #15689657C22semidirect
93. #15689656C22semidirect
94. #15689655C22semidirect
95. #15689654C22semidirect
96. #15689653C22semidirect
97. #15689652C22semidirect
98. #15689651C22semidirect
99. #15689650C22semidirect
130. C47×#564C22semidirect
131. C47×#562C22semidirect
132. C47×#553C22semidirect
133. C47×#552C22semidirect
134. C47×#540C22semidirect
135. C47×#539C22semidirect
136. C47×#529C22semidirect
610. #3567D47direct (N × H)
623. D47#3567direct (N × H)
627. #564C2×D47semidirect
637. #562C2×D47semidirect
653. #553C2×D47semidirect
669. #552C2×D47semidirect
685. #540C2×D47semidirect
701. #539C2×D47semidirect
714. #529C2×D47semidirect
745. C47C2×#3567semidirect

Maximal subgroups

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

subgroupindex
#202580782
#202580772
#202580762
#202580752
#202580742
#202580732
#202580722
#564×D472
#562×D472
#553×D472
#552×D472
#540×D472
#539×D472
#529×D472
C47×#35672
C2×#356747