Finite Group Databasebeta

← D47×#3529 #27123165

Subgroups — D47×#3529 #27123165

Order 12032.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257529C213yesmaximal, complemented
2#20257528C211yesmaximal, characteristic, complemented
3#20257527C216yesmaximal, complemented
4#20257526C216yesmaximal, complemented
5#20257525C216yesmaximal, complemented
6#20257524C213yesmaximal, complemented
7#20257523C216yesmaximal, complemented
8#563×D47C213yesmaximal, complemented
9#562×D47C216yesmaximal, complemented
10H(3,𝔽4)×D47C211yesmaximal, characteristic, complemented
11#560×D47C216yesmaximal, complemented
12#532×D47C213yesmaximal, complemented
13#529×D47C216yesmaximal, complemented
14#525×D47C216yesmaximal, complemented
15C47×#3529C211yesmaximal, characteristic, complemented
16C2×#41×D47C2213yes—
17C2×#41×D47C2211yescharacteristic, complemented
18C23×C4×D47C2212yescomplemented
19#15689877C2216yescomplemented
20#15689876C2216yescomplemented
21#15689875C22112yescomplemented
22#15689874C22112yescomplemented
23#15689873C2213yescomplemented
24#15689872C2216yescomplemented
25#15689871C2216yescomplemented
26#15689870C22112yescomplemented
27#15689870C22112yescomplemented
28#15689869C22112yescomplemented
29#15689869C22112yescomplemented
30#15689868C22112yescomplemented
31#15689868C22112yescomplemented
32#15689867C2216yescomplemented
33#15689867C2216yescomplemented
34#15689866C2216yescomplemented
35#15689865C2213yescomplemented
36#15689865C2216yescomplemented
37#15689864C22112yescomplemented
38#15689863C2216yescomplemented
39#15689863C22112yescomplemented
40#15689862C2216yescomplemented
41#15689862C22112yescomplemented
42#15689861C22112yescomplemented
43#15689861C22112yescomplemented
44#15689861C22112yescomplemented
45#15689860C2216yescomplemented
46#15689674C2213yescomplemented
47#15689673C2213yescomplemented
48#15689672C2213yescomplemented
49#15689672C2213yescomplemented
50#15689671C2213yescomplemented
51#15689670C22112yescomplemented
52#15689669C2213yescomplemented
53#15689669C2213yescomplemented
54#15689668C22112yescomplemented
55C4⋊Q8×D47C2213yescomplemented
56#127×D47C2213yes—
57#15689660C2216yescomplemented
58#15689659C2216yescomplemented
59#15689658C2216yescomplemented
60#15689657C2216yescomplemented
61#15689656C22112yescomplemented
62#15689655C2216yescomplemented
63#15689654C2216yescomplemented
64#15689653C22112yescomplemented
65#15689652C2216yescomplemented
66#15689651C22112yescomplemented
67#15689650C22112yescomplemented
68#126×D47C22112yescomplemented
69#125×D47C2216yescomplemented
70#124×D47C2216yes—
71#124×D47C2213yes—
72#124×D47C2213yescomplemented
73#15689636C22112yescomplemented
74#15689635C2216yescomplemented
75#15689634C2216yescomplemented
76#15689633C22112yescomplemented
77#15689632C22112yescomplemented
78#15689632C22112yescomplemented
79#15689631C2216yescomplemented
80#15689631C2216yescomplemented
81#15689630C2216yescomplemented
82#15689629C2216yescomplemented
83#15689629C2216yescomplemented
84#123×D47C2216yes—
85#123×D47C2216yescomplemented
86#123×D47C22112yescomplemented
87C22⋊Q8×D47C22112yescomplemented
88C22⋊Q8×D47C2216yescomplemented
89#121×D47C22112yes—
90#121×D47C2216yes—
91#121×D47C22112yescomplemented
92#120×D47C2216yes—
93#120×D47C2216yescomplemented
94C4×Q8×D47C2212yescomplemented
95C4×D4×D47C2216yes—
96C4×D4×D47C22112yescomplemented
97#117×D47C2216yescomplemented
98C2×C42×D47C2213yescomplemented
99C47×#563C2213yescomplemented
100C47×#562C2216yescomplemented
101C47×H(3,𝔽4)C2211yescharacteristic, complemented
102C47×#560C2216yescomplemented
103C47×#532C2213yescomplemented
104C47×#529C2216yescomplemented
105C47×#525C2216yescomplemented
106C24×D47C2312yes—
107C2×#10625354C2313yes—
108C2×#10625354C2311yescharacteristic, complemented
109C2×#10625350C2313yes—
110C2×#10625350C2316yes—
111C2×#10625350C2313yescomplemented
112C2×#10625352C2313yes—
113C2×#10625352C2316yes—
114C2×#10625352C2313yescomplemented
115#41×D47—412no—
116#41×D47—44no—
117C2×Q8×D47C2312yes—
118C2×Q8×D47C2313yes—
119C2×Q8×D47C2311yescharacteristic
120C2×D4×D47C2316yes—
121C2×D4×D47C23112yes—
122C2×D4×D47C2313yes—
123C2×D4×D47C2316yes—
124C2×D4×D47C2313yes—
125C23×Dic47C2312yescomplemented
126C22×C4×D47—48no—
127C22×C4×D47C2313yes—
128C22×C4×D47C2316yes—
129C22×C4×D47C2316yes—
130C22×C4×D47C2316yes—
131C22×C4×D47C2316yescomplemented
132C22×C4×D47C2316yescomplemented
133#13094024C2313yescomplemented
134#13094023C23112yescomplemented
135#13094022C2313yescomplemented
136#13094022C2313yescomplemented
137#13094021C2313yes—
138#13094020C2313yes—
139#13094020C23112yes—
140#13094020C2313yes—
141#13094019C23112yescomplemented
142#13094019C23112yescomplemented
143#13094019C23112yescomplemented
144#13094018C23112yescomplemented
145#13094017C23112yescomplemented
146#13094017C23112yescomplemented
147#13094017C23112yescomplemented
148#13094016C2316yescomplemented
149#13094015C2316yescomplemented
150#13094015C2316yescomplemented
151#13094014C23112yescomplemented
152#13094014C23112yescomplemented
153#13094013C2316yes—
154#13094013C2313yes—
155#13094013C2313yescomplemented
156#13094012C2316yes—
157#13094012C2313yes—
158#13094012C2313yescomplemented
159#13094011C2316yes—
160#13094011C2313yes—
161#13094011C2313yescomplemented
162#13094010C23112yes—
163#13094010C23112yes—
164#13094010C23112yes—
165#13094010C23112yescomplemented
166#13094009C23112yes—
167#13094009C23112yescomplemented
168#13094009C23112yescomplemented
169#13094009C23112yescomplemented
170#13094008C2316yes—
171#13094008C23112yescomplemented
172#13094008C2316yescomplemented
173#13094007C2316yes—
174#13094007C23112yescomplemented
175#13094007C2316yescomplemented
176#13094006C23112yes—
177#13094006C23112yescomplemented
178#13094006C23112yescomplemented
179#13094006C23112yescomplemented
180#13094005C2316yes—
181#13094005C23112yescomplemented
182#13094005C2316yescomplemented
183#13094004C2316yescomplemented
184#13094004C23112yescomplemented
185#13094003C2316yescomplemented
186#13094003C23112yescomplemented
187#13094002C23112yescomplemented
188#13094002C23112yescomplemented
189#13094002C23112yescomplemented
190#13094001C23112yescomplemented
191#13094001C23112yescomplemented
192#13094001C23112yescomplemented
193#13094000C2316yescomplemented
194#13094000C23112yescomplemented
195#13093999C2316yes—
196#13093999C23112yes—
197#13093999C23112yescomplemented
198#13093998C2316yes—
199#13093998C23112yes—
200#13093998C23112yescomplemented
201#13093997C23112yes—
202#13093997C23112yes—
203#13093997C23112yes—
204#13093997C23112yescomplemented
205#13093997C23112yescomplemented
206#13093996C23112yes—
207#13093996C23112yes—
208#13093996C23112yes—
209#13093996C23112yescomplemented
210#13093996C23112yescomplemented
211#13093995C2316yes—
212#13093995C23112yes—
213#13093995C23112yescomplemented
214#13093994C23112yes—
215#13093994C2316yes—
216#13093994C2316yescomplemented
217#13093994C23112yescomplemented
218#13093993C2316yes—
219#13093993C2316yescomplemented
220#13093992C2316yes—
221#13093992C23112yes—
222#13093992C23112yescomplemented
223#13093992C2316yescomplemented
224Q8×Dic47C2312yescomplemented
225C4×Dic94C2316yescomplemented
226#13093989C2316yescomplemented
227C4×D188C2316yes—
228C4×D188C23112yescomplemented
229D4×Dic47C2316yes—
230D4×Dic47C23112yescomplemented
231#13093986C2316yes—
232#13093986C23112yescomplemented
233C4×C22⋊D47C23112yes—
234C4×C22⋊D47C23112yescomplemented
235C4×C22⋊D47C23112yescomplemented
236(C22⋊D47)⋊C4C23112yes—
237(C22⋊D47)⋊C4C23112yescomplemented
238(C22⋊D47)⋊C4C23112yescomplemented
239#13093983C2316yescomplemented
240#13093982C23112yescomplemented
241#13093981C23112yescomplemented
242#13093980C2316yescomplemented
243#13093980C2316yescomplemented
244C4⋊C4×D47C23112yes—
245C4⋊C4×D47C2316yes—
246C4⋊C4×D47C23112yes—
247C4⋊C4×D47C2316yes—
248C22⋊C4×D47C2316yes—
249C22⋊C4×D47C2316yes—
250C22⋊C4×D47C23112yes—
251C22⋊C4×D47C23112yes—
252C22⋊C4×D47C23112yes—
253C2×C4×Dic47C2316yescomplemented
254C2×C4×Dic47C2313yescomplemented
255C42×D47C2316yes—
256C42×D47C2313yes—
257C42×D47C2313yes—
258C42×D47C2316yescomplemented
259C42×D47C2313yescomplemented
260C42×D47C2313yescomplemented
261C2×#41×C47C2313yes—
262C2×#41×C47C2311yescharacteristic, complemented
263C23×C4×C47C2312yescomplemented
264C4⋊Q8×C47C2313yescomplemented
265#127×C47C2313yes—
266#126×C47C23112yescomplemented
267#125×C47C2316yescomplemented
268#124×C47C2316yes—
269#124×C47C2313yes—
270#124×C47C2313yescomplemented
271#123×C47C2316yes—
272#123×C47C2316yescomplemented
273#123×C47C23112yescomplemented
274C22⋊Q8×C47C23112yescomplemented
275C22⋊Q8×C47C2316yescomplemented
276#121×C47C23112yes—
277#121×C47C2316yes—
278#121×C47C23112yescomplemented
279#120×C47C2316yes—
280#120×C47C2316yescomplemented
281C4×Q8×C47C2312yescomplemented
282C4×D4×C47C2316yes—
283C4×D4×C47C23112yescomplemented
284#117×C47C2316yescomplemented
285C2×C42×C47C2313yescomplemented
286C24×C47C2412yes—
287C23×D47—44no—
288C23×D47—48no—
289C23×D47C2416yes—
290C23×D47C2413yes—
291C23×D47C2416yes—
292#41×C47—46no—
293#41×C47—42no—
294C2×Q8×C47C2412yes—
295C2×Q8×C47C2413yes—
296C2×Q8×C47C2411yescharacteristic
297C2×D4×C47C2416yes—
298C2×D4×C47C24112yes—
299C2×D4×C47C2413yes—
300C2×D4×C47C2416yes—
301C2×D4×C47C2413yes—
302C22×C4×C47—44no—
303C22×C4×C47C2413yes—
304C22×C4×C47C2416yes—
305C22×C4×C47C2416yes—
306C22×C4×C47C2416yes—
307C2×C22⋊D47C24112yes—
308C2×C22⋊D47C24112yes—
309C2×C22⋊D47C24112yes—
310C2×C22⋊D47C2416yes—
311C2×C22⋊D47C2416yes—
312C2×C22⋊D47C2416yes—
313C2×C22⋊D47C2416yes—
314C22×Dic47—44no—
315C22×Dic47C2413yes—
316C22×Dic47C2416yes—
317C22×Dic47C2416yes—
318C22×Dic47C2416yes—
319#10625354—46no—
320#10625354—42no—
321Q8×D47—44no—
322Q8×D47—46no—
323Q8×D47—42no—
324#10625352—412no—
325#10625352—46no—
326#10625352—46no—
327D4×D47—424no—
328D4×D47—412no—
329D4×D47—412no—
330D4×D47—46no—
331D4×D47—46no—
332#10625350—46no—
333#10625350—412no—
334#10625350—46no—
335C2×D188C2416yes—
336C2×D188C24112yes—
337C2×D188C2413yes—
338C2×D188C2416yes—
339C2×D188C2413yes—
340C2×C4×D47—224no—
341C2×C4×D47—212no—
342C2×C4×D47—412no—
343C2×C4×D47—412no—
344C2×C4×D47—412no—
345C2×C4×D47—412no—
346C2×C4×D47C2416yes—
347C2×C4×D47C2416yes—
348C2×C4×D47C2413yes—
349C2×C4×D47C2413yes—
350C2×C4×D47C2413yes—
351C2×C4×D47C2416yes—
352C2×C4×D47C2416yes—
353C2×C4×D47C2416yes—
354C2×C4×D47C2416yes—
355C2×C4×D47C2416yes—
356C2×C4×D47C24112yes—
357C2×C4×D47C2411yescharacteristic
358C2×Dic94C2416yes—
359C2×Dic94C2413yes—
360C2×Dic94C2416yes—
361C2×Dic94C2413yes—
362C4⋊C4×C47C24112yes—
363C4⋊C4×C47C2416yes—
364C4⋊C4×C47C24112yes—
365C4⋊C4×C47C2416yes—
366C22⋊C4×C47C2416yes—
367C22⋊C4×C47C2416yes—
368C22⋊C4×C47C24112yes—
369C22⋊C4×C47C24112yes—
370C22⋊C4×C47C24112yes—
371C42×C47C2416yes—
372C42×C47C2413yes—
373C42×C47C2413yes—
374C22⋊Dic47C2416yes—
375C22⋊Dic47C2416yes—
376C22⋊Dic47C24112yes—
377C22⋊Dic47C24112yes—
378C22⋊Dic47C24112yes—
379(C2×D47)⋊C4C24112yes—
380(C2×D47)⋊C4C24112yes—
381(C2×D47)⋊C4C24112yes—
382(C2×D47)⋊C4C24112yes—
383(C2×D47)⋊C4C24112yes—
384(C2×D47)⋊C4C24112yes—
385(C2×D47)⋊C4C24112yes—
386(C2×D47)⋊C4C24112yes—
387C4⋊Dic47C24112yes—
388C4⋊Dic47C2416yes—
389C4⋊Dic47C24112yes—
390C4⋊Dic47C2416yes—
391Dic47⋊C4C24112yes—
392Dic47⋊C4C24112yes—
393Dic47⋊C4C24112yes—
394Dic47⋊C4C24112yes—
395Dic47⋊C4C24112yes—
396Dic47⋊C4C24112yes—
397C4×Dic47C2416yes—
398C4×Dic47C2416yes—
399C4×Dic47C2416yes—
400C4×Dic47C2416yes—
401C4×Dic47C2413yes—
402C4×Dic47C2413yes—
403C4×Dic47C2416yes—
404C23×C47—42no—
405C23×C47—44no—
406C23×C47C2516yes—
407C23×C47C2513yes—
408C22×D47—212no—
409C22×D47—26no—
410C22×D47—212no—
411C22×D47—224no—
412C22×D47—46no—
413C22×D47—412no—
414C22×D47—432no—
415C22×D47C2516yes—
416C22×D47C2513yes—
417C22×D47C2511yescharacteristic
418Q8×C47—41no—
419Q8×C47—43no—
420Q8×C47—42no—
421D4×C47—43no—
422D4×C47—43no—
423D4×C47—46no—
424D4×C47—46no—
425D4×C47—412no—
426C2×C4×C47—212no—
427C2×C4×C47—26no—
428C2×C4×C47—46no—
429C2×C4×C47—46no—
430C2×C4×C47C2516yes—
431C2×C4×C47C2513yes—
432C2×C4×C47C2516yes—
433C2×C4×C47C2516yes—
434C2×C4×C47C2511yescharacteristic
435C22⋊D47—46no—
436C22⋊D47—46no—
437C22⋊D47—46no—
438C22⋊D47—46no—
439C22⋊D47—412no—
440C22⋊D47—412no—
441C22⋊D47—412no—
442C2×Dic47—212no—
443C2×Dic47—26no—
444C2×Dic47—46no—
445C2×Dic47—46no—
446C2×Dic47C2516yes—
447C2×Dic47C2516yes—
448C2×Dic47C2513yes—
449C2×Dic47C2516yes—
450C2×Dic47C2511yescharacteristic
451D188—43no—
452D188—43no—
453D188—46no—
454D188—46no—
455D188—412no—
456C4×D47—212no—
457C4×D47—26no—
458C4×D47—212no—
459C4×D47—212no—
460C4×D47—212no—
461C4×D47—26no—
462C4×D47—212no—
463C4×D47—26no—
464C4×D47—412no—
465C4×D47—46no—
466C4×D47—46no—
467C4×D47H(5,𝔽2)14yes—
468Dic94—43no—
469Dic94—46no—
470Dic94—43no—
471Dic94—46no—
472C2×#3529—471nomaximal, Sylow
473C22×C47—26no—
474C22×C47—23no—
475C22×C47—26no—
476C22×C47—212no—
477C22×C47—48no—
478C22×C47C2611yescharacteristic
479C2×D47—26no—
480C2×D47—23no—
481C2×D47—26no—
482C2×D47—212no—
483C2×D47—424no—
484C2×D47—412no—
485C2×D47—424no—
486C2×D47C2×H(5,𝔽2)12yes—
487C2×D47#58514yes—
488C4×C47—23no—
489C4×C47—26no—
490C4×C47—26no—
491C4×C47—26no—
492C4×C47C2×H(5,𝔽2)12yes—
493Dic47—23no—
494Dic47—26no—
495Dic47—26no—
496Dic47—26no—
497Dic47C2×H(5,𝔽2)12yes—
498#3529—473no—
499#3529—476no—
500#3529—471no—
501#3529—476no—
502#3529—473no—
503#3529—476no—
504#3529—476no—
505#3529D4711yescharacteristic, direct product factor
506C2×#563—473no—
507C2×#562—476no—
508C2×H(3,𝔽4)—471no—
509C2×#560—476no—
510C2×#532—473no—
511C2×#529—476no—
512C2×#525—476no—
513C2×C47—46no—
514C2×C47—43no—
515C2×C47C22×H(5,𝔽2)11yescharacteristic
516C2×C47C2×#58512yes—
517D47—43no—
518D47—46no—
519D47#352914yesdirect product factor
520C22×#41—473no—
521C22×#41—471no—
522C24×C4—472no—
523#563—476no—
524#563—4712no—
525#563—476no—
526#563—473no—
527#563—476no—
528#563—4712no—
529#563C2×D4713yescomplemented
530#562—476no—
531#562—476no—
532#562—476no—
533#562—4712no—
534#562—4712no—
535#562—4712no—
536#562—4712no—
537#562—4712no—
538#562—4712no—
539#562C2×D4716yescomplemented
540H(3,𝔽4)—476no—
541H(3,𝔽4)—473no—
542H(3,𝔽4)—476no—
543H(3,𝔽4)C2×D4711yescharacteristic, complemented
544#560—476no—
545#560—4712no—
546#560—476no—
547#560—4712no—
548#560—4712no—
549#560—4712no—
550#560—4712no—
551#560—476no—
552#560—4712no—
553#560C2×D4716yescomplemented
554#532—473no—
555#532—473no—
556#532—473no—
557#532—473no—
558#532—473no—
559#532—473no—
560#532—4712no—
561#532—4712no—
562#532—473no—
563#532C2×D4713yescomplemented
564C2×C4⋊Q8—473no—
565C2×#127—473no—
566#529—4712no—
567#529—476no—
568#529—476no—
569#529—4712no—
570#529—476no—
571#529—476no—
572#529—476no—
573#529—476no—
574#529—4712no—
575#529—4712no—
576#529—476no—
577#529C2×D4716yescomplemented
578C2×#126—4712no—
579C2×#125—476no—
580C2×#124—476no—
581C2×#124—473no—
582C2×#124—473no—
583#525—476no—
584#525—476no—
585#525—476no—
586#525—476no—
587#525—4712no—
588#525—4712no—
589#525—476no—
590#525—476no—
591#525—4712no—
592#525—4712no—
593#525—476no—
594#525C2×D4716yescomplemented
595C2×#123—476no—
596C2×#123—476no—
597C2×#123—4712no—
598C2×C22⋊Q8—4712no—
599C2×C22⋊Q8—476no—
600C2×#121—4712no—
601C2×#121—476no—
602C2×#121—4712no—
603C2×#120—476no—
604C2×#120—476no—
605C2×C4×Q8—472no—
606C2×C4×D4—476no—
607C2×C4×D4—4712no—
608C2×#117—476no—
609C22×C42—473no—
610C47C2×#352911yescharacteristic, complemented, Sylow
611C25—472no—
612C2×#41—473no—
613C2×#41—471no—
614C2×#41—476no—
615C2×#41—473no—
616C2×#41—473no—
617C2×#41—476no—
618C2×#41—473no—
619C2×#41—473no—
620C2×#41—18812no—
621C2×#41—1884no—
622C2×#41C22×D4713yes—
623C2×#41C22×D4711yescharacteristic, complemented
624C22×Q8—472no—
625C22×Q8—473no—
626C22×Q8—471no—
627C22×D4—476no—
628C22×D4—4712no—
629C22×D4—473no—
630C22×D4—476no—
631C22×D4—473no—
632C23×C4—472no—
633C23×C4—476no—
634C23×C4—473no—
635C23×C4—476no—
636C23×C4—476no—
637C23×C4—476no—
638C23×C4—476no—
639C23×C4—1888no—
640C23×C4C22×D4712yescomplemented
641C4⋊Q8—473no—
642C4⋊Q8—473no—
643C4⋊Q8—4712no—
644C4⋊Q8—473no—
645C4⋊Q8C22×D4713yescomplemented
646#127—473no—
647#127—473no—
648#127—4712no—
649#127—473no—
650#127C22×D4713yes—
651#126—4712no—
652#126—4712no—
653#126—4712no—
654#126—4712no—
655#126—4712no—
656#126—4712no—
657#126—4712no—
658#126C22×D47112yescomplemented
659#125—4712no—
660#125—4712no—
661#125—476no—
662#125—476no—
663#125—476no—
664#125C22×D4716yescomplemented
665#124—476no—
666#124—473no—
667#124—473no—
668#124—476no—
669#124—473no—
670#124—473no—
671#124—4712no—
672#124—4712no—
673#124—4712no—
674#124—4712no—
675#124—476no—
676#124—473no—
677#124—473no—
678#124C22×D4716yes—
679#124C22×D4713yes—
680#124C22×D4713yescomplemented
681#123—476no—
682#123—476no—
683#123—4712no—
684#123—476no—
685#123—476no—
686#123—4712no—
687#123—4712no—
688#123—4712no—
689#123—4712no—
690#123—4712no—
691#123—4712no—
692#123—476no—
693#123—4712no—
694#123—476no—
695#123—4712no—
696#123—4712no—
697#123—4712no—
698#123C22×D4716yes—
699#123C22×D4716yescomplemented
700#123C22×D47112yescomplemented
701C22⋊Q8—4712no—
702C22⋊Q8—476no—
703C22⋊Q8—4712no—
704C22⋊Q8—476no—
705C22⋊Q8—4712no—
706C22⋊Q8—4712no—
707C22⋊Q8—4712no—
708C22⋊Q8—4712no—
709C22⋊Q8—476no—
710C22⋊Q8—4712no—
711C22⋊Q8—4712no—
712C22⋊Q8—4712no—
713C22⋊Q8C22×D47112yescomplemented
714C22⋊Q8C22×D4716yescomplemented
715#121—4712no—
716#121—4712no—
717#121—4712no—
718#121—476no—
719#121—4712no—
720#121—4712no—
721#121—4712no—
722#121—4712no—
723#121—4712no—
724#121—476no—
725#121—4712no—
726#121—4712no—
727#121—476no—
728#121—4712no—
729#121—4712no—
730#121—4712no—
731#121—4712no—
732#121—4712no—
733#121—4712no—
734#121C22×D47112yes—
735#121C22×D4716yes—
736#121C22×D47112yescomplemented
737#120—476no—
738#120—476no—
739#120—476no—
740#120—4712no—
741#120—476no—
742#120—4712no—
743#120—4712no—
744#120—476no—
745#120—4712no—
746#120—476no—
747#120C22×D4716yes—
748#120C22×D4716yescomplemented
749C4×Q8—472no—
750C4×Q8—476no—
751C4×Q8—476no—
752C4×Q8C22×D4712yescomplemented
753C4×D4—476no—
754C4×D4—4712no—
755C4×D4—4712no—
756C4×D4—4712no—
757C4×D4—4712no—
758C4×D4—476no—
759C4×D4—4712no—
760C4×D4—4712no—
761C4×D4—4712no—
762C4×D4—4712no—
763C4×D4—476no—
764C4×D4—4712no—
765C4×D4C22×D4716yes—
766C4×D4C22×D47112yescomplemented
767#117—476no—
768#117—4712no—
769#117—476no—
770#117—476no—
771#117—4712no—
772#117C22×D4716yescomplemented
773C2×C4⋊C4—4712no—
774C2×C4⋊C4—4712no—
775C2×C4⋊C4—476no—
776C2×C4⋊C4—476no—
777C2×C22⋊C4—476no—
778C2×C22⋊C4—476no—
779C2×C22⋊C4—4712no—
780C2×C22⋊C4—4712no—
781C2×C22⋊C4—4712no—
782C2×C42—476no—
783C2×C42—473no—
784C2×C42—476no—
785C2×C42—473no—
786C2×C42—473no—
787C2×C42—473no—
788C2×C42—473no—
789C2×C42—476no—
790C2×C42C22×D4713yescomplemented
791C24—476no—
792C24—473no—
793C24—476no—
794C24—1884no—
795C24—1888no—
796C24C23×D4712yes—
797#41—46no—
798#41—42no—
799#41—18812no—
800#41—1886no—
801#41—1886no—
802#41—18812no—
803#41—1886no—
804#41—1886no—
805#41—1886no—
806#41—1882no—
807C2×Q8—476no—
808C2×Q8—476no—
809C2×Q8—473no—
810C2×Q8—473no—
811C2×Q8—1884no—
812C2×Q8—1886no—
813C2×Q8—1882no—
814C2×Q8C23×D4712yes—
815C2×Q8C23×D4713yes—
816C2×Q8C23×D4711yescharacteristic
817C2×D4—4712no—
818C2×D4—4712no—
819C2×D4—4712no—
820C2×D4—476no—
821C2×D4—476no—
822C2×D4—476no—
823C2×D4—476no—
824C2×D4—476no—
825C2×D4—4712no—
826C2×D4—473no—
827C2×D4—476no—
828C2×D4—473no—
829C2×D4—18824no—
830C2×D4—18812no—
831C2×D4—18812no—
832C2×D4—1886no—
833C2×D4—1886no—
834C2×D4C23×D4716yes—
835C2×D4C23×D47112yes—
836C2×D4C23×D4713yes—
837C2×D4C23×D4716yes—
838C2×D4C23×D4713yes—
839C22×C4—44no—
840C22×C4—471no—
841C22×C4—473no—
842C22×C4—476no—
843C22×C4—476no—
844C22×C4—476no—
845C22×C4—476no—
846C22×C4—476no—
847C22×C4—473no—
848C22×C4—473no—
849C22×C4—476no—
850C22×C4—476no—
851C22×C4—473no—
852C22×C4—476no—
853C22×C4—476no—
854C22×C4—476no—
855C22×C4—4712no—
856C22×C4—9424no—
857C22×C4—9412no—
858C22×C4—18812no—
859C22×C4—18812no—
860C22×C4—18812no—
861C22×C4—18812no—
862C22×C4—1884no—
863C22×C4C23×D4713yes—
864C22×C4C23×D4716yes—
865C22×C4C23×D4716yes—
866C22×C4C23×D4716yes—
867C4⋊C4—4712no—
868C4⋊C4—4712no—
869C4⋊C4—4712no—
870C4⋊C4—4712no—
871C4⋊C4—4712no—
872C4⋊C4—4712no—
873C4⋊C4—4712no—
874C4⋊C4—4712no—
875C4⋊C4—476no—
876C4⋊C4—476no—
877C4⋊C4C23×D47112yes—
878C4⋊C4C23×D4716yes—
879C4⋊C4C23×D47112yes—
880C4⋊C4C23×D4716yes—
881C22⋊C4—476no—
882C22⋊C4—476no—
883C22⋊C4—4712no—
884C22⋊C4—4712no—
885C22⋊C4—4712no—
886C22⋊C4—4712no—
887C22⋊C4—4712no—
888C22⋊C4—4712no—
889C22⋊C4—4712no—
890C22⋊C4—4712no—
891C22⋊C4—4712no—
892C22⋊C4—4712no—
893C22⋊C4—4712no—
894C22⋊C4C23×D4716yes—
895C22⋊C4C23×D4716yes—
896C22⋊C4C23×D47112yes—
897C22⋊C4C23×D47112yes—
898C22⋊C4C23×D47112yes—
899C42—476no—
900C42—476no—
901C42—473no—
902C42—476no—
903C42—473no—
904C42—476no—
905C42—476no—
906C42C23×D4713yes—
907C42C23×D4713yes—
908C42C23×D4716yes—
909C23—42no—
910C23—44no—
911C23—471no—
912C23—476no—
913C23—473no—
914C23—9412no—
915C23—946no—
916C23—9412no—
917C23—9424no—
918C23—1886no—
919C23—18812no—
920C23—18832no—
921C23C24×D4716yes—
922C23C24×D4713yes—
923Q8—42no—
924Q8—43no—
925Q8—41no—
926Q8—1886no—
927Q8—1886no—
928Q8—1883no—
929Q8—1883no—
930D4—412no—
931D4—46no—
932D4—46no—
933D4—43no—
934D4—43no—
935D4—18812no—
936D4—1886no—
937D4—1886no—
938D4—1883no—
939D4—1883no—
940D4—18812no—
941D4—18812no—
942D4—18812no—
943D4—1886no—
944D4—1886no—
945D4—1886no—
946D4—1886no—
947C2×C4—212no—
948C2×C4—26no—
949C2×C4—46no—
950C2×C4—46no—
951C2×C4—471no—
952C2×C4—474no—
953C2×C4—476no—
954C2×C4—476no—
955C2×C4—473no—
956C2×C4—476no—
957C2×C4—9412no—
958C2×C4—946no—
959C2×C4—9412no—
960C2×C4—946no—
961C2×C4—9412no—
962C2×C4—9412no—
963C2×C4—9412no—
964C2×C4—946no—
965C2×C4—9412no—
966C2×C4—946no—
967C2×C4—1886no—
968C2×C4—1886no—
969C2×C4—18812no—
970C2×C4—1886no—
971C2×C4—1886no—
972C2×C4C24×D4716yes—
973C2×C4C24×D4716yes—
974C2×C4C24×D4713yes—
975C2×C4C24×D4716yes—
976C2×C4C24×D4711yescharacteristic
977C22—26no—
978C22—23no—
979C22—26no—
980C22—212no—
981C22—48no—
982C22—472no—
983C22—474no—
984C22—946no—
985C22—943no—
986C22—946no—
987C22—9412no—
988C22—18824no—
989C22—18812no—
990C22—18824no—
991C22C25×D4711yescharacteristic
992C4—26no—
993C4—23no—
994C4—26no—
995C4—26no—
996C4—472no—
997C4—946no—
998C4—943no—
999C4—946no—
1000C4—946no—
1001C4H(5,𝔽2)×D4712yes—
1002C2—46no—
1003C2—43no—
1004C2—474no—
1005C2—1886no—
1006C2—1883no—
1007C2C2×H(5,𝔽2)×D4711yescharacteristic
1008C2#585×D4712yes—
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC47×#3529C2
hypercenter#3529D47
hypocenterC47C2×#3529
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #20257529C2semidirect
2. #20257528C2semidirect
3. #20257527C2semidirect
4. #20257526C2semidirect
5. #20257525C2semidirect
6. #20257524C2semidirect
7. #20257523C2semidirect
8. #563×D47C2semidirect
9. #562×D47C2semidirect
10. H(3,𝔽4)×D47C2semidirect
11. #560×D47C2semidirect
12. #532×D47C2semidirect
13. #529×D47C2semidirect
14. #525×D47C2semidirect
15. C47×#3529C2semidirect
17. C2×#41×D47C22semidirect
18. C23×C4×D47C22semidirect
19. #15689877C22semidirect
20. #15689876C22semidirect
21. #15689875C22semidirect
22. #15689874C22semidirect
23. #15689873C22semidirect
24. #15689872C22semidirect
25. #15689871C22semidirect
26. #15689870C22semidirect
27. #15689870C22semidirect
28. #15689869C22semidirect
29. #15689869C22semidirect
30. #15689868C22semidirect
31. #15689868C22semidirect
32. #15689867C22semidirect
33. #15689867C22semidirect
34. #15689866C22semidirect
35. #15689865C22semidirect
36. #15689865C22semidirect
37. #15689864C22semidirect
38. #15689863C22semidirect
39. #15689863C22semidirect
40. #15689862C22semidirect
41. #15689862C22semidirect
42. #15689861C22semidirect
43. #15689861C22semidirect
44. #15689861C22semidirect
45. #15689860C22semidirect
46. #15689674C22semidirect
47. #15689673C22semidirect
48. #15689672C22semidirect
49. #15689672C22semidirect
50. #15689671C22semidirect
51. #15689670C22semidirect
52. #15689669C22semidirect
53. #15689669C22semidirect
54. #15689668C22semidirect
55. C4⋊Q8×D47C22semidirect
57. #15689660C22semidirect
58. #15689659C22semidirect
59. #15689658C22semidirect
60. #15689657C22semidirect
61. #15689656C22semidirect
62. #15689655C22semidirect
63. #15689654C22semidirect
64. #15689653C22semidirect
65. #15689652C22semidirect
66. #15689651C22semidirect
67. #15689650C22semidirect
68. #126×D47C22semidirect
69. #125×D47C22semidirect
72. #124×D47C22semidirect
73. #15689636C22semidirect
74. #15689635C22semidirect
75. #15689634C22semidirect
76. #15689633C22semidirect
77. #15689632C22semidirect
78. #15689632C22semidirect
79. #15689631C22semidirect
80. #15689631C22semidirect
81. #15689630C22semidirect
82. #15689629C22semidirect
83. #15689629C22semidirect
85. #123×D47C22semidirect
86. #123×D47C22semidirect
87. C22⋊Q8×D47C22semidirect
88. C22⋊Q8×D47C22semidirect
91. #121×D47C22semidirect
93. #120×D47C22semidirect
94. C4×Q8×D47C22semidirect
96. C4×D4×D47C22semidirect
97. #117×D47C22semidirect
98. C2×C42×D47C22semidirect
99. C47×#563C22semidirect
100. C47×#562C22semidirect
101. C47×H(3,𝔽4)C22semidirect
102. C47×#560C22semidirect
103. C47×#532C22semidirect
104. C47×#529C22semidirect
105. C47×#525C22semidirect
108. C2×#10625354C23semidirect
111. C2×#10625350C23semidirect
114. C2×#10625352C23semidirect
125. C23×Dic47C23semidirect
131. C22×C4×D47C23semidirect
132. C22×C4×D47C23semidirect
133. #13094024C23semidirect
134. #13094023C23semidirect
135. #13094022C23semidirect
136. #13094022C23semidirect
141. #13094019C23semidirect
142. #13094019C23semidirect
143. #13094019C23semidirect
144. #13094018C23semidirect
145. #13094017C23semidirect
146. #13094017C23semidirect
147. #13094017C23semidirect
148. #13094016C23semidirect
149. #13094015C23semidirect
150. #13094015C23semidirect
151. #13094014C23semidirect
152. #13094014C23semidirect
155. #13094013C23semidirect
158. #13094012C23semidirect
161. #13094011C23semidirect
165. #13094010C23semidirect
167. #13094009C23semidirect
168. #13094009C23semidirect
169. #13094009C23semidirect
171. #13094008C23semidirect
172. #13094008C23semidirect
174. #13094007C23semidirect
175. #13094007C23semidirect
177. #13094006C23semidirect
178. #13094006C23semidirect
179. #13094006C23semidirect
181. #13094005C23semidirect
182. #13094005C23semidirect
183. #13094004C23semidirect
184. #13094004C23semidirect
185. #13094003C23semidirect
186. #13094003C23semidirect
187. #13094002C23semidirect
188. #13094002C23semidirect
189. #13094002C23semidirect
190. #13094001C23semidirect
191. #13094001C23semidirect
192. #13094001C23semidirect
193. #13094000C23semidirect
194. #13094000C23semidirect
197. #13093999C23semidirect
200. #13093998C23semidirect
204. #13093997C23semidirect
205. #13093997C23semidirect
209. #13093996C23semidirect
210. #13093996C23semidirect
213. #13093995C23semidirect
216. #13093994C23semidirect
217. #13093994C23semidirect
219. #13093993C23semidirect
222. #13093992C23semidirect
223. #13093992C23semidirect
224. Q8×Dic47C23semidirect
225. C4×Dic94C23semidirect
226. #13093989C23semidirect
228. C4×D188C23semidirect
230. D4×Dic47C23semidirect
232. #13093986C23semidirect
234. C4×C22⋊D47C23semidirect
235. C4×C22⋊D47C23semidirect
237. (C22⋊D47)⋊C4C23semidirect
238. (C22⋊D47)⋊C4C23semidirect
239. #13093983C23semidirect
240. #13093982C23semidirect
241. #13093981C23semidirect
242. #13093980C23semidirect
243. #13093980C23semidirect
253. C2×C4×Dic47C23semidirect
254. C2×C4×Dic47C23semidirect
258. C42×D47C23semidirect
259. C42×D47C23semidirect
260. C42×D47C23semidirect
262. C2×#41×C47C23semidirect
263. C23×C4×C47C23semidirect
264. C4⋊Q8×C47C23semidirect
266. #126×C47C23semidirect
267. #125×C47C23semidirect
270. #124×C47C23semidirect
272. #123×C47C23semidirect
273. #123×C47C23semidirect
274. C22⋊Q8×C47C23semidirect
275. C22⋊Q8×C47C23semidirect
278. #121×C47C23semidirect
280. #120×C47C23semidirect
281. C4×Q8×C47C23semidirect
283. C4×D4×C47C23semidirect
284. #117×C47C23semidirect
285. C2×C42×C47C23semidirect
505. #3529D47direct (N × H)
519. D47#3529direct (N × H)
529. #563C2×D47semidirect
539. #562C2×D47semidirect
543. H(3,𝔽4)C2×D47semidirect
553. #560C2×D47semidirect
563. #532C2×D47semidirect
577. #529C2×D47semidirect
594. #525C2×D47semidirect
610. C47C2×#3529semidirect
623. C2×#41C22×D47semidirect
640. C23×C4C22×D47semidirect
645. C4⋊Q8C22×D47semidirect
658. #126C22×D47semidirect
664. #125C22×D47semidirect
680. #124C22×D47semidirect
699. #123C22×D47semidirect
700. #123C22×D47semidirect
713. C22⋊Q8C22×D47semidirect
714. C22⋊Q8C22×D47semidirect
736. #121C22×D47semidirect
748. #120C22×D47semidirect
752. C4×Q8C22×D47semidirect
766. C4×D4C22×D47semidirect
772. #117C22×D47semidirect
790. C2×C42C22×D47semidirect

Maximal subgroups

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

subgroupindex
#202575292
#202575282
#202575272
#202575262
#202575252
#202575242
#202575232
#563×D472
#562×D472
H(3,𝔽4)×D472
#560×D472
#532×D472
#529×D472
#525×D472
C47×#35292
C2×#352947