Finite Group Databasebeta

← D47×#3509 #27124712

Subgroups — D47×#3509 #27124712

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257275C211yesmaximal, characteristic, complemented
2#20257274C211yesmaximal, characteristic, complemented
3#20257273C212yesmaximal, complemented
4#20257272C211yesmaximal, characteristic, complemented
5#20257271C214yesmaximal, complemented
6#20257270C214yesmaximal, complemented
7#20257269C212yesmaximal, complemented
8#20257268C214yesmaximal, complemented
9#20257267C214yesmaximal, complemented
10#20257266C218yesmaximal, complemented
11#557×D47C214yesmaximal, complemented
12#556×D47C214yesmaximal, complemented
13#552×D47C218yesmaximal, complemented
14#541×D47C214yesmaximal, complemented
15#536×D47C212yesmaximal
16#533×D47C214yesmaximal, complemented
17#533×D47C211yesmaximal, characteristic, complemented
18C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
19#519×D47C212yesmaximal, complemented
20C4×#41×D47C211yesmaximal, characteristic
21C47×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D47C2211yescharacteristic
23C22×Q8×D47C2212yes—
24#15689852C2214yescomplemented
25#15689851C2218yescomplemented
26#15689851C2214yescomplemented
27#15689850C2218yescomplemented
28#15689850C22116yescomplemented
29#15689849C2218yescomplemented
30#15689848C2214yescomplemented
31#15689848C2218yescomplemented
32#15689847C2214yescomplemented
33#15689846C2214yescomplemented
34#15689845C2218yescomplemented
35#15689844C2218yescomplemented
36#15689843C2214yescomplemented
37#15689842C2218yescomplemented
38#15689841C2218yescomplemented
39#15689840C22116yescomplemented
40#15689815C2218yescomplemented
41#15689814C2218yescomplemented
42#15689813C2218yescomplemented
43#15689812C2218yescomplemented
44#15689811C2218yescomplemented
45#15689810C22116yescomplemented
46#15689809C22116yescomplemented
47#15689808C2218yescomplemented
48#15689807C2218yescomplemented
49#15689806C22116yescomplemented
50#15689805C22116yescomplemented
51#15689736C2214yescomplemented
52#15689735C2214yescomplemented
53#15689734C2214yescomplemented
54#15689733C2218yescomplemented
55#15689732C22116yescomplemented
56#15689731C2218yescomplemented
57#15689730C22116yescomplemented
58#15689699C2212yes—
59#15689698C2214yes—
60#15689697C2212yes—
61#15689696C2218yes—
62#15689695C2218yes—
63#15689694C2212yes—
64#15689693C2214yes—
65#15689680C2214yescomplemented
66#15689680C2211yescharacteristic, complemented
67#15689679C2218yescomplemented
68#15689679C2212yescomplemented
69#15689678C2212yescomplemented
70#15689678C2214yescomplemented
71#15689678C2214yescomplemented
72#15689677C2218yescomplemented
73#15689677C2214yescomplemented
74#15689677C2218yescomplemented
75#15689676C2218yescomplemented
76#15689676C2212yescomplemented
77#15689675C2214yescomplemented
78#15689675C2218yescomplemented
79#15689675C2218yescomplemented
80C2×#13094024C2211yescharacteristic, complemented
81C2×#13094023C2214yescomplemented
82C2×#13094022C2212yescomplemented
83C4⋊Q8×D47C2212yes—
84C4⋊Q8×D47C2214yes—
85C4⋊Q8×D47C2212yes—
86C4⋊Q8×D47C2212yes—
87C4⋊Q8×D47C2214yes—
88C4⋊Q8×D47C2212yescomplemented
89C4⋊Q8×D47C2214yescomplemented
90C4⋊Q8×D47C2212yescomplemented
91#126×D47C22116yes—
92#125×D47C2218yes—
93#125×D47C22116yes—
94#125×D47C2212yes—
95#124×D47C2214yes—
96#123×D47C2218yes—
97C22⋊Q8×D47C2214yes—
98C22⋊Q8×D47C2218yes—
99C22⋊Q8×D47C2218yes—
100#15689601C2212yescomplemented
101#15689600C2218yescomplemented
102#15689600C2212yescomplemented
103#15689600C2212yescomplemented
104#15689599C2218yescomplemented
105#15689599C2218yescomplemented
106#41×Dic47C2211yescharacteristic
107C4×#10625354C2212yes—
108C4×#10625350C2212yes—
109C4×#10625350C2211yescharacteristic
110#15689591C2211yescharacteristic
111#15689591C2212yes—
112C4×#10625352C2214yes—
113C4×#10625352C2212yes—
114C4×Q8×D47C2212yes—
115C4×Q8×D47C2218yes—
116C4×Q8×D47C2218yes—
117C4×Q8×D47C2218yes—
118C4×Q8×D47C2214yes—
119C4×D4×D47C2214yes—
120C4×D4×D47C2212yes—
121#117×D47C2211yescharacteristic
122#117×D47C2212yes—
123#117×D47C2218yes—
124#117×D47C2212yes—
125#117×D47C2218yes—
126C2×C4⋊C4×D47C2214yes—
127C2×C42×D47C2211yescharacteristic
128C2×C42×D47C2212yes—
129C47×#557C2214yescomplemented
130C47×#556C2214yescomplemented
131C47×#552C2218yescomplemented
132C47×#541C2214yescomplemented
133C47×#536C2212yes—
134C47×#533C2214yescomplemented
135C47×#533C2211yescharacteristic, complemented
136C2×C4⋊Q8×C47C2211yescharacteristic, complemented
137C47×#519C2212yescomplemented
138C4×#41×C47C2211yescharacteristic
139C2×#10625354C2311yescharacteristic
140C2×#10625350C2312yes—
141C2×#10625350C2311yescharacteristic
142C2×#10625352C2311yescharacteristic
143C2×#10625352C2312yes—
144#41×D47—28no—
145C22×Dic94C2312yes—
146C22×Dic94C2314yes—
147C2×Q8×D47—216no—
148C2×Q8×D47C2314yes—
149C2×Q8×D47C2314yes—
150C2×Q8×D47C2314yes—
151C2×Q8×D47C2311yescharacteristic
152C2×Q8×D47C2314yes—
153C2×Q8×D47C2314yes—
154C2×D4×D47C2312yes—
155C2×D4×D47C2311yescharacteristic
156C22×C4×D47C2312yes—
157C22×C4×D47C2314yes—
158C22×C4×D47C2312yes—
159C22×C4×D47C2314yes—
160C22×C4×D47C2311yescharacteristic
161#13094024C2312yes—
162#13094024C2314yes—
163#13094024C2314yes—
164#13094024C2312yes—
165#13094024C2312yes—
166#13094023C2318yes—
167#13094023C2318yes—
168#13094023C2318yes—
169#13094023C23116yes—
170#13094023C2318yes—
171#13094023C2314yes—
172#13094023C2314yes—
173#13094022C2314yes—
174#13094022C2318yes—
175#13094022C2314yes—
176#13094022C2314yes—
177#13094022C2314yes—
178#13094022C2314yes—
179#13094019C23116yes—
180#13094019C23116yes—
181#13094019C23116yes—
182#13094018C23116yes—
183#13094017C23116yes—
184#13094017C23116yes—
185#13094017C23116yes—
186#13094016C23116yes—
187#13094016C2312yes—
188#13094016C2318yes—
189#13094015C23116yes—
190#13094015C2314yes—
191#13094015C23116yes—
192#13094015C2318yes—
193#13094015C2318yes—
194#13094014C2318yes—
195#13094014C23116yes—
196#13094014C23116yes—
197#13094014C23116yes—
198#13094014C23116yes—
199#13094014C23116yes—
200#13094014C23116yes—
201#13094013C2314yes—
202#13094012C2314yes—
203#13094011C2314yes—
204#13094010C23116yes—
205#13094009C23116yes—
206#13094008C2318yes—
207#13094007C2318yes—
208#13094006C23116yes—
209#13094005C2318yes—
210#13094004C2318yes—
211#13094004C2318yes—
212#13094004C2314yes—
213#13094003C2318yes—
214#13094003C2314yes—
215#13094003C2318yes—
216#13094002C23116yes—
217#13094002C2318yes—
218#13094002C23116yes—
219#13094001C23116yes—
220#13094001C2318yes—
221#13094001C23116yes—
222#13094000C2318yes—
223#13094000C2314yes—
224#13094000C2318yes—
225Q8×Dic47C2318yes—
226Q8×Dic47C2318yes—
227Q8×Dic47C2318yes—
228Q8×Dic47C2314yes—
229Q8×Dic47C2312yes—
230C4×Dic94C23116yes—
231C4×Dic94C2318yes—
232C4×Dic94C23116yes—
233C4×Dic94C2318yes—
234C4×Dic94C23116yes—
235C4×Dic94C2318yes—
236C4×Dic94C2318yes—
237C4×Dic94C2314yes—
238C4×Dic94C2312yes—
239C4×Dic94C2314yes—
240#13093989C23116yes—
241#13093989C2318yes—
242#13093989C23116yes—
243#13093989C2318yes—
244#13093989C2318yes—
245#13093989C23116yes—
246#13093989C2314yes—
247#13093989C2318yes—
248#13093989C2314yes—
249#13093989C2312yes—
250C4×D188C2314yes—
251C4×D188C2312yes—
252D4×Dic47C2314yes—
253D4×Dic47C2312yes—
254#13093986C2314yes—
255#13093986C2312yes—
256C4×C22⋊D47C2314yes—
257C4×C22⋊D47C2314yes—
258C4×C22⋊D47C2314yes—
259(C22⋊D47)⋊C4C2314yes—
260(C22⋊D47)⋊C4C2314yes—
261(C22⋊D47)⋊C4C2314yes—
262#13093983C2312yes—
263#13093983C2318yes—
264#13093983C2318yes—
265#13093983C2311yescharacteristic
266#13093983C2312yes—
267#13093982C2314yes—
268#13093982C23116yes—
269#13093982C2318yes—
270#13093982C2318yes—
271#13093982C2312yes—
272#13093982C2314yes—
273#13093981C2312yes—
274#13093981C2312yes—
275#13093981C23116yes—
276#13093981C23116yes—
277#13093981C2312yes—
278#13093981C2314yes—
279#13093980C2314yes—
280#13093980C2318yes—
281#13093980C23116yes—
282#13093980C2318yes—
283#13093980C2312yes—
284#13093980C2314yes—
285C2×C4⋊Dic47C2314yes—
286C2×Dic47⋊C4C2318yes—
287C4⋊C4×D47C2318yes—
288C4⋊C4×D47C2318yes—
289C4⋊C4×D47C2318yes—
290C4⋊C4×D47C2318yes—
291C4⋊C4×D47C2314yes—
292C4⋊C4×D47C2312yes—
293C4⋊C4×D47C2314yes—
294C4⋊C4×D47C2314yes—
295C4⋊C4×D47C23116yes—
296C4⋊C4×D47C23116yes—
297C4⋊C4×D47C2318yes—
298C22⋊C4×D47C2312yes—
299C22⋊C4×D47C2314yes—
300C22⋊C4×D47C2314yes—
301C22⋊C4×D47C23116yes—
302C2×C4×Dic47C2312yes—
303C2×C4×Dic47C2314yes—
304C2×C4×Dic47C2311yescharacteristic
305C2×C4×Dic47C2312yes—
306C42×D47C2311yescharacteristic
307C42×D47C2312yes—
308C42×D47C2311yescharacteristic
309C42×D47C2314yes—
310C42×D47C2312yes—
311C42×D47C2312yes—
312C42×D47C2314yes—
313C42×D47C2311yescharacteristic
314C42×D47C2312yes—
315C42×D47C2311yescharacteristic
316C42×D47C2312yes—
317C42×D47C23116yes—
318C42×D47C2314yes—
319C2×#41×C47C2311yescharacteristic
320C22×Q8×C47C2312yes—
321C4⋊Q8×C47C2312yes—
322C4⋊Q8×C47C2312yes—
323C4⋊Q8×C47C2314yes—
324C4⋊Q8×C47C2312yes—
325C4⋊Q8×C47C2314yes—
326#126×C47C23116yes—
327#125×C47C23116yes—
328#125×C47C2312yes—
329#125×C47C2318yes—
330#124×C47C2314yes—
331#123×C47C2318yes—
332C22⋊Q8×C47C2318yes—
333C22⋊Q8×C47C2318yes—
334C22⋊Q8×C47C2314yes—
335C4×Q8×C47C2318yes—
336C4×Q8×C47C2312yes—
337C4×Q8×C47C2318yes—
338C4×Q8×C47C2318yes—
339C4×Q8×C47C2314yes—
340C4×D4×C47C2314yes—
341C4×D4×C47C2312yes—
342#117×C47C2312yes—
343#117×C47C2311yescharacteristic
344#117×C47C2318yes—
345#117×C47C2312yes—
346#117×C47C2318yes—
347C2×C4⋊C4×C47C2314yes—
348C2×C42×C47C2311yescharacteristic
349C2×C42×C47C2312yes—
350C23×D47C2412yes—
351C23×D47C2411yescharacteristic
352#41×C47—24no—
353C2×Q8×C47—28no—
354C2×Q8×C47C2414yes—
355C2×Q8×C47C2414yes—
356C2×Q8×C47C2414yes—
357C2×Q8×C47C2411yescharacteristic
358C2×D4×C47C2412yes—
359C2×D4×C47C2411yescharacteristic
360C22×C4×C47C2412yes—
361C22×C4×C47C2414yes—
362C22×C4×C47C2412yes—
363C22×C4×C47C2414yes—
364C22×C4×C47C2411yescharacteristic
365C2×C22⋊D47C2412yes—
366C2×C22⋊D47C2412yes—
367C2×C22⋊D47C2412yes—
368C22×Dic47C2412yes—
369C22×Dic47C2414yes—
370C22×Dic47C2412yes—
371C22×Dic47C2414yes—
372C22×Dic47C2411yescharacteristic
373#10625354—24no—
374Q8×D47—216no—
375Q8×D47—216no—
376Q8×D47—216no—
377Q8×D47—216no—
378Q8×D47—24no—
379Q8×D47—216no—
380#10625352—28no—
381#10625352—24no—
382D4×D47—28no—
383D4×D47—24no—
384#10625350—24no—
385#10625350—28no—
386C2×D188C2412yes—
387C2×D188C2411yescharacteristic
388C2×C4×D47—216no—
389C2×C4×D47—28no—
390C2×C4×D47—28no—
391C2×C4×D47—216no—
392C2×C4×D47#4118yes—
393C2×C4×D47C2414yes—
394C2×C4×D47C2418yes—
395C2×C4×D47C2412yes—
396C2×C4×D47C2418yes—
397C2×C4×D47C2412yes—
398C2×C4×D47C2412yes—
399C2×C4×D47C2412yes—
400C2×C4×D47C2414yes—
401C2×C4×D47C2412yes—
402C2×C4×D47C2414yes—
403C2×C4×D47C2412yes—
404C2×C4×D47C2418yes—
405C2×C4×D47C2411yescharacteristic
406C2×C4×D47C2411yescharacteristic
407C2×C4×D47C2411yescharacteristic
408C2×C4×D47C2411yescharacteristic
409C2×C4×D47C2412yes—
410C2×Dic94—28no—
411C2×Dic94—216no—
412C2×Dic94C2418yes—
413C2×Dic94C2414yes—
414C2×Dic94C2418yes—
415C2×Dic94C2414yes—
416C2×Dic94C2418yes—
417C2×Dic94C2414yes—
418C2×Dic94C2411yescharacteristic
419C2×Dic94C2412yes—
420C4⋊C4×C47C2418yes—
421C4⋊C4×C47C2418yes—
422C4⋊C4×C47C2414yes—
423C4⋊C4×C47C2412yes—
424C4⋊C4×C47C2414yes—
425C4⋊C4×C47C2414yes—
426C4⋊C4×C47C24116yes—
427C4⋊C4×C47C24116yes—
428C4⋊C4×C47C2418yes—
429C22⋊C4×C47C2412yes—
430C22⋊C4×C47C2414yes—
431C22⋊C4×C47C2414yes—
432C22⋊C4×C47C24116yes—
433C42×C47C2411yescharacteristic
434C42×C47C2412yes—
435C42×C47C2411yescharacteristic
436C42×C47C2414yes—
437C42×C47C2412yes—
438C42×C47C24116yes—
439C42×C47C2414yes—
440C22⋊Dic47C2412yes—
441C22⋊Dic47C2414yes—
442C22⋊Dic47C2414yes—
443C22⋊Dic47C24116yes—
444(C2×D47)⋊C4C2414yes—
445(C2×D47)⋊C4C2418yes—
446(C2×D47)⋊C4C2414yes—
447(C2×D47)⋊C4C2414yes—
448(C2×D47)⋊C4C24116yes—
449(C2×D47)⋊C4C24116yes—
450C4⋊Dic47C2418yes—
451C4⋊Dic47C2418yes—
452C4⋊Dic47C2414yes—
453C4⋊Dic47C2412yes—
454C4⋊Dic47C2414yes—
455C4⋊Dic47C2414yes—
456C4⋊Dic47C24116yes—
457C4⋊Dic47C24116yes—
458C4⋊Dic47C2418yes—
459Dic47⋊C4C24116yes—
460Dic47⋊C4C24116yes—
461Dic47⋊C4C2418yes—
462Dic47⋊C4C2414yes—
463Dic47⋊C4C2414yes—
464Dic47⋊C4C2414yes—
465Dic47⋊C4C24116yes—
466Dic47⋊C4C2418yes—
467Dic47⋊C4C24116yes—
468Dic47⋊C4C24116yes—
469Dic47⋊C4C2418yes—
470Dic47⋊C4C24116yes—
471Dic47⋊C4C2418yes—
472C4×Dic47C2411yescharacteristic
473C4×Dic47C2412yes—
474C4×Dic47C2414yes—
475C4×Dic47C2412yes—
476C4×Dic47C2412yes—
477C4×Dic47C2411yescharacteristic
478C4×Dic47C2412yes—
479C4×Dic47C2414yes—
480C4×Dic47C2414yes—
481C4×Dic47C2412yes—
482C4×Dic47C2414yes—
483C4×Dic47C2412yes—
484C4×Dic47C24116yes—
485C4×Dic47C24116yes—
486C4×Dic47C24116yes—
487C4×Dic47C2418yes—
488C4×Dic47C2414yes—
489C23×C47C2512yes—
490C23×C47C2511yescharacteristic
491C22×D47—24no—
492C22×D47—24no—
493C22×D47—28no—
494C22×D47C2×#4114yes—
495C22×D47C2512yes—
496C22×D47C2511yescharacteristic
497C22×D47C2511yescharacteristic
498Q8×C47—28no—
499Q8×C47—28no—
500Q8×C47—22no—
501Q8×C47—28no—
502D4×C47—24no—
503D4×C47—22no—
504C2×C4×C47—28no—
505C2×C4×C47—24no—
506C2×C4×C47—24no—
507C2×C4×C47—28no—
508C2×C4×C47C2×#4114yes—
509C2×C4×C47C2514yes—
510C2×C4×C47C2518yes—
511C2×C4×C47C2512yes—
512C2×C4×C47C2512yes—
513C2×C4×C47C2518yes—
514C2×C4×C47C2511yescharacteristic
515C2×C4×C47C2511yescharacteristic
516C2×C4×C47C2512yes—
517C22⋊D47—24no—
518C22⋊D47—24no—
519C22⋊D47—24no—
520C2×Dic47—28no—
521C2×Dic47—24no—
522C2×Dic47—24no—
523C2×Dic47—28no—
524C2×Dic47C2×#4114yes—
525C2×Dic47C2514yes—
526C2×Dic47C2518yes—
527C2×Dic47C2512yes—
528C2×Dic47C2512yes—
529C2×Dic47C2518yes—
530C2×Dic47C2511yescharacteristic
531C2×Dic47C2511yescharacteristic
532C2×Dic47C2512yes—
533D188—24no—
534D188—22no—
535C4×D47—24no—
536C4×D47—216no—
537C4×D47—216no—
538C4×D47—28no—
539C4×D47—24no—
540C4×D47—216no—
541C4×D47—24no—
542C4×D47—24no—
543C4×D47—28no—
544C4×D47—24no—
545C4×D47—24no—
546C4×D47—28no—
547C4×D47C2×#4114yes—
548C4×D47C2×#4114yes—
549C4×D47C2×#4114yes—
550C4×D47C2×#4114yes—
551C4×D472−1+418yes—
552Dic94—28no—
553Dic94—28no—
554Dic94—22no—
555Dic94—28no—
556Dic94—216no—
557Dic94—216no—
558Dic94—24no—
559Dic94—216no—
560C2×#3509—471nomaximal, Sylow
561C22×C47—22no—
562C22×C47—22no—
563C22×C47—24no—
564C22×C47C22×#4112yes—
565C22×C47C2611yescharacteristic
566C2×D47—22no—
567C2×D47—28no—
568C2×D47—22no—
569C2×D47—24no—
570C2×D47—48no—
571C2×D47C22×#4112yes—
572C2×D47C22×#4112yes—
573C2×D47C2×2−1+414yes—
574C4×C47—28no—
575C4×C47—22no—
576C4×C47—28no—
577C4×C47—24no—
578C4×C47—22no—
579C4×C47C22×#4112yes—
580C4×C47C22×#4112yes—
581C4×C47C2×2−1+414yes—
582Dic47—28no—
583Dic47—22no—
584Dic47—28no—
585Dic47—24no—
586Dic47—22no—
587Dic47C22×#4112yes—
588Dic47C22×#4112yes—
589Dic47C2×2−1+414yes—
590#3509—474no—
591#3509—474no—
592#3509—478no—
593#3509—474no—
594#3509—472no—
595#3509—474no—
596#3509—471no—
597#3509—471no—
598#3509—472no—
599#3509—471no—
600#3509D4711yescharacteristic, direct product factor
601C2×#557—474no—
602C2×#556—474no—
603C2×#552—478no—
604C2×#541—474no—
605C2×#536—472no—
606C2×#533—471no—
607C2×#533—474no—
608C22×C4⋊Q8—471no—
609C2×#519—472no—
610C2×C4×#41—471no—
611C2×C47—22no—
612C2×C47—42no—
613C2×C47C23×#4111yescharacteristic
614C2×C47C22×2−1+412yes—
615D47—22no—
616D47—42no—
617D47#350914yesdirect product factor
618C22×#41—471no—
619C23×Q8—472no—
620#557—478no—
621#557—474no—
622#557—4716no—
623#557—478no—
624#557—478no—
625#557—478no—
626#557—474no—
627#557—474no—
628#557C2×D4714yescomplemented
629#556—474no—
630#556—4716no—
631#556—478no—
632#556—478no—
633#556—478no—
634#556—474no—
635#556—474no—
636#556—478no—
637#556C2×D4714yescomplemented
638#552—4716no—
639#552—4716no—
640#552—478no—
641#552—4716no—
642#552—478no—
643#552—478no—
644#552—478no—
645#552—478no—
646#552—4716no—
647#552—478no—
648#552—478no—
649#552C2×D4718yescomplemented
650#541—474no—
651#541—4716no—
652#541—4716no—
653#541—474no—
654#541—478no—
655#541—478no—
656#541—474no—
657#541C2×D4714yescomplemented
658#536—472no—
659#536—472no—
660#536—474no—
661#536—474no—
662#536—478no—
663#536—478no—
664#536—472no—
665#536C2×D4712yes—
666#533—472no—
667#533—474no—
668#533—474no—
669#533—472no—
670#533—478no—
671#533—474no—
672#533—478no—
673#533—478no—
674#533—474no—
675#533—478no—
676#533—478no—
677#533—472no—
678#533—478no—
679#533—471no—
680#533—474no—
681#533C2×D4711yescharacteristic, complemented
682#533C2×D4714yescomplemented
683C2×C4⋊Q8—472no—
684C2×C4⋊Q8—472no—
685C2×C4⋊Q8—472no—
686C2×C4⋊Q8—474no—
687C2×C4⋊Q8—472no—
688C2×C4⋊Q8—472no—
689C2×C4⋊Q8—474no—
690C2×C4⋊Q8—472no—
691C2×C4⋊Q8—474no—
692C2×C4⋊Q8—474no—
693C2×C4⋊Q8—471no—
694C2×C4⋊Q8C2×D4711yescharacteristic, complemented
695C2×#126—4716no—
696C2×#125—472no—
697C2×#125—478no—
698C2×#125—4716no—
699C2×#124—474no—
700C2×#123—478no—
701C2×C22⋊Q8—478no—
702C2×C22⋊Q8—474no—
703C2×C22⋊Q8—478no—
704#519—472no—
705#519—478no—
706#519—478no—
707#519—472no—
708#519—472no—
709#519—478no—
710#519C2×D4712yescomplemented
711C4×#41—471no—
712C4×#41—472no—
713C4×#41—474no—
714C4×#41—472no—
715C4×#41—471no—
716C4×#41—472no—
717C4×#41—472no—
718C4×#41—471no—
719C4×#41C2×D4711yescharacteristic
720C2×C4×Q8—472no—
721C2×C4×Q8—478no—
722C2×C4×Q8—478no—
723C2×C4×Q8—478no—
724C2×C4×Q8—474no—
725C2×C4×D4—474no—
726C2×C4×D4—472no—
727C2×#117—471no—
728C2×#117—472no—
729C2×#117—472no—
730C2×#117—478no—
731C2×#117—478no—
732C22×C4⋊C4—474no—
733C22×C42—471no—
734C22×C42—472no—
735C47C2×#350911yescharacteristic, complemented, Sylow
736C2×#41—471no—
737C2×#41—472no—
738C2×#41—471no—
739C2×#41—472no—
740C2×#41—471no—
741C2×#41—948no—
742C2×#41C22×D4711yescharacteristic
743C22×Q8—474no—
744C22×Q8—474no—
745C22×Q8—474no—
746C22×Q8—471no—
747C22×Q8—474no—
748C22×Q8—474no—
749C22×Q8—474no—
750C22×Q8—472no—
751C22×Q8—9416no—
752C22×Q8C22×D4712yes—
753C22×D4—472no—
754C22×D4—471no—
755C23×C4—471no—
756C23×C4—474no—
757C23×C4—472no—
758C23×C4—474no—
759C23×C4—472no—
760C4⋊Q8—474no—
761C4⋊Q8—474no—
762C4⋊Q8—478no—
763C4⋊Q8—474no—
764C4⋊Q8—474no—
765C4⋊Q8—474no—
766C4⋊Q8—478no—
767C4⋊Q8—478no—
768C4⋊Q8—478no—
769C4⋊Q8—478no—
770C4⋊Q8—474no—
771C4⋊Q8—474no—
772C4⋊Q8—4716no—
773C4⋊Q8—472no—
774C4⋊Q8—472no—
775C4⋊Q8—474no—
776C4⋊Q8—472no—
777C4⋊Q8—474no—
778C4⋊Q8C22×D4712yes—
779C4⋊Q8C22×D4712yes—
780C4⋊Q8C22×D4714yes—
781C4⋊Q8C22×D4712yes—
782C4⋊Q8C22×D4714yes—
783#126—4716no—
784#126—4716no—
785#126—4716no—
786#126—4716no—
787#126—4716no—
788#126—4716no—
789#126—4716no—
790#126C22×D47116yes—
791#125—478no—
792#125—474no—
793#125—4716no—
794#125—4716no—
795#125—478no—
796#125—478no—
797#125—4716no—
798#125—4716no—
799#125—4716no—
800#125—4716no—
801#125—4716no—
802#125—4716no—
803#125—472no—
804#125—478no—
805#125—4716no—
806#125C22×D4712yes—
807#125C22×D4718yes—
808#125C22×D47116yes—
809#124—474no—
810#124—474no—
811#124—4716no—
812#124—474no—
813#124C22×D4714yes—
814#123—478no—
815#123—478no—
816#123—4716no—
817#123—4716no—
818#123—478no—
819#123C22×D4718yes—
820C22⋊Q8—478no—
821C22⋊Q8—474no—
822C22⋊Q8—478no—
823C22⋊Q8—478no—
824C22⋊Q8—474no—
825C22⋊Q8—478no—
826C22⋊Q8—4716no—
827C22⋊Q8—478no—
828C22⋊Q8—478no—
829C22⋊Q8—474no—
830C22⋊Q8—4716no—
831C22⋊Q8—478no—
832C22⋊Q8—4716no—
833C22⋊Q8—478no—
834C22⋊Q8—4716no—
835C22⋊Q8C22×D4718yes—
836C22⋊Q8C22×D4714yes—
837C22⋊Q8C22×D4718yes—
838C4×Q8—472no—
839C4×Q8—478no—
840C4×Q8—478no—
841C4×Q8—478no—
842C4×Q8—474no—
843C4×Q8—474no—
844C4×Q8—472no—
845C4×Q8—4716no—
846C4×Q8—478no—
847C4×Q8—4716no—
848C4×Q8—478no—
849C4×Q8—4716no—
850C4×Q8—478no—
851C4×Q8—478no—
852C4×Q8—474no—
853C4×Q8—472no—
854C4×Q8—474no—
855C4×Q8—4716no—
856C4×Q8—478no—
857C4×Q8—478no—
858C4×Q8—4716no—
859C4×Q8—4716no—
860C4×Q8—478no—
861C4×Q8—478no—
862C4×Q8—474no—
863C4×Q8C22×D4712yes—
864C4×Q8C22×D4718yes—
865C4×Q8C22×D4718yes—
866C4×Q8C22×D4718yes—
867C4×Q8C22×D4714yes—
868C4×D4—474no—
869C4×D4—472no—
870C4×D4—474no—
871C4×D4—474no—
872C4×D4—474no—
873C4×D4—474no—
874C4×D4—472no—
875C4×D4—474no—
876C4×D4—474no—
877C4×D4—474no—
878C4×D4—474no—
879C4×D4—472no—
880C4×D4C22×D4714yes—
881C4×D4C22×D4712yes—
882#117—471no—
883#117—472no—
884#117—472no—
885#117—478no—
886#117—478no—
887#117—472no—
888#117—474no—
889#117—474no—
890#117—4716no—
891#117—478no—
892#117—478no—
893#117—472no—
894#117—474no—
895#117—474no—
896#117—478no—
897#117—478no—
898#117—4716no—
899#117—472no—
900#117—472no—
901#117—472no—
902#117—474no—
903#117—4716no—
904#117—4716no—
905#117C22×D4711yescharacteristic
906#117C22×D4712yes—
907#117C22×D4712yes—
908#117C22×D4718yes—
909#117C22×D4718yes—
910C2×C4⋊C4—478no—
911C2×C4⋊C4—474no—
912C2×C4⋊C4—478no—
913C2×C4⋊C4—478no—
914C2×C4⋊C4—478no—
915C2×C4⋊C4—478no—
916C2×C4⋊C4—474no—
917C2×C4⋊C4—472no—
918C2×C4⋊C4—474no—
919C2×C4⋊C4—474no—
920C2×C4⋊C4—4716no—
921C2×C4⋊C4—4716no—
922C2×C4⋊C4—478no—
923C2×C4⋊C4C22×D4714yes—
924C2×C22⋊C4—472no—
925C2×C22⋊C4—474no—
926C2×C22⋊C4—474no—
927C2×C22⋊C4—4716no—
928C2×C42—472no—
929C2×C42—471no—
930C2×C42—472no—
931C2×C42—474no—
932C2×C42—472no—
933C2×C42—4716no—
934C2×C42—471no—
935C2×C42—474no—
936C2×C42—474no—
937C2×C42—472no—
938C2×C42—472no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42—474no—
942C2×C42—472no—
943C2×C42—472no—
944C2×C42—471no—
945C2×C42C22×D4711yescharacteristic
946C2×C42C22×D4712yes—
947C24—471no—
948C24—472no—
949#41—24no—
950#41—948no—
951#41—948no—
952#41—944no—
953#41—944no—
954#41—944no—
955C2×Q8—28no—
956C2×Q8—478no—
957C2×Q8—474no—
958C2×Q8—478no—
959C2×Q8—474no—
960C2×Q8—478no—
961C2×Q8—474no—
962C2×Q8—472no—
963C2×Q8—471no—
964C2×Q8—9416no—
965C2×Q8—9416no—
966C2×Q8—9416no—
967C2×Q8—9416no—
968C2×Q8—9416no—
969C2×Q8—9416no—
970C2×Q8—944no—
971C2×Q8—948no—
972C2×Q8C23×D4714yes—
973C2×Q8C23×D4714yes—
974C2×Q8C23×D4714yes—
975C2×Q8C23×D4711yescharacteristic
976C2×D4—472no—
977C2×D4—472no—
978C2×D4—472no—
979C2×D4—472no—
980C2×D4—471no—
981C2×D4—944no—
982C2×D4—948no—
983C2×D4C23×D4712yes—
984C2×D4C23×D4711yescharacteristic
985C22×C4—471no—
986C22×C4—478no—
987C22×C4—471no—
988C22×C4—472no—
989C22×C4—471no—
990C22×C4—471no—
991C22×C4—471no—
992C22×C4—472no—
993C22×C4—474no—
994C22×C4—472no—
995C22×C4—474no—
996C22×C4—474no—
997C22×C4—478no—
998C22×C4—472no—
999C22×C4—478no—
1000C22×C4—472no—
1001C22×C4—472no—
1002C22×C4—472no—
1003C22×C4—474no—
1004C22×C4—474no—
1005C22×C4—472no—
1006C22×C4—472no—
1007C22×C4—478no—
1008C22×C4—948no—
1009C22×C4—9416no—
1010C22×C4—948no—
1011C22×C4—9416no—
1012C22×C4C23×D4712yes—
1013C22×C4C23×D4714yes—
1014C22×C4C23×D4712yes—
1015C22×C4C23×D4714yes—
1016C22×C4C23×D4711yescharacteristic
1017C4⋊C4—4716no—
1018C4⋊C4—4716no—
1019C4⋊C4—478no—
1020C4⋊C4—474no—
1021C4⋊C4—474no—
1022C4⋊C4—474no—
1023C4⋊C4—478no—
1024C4⋊C4—4716no—
1025C4⋊C4—4716no—
1026C4⋊C4—4716no—
1027C4⋊C4—4716no—
1028C4⋊C4—478no—
1029C4⋊C4—478no—
1030C4⋊C4—478no—
1031C4⋊C4—478no—
1032C4⋊C4—474no—
1033C4⋊C4—472no—
1034C4⋊C4—474no—
1035C4⋊C4—474no—
1036C4⋊C4—4716no—
1037C4⋊C4—4716no—
1038C4⋊C4—478no—
1039C4⋊C4C23×D4718yes—
1040C4⋊C4C23×D4718yes—
1041C4⋊C4C23×D4714yes—
1042C4⋊C4C23×D4712yes—
1043C4⋊C4C23×D4714yes—
1044C4⋊C4C23×D4714yes—
1045C4⋊C4C23×D47116yes—
1046C4⋊C4C23×D47116yes—
1047C4⋊C4C23×D4718yes—
1048C22⋊C4—472no—
1049C22⋊C4—474no—
1050C22⋊C4—474no—
1051C22⋊C4—4716no—
1052C22⋊C4—474no—
1053C22⋊C4—478no—
1054C22⋊C4—474no—
1055C22⋊C4—474no—
1056C22⋊C4—4716no—
1057C22⋊C4—4716no—
1058C22⋊C4C23×D4712yes—
1059C22⋊C4C23×D4714yes—
1060C22⋊C4C23×D4714yes—
1061C22⋊C4C23×D47116yes—
1062C42—471no—
1063C42—472no—
1064C42—474no—
1065C42—472no—
1066C42—472no—
1067C42—471no—
1068C42—474no—
1069C42—474no—
1070C42—474no—
1071C42—472no—
1072C42—472no—
1073C42—472no—
1074C42—4716no—
1075C42—4716no—
1076C42—4716no—
1077C42—478no—
1078C42—474no—
1079C42C23×D4711yescharacteristic
1080C42C23×D4712yes—
1081C42C23×D4711yescharacteristic
1082C42C23×D4714yes—
1083C42C23×D4712yes—
1084C42C23×D47116yes—
1085C42C23×D4714yes—
1086C23—471no—
1087C23—474no—
1088C23—471no—
1089C23—472no—
1090C23—944no—
1091C23—944no—
1092C23—948no—
1093C23C24×D4712yes—
1094C23C24×D4711yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—22no—
1098Q8—28no—
1099Q8—9416no—
1100Q8—9416no—
1101Q8—9416no—
1102Q8—944no—
1103Q8—948no—
1104Q8—948no—
1105Q8—942no—
1106Q8—948no—
1107D4—24no—
1108D4—22no—
1109D4—944no—
1110D4—944no—
1111D4—944no—
1112D4—944no—
1113D4—942no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—474no—
1119C2×C4—471no—
1120C2×C4—472no—
1121C2×C4—471no—
1122C2×C4—474no—
1123C2×C4—474no—
1124C2×C4—474no—
1125C2×C4—474no—
1126C2×C4—478no—
1127C2×C4—474no—
1128C2×C4—478no—
1129C2×C4—472no—
1130C2×C4—478no—
1131C2×C4—472no—
1132C2×C4—944no—
1133C2×C4—948no—
1134C2×C4—944no—
1135C2×C4—948no—
1136C2×C4—944no—
1137C2×C4—944no—
1138C2×C4—9416no—
1139C2×C4—9416no—
1140C2×C4—9416no—
1141C2×C4—944no—
1142C2×C4—948no—
1143C2×C4—944no—
1144C2×C4—948no—
1145C2×C4—944no—
1146C2×C4—944no—
1147C2×C4—948no—
1148C2×C4#41×D4714yes—
1149C2×C4C24×D4714yes—
1150C2×C4C24×D4718yes—
1151C2×C4C24×D4712yes—
1152C2×C4C24×D4718yes—
1153C2×C4C24×D4712yes—
1154C2×C4C24×D4711yescharacteristic
1155C2×C4C24×D4711yescharacteristic
1156C2×C4C24×D4712yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—472no—
1161C22—474no—
1162C22—472no—
1163C22—948no—
1164C22—942no—
1165C22—942no—
1166C22—944no—
1167C22—1888no—
1168C22C2×#41×D4712yes—
1169C22C25×D4711yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—472no—
1176C4—472no—
1177C4—474no—
1178C4—942no—
1179C4—948no—
1180C4—944no—
1181C4—942no—
1182C4—948no—
1183C4C2×#41×D4712yes—
1184C4C2×#41×D4712yes—
1185C42−1+4×D4714yes—
1186C2—22no—
1187C2—42no—
1188C2—474no—
1189C2—942no—
1190C2—1882no—
1191C2C22×#41×D4711yescharacteristic
1192C2C2×2−1+4×D4712yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3509C2
prime radicalC2×#41×D47C22
hypercenter#3509D47
hypocenterC47C2×#3509
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #20257275C2semidirect
2. #20257274C2semidirect
3. #20257273C2semidirect
4. #20257272C2semidirect
5. #20257271C2semidirect
6. #20257270C2semidirect
7. #20257269C2semidirect
8. #20257268C2semidirect
9. #20257267C2semidirect
10. #20257266C2semidirect
11. #557×D47C2semidirect
12. #556×D47C2semidirect
13. #552×D47C2semidirect
14. #541×D47C2semidirect
16. #533×D47C2semidirect
17. #533×D47C2semidirect
18. C2×C4⋊Q8×D47C2semidirect
19. #519×D47C2semidirect
21. C47×#3509C2semidirect
24. #15689852C22semidirect
25. #15689851C22semidirect
26. #15689851C22semidirect
27. #15689850C22semidirect
28. #15689850C22semidirect
29. #15689849C22semidirect
30. #15689848C22semidirect
31. #15689848C22semidirect
32. #15689847C22semidirect
33. #15689846C22semidirect
34. #15689845C22semidirect
35. #15689844C22semidirect
36. #15689843C22semidirect
37. #15689842C22semidirect
38. #15689841C22semidirect
39. #15689840C22semidirect
40. #15689815C22semidirect
41. #15689814C22semidirect
42. #15689813C22semidirect
43. #15689812C22semidirect
44. #15689811C22semidirect
45. #15689810C22semidirect
46. #15689809C22semidirect
47. #15689808C22semidirect
48. #15689807C22semidirect
49. #15689806C22semidirect
50. #15689805C22semidirect
51. #15689736C22semidirect
52. #15689735C22semidirect
53. #15689734C22semidirect
54. #15689733C22semidirect
55. #15689732C22semidirect
56. #15689731C22semidirect
57. #15689730C22semidirect
65. #15689680C22semidirect
66. #15689680C22semidirect
67. #15689679C22semidirect
68. #15689679C22semidirect
69. #15689678C22semidirect
70. #15689678C22semidirect
71. #15689678C22semidirect
72. #15689677C22semidirect
73. #15689677C22semidirect
74. #15689677C22semidirect
75. #15689676C22semidirect
76. #15689676C22semidirect
77. #15689675C22semidirect
78. #15689675C22semidirect
79. #15689675C22semidirect
80. C2×#13094024C22semidirect
81. C2×#13094023C22semidirect
82. C2×#13094022C22semidirect
88. C4⋊Q8×D47C22semidirect
89. C4⋊Q8×D47C22semidirect
90. C4⋊Q8×D47C22semidirect
100. #15689601C22semidirect
101. #15689600C22semidirect
102. #15689600C22semidirect
103. #15689600C22semidirect
104. #15689599C22semidirect
105. #15689599C22semidirect
129. C47×#557C22semidirect
130. C47×#556C22semidirect
131. C47×#552C22semidirect
132. C47×#541C22semidirect
134. C47×#533C22semidirect
135. C47×#533C22semidirect
136. C2×C4⋊Q8×C47C22semidirect
137. C47×#519C22semidirect
600. #3509D47direct (N × H)
617. D47#3509direct (N × H)
628. #557C2×D47semidirect
637. #556C2×D47semidirect
649. #552C2×D47semidirect
657. #541C2×D47semidirect
681. #533C2×D47semidirect
682. #533C2×D47semidirect
694. C2×C4⋊Q8C2×D47semidirect
710. #519C2×D47semidirect
735. C47C2×#3509semidirect

Maximal subgroups

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

subgroupindex
#202572752
#202572742
#202572732
#202572722
#202572712
#202572702
#202572692
#202572682
#202572672
#202572662
#557×D472
#556×D472
#552×D472
#541×D472
#536×D472
#533×D472
C2×C4⋊Q8×D472
#519×D472
C4×#41×D472
C47×#35092
C2×#350947