Finite Group Databasebeta

← #26232754

Subgroups — #26232754

Order 12032.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256946C211yesmaximal, characteristic
2C4×D4×Dic47C211yesmaximal, characteristic, complemented
3#20244364C211yesmaximal, characteristic, complemented
4#20244332C211yesmaximal, characteristic, complemented
5#20243829C212yesmaximal, complemented
6#20243690C212yesmaximal, complemented
7#20243485C212yesmaximal, complemented
8#20243405C211yesmaximal, characteristic, complemented
9C4×#13093950C211yesmaximal, characteristic, complemented
10C2×#15688884C212yesmaximal, complemented
11D4×M16×C47C211yesmaximal, characteristic, complemented
12#15689843C411yescharacteristic, complemented
13#15689838C411yescharacteristic, complemented
14#15689830C411yescharacteristic, complemented
15#15689819C412yescomplemented
16#15689813C412yescomplemented
17#15689808—21no—
18#15689799—22no—
19#15689777C411yescharacteristic, complemented
20#15689767—21no—
21#15689680C2211yescharacteristic
22#15689655—21no—
23#15689653—22no—
24#15689634C2212yes—
25C4×#10625350C2211yescharacteristic
26C4×#10625352—21no—
27C2×D4×Dic47—21no—
28C2×#13093983C2212yes—
29C22×C4×Dic47C2212yes—
30C2×#13093950C2211yescharacteristic
31C2×#13093950C2211yescharacteristic
32C2×#13093950C2212yes—
33C4⋊C4×Dic47—21no—
34C4×C4⋊Dic47C2211yescharacteristic
35C22⋊C4×Dic47—22no—
36C4×C22⋊Dic47C2212yes—
37C42×Dic47C2211yescharacteristic
38#15688884C2211yescharacteristic
39#15688884C2212yes—
40#15688884C2212yes—
41#15688884C2212yes—
42#15688884C2212yes—
43#15688884C2212yes—
44#15688884C2211yescharacteristic
45C22×M16×C47C2212yes—
46C2×C4×D4×C47C2211yescharacteristic
47C47×#436—21no—
48C47×#435—22no—
49C8×D4×C47—21no—
50C47×#423C2211yescharacteristic
51C47×#407C2212yes—
52C4×M16×C47C2211yescharacteristic
53C2×#10625350C2311yescharacteristic
54C2×#10625352—21no—
55C23×Dic47—22no—
56#13094024C2×C411yescharacteristic, complemented
57#13094024C2×C411yescharacteristic, complemented
58#13094019—22no—
59#13094017—22no—
60#13094017—22no—
61#13094016C2×C412yescomplemented
62#13094015—21no—
63#13094014—22no—
64#13094011—21no—
65#13094010—22no—
66#13094008—22no—
67#13094007—22no—
68#13094006—22no—
69#13094005—22no—
70#13094004—21no—
71#13094003—21no—
72#13094003—21no—
73#13094003C2×C412yescomplemented
74#13094003C2×C412yescomplemented
75#13094001—22no—
76#13093998C2×C412yescomplemented
77#13093998C2×C412yescomplemented
78#13093996—22no—
79#13093995—21no—
80#13093993—22no—
81C4×Dic94—21no—
82C4×Dic94—21no—
83C4×Dic94C2×C411yescharacteristic, complemented
84C4×Dic94C2×C411yescharacteristic, complemented
85#13093989—21no—
86C4×D188C2×C411yescharacteristic, complemented
87C4×D188C2×C411yescharacteristic, complemented
88D4×Dic47—28no—
89D4×Dic47—21no—
90C4×C22⋊D47—21no—
91C4×C22⋊D47—21no—
92C4×C22⋊D47—22no—
93C4×C22⋊D47—22no—
94(C22⋊D47)⋊C4—22no—
95#13093983—22no—
96#13093983—22no—
97#13093983C2×C412yescomplemented
98#13093983C2×C412yescomplemented
99#13093983C2311yescharacteristic
100#13093983C2312yes—
101#13093982—21no—
102#13093981—21no—
103#13093980—22no—
104C2×C4⋊Dic47—21no—
105C2×C4⋊Dic47C2×C412yescomplemented
106C2×C4⋊Dic47C2×C412yescomplemented
107C2×C22⋊Dic47—22no—
108C2×C22⋊Dic47—22no—
109C2×C4×Dic47—21no—
110C2×C4×Dic47—22no—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—21no—
113C2×C4×Dic47—22no—
114C2×C4×Dic47—42no—
115C2×C4×Dic47C2311yescharacteristic
116C2×C4×Dic47C2312yes—
117C2×C4×Dic47C2311yescharacteristic
118C42×D47—21no—
119#13093950—22no—
120#13093950—22no—
121#13093950—42no—
122C47⋊#95—22no—
123C47⋊#95—21no—
124C22×D4×C47D411yescharacteristic
125C23×C4×C47C2312yes—
126C2×M16×C47—22no—
127C2×M16×C47—24no—
128C2×M16×C47—42no—
129C2×M16×C47C2312yes—
130C2×M16×C47C2311yescharacteristic
131C2×M16×C47C2311yescharacteristic
132C22×C8×C47—22no—
133C4×D4×C47C2×C411yescharacteristic
134C4×D4×C47C2×C412yes—
135C4×D4×C47C2×C411yescharacteristic
136C4×D4×C47D411yescharacteristic
137C4×D4×C47D412yes—
138C4×D4×C47D411yescharacteristic
139C2×C4⋊C4×C47D411yescharacteristic
140C2×C22⋊C4×C47D412yes—
141C2×C42×C47C2311yescharacteristic
142C4⋊C8×C47—21no—
143C4⋊C8×C47—21no—
144C22⋊C8×C47—22no—
145C22⋊C8×C47—22no—
146#97×C47—21no—
147C4×C8×C47—21no—
148C24×C47C2×D412yes—
149C2×D4×C47—24no—
150C2×D4×C47C22⋊C411yescharacteristic
151C2×D4×C47C22⋊C412yes—
152C2×D4×C47C22⋊C411yescharacteristic
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2411yescharacteristic
165C2×C22⋊D47—22no—
166C2×C22⋊D47—21no—
167C2×C22⋊D47—22no—
168C22×Dic47—21no—
169C22×Dic47—28no—
170C22×Dic47—22no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—44no—
175C22×Dic47—44no—
176#10625352—44no—
177#10625350—21no—
178#10625350—21no—
179#10625350—21no—
180#10625350—21no—
181C2×D188C22×C411yescharacteristic
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×Dic94—21no—
186C2×Dic94—21no—
187C2×Dic94C22×C411yescharacteristic
188M16×C47—21no—
189M16×C47—22no—
190M16×C47—21no—
191M16×C47—22no—
192M16×C47—21no—
193M16×C47—44no—
194M16×C47#4112yescomplemented
195C2×C8×C47—21no—
196C2×C8×C47—22no—
197C2×C8×C47—21no—
198C2×C8×C47—44no—
199C4⋊C4×C47C22⋊C411yescharacteristic
200C4⋊C4×C47C22⋊C411yescharacteristic
201C4⋊C4×C47C22⋊C412yes—
202C22⋊C4×C47C22⋊C412yes—
203C22⋊C4×C47C22⋊C412yes—
204C22⋊C4×C47C22⋊C412yes—
205C22⋊C4×C47C22⋊C412yes—
206C42×C47C22×C411yescharacteristic
207C42×C47C22×C411yescharacteristic
208C42×C47C2×D411yescharacteristic
209C42×C47C2×D411yescharacteristic
210C22⋊Dic47—28no—
211C22⋊Dic47—22no—
212C22⋊Dic47—22no—
213C22⋊Dic47—22no—
214C22⋊Dic47—22no—
215C22⋊Dic47—21no—
216C22⋊Dic47—22no—
217(C2×D47)⋊C4—21no—
218(C2×D47)⋊C4—21no—
219(C2×D47)⋊C4—22no—
220(C2×D47)⋊C4—22no—
221C4⋊Dic47—24no—
222C4⋊Dic47—22no—
223C4⋊Dic47—22no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47C22×C411yescharacteristic
227C4⋊Dic47C22×C411yescharacteristic
228C4⋊Dic47C22×C412yes—
229C4⋊Dic47C22×C412yes—
230Dic47⋊C4—22no—
231Dic47⋊C4—22no—
232Dic47⋊C4—21no—
233Dic47⋊C4—21no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236C4×Dic47—24no—
237C4×Dic47—21no—
238C4×Dic47—21no—
239C4×Dic47—22no—
240C4×Dic47—22no—
241C4×Dic47—21no—
242C4×Dic47—22no—
243C4×Dic47—21no—
244C4×Dic47—21no—
245C4×Dic47—22no—
246C4×Dic47—22no—
247C4×Dic47—21no—
248C4×Dic47—44no—
249C4×Dic47—42no—
250C4×Dic47#4112yescomplemented
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—24no—
254C23×C47—42no—
255C23×C47C2×C22⋊C412yes—
256C23×C47C2×C22⋊C412yes—
257C23×C47C22×D411yescharacteristic
258C22×D47—21no—
259D4×C47—24no—
260D4×C47—22no—
261D4×C47#10414yescomplemented
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—41no—
274C2×C4×C47C2×C22⋊C412yes—
275C2×C4×C47C2×C22⋊C411yescharacteristic
276C2×C4×C47C2×C22⋊C411yescharacteristic
277C2×C4×C47C2×C22⋊C412yes—
278C2×C4×C47C2×C22⋊C411yescharacteristic
279C2×C4×C47C2×C22⋊C411yescharacteristic
280C2×C4×C47C23×C411yescharacteristic
281C2×C4×C47C22×D411yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47H(5,𝔽2)11yescharacteristic
285C2×C4×C472−1+411yescharacteristic
286C22⋊D47—41no—
287C22⋊D47—41no—
288C22⋊D47—44no—
289C22⋊D47—82no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—24no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—416no—
301C2×Dic47—41no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—41no—
305C2×Dic47—44no—
306C2×Dic47—82no—
307D188—21no—
308D188—21no—
309C4×D47—41no—
310C4×D47—41no—
311C4×D47—42no—
312C4×D47—81no—
313Dic94—21no—
314Dic94—21no—
315Dic94—42no—
316Dic94—81no—
317C8×C47—22no—
318C8×C47—42no—
319C8×C47—41no—
320#22505—471nomaximal, Sylow
321C22×C47—22no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—44no—
329C22×C47—44no—
330C22×C47C2×#10414yes—
331C22×C47C22×C22⋊C411yescharacteristic
332C22×C47#54611yescharacteristic
333C22×C47#54711yescharacteristic
334C2×D47—41no—
335C2×D47—41no—
336C2×D47—41no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—21no—
340C4×C47—21no—
341C4×C47—21no—
342C4×C47C2×#10412yes—
343C4×C47C4×#4111yescharacteristic
344C4×C47#52011yescharacteristic
345C4×C47#54611yescharacteristic
346C4×C47#54711yescharacteristic
347Dic47—24no—
348Dic47—42no—
349Dic47—44no—
350Dic47—41no—
351Dic47—42no—
352Dic47—41no—
353Dic47—42no—
354Dic47—41no—
355#3475—471no—
356D4×M16D4711yescharacteristic, complemented
357C42×D4—471no—
358#1994—471no—
359#1986—471no—
360#1896—472no—
361#1871—472no—
362#1826—472no—
363#1806—471no—
364C4×#104—471no—
365C2×#339—472no—
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—24no—
369C2×C47—42no—
370C2×C47#233911yescharacteristic
371C2×C47C22×#10411yescharacteristic
372C2×C47#290111yescharacteristic
373D47—81no—
374C22×M16C2×D4712yes—
375#556—471no—
376#555—471no—
377#554—471no—
378#553—472no—
379#552—472no—
380#552—941no—
381#551—942no—
382#547—471no—
383#546—941no—
384#533—471no—
385#529—942no—
386#529—941no—
387#525—472no—
388C4×#41—471no—
389C4×#41—941no—
390C2×C4×D4—941no—
391C2×C4×D4C2×D4711yescharacteristic
392C2×#117—472no—
393C22×C42—472no—
394#436—21no—
395#435—22no—
396C8×D4—21no—
397#423C2×D4711yescharacteristic
398C2×#104—471no—
399C2×#104—471no—
400C2×#104—472no—
401#407C2×D4712yes—
402C4×M16C2×D4711yescharacteristic
403C4×C4⋊C4—471no—
404C4×C4⋊C4—941no—
405C4×C22⋊C4—472no—
406C4×C22⋊C4—942no—
407C43—471no—
408#339—472no—
409#339—471no—
410#339—472no—
411#339—472no—
412#339—472no—
413#339—472no—
414#339—471no—
415C47#2250511yescharacteristic, complemented, Sylow
416C2×#41—471no—
417C2×#41—941no—
418C22×D4D18811yescharacteristic
419C23×C4—942no—
420C23×C4C22×D4712yes—
421C2×M16—22no—
422C2×M16—24no—
423C2×M16—42no—
424C2×M16C22×D4712yes—
425C2×M16C22×D4711yescharacteristic
426C2×M16C22×D4711yescharacteristic
427C22×C8—22no—
428C4⋊Q8—471no—
429C4⋊Q8—471no—
430#126—942no—
431#126—942no—
432#126—942no—
433#125—472no—
434#125—942no—
435#125—941no—
436#124—941no—
437#124—942no—
438#123—942no—
439#123—942no—
440#123—942no—
441#123—942no—
442C22⋊Q8—472no—
443C22⋊Q8—472no—
444C22⋊Q8—941no—
445C22⋊Q8—941no—
446C22⋊Q8—941no—
447C22⋊Q8—942no—
448#121—472no—
449#121—472no—
450#121—942no—
451#121—941no—
452#120—942no—
453C4×Q8—471no—
454C4×Q8—471no—
455C4×Q8—941no—
456C4×Q8—941no—
457C4×Q8—941no—
458C4×D4—471no—
459C4×D4—471no—
460C4×D4—948no—
461C4×D4—941no—
462C4×D4—941no—
463C4×D4—941no—
464C4×D4—942no—
465C4×D4—942no—
466C4×D4—942no—
467C4×D4C4×D4711yescharacteristic
468C4×D4C4×D4712yes—
469C4×D4C4×D4711yescharacteristic
470C4×D4C22⋊D4711yescharacteristic
471C4×D4C22⋊D4712yes—
472C4×D4C22⋊D4711yescharacteristic
473#117—472no—
474#117—472no—
475#117—471no—
476#117—472no—
477#117—942no—
478#117—942no—
479#117—941no—
480#117—942no—
481#117—941no—
482C2×C4⋊C4—472no—
483C2×C4⋊C4—472no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4D18811yescharacteristic
486C2×C22⋊C4—942no—
487C2×C22⋊C4—942no—
488C2×C22⋊C4D18812yes—
489C2×C42—471no—
490C2×C42—471no—
491C2×C42—472no—
492C2×C42—944no—
493C2×C42—941no—
494C2×C42—942no—
495C2×C42—941no—
496C2×C42—941no—
497C2×C42—942no—
498C2×C42—1882no—
499C2×C42C22×D4711yescharacteristic
500C4⋊C8—21no—
501C4⋊C8—21no—
502#104—942no—
503#104—942no—
504#104—1882no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507#97—21no—
508C4×C8—21no—
509#95—942no—
510#95—941no—
511C24C2×D18812yes—
512#41—941no—
513#41—941no—
514#41—941no—
515#41—941no—
516#41—1884no—
517C2×Q8—471no—
518C2×Q8—941no—
519C2×Q8—941no—
520C2×D4—24no—
521C2×D4—471no—
522C2×D4—942no—
523C2×D4—942no—
524C2×D4—941no—
525C2×D4(C2×D47)⋊C412yes—
526C2×D4(C2×D47)⋊C411yescharacteristic
527C2×D4(C2×D47)⋊C411yescharacteristic
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—941no—
533C22×C4—942no—
534C22×C4—948no—
535C22×C4—942no—
536C22×C4—941no—
537C22×C4—942no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—1884no—
542C22×C4—1884no—
543C22×C4C2×C4×D4712yes—
544C22×C4C2×C4×D4712yes—
545C22×C4C2×D18812yes—
546C22×C4C2×D18811yescharacteristic
547C22×C4C2×D18811yescharacteristic
548C22×C4C2×C22⋊D4712yes—
549C22×C4C2×C22⋊D4712yes—
550C22×C4C23×D4711yescharacteristic
551M16—21no—
552M16—21no—
553M16—22no—
554M16—22no—
555M16—21no—
556M16—44no—
557M16#1062535212yescomplemented
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—22no—
561C2×C8—44no—
562C4⋊C4—471no—
563C4⋊C4—471no—
564C4⋊C4—472no—
565C4⋊C4—472no—
566C4⋊C4—944no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—942no—
570C4⋊C4—942no—
571C4⋊C4—942no—
572C4⋊C4—942no—
573C4⋊C4—942no—
574C4⋊C4—942no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4(C2×D47)⋊C411yescharacteristic
578C4⋊C4(C2×D47)⋊C411yescharacteristic
579C4⋊C4(C2×D47)⋊C412yes—
580C22⋊C4—948no—
581C22⋊C4—942no—
582C22⋊C4—942no—
583C22⋊C4—942no—
584C22⋊C4—942no—
585C22⋊C4—941no—
586C22⋊C4—942no—
587C22⋊C4—941no—
588C22⋊C4—941no—
589C22⋊C4—942no—
590C22⋊C4—942no—
591C22⋊C4(C2×D47)⋊C412yes—
592C22⋊C4(C2×D47)⋊C412yes—
593C22⋊C4(C2×D47)⋊C412yes—
594C22⋊C4(C2×D47)⋊C412yes—
595C42—472no—
596C42—944no—
597C42—942no—
598C42—942no—
599C42—941no—
600C42—941no—
601C42—941no—
602C42—942no—
603C42—941no—
604C42—942no—
605C42—941no—
606C42—942no—
607C42—941no—
608C42—1884no—
609C42—1882no—
610C42C2×C4×D4711yescharacteristic
611C42C2×C4×D4711yescharacteristic
612C42C2×C22⋊D4711yescharacteristic
613C42C2×C22⋊D4711yescharacteristic
614C23—22no—
615C23—22no—
616C23—24no—
617C23—42no—
618C23—941no—
619C23C2×(C2×D47)⋊C412yes—
620C23C2×(C2×D47)⋊C412yes—
621C23C22×D18811yescharacteristic
622Q8—941no—
623Q8—941no—
624Q8—3761no—
625Q8—1882no—
626D4—24no—
627D4—22no—
628D4—941no—
629D4—941no—
630D4—3762no—
631D4—1881no—
632D4—1881no—
633D4—1884no—
634D4#1309395014yescomplemented
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—944no—
652C2×C4—941no—
653C2×C4—941no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—941no—
657C2×C4—3761no—
658C2×C4—3762no—
659C2×C4—18816no—
660C2×C4—1881no—
661C2×C4—1882no—
662C2×C4—1882no—
663C2×C4—1881no—
664C2×C4—1884no—
665C2×C4—1881no—
666C2×C4—1881no—
667C2×C4—1882no—
668C2×C4C2×(C2×D47)⋊C412yes—
669C2×C4C2×(C2×D47)⋊C411yescharacteristic
670C2×C4C2×(C2×D47)⋊C411yescharacteristic
671C2×C4C2×(C2×D47)⋊C411yescharacteristic
672C2×C4C2×(C2×D47)⋊C412yes—
673C2×C4C2×(C2×D47)⋊C411yescharacteristic
674C2×C4C22×C4×D4711yescharacteristic
675C2×C4C22×C22⋊D4711yescharacteristic
676C2×C4#41×D4711yescharacteristic
677C2×C4C2×#1062535211yescharacteristic
678C2×C4#1309406911yescharacteristic
679C2×C4#1309407111yescharacteristic
680C8—22no—
681C8—42no—
682C8—41no—
683C22—21no—
684C22—21no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—44no—
691C22—44no—
692C22—1881no—
693C22—1881no—
694C22—1881no—
695C22C2×#1309395014yes—
696C22C22×(C2×D47)⋊C411yescharacteristic
697C22#1568976811yescharacteristic
698C22#1568977711yescharacteristic
699C4—21no—
700C4—21no—
701C4—21no—
702C4—22no—
703C4—22no—
704C4—944no—
705C4—1884no—
706C4—1882no—
707C4—1881no—
708C4—1882no—
709C4—1881no—
710C4—1882no—
711C4—1881no—
712C4C2×#1309395012yes—
713C4C4×#1062535211yescharacteristic
714C4#1568960211yescharacteristic
715C4#1568976711yescharacteristic
716C4#1568977211yescharacteristic
717C2—21no—
718C2—21no—
719C2—24no—
720C2—42no—
721C2—3761no—
722C2#2024621311yescharacteristic
723C2C22×#1309395011yescharacteristic
724C2#2025193311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×M16×C47C2
socleC22×C47C22×C22⋊C4
prime radical#20256946C2
cosocleC22×C4×C47C24
hypercenterD4×M16D47
hypocenterC47#22505
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. C4×D4×Dic47C2semidirect
3. #20244364C2semidirect
4. #20244332C2semidirect
5. #20243829C2semidirect
6. #20243690C2semidirect
7. #20243485C2semidirect
8. #20243405C2semidirect
9. C4×#13093950C2semidirect
10. C2×#15688884C2semidirect
11. D4×M16×C47C2semidirect
12. #15689843C4semidirect
13. #15689838C4semidirect
14. #15689830C4semidirect
15. #15689819C4semidirect
16. #15689813C4semidirect
19. #15689777C4semidirect
56. #13094024C2×C4semidirect
57. #13094024C2×C4semidirect
61. #13094016C2×C4semidirect
73. #13094003C2×C4semidirect
74. #13094003C2×C4semidirect
76. #13093998C2×C4semidirect
77. #13093998C2×C4semidirect
83. C4×Dic94C2×C4semidirect
84. C4×Dic94C2×C4semidirect
86. C4×D188C2×C4semidirect
87. C4×D188C2×C4semidirect
97. #13093983C2×C4semidirect
98. #13093983C2×C4semidirect
105. C2×C4⋊Dic47C2×C4semidirect
106. C2×C4⋊Dic47C2×C4semidirect
194. M16×C47#41semidirect
250. C4×Dic47#41semidirect
261. D4×C47#104semidirect
356. D4×M16D47semidirect
415. C47#22505semidirect
557. M16#10625352semidirect
634. D4#13093950semidirect

Maximal subgroups

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

subgroupindex
#202569462
C4×D4×Dic472
#202443642
#202443322
#202438292
#202436902
#202434852
#202434052
C4×#130939502
C2×#156888842
D4×M16×C472
#2250547