Finite Group Databasebeta

← #27101180

Subgroups — #27101180

Order 12032.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257227C211yesmaximal, characteristic, complemented
2#20255484C214yesmaximal, complemented
3#20255364C214yesmaximal, complemented
4#20254939C214yesmaximal, complemented
5#20254914C214yesmaximal, complemented
6#20254415C212yesmaximal, complemented
7#20254209C211yesmaximal, characteristic, complemented
8#20254190C211yesmaximal, characteristic, complemented
9#20254169C212yesmaximal, complemented
10#20253526C212yesmaximal, complemented
11#20252648C211yesmaximal, characteristic, complemented
12#20252640C211yesmaximal, characteristic, complemented
13#20252606C212yesmaximal, complemented
14#20252417C211yesmaximal, characteristic, complemented
15C2×C47×#547C211yesmaximal, characteristic, complemented
16C2×#13094054C2212yescomplemented
17C2×#13094049C2212yescomplemented
18C2×#13094044C2214yescomplemented
19#15689822—22no—
20#15689819C2212yescomplemented
21#15689813C2212yescomplemented
22#15689802—22no—
23#15689782C2212yescomplemented
24#15689769C2212yescomplemented
25#15689720—21no—
26#15689711—21no—
27#15689682—21no—
28#15689657C2212yes—
29#15689634C2212yes—
30C2×#13094003C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32#15689596—21no—
33#15689515C2214yescomplemented
34#15689491C2214yescomplemented
35#15689461C2214yescomplemented
36#15689456C2212yescomplemented
37#15689453C2212yescomplemented
38#15689451C2212yescomplemented
39#15689436C2212yes—
40#15689423C2214yescomplemented
41#15689379C2214yescomplemented
42#15689371C2214yescomplemented
43#15689362C2214yescomplemented
44#15689354C2214yescomplemented
45#15689338C2214yescomplemented
46#15689330C2214yescomplemented
47#15689325C2214yescomplemented
48#15689285C2214yescomplemented
49#15689285C2214yescomplemented
50#15689283C2214yescomplemented
51#15689279C2212yescomplemented
52#15689279C2212yescomplemented
53#15689278C2212yescomplemented
54#15689274C2212yescomplemented
55#15689273C2212yescomplemented
56#15689268C2214yescomplemented
57#15689268C2214yescomplemented
58#15689262C2212yes—
59#15689262C2212yes—
60#15689257C2212yes—
61#15689233C2214yescomplemented
62#15689223C2214yescomplemented
63#15689195C2214yescomplemented
64#15689195C2214yescomplemented
65#15689180C2212yescomplemented
66#15689124C2212yescomplemented
67#15689124C2212yescomplemented
68#15689119C2214yescomplemented
69#15689087C2211yescharacteristic
70#15689087C2211yescharacteristic
71C2×C22⋊(C47⋊C8)C2212yescomplemented
72C22×#41×C47C2211yescharacteristic
73C22×#41×C47C2211yescharacteristic, complemented
74C47×#547—22no—
75C47×#547—22no—
76C47×#547C2214yes—
77C47×#547C2214yescomplemented
78C2×C4⋊Q8×C47C2211yescharacteristic, complemented
79C2×#123×C47—21no—
80C2×#123×C47—21no—
81C2×C22⋊Q8×C47C2211yescharacteristic
82C2×C22⋊Q8×C47C2211yescharacteristic, complemented
83C2×#121×C47—21no—
84C2×C4×D4×C47C2211yescharacteristic
85C2×C4×D4×C47C2211yescharacteristic, complemented
86C22×C4⋊C4×C47—21no—
87C2×#10625350C2312yes—
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91#13094054—44no—
92#13094049—44no—
93#13094044—48no—
94C2×#10625337C2314yes—
95C2×#10625337C2314yes—
96C2×#10625335C2314yes—
97C2×#10625336C2314yes—
98C2×#10625336C2314yes—
99C2×#10625334C2314yes—
100C2×#10625329C2312yes—
101C2×#10625329C2312yes—
102C22×C47⋊C8C2314yes—
103#13094019—22no—
104#13094018—22no—
105#13094017—22no—
106#13094016C2312yes—
107#13094014—22no—
108#13094012C2312yes—
109#13094010—22no—
110#13094009—22no—
111#13094007—22no—
112#13094007—22no—
113#13094006—22no—
114#13094005—22no—
115#13094003—21no—
116#13094003—21no—
117#13094003C2312yes—
118#13094003C2312yes—
119#13094003C2312yes—
120#13094002—22no—
121#13093998—21no—
122#13093998—21no—
123#13093998C2312yes—
124#13093998C2312yes—
125#13093998C2312yes—
126#13093997—22no—
127#13093996—22no—
128#13093996—22no—
129#13093993—22no—
130#13093992—22no—
131C4×Dic94C2312yes—
132C4×D188C2312yes—
133C4×C22⋊D47—22no—
134C4×C22⋊D47—22no—
135C4×C22⋊D47—22no—
136(C22⋊D47)⋊C4—22no—
137(C22⋊D47)⋊C4—22no—
138#13093983C2312yes—
139#13093981—22no—
140#13093980—22no—
141C2×C4⋊Dic47C2311yescharacteristic
142C2×C4⋊Dic47C2311yescharacteristic
143C2×Dic47⋊C4—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C22⋊C4×D47—22no—
147#13093957C2314yes—
148#13093955C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093947C2314yes—
155#13093945C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158C22⋊(C47⋊C8)C2312yes—
159C22⋊(C47⋊C8)C2312yes—
160C22⋊(C47⋊C8)C2312yes—
161C22⋊(C47⋊C8)C2314yes—
162C22⋊(C47⋊C8)C2312yes—
163#13093935C2314yes—
164C2×#41×C47—21no—
165C2×#41×C47—21no—
166C2×#41×C47—22no—
167C2×#41×C47—44no—
168C2×#41×C47—44no—
169C2×#41×C47C2312yes—
170C2×#41×C47C2314yes—
171C2×#41×C47C2312yes—
172C22×Q8×C47C2311yescharacteristic
173C22×Q8×C47C2311yescharacteristic
174C22×D4×C47—21no—
175C22×D4×C47—21no—
176C22×D4×C47D411yescharacteristic
177C22×D4×C47C2311yescharacteristic
178C23×C4×C47—21no—
179C23×C4×C47—21no—
180C23×C4×C47—21no—
181C23×C4×C47C2311yescharacteristic
182C23×C4×C47C2311yescharacteristic
183C4⋊Q8×C47—22no—
184C4⋊Q8×C47C2314yes—
185#123×C47—24no—
186#123×C47—24no—
187#123×C47—24no—
188#123×C47—24no—
189C22⋊Q8×C47—21no—
190C22⋊Q8×C47—21no—
191C22⋊Q8×C47—22no—
192C22⋊Q8×C47C2312yes—
193C22⋊Q8×C47C2312yes—
194C22⋊Q8×C47C2314yes—
195#121×C47—24no—
196#121×C47—24no—
197C4×D4×C47—22no—
198C4×D4×C47D412yes—
199C4×D4×C47D412yes—
200C4×D4×C47C2314yes—
201C4×D4×C47C2312yes—
202C4×D4×C47C2312yes—
203C2×C4⋊C4×C47—21no—
204C2×C4⋊C4×C47—21no—
205C2×C4⋊C4×C47—21no—
206C2×C4⋊C4×C47—21no—
207C2×C4⋊C4×C47—24no—
208C2×C4⋊C4×C47—24no—
209C2×C4⋊C4×C47D411yescharacteristic
210C2×C4⋊C4×C47C2311yescharacteristic
211C2×C22⋊C4×C47—21no—
212C2×C22⋊C4×C47—21no—
213C2×C22⋊C4×C47—21no—
214C2×C22⋊C4×C47D411yescharacteristic
215C2×C22⋊C4×C47D411yescharacteristic
216C2×C42×C47C2311yescharacteristic
217C24×C47—21no—
218C24×C47C2×D411yescharacteristic
219C24×C47C2×D411yescharacteristic
220C23×D47—21no—
221#41×C47—28no—
222#41×C47—24no—
223#41×C47—24no—
224#41×C47—44no—
225#41×C47—42no—
226#41×C47—42no—
227#41×C47—44no—
228#41×C47—44no—
229#41×C47—48no—
230C2×Q8×C47—21no—
231C2×Q8×C47—21no—
232C2×Q8×C47—42no—
233C2×Q8×C47—42no—
234C2×Q8×C47C2412yes—
235C2×Q8×C47C2412yes—
236C2×D4×C47—24no—
237C2×D4×C47—22no—
238C2×D4×C47—24no—
239C2×D4×C47—22no—
240C2×D4×C47—21no—
241C2×D4×C47—42no—
242C2×D4×C47—44no—
243C2×D4×C47—44no—
244C2×D4×C47C2×D412yes—
245C2×D4×C47C2×D412yes—
246C2×D4×C47C2412yes—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—24no—
251C22×C4×C47—24no—
252C22×C4×C47—22no—
253C22×C4×C47—22no—
254C22×C4×C47—42no—
255C22×C4×C47—42no—
256C22×C4×C47—44no—
257C22×C4×C47—44no—
258C22×C4×C47—44no—
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D412yes—
266C22×C4×C47C2411yescharacteristic
267C22×C4×C47C2411yescharacteristic
268C22×C4×C47C2411yescharacteristic
269C22×C4×C47C2412yes—
270C2×C22⋊D47—22no—
271C2×C22⋊D47—22no—
272C2×C22⋊D47—22no—
273C2×C22⋊D47—22no—
274C2×C22⋊D47—44no—
275C22×Dic47—21no—
276C22×Dic47—21no—
277C22×Dic47—21no—
278#10625350—44no—
279C2×D188—21no—
280C2×D188—42no—
281C2×D188C2412yes—
282C2×C4×D47—22no—
283C2×C4×D47—22no—
284C2×Dic94—21no—
285C2×Dic94—42no—
286C2×Dic94C2412yes—
287C4⋊C4×C47—24no—
288C4⋊C4×C47—24no—
289C4⋊C4×C47—22no—
290C4⋊C4×C47—22no—
291C4⋊C4×C47—24no—
292C4⋊C4×C47—21no—
293C4⋊C4×C47C2×D412yes—
294C4⋊C4×C47C2×D412yes—
295C4⋊C4×C47C2412yes—
296C22⋊C4×C47—22no—
297C22⋊C4×C47—24no—
298C22⋊C4×C47—22no—
299C22⋊C4×C47—24no—
300C22⋊C4×C47C2×D412yes—
301C22⋊C4×C47C2×D412yes—
302C22⋊C4×C47C2×D412yes—
303C22⋊C4×C47C2×D412yes—
304C42×C47C2×D412yes—
305C42×C47C2412yes—
306C22⋊Dic47—22no—
307C22⋊Dic47—22no—
308C22⋊Dic47—22no—
309C22⋊Dic47—22no—
310#10625337—44no—
311#10625337—44no—
312#10625336—44no—
313#10625336—44no—
314#10625335—28no—
315#10625334—28no—
316(C2×D47)⋊C4—22no—
317(C2×D47)⋊C4—22no—
318(C2×D47)⋊C4—22no—
319(C2×D47)⋊C4—22no—
320(C2×D47)⋊C4—22no—
321(C2×D47)⋊C4—22no—
322C4⋊Dic47—21no—
323C4⋊Dic47—21no—
324C4⋊Dic47C2412yes—
325C4⋊Dic47C2412yes—
326Dic47⋊C4—22no—
327Dic47⋊C4—22no—
328Dic47⋊C4—22no—
329Dic47⋊C4—22no—
330Dic47⋊C4—22no—
331Dic47⋊C4—22no—
332C4×Dic47—22no—
333C4×Dic47—22no—
334#10625329—42no—
335#10625329—42no—
336C2×C47⋊C8—44no—
337C2×C47⋊C8C2414yes—
338C2×C47⋊C8C2414yes—
339C23×C47—24no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—42no—
348C23×C47—42no—
349C23×C47C22×D411yescharacteristic
350C23×C47C22×D412yes—
351C23×C47C22×D411yescharacteristic
352C23×C47C22×D411yescharacteristic
353C22×D47—22no—
354C22×D47—42no—
355C22×D47—81no—
356C22×D47—81no—
357Q8×C47—22no—
358Q8×C47—24no—
359Q8×C47—22no—
360Q8×C47—42no—
361Q8×C47—42no—
362D4×C47—24no—
363D4×C47—22no—
364D4×C47—42no—
365D4×C47—42no—
366D4×C47—44no—
367D4×C47—48no—
368D4×C47—44no—
369D4×C47H(5,𝔽2)14yes—
370C2×C4×C47—22no—
371C2×C4×C47—24no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—42no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—44no—
385C2×C4×C47—48no—
386C2×C4×C47—44no—
387C2×C4×C47—48no—
388C2×C4×C47—42no—
389C2×C4×C47—42no—
390C2×C4×C47—42no—
391C2×C4×C47C22×D412yes—
392C2×C4×C47C22×D412yes—
393C2×C4×C47C22×D411yescharacteristic
394C2×C4×C47C22×D411yescharacteristic
395C2×C4×C47C22×D412yes—
396C2×C4×C47C22×D411yescharacteristic
397C2×C4×C47C2511yescharacteristic
398C22⋊D47—44no—
399C22⋊D47—44no—
400C22⋊D47—82no—
401C22⋊D47—82no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—42no—
406C2×Dic47—81no—
407C2×Dic47—81no—
408D188—24no—
409D188—81no—
410C4×D47—82no—
411C4×D47—82no—
412Dic94—24no—
413Dic94—81no—
414C47⋊C8—24no—
415C47⋊C8—24no—
416#61575—471nomaximal, Sylow
417C22×C47—21no—
418C22×C47—21no—
419C22×C47—21no—
420C22×C47—22no—
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—22no—
424C22×C47—21no—
425C22×C47—24no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—22no—
429C22×C47—48no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—82no—
433C22×C47—82no—
434C22×C47#57512yes—
435C22×C47C23×D411yescharacteristic
436C2×D47—42no—
437C2×D47—42no—
438C2×D47—42no—
439C2×D47—162no—
440C4×C47—22no—
441C4×C47—21no—
442C4×C47—22no—
443C4×C47—21no—
444C4×C47—21no—
445C4×C47—22no—
446C4×C47—42no—
447C4×C47—42no—
448C4×C47—42no—
449C4×C47C2×H(5,𝔽2)12yes—
450Dic47—42no—
451Dic47—42no—
452Dic47—42no—
453#3505—471no—
454C2×#547D4711yescharacteristic, complemented
455#3315—474no—
456#3307—474no—
457#3269—474no—
458#3267—474no—
459#3218—472no—
460#3195—471no—
461#3193—471no—
462#3190—472no—
463#3114—472no—
464#3007—471no—
465#3006—471no—
466#3002—472no—
467#2973—471no—
468C2×C47—22no—
469C2×C47—41no—
470C2×C47—41no—
471C2×C47—42no—
472C2×C47—44no—
473C2×C47#348411yescharacteristic
474C2×C47C2×#57511yescharacteristic
475C2×C47#358611yescharacteristic
476D47—82no—
477C22×#41C2×D4711yescharacteristic
478C22×#41C2×D4711yescharacteristic, complemented
479C2×#137—472no—
480C2×AGL(1,ℤ/8)—472no—
481C2×#135—474no—
482#553—472no—
483#553—942no—
484#552—472no—
485#551—942no—
486#548—472no—
487#547—22no—
488#547—22no—
489#547C2×D4714yes—
490#547C2×D4714yescomplemented
491#546—472no—
492#539—941no—
493#538—941no—
494#534—941no—
495C2×C4⋊Q8C2×D4711yescharacteristic, complemented
496#529—472no—
497#525—472no—
498C2×#123—21no—
499C2×#123—21no—
500C2×C22⋊Q8—471no—
501C2×C22⋊Q8C2×D4711yescharacteristic
502C2×C22⋊Q8C2×D4711yescharacteristic, complemented
503C2×#121—21no—
504C2×#121—471no—
505#518—941no—
506C2×C4×D4C2×D4711yescharacteristic
507C2×C4×D4C2×D4711yescharacteristic, complemented
508C22×C4⋊C4—21no—
509#497—474no—
510#491—474no—
511#485—474no—
512#484—472no—
513#483—472no—
514#483—472no—
515#480—472no—
516#478—474no—
517#470—474no—
518#468—474no—
519#467—474no—
520#465—474no—
521#463—474no—
522#462—474no—
523#461—474no—
524#452—474no—
525#452—474no—
526#452—474no—
527#451—472no—
528#451—472no—
529#451—472no—
530#450—472no—
531#450—472no—
532#449—474no—
533#449—474no—
534#448—472no—
535#448—472no—
536#447—472no—
537#442—474no—
538#440—474no—
539#435—474no—
540#435—474no—
541#432—472no—
542#417—472no—
543#417—472no—
544#416—474no—
545#407—471no—
546#407—471no—
547C2×C22⋊C8—472no—
548C47#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—22no—
552C2×#41—44no—
553C2×#41—44no—
554C2×#41—472no—
555C2×#41C22×D4712yes—
556C2×#41C22×D4714yes—
557C2×#41C22×D4712yes—
558C22×Q8—471no—
559C22×Q8C22×D4711yescharacteristic
560C22×Q8C22×D4711yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—471no—
564C22×D4—941no—
565C22×D4C22⋊D4711yescharacteristic
566C22×D4C22×D4711yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D4711yescharacteristic
571C23×C4C22×D4711yescharacteristic
572#137—1884no—
573AGL(1,ℤ/8)—1884no—
574#135—1888no—
575C2×Q16—474no—
576C2×Q16—474no—
577C2×SD16—474no—
578C2×SD16—474no—
579C2×SD16—474no—
580C2×D8—474no—
581C2×M16—472no—
582C2×M16—472no—
583C22×C8—474no—
584C4⋊Q8—22no—
585C4⋊Q8C22×D4714yes—
586#126—942no—
587#126—942no—
588#126—942no—
589#125—472no—
590#125—942no—
591#124—472no—
592#124—942no—
593#123—24no—
594#123—24no—
595#123—24no—
596#123—24no—
597#123—942no—
598#123—942no—
599#123—942no—
600#123—942no—
601#123—942no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—22no—
605C22⋊Q8—472no—
606C22⋊Q8—472no—
607C22⋊Q8—472no—
608C22⋊Q8—941no—
609C22⋊Q8—941no—
610C22⋊Q8—942no—
611C22⋊Q8C22×D4712yes—
612C22⋊Q8C22×D4712yes—
613C22⋊Q8C22×D4714yes—
614#121—24no—
615#121—24no—
616#121—472no—
617#121—472no—
618#121—472no—
619#121—942no—
620#121—942no—
621#121—941no—
622#121—941no—
623#121—942no—
624#120—942no—
625#120—942no—
626C4×Q8—472no—
627C4×D4—22no—
628C4×D4—472no—
629C4×D4—942no—
630C4×D4—942no—
631C4×D4—942no—
632C4×D4—942no—
633C4×D4—942no—
634C4×D4C22⋊D4712yes—
635C4×D4C22⋊D4712yes—
636C4×D4C22×D4714yes—
637C4×D4C22×D4712yes—
638C4×D4C22×D4712yes—
639#117—472no—
640#117—942no—
641#117—942no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—471no—
649C2×C4⋊C4—471no—
650C2×C4⋊C4—941no—
651C2×C4⋊C4C22⋊D4711yescharacteristic
652C2×C4⋊C4C22×D4711yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—941no—
657C2×C22⋊C4—941no—
658C2×C22⋊C4—942no—
659C2×C22⋊C4C22⋊D4711yescharacteristic
660C2×C22⋊C4C22⋊D4711yescharacteristic
661C2×C42C22×D4711yescharacteristic
662#107—474no—
663#106—474no—
664C4⋊C8—474no—
665#103—474no—
666#103—474no—
667#103—474no—
668#103—474no—
669#103—474no—
670#102—474no—
671#102—474no—
672#102—474no—
673C22⋊C8—472no—
674C22⋊C8—472no—
675C22⋊C8—474no—
676C22⋊C8—472no—
677C22⋊C8—472no—
678#97—474no—
679C24—21no—
680C24—941no—
681C24C2×C22⋊D4711yescharacteristic
682C24C2×C22⋊D4711yescharacteristic
683#41—28no—
684#41—24no—
685#41—24no—
686#41—44no—
687#41—42no—
688#41—42no—
689#41—44no—
690#41—44no—
691#41—48no—
692#41—1884no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—472no—
698C2×Q8—941no—
699C2×Q8—1882no—
700C2×Q8C23×D4712yes—
701C2×Q8C23×D4712yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—472no—
711C2×D4—942no—
712C2×D4—942no—
713C2×D4—942no—
714C2×D4—942no—
715C2×D4—941no—
716C2×D4—1882no—
717C2×D4—1884no—
718C2×D4C2×C22⋊D4712yes—
719C2×D4C2×C22⋊D4712yes—
720C2×D4C23×D4712yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4C2×C22⋊D4711yescharacteristic
739C22×C4C2×C22⋊D4711yescharacteristic
740C22×C4C2×C22⋊D4711yescharacteristic
741C22×C4C2×C22⋊D4711yescharacteristic
742C22×C4C2×C22⋊D4711yescharacteristic
743C22×C4C2×C22⋊D4711yescharacteristic
744C22×C4C2×C22⋊D4712yes—
745C22×C4C23×D4711yescharacteristic
746C22×C4C23×D4711yescharacteristic
747C22×C4C23×D4711yescharacteristic
748C22×C4C23×D4712yes—
749Q16—1884no—
750Q16—1884no—
751SD16—948no—
752SD16—1884no—
753SD16—1884no—
754D8—948no—
755M16—1882no—
756M16—1882no—
757C2×C8—474no—
758C2×C8—474no—
759C2×C8—1884no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—24no—
765C4⋊C4—21no—
766C4⋊C4—472no—
767C4⋊C4—472no—
768C4⋊C4—942no—
769C4⋊C4—942no—
770C4⋊C4—942no—
771C4⋊C4—942no—
772C4⋊C4—942no—
773C4⋊C4—942no—
774C4⋊C4—941no—
775C4⋊C4—941no—
776C4⋊C4C2×C22⋊D4712yes—
777C4⋊C4C2×C22⋊D4712yes—
778C4⋊C4C23×D4712yes—
779C22⋊C4—22no—
780C22⋊C4—24no—
781C22⋊C4—22no—
782C22⋊C4—24no—
783C22⋊C4—942no—
784C22⋊C4—942no—
785C22⋊C4—942no—
786C22⋊C4—942no—
787C22⋊C4—942no—
788C22⋊C4—942no—
789C22⋊C4—942no—
790C22⋊C4—942no—
791C22⋊C4—942no—
792C22⋊C4—942no—
793C22⋊C4C2×C22⋊D4712yes—
794C22⋊C4C2×C22⋊D4712yes—
795C22⋊C4C2×C22⋊D4712yes—
796C22⋊C4C2×C22⋊D4712yes—
797C42—942no—
798C42—942no—
799C42C2×C22⋊D4712yes—
800C42C23×D4712yes—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—942no—
812C23—3761no—
813C23—3761no—
814C23—1882no—
815C23C22×C22⋊D4711yescharacteristic
816C23C22×C22⋊D4712yes—
817C23C22×C22⋊D4711yescharacteristic
818C23C22×C22⋊D4711yescharacteristic
819Q8—22no—
820Q8—24no—
821Q8—22no—
822Q8—42no—
823Q8—42no—
824Q8—944no—
825Q8—3761no—
826D4—24no—
827D4—22no—
828D4—42no—
829D4—42no—
830D4—44no—
831D4—48no—
832D4—44no—
833D4—944no—
834D4—3761no—
835D4—3762no—
836D4—3762no—
837D4—1884no—
838D4—1884no—
839D4#1309406914yes—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—3762no—
865C2×C4—3762no—
866C2×C4—3761no—
867C2×C4—3761no—
868C2×C4—1882no—
869C2×C4C22×C22⋊D4712yes—
870C2×C4C22×C22⋊D4712yes—
871C2×C4C22×C22⋊D4711yescharacteristic
872C2×C4C22×C22⋊D4712yes—
873C2×C4C22×C22⋊D4711yescharacteristic
874C2×C4C22×C22⋊D4711yescharacteristic
875C2×C4C24×D4711yescharacteristic
876C8—944no—
877C8—944no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—24no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—82no—
895C22—1882no—
896C22—1882no—
897C22—1882no—
898C22—7522no—
899C22#1568992112yes—
900C22C23×C22⋊D4711yescharacteristic
901C4—22no—
902C4—22no—
903C4—22no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—1882no—
911C4—1882no—
912C4—1882no—
913C4C2×#1309406912yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—44no—
919C2—3762no—
920C2#2025702311yescharacteristic
921C2C2×#1568992111yescharacteristic
922C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#547C2
socleC22×C47C23×D4
hypercenterC2×#547D47
hypocenterC47#61575
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #20257227C2semidirect
2. #20255484C2semidirect
3. #20255364C2semidirect
4. #20254939C2semidirect
5. #20254914C2semidirect
6. #20254415C2semidirect
7. #20254209C2semidirect
8. #20254190C2semidirect
9. #20254169C2semidirect
10. #20253526C2semidirect
11. #20252648C2semidirect
12. #20252640C2semidirect
13. #20252606C2semidirect
14. #20252417C2semidirect
15. C2×C47×#547C2semidirect
16. C2×#13094054C22semidirect
17. C2×#13094049C22semidirect
18. C2×#13094044C22semidirect
20. #15689819C22semidirect
21. #15689813C22semidirect
23. #15689782C22semidirect
24. #15689769C22semidirect
33. #15689515C22semidirect
34. #15689491C22semidirect
35. #15689461C22semidirect
36. #15689456C22semidirect
37. #15689453C22semidirect
38. #15689451C22semidirect
40. #15689423C22semidirect
41. #15689379C22semidirect
42. #15689371C22semidirect
43. #15689362C22semidirect
44. #15689354C22semidirect
45. #15689338C22semidirect
46. #15689330C22semidirect
47. #15689325C22semidirect
48. #15689285C22semidirect
49. #15689285C22semidirect
50. #15689283C22semidirect
51. #15689279C22semidirect
52. #15689279C22semidirect
53. #15689278C22semidirect
54. #15689274C22semidirect
55. #15689273C22semidirect
56. #15689268C22semidirect
57. #15689268C22semidirect
61. #15689233C22semidirect
62. #15689223C22semidirect
63. #15689195C22semidirect
64. #15689195C22semidirect
65. #15689180C22semidirect
66. #15689124C22semidirect
67. #15689124C22semidirect
68. #15689119C22semidirect
71. C2×C22⋊(C47⋊C8)C22semidirect
73. C22×#41×C47C22semidirect
77. C47×#547C22semidirect
78. C2×C4⋊Q8×C47C22semidirect
82. C2×C22⋊Q8×C47C22semidirect
85. C2×C4×D4×C47C22semidirect
454. C2×#547D47semidirect
478. C22×#41C2×D47semidirect
490. #547C2×D47semidirect
495. C2×C4⋊Q8C2×D47semidirect
502. C2×C22⋊Q8C2×D47semidirect
507. C2×C4×D4C2×D47semidirect
548. C47#61575semidirect

Maximal subgroups

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

subgroupindex
#202572272
#202554842
#202553642
#202549392
#202549142
#202544152
#202542092
#202541902
#202541692
#202535262
#202526482
#202526402
#202526062
#202524172
C2×C47×#5472
#6157547