Finite Group Databasebeta

← #27101210

Subgroups — #27101210

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257227C211yesmaximal, characteristic, complemented
2#20255514C214yesmaximal, complemented
3#20255394C214yesmaximal, complemented
4#20254969C214yesmaximal, complemented
5#20254929C214yesmaximal, complemented
6#20254406C212yesmaximal, complemented
7#20254194C211yesmaximal, characteristic, complemented
8#20254185C211yesmaximal, characteristic, complemented
9#20254153C212yesmaximal, complemented
10#20253559C212yesmaximal, complemented
11#20252648C211yesmaximal, characteristic, complemented
12#20252640C211yesmaximal, characteristic, complemented
13#20252606C212yesmaximal, complemented
14#20252417C211yesmaximal, characteristic, complemented
15C2×C47×#550C211yesmaximal, 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#15689510C2214yescomplemented
34#15689487C2214yescomplemented
35#15689458C2212yescomplemented
36#15689444C2214yescomplemented
37#15689441C2212yes—
38#15689439C2212yescomplemented
39#15689434C2212yescomplemented
40#15689430C2214yescomplemented
41#15689374C2214yescomplemented
42#15689367C2214yescomplemented
43#15689357C2214yescomplemented
44#15689350C2214yescomplemented
45#15689345C2214yescomplemented
46#15689320C2214yescomplemented
47#15689315C2214yescomplemented
48#15689285C2214yescomplemented
49#15689285C2214yescomplemented
50#15689279C2212yescomplemented
51#15689274C2212yescomplemented
52#15689274C2212yescomplemented
53#15689268C2214yescomplemented
54#15689268C2214yescomplemented
55#15689266C2214yescomplemented
56#15689262C2212yes—
57#15689261C2212yescomplemented
58#15689257C2212yes—
59#15689257C2212yes—
60#15689256C2212yescomplemented
61#15689228C2214yescomplemented
62#15689221C2214yescomplemented
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×#550—22no—
75C47×#550—22no—
76C47×#550C2214yes—
77C47×#550C2214yescomplemented
78C2×#127×C47—21no—
79C2×#127×C47C2211yescharacteristic, complemented
80C2×#121×C47—21no—
81C2×#121×C47—21no—
82C2×#121×C47C2211yescharacteristic
83C2×#121×C47C2211yescharacteristic, complemented
84C2×C4×Q8×C47C2211yescharacteristic, complemented
85C2×C4×D4×C47—21no—
86C2×C4×D4×C47C2211yescharacteristic
87C2×#10625350C2312yes—
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91#13094054—44no—
92#13094049—44no—
93#13094044—48no—
94C2×#10625337C2314yes—
95C2×#10625335C2314yes—
96C2×#10625335C2314yes—
97C2×#10625336C2314yes—
98C2×#10625334C2314yes—
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#13093947C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158C22⋊(C47⋊C8)C2312yes—
159C22⋊(C47⋊C8)C2312yes—
160C22⋊(C47⋊C8)C2312yes—
161C22⋊(C47⋊C8)C2312yes—
162C22⋊(C47⋊C8)C2314yes—
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×D4×C47—21no—
174C22×D4×C47—21no—
175C22×D4×C47—21no—
176C22×D4×C47—21no—
177C22×D4×C47—21no—
178C22×D4×C47—21no—
179C22×D4×C47D411yescharacteristic
180C22×D4×C47C2311yescharacteristic
181C22×D4×C47C2311yescharacteristic
182C23×C4×C47—21no—
183C23×C4×C47—21no—
184C23×C4×C47C2311yescharacteristic
185C23×C4×C47C2311yescharacteristic
186#127×C47—24no—
187#127×C47—24no—
188#127×C47—22no—
189#127×C47C2314yes—
190#121×C47—21no—
191#121×C47—21no—
192#121×C47—22no—
193#121×C47—24no—
194#121×C47—24no—
195#121×C47—24no—
196#121×C47—24no—
197#121×C47C2312yes—
198#121×C47C2312yes—
199#121×C47C2314yes—
200C4×Q8×C47—22no—
201C4×Q8×C47C2314yes—
202C4×D4×C47—24no—
203C4×D4×C47—24no—
204C4×D4×C47D412yes—
205C4×D4×C47D412yes—
206C4×D4×C47C2312yes—
207C4×D4×C47C2312yes—
208C2×C4⋊C4×C47—21no—
209C2×C4⋊C4×C47D411yescharacteristic
210C2×C4⋊C4×C47C2311yescharacteristic
211C2×C22⋊C4×C47—21no—
212C2×C22⋊C4×C47—21no—
213C2×C22⋊C4×C47D411yescharacteristic
214C2×C22⋊C4×C47D411yescharacteristic
215C2×C42×C47—21no—
216C2×C42×C47C2311yescharacteristic
217C24×C47—21no—
218C24×C47—21no—
219C24×C47C2×D411yescharacteristic
220C24×C47C2×D411yescharacteristic
221C23×D47—21no—
222#41×C47—28no—
223#41×C47—24no—
224#41×C47—24no—
225#41×C47—44no—
226#41×C47—42no—
227#41×C47—42no—
228#41×C47—44no—
229#41×C47—44no—
230#41×C47—48no—
231C2×Q8×C47—24no—
232C2×Q8×C47—21no—
233C2×Q8×C47C2412yes—
234C2×D4×C47—22no—
235C2×D4×C47—24no—
236C2×D4×C47—22no—
237C2×D4×C47—22no—
238C2×D4×C47—24no—
239C2×D4×C47—22no—
240C2×D4×C47—24no—
241C2×D4×C47—21no—
242C2×D4×C47—21no—
243C2×D4×C47—24no—
244C2×D4×C47—42no—
245C2×D4×C47—42no—
246C2×D4×C47—42no—
247C2×D4×C47—44no—
248C2×D4×C47—44no—
249C2×D4×C47—44no—
250C2×D4×C47—82no—
251C2×D4×C47—82no—
252C2×D4×C47—82no—
253C2×D4×C47C2×D412yes—
254C2×D4×C47C2×D412yes—
255C2×D4×C47C2412yes—
256C2×D4×C47C2412yes—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—24no—
260C22×C4×C47—22no—
261C22×C4×C47—22no—
262C22×C4×C47—42no—
263C22×C4×C47—42no—
264C22×C4×C47—44no—
265C22×C4×C47—44no—
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D412yes—
273C22×C4×C47C2411yescharacteristic
274C22×C4×C47C2411yescharacteristic
275C22×C4×C47C2411yescharacteristic
276C22×C4×C47C2412yes—
277C2×C22⋊D47—22no—
278C2×C22⋊D47—22no—
279C2×C22⋊D47—22no—
280C2×C22⋊D47—22no—
281C2×C22⋊D47—44no—
282C22×Dic47—21no—
283C22×Dic47—21no—
284C22×Dic47—21no—
285#10625350—44no—
286C2×D188—21no—
287C2×D188—42no—
288C2×D188C2412yes—
289C2×C4×D47—22no—
290C2×C4×D47—22no—
291C2×Dic94—21no—
292C2×Dic94—42no—
293C2×Dic94C2412yes—
294C4⋊C4×C47—24no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47C2×D412yes—
297C4⋊C4×C47C2×D412yes—
298C4⋊C4×C47C2412yes—
299C22⋊C4×C47—24no—
300C22⋊C4×C47—22no—
301C22⋊C4×C47—22no—
302C22⋊C4×C47C2×D412yes—
303C22⋊C4×C47C2×D412yes—
304C22⋊C4×C47C2×D412yes—
305C22⋊C4×C47C2×D412yes—
306C42×C47—24no—
307C42×C47C2×D412yes—
308C42×C47C2412yes—
309C22⋊Dic47—22no—
310C22⋊Dic47—22no—
311C22⋊Dic47—22no—
312C22⋊Dic47—22no—
313#10625337—28no—
314#10625336—28no—
315#10625335—44no—
316#10625335—44no—
317#10625334—44no—
318#10625334—44no—
319(C2×D47)⋊C4—22no—
320(C2×D47)⋊C4—22no—
321(C2×D47)⋊C4—22no—
322(C2×D47)⋊C4—22no—
323(C2×D47)⋊C4—22no—
324(C2×D47)⋊C4—22no—
325C4⋊Dic47—21no—
326C4⋊Dic47—21no—
327C4⋊Dic47C2412yes—
328C4⋊Dic47C2412yes—
329Dic47⋊C4—22no—
330Dic47⋊C4—22no—
331Dic47⋊C4—22no—
332Dic47⋊C4—22no—
333Dic47⋊C4—22no—
334Dic47⋊C4—22no—
335C4×Dic47—22no—
336C4×Dic47—22no—
337#10625329—42no—
338#10625329—42no—
339C2×C47⋊C8—44no—
340C2×C47⋊C8C2414yes—
341C2×C47⋊C8C2414yes—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47—41no—
349C23×C47—41no—
350C23×C47—42no—
351C23×C47—42no—
352C23×C47—42no—
353C23×C47—42no—
354C23×C47—42no—
355C23×C47—42no—
356C23×C47C22×D411yescharacteristic
357C23×C47C22×D412yes—
358C23×C47C22×D411yescharacteristic
359C23×C47C22×D411yescharacteristic
360C22×D47—22no—
361C22×D47—42no—
362C22×D47—81no—
363C22×D47—81no—
364Q8×C47—24no—
365Q8×C47—22no—
366Q8×C47H(5,𝔽2)14yes—
367D4×C47—22no—
368D4×C47—24no—
369D4×C47—22no—
370D4×C47—42no—
371D4×C47—42no—
372D4×C47—44no—
373D4×C47—48no—
374D4×C47—44no—
375D4×C47—48no—
376D4×C47—42no—
377D4×C47—42no—
378D4×C47—84no—
379D4×C47—82no—
380D4×C47—84no—
381D4×C47—82no—
382C2×C4×C47—24no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—24no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—42no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—44no—
397C2×C4×C47—48no—
398C2×C4×C47—44no—
399C2×C4×C47—42no—
400C2×C4×C47C22×D412yes—
401C2×C4×C47C22×D412yes—
402C2×C4×C47C22×D411yescharacteristic
403C2×C4×C47C22×D412yes—
404C2×C4×C47C22×D411yescharacteristic
405C2×C4×C47C22×D411yescharacteristic
406C2×C4×C47C2511yescharacteristic
407C22⋊D47—44no—
408C22⋊D47—44no—
409C22⋊D47—82no—
410C22⋊D47—82no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—42no—
415C2×Dic47—81no—
416C2×Dic47—81no—
417D188—24no—
418D188—81no—
419C4×D47—82no—
420C4×D47—82no—
421Dic94—24no—
422Dic94—81no—
423C47⋊C8—24no—
424C47⋊C8—24no—
425#61577—471nomaximal, Sylow
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—21no—
429C22×C47—22no—
430C22×C47—21no—
431C22×C47—21no—
432C22×C47—22no—
433C22×C47—21no—
434C22×C47—21no—
435C22×C47—21no—
436C22×C47—22no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—82no—
444C22×C47—82no—
445C22×C47—84no—
446C22×C47—84no—
447C22×C47#57512yes—
448C22×C47C23×D411yescharacteristic
449C2×D47—42no—
450C2×D47—42no—
451C2×D47—42no—
452C2×D47—162no—
453C4×C47—22no—
454C4×C47—21no—
455C4×C47—22no—
456C4×C47—21no—
457C4×C47—24no—
458C4×C47—21no—
459C4×C47—22no—
460C4×C47—42no—
461C4×C47C2×H(5,𝔽2)12yes—
462Dic47—42no—
463Dic47—42no—
464Dic47—42no—
465#3505—471no—
466C2×#550D4711yescharacteristic, complemented
467#3317—474no—
468#3309—474no—
469#3271—474no—
470#3268—474no—
471#3217—472no—
472#3193—471no—
473#3192—471no—
474#3188—472no—
475#3117—472no—
476#3007—471no—
477#3006—471no—
478#3002—472no—
479#2973—471no—
480C2×C47—22no—
481C2×C47—41no—
482C2×C47—41no—
483C2×C47—42no—
484C2×C47—82no—
485C2×C47—82no—
486C2×C47#348411yescharacteristic
487C2×C47C2×#57511yescharacteristic
488C2×C47#358511yescharacteristic
489D47—82no—
490C22×#41C2×D4711yescharacteristic
491C22×#41C2×D4711yescharacteristic, complemented
492C2×#137—472no—
493C2×AGL(1,ℤ/8)—472no—
494C2×#135—474no—
495#553—472no—
496#553—942no—
497#552—472no—
498#551—942no—
499#550—22no—
500#550—22no—
501#550C2×D4714yes—
502#550C2×D4714yescomplemented
503#548—472no—
504#546—472no—
505#539—941no—
506#538—941no—
507#534—941no—
508C2×#127—21no—
509C2×#127C2×D4711yescharacteristic, complemented
510#529—472no—
511#525—472no—
512C2×C22⋊Q8—471no—
513C2×#121—21no—
514C2×#121—21no—
515C2×#121—471no—
516C2×#121C2×D4711yescharacteristic
517C2×#121C2×D4711yescharacteristic, complemented
518#518—941no—
519C2×C4×Q8C2×D4711yescharacteristic, complemented
520C2×C4×D4—21no—
521C2×C4×D4C2×D4711yescharacteristic
522#496—474no—
523#490—474no—
524#484—472no—
525#482—474no—
526#481—472no—
527#481—472no—
528#480—472no—
529#479—474no—
530#469—474no—
531#468—474no—
532#466—474no—
533#465—474no—
534#464—474no—
535#460—474no—
536#459—474no—
537#452—474no—
538#452—474no—
539#451—472no—
540#450—472no—
541#450—472no—
542#449—474no—
543#449—474no—
544#449—474no—
545#448—472no—
546#448—472no—
547#447—472no—
548#447—472no—
549#447—472no—
550#441—474no—
551#440—474no—
552#435—474no—
553#435—474no—
554#432—472no—
555#417—472no—
556#417—472no—
557#416—474no—
558#407—471no—
559#407—471no—
560C2×C22⋊C8—472no—
561C47#6157711yescharacteristic, complemented, Sylow
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—22no—
565C2×#41—44no—
566C2×#41—44no—
567C2×#41—472no—
568C2×#41C22×D4712yes—
569C2×#41C22×D4714yes—
570C2×#41C22×D4712yes—
571C22×Q8—471no—
572C22×Q8C22×D4711yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—471no—
580C22×D4—941no—
581C22×D4C22⋊D4711yescharacteristic
582C22×D4C22×D4711yescharacteristic
583C22×D4C22×D4711yescharacteristic
584C23×C4—21no—
585C23×C4—21no—
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588#137—1884no—
589AGL(1,ℤ/8)—1884no—
590#135—1888no—
591C2×Q16—474no—
592C2×SD16—474no—
593C2×SD16—474no—
594C2×SD16—474no—
595C2×D8—474no—
596C2×D8—474no—
597C2×M16—472no—
598C2×M16—472no—
599C22×C8—474no—
600#127—24no—
601#127—24no—
602#127—22no—
603#127C22×D4714yes—
604#126—942no—
605#126—942no—
606#126—942no—
607#125—472no—
608#125—942no—
609#124—472no—
610#124—942no—
611#123—942no—
612#123—942no—
613#123—942no—
614#123—942no—
615#123—942no—
616C22⋊Q8—472no—
617C22⋊Q8—472no—
618C22⋊Q8—472no—
619C22⋊Q8—941no—
620C22⋊Q8—941no—
621C22⋊Q8—942no—
622#121—21no—
623#121—21no—
624#121—22no—
625#121—24no—
626#121—24no—
627#121—24no—
628#121—24no—
629#121—472no—
630#121—472no—
631#121—472no—
632#121—942no—
633#121—942no—
634#121—941no—
635#121—941no—
636#121—942no—
637#121C22×D4712yes—
638#121C22×D4712yes—
639#121C22×D4714yes—
640#120—942no—
641#120—942no—
642C4×Q8—22no—
643C4×Q8—472no—
644C4×Q8C22×D4714yes—
645C4×D4—24no—
646C4×D4—24no—
647C4×D4—472no—
648C4×D4—942no—
649C4×D4—942no—
650C4×D4—942no—
651C4×D4—942no—
652C4×D4—942no—
653C4×D4C22⋊D4712yes—
654C4×D4C22⋊D4712yes—
655C4×D4C22×D4712yes—
656C4×D4C22×D4712yes—
657#117—472no—
658#117—942no—
659#117—942no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—471no—
662C2×C4⋊C4—471no—
663C2×C4⋊C4—941no—
664C2×C4⋊C4C22⋊D4711yescharacteristic
665C2×C4⋊C4C22×D4711yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—941no—
669C2×C22⋊C4—941no—
670C2×C22⋊C4—942no—
671C2×C22⋊C4C22⋊D4711yescharacteristic
672C2×C22⋊C4C22⋊D4711yescharacteristic
673C2×C42—21no—
674C2×C42C22×D4711yescharacteristic
675#107—474no—
676#106—474no—
677C4⋊C8—474no—
678#103—474no—
679#103—474no—
680#103—474no—
681#102—474no—
682#102—474no—
683#102—474no—
684#102—474no—
685#102—474no—
686C22⋊C8—472no—
687C22⋊C8—472no—
688C22⋊C8—474no—
689C22⋊C8—472no—
690C22⋊C8—472no—
691#97—474no—
692C24—21no—
693C24—21no—
694C24—941no—
695C24C2×C22⋊D4711yescharacteristic
696C24C2×C22⋊D4711yescharacteristic
697#41—28no—
698#41—24no—
699#41—24no—
700#41—44no—
701#41—42no—
702#41—42no—
703#41—44no—
704#41—44no—
705#41—48no—
706#41—1884no—
707C2×Q8—24no—
708C2×Q8—21no—
709C2×Q8—472no—
710C2×Q8—941no—
711C2×Q8—1882no—
712C2×Q8C23×D4712yes—
713C2×D4—22no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—24no—
718C2×D4—22no—
719C2×D4—24no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—24no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—82no—
730C2×D4—82no—
731C2×D4—82no—
732C2×D4—472no—
733C2×D4—942no—
734C2×D4—942no—
735C2×D4—942no—
736C2×D4—942no—
737C2×D4—941no—
738C2×D4—1882no—
739C2×D4—1884no—
740C2×D4C2×C22⋊D4712yes—
741C2×D4C2×C22⋊D4712yes—
742C2×D4C23×D4712yes—
743C2×D4C23×D4712yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—942no—
757C22×C4—942no—
758C22×C4C2×C22⋊D4711yescharacteristic
759C22×C4C2×C22⋊D4711yescharacteristic
760C22×C4C2×C22⋊D4711yescharacteristic
761C22×C4C2×C22⋊D4711yescharacteristic
762C22×C4C2×C22⋊D4711yescharacteristic
763C22×C4C2×C22⋊D4711yescharacteristic
764C22×C4C2×C22⋊D4712yes—
765C22×C4C23×D4711yescharacteristic
766C22×C4C23×D4711yescharacteristic
767C22×C4C23×D4711yescharacteristic
768C22×C4C23×D4712yes—
769Q16—948no—
770SD16—948no—
771SD16—1884no—
772SD16—1884no—
773D8—1884no—
774D8—1884no—
775M16—1882no—
776M16—1882no—
777C2×C8—474no—
778C2×C8—474no—
779C2×C8—1884no—
780C4⋊C4—24no—
781C4⋊C4—21no—
782C4⋊C4—472no—
783C4⋊C4—472no—
784C4⋊C4—942no—
785C4⋊C4—942no—
786C4⋊C4—942no—
787C4⋊C4—942no—
788C4⋊C4—942no—
789C4⋊C4—942no—
790C4⋊C4—941no—
791C4⋊C4—941no—
792C4⋊C4C2×C22⋊D4712yes—
793C4⋊C4C2×C22⋊D4712yes—
794C4⋊C4C23×D4712yes—
795C22⋊C4—24no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—942no—
799C22⋊C4—942no—
800C22⋊C4—942no—
801C22⋊C4—942no—
802C22⋊C4—942no—
803C22⋊C4—942no—
804C22⋊C4—942no—
805C22⋊C4—942no—
806C22⋊C4—942no—
807C22⋊C4—942no—
808C22⋊C4C2×C22⋊D4712yes—
809C22⋊C4C2×C22⋊D4712yes—
810C22⋊C4C2×C22⋊D4712yes—
811C22⋊C4C2×C22⋊D4712yes—
812C42—24no—
813C42—942no—
814C42—942no—
815C42C2×C22⋊D4712yes—
816C42C23×D4712yes—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—942no—
832C23—3761no—
833C23—3761no—
834C23—1882no—
835C23C22×C22⋊D4711yescharacteristic
836C23C22×C22⋊D4712yes—
837C23C22×C22⋊D4711yescharacteristic
838C23C22×C22⋊D4711yescharacteristic
839Q8—24no—
840Q8—22no—
841Q8—944no—
842Q8—3761no—
843Q8#1309406914yes—
844D4—22no—
845D4—24no—
846D4—22no—
847D4—42no—
848D4—42no—
849D4—44no—
850D4—48no—
851D4—44no—
852D4—48no—
853D4—42no—
854D4—42no—
855D4—84no—
856D4—82no—
857D4—84no—
858D4—82no—
859D4—944no—
860D4—3761no—
861D4—3762no—
862D4—3762no—
863D4—1884no—
864D4—1884no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—48no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—3762no—
887C2×C4—3762no—
888C2×C4—3761no—
889C2×C4—3761no—
890C2×C4—1882no—
891C2×C4C22×C22⋊D4712yes—
892C2×C4C22×C22⋊D4712yes—
893C2×C4C22×C22⋊D4712yes—
894C2×C4C22×C22⋊D4711yescharacteristic
895C2×C4C22×C22⋊D4711yescharacteristic
896C2×C4C22×C22⋊D4711yescharacteristic
897C2×C4C24×D4711yescharacteristic
898C8—944no—
899C8—944no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—22no—
905C22—21no—
906C22—22no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—21no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—82no—
918C22—82no—
919C22—84no—
920C22—84no—
921C22—1882no—
922C22—1882no—
923C22—1882no—
924C22—7522no—
925C22#1568992112yes—
926C22C23×C22⋊D4711yescharacteristic
927C4—22no—
928C4—22no—
929C4—24no—
930C4—22no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—42no—
935C4—1882no—
936C4—1882no—
937C4—1882no—
938C4C2×#1309406912yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—42no—
943C2—82no—
944C2—82no—
945C2—3762no—
946C2#2025702311yescharacteristic
947C2C2×#1568992111yescharacteristic
948C2#2025816811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#550C2
socleC22×C47C23×D4
hypercenterC2×#550D47
hypocenterC47#61577
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #20257227C2semidirect
2. #20255514C2semidirect
3. #20255394C2semidirect
4. #20254969C2semidirect
5. #20254929C2semidirect
6. #20254406C2semidirect
7. #20254194C2semidirect
8. #20254185C2semidirect
9. #20254153C2semidirect
10. #20253559C2semidirect
11. #20252648C2semidirect
12. #20252640C2semidirect
13. #20252606C2semidirect
14. #20252417C2semidirect
15. C2×C47×#550C2semidirect
16. C2×#13094054C22semidirect
17. C2×#13094049C22semidirect
18. C2×#13094044C22semidirect
20. #15689819C22semidirect
21. #15689813C22semidirect
23. #15689782C22semidirect
24. #15689769C22semidirect
33. #15689510C22semidirect
34. #15689487C22semidirect
35. #15689458C22semidirect
36. #15689444C22semidirect
38. #15689439C22semidirect
39. #15689434C22semidirect
40. #15689430C22semidirect
41. #15689374C22semidirect
42. #15689367C22semidirect
43. #15689357C22semidirect
44. #15689350C22semidirect
45. #15689345C22semidirect
46. #15689320C22semidirect
47. #15689315C22semidirect
48. #15689285C22semidirect
49. #15689285C22semidirect
50. #15689279C22semidirect
51. #15689274C22semidirect
52. #15689274C22semidirect
53. #15689268C22semidirect
54. #15689268C22semidirect
55. #15689266C22semidirect
57. #15689261C22semidirect
60. #15689256C22semidirect
61. #15689228C22semidirect
62. #15689221C22semidirect
63. #15689195C22semidirect
64. #15689195C22semidirect
65. #15689180C22semidirect
66. #15689124C22semidirect
67. #15689124C22semidirect
68. #15689119C22semidirect
71. C2×C22⋊(C47⋊C8)C22semidirect
73. C22×#41×C47C22semidirect
77. C47×#550C22semidirect
79. C2×#127×C47C22semidirect
83. C2×#121×C47C22semidirect
84. C2×C4×Q8×C47C22semidirect
466. C2×#550D47semidirect
491. C22×#41C2×D47semidirect
502. #550C2×D47semidirect
509. C2×#127C2×D47semidirect
517. C2×#121C2×D47semidirect
519. C2×C4×Q8C2×D47semidirect
561. C47#61577semidirect

Maximal subgroups

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

subgroupindex
#202572272
#202555142
#202553942
#202549692
#202549292
#202544062
#202541942
#202541852
#202541532
#202535592
#202526482
#202526402
#202526062
#202524172
C2×C47×#5502
#6157747