Finite Group Databasebeta

← #28254232

Subgroups — #28254232

Order 13568.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288011C211yesmaximal, characteristic, complemented
2C2×#16811157C211yesmaximal, characteristic, complemented
3#20285444C214yesmaximal, complemented
4#20285424C212yesmaximal, complemented
5#20285413C212yesmaximal, complemented
6#20285321C212yesmaximal, complemented
7#20285310C212yesmaximal, complemented
8#20285285C214yesmaximal, complemented
9#20285267C211yesmaximal, characteristic, complemented
10#20285181C211yesmaximal, characteristic, complemented
11#20285116C211yesmaximal, characteristic, complemented
12#20285102C211yesmaximal, characteristic, complemented
13#20284345C212yesmaximal, complemented
14#20284334C212yesmaximal, complemented
15C4×#13133250C212yesmaximal, complemented
16C4×#13133245C212yesmaximal, complemented
17C2×C4×M16×C53C211yesmaximal, characteristic, complemented
18C2×#13133250C2212yes—
19C2×#13133245C2212yes—
20#16811180C2211yescharacteristic
21#16811180C2211yescharacteristic, complemented
22#16811180C2211yescharacteristic, complemented
23#16811173C2211yescharacteristic
24#16811173C2211yescharacteristic, complemented
25#16811173C2211yescharacteristic, complemented
26#16811157—21no—
27#16811157—21no—
28#16811157—21no—
29#16811157—21no—
30#16811157—21no—
31#16811157—21no—
32#16811157—21no—
33#16811157—21no—
34#16811157C2212yes—
35#16811157C2212yes—
36#16811157C2212yes—
37#16811157C2212yes—
38#16811157C2212yescomplemented
39#16811157C2212yescomplemented
40C2×#13133211—21no—
41C2×#13133209C2211yescharacteristic
42C2×#13133205C2211yescharacteristic
43#16811134—21no—
44#16811134—21no—
45#16811134C2212yes—
46C2×#13133200—21no—
47C2×#13133196C2211yescharacteristic
48C2×#13133191C2211yescharacteristic
49C4×#11719945—21no—
50C4×#11719945—21no—
51C4×#11719945C2212yes—
52C2×C4×Dic106C2211yescharacteristic
53C2×C4×D212C2211yescharacteristic
54C2×C4×C22⋊D53—21no—
55C2×#13133174—21no—
56#16811032C2212yescomplemented
57#16811032C2212yescomplemented
58#16811025C2214yescomplemented
59#16811017C2212yescomplemented
60#16811012C2212yescomplemented
61#16811007C2214yescomplemented
62#16810992C2212yescomplemented
63#16810988C2212yescomplemented
64#16810983C2212yescomplemented
65#16810983C2212yescomplemented
66#16810978C2214yescomplemented
67#16810978C2214yescomplemented
68#16810881C2214yescomplemented
69#16810876C2214yes—
70#16810869C2214yes—
71#16810869C2214yescomplemented
72#16810864C2214yescomplemented
73#16810859C2214yes—
74#16810852C2214yes—
75#16810852C2214yescomplemented
76#16810736C2214yescomplemented
77#16810731C2214yescomplemented
78#16810725C2214yescomplemented
79#16810725C2214yescomplemented
80C4×Dic212C2214yescomplemented
81C4×#11719913C2214yescomplemented
82C4×#11719913C2214yescomplemented
83C4×D424C2214yescomplemented
84#16810665C2212yes—
85#16810665C2212yes—
86#16810633C2212yes—
87#16810629C2212yes—
88#16810625C2212yes—
89#16810625C2212yes—
90C22×M16×C53C2212yes—
91C22×C42×C53C2211yescharacteristic
92C4×M16×C53C2211yescharacteristic
93C4×M16×C53C2212yes—
94C4×M16×C53C2211yescharacteristic
95C4×M16×C53C2212yescomplemented
96C4×M16×C53C2212yescomplemented
97C2×#97×C53C2212yescomplemented
98C2×C4×C8×C53C2212yescomplemented
99C2×#11719945—21no—
100C2×#11719945—21no—
101C2×#11719945C2312yes—
102C22×Dic106C2311yescharacteristic
103C22×D212C2311yescharacteristic
104C22×C22⋊D53—21no—
105C22×C4×D53—21no—
106#13133250—28no—
107#13133245—28no—
108C2×Dic212C2314yes—
109C2×#11719913C2314yes—
110C2×#11719913C2314yes—
111C2×D424C2314yes—
112#13133217C2311yescharacteristic
113#13133217C2311yescharacteristic
114#13133217C2311yescharacteristic
115#13133214C2311yescharacteristic
116#13133211—22no—
117#13133211—22no—
118#13133211—22no—
119#13133211—22no—
120#13133211—22no—
121#13133211—22no—
122#13133209—21no—
123#13133209—21no—
124#13133209—21no—
125#13133209—21no—
126#13133209C2312yes—
127#13133209C2312yes—
128#13133209C2312yes—
129#13133205—21no—
130#13133205—21no—
131#13133205—21no—
132#13133205—21no—
133#13133205C2312yes—
134#13133205C2312yes—
135#13133205C2312yes—
136#13133200—22no—
137#13133200—22no—
138#13133200—22no—
139#13133200—22no—
140#13133200—22no—
141#13133200—22no—
142#13133200—22no—
143#13133196—21no—
144#13133196—21no—
145#13133196—21no—
146#13133196—21no—
147#13133196—21no—
148#13133196—21no—
149#13133196C2312yes—
150#13133196C2312yes—
151#13133196C2312yes—
152#13133196C2312yes—
153#13133191—21no—
154#13133191—21no—
155#13133191—21no—
156#13133191—21no—
157#13133191—21no—
158#13133191—21no—
159#13133191C2312yes—
160#13133191C2312yes—
161#13133191C2312yes—
162#13133191C2312yes—
163#13133186—22no—
164C4×Dic106—21no—
165C4×Dic106—21no—
166C4×Dic106—21no—
167C4×Dic106—21no—
168C4×Dic106—21no—
169C4×Dic106—21no—
170C4×Dic106C2312yes—
171C4×Dic106C2312yes—
172C4×Dic106C2312yes—
173C4×Dic106C2312yes—
174C4×D212—21no—
175C4×D212—21no—
176C4×D212—21no—
177C4×D212—21no—
178C4×D212—21no—
179C4×D212—21no—
180C4×D212C2312yes—
181C4×D212C2312yes—
182C4×D212C2312yes—
183C4×D212C2312yes—
184C4×C22⋊D53—22no—
185C4×C22⋊D53—22no—
186C4×C22⋊D53—22no—
187C4×C22⋊D53—22no—
188C4×C22⋊D53—22no—
189C4×C22⋊D53—22no—
190C4×C22⋊D53—22no—
191C4×C22⋊D53—22no—
192C4×C22⋊D53—22no—
193C4×C22⋊D53—22no—
194#13133176—21no—
195#13133176—21no—
196#13133176C2312yes—
197#13133174—22no—
198#13133174—22no—
199#13133174—22no—
200#13133174—22no—
201#13133174—22no—
202#13133174—22no—
203#13133174—22no—
204C2×C4⋊Dic53C2311yescharacteristic
205C2×C4⋊Dic53C2311yescharacteristic
206C2×#11719919—21no—
207C2×#11719919—21no—
208C2×#11719919—21no—
209C2×#11719919—21no—
210C2×C22⋊Dic53—21no—
211C2×#11719921—21no—
212C2×#11719921—21no—
213C2×#11719921—21no—
214C2×#11719921—21no—
215C2×C4×Dic53—21no—
216C42×D53—22no—
217#13133151C2314yes—
218#13133151C2314yes—
219#13133149C2314yes—
220#13133149C2314yes—
221#13133142C2314yes—
222#13133142C2314yes—
223#13133142C2314yes—
224#13133142C2314yes—
225#13133139C2314yes—
226#13133139C2314yes—
227#13133139C2314yes—
228#13133139C2314yes—
229C23×C4×C53D411yescharacteristic
230C23×C4×C53D411yescharacteristic
231C23×C4×C53C2311yescharacteristic
232C2×M16×C53—28no—
233C2×M16×C53C2314yes—
234C2×M16×C53C2312yes—
235C2×M16×C53C2312yes—
236C22×C8×C53C2314yes—
237C2×C42×C53D411yescharacteristic
238C2×C42×C53D411yescharacteristic
239C2×C42×C53D411yescharacteristic
240C2×C42×C53D411yescharacteristic
241C2×C42×C53D411yescharacteristic
242C2×C42×C53D411yescharacteristic
243C2×C42×C53C2311yescharacteristic
244C2×C42×C53C2311yescharacteristic
245C2×C42×C53C2311yescharacteristic
246C2×C42×C53C2311yescharacteristic
247C2×C42×C53C2311yescharacteristic
248C2×C42×C53C2311yescharacteristic
249#97×C53C2312yes—
250#97×C53C2314yes—
251#97×C53C2312yes—
252C4×C8×C53C2312yes—
253C4×C8×C53C2314yes—
254C4×C8×C53C2312yes—
255C24×C53C2×D411yescharacteristic
256C23×D53—21no—
257C22×C4×C53—24no—
258C22×C4×C53—42no—
259C22×C4×C53—42no—
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2×D411yescharacteristic
275C22×C4×C53C2411yescharacteristic
276C22×C4×C53C2411yescharacteristic
277C22×C4×C53C2411yescharacteristic
278C2×C22⋊D53—22no—
279C2×C22⋊D53—22no—
280C2×C22⋊D53—22no—
281C2×C22⋊D53—22no—
282C2×C22⋊D53—22no—
283C2×C22⋊D53—44no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287#11719945—24no—
288#11719945—24no—
289#11719945—44no—
290#11719945—44no—
291C2×D212—24no—
292C2×D212—21no—
293C2×D212—21no—
294C2×D212—21no—
295C2×D212C2412yes—
296C2×D212C2412yes—
297C2×C4×D53—22no—
298C2×C4×D53—22no—
299C2×C4×D53—22no—
300C2×C4×D53—22no—
301C2×C4×D53—22no—
302C2×C4×D53—44no—
303C2×Dic106—24no—
304C2×Dic106—21no—
305C2×Dic106—21no—
306C2×Dic106—21no—
307C2×Dic106C2412yes—
308C2×Dic106C2412yes—
309M16×C53—24no—
310M16×C53—28no—
311M16×C53#4118yescomplemented
312C2×C8×C53—28no—
313C2×C8×C53C2414yes—
314C2×C8×C53C2414yes—
315C42×C53C2×D411yescharacteristic
316C42×C53C2×D411yescharacteristic
317C42×C53C2×D411yescharacteristic
318C42×C53C2×D411yescharacteristic
319C42×C53C2×D411yescharacteristic
320C42×C53C2×D411yescharacteristic
321C42×C53C2×D411yescharacteristic
322C42×C53C2×D411yescharacteristic
323C42×C53C2×D411yescharacteristic
324C42×C53C2×D411yescharacteristic
325C42×C53C2×D411yescharacteristic
326C42×C53C2×D411yescharacteristic
327C42×C53C2411yescharacteristic
328C42×C53C2411yescharacteristic
329C42×C53C2411yescharacteristic
330C42×C53C2411yescharacteristic
331C22⋊Dic53—22no—
332C22⋊Dic53—22no—
333C22⋊Dic53—22no—
334C22⋊Dic53—22no—
335C22⋊Dic53—22no—
336#11719921—22no—
337#11719921—22no—
338#11719921—22no—
339#11719921—22no—
340#11719921—22no—
341#11719921—22no—
342#11719921—22no—
343#11719921—22no—
344#11719921—22no—
345#11719921—22no—
346#11719921—22no—
347#11719921—22no—
348#11719921—22no—
349#11719921—22no—
350C4⋊Dic53—21no—
351C4⋊Dic53—21no—
352C4⋊Dic53—21no—
353C4⋊Dic53—21no—
354C4⋊Dic53—21no—
355C4⋊Dic53—21no—
356C4⋊Dic53C2412yes—
357C4⋊Dic53C2412yes—
358C4⋊Dic53C2412yes—
359C4⋊Dic53C2412yes—
360#11719919—22no—
361#11719919—22no—
362#11719919—22no—
363#11719919—22no—
364#11719919—22no—
365#11719919—22no—
366#11719919—22no—
367#11719919—22no—
368#11719919—22no—
369#11719919—22no—
370#11719919—22no—
371#11719919—22no—
372#11719919—22no—
373#11719919—22no—
374C4×Dic53—22no—
375C4×Dic53—22no—
376C4×Dic53—22no—
377C4×Dic53—22no—
378C4×Dic53—22no—
379Dic212—28no—
380D424—28no—
381#11719913—28no—
382#11719913—28no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—41no—
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C22×D411yescharacteristic
389C22×D53—22no—
390C22×D53—22no—
391C22×D53—42no—
392C22×D53—42no—
393C22×D53—42no—
394C2×C4×C53—22no—
395C2×C4×C53—22no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53C22×D411yescharacteristic
412C2×C4×C53C22×D411yescharacteristic
413C2×C4×C53C22×D411yescharacteristic
414C2×C4×C53C22×D411yescharacteristic
415C2×C4×C53C22×D411yescharacteristic
416C2×C4×C53C22×D411yescharacteristic
417C2×C4×C53C22×D411yescharacteristic
418C2×C4×C53C22×D411yescharacteristic
419C2×C4×C53C22×D411yescharacteristic
420C2×C4×C53C22×D411yescharacteristic
421C2×C4×C53C22×D411yescharacteristic
422C2×C4×C53C2×#4114yes—
423C2×C4×C53C2511yescharacteristic
424C22⋊D53—44no—
425C22⋊D53—44no—
426C22⋊D53—44no—
427C22⋊D53—44no—
428C22⋊D53—44no—
429C2×Dic53—22no—
430C2×Dic53—22no—
431C2×Dic53—22no—
432C2×Dic53—22no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—42no—
436C2×Dic53—42no—
437C2×Dic53—42no—
438D212—24no—
439D212—22no—
440D212—22no—
441D212—42no—
442D212—42no—
443D212—42no—
444C4×D53—44no—
445C4×D53—44no—
446C4×D53—44no—
447C4×D53—44no—
448C4×D53—44no—
449Dic106—24no—
450Dic106—22no—
451Dic106—22no—
452Dic106—42no—
453Dic106—42no—
454Dic106—42no—
455C8×C53—24no—
456C8×C53C2×#4118yes—
457#60702—531nomaximal, Sylow
458C22×C53—21no—
459C22×C53—21no—
460C22×C53—21no—
461C22×C53—21no—
462C22×C53—21no—
463C22×C53—21no—
464C22×C53—21no—
465C22×C53—44no—
466C22×C53#53212yes—
467C22×C53#57512yes—
468C22×C53C23×D411yescharacteristic
469C2×D53—42no—
470C2×D53—42no—
471C2×D53—42no—
472C2×D53—42no—
473C2×D53—42no—
474C2×D53—42no—
475C2×D53—84no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53#53212yes—
486C4×C53#57512yes—
487C4×C53C22×#4112yes—
488Dic53—42no—
489Dic53—42no—
490Dic53—42no—
491Dic53—42no—
492Dic53—42no—
493Dic53—42no—
494#3444—531no—
495C2×#529—531no—
496#3183—534no—
497#3181—532no—
498#3180—532no—
499#3172—532no—
500#3171—532no—
501#3168—534no—
502#3166—531no—
503#3153—531no—
504#3142—531no—
505#3140—531no—
506#3056—532no—
507#3055—532no—
508C4×#137—532no—
509C4×AGL(1,ℤ/8)—532no—
510C2×C4×M16D5311yescharacteristic, complemented
511C2×C53—22no—
512C2×C53—22no—
513C2×C53—41no—
514C2×C53C2×#53211yescharacteristic
515C2×C53C2×#57511yescharacteristic
516C2×C53C2×#57511yescharacteristic
517D53—82no—
518D53—82no—
519C2×#137—532no—
520C2×AGL(1,ℤ/8)—532no—
521C22×M16C2×D5312yes—
522#533—531no—
523#533—531no—
524#533—531no—
525#532—531no—
526#532—531no—
527#532—531no—
528#529—532no—
529#529—532no—
530#529—532no—
531#529—532no—
532#529—532no—
533#529—532no—
534#529—1061no—
535#529—1061no—
536#529—1061no—
537#529—1061no—
538#529—1061no—
539#529—1061no—
540#529—1061no—
541#529—1061no—
542C2×#126—1061no—
543C2×#125—531no—
544C2×#124—531no—
545#525—532no—
546#525—1061no—
547#525—1061no—
548C2×#123—1061no—
549C2×C22⋊Q8—531no—
550C2×#121—531no—
551C4×#41—532no—
552C4×#41—1061no—
553C4×#41—1061no—
554C2×C4×Q8—531no—
555C2×C4×D4—531no—
556C2×C4×D4—1061no—
557C2×#117—1061no—
558C22×C42C2×D5311yescharacteristic
559#501—532no—
560#501—532no—
561#499—534no—
562#497—532no—
563#496—532no—
564#495—534no—
565#491—532no—
566#490—532no—
567#489—532no—
568#489—532no—
569#488—534no—
570#488—534no—
571#470—534no—
572#469—534no—
573#468—534no—
574#468—534no—
575#467—534no—
576#466—534no—
577#465—534no—
578#465—534no—
579#442—534no—
580#441—534no—
581#440—534no—
582#440—534no—
583C4×Q16—534no—
584C4×SD16—534no—
585C4×SD16—534no—
586C4×D8—534no—
587#428—532no—
588#428—532no—
589#419—532no—
590#418—532no—
591#417—532no—
592#417—532no—
593C4×M16C2×D5311yescharacteristic
594C4×M16C2×D5311yescharacteristic
595C4×M16C2×D5312yes—
596C4×M16C2×D5312yescomplemented
597C4×M16C2×D5312yescomplemented
598C2×#97C2×D5312yescomplemented
599C2×C4×C8C2×D5312yescomplemented
600C53#6070211yescharacteristic, complemented, Sylow
601C2×#41—532no—
602C2×#41—1061no—
603C2×#41—1061no—
604C22×Q8—531no—
605C22×D4—531no—
606C22×D4—1061no—
607C23×C4—1061no—
608C23×C4D21211yescharacteristic
609C23×C4D21211yescharacteristic
610C23×C4C22×D5311yescharacteristic
611#137—1068no—
612AGL(1,ℤ/8)—1068no—
613C2×Q16—534no—
614C2×SD16—534no—
615C2×SD16—534no—
616C2×D8—534no—
617C2×M16—28no—
618C2×M16C22×D5312yes—
619C2×M16C22×D5314yes—
620C2×M16C22×D5312yes—
621C22×C8C22×D5314yes—
622C4⋊Q8—531no—
623C4⋊Q8—531no—
624C4⋊Q8—531no—
625#127—531no—
626#126—1062no—
627#126—1062no—
628#126—1062no—
629#126—1062no—
630#126—1062no—
631#126—1062no—
632#125—532no—
633#125—532no—
634#125—532no—
635#125—1061no—
636#125—1061no—
637#125—1061no—
638#125—1061no—
639#124—532no—
640#124—532no—
641#124—532no—
642#124—1061no—
643#124—1061no—
644#124—1061no—
645#124—1061no—
646#123—1062no—
647#123—1062no—
648#123—1062no—
649#123—1062no—
650#123—1062no—
651#123—1062no—
652#123—1062no—
653C22⋊Q8—532no—
654C22⋊Q8—532no—
655C22⋊Q8—532no—
656C22⋊Q8—532no—
657C22⋊Q8—1061no—
658C22⋊Q8—1061no—
659C22⋊Q8—1061no—
660C22⋊Q8—1061no—
661C22⋊Q8—1061no—
662C22⋊Q8—1061no—
663#121—532no—
664#121—532no—
665#121—532no—
666#121—532no—
667#121—1061no—
668#121—1061no—
669#121—1061no—
670#121—1061no—
671#121—1061no—
672#121—1061no—
673#120—1062no—
674C4×Q8—532no—
675C4×Q8—532no—
676C4×Q8—532no—
677C4×Q8—532no—
678C4×Q8—1061no—
679C4×Q8—1061no—
680C4×Q8—1061no—
681C4×Q8—1061no—
682C4×Q8—1061no—
683C4×Q8—1061no—
684C4×D4—532no—
685C4×D4—532no—
686C4×D4—532no—
687C4×D4—532no—
688C4×D4—1062no—
689C4×D4—1062no—
690C4×D4—1062no—
691C4×D4—1062no—
692C4×D4—1062no—
693C4×D4—1062no—
694C4×D4—1062no—
695C4×D4—1062no—
696C4×D4—1062no—
697C4×D4—1062no—
698C4×D4—1061no—
699C4×D4—1061no—
700C4×D4—1061no—
701C4×D4—1061no—
702C4×D4—1061no—
703C4×D4—1061no—
704#117—532no—
705#117—1061no—
706#117—1061no—
707#117—1062no—
708#117—1062no—
709#117—1062no—
710#117—1062no—
711#117—1062no—
712#117—1062no—
713#117—1062no—
714C2×C4⋊C4—531no—
715C2×C4⋊C4—531no—
716C2×C4⋊C4—1061no—
717C2×C4⋊C4—1061no—
718C2×C4⋊C4—1061no—
719C2×C4⋊C4—1061no—
720C2×C22⋊C4—1061no—
721C2×C22⋊C4—1061no—
722C2×C22⋊C4—1061no—
723C2×C22⋊C4—1061no—
724C2×C22⋊C4—1061no—
725C2×C42—1061no—
726C2×C42—1062no—
727C2×C42D21211yescharacteristic
728C2×C42D21211yescharacteristic
729C2×C42D21211yescharacteristic
730C2×C42D21211yescharacteristic
731C2×C42D21211yescharacteristic
732C2×C42D21211yescharacteristic
733C2×C42C22×D5311yescharacteristic
734C2×C42C22×D5311yescharacteristic
735C2×C42C22×D5311yescharacteristic
736C2×C42C22×D5311yescharacteristic
737C2×C42C22×D5311yescharacteristic
738C2×C42C22×D5311yescharacteristic
739#107—534no—
740#107—534no—
741#106—534no—
742#106—534no—
743#103—534no—
744#103—534no—
745#103—534no—
746#103—534no—
747#102—534no—
748#102—534no—
749#102—534no—
750#102—534no—
751#97C22×D5314yes—
752#97C22×D5312yes—
753#97C22×D5312yes—
754C4×C8C22×D5314yes—
755C4×C8C22×D5312yes—
756C4×C8C22×D5312yes—
757C24—1061no—
758C24C2×D21211yescharacteristic
759#41—1064no—
760#41—1064no—
761#41—2124no—
762#41—2124no—
763C2×Q8—532no—
764C2×Q8—532no—
765C2×Q8—1061no—
766C2×Q8—1061no—
767C2×Q8—1061no—
768C2×Q8—1064no—
769C2×D4—532no—
770C2×D4—532no—
771C2×D4—1062no—
772C2×D4—1062no—
773C2×D4—1062no—
774C2×D4—1062no—
775C2×D4—1062no—
776C2×D4—1061no—
777C2×D4—1061no—
778C2×D4—1061no—
779C2×D4—1064no—
780C2×D4—2124no—
781C22×C4—24no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—1061no—
785C22×C4—1061no—
786C22×C4—1061no—
787C22×C4—1062no—
788C22×C4—1062no—
789C22×C4—1062no—
790C22×C4—1062no—
791C22×C4—1062no—
792C22×C4—2124no—
793C22×C4C2×D21211yescharacteristic
794C22×C4C2×D21211yescharacteristic
795C22×C4C2×D21211yescharacteristic
796C22×C4C2×D21211yescharacteristic
797C22×C4C2×D21211yescharacteristic
798C22×C4C2×D21211yescharacteristic
799C22×C4C2×D21211yescharacteristic
800C22×C4C2×D21211yescharacteristic
801C22×C4C2×D21211yescharacteristic
802C22×C4C2×D21211yescharacteristic
803C22×C4C2×D21211yescharacteristic
804C22×C4C2×D21211yescharacteristic
805C22×C4C2×D21211yescharacteristic
806C22×C4C2×D21211yescharacteristic
807C22×C4C2×D21211yescharacteristic
808C22×C4C23×D5311yescharacteristic
809C22×C4C23×D5311yescharacteristic
810C22×C4C23×D5311yescharacteristic
811Q16—1068no—
812SD16—1068no—
813SD16—1068no—
814D8—1068no—
815M16—24no—
816M16—28no—
817M16#1171994518yescomplemented
818C2×C8—28no—
819C2×C8C23×D5314yes—
820C2×C8C23×D5314yes—
821C4⋊C4—532no—
822C4⋊C4—532no—
823C4⋊C4—532no—
824C4⋊C4—532no—
825C4⋊C4—1061no—
826C4⋊C4—1061no—
827C4⋊C4—1062no—
828C4⋊C4—1062no—
829C4⋊C4—1062no—
830C4⋊C4—1062no—
831C4⋊C4—1062no—
832C4⋊C4—1062no—
833C4⋊C4—1062no—
834C4⋊C4—1062no—
835C4⋊C4—1062no—
836C4⋊C4—1062no—
837C4⋊C4—1061no—
838C4⋊C4—1061no—
839C4⋊C4—1061no—
840C4⋊C4—1061no—
841C4⋊C4—1062no—
842C4⋊C4—1062no—
843C4⋊C4—1062no—
844C4⋊C4—1062no—
845C22⋊C4—1062no—
846C22⋊C4—1062no—
847C22⋊C4—1062no—
848C22⋊C4—1062no—
849C22⋊C4—1062no—
850C22⋊C4—1062no—
851C22⋊C4—1062no—
852C22⋊C4—1062no—
853C22⋊C4—1062no—
854C22⋊C4—1062no—
855C22⋊C4—1062no—
856C22⋊C4—1062no—
857C22⋊C4—1062no—
858C22⋊C4—1062no—
859C22⋊C4—1062no—
860C22⋊C4—1062no—
861C22⋊C4—1062no—
862C22⋊C4—1062no—
863C22⋊C4—1062no—
864C42—1062no—
865C42—1062no—
866C42—1062no—
867C42—1062no—
868C42—1062no—
869C42C2×D21211yescharacteristic
870C42C2×D21211yescharacteristic
871C42C2×D21211yescharacteristic
872C42C2×D21211yescharacteristic
873C42C2×D21211yescharacteristic
874C42C2×D21211yescharacteristic
875C42C2×D21211yescharacteristic
876C42C2×D21211yescharacteristic
877C42C2×D21211yescharacteristic
878C42C2×D21211yescharacteristic
879C42C2×D21211yescharacteristic
880C42C2×D21211yescharacteristic
881C42C23×D5311yescharacteristic
882C42C23×D5311yescharacteristic
883C42C23×D5311yescharacteristic
884C42C23×D5311yescharacteristic
885C23—22no—
886C23—22no—
887C23—41no—
888C23—1062no—
889C23—1062no—
890C23—2122no—
891C23—2122no—
892C23—2122no—
893C23C22×D21211yescharacteristic
894C23C22×D21211yescharacteristic
895C23C22×D21211yescharacteristic
896Q8—1062no—
897Q8—1064no—
898Q8—1062no—
899Q8—2122no—
900Q8—2122no—
901Q8—2122no—
902D4—1062no—
903D4—1064no—
904D4—1062no—
905D4—2122no—
906D4—2122no—
907D4—2124no—
908D4—2124no—
909D4—2124no—
910D4—2124no—
911D4—2124no—
912D4—2122no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—1062no—
931C2×C4—1062no—
932C2×C4—1062no—
933C2×C4—1062no—
934C2×C4—1062no—
935C2×C4—1062no—
936C2×C4—2124no—
937C2×C4—2124no—
938C2×C4—2122no—
939C2×C4—2122no—
940C2×C4—2122no—
941C2×C4—2124no—
942C2×C4—2124no—
943C2×C4—2124no—
944C2×C4C22×D21211yescharacteristic
945C2×C4C22×D21211yescharacteristic
946C2×C4C22×D21211yescharacteristic
947C2×C4C22×D21211yescharacteristic
948C2×C4C22×D21211yescharacteristic
949C2×C4C22×D21211yescharacteristic
950C2×C4C22×D21211yescharacteristic
951C2×C4C22×D21211yescharacteristic
952C2×C4C22×D21211yescharacteristic
953C2×C4C22×D21211yescharacteristic
954C2×C4C22×D21211yescharacteristic
955C2×C4C2×#1171994514yes—
956C2×C4C24×D5311yescharacteristic
957C8—24no—
958C8C2×#1171994518yes—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—44no—
967C22—4244no—
968C22—2122no—
969C22—2122no—
970C22—2122no—
971C22—2122no—
972C22—2122no—
973C22—2122no—
974C22#1681117312yes—
975C22#1681142312yes—
976C22C23×D21211yescharacteristic
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—2122no—
987C4—2122no—
988C4—2122no—
989C4—2122no—
990C4—2122no—
991C4—2122no—
992C4#1681117312yes—
993C4#1681142312yes—
994C4C22×#1171994512yes—
995C2—22no—
996C2—22no—
997C2—41no—
998C2—4242no—
999C2—4242no—
1000C2C2×#1681117311yescharacteristic
1001C2C2×#1681142311yescharacteristic
1002C2C2×#1681142311yescharacteristic
subgroupG/H
centerC2×C4C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×M16×C53C2
socleC22×C53C23×D4
hypercenterC2×C4×M16D53
hypocenterC53#60702
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. #20288011C2semidirect
2. C2×#16811157C2semidirect
3. #20285444C2semidirect
4. #20285424C2semidirect
5. #20285413C2semidirect
6. #20285321C2semidirect
7. #20285310C2semidirect
8. #20285285C2semidirect
9. #20285267C2semidirect
10. #20285181C2semidirect
11. #20285116C2semidirect
12. #20285102C2semidirect
13. #20284345C2semidirect
14. #20284334C2semidirect
15. C4×#13133250C2semidirect
16. C4×#13133245C2semidirect
17. C2×C4×M16×C53C2semidirect
21. #16811180C22semidirect
22. #16811180C22semidirect
24. #16811173C22semidirect
25. #16811173C22semidirect
38. #16811157C22semidirect
39. #16811157C22semidirect
56. #16811032C22semidirect
57. #16811032C22semidirect
58. #16811025C22semidirect
59. #16811017C22semidirect
60. #16811012C22semidirect
61. #16811007C22semidirect
62. #16810992C22semidirect
63. #16810988C22semidirect
64. #16810983C22semidirect
65. #16810983C22semidirect
66. #16810978C22semidirect
67. #16810978C22semidirect
68. #16810881C22semidirect
71. #16810869C22semidirect
72. #16810864C22semidirect
75. #16810852C22semidirect
76. #16810736C22semidirect
77. #16810731C22semidirect
78. #16810725C22semidirect
79. #16810725C22semidirect
80. C4×Dic212C22semidirect
81. C4×#11719913C22semidirect
82. C4×#11719913C22semidirect
83. C4×D424C22semidirect
95. C4×M16×C53C22semidirect
96. C4×M16×C53C22semidirect
97. C2×#97×C53C22semidirect
98. C2×C4×C8×C53C22semidirect
311. M16×C53#41semidirect
510. C2×C4×M16D53semidirect
596. C4×M16C2×D53semidirect
597. C4×M16C2×D53semidirect
598. C2×#97C2×D53semidirect
599. C2×C4×C8C2×D53semidirect
600. C53#60702semidirect
817. M16#11719945semidirect

Maximal subgroups

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

subgroupindex
#202880112
C2×#168111572
#202854442
#202854242
#202854132
#202853212
#202853102
#202852852
#202852672
#202851812
#202851162
#202851022
#202843452
#202843342
C4×#131332502
C4×#131332452
C2×C4×M16×C532
#6070253