Finite Group Databasebeta

← #28329570

Subgroups — #28329570

Order 13568.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811703C211yesmaximal, characteristic, complemented
2D53⋊#568C211yesmaximal, characteristic, complemented
3#20291495C214yesmaximal, complemented
4#20291493C214yesmaximal, complemented
5#20291490C218yesmaximal, complemented
6#20291488C218yesmaximal, complemented
7D53⋊#430C211yesmaximal, characteristic, complemented
8C2×#16811622C211yesmaximal, characteristic, complemented
9D53⋊#421C211yesmaximal, characteristic, complemented
10#20291278C211yesmaximal, characteristic, complemented
11C2×#16811422C211yesmaximal, characteristic
12#16811703—22no—
13#16811703—22no—
14#16811703C2212yescomplemented
15#16811703C2214yescomplemented
16#16811703C2214yescomplemented
17#16811702—22no—
18#16811702C2214yescomplemented
19#16811701—22no—
20#16811701C2212yescomplemented
21C2×#13133305—22no—
22C2×#13133305C2214yescomplemented
23D53⋊#131—22no—
24D53⋊#131C2214yescomplemented
25C2×D53⋊M16—22no—
26C2×D53⋊M16—22no—
27C2×D53⋊M16C2211yescharacteristic
28C2×D53⋊M16C2211yescharacteristic
29C2×D53⋊M16C2211yescharacteristic
30C2×#13133296C2211yescharacteristic
31#16811669C22116yescomplemented
32#16811668C22116yescomplemented
33#16811667C22116yescomplemented
34#16811666C22116yescomplemented
35#16811638C2214yescomplemented
36#16811638C2214yescomplemented
37D53⋊#108C2214yescomplemented
38#16811622C2212yescomplemented
39#16811622C2214yescomplemented
40#16811622C2214yescomplemented
41#16811621C2212yescomplemented
42#16811620C2214yescomplemented
43C2×#13133282C2214yescomplemented
44D53⋊#104C2214yescomplemented
45#16811589C2214yescomplemented
46#16811586C2214yescomplemented
47M16×#6157C2214yescomplemented
48C22×#11719949C2211yescharacteristic
49C2×#41×D53C2211yescharacteristic
50#16811422C414yescomplemented
51#16811422C414yescomplemented
52#16811422C2214yes—
53#16811422C2214yes—
54C2×#13133249C412yescomplemented
55C2×#13133248C411yescharacteristic, complemented
56C2×#13133245C411yescharacteristic, complemented
57C2×#13133244C412yescomplemented
58C2×#13133242C411yescharacteristic, complemented
59C2×#13133240C2212yes—
60C2×#13133238C2212yes—
61C2×M16×D53C2211yescharacteristic
62C2×#137×C53C411yescharacteristic, complemented
63#13133305—28no—
64#13133305—24no—
65#13133305—28no—
66#13133305—28no—
67#13133305C23116yescomplemented
68#13133305C2318yescomplemented
69#13133304—28no—
70#13133304—28no—
71#13133304—24no—
72#13133304C2318yescomplemented
73C2×#11719936—24no—
74C2×#11719936—24no—
75C2×#11719936D412yes—
76C2×#11719936C2312yes—
77C2×#11719936C2312yes—
78D53⋊M16—24no—
79D53⋊M16—21no—
80D53⋊M16—21no—
81D53⋊M16—21no—
82D53⋊M16—21no—
83D53⋊M16—24no—
84D53⋊M16—28no—
85D53⋊M16—28no—
86D53⋊M16—24no—
87D53⋊M16D412yes—
88D53⋊M16D412yes—
89D53⋊M16C2312yes—
90D53⋊M16C2312yes—
91D53⋊M16C2312yes—
92D53⋊M16C2312yes—
93D53⋊M16C2312yes—
94D53⋊M16C2312yes—
95C2×#11719940—21no—
96C2×#11719940—21no—
97C2×#11719940—24no—
98C2×#11719940D412yes—
99C2×D53⋊C8—24no—
100C2×D53⋊C8—21no—
101C2×D53⋊C8—21no—
102C2×D53⋊C8—24no—
103C2×D53⋊C8C2312yes—
104#13133296—21no—
105#13133296—21no—
106#13133296C2312yes—
107#13133296C2312yes—
108C2×C4⋊#6157—21no—
109C2×C22⋊#6157—21no—
110C2×C4×#6157C2312yes—
111#13133288C2318yescomplemented
112#13133287C2318yescomplemented
113#13133282C2318yescomplemented
114#13133282C23116yescomplemented
115#13133281C2318yescomplemented
116#13133271C2318yescomplemented
117C8×#6157C2318yescomplemented
118C2×#11719949—21no—
119C2×#11719949—21no—
120C2×#11719949—21no—
121C2×#11719949—21no—
122C2×#11719949—21no—
123C2×#11719949—21no—
124C2×#11719949C2×C412yes—
125C2×#11719949C2×C412yes—
126C2×#11719949C2×C412yes—
127C2×#11719949C2312yes—
128C2×#11719949C2312yes—
129C2×#11719949C2311yescharacteristic
130C2×#11719949C2312yes—
131C2×#11719945—21no—
132C2×#11719945C2×C411yescharacteristic
133C2×#11719947—21no—
134C2×#11719947C2311yescharacteristic
135#41×D53—21no—
136#41×D53—21no—
137#41×D53—21no—
138#41×D53—21no—
139#41×D53C2×C412yes—
140#41×D53C2×C412yes—
141#41×D53C2312yes—
142#41×D53C2312yes—
143C2×Q8×D53C2×C411yescharacteristic
144C22×D212—21no—
145C22×D212C2×C411yescharacteristic
146C2×D4×D53—21no—
147C2×D4×D53C2×C411yescharacteristic
148C22×C4×D53—21no—
149C22×C4×D53—21no—
150C22×C4×D53C2311yescharacteristic
151#13133249C2×C418yes—
152#13133249C2×C418yescomplemented
153#13133248C2×C414yes—
154#13133248C2×C414yescomplemented
155#13133245C2×C414yes—
156#13133245C2×C414yescomplemented
157#13133244C2×C418yes—
158#13133244C2×C418yescomplemented
159#13133242C2×C414yes—
160#13133242C2×C414yescomplemented
161#13133240C2×C418yescomplemented
162#13133240C2318yes—
163#13133238C2×C418yescomplemented
164#13133238C2318yes—
165C2×#11719925C2×C412yescomplemented
166C2×#11719913C2×C412yescomplemented
167C2×#11719924C2×C412yescomplemented
168C2×#11719924C2×C412yescomplemented
169C2×D424C2×C412yescomplemented
170C2×#11719922C2×C412yescomplemented
171C2×#11719917C2×C411yescharacteristic
172C2×#11719912C2×C412yes—
173M16×D53C2×C412yes—
174M16×D53C2×C412yes—
175M16×D53C2312yes—
176M16×D53C2312yes—
177C2×C8×D53C2312yes—
178C2×#41×C53C2×C411yescharacteristic
179C22×Q8×C53C2×C411yescharacteristic
180#137×C53C2×C414yes—
181#137×C53C2×C414yescomplemented
182C2×Q16×C53C2×C412yescomplemented
183C2×SD16×C53C2×C412yescomplemented
184C2×M16×C53C2×C411yescharacteristic
185C23×D53—21no—
186C23×D53—21no—
187C23×D53#4111yescharacteristic
188C22×#6157—22no—
189#41×C53—21no—
190#41×C53—21no—
191#41×C53C22×C412yes—
192#41×C53C22×C412yes—
193C2×Q8×C53—21no—
194C2×Q8×C53—21no—
195C2×Q8×C53—21no—
196C2×Q8×C53C22×C412yes—
197C2×Q8×C53C22×C411yescharacteristic
198C2×Q8×C53C22×C412yes—
199C2×Q8×C53C22×C412yes—
200C2×D4×C53—21no—
201C2×D4×C53C22×C411yescharacteristic
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53C22×C411yescharacteristic
205C2×C22⋊D53—21no—
206C2×C22⋊D53—21no—
207C2×C22⋊D53—21no—
208C22×Dic53—21no—
209C22×Dic53C2×D411yescharacteristic
210#11719949—22no—
211#11719949—22no—
212#11719949—22no—
213#11719949—22no—
214#11719949—22no—
215#11719949—22no—
216#11719949—21no—
217#11719949—22no—
218#11719949—22no—
219#11719949—22no—
220#11719949—21no—
221#11719949—22no—
222#11719949—22no—
223#11719949—22no—
224#11719949C22×C414yes—
225#11719949C22×C412yes—
226#11719949C22×C414yes—
227#11719949C22×C414yes—
228#11719949C2414yes—
229#11719949C2412yes—
230Q8×D53—21no—
231Q8×D53—21no—
232Q8×D53C22×C412yes—
233Q8×D53C22×C412yes—
234#11719947—22no—
235#11719947—22no—
236#11719947—22no—
237#11719947—22no—
238#11719947—21no—
239#11719947—21no—
240#11719947C22×C412yes—
241#11719947C2412yes—
242D4×D53—22no—
243D4×D53—22no—
244D4×D53—22no—
245D4×D53—22no—
246D4×D53—21no—
247D4×D53—21no—
248D4×D53C22×C412yes—
249D4×D53C22×C412yes—
250#11719945—21no—
251#11719945—21no—
252#11719945—22no—
253#11719945—22no—
254#11719945—22no—
255#11719945—22no—
256#11719945C22×C412yes—
257#11719945C22×C412yes—
258C2×D212—22no—
259C2×D212—22no—
260C2×D212—22no—
261C2×D212—21no—
262C2×D212—22no—
263C2×D212—22no—
264C2×D212—22no—
265C2×D212—21no—
266C2×D212—21no—
267C2×D212—21no—
268C2×D212C22×C412yes—
269C2×D212C22×C411yescharacteristic
270C2×D212C22×C412yes—
271C2×D212C22×C412yes—
272C2×C4×D53—21no—
273C2×C4×D53—21no—
274C2×C4×D53—22no—
275C2×C4×D53—22no—
276C2×C4×D53—22no—
277C2×C4×D53—21no—
278C2×C4×D53—22no—
279C2×C4×D53—22no—
280C2×C4×D53—22no—
281C2×C4×D53—22no—
282C2×C4×D53—22no—
283C2×C4×D53—22no—
284C2×C4×D53—22no—
285C2×C4×D53C22×C411yescharacteristic
286C2×C4×D53C22×C411yescharacteristic
287C2×C4×D53C22×C411yescharacteristic
288C2×C4×D53C2×D411yescharacteristic
289C2×C4×D53C2×D411yescharacteristic
290C2×C4×D53C2×D411yescharacteristic
291C2×C4×D53#4111yescharacteristic
292C2×C4×D53#4111yescharacteristic
293C2×C4×D53#4111yescharacteristic
294C2×C4×D53C2411yescharacteristic
295C2×C4×D53C2411yescharacteristic
296C2×C4×D53C2411yescharacteristic
297C2×Dic106—21no—
298C2×Dic106C22×C411yescharacteristic
299C22⋊#6157—22no—
300C22⋊#6157—22no—
301#11719940—22no—
302#11719940—22no—
303#11719940—22no—
304#11719940—22no—
305#11719940—28no—
306#11719940C2×D414yes—
307#11719940C2×D414yes—
308C2×#88324—22no—
309C2×#88324—22no—
310C2×#88324—28no—
311C2×#88324C2×D414yes—
312C4⋊#6157—22no—
313C4⋊#6157—22no—
314C4×#6157—22no—
315C4×#6157C2414yes—
316#11719936—22no—
317#11719936—22no—
318#11719936—28no—
319#11719936—216no—
320#11719936C2×D414yes—
321#11719936C2×D414yes—
322#11719936C2414yes—
323#11719936C2414yes—
324D53⋊C8—22no—
325D53⋊C8—22no—
326D53⋊C8—22no—
327D53⋊C8—22no—
328D53⋊C8—28no—
329D53⋊C8—216no—
330D53⋊C8C2×D414yes—
331D53⋊C8C2414yes—
332Q16×C53C22×C418yes—
333SD16×C53C22×C418yes—
334M16×C53C22×C412yes—
335M16×C53C22×C412yes—
336C2×C8×C53C22×C412yes—
337#11719925C22×C418yes—
338#11719924C22×C418yes—
339#11719924C22×C418yes—
340#11719922C22×C418yes—
341#11719917C22×C412yes—
342#11719917C22×C412yes—
343C2×#88322C22×C412yes—
344D424C22×C418yes—
345#11719913C22×C418yes—
346#11719912C22×C414yes—
347#11719912C22×C414yes—
348C8×D53C22×C414yes—
349C8×D53C2414yes—
350C23×C53—21no—
351C23×C53C4×D411yescharacteristic
352C22×D53—22no—
353C22×D53—22no—
354C22×D53—22no—
355C22×D53—21no—
356C22×D53—22no—
357C22×D53—22no—
358C22×D53—81no—
359C22×D53—82no—
360C22×D53—82no—
361C22×D53C4×D411yescharacteristic
362C22×D53C4×D411yescharacteristic
363C22×D53C4×D411yescharacteristic
364C22×D53C2×#4111yescharacteristic
365C22×D53C2×#4111yescharacteristic
366C22×D53C2×#4111yescharacteristic
367C2×#6157—24no—
368C2×#6157—82no—
369Q8×C53—21no—
370Q8×C53—22no—
371Q8×C53—22no—
372Q8×C53—22no—
373Q8×C53C23×C412yes—
374Q8×C53C23×C414yes—
375D4×C53—22no—
376D4×C53—22no—
377D4×C53—21no—
378D4×C53C23×C412yes—
379C2×C4×C53—21no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53C4×D411yescharacteristic
386C2×C4×C53C4×D411yescharacteristic
387C2×C4×C53C4×D411yescharacteristic
388C2×C4×C53C23×C411yescharacteristic
389C2×C4×C53C23×C411yescharacteristic
390C2×C4×C53C23×C411yescharacteristic
391C22⋊D53—22no—
392C22⋊D53—22no—
393C22⋊D53—22no—
394C22⋊D53—22no—
395C22⋊D53—22no—
396C22⋊D53—22no—
397C2×Dic53—21no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53C4×D411yescharacteristic
401C2×Dic53C4×D411yescharacteristic
402C2×Dic53C4×D411yescharacteristic
403C2×Dic53C22×D411yescharacteristic
404C2×Dic53C22×D411yescharacteristic
405C2×Dic53C22×D411yescharacteristic
406D212—24no—
407D212—24no—
408D212—24no—
409D212—22no—
410D212—24no—
411D212—22no—
412D212—22no—
413D212—22no—
414D212—22no—
415D212—21no—
416D212C23×C414yes—
417D212C23×C412yes—
418C4×D53—22no—
419C4×D53—22no—
420C4×D53—22no—
421C4×D53—22no—
422C4×D53—22no—
423C4×D53—24no—
424C4×D53—24no—
425C4×D53—24no—
426C4×D53—22no—
427C4×D53—24no—
428C4×D53C4×D411yescharacteristic
429C4×D53C4×D411yescharacteristic
430C4×D53C4×D411yescharacteristic
431C4×D53C4×D411yescharacteristic
432C4×D53C4×D411yescharacteristic
433C4×D53C4×D411yescharacteristic
434C4×D53C23×C411yescharacteristic
435C4×D53C23×C411yescharacteristic
436C4×D53C23×C411yescharacteristic
437C4×D53C22×D411yescharacteristic
438C4×D53C22×D411yescharacteristic
439C4×D53C22×D411yescharacteristic
440C4×D53C2×#4111yescharacteristic
441C4×D53C2×#4111yescharacteristic
442C4×D53C2×#4111yescharacteristic
443C4×D53C2511yescharacteristic
444Dic106—21no—
445Dic106—22no—
446Dic106—22no—
447Dic106C23×C412yes—
448#88324—24no—
449#88324—24no—
450#88324C22×D418yes—
451C8×C53C23×C414yes—
452#88322C23×C414yes—
453#60182—531nomaximal, Sylow
454C22×C53—22no—
455C22×C53—41no—
456C22×C53—81no—
457C22×C53C2×C4×D411yescharacteristic
458C22×C53C2×C4×D411yescharacteristic
459C22×C53C2×C4×D411yescharacteristic
460C2×D53—24no—
461C2×D53—22no—
462C2×D53—41no—
463C2×D53—41no—
464C2×D53—41no—
465C2×D53—41no—
466C2×D53—41no—
467C2×D53—41no—
468C2×D53—44no—
469C2×D53—44no—
470C2×D53—82no—
471C2×D53—82no—
472C2×D53—81no—
473C2×D53—82no—
474C2×D53C2×C4×D411yescharacteristic
475C2×D53C2×C4×D411yescharacteristic
476C2×D53C2×C4×D411yescharacteristic
477C2×D53C22×#4111yescharacteristic
478#6157—44no—
479C4×C53—22no—
480C4×C53—24no—
481C4×C53C2×C4×D411yescharacteristic
482C4×C53C2×C4×D411yescharacteristic
483C4×C53C2×C4×D411yescharacteristic
484C4×C53C24×C411yescharacteristic
485Dic53—22no—
486Dic53C2×C4×D411yescharacteristic
487Dic53C2×C4×D411yescharacteristic
488Dic53C2×C4×D411yescharacteristic
489Dic53C23×D411yescharacteristic
490C2×#575—531no—
491C2×#568—531no—
492C2×#568—531no—
493#2957—534no—
494#2957—534no—
495#2956—538no—
496#2955—538no—
497C2×#430—531no—
498C2×#421—531no—
499C2×#421—531no—
500#2873—531no—
501C2×C53—21no—
502C2×C53—21no—
503C2×C53—21no—
504C2×C53—42no—
505C2×C53C22×C4×D411yescharacteristic
506D53—21no—
507D53—21no—
508D53—21no—
509D53—21no—
510D53—44no—
511D53—42no—
512C22×#41—531no—
513C22×#41—531no—
514#575—534no—
515#575—534no—
516#575—534no—
517#575—534no—
518C2×#137—531no—
519C2×#137—532no—
520C2×#137#615711yescharacteristic, complemented
521C2×AGL(1,ℤ/8)—531no—
522C2×AGL(1,ℤ/8)—532no—
523C2×AGL(1,ℤ/8)—531no—
524C2×#135—532no—
525C2×#135—532no—
526#568—534no—
527#568—534no—
528#568—532no—
529#568—534no—
530#568—532no—
531#568—1062no—
532#568—1062no—
533#568—1062no—
534#568—1062no—
535C2×#131—534no—
536C2×#131—534no—
537C2×#131—1062no—
538C2×#131—1062no—
539C22×M16—531no—
540C22×M16—531no—
541C22×M16—531no—
542C22×M16—531no—
543C22×M16—1062no—
544C22×M16—1062no—
545C2×#117—531no—
546#444—5316no—
547#444—5316no—
548#443—5316no—
549#443—5316no—
550#430—534no—
551#430—534no—
552C2×#108—534no—
553#421—534no—
554#421—532no—
555#421—534no—
556#421—532no—
557#421—534no—
558C2×#104—534no—
559C2×#104—534no—
560#405—534no—
561#405—534no—
562C4×M16—534no—
563C53#6018211yescharacteristic, complemented, Sylow
564C2×#41—532no—
565C2×#41—532no—
566C2×#41—532no—
567C2×#41—532no—
568C2×#41—532no—
569C2×#41—531no—
570C2×#41—532no—
571C2×#41—532no—
572C2×#41—532no—
573C2×#41—532no—
574C2×#41—532no—
575C2×#41—531no—
576C2×#41—531no—
577C2×#41—1061no—
578C2×#41—1061no—
579C2×#41—1061no—
580C2×#41—1061no—
581C2×#41—1061no—
582C2×#41—1061no—
583C2×#41—1061no—
584C2×#41—1061no—
585C2×#41—1061no—
586C2×#41—1061no—
587C2×#41—1061no—
588C2×#41—1061no—
589C2×#41C2×#615711yescharacteristic
590C22×Q8—531no—
591C22×Q8C2×#615711yescharacteristic
592C22×D4—531no—
593C22×D4—531no—
594C22×D4—1061no—
595C22×D4—1061no—
596C23×C4—531no—
597C23×C4—1061no—
598C23×C4—1061no—
599#137—534no—
600#137—534no—
601#137—538no—
602#137—538no—
603#137C2×#615714yes—
604#137C2×#615714yescomplemented
605AGL(1,ℤ/8)—534no—
606AGL(1,ℤ/8)—534no—
607AGL(1,ℤ/8)—538no—
608AGL(1,ℤ/8)—538no—
609AGL(1,ℤ/8)—534no—
610AGL(1,ℤ/8)—534no—
611#135—538no—
612#135—538no—
613#135—538no—
614#135—538no—
615C2×Q16—532no—
616C2×Q16C2×#615712yescomplemented
617C2×SD16—532no—
618C2×SD16—532no—
619C2×SD16—532no—
620C2×SD16C2×#615712yescomplemented
621C2×D8—532no—
622C2×D8—532no—
623#131—538no—
624#131—538no—
625#131—5316no—
626#131—1068no—
627#131—1068no—
628#131—1064no—
629#131—1068no—
630#131—1068no—
631#131—1064no—
632#131—1068no—
633C2×M16—532no—
634C2×M16—532no—
635C2×M16—532no—
636C2×M16—532no—
637C2×M16—532no—
638C2×M16—532no—
639C2×M16—531no—
640C2×M16—532no—
641C2×M16—532no—
642C2×M16—532no—
643C2×M16—532no—
644C2×M16—532no—
645C2×M16—532no—
646C2×M16—532no—
647C2×M16—532no—
648C2×M16—532no—
649C2×M16—532no—
650C2×M16—532no—
651C2×M16—1064no—
652C2×M16—1064no—
653C2×M16—1064no—
654C2×M16—1064no—
655C2×M16—1064no—
656C2×M16—1068no—
657C2×M16—1068no—
658C2×M16—1064no—
659C2×M16—1061no—
660C2×M16—1061no—
661C2×M16—1061no—
662C2×M16—1061no—
663C2×M16—1061no—
664C2×M16—1061no—
665C2×M16C2×#615711yescharacteristic
666C22×C8—532no—
667C22×C8—532no—
668C22×C8—1064no—
669C22×C8—1064no—
670C22×C8—1061no—
671C22×C8—1061no—
672#117—532no—
673#117—532no—
674#117—1061no—
675#117—1061no—
676C2×C4⋊C4—1061no—
677C2×C22⋊C4—1061no—
678C2×C42—532no—
679#108—538no—
680#108—538no—
681#104—538no—
682#104—538no—
683#104—5316no—
684#97—538no—
685C4×C8—538no—
686C24—531no—
687C24—1061no—
688C24—1061no—
689#41—21no—
690#41—21no—
691#41—532no—
692#41—534no—
693#41—534no—
694#41—534no—
695#41—532no—
696#41—534no—
697#41—532no—
698#41—532no—
699#41—532no—
700#41—532no—
701#41—1062no—
702#41—1062no—
703#41—1062no—
704#41—1062no—
705#41—1062no—
706#41—1062no—
707#41—1061no—
708#41—1062no—
709#41—1062no—
710#41—1061no—
711#41—1062no—
712#41—1062no—
713#41—1061no—
714#41—1062no—
715#41—1062no—
716#41—1062no—
717#41—1062no—
718#41—1062no—
719#41—1062no—
720#41—1062no—
721#41—1062no—
722#41—1062no—
723#41—1062no—
724#41—1061no—
725#41—1061no—
726#41—1061no—
727#41C22×#615712yes—
728#41C22×#615712yes—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—532no—
733C2×Q8—532no—
734C2×Q8—531no—
735C2×Q8—1061no—
736C2×Q8—1061no—
737C2×Q8—1061no—
738C2×Q8C22×#615711yescharacteristic
739C2×Q8C22×#615712yes—
740C2×Q8C22×#615712yes—
741C2×Q8C22×#615712yes—
742C2×D4—21no—
743C2×D4—532no—
744C2×D4—532no—
745C2×D4—532no—
746C2×D4—531no—
747C2×D4—532no—
748C2×D4—532no—
749C2×D4—1061no—
750C2×D4—1062no—
751C2×D4—1062no—
752C2×D4—1062no—
753C2×D4—1062no—
754C2×D4—1062no—
755C2×D4—1062no—
756C2×D4—1061no—
757C2×D4—1061no—
758C2×D4—1061no—
759C2×D4—1062no—
760C2×D4—1062no—
761C2×D4—1062no—
762C2×D4—1062no—
763C2×D4—1061no—
764C2×D4—1061no—
765C2×D4—1061no—
766C2×D4—1061no—
767C2×D4—1061no—
768C2×D4C22×#615711yescharacteristic
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—531no—
772C22×C4—531no—
773C22×C4—531no—
774C22×C4—531no—
775C22×C4—531no—
776C22×C4—531no—
777C22×C4—531no—
778C22×C4—531no—
779C22×C4—531no—
780C22×C4—531no—
781C22×C4—531no—
782C22×C4—531no—
783C22×C4—531no—
784C22×C4—1062no—
785C22×C4—1062no—
786C22×C4—1061no—
787C22×C4—1062no—
788C22×C4—1062no—
789C22×C4—1062no—
790C22×C4—1062no—
791C22×C4—1062no—
792C22×C4—1062no—
793C22×C4—1062no—
794C22×C4—1062no—
795C22×C4—1061no—
796C22×C4—1061no—
797C22×C4—1061no—
798C22×C4—1062no—
799C22×C4C22×#615711yescharacteristic
800Q16—538no—
801Q16C22×#615718yes—
802SD16—538no—
803SD16—538no—
804SD16—538no—
805SD16C22×#615718yes—
806D8—538no—
807D8—538no—
808M16—534no—
809M16—534no—
810M16—534no—
811M16—534no—
812M16—532no—
813M16—532no—
814M16—534no—
815M16—534no—
816M16—534no—
817M16—534no—
818M16—1068no—
819M16—10616no—
820M16—1068no—
821M16—1062no—
822M16—1062no—
823M16—1062no—
824M16—1062no—
825M16—1062no—
826M16—1062no—
827M16C22×#615712yes—
828M16C22×#615712yes—
829C2×C8—534no—
830C2×C8—534no—
831C2×C8—534no—
832C2×C8—532no—
833C2×C8—534no—
834C2×C8—534no—
835C2×C8—1068no—
836C2×C8—1068no—
837C2×C8—10616no—
838C2×C8—1062no—
839C2×C8—1062no—
840C2×C8—1062no—
841C2×C8—1062no—
842C2×C8—1062no—
843C2×C8—1062no—
844C2×C8C22×#615712yes—
845C4⋊C4—1062no—
846C4⋊C4—1062no—
847C22⋊C4—1062no—
848C22⋊C4—1062no—
849C42—534no—
850C42—1062no—
851C23—21no—
852C23—531no—
853C23—531no—
854C23—531no—
855C23—531no—
856C23—531no—
857C23—531no—
858C23—1062no—
859C23—1062no—
860C23—1062no—
861C23—1061no—
862C23—1062no—
863C23—1062no—
864C23—4242no—
865C23—4241no—
866C23—4242no—
867C23D4×#615711yescharacteristic
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—21no—
872Q8—532no—
873Q8—1062no—
874Q8—1062no—
875Q8—1061no—
876Q8C23×#615712yes—
877Q8C23×#615714yes—
878D4—22no—
879D4—22no—
880D4—21no—
881D4—534no—
882D4—532no—
883D4—1062no—
884D4—1062no—
885D4—1064no—
886D4—1064no—
887D4—1064no—
888D4—1064no—
889D4—1062no—
890D4—1062no—
891D4—1062no—
892D4—1062no—
893D4—1062no—
894D4—1062no—
895D4—1062no—
896D4—1062no—
897D4—1062no—
898D4—1061no—
899D4C23×#615712yes—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—531no—
907C2×C4—531no—
908C2×C4—531no—
909C2×C4—531no—
910C2×C4—531no—
911C2×C4—531no—
912C2×C4—531no—
913C2×C4—531no—
914C2×C4—531no—
915C2×C4—531no—
916C2×C4—531no—
917C2×C4—531no—
918C2×C4—531no—
919C2×C4—531no—
920C2×C4—531no—
921C2×C4—531no—
922C2×C4—531no—
923C2×C4—531no—
924C2×C4—531no—
925C2×C4—531no—
926C2×C4—531no—
927C2×C4—531no—
928C2×C4—1062no—
929C2×C4—1064no—
930C2×C4—1062no—
931C2×C4—1064no—
932C2×C4—1064no—
933C2×C4—1064no—
934C2×C4—1062no—
935C2×C4—1062no—
936C2×C4—1062no—
937C2×C4—1062no—
938C2×C4—1061no—
939C2×C4—1062no—
940C2×C4—1062no—
941C2×C4—1064no—
942C2×C4—4242no—
943C2×C4D4×#615711yescharacteristic
944C2×C4D4×#615711yescharacteristic
945C2×C4D4×#615711yescharacteristic
946C2×C4C23×#615711yescharacteristic
947C2×C4C23×#615711yescharacteristic
948C2×C4C23×#615711yescharacteristic
949C8—538no—
950C8—534no—
951C8—1064no—
952C8—1064no—
953C8C23×#615714yes—
954C22—22no—
955C22—41no—
956C22—81no—
957C22—531no—
958C22—531no—
959C22—531no—
960C22—531no—
961C22—1064no—
962C22—1062no—
963C22—4242no—
964C22—4241no—
965C22—4242no—
966C22—4242no—
967C22—2121no—
968C22—2121no—
969C22—2121no—
970C22—2121no—
971C22—2121no—
972C22—2121no—
973C22—2124no—
974C22—2124no—
975C22C2×D4×#615711yescharacteristic
976C22C2×D4×#615711yescharacteristic
977C22C2×D4×#615711yescharacteristic
978C4—22no—
979C4—24no—
980C4—531no—
981C4—531no—
982C4—531no—
983C4—531no—
984C4—1062no—
985C4—2124no—
986C4C2×D4×#615711yescharacteristic
987C4C2×D4×#615711yescharacteristic
988C4C2×D4×#615711yescharacteristic
989C4C24×#615711yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—42no—
994C2—1061no—
995C2—1061no—
996C2—1061no—
997C2—1061no—
998C2—2124no—
999C2—2122no—
1000C2C22×D4×#615711yescharacteristic
subgroupG/H
centerC2C22×D4×#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC2×#137×C53C4
socleC2×C53C22×C4×D4
prime radicalC2×#16811422C2
cosocleC4×D53C25
hypercenterC2×#137#6157
hypocenterC53#60182
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16811703C2semidirect
2. D53⋊#568C2semidirect
3. #20291495C2semidirect
4. #20291493C2semidirect
5. #20291490C2semidirect
6. #20291488C2semidirect
7. D53⋊#430C2semidirect
8. C2×#16811622C2semidirect
9. D53⋊#421C2semidirect
10. #20291278C2semidirect
14. #16811703C22semidirect
15. #16811703C22semidirect
16. #16811703C22semidirect
18. #16811702C22semidirect
20. #16811701C22semidirect
22. C2×#13133305C22semidirect
24. D53⋊#131C22semidirect
31. #16811669C22semidirect
32. #16811668C22semidirect
33. #16811667C22semidirect
34. #16811666C22semidirect
35. #16811638C22semidirect
36. #16811638C22semidirect
37. D53⋊#108C22semidirect
38. #16811622C22semidirect
39. #16811622C22semidirect
40. #16811622C22semidirect
41. #16811621C22semidirect
42. #16811620C22semidirect
43. C2×#13133282C22semidirect
44. D53⋊#104C22semidirect
45. #16811589C22semidirect
46. #16811586C22semidirect
47. M16×#6157C22semidirect
50. #16811422C4semidirect
51. #16811422C4semidirect
54. C2×#13133249C4semidirect
55. C2×#13133248C4semidirect
56. C2×#13133245C4semidirect
57. C2×#13133244C4semidirect
58. C2×#13133242C4semidirect
62. C2×#137×C53C4semidirect
67. #13133305C23semidirect
68. #13133305C23semidirect
72. #13133304C23semidirect
111. #13133288C23semidirect
112. #13133287C23semidirect
113. #13133282C23semidirect
114. #13133282C23semidirect
115. #13133281C23semidirect
116. #13133271C23semidirect
117. C8×#6157C23semidirect
152. #13133249C2×C4semidirect
154. #13133248C2×C4semidirect
156. #13133245C2×C4semidirect
158. #13133244C2×C4semidirect
160. #13133242C2×C4semidirect
161. #13133240C2×C4semidirect
163. #13133238C2×C4semidirect
165. C2×#11719925C2×C4semidirect
166. C2×#11719913C2×C4semidirect
167. C2×#11719924C2×C4semidirect
168. C2×#11719924C2×C4semidirect
169. C2×D424C2×C4semidirect
170. C2×#11719922C2×C4semidirect
181. #137×C53C2×C4semidirect
182. C2×Q16×C53C2×C4semidirect
183. C2×SD16×C53C2×C4semidirect
520. C2×#137#6157semidirect
563. C53#60182semidirect
604. #137C2×#6157semidirect
616. C2×Q16C2×#6157semidirect
620. C2×SD16C2×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#168117032
D53⋊#5682
#202914952
#202914932
#202914902
#202914882
D53⋊#4302
C2×#168116222
D53⋊#4212
#202912782
C2×#168114222
#6018253