Finite Group Databasebeta

← #28248300

Subgroups — #28248300

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811421C211yesmaximal, characteristic
2#20287916C211yesmaximal, characteristic, complemented
3#20283596C214yesmaximal, complemented
4#20283588C214yesmaximal, complemented
5#20283554C214yesmaximal, complemented
6#20283543C214yesmaximal, complemented
7C4×#13133248C214yesmaximal, complemented
8C4×#13133243C214yesmaximal, complemented
9C2×#16810663C211yesmaximal, characteristic, complemented
10#20283234C211yesmaximal, characteristic, complemented
11C2×#16810622C211yesmaximal, characteristic, complemented
12#20283134C211yesmaximal, characteristic, complemented
13C2×C53×#520C211yesmaximal, characteristic, complemented
14C22×#11719945C2211yescharacteristic
15#16811421C4116yescomplemented
16C2×#13133248C2212yes—
17C2×#13133247C2212yes—
18C2×#13133243C2212yes—
19C2×#13133242C2212yes—
20C2×#13133237C2214yes—
21C22×#11719917C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23#16811104—21no—
24#16811104—21no—
25#16811103C2212yescomplemented
26#16811103C2212yescomplemented
27#16811100C2212yescomplemented
28#16811097C2212yescomplemented
29#16811096—22no—
30C4×#11719945C2214yes—
31#16811091—22no—
32C2×#13133176C2211yescharacteristic
33#117×D53—22no—
34#16810733C2218yescomplemented
35#16810728C2218yescomplemented
36#16810723C2218yescomplemented
37#16810721C2218yescomplemented
38C4×#11719925C2218yescomplemented
39C4×#11719924C2218yescomplemented
40C4×#11719923C2218yescomplemented
41C4×#11719922C2218yescomplemented
42#16810663C2214yescomplemented
43#16810663C2214yescomplemented
44C2×#13133150C2212yescomplemented
45C2×#13133148C2212yescomplemented
46#16810632C2212yescomplemented
47#16810628C2212yescomplemented
48#16810624C2212yescomplemented
49#16810624C2212yescomplemented
50#16810622C2214yes—
51#16810622C2214yescomplemented
52#16810619C2214yes—
53C2×#13133140C2212yescomplemented
54C2×#13133137C2212yescomplemented
55#16810579C2214yescomplemented
56#16810579C2214yescomplemented
57C4×#11719917C2214yescomplemented
58C22×#41×C53C2211yescharacteristic
59C53×#520—22no—
60C53×#520—22no—
61C53×#520C2214yes—
62C53×#520C2214yescomplemented
63C2×C4×Q8×C53C2212yescomplemented
64C2×C4×D4×C53—22no—
65C2×C4×D4×C53C2212yescomplemented
66C2×#117×C53—21no—
67C2×#117×C53C2211yescharacteristic
68C22×C4⋊C4×C53—21no—
69C22×C4⋊C4×C53C2211yescharacteristic
70C2×#11719945—21no—
71C2×#11719945—21no—
72C2×#11719945—24no—
73C2×#11719945C2×C418yescomplemented
74C2×#11719945C2312yes—
75C2×#11719945C2312yes—
76C22×Dic106C2311yescharacteristic
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C4×D53—21no—
80#13133248C2×C4116yescomplemented
81#13133247C2×C4116yescomplemented
82#13133243C2×C4116yescomplemented
83#13133242C2×C4116yescomplemented
84#13133237C2×C4132yescomplemented
85C2×#11719925C2314yes—
86C2×#11719923C2314yes—
87C2×#11719924C2314yes—
88C2×#11719922C2314yes—
89C2×#11719917—24no—
90C2×#11719917C2×C418yescomplemented
91C2×#11719917C2312yes—
92C2×#11719917C2312yes—
93C2×#11719917C2312yes—
94C2×#11719917C2312yes—
95C22×#88322C2312yes—
96C22×#88322C2312yes—
97C4×Dic106C2314yes—
98C4×Dic106C2314yes—
99#13133182—22no—
100#13133182—22no—
101C4×D212C2314yes—
102C4×D212C2314yes—
103#13133179—22no—
104#13133179—22no—
105C4×C22⋊D53—24no—
106C4×C22⋊D53—24no—
107#13133177—24no—
108#13133177—24no—
109#13133176—21no—
110#13133176—21no—
111#13133176C2312yes—
112#13133176C2312yes—
113#13133175—22no—
114#13133175—22no—
115#13133174—24no—
116#13133173—24no—
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2311yescharacteristic
119C4⋊C4×D53—22no—
120C4⋊C4×D53—22no—
121C2×C22⋊Dic53—21no—
122C22⋊C4×D53—24no—
123C2×C4×Dic53—21no—
124C42×D53—24no—
125#13133150C2318yes—
126#13133148C2318yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133140C2318yes—
130#13133138C2314yes—
131#13133138C2314yes—
132#13133137C2318yes—
133#13133128C2318yes—
134C4×#88322C2318yes—
135C2×#41×C53—21no—
136C2×#41×C53—21no—
137C2×#41×C53—24no—
138C2×#41×C53C2×C418yescomplemented
139C2×#41×C53C2312yes—
140C2×#41×C53C2312yes—
141C22×Q8×C53C2311yescharacteristic
142C22×D4×C53—21no—
143C22×D4×C53C2311yescharacteristic
144C23×C4×C53—21no—
145C23×C4×C53—21no—
146C23×C4×C53—22no—
147C23×C4×C53C2311yescharacteristic
148C4×Q8×C53—24no—
149C4×Q8×C53C2318yes—
150C4×D4×C53—28no—
151C4×D4×C53—28no—
152C4×D4×C53—24no—
153C4×D4×C53C2318yes—
154#117×C53—24no—
155#117×C53—24no—
156#117×C53D412yes—
157#117×C53D412yes—
158#117×C53C2312yes—
159#117×C53C2312yes—
160C2×C4⋊C4×C53—24no—
161C2×C4⋊C4×C53—24no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—22no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2312yes—
169C2×C4⋊C4×C53C2312yes—
170C2×C4⋊C4×C53C2312yes—
171C2×C22⋊C4×C53—22no—
172C2×C22⋊C4×C53D412yes—
173C2×C42×C53—22no—
174C2×C42×C53C2312yes—
175C24×C53—21no—
176C24×C53C2×D411yescharacteristic
177C23×D53—21no—
178#41×C53—28no—
179#41×C53—28no—
180#41×C53—24no—
181#41×C53—24no—
182#41×C53C22×C418yes—
183#41×C53C22×C418yes—
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53C22×C414yes—
187C2×Q8×C53C2412yes—
188C2×D4×C53—28no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53C22×C414yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—28no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—28no—
203C22×C4×C53—84no—
204C22×C4×C53—82no—
205C22×C4×C53C22×C414yes—
206C22×C4×C53C2×D412yes—
207C22×C4×C53C2×D412yes—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53#4114yes—
212C22×C4×C53C2411yescharacteristic
213C22×C4×C53C2411yescharacteristic
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—28no—
216C2×C22⋊D53—22no—
217C2×C22⋊D53—22no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221#11719945—28no—
222#11719945—28no—
223#11719945—24no—
224#11719945—24no—
225#11719945C22×C418yes—
226#11719945C22×C418yescomplemented
227C2×D212—21no—
228C2×D212—22no—
229C2×D212C22×C414yescomplemented
230C2×D212C2412yes—
231C2×C4×D53—28no—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×Dic106—21no—
237C2×Dic106—22no—
238C2×Dic106C22×C414yescomplemented
239C2×Dic106C2412yes—
240C4⋊C4×C53—22no—
241C4⋊C4×C53—22no—
242C4⋊C4×C53—28no—
243C4⋊C4×C53—22no—
244C4⋊C4×C53C2×D412yes—
245C4⋊C4×C53C2×D412yes—
246C4⋊C4×C53C2×D412yes—
247C4⋊C4×C53C2×D412yes—
248C4⋊C4×C53C2414yes—
249C22⋊C4×C53—28no—
250C22⋊C4×C53C2×D414yes—
251C22⋊C4×C53C2×D414yes—
252C42×C53—28no—
253C42×C53C2×D414yes—
254C42×C53C2414yes—
255C22⋊Dic53—22no—
256C22⋊Dic53—22no—
257#11719925C22×C4116yescomplemented
258#11719924C22×C4116yescomplemented
259#11719923C22×C4116yescomplemented
260#11719922C22×C4116yescomplemented
261#11719921—24no—
262#11719921—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53C2412yes—
266C4⋊Dic53C2412yes—
267#11719919—24no—
268#11719919—24no—
269C4×Dic53—22no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53—22no—
273#11719917—24no—
274#11719917—24no—
275#11719917C22×C418yes—
276#11719917C22×C418yescomplemented
277C2×#88322—24no—
278C2×#88322C22×C418yescomplemented
279C2×#88322C2414yes—
280C2×#88322C2414yes—
281C23×C53—24no—
282C23×C53—22no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C4×D414yes—
288C23×C53C22×D411yescharacteristic
289C23×C53C22×D411yescharacteristic
290C23×C53C22×D411yescharacteristic
291C22×D53—22no—
292C22×D53—24no—
293C22×D53—81no—
294C22×D53—81no—
295Q8×C53—24no—
296Q8×C53—22no—
297Q8×C53C23×C414yes—
298D4×C53—28no—
299D4×C53—28no—
300D4×C53—24no—
301D4×C53—22no—
302D4×C53C23×C414yes—
303C2×C4×C53—24no—
304C2×C4×C53—22no—
305C2×C4×C53—28no—
306C2×C4×C53—28no—
307C2×C4×C53—24no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—44no—
311C2×C4×C53—88no—
312C2×C4×C53—82no—
313C2×C4×C53—82no—
314C2×C4×C53C4×D414yes—
315C2×C4×C53C4×D414yes—
316C2×C4×C53C4×D414yes—
317C2×C4×C53C23×C412yes—
318C2×C4×C53C23×C412yes—
319C2×C4×C53C23×C412yes—
320C2×C4×C53C22×D414yes—
321C2×C4×C53C22×D414yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4112yes—
326C2×C4×C53C2×#4112yes—
327C2×C4×C53C2×#4112yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—28no—
330C22⋊D53—28no—
331C2×Dic53—24no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—81no—
336C2×Dic53—81no—
337D212—24no—
338D212—22no—
339D212C23×C414yes—
340C4×D53—28no—
341C4×D53—28no—
342C4×D53—84no—
343C4×D53—84no—
344Dic106—24no—
345Dic106—22no—
346Dic106C23×C414yes—
347#88322—24no—
348#88322C23×C418yes—
349#60170—531nomaximal, Sylow
350C22×C53—21no—
351C22×C53—21no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—24no—
357C22×C53—44no—
358C22×C53—48no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53C2×C4×D412yes—
362C22×C53C2×C4×D412yes—
363C22×C53C2×C4×D412yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—24no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—84no—
369C4×C53—24no—
370C4×C53—24no—
371C4×C53—24no—
372C4×C53—44no—
373C4×C53C2×C4×D412yes—
374C4×C53C2×C4×D412yes—
375C4×C53C2×C4×D412yes—
376C4×C53C24×C411yescharacteristic
377C4×C53C22×#4111yescharacteristic
378Dic53—24no—
379Dic53—42no—
380Dic53—42no—
381C2×#575—531no—
382#3428—531no—
383C2×#520D5311yescharacteristic, complemented
384#2952—534no—
385#2951—534no—
386#2947—534no—
387#2946—534no—
388C4×#137—534no—
389C4×AGL(1,ℤ/8)—534no—
390C2×#428—531no—
391#2896—531no—
392C2×#417—531no—
393#2873—531no—
394C2×C53—22no—
395C2×C53—22no—
396C2×C53—22no—
397C2×C53—44no—
398C2×C53C22×C4×D411yescharacteristic
399C2×C53#358511yescharacteristic
400C2×C53#358611yescharacteristic
401D53—44no—
402C22×#41—531no—
403C22×#41C2×D5311yescharacteristic
404#575—5316no—
405C2×#137—532no—
406C2×#137—532no—
407C2×AGL(1,ℤ/8)—532no—
408C2×AGL(1,ℤ/8)—532no—
409C2×#135—534no—
410C22×M16—531no—
411C22×M16—531no—
412#520—22no—
413#520—22no—
414#520—532no—
415#520—532no—
416#520—1061no—
417#520—1061no—
418#520C2×D5314yes—
419#520C2×D5314yescomplemented
420#519—532no—
421#518—532no—
422#518—1062no—
423C4×#41—534no—
424C4×#41—1062no—
425C2×C4×Q8C2×D5312yescomplemented
426C2×C4×D4—22no—
427C2×C4×D4C2×D5312yescomplemented
428C2×#117—21no—
429C2×#117—531no—
430C2×#117—1062no—
431C2×#117C2×D5311yescharacteristic
432C22×C4⋊C4—21no—
433C22×C4⋊C4C2×D5311yescharacteristic
434#442—538no—
435#441—538no—
436#440—538no—
437#440—538no—
438C4×Q16—538no—
439C4×SD16—538no—
440C4×SD16—538no—
441C4×D8—538no—
442#428—534no—
443#428—534no—
444C2×#107—532no—
445C2×#106—532no—
446#419—532no—
447#418—532no—
448#417—532no—
449#417—532no—
450#417—534no—
451#417—534no—
452#416—534no—
453C2×#103—532no—
454C2×#102—532no—
455#405—534no—
456#405—534no—
457C4×M16—534no—
458C53#6017011yescharacteristic, complemented, Sylow
459C2×#41—24no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—538no—
463C2×#41—532no—
464C2×#41—532no—
465C2×#41—1064no—
466C2×#41—1061no—
467C2×#41—1061no—
468C2×#41C4×D5318yescomplemented
469C2×#41C22×D5312yes—
470C2×#41C22×D5312yes—
471C22×Q8—531no—
472C22×Q8C22×D5311yescharacteristic
473C22×D4—21no—
474C22×D4—531no—
475C22×D4—1061no—
476C22×D4C22×D5311yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—22no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482#137—5316no—
483#137—5316no—
484AGL(1,ℤ/8)—5316no—
485AGL(1,ℤ/8)—5316no—
486#135—5332no—
487C2×Q16—534no—
488C2×SD16—534no—
489C2×SD16—534no—
490C2×D8—534no—
491C2×M16—538no—
492C2×M16—532no—
493C2×M16—532no—
494C2×M16—532no—
495C2×M16—532no—
496C2×M16—1064no—
497C22×C8—532no—
498C22×C8—532no—
499C4×Q8—24no—
500C4×Q8—534no—
501C4×Q8—534no—
502C4×Q8—1062no—
503C4×Q8—1062no—
504C4×Q8C22×D5318yes—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—24no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1064no—
511C4×D4—1064no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1064no—
515C4×D4—1064no—
516C4×D4C22×D5318yes—
517#117—24no—
518#117—24no—
519#117—532no—
520#117—532no—
521#117—1061no—
522#117—1061no—
523#117—1062no—
524#117—1062no—
525#117—1064no—
526#117—1064no—
527#117C22⋊D5312yes—
528#117C22⋊D5312yes—
529#117C22×D5312yes—
530#117C22×D5312yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—1062no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4C22⋊D5311yescharacteristic
542C2×C4⋊C4C22⋊D5311yescharacteristic
543C2×C4⋊C4C22×D5312yes—
544C2×C4⋊C4C22×D5312yes—
545C2×C4⋊C4C22×D5312yes—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1064no—
549C2×C22⋊C4C22⋊D5312yes—
550C2×C42—22no—
551C2×C42—1061no—
552C2×C42—1064no—
553C2×C42C22×D5312yes—
554#107—538no—
555#106—538no—
556#103—534no—
557#103—534no—
558#103—538no—
559#102—534no—
560#102—534no—
561#102—538no—
562#97—538no—
563C4×C8—538no—
564C24—21no—
565C24—1061no—
566C24C2×C22⋊D5311yescharacteristic
567#41—28no—
568#41—28no—
569#41—24no—
570#41—24no—
571#41—538no—
572#41—538no—
573#41—1068no—
574#41—1068no—
575#41—1064no—
576#41—1064no—
577#41C2×C4×D5318yes—
578#41C2×C4×D5318yes—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—534no—
582C2×Q8—532no—
583C2×Q8—1061no—
584C2×Q8—1062no—
585C2×Q8C2×C4×D5314yes—
586C2×Q8C23×D5312yes—
587C2×D4—28no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—534no—
593C2×D4—532no—
594C2×D4—1068no—
595C2×D4—1062no—
596C2×D4—1062no—
597C2×D4—1061no—
598C2×D4—1062no—
599C2×D4C2×C4×D5314yes—
600C2×D4C23×D5312yes—
601C22×C4—21no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4—1061no—
612C22×C4—1068no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1064no—
618C22×C4—1064no—
619C22×C4C2×C4×D5314yes—
620C22×C4#1171994514yes—
621C22×C4C2×C22⋊D5312yes—
622C22×C4C2×C22⋊D5312yes—
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C23×D5311yescharacteristic
627C22×C4C23×D5311yescharacteristic
628C22×C4C23×D5311yescharacteristic
629Q16—5316no—
630SD16—5316no—
631SD16—5316no—
632D8—5316no—
633M16—538no—
634M16—538no—
635M16—1064no—
636M16—1064no—
637C2×C8—538no—
638C2×C8—534no—
639C2×C8—534no—
640C2×C8—1064no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—28no—
644C4⋊C4—22no—
645C4⋊C4—532no—
646C4⋊C4—532no—
647C4⋊C4—1061no—
648C4⋊C4—1061no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4C2×C22⋊D5312yes—
652C4⋊C4C2×C22⋊D5312yes—
653C4⋊C4C2×C22⋊D5312yes—
654C4⋊C4C2×C22⋊D5312yes—
655C4⋊C4C23×D5314yes—
656C22⋊C4—28no—
657C22⋊C4—1062no—
658C22⋊C4—1062no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4C2×C22⋊D5314yes—
662C22⋊C4C2×C22⋊D5314yes—
663C42—28no—
664C42—1062no—
665C42—1062no—
666C42—1064no—
667C42—1064no—
668C42C2×C22⋊D5314yes—
669C42C23×D5314yes—
670C23—24no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—1064no—
677C23—1062no—
678C23—4241no—
679C23—4241no—
680C23C4×C22⋊D5314yes—
681C23C22×C22⋊D5311yescharacteristic
682C23C22×C22⋊D5311yescharacteristic
683C23C22×C22⋊D5311yescharacteristic
684Q8—24no—
685Q8—22no—
686Q8—534no—
687Q8—1064no—
688Q8—1062no—
689Q8C22×C4×D5314yes—
690D4—28no—
691D4—28no—
692D4—24no—
693D4—22no—
694D4—534no—
695D4—1068no—
696D4—1068no—
697D4—1064no—
698D4—1062no—
699D4C22×C4×D5314yes—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—88no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1068no—
714C2×C4—1068no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—4244no—
718C2×C4—4244no—
719C2×C4—4241no—
720C2×C4—4241no—
721C2×C4C4×C22⋊D5314yes—
722C2×C4C4×C22⋊D5314yes—
723C2×C4C4×C22⋊D5314yes—
724C2×C4C22×C4×D5312yes—
725C2×C4C22×C4×D5312yes—
726C2×C4C22×C4×D5312yes—
727C2×C4C22×C22⋊D5314yes—
728C2×C4C22×C22⋊D5314yes—
729C2×C4C22×C22⋊D5311yescharacteristic
730C2×C4C22×C22⋊D5311yescharacteristic
731C2×C4C22×C22⋊D5311yescharacteristic
732C2×C4C2×#1171994512yes—
733C2×C4C2×#1171994512yes—
734C2×C4C2×#1171994512yes—
735C2×C4C24×D5311yescharacteristic
736C8—538no—
737C8—1064no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—24no—
745C22—44no—
746C22—48no—
747C22—42no—
748C22—42no—
749C22—1064no—
750C22—4244no—
751C22—2122no—
752C22—2122no—
753C22C2×C4×C22⋊D5312yes—
754C22C2×C4×C22⋊D5312yes—
755C22C2×C4×C22⋊D5312yes—
756C22C23×C22⋊D5311yescharacteristic
757C4—24no—
758C4—24no—
759C4—24no—
760C4—44no—
761C4—1064no—
762C4—2122no—
763C4—2122no—
764C4C2×C4×C22⋊D5312yes—
765C4C2×C4×C22⋊D5312yes—
766C4C2×C4×C22⋊D5312yes—
767C4C23×C4×D5311yescharacteristic
768C4C22×#1171994511yescharacteristic
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—2124no—
774C2C22×C4×C22⋊D5311yescharacteristic
775C2#2028949511yescharacteristic
776C2#2028950211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C53×#520C2
socleC22×C53C23×D4
prime radicalC2×#16811421C2
cosocleC2×C4×C53C25
hypercenterC2×#520D53
hypocenterC53#60170
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. #20287916C2semidirect
3. #20283596C2semidirect
4. #20283588C2semidirect
5. #20283554C2semidirect
6. #20283543C2semidirect
7. C4×#13133248C2semidirect
8. C4×#13133243C2semidirect
9. C2×#16810663C2semidirect
10. #20283234C2semidirect
11. C2×#16810622C2semidirect
12. #20283134C2semidirect
13. C2×C53×#520C2semidirect
15. #16811421C4semidirect
25. #16811103C22semidirect
26. #16811103C22semidirect
27. #16811100C22semidirect
28. #16811097C22semidirect
34. #16810733C22semidirect
35. #16810728C22semidirect
36. #16810723C22semidirect
37. #16810721C22semidirect
38. C4×#11719925C22semidirect
39. C4×#11719924C22semidirect
40. C4×#11719923C22semidirect
41. C4×#11719922C22semidirect
42. #16810663C22semidirect
43. #16810663C22semidirect
44. C2×#13133150C22semidirect
45. C2×#13133148C22semidirect
46. #16810632C22semidirect
47. #16810628C22semidirect
48. #16810624C22semidirect
49. #16810624C22semidirect
51. #16810622C22semidirect
53. C2×#13133140C22semidirect
54. C2×#13133137C22semidirect
55. #16810579C22semidirect
56. #16810579C22semidirect
57. C4×#11719917C22semidirect
62. C53×#520C22semidirect
63. C2×C4×Q8×C53C22semidirect
65. C2×C4×D4×C53C22semidirect
73. C2×#11719945C2×C4semidirect
80. #13133248C2×C4semidirect
81. #13133247C2×C4semidirect
82. #13133243C2×C4semidirect
83. #13133242C2×C4semidirect
84. #13133237C2×C4semidirect
90. C2×#11719917C2×C4semidirect
138. C2×#41×C53C2×C4semidirect
226. #11719945C22×C4semidirect
229. C2×D212C22×C4semidirect
238. C2×Dic106C22×C4semidirect
257. #11719925C22×C4semidirect
258. #11719924C22×C4semidirect
259. #11719923C22×C4semidirect
260. #11719922C22×C4semidirect
276. #11719917C22×C4semidirect
278. C2×#88322C22×C4semidirect
383. C2×#520D53semidirect
419. #520C2×D53semidirect
425. C2×C4×Q8C2×D53semidirect
427. C2×C4×D4C2×D53semidirect
458. C53#60170semidirect
468. C2×#41C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114212
#202879162
#202835962
#202835882
#202835542
#202835432
C4×#131332482
C4×#131332432
C2×#168106632
#202832342
C2×#168106222
#202831342
C2×C53×#5202
#6017053