Finite Group Databasebeta

← #27385963

Subgroups — #27385963

Order 13568.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811421C211yesmaximal, characteristic
2C2×#16811390C211yesmaximal, characteristic, complemented
3#20283232C211yesmaximal, characteristic, complemented
4C2×#16810605C211yesmaximal, characteristic, complemented
5#20275193C214yesmaximal, complemented
6#20275186C214yesmaximal, complemented
7C2×#16810393C211yesmaximal, characteristic, complemented
8C2×#16810381C211yesmaximal, characteristic, complemented
9C2×C53×#421C211yesmaximal, characteristic, complemented
10C22×#11719945C2211yescharacteristic
11#16811421—22no—
12#16811421—22no—
13#16811421—22no—
14#16811421—22no—
15C2×#13133248C412yescomplemented
16C2×#13133247C2212yes—
17C2×#13133243C412yescomplemented
18C2×#13133242C2212yes—
19C2×#13133237C414yescomplemented
20#16811390—22no—
21#16811390—22no—
22#16811390—22no—
23#16811390C2214yes—
24C2×#13133224—22no—
25C2×#13133224—22no—
26C22×#11719917—22no—
27C22×#11719917C2211yescharacteristic
28C22×#11719917C2211yescharacteristic
29C22×#11719917C2211yescharacteristic
30#16810631C2212yescomplemented
31#16810627C2212yescomplemented
32#16810622—22no—
33#16810617—22no—
34#16810605—22no—
35#16810605—22no—
36C2×#13133135C2212yescomplemented
37C2×#13133133C2212yescomplemented
38#16810393C2214yescomplemented
39#16810381C2214yescomplemented
40C22×#41×C53C2211yescharacteristic
41C22×M16×C53C2211yescharacteristic
42C2×#117×C53C2211yescharacteristic
43C53×#421—22no—
44C53×#421C2214yes—
45C2×#104×C53—22no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945—21no—
54C2×#11719945—21no—
55C2×#11719945—21no—
56C2×#11719945C2×C412yes—
57C2×#11719945C2×C412yes—
58C22×Dic106C2311yescharacteristic
59C22×D212C2311yescharacteristic
60C22×C22⋊D53—21no—
61C22×C4×D53—21no—
62#13133248—24no—
63#13133248—24no—
64#13133247—24no—
65#13133247—24no—
66#13133243—24no—
67#13133243—24no—
68#13133242—24no—
69#13133242—24no—
70#13133237—28no—
71#13133237—28no—
72C2×#11719925C2×C414yescomplemented
73C2×#11719923C2×C414yescomplemented
74C2×#11719924C2×C414yescomplemented
75C2×#11719922C2×C414yescomplemented
76#13133224—28no—
77#13133224—28no—
78#13133224—28no—
79#13133224—28no—
80C2×#11719917—24no—
81C2×#11719917—28no—
82C2×#11719917—28no—
83C2×#11719917—21no—
84C2×#11719917—21no—
85C2×#11719917—21no—
86C2×#11719917—21no—
87C2×#11719917—21no—
88C2×#11719917—21no—
89C2×#11719917—21no—
90C2×#11719917—21no—
91C2×#11719917—21no—
92C2×#11719917—21no—
93C2×#11719917—21no—
94C2×#11719917C2×C412yes—
95C2×#11719917D412yes—
96C2×#11719917D412yes—
97C2×#11719917D412yes—
98C2×#11719917C2312yes—
99C2×#11719917C2312yes—
100C2×#11719917C2312yes—
101C22×#88322—24no—
102C22×#88322—21no—
103C22×#88322C2×C412yes—
104C22×#88322D412yes—
105#13133140—24no—
106#13133137—24no—
107#13133135—24no—
108#13133133—24no—
109C2×#41×C53—21no—
110C2×#41×C53—21no—
111C2×#41×C53—21no—
112C2×#41×C53—21no—
113C2×#41×C53—21no—
114C2×#41×C53—21no—
115C2×#41×C53C2×C412yes—
116C2×#41×C53D412yes—
117C2×#41×C53D412yes—
118C2×#41×C53D412yes—
119C2×#41×C53D412yes—
120C2×#41×C53C2312yes—
121C22×Q8×C53C2×C411yescharacteristic
122C22×D4×C53—21no—
123C22×D4×C53C2×C411yescharacteristic
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126C2×M16×C53—21no—
127C2×M16×C53—21no—
128C2×M16×C53—21no—
129C2×M16×C53—21no—
130C2×M16×C53—21no—
131C2×M16×C53C2312yes—
132C22×C8×C53—21no—
133#117×C53—21no—
134#117×C53—21no—
135#117×C53—21no—
136#117×C53C2312yes—
137C2×C4⋊C4×C53—21no—
138C2×C22⋊C4×C53—21no—
139C2×C42×C53—21no—
140#104×C53—28no—
141C24×C53—21no—
142C24×C53#4111yescharacteristic
143C23×D53—21no—
144#41×C53—22no—
145#41×C53—22no—
146#41×C53—22no—
147#41×C53—22no—
148#41×C53—22no—
149#41×C53—22no—
150#41×C53—22no—
151#41×C53—22no—
152#41×C53—22no—
153#41×C53—22no—
154#41×C53—22no—
155#41×C53—22no—
156#41×C53C22⋊C414yes—
157#41×C53C22⋊C414yes—
158#41×C53C2×D414yes—
159#41×C53C2×D414yes—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53C22⋊C412yes—
164C2×Q8×C53C22⋊C412yes—
165C2×Q8×C53C22×C412yes—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—22no—
169C2×D4×C53—22no—
170C2×D4×C53—22no—
171C2×D4×C53—22no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53C22⋊C412yes—
176C2×D4×C53C22⋊C412yes—
177C2×D4×C53C22×C412yes—
178C22×C4×C53—21no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—41no—
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C22×C411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53#4111yescharacteristic
197C22×C4×C53#4111yescharacteristic
198C22×C4×C53#4111yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—22no—
201C2×C22⋊D53—22no—
202C2×C22⋊D53—41no—
203C2×C22⋊D53—41no—
204C2×C22⋊D53—41no—
205C2×C22⋊D53—41no—
206C22×Dic53—21no—
207#11719945—22no—
208#11719945—22no—
209#11719945—22no—
210#11719945—22no—
211#11719945—22no—
212#11719945—22no—
213#11719945—22no—
214#11719945—22no—
215#11719945—41no—
216#11719945—41no—
217#11719945—41no—
218#11719945—41no—
219#11719945—41no—
220#11719945—41no—
221#11719945—41no—
222#11719945—41no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—21no—
226C2×D212—21no—
227C2×D212—21no—
228C2×D212C22×C412yes—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—41no—
232C2×C4×D53—41no—
233C2×C4×D53—41no—
234C2×C4×D53—41no—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106C22×C412yes—
241M16×C53—22no—
242M16×C53—22no—
243M16×C53—41no—
244M16×C53—41no—
245C2×C8×C53—22no—
246C2×C8×C53—41no—
247C2×C8×C53—41no—
248C4⋊C4×C53—22no—
249C4⋊C4×C53—41no—
250C22⋊C4×C53—22no—
251C22⋊C4×C53—41no—
252C42×C53—22no—
253C42×C53—41no—
254#11719925—28no—
255#11719924—28no—
256#11719923—28no—
257#11719922—28no—
258#11719917—216no—
259#11719917—22no—
260#11719917—22no—
261#11719917—22no—
262#11719917—22no—
263#11719917—22no—
264#11719917—22no—
265#11719917—22no—
266#11719917—22no—
267#11719917—22no—
268#11719917—22no—
269#11719917—22no—
270#11719917C2×D414yes—
271C2×#88322—216no—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C22×C414yes—
280C2×#88322C2×D414yes—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—81no—
285C23×C53—82no—
286C23×C53C4×D411yescharacteristic
287C23×C53C4×D411yescharacteristic
288C23×C53#12111yescharacteristic
289C23×C53#12111yescharacteristic
290C23×C53#12311yescharacteristic
291C23×C53#12311yescharacteristic
292C23×C53C2×#4111yescharacteristic
293C22×D53—22no—
294C22×D53—41no—
295C22×D53—41no—
296C22×D53—82no—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53C2×C22⋊C414yes—
301D4×C53—24no—
302D4×C53—24no—
303D4×C53—24no—
304D4×C53—24no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53C2×C22⋊C414yes—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—24no—
313C2×C4×C53—24no—
314C2×C4×C53—24no—
315C2×C4×C53—24no—
316C2×C4×C53—42no—
317C2×C4×C53—82no—
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C2×C22⋊C411yescharacteristic
321C2×C4×C53C2×C22⋊C411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53C4×D411yescharacteristic
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53#12011yescharacteristic
332C2×C4×C53#12111yescharacteristic
333C2×C4×C53#12111yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12311yescharacteristic
339C2×C4×C53#12311yescharacteristic
340C2×C4×C53C23×C411yescharacteristic
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53C2×#4111yescharacteristic
346C22⋊D53—42no—
347C22⋊D53—42no—
348C22⋊D53—42no—
349C22⋊D53—42no—
350C2×Dic53—22no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353D212—22no—
354D212—22no—
355D212—41no—
356D212—41no—
357C4×D53—42no—
358C4×D53—42no—
359C4×D53—42no—
360C4×D53—42no—
361Dic106—22no—
362Dic106—22no—
363Dic106—41no—
364Dic106—41no—
365C8×C53—42no—
366#88322—24no—
367#88322—24no—
368#88322—24no—
369#20995—531nomaximal, Sylow
370C22×C53—24no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—44no—
379C22×C53—82no—
380C22×C53—82no—
381C22×C53#38611yescharacteristic
382C22×C53#38611yescharacteristic
383C22×C53#38611yescharacteristic
384C22×C53#38611yescharacteristic
385C22×C53C2×C4×D411yescharacteristic
386C22×C53C2×#12111yescharacteristic
387C22×C53C2×#12311yescharacteristic
388C2×D53—42no—
389C2×D53—82no—
390C2×D53—82no—
391C2×D53—82no—
392C4×C53—24no—
393C4×C53—82no—
394C4×C53#38611yescharacteristic
395C4×C53#38611yescharacteristic
396C4×C53#38611yescharacteristic
397C4×C53#38611yescharacteristic
398C4×C53C22×C22⋊C411yescharacteristic
399C4×C53C2×C4×D411yescharacteristic
400C4×C53C2×#12011yescharacteristic
401C4×C53C2×#12111yescharacteristic
402Dic53—42no—
403C2×#575—531no—
404C2×#568—531no—
405C2×#421D5311yescharacteristic, complemented
406#2896—531no—
407C2×#413—531no—
408#1903—534no—
409#1902—534no—
410C2×#344—531no—
411C2×#338—531no—
412C2×C53—21no—
413C2×C53—21no—
414C2×C53—21no—
415C2×C53—21no—
416C2×C53—21no—
417C2×C53—21no—
418C2×C53—21no—
419C2×C53—44no—
420C2×C53C2×#38611yescharacteristic
421D53—82no—
422C22×#41—531no—
423C22×#41C2×D5311yescharacteristic
424#575—1062no—
425#575—1062no—
426#575—1062no—
427#575—1062no—
428C2×#137—532no—
429C2×#137—532no—
430C2×AGL(1,ℤ/8)—532no—
431C2×AGL(1,ℤ/8)—532no—
432C2×#135—534no—
433#568—534no—
434#568—1062no—
435#568—1062no—
436#568—1062no—
437C2×#131—1062no—
438C2×#131—1062no—
439C22×M16—531no—
440C22×M16—531no—
441C22×M16—531no—
442C22×M16—1062no—
443C22×M16C2×D5311yescharacteristic
444C2×#117C2×D5311yescharacteristic
445#421—22no—
446#421C2×D5314yes—
447C2×#104—22no—
448#419—532no—
449#418—532no—
450#417—1062no—
451#416—1062no—
452#413—1062no—
453#413—1062no—
454C2×#101—532no—
455C2×#100—532no—
456#344—534no—
457#338—534no—
458C53#2099511yescharacteristic, complemented, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—532no—
466C2×#41—532no—
467C2×#41—1061no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—1061no—
471C2×#41—1061no—
472C2×#41—1061no—
473C2×#41—1061no—
474C2×#41—1061no—
475C2×#41—1061no—
476C2×#41—1061no—
477C2×#41C4×D5312yes—
478C2×#41D21212yes—
479C2×#41D21212yes—
480C2×#41C22⋊D5312yes—
481C2×#41C22⋊D5312yes—
482C2×#41C22×D5312yes—
483C22×Q8—531no—
484C22×Q8C4×D5311yescharacteristic
485C22×D4—21no—
486C22×D4—531no—
487C22×D4—1061no—
488C22×D4C4×D5311yescharacteristic
489C23×C4—21no—
490C23×C4—1061no—
491C23×C4C22×D5311yescharacteristic
492#137—1064no—
493#137—1064no—
494#137—1064no—
495#137—1064no—
496AGL(1,ℤ/8)—1064no—
497AGL(1,ℤ/8)—1064no—
498AGL(1,ℤ/8)—1064no—
499AGL(1,ℤ/8)—1064no—
500#135—1068no—
501#135—1068no—
502C2×Q16—534no—
503C2×SD16—534no—
504C2×SD16—534no—
505C2×D8—534no—
506#131—1068no—
507#131—1068no—
508#131—1068no—
509#131—1068no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—532no—
516C2×M16—532no—
517C2×M16—532no—
518C2×M16—532no—
519C2×M16—532no—
520C2×M16—532no—
521C2×M16—532no—
522C2×M16—1068no—
523C2×M16—1064no—
524C2×M16—1068no—
525C2×M16—1061no—
526C2×M16—1061no—
527C2×M16—1061no—
528C2×M16—1061no—
529C2×M16—1061no—
530C2×M16—1061no—
531C2×M16—1061no—
532C2×M16—1061no—
533C2×M16—1061no—
534C2×M16—1061no—
535C2×M16—1061no—
536C2×M16C22×D5312yes—
537C22×C8—21no—
538C22×C8—532no—
539C22×C8—532no—
540C22×C8—1064no—
541C22×C8—1061no—
542#117—21no—
543#117—21no—
544#117—21no—
545#117C22×D5312yes—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C42—21no—
549#104—28no—
550#103—1064no—
551#102—1064no—
552#101—1064no—
553#100—1064no—
554C24—21no—
555C24—1061no—
556C24#1171994711yescharacteristic
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—1062no—
570#41—1062no—
571#41—1062no—
572#41—1062no—
573#41—1062no—
574#41—1062no—
575#41—1062no—
576#41—1062no—
577#41—2121no—
578#41—2121no—
579#41—2121no—
580#41—2121no—
581#41—2121no—
582#41—2121no—
583#41—2121no—
584#41—2121no—
585#41#1171992114yes—
586#41#1171992114yes—
587#41C2×D21214yes—
588#41C2×C22⋊D5314yes—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—532no—
593C2×Q8—1061no—
594C2×Q8—1061no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×Q8#1171992112yes—
599C2×Q8#1171992112yes—
600C2×Q8C2×C4×D5312yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—532no—
611C2×D4—1062no—
612C2×D4—1062no—
613C2×D4—1061no—
614C2×D4—1061no—
615C2×D4—1061no—
616C2×D4—1061no—
617C2×D4—1061no—
618C2×D4—2121no—
619C2×D4—2121no—
620C2×D4—2121no—
621C2×D4—2121no—
622C2×D4#1171992112yes—
623C2×D4#1171992112yes—
624C2×D4C2×C4×D5312yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—41no—
633C22×C4—1061no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—2121no—
637C22×C4—2121no—
638C22×C4—2121no—
639C22×C4—2121no—
640C22×C4C2×C4×D5311yescharacteristic
641C22×C4C2×C4×D5311yescharacteristic
642C22×C4C2×D21211yescharacteristic
643C22×C4C2×D21211yescharacteristic
644C22×C4D4×D5311yescharacteristic
645C22×C4D4×D5311yescharacteristic
646C22×C4D4×D5311yescharacteristic
647C22×C4D4×D5311yescharacteristic
648C22×C4#1171994711yescharacteristic
649C22×C4#1171994711yescharacteristic
650C22×C4#1171994711yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5311yescharacteristic
654Q16—1068no—
655SD16—1068no—
656SD16—1068no—
657D8—1068no—
658M16—22no—
659M16—22no—
660M16—41no—
661M16—41no—
662M16—534no—
663M16—10616no—
664M16—1062no—
665M16—1062no—
666M16—1062no—
667M16—1062no—
668M16—1062no—
669M16—1062no—
670M16—1062no—
671M16—1062no—
672M16—1062no—
673M16—1062no—
674M16—1062no—
675C2×C8—22no—
676C2×C8—41no—
677C2×C8—41no—
678C2×C8—534no—
679C2×C8—534no—
680C2×C8—10616no—
681C2×C8—1062no—
682C2×C8—1062no—
683C2×C8—1062no—
684C2×C8—1062no—
685C2×C8—1062no—
686C2×C8—1062no—
687C2×C8—1062no—
688C4⋊C4—22no—
689C4⋊C4—41no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C42—22no—
693C42—41no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—81no—
698C23—82no—
699C23—1062no—
700C23—4242no—
701C23—2121no—
702C23—2121no—
703C23#1313317711yescharacteristic
704C23#1313317711yescharacteristic
705C23#1313318911yescharacteristic
706C23#1313318911yescharacteristic
707C23#1313320111yescharacteristic
708C23#1313320111yescharacteristic
709C23C2×#1171994711yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—1062no—
714Q8—1062no—
715Q8—2121no—
716Q8—2121no—
717Q8C2×#1171992114yes—
718D4—24no—
719D4—24no—
720D4—24no—
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—1062no—
726D4—1062no—
727D4—2122no—
728D4—2122no—
729D4—2122no—
730D4—2122no—
731D4—2121no—
732D4—2121no—
733D4C2×#1171992114yes—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—42no—
742C2×C4—82no—
743C2×C4—1062no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4C2×#1171992111yescharacteristic
751C2×C4C2×#1171992111yescharacteristic
752C2×C4C2×#1171992111yescharacteristic
753C2×C4C2×#1171992111yescharacteristic
754C2×C4#1313317711yescharacteristic
755C2×C4#1313317711yescharacteristic
756C2×C4#1313317711yescharacteristic
757C2×C4#1313317711yescharacteristic
758C2×C4#1313317711yescharacteristic
759C2×C4#1313317711yescharacteristic
760C2×C4#1313318711yescharacteristic
761C2×C4#1313318711yescharacteristic
762C2×C4#1313318711yescharacteristic
763C2×C4#1313318711yescharacteristic
764C2×C4#1313318911yescharacteristic
765C2×C4#1313318911yescharacteristic
766C2×C4#1313318911yescharacteristic
767C2×C4#1313318911yescharacteristic
768C2×C4#1313318911yescharacteristic
769C2×C4#1313318911yescharacteristic
770C2×C4#1313320111yescharacteristic
771C2×C4#1313320111yescharacteristic
772C2×C4C22×C4×D5311yescharacteristic
773C2×C4C2×D4×D5311yescharacteristic
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4C22×C22⋊D5311yescharacteristic
776C2×C4C22×D21211yescharacteristic
777C2×C4C2×#1171994711yescharacteristic
778C8—42no—
779C8—1064no—
780C8—1064no—
781C8—1064no—
782C22—24no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—44no—
791C22—82no—
792C22—82no—
793C22—4242no—
794C22—4242no—
795C22—4242no—
796C22—2122no—
797C22#1681050011yescharacteristic
798C22#1681050011yescharacteristic
799C22#1681050011yescharacteristic
800C22#1681050011yescharacteristic
801C22C2×#1313317711yescharacteristic
802C22C2×#1313318911yescharacteristic
803C22C2×#1313320111yescharacteristic
804C4—24no—
805C4—82no—
806C4—2122no—
807C4#1681050011yescharacteristic
808C4#1681050011yescharacteristic
809C4#1681050011yescharacteristic
810C4#1681050011yescharacteristic
811C4C22×#1171992111yescharacteristic
812C4C2×#1313317711yescharacteristic
813C4C2×#1313318711yescharacteristic
814C4C2×#1313318911yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—44no—
823C2—4242no—
824C2C2×#1681050011yescharacteristic
subgroupG/H
centerC4#16810500
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC2×C53C2×#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53#20995
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16811390C2semidirect
3. #20283232C2semidirect
4. C2×#16810605C2semidirect
5. #20275193C2semidirect
6. #20275186C2semidirect
7. C2×#16810393C2semidirect
8. C2×#16810381C2semidirect
9. C2×C53×#421C2semidirect
15. C2×#13133248C4semidirect
17. C2×#13133243C4semidirect
19. C2×#13133237C4semidirect
30. #16810631C22semidirect
31. #16810627C22semidirect
36. C2×#13133135C22semidirect
37. C2×#13133133C22semidirect
38. #16810393C22semidirect
39. #16810381C22semidirect
72. C2×#11719925C2×C4semidirect
73. C2×#11719923C2×C4semidirect
74. C2×#11719924C2×C4semidirect
75. C2×#11719922C2×C4semidirect
405. C2×#421D53semidirect
458. C53#20995semidirect

Maximal subgroups

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

subgroupindex
C2×#168114212
C2×#168113902
#202832322
C2×#168106052
#202751932
#202751862
C2×#168103932
C2×#168103812
C2×C53×#4212
#2099553