Finite Group Databasebeta

← #27290949

Subgroups — #27290949

Order 13568.

1252 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810640C211yesmaximal, characteristic, complemented
2C2×#16810640C211yesmaximal, characteristic, complemented
3C2×#16810607C211yesmaximal, characteristic, complemented
4#20283160C211yesmaximal, characteristic, complemented
5#20274453C211yesmaximal, characteristic, complemented
6#20274441C211yesmaximal, characteristic, complemented
7C2×C53×#575C211yesmaximal, characteristic
8C22×#11719917C2211yescharacteristic
9C22×#11719917C2211yescharacteristic
10C22×#11719917C2211yescharacteristic
11C2×#13133176C2211yescharacteristic
12#16810640—22no—
13#16810640—22no—
14#16810640—22no—
15#16810640—22no—
16C2×#13133144—22no—
17C2×#13133144—22no—
18#16810607—22no—
19#16810607—22no—
20C2×#13133136—21no—
21C2×#13133134—21no—
22#16810590—22no—
23#16810590—22no—
24#16810587—22no—
25#16810391—22no—
26#16810387—22no—
27C22×#41×C53C2211yescharacteristic
28C22×#41×C53C2211yescharacteristic
29C53×#575—22no—
30C53×#575—22no—
31C53×#575—22no—
32C53×#575—22no—
33C2×#137×C53—21no—
34C2×#137×C53C412yescomplemented
35C2×AGL(1,ℤ/8)×C53—21no—
36C2×AGL(1,ℤ/8)×C53C412yescomplemented
37C2×#135×C53—22no—
38C22×M16×C53C2211yescharacteristic
39C2×#11719917—21no—
40C2×#11719917—21no—
41C2×#11719917—21no—
42C2×#11719917—21no—
43C2×#11719917—21no—
44C2×#11719917—21no—
45C2×#11719917—21no—
46C2×#11719917—21no—
47C2×#11719917—21no—
48C2×#11719917—21no—
49C2×#11719917—21no—
50C2×#11719917—21no—
51C2×#11719917—21no—
52C2×#11719917—21no—
53C2×#11719917—21no—
54C2×#11719917D412yes—
55C2×#11719917D412yes—
56C2×#11719917D412yes—
57C22×#88322—21no—
58C22×#88322—21no—
59C22×#88322—21no—
60#13133176—21no—
61#13133176—21no—
62#13133176—21no—
63#13133176—21no—
64C2×C4⋊Dic53—21no—
65C2×C22⋊Dic53—21no—
66C2×C4×Dic53D412yes—
67#13133144—28no—
68#13133144—28no—
69#13133136—24no—
70#13133134—24no—
71C22⋊#88322—28no—
72C2×#41×C53—21no—
73C2×#41×C53—21no—
74C2×#41×C53—21no—
75C2×#41×C53—21no—
76C2×#41×C53—21no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—21no—
82C2×#41×C53—21no—
83C2×#41×C53—21no—
84C2×#41×C53—21no—
85C2×#41×C53—21no—
86C2×#41×C53—21no—
87C2×#41×C53—21no—
88C2×#41×C53—21no—
89C2×#41×C53—21no—
90C2×#41×C53—21no—
91C2×#41×C53—21no—
92C2×#41×C53C2×C412yes—
93C2×#41×C53D412yes—
94C2×#41×C53D412yes—
95C2×#41×C53D412yes—
96C22×Q8×C53C2×C411yescharacteristic
97C22×Q8×C53D411yescharacteristic
98C22×D4×C53—21no—
99C22×D4×C53—21no—
100C22×D4×C53C2×C411yescharacteristic
101C22×D4×C53D411yescharacteristic
102C23×C4×C53—21no—
103C23×C4×C53—21no—
104C23×C4×C53C2311yescharacteristic
105#137×C53—24no—
106#137×C53—24no—
107#137×C53—24no—
108#137×C53—24no—
109AGL(1,ℤ/8)×C53—24no—
110AGL(1,ℤ/8)×C53—24no—
111AGL(1,ℤ/8)×C53—24no—
112AGL(1,ℤ/8)×C53—24no—
113#135×C53—28no—
114#135×C53—28no—
115C2×Q16×C53—22no—
116C2×SD16×C53—22no—
117C2×SD16×C53—22no—
118C2×D8×C53—22no—
119C2×M16×C53—21no—
120C2×M16×C53—21no—
121C2×M16×C53—21no—
122C2×M16×C53C2×C412yes—
123C2×M16×C53D412yes—
124C2×M16×C53D412yes—
125C22×C8×C53—21no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53#4111yescharacteristic
129#41×C53—22no—
130#41×C53—22no—
131#41×C53—22no—
132#41×C53—22no—
133#41×C53—22no—
134#41×C53—22no—
135#41×C53—22no—
136#41×C53—22no—
137#41×C53—22no—
138#41×C53—22no—
139#41×C53—22no—
140#41×C53—22no—
141#41×C53—22no—
142#41×C53—22no—
143#41×C53—22no—
144#41×C53—22no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53C22⋊C412yes—
172C2×Q8×C53C22⋊C412yes—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—41no—
188C2×D4×C53—41no—
189C2×D4×C53—41no—
190C2×D4×C53—41no—
191C2×D4×C53—41no—
192C2×D4×C53—41no—
193C2×D4×C53—41no—
194C2×D4×C53—41no—
195C2×D4×C53C22⋊C412yes—
196C2×D4×C53C22⋊C412yes—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—41no—
204C22×C4×C53—41no—
205C22×C4×C53—41no—
206C22×C4×C53—41no—
207C22×C4×C53—41no—
208C22×C4×C53—41no—
209C22×C4×C53—41no—
210C22×C4×C53—41no—
211C22×C4×C53C22×C411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53#4111yescharacteristic
223C22×C4×C53#4111yescharacteristic
224C22×C4×C53#4111yescharacteristic
225C22×Dic53—22no—
226Q16×C53—28no—
227SD16×C53—28no—
228SD16×C53—28no—
229D8×C53—28no—
230M16×C53—22no—
231M16×C53—22no—
232M16×C53—22no—
233M16×C53C22⋊C414yes—
234C2×C8×C53—22no—
235C2×C8×C53—22no—
236C2×C8×C53—22no—
237C22⋊Dic53—41no—
238C22⋊Dic53—41no—
239C4⋊Dic53—41no—
240C4⋊Dic53—41no—
241C4×Dic53—22no—
242C4×Dic53—22no—
243#11719917—22no—
244#11719917—22no—
245#11719917—22no—
246#11719917—22no—
247#11719917—22no—
248#11719917—22no—
249#11719917—41no—
250#11719917—41no—
251#11719917—41no—
252#11719917—41no—
253#11719917—41no—
254#11719917—41no—
255C2×#88322—22no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—41no—
259C2×#88322—41no—
260C2×#88322—41no—
261C2×#88322—41no—
262C2×#88322—41no—
263C2×#88322—41no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—81no—
271C23×C53—82no—
272C23×C53—82no—
273C23×C53C4×D411yescharacteristic
274C23×C53#12111yescharacteristic
275C23×C53#12111yescharacteristic
276C23×C53#12111yescharacteristic
277C23×C53#12311yescharacteristic
278C23×C53#12311yescharacteristic
279C23×C53#12411yescharacteristic
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—41no—
285Q8×C53—41no—
286Q8×C53—41no—
287Q8×C53—41no—
288D4×C53—22no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—42no—
298D4×C53—42no—
299D4×C53—42no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53—41no—
303D4×C53—41no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C2×C22⋊C411yescharacteristic
321C2×C4×C53C4×D411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53#12011yescharacteristic
325C2×C4×C53#12011yescharacteristic
326C2×C4×C53#12011yescharacteristic
327C2×C4×C53#12011yescharacteristic
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#12111yescharacteristic
339C2×C4×C53#12111yescharacteristic
340C2×C4×C53#12111yescharacteristic
341C2×C4×C53#12311yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12411yescharacteristic
344C2×C4×C53#12711yescharacteristic
345C2×C4×C53#12711yescharacteristic
346C2×Dic53—42no—
347C2×Dic53—82no—
348C8×C53—24no—
349#88322—42no—
350#88322—42no—
351#88322—42no—
352#11032—531nomaximal, Sylow
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—44no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—82no—
364C22×C53—82no—
365C22×C53—82no—
366C22×C53—82no—
367C22×C53—82no—
368C22×C53#38611yescharacteristic
369C22×C53#38611yescharacteristic
370C22×C53#39011yescharacteristic
371C22×C53#39211yescharacteristic
372C22×C53#39411yescharacteristic
373C22×C53#39411yescharacteristic
374C22×C53#39411yescharacteristic
375C4×C53—42no—
376C4×C53—42no—
377C4×C53#37911yescharacteristic
378C4×C53#38611yescharacteristic
379C4×C53#38611yescharacteristic
380C4×C53#39011yescharacteristic
381C4×C53#39211yescharacteristic
382C4×C53#39211yescharacteristic
383C4×C53#39211yescharacteristic
384C4×C53#39411yescharacteristic
385Dic53—82no—
386C2×#575D5311yescharacteristic
387C2×#421—531no—
388C2×#421—531no—
389C2×#413—531no—
390#2879—531no—
391#1742—531no—
392#1738—531no—
393C2×C53—21no—
394C2×C53—21no—
395C2×C53—21no—
396C2×C53—21no—
397C2×C53—21no—
398C2×C53—21no—
399C2×C53—21no—
400C2×C53—82no—
401C2×C53—82no—
402C2×C53#143811yescharacteristic
403C22×#41C2×D5311yescharacteristic
404C22×#41C2×D5311yescharacteristic
405#575—22no—
406#575—22no—
407#575—22no—
408#575—22no—
409C2×#137—21no—
410C2×#137Dic5312yescomplemented
411C2×AGL(1,ℤ/8)—21no—
412C2×AGL(1,ℤ/8)Dic5312yescomplemented
413C2×#135—22no—
414C22×M16—531no—
415C22×M16—531no—
416C22×M16—531no—
417C22×M16C2×D5311yescharacteristic
418C2×#117—531no—
419#421—1062no—
420#421—1062no—
421#421—1062no—
422#421—1062no—
423C2×#104—1062no—
424C2×#104—1062no—
425#413—1062no—
426#413—1062no—
427C2×#101—1061no—
428C2×#100—1061no—
429#408—1062no—
430#408—1062no—
431#407—1062no—
432#343—1062no—
433#341—1062no—
434C53#1103211yescharacteristic, complemented, Sylow
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41C2×Dic5312yes—
456C2×#41C22⋊D5312yes—
457C2×#41C22⋊D5312yes—
458C2×#41C22⋊D5312yes—
459C22×Q8C2×Dic5311yescharacteristic
460C22×Q8C22⋊D5311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C2×Dic5311yescharacteristic
464C22×D4C22⋊D5311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C22×D5311yescharacteristic
468#137—24no—
469#137—24no—
470#137—24no—
471#137—24no—
472AGL(1,ℤ/8)—24no—
473AGL(1,ℤ/8)—24no—
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—24no—
476#135—28no—
477#135—28no—
478C2×Q16—22no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×D8—22no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—532no—
486C2×M16—532no—
487C2×M16—532no—
488C2×M16—1061no—
489C2×M16—1061no—
490C2×M16—1061no—
491C2×M16—1061no—
492C2×M16—1061no—
493C2×M16—1061no—
494C2×M16—1061no—
495C2×M16—1061no—
496C2×M16—1061no—
497C2×M16—1061no—
498C2×M16—1061no—
499C2×M16—1061no—
500C2×M16—1061no—
501C2×M16—1061no—
502C2×M16—1061no—
503C2×M16C2×Dic5312yes—
504C2×M16C22⋊D5312yes—
505C2×M16C22⋊D5312yes—
506C22×C8—21no—
507C22×C8—1061no—
508C22×C8—1061no—
509C22×C8—1061no—
510#117—1061no—
511#117—1061no—
512#117—1061no—
513#117—1061no—
514C2×C4⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C42—532no—
517#104—1068no—
518#104—1068no—
519#101—1064no—
520#100—1064no—
521C22⋊C8—1068no—
522C24—21no—
523C24—21no—
524C24#1171994711yescharacteristic
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C22⋊Dic5312yes—
568C2×Q8C22⋊Dic5312yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4C22⋊Dic5312yes—
592C2×D4C22⋊Dic5312yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—1062no—
608C22×C4D4×D5311yescharacteristic
609C22×C4D4×D5311yescharacteristic
610C22×C4D4×D5311yescharacteristic
611C22×C4D4×D5311yescharacteristic
612C22×C4#1171994711yescharacteristic
613C22×C4#1171994711yescharacteristic
614C22×C4#1171994711yescharacteristic
615C22×C4C22×Dic5311yescharacteristic
616C22×C4C2×C22⋊D5311yescharacteristic
617C22×C4C2×C22⋊D5311yescharacteristic
618C22×C4C2×C22⋊D5311yescharacteristic
619C22×C4C2×C22⋊D5311yescharacteristic
620C22×C4C2×C22⋊D5311yescharacteristic
621C22×C4C2×C22⋊D5311yescharacteristic
622Q16—28no—
623SD16—28no—
624SD16—28no—
625D8—28no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—1062no—
630M16—1062no—
631M16—1062no—
632M16—1062no—
633M16—1062no—
634M16—1062no—
635M16—2121no—
636M16—2121no—
637M16—2121no—
638M16—2121no—
639M16—2121no—
640M16—2121no—
641M16C22⋊Dic5314yes—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—1062no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—2121no—
649C2×C8—2121no—
650C2×C8—2121no—
651C2×C8—2121no—
652C2×C8—2121no—
653C2×C8—2121no—
654C4⋊C4—2121no—
655C4⋊C4—2121no—
656C22⋊C4—2121no—
657C22⋊C4—2121no—
658C42—1062no—
659C42—1062no—
660C23—22no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—81no—
667C23—82no—
668C23—82no—
669C23D4×Dic5311yescharacteristic
670C23#1313318811yescharacteristic
671C23#1313318911yescharacteristic
672C23#1313318911yescharacteristic
673C23#1313319811yescharacteristic
674C23#1313319811yescharacteristic
675C23#1313320411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—4242no—
715C2×C4—2122no—
716C2×C4C2×C22⋊Dic5311yescharacteristic
717C2×C4C2×C22⋊Dic5311yescharacteristic
718C2×C4C2×C22⋊Dic5311yescharacteristic
719C2×C4D4×Dic5311yescharacteristic
720C2×C4D4×Dic5311yescharacteristic
721C2×C4D4×Dic5311yescharacteristic
722C2×C4#1313318511yescharacteristic
723C2×C4#1313318511yescharacteristic
724C2×C4#1313318511yescharacteristic
725C2×C4#1313318511yescharacteristic
726C2×C4#1313318611yescharacteristic
727C2×C4#1313318611yescharacteristic
728C2×C4#1313318611yescharacteristic
729C2×C4#1313318611yescharacteristic
730C2×C4#1313318811yescharacteristic
731C2×C4#1313318811yescharacteristic
732C2×C4#1313318811yescharacteristic
733C2×C4#1313318911yescharacteristic
734C2×C4#1313318911yescharacteristic
735C2×C4#1313318911yescharacteristic
736C2×C4#1313318911yescharacteristic
737C2×C4#1313318911yescharacteristic
738C2×C4#1313318911yescharacteristic
739C2×C4#1313319811yescharacteristic
740C2×C4#1313319811yescharacteristic
741C2×C4#1313320411yescharacteristic
742C2×C4#1313321311yescharacteristic
743C2×C4#1313321311yescharacteristic
744C8—24no—
745C8—2122no—
746C8—2122no—
747C8—2122no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22#1681050311yescharacteristic
764C22#1681050311yescharacteristic
765C22#1681052611yescharacteristic
766C22#1681053111yescharacteristic
767C22#1681053711yescharacteristic
768C22#1681053711yescharacteristic
769C22#1681053711yescharacteristic
770C4—42no—
771C4—42no—
772C4—4242no—
773C4#1681047911yescharacteristic
774C4#1681050311yescharacteristic
775C4#1681050311yescharacteristic
776C4#1681052611yescharacteristic
777C4#1681053111yescharacteristic
778C4#1681053111yescharacteristic
779C4#1681053111yescharacteristic
780C4#1681053711yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—82no—
789C2—82no—
790C2#2027295611yescharacteristic
subgroupG/H
centerC4#16810531
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
Fitting, prime radicalC2×C53×#575C2
socleC2×C53#1438
cosocleC23×C4×C53C23
hypercenterC2×#575D53
hypocenterC53#11032
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16810640C2semidirect
2. C2×#16810640C2semidirect
3. C2×#16810607C2semidirect
4. #20283160C2semidirect
5. #20274453C2semidirect
6. #20274441C2semidirect
34. C2×#137×C53C4semidirect
36. C2×AGL(1,ℤ/8)×C53C4semidirect
410. C2×#137Dic53semidirect
412. C2×AGL(1,ℤ/8)Dic53semidirect
434. C53#11032semidirect

Maximal subgroups

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

subgroupindex
C2×#168106402
C2×#168106072
#202831602
#202744532
#202744412
C2×C53×#5752
#1103253