Finite Group Databasebeta

← #27404443

Subgroups — #27404443

Order 13568.

1174 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810735C211yesmaximal, characteristic, complemented
2C2×#16810619C211yesmaximal, characteristic, complemented
3#20277757C211yesmaximal, characteristic, complemented
4#20277545C211yesmaximal, characteristic, complemented
5#20275598C211yesmaximal, characteristic, complemented
6#20275407C211yesmaximal, characteristic, complemented
7#20275351C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275065C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20274964C211yesmaximal, characteristic, complemented
12#20274916C211yesmaximal, characteristic, complemented
13#20274542C211yesmaximal, characteristic, complemented
14#20274494C211yesmaximal, characteristic, complemented
15C2×C53×#449C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×D4×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810735—24no—
22C2×#13133151C2211yescharacteristic
23C2×#13133149C2211yescharacteristic
24#16810619—24no—
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33#16810530C2211yescharacteristic
34#16810530C2211yescharacteristic
35#16810526—21no—
36#16810526C2211yescharacteristic
37#16810522C2211yescharacteristic
38#16810516—21no—
39#16810503—21no—
40#16810503—21no—
41#16810503—21no—
42#16810486—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45C22⋊C4×Dic53—21no—
46C4×C22⋊Dic53C2211yescharacteristic
47C2×#13133124—21no—
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×#41×C53C2211yescharacteristic
55C22×SD16×C53C2211yescharacteristic
56C22×D8×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C53×#449C418yescomplemented
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C23×Dic53—21no—
63C23×Dic53—21no—
64C23×Dic53—21no—
65C22×#88322—22no—
66C22×#88322—22no—
67C22×#88322—41no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70D4×Dic53—22no—
71D4×Dic53—22no—
72D4×Dic53—22no—
73D4×Dic53—41no—
74D4×Dic53—41no—
75D4×Dic53—41no—
76#13133176—22no—
77#13133176—41no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53D411yescharacteristic
91C2×C22⋊Dic53D411yescharacteristic
92C2×C4×Dic53—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53C2311yescharacteristic
95C2×C4×Dic53C2311yescharacteristic
96#13133151—41no—
97#13133149—22no—
98#13133141—22no—
99#13133141—22no—
100#13133138—22no—
101#13133138—22no—
102#13133138—41no—
103#13133138D414yescomplemented
104#13133127—22no—
105#13133127—41no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124D411yescharacteristic
114#13133124D411yescharacteristic
115C2×#41×C53—22no—
116C2×#41×C53—22no—
117C2×#41×C53—22no—
118C2×#41×C53—41no—
119C2×#41×C53—41no—
120C2×#41×C53C2×C414yescomplemented
121C22×Q8×C53C2311yescharacteristic
122C22×D4×C53—21no—
123C22×D4×C53—21no—
124C22×D4×C53C2311yescharacteristic
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128C2×SD16×C53—41no—
129C2×SD16×C53—41no—
130C2×SD16×C53C2×C414yescomplemented
131C2×D8×C53—22no—
132C2×D8×C53—22no—
133C2×D8×C53C2×C414yes—
134C22×C8×C53C2311yescharacteristic
135C22×C8×C53C2311yescharacteristic
136#121×C53—22no—
137#121×C53C2×C414yescomplemented
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140#103×C53C2×C414yescomplemented
141#102×C53C2×C414yescomplemented
142C22⋊C8×C53C2×C414yescomplemented
143C24×C53—21no—
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146#41×C53—28no—
147#41×C53—44no—
148#41×C53—44no—
149#41×C53—44no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53C22×C412yes—
156C2×D4×C53—24no—
157C2×D4×C53—24no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—42no—
167C2×D4×C53—42no—
168C2×D4×C53—81no—
169C2×D4×C53—81no—
170C2×D4×C53C22×C412yes—
171C2×D4×C53C22×C412yes—
172C2×D4×C53C2×D412yes—
173C2×D4×C53#4112yes—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—24no—
181C22×C4×C53—42no—
182C22×C4×C53—42no—
183C22×C4×C53C22×C412yes—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53#4112yes—
186C22×C4×C53C2411yescharacteristic
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—42no—
192C22×Dic53—42no—
193C22×Dic53—42no—
194C22×Dic53—42no—
195C22×Dic53—42no—
196C22×Dic53—42no—
197C22×Dic53—81no—
198C22×Dic53—81no—
199C22×Dic53—81no—
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204SD16×C53—44no—
205D8×C53—28no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53C22×C412yes—
211C2×C8×C53C22×C412yes—
212C4⋊C4×C53—21no—
213C4⋊C4×C53C22×C412yes—
214C22⋊C4×C53—24no—
215C22⋊Dic53—41no—
216C22⋊Dic53—41no—
217C22⋊Dic53—42no—
218C22⋊Dic53—42no—
219C22⋊Dic53—42no—
220C22⋊Dic53—42no—
221C22⋊Dic53—42no—
222C22⋊Dic53—81no—
223C22⋊Dic53—81no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—81no—
232C4⋊Dic53C2×D412yes—
233C4×Dic53—21no—
234C4×Dic53—21no—
235C4×Dic53—21no—
236C4×Dic53—21no—
237C4×Dic53—42no—
238C4×Dic53—81no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—44no—
245C2×#88322C2×D412yes—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—21no—
249C23×C53—22no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53C4×D412yes—
267C23×C53C22×D411yescharacteristic
268Q8×C53—22no—
269Q8×C53—22no—
270Q8×C53—41no—
271Q8×C53—41no—
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—22no—
275D4×C53—22no—
276D4×C53—22no—
277D4×C53—48no—
278D4×C53—41no—
279D4×C53—41no—
280D4×C53—84no—
281D4×C53C4×D414yes—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—48no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53C4×D412yes—
296C2×C4×C53C23×C411yescharacteristic
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×C4×C53H(5,𝔽2)11yescharacteristic
302C2×Dic53—22no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—84no—
327C2×Dic53—84no—
328C2×Dic53—84no—
329C8×C53—22no—
330C8×C53—22no—
331#88322—22no—
332#88322—41no—
333#22860—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—24no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—41no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—81no—
352C22×C53—81no—
353C22×C53—81no—
354C22×C53—81no—
355C22×C53C2×C4×D411yescharacteristic
356C22×C53D4211yescharacteristic
357C22×C53#54611yescharacteristic
358C22×C53#57511yescharacteristic
359C22×C53#57511yescharacteristic
360C22×C53#57611yescharacteristic
361C22×C53#57711yescharacteristic
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53C2×C4×D411yescharacteristic
366C4×C53#51811yescharacteristic
367C4×C53#54611yescharacteristic
368C4×C53#55111yescharacteristic
369Dic53—41no—
370Dic53—42no—
371Dic53—41no—
372Dic53—41no—
373Dic53—41no—
374Dic53—81no—
375Dic53—81no—
376Dic53—81no—
377C2×#449D5311yescharacteristic
378C2×#442—531no—
379C2×#416—531no—
380#2363—531no—
381#2339—531no—
382#1973—531no—
383#1935—531no—
384#1927—531no—
385#1893—531no—
386#1879—531no—
387#1877—531no—
388#1862—531no—
389#1854—531no—
390#1762—531no—
391#1752—531no—
392C2×C53—42no—
393C2×C53—44no—
394C2×C53—82no—
395C2×C53#235811yescharacteristic
396C2×C53#294311yescharacteristic
397C2×C53#294611yescharacteristic
398C2×C53#326711yescharacteristic
399C2×C53#326811yescharacteristic
400C2×C53#330711yescharacteristic
401C2×C53#331911yescharacteristic
402C22×#41C2×D5311yescharacteristic
403C22×SD16C2×D5311yescharacteristic
404C22×D8C2×D5311yescharacteristic
405C23×C8—531no—
406C2×#121C2×D5311yescharacteristic
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×#117—531no—
411#449Dic5318yescomplemented
412#442—1064no—
413C2×#107—531no—
414C2×#106—531no—
415#416—1064no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103C2×D5311yescharacteristic
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102C2×D5311yescharacteristic
424C2×C22⋊C8C2×D5311yescharacteristic
425C2×#97—531no—
426C2×#97—531no—
427#391—531no—
428#391—531no—
429#390—531no—
430#390—1061no—
431#389—531no—
432#388—1061no—
433#386—1061no—
434#386—1061no—
435#386—1061no—
436#381—1061no—
437#380—531no—
438C4×C4⋊C4—531no—
439C4×C22⋊C4—531no—
440C4×C22⋊C4—1061no—
441C2×#95—1061no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446#336—531no—
447#336—531no—
448C53#2286011yescharacteristic, complemented, Sylow
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C2×#41C2×Dic5314yescomplemented
455C22×Q8C22×D5311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C22×D5311yescharacteristic
459C22×D4C22×D5311yescharacteristic
460C23×C4—21no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C23×C4C22×D5311yescharacteristic
465C2×SD16—41no—
466C2×SD16—41no—
467C2×SD16C2×Dic5314yescomplemented
468C2×D8—22no—
469C2×D8—22no—
470C2×D8C2×Dic5314yes—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—1062no—
474C22×C8—1062no—
475C22×C8—2121no—
476C22×C8C22×D5311yescharacteristic
477C22×C8C22×D5311yescharacteristic
478#121—22no—
479#121C2×Dic5314yescomplemented
480C4×D4—1062no—
481C4×D4—1062no—
482C4×D4—1062no—
483C4×D4—2121no—
484C4×D4—2121no—
485C4×D4—2121no—
486#117—1062no—
487#117—2121no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4C22×D5311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—531no—
496C2×C22⋊C4—531no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C42—531no—
505C2×C42—531no—
506C2×C42—1061no—
507C2×C42—1061no—
508#107—2121no—
509#106—1062no—
510#103—1062no—
511#103—1062no—
512#103C2×Dic5314yescomplemented
513#102—534no—
514#102—1062no—
515#102—1062no—
516#102—2121no—
517#102C2×Dic5314yescomplemented
518C22⋊C8C2×Dic5314yescomplemented
519#97—1062no—
520#97—2121no—
521#95—531no—
522#95—531no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526#95—1061no—
527#95—1061no—
528#95—1061no—
529#95—1061no—
530C24—21no—
531C24—21no—
532C24D4×D5311yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C22×Dic5312yes—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4D4×D5312yes—
558C2×D4#1171994712yes—
559C2×D4C22×Dic5312yes—
560C2×D4C22×Dic5312yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—531no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—4241no—
579C22×C4—4241no—
580C22×C4—4241no—
581C22×C4—2122no—
582C22×C4—2122no—
583C22×C4—2122no—
584C22×C4—2122no—
585C22×C4—2122no—
586C22×C4—2122no—
587C22×C4D4×D5311yescharacteristic
588C22×C4#1171994712yes—
589C22×C4C22×Dic5312yes—
590C22×C4C23×D5311yescharacteristic
591SD16—44no—
592D8—28no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—532no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—2124no—
604C2×C8C22×Dic5312yes—
605C2×C8C22×Dic5312yes—
606C4⋊C4—21no—
607C4⋊C4—532no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—4241no—
616C4⋊C4C22×Dic5312yes—
617C22⋊C4—24no—
618C22⋊C4—4241no—
619C22⋊C4—4241no—
620C22⋊C4—2121no—
621C22⋊C4—2121no—
622C22⋊C4—2122no—
623C22⋊C4—2122no—
624C22⋊C4—2122no—
625C22⋊C4—2122no—
626C22⋊C4—2122no—
627C42—1061no—
628C42—1061no—
629C42—1061no—
630C42—1061no—
631C42—4241no—
632C42—2122no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23D4×Dic5312yes—
654C23C2×D4×D5311yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—48no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4D4×Dic5314yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—1061no—
691C2×C4—1061no—
692C2×C4—1062no—
693C2×C4—1061no—
694C2×C4—1061no—
695C2×C4—4244no—
696C2×C4—4244no—
697C2×C4—4244no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4D4×Dic5312yes—
710C2×C4C23×Dic5311yescharacteristic
711C2×C4C2×D4×D5311yescharacteristic
712C2×C4C2×#1171994711yescharacteristic
713C2×C4C2×#1171994711yescharacteristic
714C2×C4#1313326211yescharacteristic
715C2×C4#1313326211yescharacteristic
716C8—22no—
717C8—22no—
718C8—1062no—
719C8—2121no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22C2×D4×Dic5311yescharacteristic
742C22#1681125511yescharacteristic
743C22#1681126011yescharacteristic
744C22#1681142011yescharacteristic
745C22#1681142011yescharacteristic
746C22#1681142711yescharacteristic
747C22#1681143311yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—4241no—
752C4—4241no—
753C4—4241no—
754C4—2121no—
755C4—2122no—
756C4—2121no—
757C4—2121no—
758C4—2121no—
759C4C2×D4×Dic5311yescharacteristic
760C4#1681109811yescharacteristic
761C4#1681126011yescharacteristic
762C4#1681130411yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#2027769911yescharacteristic
767C2#2028351611yescharacteristic
768C2#2028354811yescharacteristic
769C2#2028623311yescharacteristic
770C2#2028625911yescharacteristic
771C2#2028669511yescharacteristic
772C2#2028687511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#449C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#449D53
hypocenterC53#22860
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16810735C2semidirect
2. C2×#16810619C2semidirect
3. #20277757C2semidirect
4. #20277545C2semidirect
5. #20275598C2semidirect
6. #20275407C2semidirect
7. #20275351C2semidirect
8. #20275144C2semidirect
9. #20275065C2semidirect
10. #20275051C2semidirect
11. #20274964C2semidirect
12. #20274916C2semidirect
13. #20274542C2semidirect
14. #20274494C2semidirect
58. C53×#449C4semidirect
103. #13133138D4semidirect
120. C2×#41×C53C2×C4semidirect
130. C2×SD16×C53C2×C4semidirect
137. #121×C53C2×C4semidirect
140. #103×C53C2×C4semidirect
141. #102×C53C2×C4semidirect
142. C22⋊C8×C53C2×C4semidirect
411. #449Dic53semidirect
448. C53#22860semidirect
454. C2×#41C2×Dic53semidirect
467. C2×SD16C2×Dic53semidirect
479. #121C2×Dic53semidirect
512. #103C2×Dic53semidirect
517. #102C2×Dic53semidirect
518. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107352
C2×#168106192
#202777572
#202775452
#202755982
#202754072
#202753512
#202751442
#202750652
#202750512
#202749642
#202749162
#202745422
#202744942
C2×C53×#4492
#2286053