Finite Group Databasebeta

← #27395427

Subgroups — #27395427

Order 13568.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810756C211yesmaximal, characteristic
2#20277295C211yesmaximal, characteristic, complemented
3#20275590C211yesmaximal, characteristic, complemented
4#20275580C211yesmaximal, characteristic, complemented
5#20275411C211yesmaximal, characteristic, complemented
6#20275397C211yesmaximal, characteristic, complemented
7#20275342C211yesmaximal, characteristic, complemented
8#20275335C211yesmaximal, characteristic, complemented
9#20275063C211yesmaximal, characteristic, complemented
10#20275063C211yesmaximal, characteristic, complemented
11#20275038C211yesmaximal, characteristic, complemented
12#20274912C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2324C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810756C418yescomplemented
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133138C2211yescharacteristic, complemented
24C2×#13133138C2211yescharacteristic, complemented
25C2×#13133137C2211yescharacteristic
26C2×#13133137C2211yescharacteristic
27C2×#13133137C2211yescharacteristic
28C2×#13133137C2211yescharacteristic
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×#13133128C2211yescharacteristic, complemented
34C2×C4×#88322C2211yescharacteristic, complemented
35#16810525C2211yescharacteristic
36#16810525C2211yescharacteristic
37#16810525C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810524—21no—
40#16810524—21no—
41#16810478—21no—
42#16810478—21no—
43#16810385C2211yescharacteristic, complemented
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810378C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49C2×#121×C53C2211yescharacteristic
50C2×C4×D4×C53C2211yescharacteristic, complemented
51C2×#117×C53C2211yescharacteristic
52C53×#390—21no—
53C53×#390C2211yescharacteristic, complemented
54C53×#389C2211yescharacteristic, complemented
55C53×#388—21no—
56C53×#386—21no—
57C53×#385—21no—
58C53×#380C2211yescharacteristic
59C4×C4⋊C4×C53C2211yescharacteristic, complemented
60C24×D53—21no—
61C22×D212—21no—
62C22×D212—22no—
63C22×D212—41no—
64C22×D212—41no—
65C22×D212—41no—
66C22×D212—41no—
67C22×D212C2×C414yescomplemented
68C22×D212C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C2×#11719922—41no—
71C2×#11719922—41no—
72C2×#11719922—41no—
73C2×#11719922—41no—
74C2×#11719922C2×C414yes—
75C2×#11719922C2×C414yes—
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80#13133176—41no—
81#13133176—41no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×#11719921—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—21no—
94#13133150—41no—
95#13133148—41no—
96#13133138—41no—
97#13133138—41no—
98#13133137—41no—
99#13133137—41no—
100#13133137—41no—
101#13133137—41no—
102#13133137C2×C414yescomplemented
103#13133137C2×C414yescomplemented
104C22⋊#88322—22no—
105C22⋊#88322C2×C414yescomplemented
106#13133128—41no—
107C4×#88322—41no—
108C22×D4×C53—21no—
109C22×D4×C53C2311yescharacteristic
110C23×C4×C53—21no—
111C23×C4×C53C2311yescharacteristic
112#121×C53—22no—
113#121×C53C2×C414yes—
114C4×D4×C53—41no—
115C4×D4×C53—41no—
116#117×C53—41no—
117#117×C53—41no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53D411yescharacteristic
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53—21no—
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137C24×C53—21no—
138C24×C53C2×D411yescharacteristic
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—24no—
142C23×D53—42no—
143C23×D53—42no—
144C23×D53—81no—
145C23×D53—81no—
146C23×D53—81no—
147C23×D53—81no—
148C2×D4×C53—24no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—81no—
155C2×D4×C53—81no—
156C2×D4×C53C22×C412yes—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—42no—
165C22×C4×C53—81no—
166C22×C4×C53—81no—
167C22×C4×C53C22×C412yes—
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53#4112yes—
174C22×C4×C53C2411yescharacteristic
175C22×Dic53—21no—
176C22×Dic53—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—21no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212—24no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—44no—
189C2×D212—44no—
190C2×D212—42no—
191C2×D212—42no—
192C2×D212—44no—
193C2×D212—44no—
194C2×D212C22×C412yes—
195C2×D212C22×C412yes—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—41no—
202C4⋊C4×C53—41no—
203C4⋊C4×C53—81no—
204C4⋊C4×C53C22×C412yes—
205C22⋊C4×C53—24no—
206C22⋊C4×C53—41no—
207C22⋊C4×C53—41no—
208C22⋊C4×C53—42no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53—81no—
211C22⋊C4×C53—81no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—81no—
217C22⋊Dic53—42no—
218#11719922—44no—
219#11719922—44no—
220#11719921—81no—
221#11719921—81no—
222#11719921—81no—
223#11719921—81no—
224#11719921—81no—
225#11719921—81no—
226#11719921—81no—
227#11719921—81no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4×Dic53—42no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322C22×C412yes—
244C2×#88322C22×C412yes—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—22no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53C4×D412yes—
259C23×C53C22×D411yescharacteristic
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—48no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—41no—
274C22×D53—41no—
275C22×D53—84no—
276C22×D53—84no—
277C22×D53—84no—
278C22×D53—84no—
279C22×D53—84no—
280C22×D53—84no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—41no—
284D4×C53—41no—
285D4×C53—84no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—84no—
314C2×C4×C53C4×D412yes—
315C2×C4×C53C23×C411yescharacteristic
316C2×C4×C53C2×#4111yescharacteristic
317C2×C4×C53H(5,𝔽2)11yescharacteristic
318C2×C4×C53H(5,𝔽2)11yescharacteristic
319C2×C4×C53H(5,𝔽2)11yescharacteristic
320C2×C4×C53H(5,𝔽2)11yescharacteristic
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—22no—
331D212—48no—
332D212—41no—
333D212—41no—
334D212—41no—
335D212—41no—
336#88322—22no—
337#88322—22no—
338#88322—41no—
339#88322—41no—
340#22056—531nomaximal, Sylow
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53—41no—
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×C53#53411yescharacteristic
357C22×C53#53511yescharacteristic
358C22×C53#57611yescharacteristic
359C22×C53#57611yescharacteristic
360C22×C53#57611yescharacteristic
361C22×C53#57711yescharacteristic
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—816no—
369C2×D53—81no—
370C2×D53—81no—
371C2×D53—81no—
372C2×D53—81no—
373C2×D53—81no—
374C2×D53—81no—
375C2×D53—81no—
376C2×D53—81no—
377C4×C53—22no—
378C4×C53—41no—
379C4×C53—41no—
380C4×C53—41no—
381C4×C53—41no—
382C4×C53—42no—
383C4×C53—81no—
384C4×C53—81no—
385C4×C53#51811yescharacteristic
386C4×C53#51811yescharacteristic
387C4×C53#53811yescharacteristic
388C4×C53#53811yescharacteristic
389Dic53—81no—
390Dic53—81no—
391C2×#447—531no—
392#2324D5311yescharacteristic, complemented
393#2309—531no—
394#1972—531no—
395#1970—531no—
396#1936—531no—
397#1934—531no—
398#1926—531no—
399#1925—531no—
400#1879—531no—
401#1879—531no—
402#1875—531no—
403#1854—531no—
404#1786—531no—
405#1750—531no—
406C2×C53—42no—
407C2×C53—82no—
408C2×C53#232111yescharacteristic
409C2×C53#294611yescharacteristic
410C2×C53#294811yescharacteristic
411C2×C53#319811yescharacteristic
412C2×C53#319911yescharacteristic
413C2×C53#322011yescharacteristic
414C2×C53#322411yescharacteristic
415D53—82no—
416D53—82no—
417C23×D4—531no—
418C22×D8—531no—
419C22×D8—531no—
420C2×#121C2×D5311yescharacteristic
421C2×C4×D4C2×D5311yescharacteristic, complemented
422C2×#117—531no—
423C2×#117C2×D5311yescharacteristic
424#447—538no—
425C2×#107—531no—
426C2×#106—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×C22⋊C8—531no—
436C2×C22⋊C8—531no—
437C2×#97—531no—
438C2×C4×C8—531no—
439#390—21no—
440#390—531no—
441#390—531no—
442#390—531no—
443#390—531no—
444#390—1061no—
445#390—1061no—
446#390C2×D5311yescharacteristic, complemented
447#389C2×D5311yescharacteristic, complemented
448#388—21no—
449#386—21no—
450#385—21no—
451#380C2×D5311yescharacteristic
452#379—1061no—
453#379—1061no—
454C4×C4⋊C4C2×D5311yescharacteristic, complemented
455#340—531no—
456#340—531no—
457#340—531no—
458#340—531no—
459#336—531no—
460#336—531no—
461C53#2205611yescharacteristic, complemented, Sylow
462C25—1061no—
463C22×D4—21no—
464C22×D4—534no—
465C22×D4—531no—
466C22×D4—531no—
467C22×D4—1062no—
468C22×D4—1061no—
469C22×D4—2121no—
470C22×D4—2121no—
471C22×D4—2121no—
472C22×D4—2121no—
473C22×D4C22×D5311yescharacteristic
474C23×C4—21no—
475C23×C4C22×D5311yescharacteristic
476C2×D8—534no—
477C2×D8—534no—
478C2×D8—2121no—
479C2×D8—2121no—
480C2×D8—2121no—
481C2×D8—2121no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8—531no—
485C22×C8—531no—
486#121—22no—
487#121C4×D5314yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—2121no—
493#117—2121no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4C22⋊D5311yescharacteristic
498C2×C4⋊C4C22⋊D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C4⋊C4C22×D5311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4C22⋊D5311yescharacteristic
517C2×C22⋊C4C22⋊D5311yescharacteristic
518C2×C42—21no—
519C2×C42—1061no—
520C2×C42C22×D5311yescharacteristic
521C2×C42C22×D5311yescharacteristic
522#107—2121no—
523#106—2121no—
524#102—534no—
525#102—534no—
526#102—2121no—
527#102—2121no—
528#102—2121no—
529#102—2121no—
530#102—2121no—
531#102—2121no—
532C22⋊C8—534no—
533C22⋊C8—1062no—
534#97—2121no—
535C4×C8—2121no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—1064no—
541C24—1061no—
542C24—1061no—
543C24—4241no—
544C24—4241no—
545C24—4241no—
546C24—4241no—
547C24—2122no—
548C24—2122no—
549C24C2×C22⋊D5311yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—532no—
559C2×D4—532no—
560C2×D4—1064no—
561C2×D4—1061no—
562C2×D4—1061no—
563C2×D4—1061no—
564C2×D4—1061no—
565C2×D4—1061no—
566C2×D4—1061no—
567C2×D4—1061no—
568C2×D4—1061no—
569C2×D4—1061no—
570C2×D4—1061no—
571C2×D4—2124no—
572C2×D4—2124no—
573C2×D4—2122no—
574C2×D4—2122no—
575C2×D4—2124no—
576C2×D4—2124no—
577C2×D4C2×C4×D5312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4C2×C4×D5312yes—
591C22×C4#1171994512yes—
592C22×C4C2×C22⋊D5311yescharacteristic
593C22×C4C2×C22⋊D5311yescharacteristic
594C22×C4C2×C22⋊D5311yescharacteristic
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598D8—2124no—
599D8—2124no—
600C2×C8—532no—
601C2×C8—532no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C2×C8—1061no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—81no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1061no—
624C4⋊C4C2×C4×D5312yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—4241no—
633C22⋊C4—4241no—
634C22⋊C4—4241no—
635C22⋊C4—4241no—
636C22⋊C4—4241no—
637C22⋊C4—4241no—
638C22⋊C4—4241no—
639C22⋊C4—4241no—
640C22⋊C4—2122no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42—2122no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—1062no—
661C23—1062no—
662C23—4244no—
663C23—4244no—
664C23—4244no—
665C23—4244no—
666C23—4244no—
667C23—4244no—
668C23—2128no—
669C23—2121no—
670C23—2121no—
671C23—2121no—
672C23—2121no—
673C23—2121no—
674C23—2121no—
675C23—2121no—
676C23—2121no—
677C23—2121no—
678C23—2121no—
679C23—2121no—
680C23—2121no—
681C23C4×C22⋊D5312yes—
682C23C22×C22⋊D5311yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—1062no—
689D4—1062no—
690D4—1062no—
691D4—1062no—
692D4—2128no—
693D4—2121no—
694D4—2121no—
695D4—2121no—
696D4—2121no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4C4×C22⋊D5312yes—
732C2×C4C22×C4×D5311yescharacteristic
733C2×C4C2×#1171994511yescharacteristic
734C2×C4#1313326211yescharacteristic
735C2×C4#1313326211yescharacteristic
736C2×C4#1313326311yescharacteristic
737C2×C4#1313326311yescharacteristic
738C8—1062no—
739C8—1062no—
740C8—2121no—
741C8—2121no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—42416no—
757C22—4241no—
758C22—4241no—
759C22—4241no—
760C22—4241no—
761C22—4241no—
762C22—4241no—
763C22—4241no—
764C22—4241no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22—2122no—
770C22—2122no—
771C22C2×C4×C22⋊D5311yescharacteristic
772C22#1681118211yescharacteristic
773C22#1681118711yescharacteristic
774C22#1681142611yescharacteristic
775C22#1681142611yescharacteristic
776C22#1681142611yescharacteristic
777C22#1681143111yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—4241no—
787C4—4241no—
788C4#1681109511yescharacteristic
789C4#1681109511yescharacteristic
790C4#1681120611yescharacteristic
791C4#1681120611yescharacteristic
792C2—42no—
793C2—82no—
794C2—4242no—
795C2—4242no—
796C2#2027736911yescharacteristic
797C2#2028354311yescharacteristic
798C2#2028356511yescharacteristic
799C2#2028556111yescharacteristic
800C2#2028557611yescharacteristic
801C2#2028575911yescharacteristic
802C2#2028580311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2324C2
socleC23×C53C22×D4
prime radicalC2×#16810756C2
cosocleC22×C4×C53C24
hypercenter#2324D53
hypocenterC53#22056
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #20277295C2semidirect
3. #20275590C2semidirect
4. #20275580C2semidirect
5. #20275411C2semidirect
6. #20275397C2semidirect
7. #20275342C2semidirect
8. #20275335C2semidirect
9. #20275063C2semidirect
10. #20275063C2semidirect
11. #20275038C2semidirect
12. #20274912C2semidirect
13. #20274645C2semidirect
14. #20274481C2semidirect
15. C53×#2324C2semidirect
20. #16810756C4semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. C2×#13133138C22semidirect
24. C2×#13133138C22semidirect
33. C2×#13133128C22semidirect
34. C2×C4×#88322C22semidirect
43. #16810385C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810378C22semidirect
48. #16810378C22semidirect
50. C2×C4×D4×C53C22semidirect
53. C53×#390C22semidirect
54. C53×#389C22semidirect
59. C4×C4⋊C4×C53C22semidirect
67. C22×D212C2×C4semidirect
102. #13133137C2×C4semidirect
103. #13133137C2×C4semidirect
105. C22⋊#88322C2×C4semidirect
392. #2324D53semidirect
421. C2×C4×D4C2×D53semidirect
446. #390C2×D53semidirect
447. #389C2×D53semidirect
454. C4×C4⋊C4C2×D53semidirect
461. C53#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#168107562
#202772952
#202755902
#202755802
#202754112
#202753972
#202753422
#202753352
#202750632
#202750382
#202749122
#202746452
#202744812
C53×#23242
#2205653