Finite Group Databasebeta

← #27395433

Subgroups — #27395433

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×#16810757C211yesmaximal, characteristic
2#20277408C211yesmaximal, characteristic, complemented
3#20275590C211yesmaximal, characteristic, complemented
4#20275580C211yesmaximal, characteristic, complemented
5#20275415C211yesmaximal, characteristic, complemented
6#20275401C211yesmaximal, characteristic, complemented
7#20275339C211yesmaximal, characteristic, complemented
8#20275332C211yesmaximal, characteristic, complemented
9#20275066C211yesmaximal, characteristic, complemented
10#20275066C211yesmaximal, characteristic, complemented
11#20275037C211yesmaximal, characteristic, complemented
12#20274914C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2309C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic, complemented
20#16810757C418yescomplemented
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133138C2211yescharacteristic
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133137C2211yescharacteristic, complemented
30C2×#13133137C2211yescharacteristic, complemented
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×#13133128C2211yescharacteristic, complemented
34C2×C4×#88322C2211yescharacteristic, complemented
35#16810525C2211yescharacteristic, complemented
36#16810523—21no—
37#16810521C2211yescharacteristic, complemented
38#16810513—21no—
39#16810499—21no—
40#16810494—21no—
41#16810483C2211yescharacteristic
42C4×C4⋊Dic53C2211yescharacteristic, complemented
43#16810385C2211yescharacteristic, complemented
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810378C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49C23×D4×C53C2211yescharacteristic
50C2×#117×C53C2211yescharacteristic
51C2×#117×C53C2211yescharacteristic
52C53×#390—21no—
53C53×#390—21no—
54C53×#390C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#379—21no—
59C53×#379—21no—
60C22×D212C2311yescharacteristic
61C22×C22⋊D53—21no—
62C22×C4×D53—21no—
63C2×#11719922—41no—
64C2×#11719922—41no—
65C2×#11719922—41no—
66C2×#11719922—41no—
67C2×#11719922C2×C414yes—
68C2×#11719922C2×C414yes—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133191—22no—
74#13133191C2×C414yes—
75C4×D212—41no—
76C4×D212—41no—
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×#11719919—21no—
81C2×C22⋊Dic53—21no—
82C2×#11719921—21no—
83C2×#11719921—21no—
84C2×#11719921—21no—
85C2×#11719921—21no—
86C2×C4×Dic53—21no—
87#13133150—41no—
88#13133148—41no—
89#13133138—41no—
90#13133138—41no—
91#13133138—41no—
92#13133138—41no—
93#13133138C2×C414yescomplemented
94#13133138C2×C414yescomplemented
95#13133137—41no—
96#13133137—41no—
97C22⋊#88322—22no—
98C22⋊#88322C2×C414yescomplemented
99#13133128—41no—
100C4×#88322—41no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104C25×C53—21no—
105C22×D4×C53—21no—
106C22×D4×C53—22no—
107C22×D4×C53—41no—
108C22×D4×C53—41no—
109C22×D4×C53—41no—
110C22×D4×C53—41no—
111C22×D4×C53C2×C414yescomplemented
112C22×D4×C53C2311yescharacteristic
113C22×D4×C53C2311yescharacteristic
114C23×C4×C53C2311yescharacteristic
115#117×C53—41no—
116#117×C53—41no—
117#117×C53—41no—
118#117×C53—41no—
119C2×C4⋊C4×C53D411yescharacteristic
120C2×C4⋊C4×C53D411yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C22⋊C4×C53—21no—
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×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C42×C53—21no—
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—24no—
140C24×C53—42no—
141C24×C53—42no—
142C24×C53—81no—
143C24×C53—81no—
144C24×C53—81no—
145C24×C53—81no—
146C24×C53C2×D411yescharacteristic
147C23×D53—21no—
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—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—44no—
160C2×D4×C53—44no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53—44no—
164C2×D4×C53—44no—
165C2×D4×C53C22×C412yes—
166C2×D4×C53C22×C412yes—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53C22×C412yes—
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53#4112yes—
180C22×C4×C53C2411yescharacteristic
181C2×C22⋊D53—24no—
182C2×C22⋊D53—81no—
183C2×C22⋊D53—81no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212C22×C412yes—
193C2×C4×D53—42no—
194C2×C4×D53—81no—
195C2×C4×D53—81no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—41no—
201C4⋊C4×C53—41no—
202C22⋊C4×C53—41no—
203C22⋊C4×C53—41no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53—81no—
206C22⋊C4×C53—81no—
207C22⋊C4×C53—81no—
208C22⋊C4×C53—81no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53—81no—
211C22⋊C4×C53—81no—
212C22⋊C4×C53—81no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—21no—
217C42×C53—42no—
218C22⋊Dic53—81no—
219#11719922—44no—
220#11719922—44no—
221#11719921—24no—
222#11719921—42no—
223#11719921—81no—
224#11719921—81no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53C22×C412yes—
231#11719919—81no—
232C4×Dic53—81no—
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—22no—
253C23×C53—48no—
254C23×C53—41no—
255C23×C53—41no—
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×C53—84no—
267C23×C53—84no—
268C23×C53—84no—
269C23×C53—84no—
270C23×C53—84no—
271C23×C53—84no—
272C23×C53C4×D412yes—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—41no—
276C22×D53—41no—
277C22×D53—41no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53—41no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—22no—
284D4×C53—22no—
285D4×C53—48no—
286D4×C53—41no—
287D4×C53—41no—
288D4×C53—41no—
289D4×C53—41no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
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—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
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
321C22⋊D53—84no—
322C2×Dic53—22no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331D212—22no—
332D212—22no—
333D212—41no—
334D212—41no—
335C4×D53—84no—
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—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—816no—
355C22×C53—81no—
356C22×C53—81no—
357C22×C53—81no—
358C22×C53—81no—
359C22×C53—81no—
360C22×C53—81no—
361C22×C53—81no—
362C22×C53—81no—
363C22×C53C2×C4×D411yescharacteristic
364C22×C53#53411yescharacteristic
365C22×C53#53511yescharacteristic
366C22×C53#57611yescharacteristic
367C22×C53#57611yescharacteristic
368C22×C53#57611yescharacteristic
369C22×C53#57711yescharacteristic
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
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—81no—
383C4×C53—81no—
384C4×C53#51811yescharacteristic
385C4×C53#51811yescharacteristic
386C4×C53#53811yescharacteristic
387C4×C53#53811yescharacteristic
388Dic53—42no—
389Dic53—81no—
390Dic53—81no—
391C2×#447—531no—
392#2324—531no—
393#2309D5311yescharacteristic, complemented
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—82no—
409C2×C53#232111yescharacteristic
410C2×C53#294611yescharacteristic
411C2×C53#294811yescharacteristic
412C2×C53#319811yescharacteristic
413C2×C53#319911yescharacteristic
414C2×C53#322011yescharacteristic
415C2×C53#322411yescharacteristic
416D53—82no—
417C23×D4C2×D5311yescharacteristic
418C22×D8—531no—
419C22×D8—531no—
420C2×#121—531no—
421C2×C4×D4—531no—
422C2×#117C2×D5311yescharacteristic
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—21no—
441#390—531no—
442#390—1061no—
443#390C2×D5311yescharacteristic
444#390C2×D5311yescharacteristic
445#390C2×D5311yescharacteristic
446#390C2×D5311yescharacteristic
447#389—531no—
448#388—1061no—
449#386—1061no—
450#385—1061no—
451#380—531no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—531no—
455#340—531no—
456#340—531no—
457#340—531no—
458#340—531no—
459#336—531no—
460#336—531no—
461C53#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4C4×D5314yescomplemented
472C22×D4C22×D5311yescharacteristic
473C22×D4C22×D5311yescharacteristic
474C23×C4—1061no—
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—534no—
487#121—1062no—
488C4×D4—2121no—
489C4×D4—2121no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—1061no—
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—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
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—1061no—
537#95—1061no—
538#95—1061no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—1061no—
549C24C2×C22⋊D5311yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—532no—
568C2×D4—1064no—
569C2×D4—1061no—
570C2×D4—1061no—
571C2×D4—1061no—
572C2×D4—1061no—
573C2×D4—1061no—
574C2×D4—4241no—
575C2×D4—4241no—
576C2×D4C2×C4×D5312yes—
577C2×D4C2×C4×D5312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—4241no—
588C22×C4—4241no—
589C22×C4—2122no—
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—41no—
617C4⋊C4—41no—
618C4⋊C4—532no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1061no—
624C4⋊C4—4241no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—1064no—
637C22⋊C4—4241no—
638C22⋊C4—4241no—
639C22⋊C4—4241no—
640C22⋊C4—2122no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—4241no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—1062no—
675C23—2121no—
676C23—2121no—
677C23—2121no—
678C23—2121no—
679C23—2121no—
680C23—2121no—
681C23C4×C22⋊D5312yes—
682C23C22×C22⋊D5311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—1062no—
693D4—1062no—
694D4—4244no—
695D4—2121no—
696D4—2121no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
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—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—1062no—
722C2×C4—4244no—
723C2×C4—2121no—
724C2×C4—2121no—
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#1313326211yescharacteristic
737C2×C4#1313326211yescharacteristic
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—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—4241no—
765C22—4241no—
766C22—4241no—
767C22—4241no—
768C22—2122no—
769C22—2122no—
770C22—2122no—
771C22C2×C4×C22⋊D5311yescharacteristic
772C22#1681118211yescharacteristic
773C22#1681119011yescharacteristic
774C22#1681142611yescharacteristic
775C22#1681142611yescharacteristic
776C22#1681142611yescharacteristic
777C22#1681143411yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—4241no—
786C4—4241no—
787C4—2122no—
788C4#1681109611yescharacteristic
789C4#1681109611yescharacteristic
790C4#1681121111yescharacteristic
791C4#1681121111yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—4242no—
796C2#2027737311yescharacteristic
797C2#2028354711yescharacteristic
798C2#2028356511yescharacteristic
799C2#2028556711yescharacteristic
800C2#2028557611yescharacteristic
801C2#2028576511yescharacteristic
802C2#2028580911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2309C2
socleC23×C53C22×D4
prime radicalC2×#16810757C2
cosocleC22×C4×C53C24
hypercenter#2309D53
hypocenterC53#22056
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #20277408C2semidirect
3. #20275590C2semidirect
4. #20275580C2semidirect
5. #20275415C2semidirect
6. #20275401C2semidirect
7. #20275339C2semidirect
8. #20275332C2semidirect
9. #20275066C2semidirect
10. #20275066C2semidirect
11. #20275037C2semidirect
12. #20274914C2semidirect
13. #20274646C2semidirect
14. #20274481C2semidirect
15. C53×#2309C2semidirect
19. C2×C4×D212C22semidirect
20. #16810757C4semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
29. C2×#13133137C22semidirect
30. C2×#13133137C22semidirect
33. C2×#13133128C22semidirect
34. C2×C4×#88322C22semidirect
35. #16810525C22semidirect
37. #16810521C22semidirect
42. C4×C4⋊Dic53C22semidirect
43. #16810385C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810378C22semidirect
48. #16810378C22semidirect
93. #13133138C2×C4semidirect
94. #13133138C2×C4semidirect
98. C22⋊#88322C2×C4semidirect
111. C22×D4×C53C2×C4semidirect
393. #2309D53semidirect
461. C53#22056semidirect
471. C22×D4C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107572
#202774082
#202755902
#202755802
#202754152
#202754012
#202753392
#202753322
#202750662
#202750372
#202749142
#202746462
#202744812
C53×#23092
#2205653