Finite Group Databasebeta

← #27400313

Subgroups — #27400313

Order 13568.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811308C211yesmaximal, characteristic
2C2×C8×C22⋊D53C211yesmaximal, characteristic
3#20277640C211yesmaximal, characteristic
4#20275678C211yesmaximal, characteristic, complemented
5#20275671C211yesmaximal, characteristic, complemented
6#20275138C211yesmaximal, characteristic, complemented
7#20275137C211yesmaximal, characteristic, complemented
8#20275026C211yesmaximal, characteristic, complemented
9#20275022C211yesmaximal, characteristic, complemented
10#20274808C211yesmaximal, characteristic, complemented
11#20274801C211yesmaximal, characteristic, complemented
12#20274729C211yesmaximal, characteristic, complemented
13#20274534C211yesmaximal, characteristic, complemented
14#20274430C211yesmaximal, characteristic, complemented
15C2×C53×#340C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17#16811308—24no—
18#16811308C418yescomplemented
19C2×#13133212—21no—
20C2×#13133208C2211yescharacteristic
21C2×#13133207—21no—
22C2×#13133200—21no—
23C2×#13133197C2211yescharacteristic
24C2×#13133196C2211yescharacteristic
25C2×#13133182C2211yescharacteristic
26C2×C4×C22⋊D53C2211yescharacteristic
27C2×#13133176—21no—
28C2×#13133175C2211yescharacteristic
29C2×#13133175C2211yescharacteristic
30C8×C22⋊D53—24no—
31C2×#13133146C2211yescharacteristic
32C2×#13133142C2211yescharacteristic
33C2×#13133142C2211yescharacteristic
34C2×#13133140C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×C8×Dic53C2211yescharacteristic
39#16810513—21no—
40#16810504—21no—
41#16810502—21no—
42#16810488C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810480C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C4×C22⋊Dic53—21no—
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C22×C4⋊C4×C53C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#340C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×Dic106C2311yescharacteristic
63C22×C22⋊D53D411yescharacteristic
64C22×C4×D53C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67C2×C8×D53—22no—
68C2×C8×D53—22no—
69C2×C8×D53—41no—
70#13133212—28no—
71#13133208—22no—
72#13133208C2×C414yescomplemented
73#13133207—28no—
74#13133200—28no—
75#13133197—22no—
76#13133197C2×C414yescomplemented
77#13133196—22no—
78#13133196C2×C414yes—
79#13133182—22no—
80#13133182C2×C414yescomplemented
81C4×C22⋊D53C2×C414yes—
82C4×C22⋊D53D414yes—
83#13133176—28no—
84#13133175—22no—
85#13133175—22no—
86#13133175—41no—
87#13133175C2×C414yescomplemented
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×#11719919—21no—
94C2×#11719919—21no—
95C2×#11719919—21no—
96C2×#11719919D411yescharacteristic
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53D411yescharacteristic
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C2×#11719921D411yescharacteristic
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109C2×C4×Dic53C2311yescharacteristic
110#13133146—22no—
111#13133142—22no—
112#13133142—41no—
113#13133140—22no—
114#13133140—41no—
115C22⋊#88322—22no—
116#13133129—22no—
117C8×Dic53—22no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123C23×C4×C53—21no—
124C23×C4×C53—21no—
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53—22no—
127C22×C8×C53—22no—
128C22×C8×C53—41no—
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53—41no—
136C2×C4⋊C4×C53C2×C414yes—
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141C24×C53C2×D411yescharacteristic
142C23×D53C2×D411yescharacteristic
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—24no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—81no—
157C22×C4×C53C22×C412yes—
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2411yescharacteristic
161C2×C22⋊D53—22no—
162C2×C22⋊D53—22no—
163C2×C22⋊D53C22⋊C414yes—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53C2×D411yescharacteristic
169C22×Dic53C2×D411yescharacteristic
170C22×Dic53C2×D411yescharacteristic
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53C22×C412yes—
176C2×C4×D53C2×D412yes—
177C2×Dic106—21no—
178C2×Dic106—21no—
179C2×Dic106—21no—
180C2×Dic106—21no—
181C2×Dic106—21no—
182C2×Dic106C22×C412yes—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—44no—
189C2×C8×C53#4112yes—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—42no—
197C4⋊C4×C53C22×C412yes—
198C4⋊C4×C53C22×C412yes—
199C4⋊C4×C53#4112yes—
200C22⋊Dic53—24no—
201C22⋊Dic53—42no—
202C22⋊Dic53C22⋊C414yes—
203#11719921—24no—
204#11719921—24no—
205#11719921—42no—
206#11719921—81no—
207#11719921C22⋊C414yes—
208C4⋊Dic53—21no—
209C4⋊Dic53—24no—
210C4⋊Dic53—24no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53C22×C412yes—
216#11719919—24no—
217#11719919—24no—
218#11719919—24no—
219#11719919C22⋊C414yes—
220C4×Dic53—24no—
221C4×Dic53—24no—
222C4×Dic53—42no—
223C4×Dic53—81no—
224C4×Dic53C22×C412yes—
225C4×Dic53C2×D412yes—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C8×D53—44no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53C2×C22⋊C412yes—
238C23×C53#13512yes—
239C23×C53#13512yes—
240C23×C53C22×D411yescharacteristic
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53C2×C22⋊C412yes—
248C2×C4×C53—21no—
249C2×C4×C53—21no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—48no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—84no—
268C2×C4×C53C2×C22⋊C412yes—
269C2×C4×C53C23×C411yescharacteristic
270C2×C4×C53C22×D411yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53H(5,𝔽2)11yescharacteristic
274C2×C4×C532−1+411yescharacteristic
275C22⋊D53—28no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53C2×C22⋊C412yes—
295C2×Dic53C2×C22⋊C412yes—
296C2×Dic53C2×C22⋊C412yes—
297C4×D53—22no—
298C4×D53—22no—
299C4×D53—22no—
300C4×D53—22no—
301Dic106—22no—
302Dic106—22no—
303Dic106—41no—
304Dic106—41no—
305C8×C53—22no—
306C8×C53—41no—
307#88322—41no—
308#88322—41no—
309#22486—531nomaximal, Sylow
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53#41614yes—
317C22×C53C22×C22⋊C411yescharacteristic
318C22×C53#54611yescharacteristic
319C22×C53#54711yescharacteristic
320C22×C53C2×#13511yescharacteristic
321C22×C53C2×#13511yescharacteristic
322C22×C53#57711yescharacteristic
323C22×C53#57811yescharacteristic
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—41no—
328C2×D53—41no—
329C2×D53—41no—
330C2×D53—41no—
331C4×C53—22no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53—81no—
336C4×C53C4×#4111yescharacteristic
337C4×C53#52011yescharacteristic
338C4×C53#54611yescharacteristic
339C4×C53#54711yescharacteristic
340Dic53—22no—
341Dic53—22no—
342Dic53—22no—
343Dic53—42no—
344Dic53—42no—
345Dic53—81no—
346Dic53—81no—
347C2×#552—531no—
348C2×C8×D4—531no—
349#2352—531no—
350#1991—531no—
351#1989—531no—
352#1892—531no—
353#1892—531no—
354#1873—531no—
355#1872—531no—
356#1825—531no—
357#1823—531no—
358#1805—531no—
359C4×#103—531no—
360#1735—531no—
361C2×#340D5311yescharacteristic, complemented
362C2×C53—24no—
363C2×C53#233911yescharacteristic
364C2×C53C2×#41611yescharacteristic
365C2×C53#289811yescharacteristic
366C2×C53#329611yescharacteristic
367C2×C53#330011yescharacteristic
368C2×C53#333611yescharacteristic
369C2×C53#333711yescharacteristic
370D53—42no—
371C23×C8—531no—
372C23×C8C2×D5311yescharacteristic
373#552—538no—
374#552—1064no—
375C2×#126—1061no—
376C2×#125—531no—
377C2×#125—1061no—
378C2×#123—1061no—
379C2×C22⋊Q8—531no—
380C2×C22⋊Q8—531no—
381C2×C4×Q8—531no—
382C2×C4×D4—531no—
383C2×#117—531no—
384C2×#117—531no—
385C2×#117—1061no—
386C22×C4⋊C4C2×D5311yescharacteristic
387C22×C4⋊C4C2×D5311yescharacteristic
388C8×D4—1064no—
389C2×C4⋊C8—531no—
390C2×#103—531no—
391C2×#103—531no—
392C2×#103—531no—
393C2×#103—531no—
394C2×C22⋊C8—531no—
395C2×C22⋊C8—531no—
396C2×C4×C8—531no—
397#388—1061no—
398#387—1061no—
399#386—1061no—
400#382—531no—
401#380—531no—
402#380—531no—
403C4×C4⋊C4—531no—
404C4×C22⋊C4—1061no—
405#340—531no—
406#340—531no—
407#340—531no—
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340C2×D5311yescharacteristic
414#340C2×D5311yescharacteristic
415#340C2×D5311yescharacteristic
416#340C2×D5311yescharacteristic
417C53#2248611yescharacteristic, complemented, Sylow
418C22×Q8—531no—
419C22×D4—531no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—531no—
423C23×C4C22×D5311yescharacteristic
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—531no—
428C22×C8—531no—
429C22×C8—1062no—
430C22×C8—1062no—
431C22×C8—2121no—
432C22×C8C22×D5311yescharacteristic
433C22×C8C22×D5311yescharacteristic
434#126—1068no—
435#125—534no—
436#125—1062no—
437#125—1068no—
438#123—1068no—
439C22⋊Q8—534no—
440C22⋊Q8—534no—
441C22⋊Q8—1062no—
442C22⋊Q8—1062no—
443C4×Q8—534no—
444C4×Q8—1062no—
445C4×D4—534no—
446C4×D4—534no—
447#117—534no—
448#117—1068no—
449#117—1062no—
450#117—1062no—
451#117—2121no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—1061no—
462C2×C4⋊C4—1061no—
463C2×C4⋊C4—1061no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4C4×D5314yes—
467C2×C4⋊C4C22×D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C4⋊C4C22×D5311yescharacteristic
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C22⋊C4—531no—
472C2×C22⋊C4—531no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C22⋊C4—1061no—
479C2×C42—531no—
480C2×C42—1061no—
481C2×C42—1061no—
482C2×C42—1061no—
483C2×C42—1061no—
484C4⋊C8—1062no—
485#103—1062no—
486#103—1062no—
487#103—2121no—
488#103—2121no—
489C22⋊C8—1062no—
490C22⋊C8—1062no—
491C4×C8—1062no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497C24—531no—
498C24D4×D5311yescharacteristic
499C2×Q8—532no—
500C2×Q8—1061no—
501C2×Q8—1061no—
502C2×Q8—1061no—
503C2×Q8—1061no—
504C2×Q8—1061no—
505C2×D4—534no—
506C2×D4—1062no—
507C2×D4—1062no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4C2×C4×D5312yes—
536C22×C4D4×D5311yescharacteristic
537C22×C4D4×D5312yes—
538C22×C4C23×D5311yescharacteristic
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—44no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—2124no—
552C2×C8#1171994512yes—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—534no—
561C4⋊C4—532no—
562C4⋊C4—1064no—
563C4⋊C4—1064no—
564C4⋊C4—1064no—
565C4⋊C4—1064no—
566C4⋊C4—1064no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4—1061no—
572C4⋊C4C2×C4×D5312yes—
573C4⋊C4C2×C4×D5312yes—
574C4⋊C4#1171994512yes—
575C22⋊C4—534no—
576C22⋊C4—534no—
577C22⋊C4—1064no—
578C22⋊C4—1064no—
579C22⋊C4—1064no—
580C22⋊C4—4241no—
581C22⋊C4—2122no—
582C22⋊C4—2122no—
583C42—532no—
584C42—532no—
585C42—1064no—
586C42—1064no—
587C42—4241no—
588C42—2122no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—532no—
594C23—1061no—
595C23—1061no—
596C23—1061no—
597C23—1061no—
598C23—1061no—
599C23—1061no—
600C23C22⋊C4×D5312yes—
601C23#1313323612yes—
602C23#1313323812yes—
603C23C2×D4×D5311yescharacteristic
604Q8—1062no—
605Q8—1062no—
606Q8—2121no—
607Q8—2121no—
608D4—1068no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—48no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4—532no—
630C2×C4—532no—
631C2×C4—532no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4C22⋊C4×D5312yes—
655C2×C4C22×C4×D5311yescharacteristic
656C2×C4C2×D4×D5311yescharacteristic
657C2×C4C2×#1171994511yescharacteristic
658C2×C4C2×#1171994511yescharacteristic
659C2×C4#1313326211yescharacteristic
660C2×C4#1313326511yescharacteristic
661C8—22no—
662C8—41no—
663C8—2121no—
664C8—2121no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—1062no—
672C22—1062no—
673C22—1062no—
674C22—2121no—
675C22—2121no—
676C22—2121no—
677C22—2121no—
678C22#1681061614yes—
679C22C2×C22⋊C4×D5311yescharacteristic
680C22#1681126311yescharacteristic
681C22#1681127411yescharacteristic
682C22C2×#1313323611yescharacteristic
683C22C2×#1313323811yescharacteristic
684C22#1681142911yescharacteristic
685C22#1681143611yescharacteristic
686C4—22no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—1062no—
692C4—1062no—
693C4—1062no—
694C4—4241no—
695C4—4241no—
696C4—2122no—
697C4—2122no—
698C4C4×#1171994511yescharacteristic
699C4#1681110411yescharacteristic
700C4#1681126311yescharacteristic
701C4#1681127411yescharacteristic
702C2—24no—
703C2—2122no—
704C2#2027754211yescharacteristic
705C2C2×#1681061611yescharacteristic
706C2#2028324311yescharacteristic
707C2#2028654611yescharacteristic
708C2#2028659811yescharacteristic
709C2#2028707911yescharacteristic
710C2#2028709011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#340C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenterC2×#340D53
hypocenterC53#22486
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #20275678C2semidirect
5. #20275671C2semidirect
6. #20275138C2semidirect
7. #20275137C2semidirect
8. #20275026C2semidirect
9. #20275022C2semidirect
10. #20274808C2semidirect
11. #20274801C2semidirect
12. #20274729C2semidirect
13. #20274534C2semidirect
14. #20274430C2semidirect
15. C2×C53×#340C2semidirect
18. #16811308C4semidirect
72. #13133208C2×C4semidirect
76. #13133197C2×C4semidirect
80. #13133182C2×C4semidirect
87. #13133175C2×C4semidirect
361. C2×#340D53semidirect
417. C53#22486semidirect

Maximal subgroups

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

subgroupindex
C2×#168113082
C2×C8×C22⋊D532
#202776402
#202756782
#202756712
#202751382
#202751372
#202750262
#202750222
#202748082
#202748012
#202747292
#202745342
#202744302
C2×C53×#3402
#2248653