Finite Group Databasebeta

← C2×#20284627 #28251858

Subgroups — C2×#20284627 #28251858

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811133C211yesmaximal, characteristic
2C2×#117×D53C211yesmaximal, characteristic, complemented
3#20284627C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810964C211yesmaximal, characteristic, complemented
8C2×#16810944C211yesmaximal, characteristic, complemented
9C2×#16810955C211yesmaximal, characteristic, complemented
10C2×#16810935C211yesmaximal, characteristic, complemented
11C2×#16810660C211yesmaximal, characteristic, complemented
12C2×#16810658C211yesmaximal, characteristic, complemented
13C2×#16810616C211yesmaximal, characteristic, complemented
14C2×#16810616C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811133—24no—
22#16811133C2218yes—
23C2×#13133199—21no—
24C2×#13133197C2211yescharacteristic
25C2×#13133196C2211yescharacteristic
26C2×#13133188C2211yescharacteristic
27C2×#13133185—21no—
28C2×D4×Dic53—21no—
29C2×#13133177—21no—
30C2×#13133176C2211yescharacteristic
31C2×#13133175C2211yescharacteristic
32C2×#13133175C2211yescharacteristic
33C2×#13133175C2211yescharacteristic
34C2×#13133174—21no—
35C2×#13133173—21no—
36#117×D53—24no—
37#117×D53C2218yescomplemented
38C2×C4⋊C4×D53C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C22⋊C4×D53—21no—
41C2×C42×D53—21no—
42#16810965C2218yescomplemented
43#16810964C2218yescomplemented
44#16810960C2218yescomplemented
45#16810955C2218yescomplemented
46#16810944C2218yescomplemented
47#16810940C2218yescomplemented
48#16810935C2218yescomplemented
49#16810660C2218yescomplemented
50#16810658C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133150C2211yescharacteristic, complemented
53C2×#13133150C2211yescharacteristic, complemented
54C2×#13133149C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810616C2218yescomplemented
58#16810616C2218yescomplemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133138C2211yescharacteristic, complemented
64C2×#13133138C2211yescharacteristic, complemented
65C2×C22⋊#88322C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C22⋊C8×D53C2218yescomplemented
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53D411yescharacteristic
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947—24no—
81C2×#11719947C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C23×Dic53—21no—
86C23×Dic53D411yescharacteristic
87C22×C4×D53—24no—
88C22×C4×D53—24no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53D411yescharacteristic
92C22×C4×D53D414yes—
93C22×C4×D53D411yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2314yes—
96C22×C4×D53C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—24no—
100C2×C8×D53—24no—
101C2×C8×D53C2314yes—
102C2×C8×D53C2314yes—
103#13133199—28no—
104#13133197—22no—
105#13133197C2314yes—
106#13133196—22no—
107#13133196C2314yes—
108#13133188—22no—
109#13133188C2314yes—
110#13133185—28no—
111D4×Dic53—28no—
112#13133177—28no—
113#13133176—22no—
114#13133176C2314yes—
115#13133175—22no—
116#13133175—22no—
117#13133175—22no—
118#13133175C2314yes—
119#13133175C2314yes—
120#13133175C2314yes—
121#13133174—28no—
122#13133173—28no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C4⋊C4×D53C2314yes—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C22⋊C4×D53—28no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C42×D53—28no—
147#13133151C2314yescomplemented
148#13133150C2314yescomplemented
149#13133150C2314yescomplemented
150#13133149C2314yescomplemented
151#13133148C2314yescomplemented
152#13133148C2314yescomplemented
153#13133142C2314yescomplemented
154#13133142C2314yescomplemented
155#13133140C2314yescomplemented
156#13133140C2314yescomplemented
157#13133138C2314yescomplemented
158#13133138C2314yescomplemented
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162C22×D4×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#121×C53—22no—
168#121×C53C2314yes—
169#117×C53—22no—
170#117×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yescomplemented
178#106×C53C2314yescomplemented
179#102×C53C2314yescomplemented
180#102×C53C2314yescomplemented
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—24no—
185C23×D53—24no—
186C23×D53—42no—
187C23×D53C2×D414yes—
188C23×D53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190C2×D4×C53—24no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—44no—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—44no—
209C22×Dic53—24no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—44no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D414yes—
218C22×Dic53C2×D411yescharacteristic
219#11719947—28no—
220#11719947—28no—
221#11719947—48no—
222C2×C4×D53—24no—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—24no—
226C2×C4×D53—216no—
227C2×C4×D53—28no—
228C2×C4×D53—28no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—44no—
232C2×C4×D53—44no—
233C2×C4×D53C2×D414yes—
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2×D414yes—
236C2×C4×D53C2×D412yes—
237C2×C4×D53#4114yes—
238C2×C4×D53#4114yes—
239C2×C4×D53C2412yes—
240C2×C4×D53C2412yes—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—21no—
244C2×Dic106C2412yes—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53C2412yes—
248C2×C8×C53C2412yes—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—24no—
257C42×C53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322C2412yes—
282C2×#88322C2412yes—
283C8×D53—28no—
284C8×D53—28no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53C22×D412yes—
293C23×C53C22×D411yescharacteristic
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—28no—
299C22×D53—28no—
300C22×D53—44no—
301C22×D53—416no—
302C22×D53#12314yes—
303C22×D53#13514yes—
304C22×D53C22×D412yes—
305C22×D53C22×D412yes—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—48no—
309D4×C53—42no—
310C2×C4×C53—22no—
311C2×C4×C53—24no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D411yescharacteristic
322C2×C4×C53C2×#4112yes—
323C2×C4×C53C2×#4112yes—
324C2×C4×C53C2511yescharacteristic
325C22⋊D53—48no—
326C22⋊D53—48no—
327C2×Dic53—22no—
328C2×Dic53—28no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—48no—
338C2×Dic53#12314yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C4×D53—28no—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—28no—
346C4×D53—48no—
347C4×D53—48no—
348C4×D53#12318yes—
349C4×D53C2×#4114yes—
350C4×D53C2×#4114yes—
351Dic106—22no—
352Dic106—22no—
353Dic106—42no—
354C8×C53—22no—
355C8×C53—22no—
356#88322—22no—
357#88322—22no—
358C2×#3091—531nomaximal, Sylow
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—44no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—84no—
367C22×C53C2×#12312yes—
368C22×C53C2×#13512yes—
369C22×C53#57512yes—
370C22×C53C23×D411yescharacteristic
371C2×D53—28no—
372C2×D53—28no—
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—22no—
377C2×D53—416no—
378C2×D53C2×#12314yes—
379C2×D53C2×#13514yes—
380C4×C53—22no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53C2×#12312yes—
385C4×C53C22×#4111yescharacteristic
386C4×C53C22×#4111yescharacteristic
387Dic53—22no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391Dic53—42no—
392Dic53C2×#12314yes—
393C2×#525—531no—
394C22×#117—531no—
395#3091—5316no—
396C2×#484—531no—
397C2×#481—531no—
398C2×#485—531no—
399C2×#485—531no—
400C2×#482—531no—
401C2×#482D5311yescharacteristic, complemented
402C2×#483—531no—
403C2×#480—531no—
404C2×#427—531no—
405C2×#427—531no—
406C2×#416—531no—
407C2×#416—531no—
408C22×C22⋊C8—531no—
409C2×C53—42no—
410C2×C53—82no—
411C2×C53#309114yescomplemented
412C2×C53C22×#12311yescharacteristic
413C2×C53C22×#13511yescharacteristic
414C2×C53C2×#57511yescharacteristic
415D53—24no—
416D53—24no—
417C22×#41—531no—
418C24×C4—531no—
419C23×C8—531no—
420C23×C8—531no—
421#525—538no—
422#525—1064no—
423C2×#123—1061no—
424C2×C22⋊Q8—531no—
425C2×C22⋊Q8—531no—
426C2×#121—531no—
427C2×#121C2×D5311yescharacteristic
428C2×#120—1061no—
429C2×C4×D4—1061no—
430C2×C4×D4—1061no—
431C2×#117—531no—
432C2×#117—538no—
433C2×#117—531no—
434C2×#117—531no—
435C2×#117—531no—
436C2×#117—1061no—
437C2×#117—1061no—
438C2×#117—1064no—
439C2×#117C2×D5311yescharacteristic
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442C22×C22⋊C4—1061no—
443C22×C42—1061no—
444#485—538no—
445#485—538no—
446#484—538no—
447#483—538no—
448#482—538no—
449#482C2×D5318yescomplemented
450#481—538no—
451#480—538no—
452#427—538no—
453#427—538no—
454C2×#107—531no—
455C2×#107—531no—
456C2×#107—531no—
457C2×#107C2×D5311yescharacteristic, complemented
458C2×#106—531no—
459C2×#106—531no—
460C2×#106—531no—
461C2×#106C2×D5311yescharacteristic, complemented
462#416—538no—
463#416—538no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102C2×D5311yescharacteristic, complemented
471C2×#102C2×D5311yescharacteristic, complemented
472C2×C22⋊C8—531no—
473C2×C22⋊C8—531no—
474C2×C22⋊C8—531no—
475C2×C22⋊C8—538no—
476C2×C22⋊C8C2×D5311yescharacteristic
477C53C2×#309111yescharacteristic, complemented, Sylow
478C25—531no—
479C2×#41—534no—
480C2×#41—1062no—
481C2×#41—1064no—
482C2×#41—1064no—
483C22×Q8—531no—
484C22×D4—21no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4C22×D5311yescharacteristic
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—531no—
491C23×C4—534no—
492C23×C4—531no—
493C23×C4—531no—
494C23×C4—534no—
495C23×C4—1064no—
496C23×C4—1064no—
497C23×C4—1061no—
498C23×C4—1061no—
499C23×C4—1061no—
500C23×C4C22×D5311yescharacteristic
501C22×C8—531no—
502C22×C8—531no—
503C22×C8—534no—
504C22×C8—534no—
505C22×C8—1064no—
506C22×C8—1064no—
507C22×C8C22×D5311yescharacteristic
508C22×C8C22×D5311yescharacteristic
509#123—1068no—
510C22⋊Q8—534no—
511C22⋊Q8—534no—
512C22⋊Q8—1062no—
513C22⋊Q8—1062no—
514#121—22no—
515#121—534no—
516#121—1062no—
517#121C22×D5314yes—
518#120—1068no—
519C4×D4—1068no—
520C4×D4—1068no—
521#117—22no—
522#117—534no—
523#117—534no—
524#117—534no—
525#117—534no—
526#117—1068no—
527#117—1068no—
528#117—1062no—
529#117—1062no—
530#117—1062no—
531#117—1062no—
532#117C22×D5314yes—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—534no—
537C2×C4⋊C4—534no—
538C2×C4⋊C4—1062no—
539C2×C4⋊C4—1062no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1068no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—21no—
558C2×C42—1068no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42—1061no—
563#107—534no—
564#107—534no—
565#107—534no—
566#107C22×D5314yescomplemented
567#106—534no—
568#106—534no—
569#106—534no—
570#106C22×D5314yescomplemented
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#102—534no—
576#102—534no—
577#102C22×D5314yescomplemented
578#102C22×D5314yescomplemented
579C22⋊C8—534no—
580C22⋊C8—534no—
581C22⋊C8—534no—
582C22⋊C8C22×D5314yes—
583C24—21no—
584C24—531no—
585C24—531no—
586C24—534no—
587C24—1064no—
588C24—1064no—
589C24—2122no—
590C24D4×D5311yescharacteristic
591#41—1068no—
592#41—1068no—
593#41—2128no—
594C2×Q8—532no—
595C2×Q8—1061no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—1064no—
604C2×D4—1064no—
605C2×D4—2124no—
606C2×D4—2124no—
607C2×D4C23×D5312yes—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—531no—
614C22×C4—532no—
615C22×C4—534no—
616C22×C4—534no—
617C22×C4—532no—
618C22×C4—534no—
619C22×C4—531no—
620C22×C4—534no—
621C22×C4—532no—
622C22×C4—534no—
623C22×C4—532no—
624C22×C4—1064no—
625C22×C4—10616no—
626C22×C4—1068no—
627C22×C4—1068no—
628C22×C4—1064no—
629C22×C4—1064no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—2124no—
640C22×C4—2124no—
641C22×C4—2124no—
642C22×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—532no—
649C2×C8—532no—
650C2×C8—1068no—
651C2×C8—1068no—
652C2×C8—1062no—
653C2×C8—1062no—
654C2×C8C23×D5312yes—
655C2×C8C23×D5312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—532no—
660C4⋊C4—532no—
661C4⋊C4—532no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1061no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4—1064no—
669C4⋊C4C23×D5312yes—
670C4⋊C4C23×D5312yes—
671C4⋊C4C23×D5312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C42—24no—
682C42—1064no—
683C42—1064no—
684C42—1064no—
685C42—1064no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—534no—
694C23—534no—
695C23—532no—
696C23—532no—
697C23—1068no—
698C23—1068no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—1062no—
703C23—2124no—
704C23—21216no—
705C23C2×D4×D5312yes—
706C23C2×D4×D5311yescharacteristic
707Q8—1062no—
708Q8—1062no—
709Q8—2122no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—2128no—
715D4—2128no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—534no—
727C2×C4—532no—
728C2×C4—538no—
729C2×C4—534no—
730C2×C4—534no—
731C2×C4—532no—
732C2×C4—1068no—
733C2×C4—1068no—
734C2×C4—1068no—
735C2×C4—1062no—
736C2×C4—1064no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—2128no—
744C2×C4—2128no—
745C2×C4—2128no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4C2×D4×D5312yes—
751C2×C4C2×D4×D5311yescharacteristic
752C2×C4#41×D5312yes—
753C2×C4#41×D5312yes—
754C2×C4C24×D5311yescharacteristic
755C8—22no—
756C8—22no—
757C8—1062no—
758C8—1062no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—534no—
768C22—534no—
769C22—1062no—
770C22—1062no—
771C22—1062no—
772C22—1062no—
773C22—1068no—
774C22—1068no—
775C22—21216no—
776C22#123×D5312yes—
777C22#135×D5312yes—
778C22#1681141912yes—
779C22C22×D4×D5311yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—534no—
785C4—1062no—
786C4—2122no—
787C4—2122no—
788C4—2122no—
789C4—2122no—
790C4#123×D5312yes—
791C4C2×#41×D5311yescharacteristic
792C4C2×#41×D5311yescharacteristic
793C2—42no—
794C2—82no—
795C2—1064no—
796C2—1064no—
797C2#2028462714yesdirect product factor
798C2C2×#123×D5311yescharacteristic
799C2C2×#135×D5311yescharacteristic
800C2C2×#1681141911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
prime radicalC2×#16811133C2
hypercenterC2×#482D53
hypocenterC53C2×#3091
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#117×D53C2semidirect
3. #20284627C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810964C2semidirect
8. C2×#16810944C2semidirect
9. C2×#16810955C2semidirect
10. C2×#16810935C2semidirect
11. C2×#16810660C2semidirect
12. C2×#16810658C2semidirect
13. C2×#16810616C2semidirect
14. C2×#16810616C2semidirect
15. C2×C22⋊C8×D53C2semidirect
16. C2×C53×#482C2semidirect
37. #117×D53C22semidirect
42. #16810965C22semidirect
43. #16810964C22semidirect
44. #16810960C22semidirect
45. #16810955C22semidirect
46. #16810944C22semidirect
47. #16810940C22semidirect
48. #16810935C22semidirect
49. #16810660C22semidirect
50. #16810658C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133150C22semidirect
53. C2×#13133150C22semidirect
54. C2×#13133149C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810616C22semidirect
58. #16810616C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133140C22semidirect
62. C2×#13133140C22semidirect
63. C2×#13133138C22semidirect
64. C2×#13133138C22semidirect
68. C22⋊C8×D53C22semidirect
71. C53×#482C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
147. #13133151C23semidirect
148. #13133150C23semidirect
149. #13133150C23semidirect
150. #13133149C23semidirect
151. #13133148C23semidirect
152. #13133148C23semidirect
153. #13133142C23semidirect
154. #13133142C23semidirect
155. #13133140C23semidirect
156. #13133140C23semidirect
157. #13133138C23semidirect
158. #13133138C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. #102×C53C23semidirect
180. #102×C53C23semidirect
401. C2×#482D53semidirect
411. C2×C53#3091semidirect
449. #482C2×D53semidirect
457. C2×#107C2×D53semidirect
461. C2×#106C2×D53semidirect
470. C2×#102C2×D53semidirect
471. C2×#102C2×D53semidirect
477. C53C2×#3091semidirect
566. #107C22×D53semidirect
570. #106C22×D53semidirect
577. #102C22×D53semidirect
578. #102C22×D53semidirect
797. C2#20284627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111332
C2×#117×D532
#202846272
C2×#168109602
C2×#168109402
C2×#168109652
C2×#168109642
C2×#168109442
C2×#168109552
C2×#168109352
C2×#168106602
C2×#168106582
C2×#168106162
C2×C22⋊C8×D532
C2×C53×#4822
C2×#309153