Finite Group Databasebeta

← C2×#20284633 #28251864

Subgroups — C2×#20284633 #28251864

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×#16811136C211yesmaximal, characteristic
2C2×#117×D53C211yesmaximal, characteristic, complemented
3#20284633C2116yesmaximal, direct product factor
4C2×#16810957C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810961C211yesmaximal, characteristic, complemented
7C2×#16810948C211yesmaximal, characteristic, complemented
8C2×#16810947C211yesmaximal, characteristic, complemented
9C2×#16810952C211yesmaximal, characteristic, complemented
10C2×#16810938C211yesmaximal, characteristic, complemented
11C2×#16810660C211yesmaximal, characteristic, complemented
12C2×#16810658C211yesmaximal, characteristic, complemented
13C2×#16810618C211yesmaximal, characteristic, complemented
14C2×#16810618C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811136—24no—
22#16811136C2218yes—
23C2×#13133202—21no—
24C2×#13133193C2211yescharacteristic
25C2×#13133192C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×#13133187—21no—
28C2×#13133179—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#16810961C2218yescomplemented
43#16810957C2218yescomplemented
44#16810952C2218yescomplemented
45#16810948C2218yescomplemented
46#16810947C2218yescomplemented
47#16810943C2218yescomplemented
48#16810938C2218yescomplemented
49#16810660C2218yescomplemented
50#16810658C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133150C2211yescharacteristic, complemented
53C2×#13133150C2211yescharacteristic, complemented
54C2×#13133149C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810618C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65C2×C22⋊#88322C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C22⋊C8×D53C2218yescomplemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53D411yescharacteristic
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949—24no—
81C2×#11719949C2314yes—
82C22×D212—21no—
83C22×D212—21no—
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C23×Dic53D411yescharacteristic
87C22×C4×D53—24no—
88C22×C4×D53—24no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53D411yescharacteristic
93C22×C4×D53D414yes—
94C22×C4×D53D411yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C22×C4×D53C2314yes—
97C22×C4×D53C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C2×C8×D53—24no—
101C2×C8×D53—24no—
102C2×C8×D53C2314yes—
103C2×C8×D53C2314yes—
104#13133202—28no—
105#13133193—22no—
106#13133193C2314yes—
107#13133192—22no—
108#13133192C2314yes—
109#13133191—22no—
110#13133191C2314yes—
111#13133187—28no—
112#13133179—28no—
113#13133177—28no—
114#13133176—22no—
115#13133176C2314yes—
116#13133175—22no—
117#13133175—22no—
118#13133175—22no—
119#13133175C2314yes—
120#13133175C2314yes—
121#13133175C2314yes—
122#13133174—28no—
123#13133173—28no—
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×#11719921—21no—
136C2×#11719921—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#13133141C2314yescomplemented
154#13133141C2314yescomplemented
155#13133139C2314yescomplemented
156#13133139C2314yescomplemented
157#13133137C2314yescomplemented
158#13133137C2314yescomplemented
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53C2314yes—
168#117×C53—22no—
169#117×C53C2314yes—
170C2×C4⋊C4×C53—21no—
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#103×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—24no—
184C23×D53—24no—
185C23×D53—21no—
186C23×D53—42no—
187C23×D53C2×D414yes—
188C23×D53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C22×Dic53—24no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D414yes—
212C22×Dic53C2×D411yescharacteristic
213#11719949—28no—
214#11719949—28no—
215#11719949—48no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—24no—
219C2×D212—24no—
220C2×D212—21no—
221C2×D212—44no—
222C2×D212—44no—
223C2×D212C2412yes—
224C2×C4×D53—24no—
225C2×C4×D53—22no—
226C2×C4×D53—22no—
227C2×C4×D53—24no—
228C2×C4×D53—216no—
229C2×C4×D53—28no—
230C2×C4×D53—28no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×C4×D53—44no—
237C2×C4×D53C2×D414yes—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2×D414yes—
240C2×C4×D53C2×D412yes—
241C2×C4×D53#4114yes—
242C2×C4×D53#4114yes—
243C2×C4×D53C2412yes—
244C2×C4×D53C2412yes—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53C2412yes—
248C2×C8×C53C2412yes—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C42×C53—24no—
259C22⋊Dic53—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
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×C53C22×D412yes—
289C23×C53C22×D411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—28no—
295C22×D53—28no—
296C22×D53—22no—
297C22×D53—44no—
298C22×D53—416no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53#12314yes—
303C22×D53#13514yes—
304C22×D53C22×D412yes—
305C22×D53C22×D412yes—
306Q8×C53—22no—
307Q8×C53—22no—
308Q8×C53—42no—
309C2×C4×C53—22no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
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×C53—42no—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4112yes—
324C2×C4×C53C2×#4112yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—48no—
327C2×Dic53—22no—
328C2×Dic53—28no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53#12314yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—22no—
339D212—22no—
340D212—48no—
341D212—48no—
342D212—42no—
343C4×D53—28no—
344C4×D53—24no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—28no—
348C4×D53—48no—
349C4×D53—48no—
350C4×D53—48no—
351C4×D53#12318yes—
352C4×D53C2×#4114yes—
353C4×D53C2×#4114yes—
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×C53C2×#12312yes—
364C22×C53C2×#13512yes—
365C22×C53#57512yes—
366C22×C53C23×D411yescharacteristic
367C2×D53—28no—
368C2×D53—28no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—416no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—84no—
378C2×D53C2×#12314yes—
379C2×D53C2×#13514yes—
380C4×C53—22no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53C2×#12312yes—
386C4×C53C22×#4111yescharacteristic
387C4×C53C22×#4111yescharacteristic
388Dic53—22no—
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×#485D5311yescharacteristic, complemented
400C2×#482—531no—
401C2×#482—531no—
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#309114yescomplemented
411C2×C53C22×#12311yescharacteristic
412C2×C53C22×#13511yescharacteristic
413C2×C53C2×#57511yescharacteristic
414D53—24no—
415D53—24no—
416D53—82no—
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⋊Q8C2×D5311yescharacteristic
426C2×#121—531no—
427C2×#121—531no—
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#485C2×D5318yescomplemented
446#484—538no—
447#483—538no—
448#482—538no—
449#482—538no—
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×#103C2×D5311yescharacteristic, complemented
467C2×#103C2×D5311yescharacteristic, complemented
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
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×Q8C22×D5311yescharacteristic
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4—1061no—
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—22no—
511C22⋊Q8—534no—
512C22⋊Q8—1062no—
513C22⋊Q8C22×D5314yes—
514#121—534no—
515#121—534no—
516#121—1062no—
517#121—1062no—
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—21no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—534no—
538C2×C4⋊C4—534no—
539C2×C4⋊C4—1062no—
540C2×C4⋊C4—1062no—
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#103C22×D5314yescomplemented
574#103C22×D5314yescomplemented
575#102—534no—
576#102—534no—
577#102—534no—
578#102—534no—
579C22⋊C8—534no—
580C22⋊C8—534no—
581C22⋊C8—534no—
582C22⋊C8C22×D5314yes—
583C24—531no—
584C24—531no—
585C24—534no—
586C24—1064no—
587C24—1064no—
588C24—1061no—
589C24—2122no—
590C24D4×D5311yescharacteristic
591#41—1068no—
592#41—1068no—
593#41—2128no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D5312yes—
598C2×D4—532no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1061no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—2124no—
606C2×D4—2124no—
607C2×D4—2124no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—531no—
615C22×C4—532no—
616C22×C4—534no—
617C22×C4—534no—
618C22×C4—532no—
619C22×C4—534no—
620C22×C4—531no—
621C22×C4—534no—
622C22×C4—532no—
623C22×C4—534no—
624C22×C4—532no—
625C22×C4—1064no—
626C22×C4—10616no—
627C22×C4—1068no—
628C22×C4—1068no—
629C22×C4—1064no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1064no—
634C22×C4—1062no—
635C22×C4—1062no—
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—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—532no—
661C4⋊C4—532no—
662C4⋊C4—532no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4—1061no—
667C4⋊C4—1061no—
668C4⋊C4—1061no—
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—534no—
690C23—534no—
691C23—532no—
692C23—532no—
693C23—1068no—
694C23—1068no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23—2124no—
701C23—21216no—
702C23—2122no—
703C23—2122no—
704C23—2122no—
705C23C2×D4×D5312yes—
706C23C2×D4×D5311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—1062no—
711D4—1062no—
712D4—2128no—
713D4—2128no—
714D4—2128no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—534no—
729C2×C4—532no—
730C2×C4—538no—
731C2×C4—534no—
732C2×C4—534no—
733C2×C4—532no—
734C2×C4—1068no—
735C2×C4—1068no—
736C2×C4—1068no—
737C2×C4—1062no—
738C2×C4—1064no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—2128no—
745C2×C4—2128no—
746C2×C4—2128no—
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—534no—
764C22—534no—
765C22—1062no—
766C22—1062no—
767C22—1062no—
768C22—1062no—
769C22—1068no—
770C22—1068no—
771C22—4244no—
772C22—21216no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22#123×D5312yes—
777C22#135×D5312yes—
778C22#1681142212yes—
779C22C22×D4×D5311yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—534no—
786C4—1062no—
787C4—2122no—
788C4—2122no—
789C4—2122no—
790C4#123×D5312yes—
791C4C2×#41×D5311yescharacteristic
792C4C2×#41×D5311yescharacteristic
793C2—42no—
794C2—1064no—
795C2—1064no—
796C2—4242no—
797C2#2028463314yesdirect product factor
798C2C2×#123×D5311yescharacteristic
799C2C2×#135×D5311yescharacteristic
800C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC2×#16811136C2
hypercenterC2×#485D53
hypocenterC53C2×#3091
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#117×D53C2semidirect
3. #20284633C2direct (N × H)
4. C2×#16810957C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810961C2semidirect
7. C2×#16810948C2semidirect
8. C2×#16810947C2semidirect
9. C2×#16810952C2semidirect
10. C2×#16810938C2semidirect
11. C2×#16810660C2semidirect
12. C2×#16810658C2semidirect
13. C2×#16810618C2semidirect
14. C2×#16810618C2semidirect
15. C2×C22⋊C8×D53C2semidirect
16. C2×C53×#485C2semidirect
37. #117×D53C22semidirect
42. #16810961C22semidirect
43. #16810957C22semidirect
44. #16810952C22semidirect
45. #16810948C22semidirect
46. #16810947C22semidirect
47. #16810943C22semidirect
48. #16810938C22semidirect
49. #16810660C22semidirect
50. #16810658C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133150C22semidirect
53. C2×#13133150C22semidirect
54. C2×#13133149C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810618C22semidirect
58. #16810618C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133141C22semidirect
61. C2×#13133139C22semidirect
62. C2×#13133139C22semidirect
63. C2×#13133137C22semidirect
64. C2×#13133137C22semidirect
68. C22⋊C8×D53C22semidirect
71. C53×#485C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
147. #13133151C23semidirect
148. #13133150C23semidirect
149. #13133150C23semidirect
150. #13133149C23semidirect
151. #13133148C23semidirect
152. #13133148C23semidirect
153. #13133141C23semidirect
154. #13133141C23semidirect
155. #13133139C23semidirect
156. #13133139C23semidirect
157. #13133137C23semidirect
158. #13133137C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. #103×C53C23semidirect
180. #103×C53C23semidirect
399. C2×#485D53semidirect
410. C2×C53#3091semidirect
445. #485C2×D53semidirect
457. C2×#107C2×D53semidirect
461. C2×#106C2×D53semidirect
466. C2×#103C2×D53semidirect
467. C2×#103C2×D53semidirect
477. C53C2×#3091semidirect
566. #107C22×D53semidirect
570. #106C22×D53semidirect
573. #103C22×D53semidirect
574. #103C22×D53semidirect
797. C2#20284633direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111362
C2×#117×D532
#202846332
C2×#168109572
C2×#168109432
C2×#168109612
C2×#168109482
C2×#168109472
C2×#168109522
C2×#168109382
C2×#168106602
C2×#168106582
C2×#168106182
C2×C22⋊C8×D532
C2×C53×#4852
C2×#309153