Finite Group Databasebeta

← C2×#20284701 #28251950

Subgroups — C2×#20284701 #28251950

Order 13568.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811203C211yesmaximal, characteristic
2C2×#16811103C211yesmaximal, characteristic, complemented
3#20284701C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810950C211yesmaximal, characteristic, complemented
8C2×#16810947C211yesmaximal, characteristic, complemented
9C2×#16810952C211yesmaximal, characteristic, complemented
10C2×#16810951C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic, complemented
12C2×#106×D53C211yesmaximal, characteristic, complemented
13C2×#16810623C211yesmaximal, characteristic, complemented
14C2×#16810618C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811203—24no—
22#16811203C2218yes—
23C2×#13133195—21no—
24C2×#13133193C2211yescharacteristic
25C2×#13133192—21no—
26C2×#13133192C2211yescharacteristic
27C2×#13133191C2211yescharacteristic
28C2×#13133190—21no—
29C2×#13133190—21no—
30#16811103—24no—
31#16811103C2218yescomplemented
32C2×C4×Dic106—21no—
33C2×C4×D212—21no—
34C2×#13133177—21no—
35C2×#13133177—21no—
36C2×#13133175C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C22×C4⋊Dic53C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810962C2218yescomplemented
43#16810952C2218yescomplemented
44#16810951C2218yescomplemented
45#16810950C2218yescomplemented
46#16810947C2218yescomplemented
47#16810943C2218yescomplemented
48#16810942C2218yescomplemented
49#16810664C2218yescomplemented
50C2×#13133150C2211yescharacteristic
51C2×#13133149C2211yescharacteristic
52C2×#13133149C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56#106×D53C2218yescomplemented
57#16810623C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—24no—
80C2×#11719949C2314yes—
81C2×#11719945—24no—
82C2×#11719945—24no—
83C2×#11719945D414yes—
84C2×#11719945C2314yes—
85C22×Dic106D411yescharacteristic
86C22×D212—21no—
87C22×D212—21no—
88C22×D212D411yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53D411yescharacteristic
92C22×C22⋊D53D411yescharacteristic
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C22×C4×D53C2311yescharacteristic
99C22×C4×D53C2311yescharacteristic
100C2×#11719912—24no—
101C2×#11719912C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C2×C8×D53—24no—
105C2×C8×D53C2314yes—
106#13133195—28no—
107#13133193—22no—
108#13133193C2314yes—
109#13133192—28no—
110#13133192—22no—
111#13133192C2314yes—
112#13133191—22no—
113#13133191C2314yes—
114#13133190—28no—
115#13133190—28no—
116C4×Dic106—28no—
117C4×D212—28no—
118#13133177—28no—
119#13133177—28no—
120#13133175—22no—
121#13133175—22no—
122#13133175C2314yes—
123#13133175C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—22no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2314yes—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53—22no—
136C4⋊C4×D53—22no—
137C4⋊C4×D53C2314yes—
138C4⋊C4×D53C2314yes—
139C4⋊C4×D53C2314yes—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147#13133150C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133148C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
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×C53C2314yes—
178#106×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C23×D53C2×D411yescharacteristic
186C2×Q8×C53—21no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53C2412yes—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—82no—
204C2×C22⋊D53C2×D414yes—
205C2×C22⋊D53C2×D414yes—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—82no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213#11719949—28no—
214#11719949—28no—
215#11719949—48no—
216#11719945—216no—
217#11719945—28no—
218#11719945—28no—
219C2×D212—24no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—24no—
223C2×D212—21no—
224C2×D212—24no—
225C2×D212—44no—
226C2×D212—82no—
227C2×D212C2×D414yes—
228C2×D212C2412yes—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—44no—
236C2×C4×D53—82no—
237C2×C4×D53—82no—
238C2×C4×D53—82no—
239C2×C4×D53C2×D412yes—
240C2×C4×D53C2×D412yes—
241C2×C4×D53#4114yes—
242C2×C4×D53#4114yes—
243C2×C4×D53C2412yes—
244C2×C4×D53C2412yes—
245C2×Dic106—24no—
246C2×Dic106C2×D414yes—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C42×C53—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⋊Dic53—24no—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322C2412yes—
282C2×#88322C2412yes—
283#11719912—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—22no—
295C22×D53—22no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53#12314yes—
300C22×D53C22×D412yes—
301C22×D53C22×D412yes—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—42no—
305C2×C4×C53—22no—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C2×#4112yes—
320C2×C4×C53C2×#4112yes—
321C2×C4×C53C2511yescharacteristic
322C22⋊D53—28no—
323C22⋊D53—28no—
324C22⋊D53—84no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—84no—
333C2×Dic53#12314yes—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336D212—28no—
337D212—22no—
338D212—22no—
339D212—48no—
340D212—42no—
341D212—84no—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—48no—
346C4×D53—84no—
347C4×D53—84no—
348C4×D53—84no—
349C4×D53#12318yes—
350C4×D53C2×#4114yes—
351C4×D53C2×#4114yes—
352Dic106—28no—
353C8×C53—22no—
354C8×C53—22no—
355#88322—22no—
356#88322—22no—
357C2×#3099—531nomaximal, Sylow
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—44no—
362C22×C53C2×#12312yes—
363C22×C53#57712yes—
364C22×C53#57712yes—
365C22×C53C23×D411yescharacteristic
366C2×D53—28no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—44no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—84no—
377C2×D53C2×#12314yes—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53C2×#12312yes—
384C4×C53C22×#4111yescharacteristic
385C4×C53C22×#4111yescharacteristic
386Dic53—22no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53C2×#12314yes—
391C2×#537—531no—
392C2×#520—531no—
393#3099—5316no—
394C2×#481—531no—
395C2×#481—531no—
396C2×#485—531no—
397C2×#485D5311yescharacteristic, complemented
398C2×#482—531no—
399C2×#482—531no—
400C2×#483—531no—
401C2×#483—531no—
402C2×#428—531no—
403C22×#106—531no—
404C2×#417—531no—
405C2×#416—531no—
406C2×#408—531no—
407C2×C53—42no—
408C2×C53#309914yescomplemented
409C2×C53C22×#12311yescharacteristic
410C2×C53C2×#57711yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—24no—
413D53—42no—
414D53—82no—
415C22×#41—531no—
416C22×#41—531no—
417C22×M16—531no—
418C23×C8—531no—
419#537—538no—
420#537—1064no—
421C2×C22⋊Q8—531no—
422C2×C22⋊Q8—1061no—
423C2×C22⋊Q8C2×D5311yescharacteristic
424C2×#121—531no—
425C2×#121—531no—
426C2×#121—1061no—
427C2×#121—1061no—
428C2×#121—1061no—
429#520—538no—
430#520—1064no—
431C2×C4×Q8—1061no—
432C2×C4×D4—1061no—
433C2×C4×D4—1061no—
434C2×C4×D4—1061no—
435C2×#117—531no—
436C2×#117—531no—
437C2×#117C2×D5311yescharacteristic
438C22×C4⋊C4—531no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442#485—538no—
443#485C2×D5318yescomplemented
444#483—538no—
445#483—538no—
446#482—538no—
447#482—538no—
448#481—538no—
449#481—538no—
450#428—538no—
451C2×#107—531no—
452C2×#107C2×D5311yescharacteristic
453C2×#106—531no—
454C2×#106—531no—
455C2×#106—531no—
456C2×#106—531no—
457C2×#106—531no—
458C2×#106—538no—
459C2×#106C2×D5311yescharacteristic
460#417—538no—
461#416—538no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103C2×D5311yescharacteristic
465C2×#103C2×D5311yescharacteristic
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470#408—538no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×C22⋊C8—531no—
474C2×C22⋊C8C2×D5311yescharacteristic
475C53C2×#309911yescharacteristic, complemented, Sylow
476C2×#41—534no—
477C2×#41—534no—
478C2×#41—534no—
479C2×#41—1064no—
480C2×#41—1064no—
481C2×#41—1062no—
482C2×#41—1064no—
483C2×#41—1064no—
484C22×Q8—531no—
485C22×Q8C22×D5311yescharacteristic
486C22×D4—531no—
487C22×D4—531no—
488C22×D4—531no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4—1061no—
492C22×D4—1061no—
493C23×C4—531no—
494C23×C4—531no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1061no—
498C23×C4—1061no—
499C23×C4—1061no—
500C23×C4C22×D5311yescharacteristic
501C2×M16—534no—
502C2×M16—1064no—
503C22×C8—531no—
504C22×C8—531no—
505C22×C8—534no—
506C22×C8—1064no—
507C22×C8C22×D5311yescharacteristic
508C22×C8C22×D5311yescharacteristic
509C22⋊Q8—22no—
510C22⋊Q8—534no—
511C22⋊Q8—1068no—
512C22⋊Q8—1062no—
513C22⋊Q8C22×D5314yes—
514#121—534no—
515#121—534no—
516#121—1068no—
517#121—1068no—
518#121—1062no—
519#121—1068no—
520#121—1062no—
521C4×Q8—1068no—
522C4×D4—1068no—
523C4×D4—1068no—
524C4×D4—1068no—
525#117—22no—
526#117—534no—
527#117—534no—
528#117—1062no—
529#117—1062no—
530#117C22×D5314yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—534no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—534no—
537C2×C4⋊C4—534no—
538C2×C4⋊C4—534no—
539C2×C4⋊C4—1062no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4—1062no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1062no—
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C4⋊C4C22×D5311yescharacteristic
550C2×C4⋊C4C22×D5311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—21no—
559C2×C42—1061no—
560C2×C42—1061no—
561#107—534no—
562#107C22×D5314yes—
563#106—534no—
564#106—534no—
565#106—534no—
566#106—534no—
567#106—534no—
568#106C22×D5314yes—
569#103—534no—
570#103—534no—
571#103C22×D5314yes—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#102—534no—
576#102—534no—
577C22⋊C8—534no—
578C22⋊C8—534no—
579C22⋊C8—534no—
580C22⋊C8C22×D5314yes—
581C24—531no—
582C24—531no—
583C24—1061no—
584C24D4×D5311yescharacteristic
585#41—10616no—
586#41—1068no—
587#41—1068no—
588#41—1068no—
589#41—1068no—
590#41—2128no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—534no—
595C2×Q8—1064no—
596C2×Q8C23×D5312yes—
597C2×D4—534no—
598C2×D4—534no—
599C2×D4—534no—
600C2×D4—532no—
601C2×D4—1064no—
602C2×D4—1064no—
603C2×D4—1064no—
604C2×D4—1064no—
605C2×D4—1064no—
606C2×D4—1064no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—1062no—
610C2×D4—4242no—
611C2×D4—4242no—
612C2×D4—2124no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—531no—
620C22×C4—532no—
621C22×C4—534no—
622C22×C4—534no—
623C22×C4—532no—
624C22×C4—531no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—1064no—
628C22×C4—1064no—
629C22×C4—1064no—
630C22×C4—1064no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1064no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—4242no—
638C22×C4—4242no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4—2124no—
642C22×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646M16—1068no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—532no—
650C2×C8—532no—
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—1064no—
667C4⋊C4—1061no—
668C4⋊C4—1061no—
669C4⋊C4—1064no—
670C4⋊C4—1061no—
671C4⋊C4C23×D5312yes—
672C4⋊C4C23×D5312yes—
673C4⋊C4C23×D5312yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C42—24no—
682C42—1064no—
683C42—1064no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—534no—
688C23—532no—
689C23—532no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—2122no—
697C23—2122no—
698C23—2122no—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—1068no—
705D4—1068no—
706D4—1068no—
707D4—1068no—
708D4—1062no—
709D4—1062no—
710D4—4244no—
711D4—4244no—
712D4—2128no—
713D4—2122no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
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—1062no—
733C2×C4—1064no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—4244no—
740C2×C4—4244no—
741C2×C4—4244no—
742C2×C4—4244no—
743C2×C4—2128no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4C2×D4×D5312yes—
748C2×C4C2×D4×D5311yescharacteristic
749C2×C4#41×D5312yes—
750C2×C4#41×D5312yes—
751C2×C4C24×D5311yescharacteristic
752C8—22no—
753C8—22no—
754C8—1062no—
755C8—1062no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—534no—
761C22—1068no—
762C22—1062no—
763C22—1062no—
764C22—1062no—
765C22—1062no—
766C22—1062no—
767C22—4244no—
768C22—2122no—
769C22—2122no—
770C22—2122no—
771C22—2124no—
772C22#123×D5312yes—
773C22#1681143012yes—
774C22#1681143212yes—
775C22C22×D4×D5311yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—534no—
782C4—1062no—
783C4—2122no—
784C4—2122no—
785C4—2122no—
786C4#123×D5312yes—
787C4C2×#41×D5311yescharacteristic
788C4C2×#41×D5311yescharacteristic
789C2—42no—
790C2—1064no—
791C2—4242no—
792C2—2122no—
793C2#2028470114yesdirect product factor
794C2C2×#123×D5311yescharacteristic
795C2C2×#1681143011yescharacteristic
796C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC2×#16811203C2
hypercenterC2×#485D53
hypocenterC53C2×#3099
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×#16811103C2semidirect
3. #20284701C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810950C2semidirect
8. C2×#16810947C2semidirect
9. C2×#16810952C2semidirect
10. C2×#16810951C2semidirect
11. C2×#16810664C2semidirect
12. C2×#106×D53C2semidirect
13. C2×#16810623C2semidirect
14. C2×#16810618C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#485C2semidirect
31. #16811103C22semidirect
42. #16810962C22semidirect
43. #16810952C22semidirect
44. #16810951C22semidirect
45. #16810950C22semidirect
46. #16810947C22semidirect
47. #16810943C22semidirect
48. #16810942C22semidirect
49. #16810664C22semidirect
56. #106×D53C22semidirect
57. #16810623C22semidirect
58. #16810618C22semidirect
65. #16810588C22semidirect
71. C53×#485C22semidirect
397. C2×#485D53semidirect
408. C2×C53#3099semidirect
443. #485C2×D53semidirect
475. C53C2×#3099semidirect
793. C2#20284701direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112032
C2×#168111032
#202847012
C2×#168109432
C2×#168109422
C2×#168109622
C2×#168109502
C2×#168109472
C2×#168109522
C2×#168109512
C2×#168106642
C2×#106×D532
C2×#168106232
C2×#168106182
C2×#168105882
C2×C53×#4852
C2×#309953