Finite Group Databasebeta

← C2×#20284705 #28251954

Subgroups — C2×#20284705 #28251954

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×#16811202C211yesmaximal, characteristic
2C2×#16811104C211yesmaximal, characteristic, complemented
3#20284705C2116yesmaximal, direct product factor
4C2×#16810940C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810945C211yesmaximal, characteristic, complemented
8C2×#16810944C211yesmaximal, characteristic, complemented
9C2×#16810955C211yesmaximal, characteristic, complemented
10C2×#16810953C211yesmaximal, characteristic, complemented
11C2×#16810662C211yesmaximal, characteristic, complemented
12C2×#106×D53C211yesmaximal, characteristic, complemented
13C2×#16810621C211yesmaximal, characteristic, complemented
14C2×#16810616C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#481C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811202—24no—
22#16811202C2218yes—
23C2×#13133197C2211yescharacteristic
24C2×#13133196C2211yescharacteristic
25C2×#13133194—21no—
26C2×#13133190—21no—
27C2×#13133189—21no—
28C2×#13133188—21no—
29C2×#13133188C2211yescharacteristic
30#16811104—24no—
31#16811104C2218yescomplemented
32C2×#13133182—21no—
33C2×#13133179—21no—
34C2×C4×C22⋊D53—21no—
35C2×C4×C22⋊D53—21no—
36C2×#13133176C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810967C2218yescomplemented
43#16810965C2218yescomplemented
44#16810955C2218yescomplemented
45#16810953C2218yescomplemented
46#16810945C2218yescomplemented
47#16810944C2218yescomplemented
48#16810940C2218yescomplemented
49#16810662C2218yescomplemented
50C2×#13133151C2211yescharacteristic
51C2×#13133150C2211yescharacteristic
52C2×#13133149C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56#106×D53C2218yescomplemented
57#16810621C2218yescomplemented
58#16810616C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#481C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—24no—
78C2×#11719945—24no—
79C2×#11719945D414yes—
80C2×#11719945C2314yes—
81C2×#11719947—22no—
82C2×#11719947—24no—
83C2×#11719947—24no—
84C2×#11719947C2314yes—
85C22×Dic106D411yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×D212D411yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53D411yescharacteristic
91C22×C22⋊D53D411yescharacteristic
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C22×C4×D53C2311yescharacteristic
98C2×#11719912—24no—
99C2×#11719912C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—24no—
103C2×C8×D53C2314yes—
104#13133197—22no—
105#13133197C2314yes—
106#13133196—22no—
107#13133196C2314yes—
108#13133194—28no—
109#13133190—28no—
110#13133189—28no—
111#13133188—28no—
112#13133188—22no—
113#13133188C2314yes—
114#13133182—28no—
115#13133179—28no—
116C4×C22⋊D53—28no—
117C4×C22⋊D53—28no—
118#13133176—22no—
119#13133176C2314yes—
120#13133175—22no—
121#13133175—22no—
122#13133175C2314yes—
123#13133175C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C4⋊C4×D53C2314yes—
137C4⋊C4×D53C2314yes—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147#13133151C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133148C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162C22×D4×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C23×C4×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168#121×C53—22no—
169#121×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—22no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#102×C53C2314yes—
180#102×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53C2×D411yescharacteristic
185C23×D53C2×D411yescharacteristic
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—82no—
191C2×D4×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—82no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—82no—
209C2×C22⋊D53C2×D414yes—
210C2×C22⋊D53C2×D414yes—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—24no—
216C22×Dic53—44no—
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719947—28no—
220#11719947—28no—
221#11719947—48no—
222#11719945—216no—
223#11719945—28no—
224#11719945—28no—
225C2×D212—24no—
226C2×D212C2×D414yes—
227C2×C4×D53—22no—
228C2×C4×D53—22no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—82no—
233C2×C4×D53—82no—
234C2×C4×D53—82no—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2×D412yes—
237C2×C4×D53#4114yes—
238C2×C4×D53#4114yes—
239C2×C4×D53C2412yes—
240C2×C4×D53C2412yes—
241C2×Dic106—24no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106C2×D414yes—
246C2×Dic106C2412yes—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—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—
275#11719919—24no—
276C4×Dic53—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×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—22no—
299C22×D53#12314yes—
300C22×D53C22×D412yes—
301C22×D53C22×D412yes—
302D4×C53—22no—
303D4×C53—22no—
304D4×C53—42no—
305D4×C53—84no—
306C2×C4×C53—22no—
307C2×C4×C53—24no—
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—84no—
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—48no—
325C22⋊D53—84no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—48no—
336C2×Dic53#12314yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339D212—28no—
340C4×D53—24no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—84no—
344C4×D53—84no—
345C4×D53—84no—
346C4×D53#12318yes—
347C4×D53C2×#4114yes—
348C4×D53C2×#4114yes—
349Dic106—28no—
350Dic106—22no—
351Dic106—22no—
352Dic106—42no—
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×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—84no—
366C22×C53C2×#12312yes—
367C22×C53#57712yes—
368C22×C53#57712yes—
369C22×C53C23×D411yescharacteristic
370C2×D53—28no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—44no—
377C2×D53C2×#12314yes—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53C2×#12312yes—
383C4×C53C22×#4111yescharacteristic
384C4×C53C22×#4111yescharacteristic
385Dic53—22no—
386Dic53—42no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53C2×#12314yes—
391C2×#537—531no—
392C2×#520—531no—
393#3099—5316no—
394C2×#481—531no—
395C2×#481D5311yescharacteristic, complemented
396C2×#485—531no—
397C2×#485—531no—
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—82no—
409C2×C53#309914yescomplemented
410C2×C53C22×#12311yescharacteristic
411C2×C53C2×#57711yescharacteristic
412C2×C53C2×#57711yescharacteristic
413D53—24no—
414D53—42no—
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—531no—
423C2×C22⋊Q8—1061no—
424C2×#121—531no—
425C2×#121—1061no—
426C2×#121—1061no—
427C2×#121—1061no—
428C2×#121C2×D5311yescharacteristic
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×#117—531no—
438C22×C4⋊C4—531no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4C2×D5311yescharacteristic
442#485—538no—
443#485—538no—
444#483—538no—
445#483—538no—
446#482—538no—
447#482—538no—
448#481—538no—
449#481C2×D5318yescomplemented
450#428—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×#106—531no—
455C2×#106—531no—
456C2×#106—531no—
457C2×#106—538no—
458C2×#106C2×D5311yescharacteristic
459C2×#106C2×D5311yescharacteristic
460#417—538no—
461#416—538no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102C2×D5311yescharacteristic
469C2×#102C2×D5311yescharacteristic
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×Q8—531no—
486C22×D4—21no—
487C22×D4—531no—
488C22×D4—531no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4—1061no—
492C22×D4C22×D5311yescharacteristic
493C23×C4—21no—
494C23×C4—531no—
495C23×C4—531no—
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—534no—
510C22⋊Q8—534no—
511C22⋊Q8—1068no—
512C22⋊Q8—1062no—
513C22⋊Q8—1062no—
514#121—22no—
515#121—534no—
516#121—1068no—
517#121—1062no—
518#121—1068no—
519#121—1068no—
520#121C22×D5314yes—
521C4×Q8—1068no—
522C4×D4—1068no—
523C4×D4—1068no—
524C4×D4—1068no—
525#117—534no—
526#117—534no—
527#117—534no—
528#117—1062no—
529#117—1062no—
530#117—1062no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
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⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C4⋊C4C22×D5311yescharacteristic
550C2×C4⋊C4C22×D5314yes—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561#107—534no—
562#107—534no—
563#106—534no—
564#106—534no—
565#106—534no—
566#106—534no—
567#106C22×D5314yes—
568#106C22×D5314yes—
569#103—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#102—534no—
574#102—534no—
575#102C22×D5314yes—
576#102C22×D5314yes—
577C22⋊C8—534no—
578C22⋊C8—534no—
579C22⋊C8—534no—
580C22⋊C8C22×D5314yes—
581C24—21no—
582C24—531no—
583C24—531no—
584C24D4×D5311yescharacteristic
585#41—10616no—
586#41—1068no—
587#41—1068no—
588#41—1068no—
589#41—1068no—
590#41—2128no—
591C2×Q8—534no—
592C2×Q8—532no—
593C2×Q8—1064no—
594C2×Q8—1061no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—82no—
602C2×D4—534no—
603C2×D4—534no—
604C2×D4—534no—
605C2×D4—1064no—
606C2×D4—1064no—
607C2×D4—1064no—
608C2×D4—1064no—
609C2×D4—1064no—
610C2×D4—4242no—
611C2×D4—2124no—
612C2×D4C23×D5312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—531no—
621C22×C4—532no—
622C22×C4—534no—
623C22×C4—534no—
624C22×C4—532no—
625C22×C4—531no—
626C22×C4—532no—
627C22×C4—532no—
628C22×C4—1064no—
629C22×C4—1064no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1061no—
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—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
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—1061no—
670C4⋊C4—1064no—
671C4⋊C4C23×D5312yes—
672C4⋊C4C23×D5312yes—
673C4⋊C4C23×D5312yes—
674C22⋊C4—24no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C42—1064no—
682C42—1064no—
683C42—1064no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—534no—
692C23—532no—
693C23—532no—
694C23—1062no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—1068no—
702Q8—1062no—
703Q8—1062no—
704Q8—2122no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—1068no—
710D4—1068no—
711D4—1068no—
712D4—4244no—
713D4—2128no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—534no—
726C2×C4—532no—
727C2×C4—538no—
728C2×C4—534no—
729C2×C4—534no—
730C2×C4—532no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1062no—
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—2128no—
743C2×C4—2122no—
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—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—534no—
765C22—1068no—
766C22—1062no—
767C22—1062no—
768C22—1062no—
769C22—1062no—
770C22—1062no—
771C22—2124no—
772C22#123×D5312yes—
773C22#1681142912yes—
774C22#1681143312yes—
775C22C22×D4×D5311yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—534no—
781C4—1062no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4—2122no—
786C4#123×D5312yes—
787C4C2×#41×D5311yescharacteristic
788C4C2×#41×D5311yescharacteristic
789C2—42no—
790C2—82no—
791C2—1064no—
792C2—2122no—
793C2#2028470514yesdirect product factor
794C2C2×#123×D5311yescharacteristic
795C2C2×#1681142911yescharacteristic
796C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#481C2
socleC23×C53C22×D4
prime radicalC2×#16811202C2
hypercenterC2×#481D53
hypocenterC53C2×#3099
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#16811104C2semidirect
3. #20284705C2direct (N × H)
4. C2×#16810940C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810945C2semidirect
8. C2×#16810944C2semidirect
9. C2×#16810955C2semidirect
10. C2×#16810953C2semidirect
11. C2×#16810662C2semidirect
12. C2×#106×D53C2semidirect
13. C2×#16810621C2semidirect
14. C2×#16810616C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#481C2semidirect
31. #16811104C22semidirect
42. #16810967C22semidirect
43. #16810965C22semidirect
44. #16810955C22semidirect
45. #16810953C22semidirect
46. #16810945C22semidirect
47. #16810944C22semidirect
48. #16810940C22semidirect
49. #16810662C22semidirect
56. #106×D53C22semidirect
57. #16810621C22semidirect
58. #16810616C22semidirect
65. #16810588C22semidirect
71. C53×#481C22semidirect
395. C2×#481D53semidirect
409. C2×C53#3099semidirect
449. #481C2×D53semidirect
475. C53C2×#3099semidirect
793. C2#20284705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112022
C2×#168111042
#202847052
C2×#168109402
C2×#168109672
C2×#168109652
C2×#168109452
C2×#168109442
C2×#168109552
C2×#168109532
C2×#168106622
C2×#106×D532
C2×#168106212
C2×#168106162
C2×#168105882
C2×C53×#4812
C2×#309953