Finite Group Databasebeta

← C2×#20284662 #28251897

Subgroups — C2×#20284662 #28251897

Order 13568.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D53C211yesmaximal, characteristic
2C2×#117×D53C211yesmaximal, characteristic
3#20284662C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810964C211yesmaximal, characteristic, complemented
8C2×#16810961C211yesmaximal, characteristic, complemented
9C2×#16810955C211yesmaximal, characteristic, complemented
10C2×#16810952C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic, complemented
12C2×#16810662C211yesmaximal, characteristic, complemented
13C2×#16810630C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#16810585C211yesmaximal, characteristic
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C2×#13133197C2211yescharacteristic
22C2×#13133196C2211yescharacteristic
23C2×#13133195—21no—
24C2×#13133194—21no—
25C2×#13133193C2211yescharacteristic
26C22⋊Q8×D53—24no—
27C22⋊Q8×D53C2218yes—
28C2×#13133176C2211yescharacteristic
29C2×#13133175C2211yescharacteristic
30C2×#13133175C2211yescharacteristic
31C2×#13133174—21no—
32C2×#13133173—21no—
33#117×D53—24no—
34#117×D53C2218yes—
35C2×C4⋊C4×D53—21no—
36C2×C4⋊C4×D53C2211yescharacteristic
37C2×C4⋊C4×D53C2211yescharacteristic
38C2×C4⋊C4×D53C2211yescharacteristic
39C2×C22⋊C4×D53—21no—
40C2×C22⋊C4×D53—21no—
41C2×C42×D53—21no—
42#16810965C2218yescomplemented
43#16810964C2218yescomplemented
44#16810961C2218yescomplemented
45#16810960C2218yescomplemented
46#16810957C2218yescomplemented
47#16810955C2218yescomplemented
48#16810952C2218yescomplemented
49#16810664C2218yescomplemented
50#16810662C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133150C2211yescharacteristic, complemented
53C2×#13133150C2211yescharacteristic, complemented
54C2×#13133149C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810630C2218yescomplemented
58#16810630C2218yescomplemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133141C2211yescharacteristic, complemented
62C2×#13133141C2211yescharacteristic, complemented
63C2×#13133140C2211yescharacteristic, complemented
64C2×#13133140C2211yescharacteristic, complemented
65#16810585C2218yes—
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
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
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53—24no—
83C2×Q8×D53C2314yes—
84C23×Dic53D411yescharacteristic
85C22×C4×D53—24no—
86C22×C4×D53—24no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53D411yescharacteristic
92C22×C4×D53D411yescharacteristic
93C22×C4×D53D414yes—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2314yes—
96C22×C4×D53C2311yescharacteristic
97C2×#11719912—24no—
98C2×#11719912—24no—
99C2×#11719912C2314yes—
100C2×#11719912C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133197—22no—
104#13133197C2314yes—
105#13133196—22no—
106#13133196C2314yes—
107#13133195—28no—
108#13133194—28no—
109#13133193—22no—
110#13133193C2314yes—
111#13133176—22no—
112#13133176C2314yes—
113#13133175—22no—
114#13133175—22no—
115#13133175C2314yes—
116#13133175C2314yes—
117#13133174—28no—
118#13133173—28no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C4⋊C4×D53—28no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C22⋊C4×D53—28no—
142C22⋊C4×D53—28no—
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#13133141C2314yescomplemented
156#13133141C2314yescomplemented
157#13133140C2314yescomplemented
158#13133140C2314yescomplemented
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—42no—
186C23×D53C2×D414yes—
187C23×D53C2×D411yescharacteristic
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—24no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D414yes—
210C22×Dic53C2×D411yescharacteristic
211Q8×D53—28no—
212Q8×D53—28no—
213Q8×D53—48no—
214C2×C4×D53—24no—
215C2×C4×D53—22no—
216C2×C4×D53—22no—
217C2×C4×D53—24no—
218C2×C4×D53—216no—
219C2×C4×D53—28no—
220C2×C4×D53—28no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—44no—
226C2×C4×D53—44no—
227C2×C4×D53—44no—
228C2×C4×D53—44no—
229C2×C4×D53C2×D414yes—
230C2×C4×D53C2×D414yes—
231C2×C4×D53C2×D412yes—
232C2×C4×D53C2×D412yes—
233C2×C4×D53#4114yes—
234C2×C4×D53#4114yes—
235C2×C4×D53C2412yes—
236C2×C4×D53C2412yes—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—21no—
240C2×Dic106—24no—
241C2×Dic106—44no—
242C2×Dic106C2412yes—
243C2×C8×C53—22no—
244C2×C8×C53—22no—
245C2×C8×C53C2412yes—
246C2×C8×C53C2412yes—
247C4⋊C4×C53—24no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C22⋊C4×C53—24no—
255C22⋊C4×C53—24no—
256C42×C53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—24no—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322C2412yes—
281C2×#88322C2412yes—
282#11719912—28no—
283#11719912—28no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—28no—
294C22×D53—28no—
295C22×D53—44no—
296C22×D53—416no—
297C22×D53#12314yes—
298C22×D53#13714yes—
299C22×D53C22×D412yes—
300C22×D53C22×D412yes—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—42no—
304C2×C4×C53—22no—
305C2×C4×C53—24no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2×#4112yes—
320C2×C4×C53C2511yescharacteristic
321C2×Dic53—22no—
322C2×Dic53—28no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53#12314yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C4×D53—28no—
335C4×D53—24no—
336C4×D53—22no—
337C4×D53—22no—
338C4×D53—28no—
339C4×D53—48no—
340C4×D53—48no—
341C4×D53—48no—
342C4×D53—48no—
343C4×D53#12318yes—
344C4×D53C2×#4114yes—
345C4×D53C2×#4114yes—
346Dic106—22no—
347Dic106—22no—
348Dic106—42no—
349Dic106—48no—
350C8×C53—22no—
351C8×C53—22no—
352#88322—22no—
353#88322—22no—
354C2×#3095—531nomaximal, Sylow
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—44no—
359C22×C53C2×#12312yes—
360C22×C53C2×#13712yes—
361C22×C53#57512yes—
362C22×C53C23×D411yescharacteristic
363C2×D53—28no—
364C2×D53—28no—
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—416no—
370C2×D53C2×#12314yes—
371C2×D53C2×#13714yes—
372C4×C53—22no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53C2×#12312yes—
378C4×C53C22×#4111yescharacteristic
379C4×C53C22×#4111yescharacteristic
380Dic53—22no—
381Dic53—42no—
382Dic53—42no—
383Dic53—42no—
384Dic53—42no—
385Dic53C2×#12314yes—
386C22×C22⋊Q8—531no—
387C22×#117—531no—
388#3095—5316no—
389C2×#484—531no—
390C2×#484—531no—
391C2×#485—531no—
392C2×#485—531no—
393C2×#485—531no—
394C2×#485D5311yescharacteristic, complemented
395C2×#483—531no—
396C2×#483—531no—
397C2×#428—531no—
398C2×#428—531no—
399C2×#419—531no—
400C2×#419—531no—
401C2×#407—531no—
402C2×C53—42no—
403C2×C53#309514yescomplemented
404C2×C53C22×#12311yescharacteristic
405C2×C53C22×#13711yescharacteristic
406C2×C53C2×#57511yescharacteristic
407D53—24no—
408D53—24no—
409C23×Q8—531no—
410C24×C4—531no—
411C22×M16—531no—
412C22×M16—531no—
413C2×C22⋊Q8—531no—
414C2×C22⋊Q8—531no—
415C2×C22⋊Q8—538no—
416C2×C22⋊Q8—531no—
417C2×C22⋊Q8—1061no—
418C2×C22⋊Q8—1061no—
419C2×C22⋊Q8—1064no—
420C2×C22⋊Q8C2×D5311yescharacteristic
421C2×#117—531no—
422C2×#117—538no—
423C2×#117—531no—
424C2×#117—531no—
425C2×#117—1061no—
426C2×#117—1061no—
427C2×#117—1064no—
428C2×#117C2×D5311yescharacteristic
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—1061no—
433C22×C22⋊C4—1061no—
434C22×C22⋊C4—1061no—
435C22×C42—1061no—
436#485—538no—
437#485—538no—
438#485—538no—
439#485C2×D5318yescomplemented
440#484—538no—
441#484—538no—
442#483—538no—
443#483—538no—
444#428—538no—
445#428—538no—
446C2×#107—531no—
447C2×#107—531no—
448C2×#107—531no—
449C2×#107C2×D5311yescharacteristic, complemented
450C2×#106—531no—
451C2×#106—531no—
452C2×#106—531no—
453C2×#106C2×D5311yescharacteristic, complemented
454#419—538no—
455#419—538no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103C2×D5311yescharacteristic, complemented
463C2×#103C2×D5311yescharacteristic, complemented
464#407—538no—
465C2×C22⋊C8—531no—
466C2×C22⋊C8—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8C2×D5311yescharacteristic
469C53C2×#309511yescharacteristic, complemented, Sylow
470C25—531no—
471C22×Q8—534no—
472C22×Q8—531no—
473C22×Q8—1061no—
474C22×Q8—1062no—
475C22×Q8—1064no—
476C22×Q8—1064no—
477C22×Q8C22×D5311yescharacteristic
478C23×C4—531no—
479C23×C4—531no—
480C23×C4—531no—
481C23×C4—534no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—534no—
485C23×C4—1064no—
486C23×C4—1064no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4C22×D5311yescharacteristic
492C2×M16—534no—
493C2×M16—534no—
494C2×M16—1064no—
495C2×M16—1064no—
496C22×C8—531no—
497C22×C8—531no—
498C22×C8C22×D5311yescharacteristic
499C22×C8C22×D5311yescharacteristic
500C22⋊Q8—22no—
501C22⋊Q8—534no—
502C22⋊Q8—534no—
503C22⋊Q8—534no—
504C22⋊Q8—1068no—
505C22⋊Q8—1068no—
506C22⋊Q8—1062no—
507C22⋊Q8—1062no—
508C22⋊Q8—1062no—
509C22⋊Q8C22×D5314yes—
510#117—22no—
511#117—534no—
512#117—534no—
513#117—534no—
514#117—1068no—
515#117—1068no—
516#117—1062no—
517#117—1062no—
518#117—1062no—
519#117C22×D5314yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—534no—
527C2×C4⋊C4—1062no—
528C2×C4⋊C4—1062no—
529C2×C4⋊C4—1062no—
530C2×C4⋊C4—1068no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4C22×D5311yescharacteristic
538C2×C4⋊C4C22×D5311yescharacteristic
539C2×C4⋊C4C22×D5311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1068no—
543C2×C22⋊C4—1068no—
544C2×C22⋊C4—1061no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C42—21no—
551C2×C42—1068no—
552C2×C42—1061no—
553C2×C42—1061no—
554C2×C42—1061no—
555#107—534no—
556#107—534no—
557#107—534no—
558#107C22×D5314yescomplemented
559#106—534no—
560#106—534no—
561#106—534no—
562#106C22×D5314yescomplemented
563#103—534no—
564#103—534no—
565#103—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103C22×D5314yescomplemented
570#103C22×D5314yescomplemented
571C22⋊C8—534no—
572C22⋊C8—534no—
573C22⋊C8—534no—
574C22⋊C8C22×D5314yes—
575C24—531no—
576C24—531no—
577C24—534no—
578C24—1064no—
579C24—1064no—
580C24—2122no—
581C24D4×D5311yescharacteristic
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—532no—
586C2×Q8—1064no—
587C2×Q8—1068no—
588C2×Q8—1068no—
589C2×Q8—1061no—
590C2×Q8—1062no—
591C2×Q8—1062no—
592C2×Q8—2124no—
593C2×Q8—2128no—
594C2×Q8C23×D5312yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—531no—
602C22×C4—532no—
603C22×C4—534no—
604C22×C4—534no—
605C22×C4—532no—
606C22×C4—534no—
607C22×C4—531no—
608C22×C4—534no—
609C22×C4—534no—
610C22×C4—532no—
611C22×C4—532no—
612C22×C4—1064no—
613C22×C4—10616no—
614C22×C4—1068no—
615C22×C4—1068no—
616C22×C4—1064no—
617C22×C4—1064no—
618C22×C4—1064no—
619C22×C4—1064no—
620C22×C4—1064no—
621C22×C4—1064no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—2124no—
629C22×C4—2124no—
630C22×C4—2124no—
631C22×C4—2124no—
632C22×C4D4×D5312yes—
633C22×C4D4×D5311yescharacteristic
634C22×C4C23×D5312yes—
635C22×C4C23×D5311yescharacteristic
636M16—1068no—
637M16—1068no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—532no—
641C2×C8—532no—
642C2×C8—1062no—
643C2×C8—1062no—
644C2×C8C23×D5312yes—
645C2×C8C23×D5312yes—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—532no—
651C4⋊C4—532no—
652C4⋊C4—532no—
653C4⋊C4—1064no—
654C4⋊C4—1064no—
655C4⋊C4—1064no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1061no—
659C4⋊C4—1061no—
660C4⋊C4—1061no—
661C4⋊C4—1064no—
662C4⋊C4C23×D5312yes—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C42—24no—
674C42—1064no—
675C42—1064no—
676C42—1064no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—534no—
681C23—534no—
682C23—532no—
683C23—532no—
684C23—1068no—
685C23—1068no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—2124no—
691C23—21216no—
692C23C2×D4×D5312yes—
693C23C2×D4×D5311yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—1062no—
698Q8—1062no—
699Q8—2128no—
700Q8—2122no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—534no—
714C2×C4—532no—
715C2×C4—538no—
716C2×C4—534no—
717C2×C4—534no—
718C2×C4—532no—
719C2×C4—1068no—
720C2×C4—1068no—
721C2×C4—1068no—
722C2×C4—1062no—
723C2×C4—1064no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—2128no—
731C2×C4—2128no—
732C2×C4—2128no—
733C2×C4—2128no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4C2×D4×D5312yes—
739C2×C4C2×D4×D5311yescharacteristic
740C2×C4#41×D5312yes—
741C2×C4#41×D5312yes—
742C2×C4C24×D5311yescharacteristic
743C8—22no—
744C8—22no—
745C8—1062no—
746C8—1062no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—534no—
752C22—534no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—1062no—
757C22—1068no—
758C22—1068no—
759C22—21216no—
760C22#123×D5312yes—
761C22#137×D5312yes—
762C22#1681142012yes—
763C22C22×D4×D5311yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—534no—
770C4—1062no—
771C4—2122no—
772C4—2122no—
773C4—2122no—
774C4—2122no—
775C4#123×D5312yes—
776C4C2×#41×D5311yescharacteristic
777C4C2×#41×D5311yescharacteristic
778C2—42no—
779C2—1064no—
780C2—1064no—
781C2#2028466214yesdirect product factor
782C2C2×#123×D5311yescharacteristic
783C2C2×#137×D5311yescharacteristic
784C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC24×D53D4
hypercenterC2×#485D53
hypocenterC53C2×#3095
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
3. #20284662C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810964C2semidirect
8. C2×#16810961C2semidirect
9. C2×#16810955C2semidirect
10. C2×#16810952C2semidirect
11. C2×#16810664C2semidirect
12. C2×#16810662C2semidirect
13. C2×#16810630C2semidirect
14. C2×#16810630C2semidirect
16. C2×C53×#485C2semidirect
42. #16810965C22semidirect
43. #16810964C22semidirect
44. #16810961C22semidirect
45. #16810960C22semidirect
46. #16810957C22semidirect
47. #16810955C22semidirect
48. #16810952C22semidirect
49. #16810664C22semidirect
50. #16810662C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133150C22semidirect
53. C2×#13133150C22semidirect
54. C2×#13133149C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810630C22semidirect
58. #16810630C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133141C22semidirect
62. C2×#13133141C22semidirect
63. C2×#13133140C22semidirect
64. C2×#13133140C22semidirect
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. #13133142C23semidirect
154. #13133142C23semidirect
155. #13133141C23semidirect
156. #13133141C23semidirect
157. #13133140C23semidirect
158. #13133140C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. #103×C53C23semidirect
180. #103×C53C23semidirect
394. C2×#485D53semidirect
403. C2×C53#3095semidirect
439. #485C2×D53semidirect
449. C2×#107C2×D53semidirect
453. C2×#106C2×D53semidirect
462. C2×#103C2×D53semidirect
463. C2×#103C2×D53semidirect
469. C53C2×#3095semidirect
558. #107C22×D53semidirect
562. #106C22×D53semidirect
569. #103C22×D53semidirect
570. #103C22×D53semidirect
781. C2#20284662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D532
C2×#117×D532
#202846622
C2×#168109602
C2×#168109572
C2×#168109652
C2×#168109642
C2×#168109612
C2×#168109552
C2×#168109522
C2×#168106642
C2×#168106622
C2×#168106302
C2×#168105852
C2×C53×#4852
C2×#309553