Finite Group Databasebeta

← C2×#20287462 #28263835

Subgroups — C2×#20287462 #28263835

Order 13568.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811333C211yesmaximal, characteristic, complemented
2#20287462C2116yesmaximal, direct product factor
3C2×#16810987C211yesmaximal, characteristic, complemented
4C2×#16810982C211yesmaximal, characteristic, complemented
5C2×#16810977C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810923C211yesmaximal, characteristic, complemented
8C2×#16810903C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810835C211yesmaximal, characteristic, complemented
11C2×#16810815C211yesmaximal, characteristic
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#559C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811333—24no—
21#16811333C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133209C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133195—21no—
26C2×#13133195—21no—
27C2×#13133193—21no—
28C2×C4×D212C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C2×C4×D212C2211yescharacteristic
31C2×C4⋊C4×D53—21no—
32#16810987C2218yescomplemented
33#16810982C2218yescomplemented
34#16810977C2218yescomplemented
35#16810930C2218yescomplemented
36#16810923C2218yescomplemented
37#16810903C2218yescomplemented
38#16810835C2218yescomplemented
39#16810835C2218yescomplemented
40#16810815C2218yes—
41#16810754C2218yescomplemented
42#16810733C2218yescomplemented
43#16810721C2218yescomplemented
44C4×#11719922C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#559—24no—
65C53×#559C2218yescomplemented
66C2×#127×C53C2211yescharacteristic
67C2×#124×C53—21no—
68C2×#124×C53C2211yescharacteristic
69C2×#124×C53C2211yescharacteristic
70C2×#123×C53—21no—
71C2×#123×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×D4×C53—21no—
75C2×C4×D4×C53C2211yescharacteristic
76C2×C4×D4×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212C2311yescharacteristic
79C22×C4×D53—21no—
80C22×C4×D53—21no—
81C22×C4×D53—21no—
82C2×#11719924—24no—
83C2×#11719924C2314yes—
84C2×#11719922—24no—
85C2×#11719922—24no—
86C2×#11719922C2314yes—
87C2×#11719922C2314yes—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133217—22no—
93#13133217C2314yes—
94#13133209—22no—
95#13133209—22no—
96#13133209C2314yes—
97#13133209C2314yes—
98#13133195—28no—
99#13133195—28no—
100#13133193—28no—
101C4×D212—22no—
102C4×D212—22no—
103C4×D212—22no—
104C4×D212C2314yes—
105C4×D212C2314yes—
106C4×D212C2314yes—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×#11719919—21no—
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×#11719919—21no—
115C4⋊C4×D53—28no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133148C2314yes—
122C4⋊#88322C2314yes—
123C4⋊#88322C2314yes—
124C4⋊#88322C2314yes—
125#13133141C2314yes—
126#13133141C2314yes—
127#13133141C2314yes—
128#13133138C2314yes—
129#13133138C2314yes—
130#13133138C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133137C2314yes—
135#13133128C2314yes—
136#13133128C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53D411yescharacteristic
139C22×Q8×C53C2311yescharacteristic
140C22×D4×C53—21no—
141C22×D4×C53—21no—
142C22×D4×C53C2311yescharacteristic
143C22×D4×C53C2311yescharacteristic
144C23×C4×C53—21no—
145C23×C4×C53—21no—
146#127×C53—22no—
147#127×C53C2314yes—
148#124×C53—22no—
149#124×C53—22no—
150#124×C53—28no—
151#124×C53C2314yes—
152#124×C53C2314yes—
153#123×C53—28no—
154#123×C53—28no—
155C4×Q8×C53—22no—
156C4×Q8×C53D414yes—
157C4×Q8×C53C2314yes—
158C4×Q8×C53C2314yes—
159C4×D4×C53—28no—
160C4×D4×C53—22no—
161C4×D4×C53—22no—
162C4×D4×C53C2314yes—
163C4×D4×C53C2314yes—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53D411yescharacteristic
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C22⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C24×C53—21no—
181C23×D53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53—42no—
186C2×Q8×C53C2×D414yes—
187C2×Q8×C53C2412yes—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—24no—
191C2×D4×C53—24no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—22no—
196C2×D4×C53—44no—
197C2×D4×C53—82no—
198C2×D4×C53C2412yes—
199C2×D4×C53C2412yes—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—24no—
203C22×C4×C53—24no—
204C22×C4×C53—82no—
205C22×C4×C53—82no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2411yescharacteristic
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C2×D212—21no—
217C2×D212—22no—
218C2×D212#4114yes—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—44no—
224C2×C4×D53—82no—
225C2×C4×D53—82no—
226C2×Dic106—24no—
227C2×Dic106—82no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2×D414yes—
231C4⋊C4×C53C2×D414yes—
232C4⋊C4×C53C2×D414yes—
233C4⋊C4×C53C2412yes—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—24no—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C42×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2×D412yes—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245C42×C53C2412yes—
246C42×C53C2412yes—
247#11719924—28no—
248#11719922—28no—
249#11719922—28no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—24no—
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—44no—
288Q8×C53—42no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—48no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—84no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—84no—
308C2×C4×C53—84no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C2×#4112yes—
317C2×C4×C532−1+412yes—
318C2×C4×C53C2511yescharacteristic
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325D212—24no—
326D212—22no—
327D212C2×#4114yes—
328C4×D53—48no—
329C4×D53—84no—
330C4×D53—84no—
331Dic106—84no—
332#88322—22no—
333#88322—22no—
334#88322—22no—
335#88322—22no—
336C2×#3370—531nomaximal, Sylow
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—84no—
344C22×C53—84no—
345C22×C53#54812yes—
346C22×C53#57512yes—
347C22×C53#57612yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—24no—
350C2×D53—48no—
351C2×D53—42no—
352C2×D53—42no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53#54812yes—
362C4×C53C22×#4111yescharacteristic
363C4×C53C2×2−1+411yescharacteristic
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#559D5311yescharacteristic, complemented
368C2×#554—531no—
369#3370—5316no—
370C2×#490—531no—
371C2×#489—531no—
372C2×#488—531no—
373C2×#479—531no—
374C2×#478—531no—
375C2×#474—531no—
376C2×#463—531no—
377C2×#463—531no—
378C2×#459—531no—
379C2×#446—531no—
380C2×#442—531no—
381C2×#440—531no—
382C2×C4×D8—531no—
383C2×C53—82no—
384C2×C53—82no—
385C2×C53#337014yescomplemented
386C2×C53C2×#54811yescharacteristic
387C2×C53C2×#57511yescharacteristic
388C2×C53C2×#57611yescharacteristic
389D53—44no—
390C22×SD16—531no—
391C22×D8—531no—
392C22×D8—531no—
393#559—24no—
394#559C2×D5318yescomplemented
395#554—538no—
396#554—1064no—
397C2×C4⋊Q8—531no—
398C2×#127C2×D5311yescharacteristic
399C2×#125—531no—
400C2×#125—531no—
401C2×#124—21no—
402C2×#124C2×D5311yescharacteristic
403C2×#124C2×D5311yescharacteristic
404C2×#123—21no—
405C2×#123—21no—
406C2×C22⋊Q8—1061no—
407C2×C22⋊Q8—1061no—
408C2×C22⋊Q8—1061no—
409C2×C4×Q8C2×D5311yescharacteristic
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—531no—
413C2×C4×D4—531no—
414C2×C4×D4—531no—
415C2×C4×D4C2×D5311yescharacteristic
416C2×C4×D4C2×D5311yescharacteristic
417C22×C4⋊C4—1061no—
418#490—538no—
419#489—538no—
420#488—538no—
421#479—538no—
422#478—538no—
423#474—538no—
424#463—538no—
425#463—538no—
426#459—538no—
427#446—538no—
428#442—538no—
429#440—538no—
430C4×D8—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×#97—531no—
448C2×#97—531no—
449C2×C4×C8—531no—
450C53C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—1061no—
452C22×Q8C22⋊D5311yescharacteristic
453C22×Q8C22×D5311yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—531no—
457C22×D4C22×D5311yescharacteristic
458C22×D4C22×D5311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C2×SD16—534no—
465C2×SD16—1064no—
466C2×D8—534no—
467C2×D8—534no—
468C2×D8—1064no—
469C2×D8—1064no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C4⋊Q8—534no—
475C4⋊Q8—1062no—
476#127—22no—
477#127C22×D5314yes—
478#125—534no—
479#125—534no—
480#125—1062no—
481#125—1062no—
482#124—28no—
483#124—22no—
484#124—22no—
485#124C22×D5314yes—
486#124C22×D5314yes—
487#123—28no—
488#123—28no—
489C22⋊Q8—1068no—
490C22⋊Q8—1068no—
491C22⋊Q8—1068no—
492C4×Q8—22no—
493C4×Q8C22⋊D5314yes—
494C4×Q8C22×D5314yes—
495C4×Q8C22×D5314yes—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1062no—
505C4×D4C22×D5314yes—
506C4×D4C22×D5314yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1068no—
517C2×C4⋊C4C22⋊D5311yescharacteristic
518C2×C4⋊C4C22⋊D5311yescharacteristic
519C2×C4⋊C4C22⋊D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—21no—
531C2×C42C22×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533C2×C42C22×D5311yescharacteristic
534#107—534no—
535#107—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#102—534no—
544#102—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548#102—534no—
549#102—534no—
550#97—534no—
551#97—534no—
552C4×C8—534no—
553C24—21no—
554C24—21no—
555C24—1061no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—1064no—
561C2×Q8—4242no—
562C2×Q8C2×C22⋊D5314yes—
563C2×Q8C23×D5312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—82no—
574C2×D4—534no—
575C2×D4—532no—
576C2×D4—1061no—
577C2×D4—1062no—
578C2×D4C23×D5312yes—
579C2×D4C23×D5312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—1064no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4—2124no—
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C2×C22⋊D5311yescharacteristic
600C22×C4C2×C22⋊D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603D8—1068no—
604D8—1068no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1062no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8—1062no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—532no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4C2×C22⋊D5314yes—
627C4⋊C4C2×C22⋊D5314yes—
628C4⋊C4C2×C22⋊D5314yes—
629C4⋊C4C23×D5312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—24no—
640C42C2×C22⋊D5312yes—
641C42C2×C22⋊D5312yes—
642C42C2×C22⋊D5312yes—
643C42C23×D5312yes—
644C42C23×D5312yes—
645C42C23×D5312yes—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1064no—
655C23—1062no—
656C23—2122no—
657C23—2122no—
658C23C22×C22⋊D5311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—4244no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—534no—
673D4—1064no—
674D4—1062no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—4244no—
691C2×C4—4244no—
692C2×C4—2128no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4C22×C22⋊D5312yes—
697C2×C4C22×C22⋊D5312yes—
698C2×C4C22×C22⋊D5312yes—
699C2×C4C22×C22⋊D5312yes—
700C2×C4C22×C22⋊D5312yes—
701C2×C4C22×C22⋊D5312yes—
702C2×C4C22×C22⋊D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—1062no—
707C8—1062no—
708C8—1062no—
709C8—1062no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—1064no—
719C22—2122no—
720C22—2122no—
721C22—2128no—
722C22#1681128012yes—
723C22#1681142112yes—
724C22#1681142612yes—
725C22C23×C22⋊D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681128012yes—
738C4C2×#41×D5311yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—82no—
741C2—82no—
742C2—2124no—
743C2#2028746214yesdirect product factor
744C2C2×#1681128011yescharacteristic
745C2C2×#1681142111yescharacteristic
746C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#559C2
socleC23×C53C22×D4
prime radicalC2×#16810815C2
hypercenterC2×#559D53
hypocenterC53C2×#3370
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16811333C2semidirect
2. #20287462C2direct (N × H)
3. C2×#16810987C2semidirect
4. C2×#16810982C2semidirect
5. C2×#16810977C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810923C2semidirect
8. C2×#16810903C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810835C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810733C2semidirect
14. C2×#16810721C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#559C2semidirect
21. #16811333C22semidirect
32. #16810987C22semidirect
33. #16810982C22semidirect
34. #16810977C22semidirect
35. #16810930C22semidirect
36. #16810923C22semidirect
37. #16810903C22semidirect
38. #16810835C22semidirect
39. #16810835C22semidirect
41. #16810754C22semidirect
42. #16810733C22semidirect
43. #16810721C22semidirect
44. C4×#11719922C22semidirect
65. C53×#559C22semidirect
367. C2×#559D53semidirect
385. C2×C53#3370semidirect
394. #559C2×D53semidirect
450. C53C2×#3370semidirect
743. C2#20287462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113332
#202874622
C2×#168109872
C2×#168109822
C2×#168109772
C2×#168109302
C2×#168109232
C2×#168109032
C2×#168108352
C2×#168108152
C2×#168107542
C2×#168107332
C2×#168107212
C2×C4×#117199222
C2×C53×#5592
C2×#337053