Finite Group Databasebeta

← C2×#20287215 #28262687

Subgroups — C2×#20287215 #28262687

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic, complemented
2#20287215C2116yesmaximal, direct product factor
3C2×#16811029C211yesmaximal, characteristic, complemented
4C2×#16810947C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810944C211yesmaximal, characteristic, complemented
7C2×#16810934C211yesmaximal, characteristic, complemented
8C2×#16810923C211yesmaximal, characteristic, complemented
9C2×#16810900C211yesmaximal, characteristic, complemented
10C2×#16810874C211yesmaximal, characteristic, complemented
11C2×#16810857C211yesmaximal, characteristic, complemented
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810666C211yesmaximal, characteristic, complemented
15C2×#16810659C211yesmaximal, characteristic, complemented
16C2×C53×#555C211yesmaximal, characteristic, complemented
17C22×#11719922C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811319—24no—
21#16811319C2218yescomplemented
22C2×#13133212—21no—
23C2×#13133209C2211yescharacteristic
24C2×#13133199—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×#13133189—21no—
28C2×C4×D212C2211yescharacteristic
29C2×#13133177—21no—
30C2×#13133176C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811029C2218yescomplemented
33#16810947C2218yescomplemented
34#16810947C2218yescomplemented
35#16810944C2218yescomplemented
36#16810934C2218yescomplemented
37#16810923C2218yescomplemented
38#16810900C2218yescomplemented
39#16810874C2218yescomplemented
40#16810857C2218yescomplemented
41#16810733C2218yescomplemented
42#16810695C2218yescomplemented
43#16810666C2218yescomplemented
44#16810659C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133150C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#555—24no—
65C53×#555C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#124×C53—21no—
68C2×#124×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×#117×C53—21no—
75C2×#117×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C2×#11719922—24no—
83C2×#11719922C2314yes—
84C2×#11719917—24no—
85C2×#11719917C2314yes—
86C22×#88322—24no—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2314yes—
91C22×#88322C2311yescharacteristic
92#13133212—28no—
93#13133209—22no—
94#13133209C2314yes—
95#13133199—28no—
96#13133191—22no—
97#13133191—22no—
98#13133191C2314yes—
99#13133191C2314yes—
100#13133189—28no—
101C4×D212—22no—
102C4×D212C2314yes—
103#13133177—28no—
104#13133176—22no—
105#13133176C2314yes—
106C2×C4⋊Dic53—22no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53C2314yes—
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×C22⋊Dic53—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133150C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128C4⋊#88322C2314yes—
129#13133138C2314yes—
130#13133138C2314yes—
131#13133138C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137#13133128C2314yes—
138C22×Q8×C53—21no—
139C22×D4×C53—21no—
140C22×D4×C53—21no—
141C22×D4×C53D411yescharacteristic
142C22×D4×C53C2311yescharacteristic
143C23×C4×C53—21no—
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C4⋊Q8×C53—22no—
147C4⋊Q8×C53C2314yes—
148#124×C53—28no—
149#124×C53—28no—
150#121×C53—28no—
151#121×C53—22no—
152#121×C53—22no—
153#121×C53C2314yes—
154#121×C53C2314yes—
155C4×D4×C53—22no—
156C4×D4×C53D414yes—
157C4×D4×C53C2314yes—
158C4×D4×C53C2314yes—
159#117×C53—28no—
160#117×C53—22no—
161#117×C53—22no—
162#117×C53C2314yes—
163#117×C53C2314yes—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53D411yescharacteristic
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
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×C53D411yescharacteristic
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C42×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C24×C53C2×D411yescharacteristic
181C24×C53C2×D411yescharacteristic
182C23×D53—21no—
183C2×Q8×C53—24no—
184C2×Q8×C53—82no—
185C2×D4×C53—24no—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—42no—
191C2×D4×C53—82no—
192C2×D4×C53—82no—
193C2×D4×C53C2×D414yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—24no—
203C22×C4×C53—44no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—82no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—24no—
221C22×Dic53—82no—
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—21no—
225C2×D212C2412yes—
226C2×C4×D53—24no—
227C2×C4×D53—82no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2×D414yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊C4×C53C2×D414yes—
242C22⋊C4×C53C2×D414yes—
243C42×C53—24no—
244C42×C53—24no—
245C42×C53C2×D412yes—
246C42×C53C2412yes—
247C22⋊Dic53—24no—
248#11719922—28no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—21no—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261C4×Dic53—24no—
262#11719917—28no—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322—28no—
267C2×#88322#4114yes—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53C22×D412yes—
283C23×C53C22×D412yes—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289Q8×C53—84no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—44no—
293D4×C53—42no—
294D4×C53—84no—
295D4×C53—84no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—24no—
301C2×C4×C53—24no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—48no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C2×#4112yes—
319C2×C4×C532−1+412yes—
320C2×C4×C53C2511yescharacteristic
321C22⋊D53—48no—
322C22⋊D53—84no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—84no—
330D212—22no—
331D212—22no—
332D212—42no—
333C4×D53—84no—
334#88322—22no—
335#88322—22no—
336#88322—22no—
337#88322C2×#4114yes—
338C2×#3347—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—44no—
346C22×C53—44no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—84no—
351C22×C53#54712yes—
352C22×C53#57512yes—
353C22×C53#57612yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53#54712yes—
367C4×C53C22×#4111yescharacteristic
368C4×C53C2×2−1+411yescharacteristic
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#555D5311yescharacteristic, complemented
373C2×#553—531no—
374#3347—5316no—
375C2×#501—531no—
376C2×#482—531no—
377C2×#482—531no—
378C2×#482—531no—
379C2×#480—531no—
380C2×#478—531no—
381C2×#474—531no—
382C2×#469—531no—
383C2×#466—531no—
384C2×#442—531no—
385C2×#435—531no—
386C2×#428—531no—
387C2×#427—531no—
388C2×C53—42no—
389C2×C53—42no—
390C2×C53—82no—
391C2×C53#334714yescomplemented
392C2×C53C2×#54711yescharacteristic
393C2×C53C2×#57511yescharacteristic
394C2×C53C2×#57611yescharacteristic
395D53—82no—
396C22×D8—531no—
397C22×M16—531no—
398C23×C8—531no—
399#555—24no—
400#555C2×D5318yescomplemented
401#553—538no—
402#553—1064no—
403C2×C4⋊Q8C2×D5311yescharacteristic
404C2×#126—1061no—
405C2×#125—531no—
406C2×#124—21no—
407C2×#124—21no—
408C2×#123—1061no—
409C2×#121—21no—
410C2×#121—531no—
411C2×#121—531no—
412C2×#121—1061no—
413C2×#121C2×D5311yescharacteristic
414C2×#121C2×D5311yescharacteristic
415C2×C4×D4—531no—
416C2×C4×D4—1061no—
417C2×C4×D4C2×D5311yescharacteristic
418C2×C4×D4C2×D5311yescharacteristic
419C2×#117—21no—
420C2×#117—531no—
421C2×#117C2×D5311yescharacteristic
422C2×#117C2×D5311yescharacteristic
423C22×C4⋊C4—531no—
424#501—538no—
425#482—538no—
426#482—538no—
427#482—538no—
428#480—538no—
429#478—538no—
430#474—538no—
431#469—538no—
432#466—538no—
433#442—538no—
434#435—538no—
435#428—538no—
436#427—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107—531no—
441C2×#107—531no—
442C2×#106—531no—
443C2×#106—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×#97—531no—
456C53C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—531no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22⋊D5311yescharacteristic
464C22×D4C22×D5311yescharacteristic
465C23×C4—21no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C2×D8—534no—
471C2×D8—1064no—
472C2×M16—534no—
473C2×M16—1064no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—534no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—1064no—
480C4⋊Q8—22no—
481C4⋊Q8C22×D5314yes—
482#126—1068no—
483#125—534no—
484#125—1062no—
485#124—28no—
486#124—28no—
487#123—1068no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—534no—
492#121—534no—
493#121—1068no—
494#121—1062no—
495#121—1062no—
496#121C22×D5314yes—
497#121C22×D5314yes—
498C4×D4—22no—
499C4×D4—534no—
500C4×D4—1068no—
501C4×D4—1062no—
502C4×D4C22⋊D5314yes—
503C4×D4C22×D5314yes—
504C4×D4C22×D5314yes—
505#117—22no—
506#117—22no—
507#117—28no—
508#117—534no—
509#117—1062no—
510#117C22×D5314yes—
511#117C22×D5314yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1062no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4C22⋊D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4C22⋊D5311yescharacteristic
535C2×C22⋊C4C22⋊D5311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540#107—534no—
541#107—534no—
542#107—534no—
543#107—534no—
544#107—534no—
545#106—534no—
546#106—534no—
547#106—534no—
548#106—534no—
549C4⋊C8—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102—534no—
556C22⋊C8—534no—
557C22⋊C8—534no—
558#97—534no—
559C24—21no—
560C24—1061no—
561C24C2×C22⋊D5311yescharacteristic
562C24C2×C22⋊D5311yescharacteristic
563C2×Q8—24no—
564C2×Q8—82no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—42no—
571C2×D4—82no—
572C2×D4—82no—
573C2×D4—532no—
574C2×D4—1064no—
575C2×D4—1064no—
576C2×D4—1061no—
577C2×D4—1062no—
578C2×D4—1062no—
579C2×D4—4242no—
580C2×D4—2124no—
581C2×D4C2×C22⋊D5314yes—
582C2×D4C23×D5312yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—44no—
592C22×C4—1064no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1064no—
597C22×C4—4242no—
598C22×C4—4242no—
599C22×C4C2×C22⋊D5312yes—
600C22×C4C2×C22⋊D5312yes—
601C22×C4C2×C22⋊D5311yescharacteristic
602C22×C4C2×C22⋊D5311yescharacteristic
603C22×C4C2×C22⋊D5311yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C23×D5312yes—
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608D8—1068no—
609M16—1068no—
610C2×C8—534no—
611C2×C8—532no—
612C2×C8—532no—
613C2×C8—532no—
614C2×C8—532no—
615C2×C8—1068no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—1062no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4—1061no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4C2×C22⋊D5314yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C4⋊C4C23×D5312yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4C2×C22⋊D5314yes—
646C22⋊C4C2×C22⋊D5314yes—
647C42—24no—
648C42—24no—
649C42—1064no—
650C42C2×C22⋊D5312yes—
651C42C23×D5312yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—1062no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23C22×C22⋊D5312yes—
667C23C22×C22⋊D5312yes—
668C23C22×C22⋊D5311yescharacteristic
669Q8—84no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—42no—
674D4—84no—
675D4—84no—
676D4—1062no—
677D4—1062no—
678D4—4244no—
679D4—2128no—
680D4—2122no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—4244no—
702C2×C4—4244no—
703C2×C4—2122no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4C22×C22⋊D5312yes—
707C2×C4C22×C22⋊D5312yes—
708C2×C4C22×C22⋊D5312yes—
709C2×C4C22×C22⋊D5312yes—
710C2×C4C22×C22⋊D5311yescharacteristic
711C2×C4#41×D5312yes—
712C2×C4#1313326412yes—
713C2×C4C24×D5311yescharacteristic
714C8—534no—
715C8—1062no—
716C8—1062no—
717C8—1062no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—4244no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22#1681127212yes—
735C22#1681142112yes—
736C22#1681142612yes—
737C22C23×C22⋊D5311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127212yes—
749C4C2×#41×D5311yescharacteristic
750C4C2×#1313326411yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—4242no—
755C2#2028721514yesdirect product factor
756C2C2×#1681127211yescharacteristic
757C2C2×#1681142111yescharacteristic
758C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#555C2
socleC23×C53C22×D4
hypercenterC2×#555D53
hypocenterC53C2×#3347
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#16811319C2semidirect
2. #20287215C2direct (N × H)
3. C2×#16811029C2semidirect
4. C2×#16810947C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810944C2semidirect
7. C2×#16810934C2semidirect
8. C2×#16810923C2semidirect
9. C2×#16810900C2semidirect
10. C2×#16810874C2semidirect
11. C2×#16810857C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810666C2semidirect
15. C2×#16810659C2semidirect
16. C2×C53×#555C2semidirect
21. #16811319C22semidirect
32. #16811029C22semidirect
33. #16810947C22semidirect
34. #16810947C22semidirect
35. #16810944C22semidirect
36. #16810934C22semidirect
37. #16810923C22semidirect
38. #16810900C22semidirect
39. #16810874C22semidirect
40. #16810857C22semidirect
41. #16810733C22semidirect
42. #16810695C22semidirect
43. #16810666C22semidirect
44. #16810659C22semidirect
65. C53×#555C22semidirect
372. C2×#555D53semidirect
391. C2×C53#3347semidirect
400. #555C2×D53semidirect
456. C53C2×#3347semidirect
755. C2#20287215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
#202872152
C2×#168110292
C2×#168109472
C2×#168109442
C2×#168109342
C2×#168109232
C2×#168109002
C2×#168108742
C2×#168108572
C2×#168107332
C2×#168106952
C2×#168106662
C2×#168106592
C2×C53×#5552
C2×#334753