Finite Group Databasebeta

← C2×#20287161 #28262629

Subgroups — C2×#20287161 #28262629

Order 13568.

2094 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×#16811315C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic
3#20287161C2116yesmaximal, direct product factor
4C2×#16811030C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810951C211yesmaximal, characteristic, complemented
8C2×#16810934C211yesmaximal, characteristic, complemented
9C2×#16810916C211yesmaximal, characteristic, complemented
10C2×#16810921C211yesmaximal, characteristic, complemented
11C2×#16810866C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810694C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C22×#13133151C211yesmaximal, characteristic, complemented
16C2×C53×#465C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719912C2211yescharacteristic
19#16811315—24no—
20#16811315C2218yescomplemented
21#16811273—24no—
22#16811273C2218yes—
23C2×#13133216C2211yescharacteristic
24C2×#13133212—21no—
25C2×#13133208—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133201—21no—
28C2×#13133199—21no—
29C2×#13133198—21no—
30C2×#13133194—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133188C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133175C2211yescharacteristic
37C2×#13133173—21no—
38C22×C4⋊Dic53C2211yescharacteristic
39C22×C4⋊Dic53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811030C2218yescomplemented
42#16810957C2218yescomplemented
43#16810951C2218yescomplemented
44#16810945C2218yescomplemented
45#16810934C2218yescomplemented
46#16810921C2218yescomplemented
47#16810916C2218yescomplemented
48#16810866C2218yescomplemented
49#16810724C2218yescomplemented
50#16810694C2218yescomplemented
51#16810662C2218yescomplemented
52C2×#13133151C2211yescharacteristic
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#465C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×C22⋊D53—21no—
81C22×C22⋊D53D411yescharacteristic
82C23×Dic53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C2×#11719912—24no—
88C2×#11719912C2314yes—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133216—22no—
92#13133216C2314yes—
93#13133212—28no—
94#13133208—28no—
95#13133208—22no—
96#13133208C2314yes—
97#13133201—28no—
98#13133199—28no—
99#13133198—28no—
100#13133194—28no—
101#13133193—22no—
102#13133193C2314yes—
103#13133188—22no—
104#13133188C2314yes—
105Q8×Dic53—22no—
106Q8×Dic53C2314yes—
107D4×Dic53—22no—
108D4×Dic53C2314yes—
109C4×C22⋊D53D414yes—
110C4×C22⋊D53C2314yes—
111#13133175—22no—
112#13133175C2314yes—
113#13133173—28no—
114C2×C4⋊Dic53—22no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2314yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53D411yescharacteristic
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142#13133151C2314yes—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133129C2314yes—
157#13133127C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53—21no—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C2×SD16×C53—24no—
163C2×SD16×C53C2314yes—
164C22×C8×C53—24no—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22⋊Q8×C53—22no—
169C22⋊Q8×C53C2314yes—
170#121×C53—22no—
171#121×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#103×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C24×C53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53C2412yes—
187C2×D4×C53—24no—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—44no—
192C2×D4×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—44no—
205C2×C22⋊D53C2×D414yes—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53—44no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719947—432no—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—44no—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2412yes—
226C2×Dic106—24no—
227C2×Dic106—44no—
228SD16×C53—28no—
229C2×C8×C53—22no—
230C2×C8×C53—28no—
231C2×C8×C53#4114yescomplemented
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53C2×D414yes—
244#11719921—24no—
245#11719921—24no—
246#11719921C2×D414yes—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919C2×D414yes—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53C2×D412yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272#11719912—28no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53AGL(1,ℤ/8)14yes—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53C22×D412yes—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—42no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—48no—
292D4×C53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—28no—
309C22⋊D53—48no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—48no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—48no—
321C2×Dic53—48no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C4×D53—24no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—48no—
331Dic106—48no—
332C8×C53—22no—
333C8×C53C2×#4114yescomplemented
334#88322—22no—
335#88322—22no—
336C2×#3343—531nomaximal, Sylow
337C22×C53—28no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—84no—
344C22×C53#54712yes—
345C22×C53C2×AGL(1,ℤ/8)14yes—
346C22×C53C2×AGL(1,ℤ/8)12yes—
347C22×C53#57812yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—44no—
353C4×C53—22no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#54712yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C2×2−1+411yescharacteristic
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#552—531no—
368C2×#547—531no—
369#3343—5316no—
370C2×#501—531no—
371C2×#484—531no—
372C2×#482—531no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#477—531no—
376C2×#478—531no—
377C2×#468—531no—
378C2×#465D5311yescharacteristic, complemented
379C2×#440—531no—
380C2×#435—531no—
381C2×#428—531no—
382C22×#107—531no—
383C2×C53—24no—
384C2×C53—82no—
385C2×C53#334314yescomplemented
386C2×C53C2×#54711yescharacteristic
387C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C53C2×#57811yescharacteristic
389D53—42no—
390C22×#41—1061no—
391C22×SD16C2×D5311yescharacteristic
392C22×M16—531no—
393C23×C8C2×D5311yescharacteristic
394#552—538no—
395#552—1064no—
396#547—538no—
397#547—1064no—
398C2×C4⋊Q8—531no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#125—1061no—
402C2×#123—1061no—
403C2×#123—1061no—
404C2×#123—1061no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—1061no—
407C2×C22⋊Q8C2×D5311yescharacteristic
408C2×#121—531no—
409C2×#121C2×D5311yescharacteristic
410C2×C4×Q8—531no—
411C2×C4×D4—531no—
412C2×C4×D4—531no—
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418#501—538no—
419#484—538no—
420#483—538no—
421#482—538no—
422#480—538no—
423#478—538no—
424#477—538no—
425#468—538no—
426#465C2×D5318yescomplemented
427#440—538no—
428#435—538no—
429#428—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—538no—
433C2×#107—531no—
434C2×#107—531no—
435C2×#107—531no—
436C2×#107—531no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#106C2×D5311yescharacteristic
440C2×C4⋊C8—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103C2×D5311yescharacteristic
444C2×#102—531no—
445C2×#102—531no—
446C2×#102C2×D5311yescharacteristic
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×#97—531no—
450C53C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1068no—
452C2×#41—2128no—
453C22×Q8—1061no—
454C22×Q8C22×D5311yescharacteristic
455C22×D4—21no—
456C22×D4—531no—
457C22×D4—1061no—
458C22×D4C22×D5311yescharacteristic
459C23×C4—531no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C23×C4C22×D5311yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D5314yes—
467C2×M16—534no—
468C2×M16—1064no—
469C22×C8—24no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5314yes—
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#125—534no—
479#125—1062no—
480#125—1068no—
481#123—1068no—
482#123—1068no—
483#123—1068no—
484C22⋊Q8—22no—
485C22⋊Q8—534no—
486C22⋊Q8—1068no—
487C22⋊Q8—1062no—
488C22⋊Q8C22×D5314yes—
489#121—22no—
490#121—534no—
491#121—1062no—
492#121C22×D5314yes—
493C4×Q8—534no—
494C4×Q8—1062no—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—534no—
498C4×D4—1062no—
499#117—534no—
500#117—1068no—
501#117—1062no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—534no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1062no—
521C2×C4⋊C4—1062no—
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C42—531no—
533C2×C42—1061no—
534C2×C42—1061no—
535#107—534no—
536#107—534no—
537#107—534no—
538#107—534no—
539#107—534no—
540#107—534no—
541#106—534no—
542#106—534no—
543#106C22×D5314yes—
544C4⋊C8—534no—
545#103—534no—
546#103—534no—
547#103C22×D5314yes—
548#102—534no—
549#102—534no—
550#102C22×D5314yes—
551C22⋊C8—534no—
552C22⋊C8—534no—
553#97—534no—
554C24—21no—
555C24—531no—
556C24D4×D5311yescharacteristic
557#41—21232no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—1064no—
562C2×Q8—2124no—
563C2×Q8C23×D5312yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—534no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—2124no—
573C2×D4C23×D5312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1064no—
589C22×C4—1064no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—2124no—
595C22×C4—2124no—
596C22×C4—2124no—
597C22×C4—2124no—
598C22×C4D4×D5312yes—
599C22×C4D4×D5311yescharacteristic
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602SD16—28no—
603M16—1068no—
604C2×C8—22no—
605C2×C8—28no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1062no—
609C2×C8—1062no—
610C2×C8#1171994714yescomplemented
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—534no—
617C4⋊C4—532no—
618C4⋊C4—532no—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1064no—
631C4⋊C4—1061no—
632C4⋊C4—1064no—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—534no—
638C22⋊C4—534no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C42—532no—
644C42—532no—
645C42—1064no—
646C42—1064no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—532no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23#1313324414yes—
658C23C2×D4×D5312yes—
659C23C2×D4×D5311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2128no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—1068no—
669D4—2128no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1064no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2128no—
694C2×C4—2128no—
695C2×C4—2128no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4—2128no—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994712yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—1062no—
708C8—1062no—
709C8C2×#1171994714yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—2124no—
721C22#1681127312yes—
722C22C2×#1313324414yes—
723C22C2×#1313324412yes—
724C22#1681143712yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1062no—
731C4—1062no—
732C4—1062no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127312yes—
738C4C22×#1171994711yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—24no—
741C2—82no—
742C2—2122no—
743C2#2028716114yesdirect product factor
744C2C2×#1681127311yescharacteristic
745C2C22×#1313324411yescharacteristic
746C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
prime radicalC2×#16811273C2
hypercenterC2×#465D53
hypocenterC53C2×#3343
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16811315C2semidirect
3. #20287161C2direct (N × H)
4. C2×#16811030C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810951C2semidirect
8. C2×#16810934C2semidirect
9. C2×#16810916C2semidirect
10. C2×#16810921C2semidirect
11. C2×#16810866C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810694C2semidirect
14. C2×#16810662C2semidirect
15. C22×#13133151C2semidirect
16. C2×C53×#465C2semidirect
20. #16811315C22semidirect
41. #16811030C22semidirect
42. #16810957C22semidirect
43. #16810951C22semidirect
44. #16810945C22semidirect
45. #16810934C22semidirect
46. #16810921C22semidirect
47. #16810916C22semidirect
48. #16810866C22semidirect
49. #16810724C22semidirect
50. #16810694C22semidirect
51. #16810662C22semidirect
56. C2×#13133151C22semidirect
73. C53×#465C22semidirect
231. C2×C8×C53#41semidirect
333. C8×C53C2×#41semidirect
378. C2×#465D53semidirect
385. C2×C53#3343semidirect
426. #465C2×D53semidirect
450. C53C2×#3343semidirect
610. C2×C8#11719947semidirect
709. C8C2×#11719947semidirect
743. C2#20287161direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113152
C2×#168112732
#202871612
C2×#168110302
C2×#168109572
C2×#168109452
C2×#168109512
C2×#168109342
C2×#168109162
C2×#168109212
C2×#168108662
C2×#168107242
C2×#168106942
C2×#168106622
C22×#131331512
C2×C53×#4652
C2×#334353