Finite Group Databasebeta

← C2×#20287508 #28263780

Subgroups — C2×#20287508 #28263780

Order 13568.

2134 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×#16811356C211yesmaximal, characteristic, complemented
2C2×D4×Dic106C211yesmaximal, characteristic, complemented
3#20287508C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810981C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic, complemented
7C2×#16810907C211yesmaximal, characteristic, complemented
8C2×#16810913C211yesmaximal, characteristic, complemented
9C2×#16810912C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810836C211yesmaximal, characteristic, complemented
12C2×#16810816C211yesmaximal, characteristic
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810732C211yesmaximal, characteristic, complemented
15C2×#16810714C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C23×Dic106—21no—
18C22×#11719923C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811356—24no—
21#16811356C2218yescomplemented
22D4×Dic106—24no—
23D4×Dic106C2218yescomplemented
24C2×#13133217C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133213C2211yescharacteristic
28C2×#13133205C2211yescharacteristic
29C2×#13133204C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133200—21no—
32C2×#13133199—21no—
33C2×#13133196—21no—
34C2×#13133194—21no—
35C2×#13133194—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42#16810983C2218yescomplemented
43#16810981C2218yescomplemented
44#16810968C2218yescomplemented
45#16810913C2218yescomplemented
46#16810912C2218yescomplemented
47#16810907C2218yescomplemented
48#16810838C2218yescomplemented
49#16810836C2218yescomplemented
50#16810816C2218yes—
51#16810751C2218yescomplemented
52#16810732C2218yescomplemented
53#16810714C2218yescomplemented
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106—28no—
81C22×Dic106—48no—
82C22×Dic106D411yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C23×Dic53—21no—
88C23×Dic53—21no—
89C22×C4×D53—21no—
90C2×#11719923—24no—
91C2×#11719923C2314yes—
92C2×#11719922—24no—
93C2×#11719922C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133217—22no—
97#13133217C2314yes—
98#13133216—22no—
99#13133216—22no—
100#13133216C2314yes—
101#13133216C2314yes—
102#13133213—22no—
103#13133213C2314yes—
104#13133205—22no—
105#13133205C2314yes—
106#13133204—22no—
107#13133204C2314yes—
108#13133203—28no—
109#13133200—28no—
110#13133199—28no—
111#13133196—28no—
112#13133194—28no—
113#13133194—28no—
114C4×Dic106D414yes—
115C4×Dic106C2314yes—
116#13133182—22no—
117#13133182C2314yes—
118D4×Dic53—22no—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121D4×Dic53C2314yes—
122#13133179—22no—
123#13133179C2314yes—
124C4×C22⋊D53—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53C2311yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144#13133148C2314yes—
145#13133148C2314yes—
146C4⋊#88322C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133142C2314yes—
151#13133140C2314yes—
152#13133139C2314yes—
153#13133139C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156#13133137C2314yes—
157#13133127C2314yes—
158C8×Dic53C2314yes—
159C22×D4×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53—21no—
162C23×C4×C53—21no—
163C2×D8×C53—24no—
164C2×D8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×D4×C53—22no—
168C4×D4×C53—22no—
169C4×D4×C53C2314yes—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53C2311yescharacteristic
176#106×C53C2314yes—
177#102×C53C2314yes—
178#102×C53C2314yes—
179#97×C53C2314yes—
180C24×C53—21no—
181C24×C53—21no—
182C23×D53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53#4114yes—
189C2×D4×C53C2412yes—
190C2×D4×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—24no—
194C22×C4×C53—24no—
195C22×C4×C53—44no—
196C22×C4×C53—82no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—44no—
203C2×C22⋊D53—82no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—24no—
209C22×Dic53—44no—
210C22×Dic53—44no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—21no—
218C2×D212C2412yes—
219C2×C4×D53—24no—
220C2×C4×D53—82no—
221C2×Dic106—24no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—21no—
225C2×Dic106—24no—
226C2×Dic106—24no—
227C2×Dic106—24no—
228C2×Dic106—432no—
229C2×Dic106—44no—
230C2×Dic106—44no—
231C2×Dic106—44no—
232C2×Dic106C2×D414yes—
233C2×Dic106C2412yes—
234D8×C53—28no—
235C2×C8×C53—22no—
236C2×C8×C53—22no—
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C2412yes—
242C4⋊C4×C53C2412yes—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C42×C53C2×D412yes—
246C42×C53C2412yes—
247C22⋊Dic53—24no—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251#11719923—28no—
252#11719922—28no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53C2×D414yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2×D412yes—
270C4×Dic53C2412yes—
271C4×Dic53C2412yes—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276C23×C53—24no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289D4×C53—24no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
294D4×C53C2×#4114yes—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—48no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—84no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53C2×#4112yes—
307C2×C4×C532−1+412yes—
308C2×C4×C53C2511yescharacteristic
309C22⋊D53—48no—
310C22⋊D53—84no—
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—42no—
321C2×Dic53—48no—
322C2×Dic53AGL(1,ℤ/8)14yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327D212—22no—
328D212—22no—
329D212—42no—
330C4×D53—84no—
331Dic106—28no—
332Dic106—22no—
333Dic106—22no—
334Dic106—48no—
335Dic106—48no—
336Dic106—42no—
337Dic106—48no—
338C8×C53—22no—
339C8×C53—22no—
340#88322—22no—
341#88322—22no—
342C2×#3373—531nomaximal, Sylow
343C22×C53—24no—
344C22×C53—48no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—84no—
351C22×C53#54812yes—
352C22×C53C2×AGL(1,ℤ/8)12yes—
353C22×C53#57712yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#54812yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53C2×AGL(1,ℤ/8)14yes—
373C2×#559—531no—
374C2×D4×Q8—531no—
375#3373—5316no—
376C2×#489—531no—
377C2×#489—531no—
378C2×#486—531no—
379C2×#475—531no—
380C2×#476—531no—
381C2×#476—531no—
382C2×#463—531no—
383C2×#463—531no—
384C2×#459—531no—
385C2×#446—531no—
386C2×#442—531no—
387C2×#442D5311yescharacteristic, complemented
388C2×C4×SD16—531no—
389C2×C53—44no—
390C2×C53—82no—
391C2×C53#337314yescomplemented
392C2×C53C2×#54811yescharacteristic
393C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C53C2×#57711yescharacteristic
395D53—82no—
396C23×Q8—1061no—
397C22×SD16—531no—
398C22×D8—531no—
399C22×D8C2×D5311yescharacteristic
400#559—538no—
401#559—1064no—
402D4×Q8—538no—
403D4×Q8—1064no—
404C2×C4⋊Q8—531no—
405C2×C4⋊Q8—531no—
406C2×C4⋊Q8—531no—
407C2×#127—531no—
408C2×#124—531no—
409C2×#124—531no—
410C2×#124—1061no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—1061no—
414C2×C22⋊Q8—1061no—
415C2×C22⋊Q8—1061no—
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×D4—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4C2×D5311yescharacteristic
423C2×C4×D4C2×D5311yescharacteristic
424#489—538no—
425#489—538no—
426#486—538no—
427#476—538no—
428#476—538no—
429#475—538no—
430#463—538no—
431#463—538no—
432#459—538no—
433#446—538no—
434#442—538no—
435#442C2×D5318yescomplemented
436C4×SD16—538no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#106C2×D5311yescharacteristic
440C2×C4⋊C8—531no—
441C2×C4⋊C8—531no—
442C2×C4⋊C8—531no—
443C2×#103—531no—
444C2×#103—531no—
445C2×#103—531no—
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×#97—531no—
454C2×#97C2×D5311yescharacteristic
455C2×C4×C8—531no—
456C53C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—531no—
458C22×Q8—531no—
459C22×Q8—1061no—
460C22×Q8—1061no—
461C22×Q8—1068no—
462C22×Q8—1061no—
463C22×Q8—2128no—
464C22×D4—531no—
465C22×D4—1061no—
466C22×D4—1061no—
467C22×D4C22×D5311yescharacteristic
468C22×D4C22×D5311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C2×SD16—534no—
475C2×SD16—1064no—
476C2×D8—24no—
477C2×D8—534no—
478C2×D8—1064no—
479C2×D8C22×D5314yes—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8C22×D5311yescharacteristic
483C22×C8C22×D5311yescharacteristic
484C4⋊Q8—534no—
485C4⋊Q8—534no—
486C4⋊Q8—534no—
487C4⋊Q8—1062no—
488C4⋊Q8—1062no—
489C4⋊Q8—1062no—
490#127—534no—
491#127—1062no—
492#124—534no—
493#124—534no—
494#124—1062no—
495#124—1068no—
496#124—1062no—
497#123—1068no—
498#123—1068no—
499C22⋊Q8—1068no—
500C22⋊Q8—1068no—
501C22⋊Q8—1068no—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—1062no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1068no—
515C4×D4C22×D5314yes—
516C4×D4C22×D5314yes—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
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⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—531no—
538C2×C42—531no—
539C2×C42—1061no—
540C2×C42C22×D5311yescharacteristic
541#106—534no—
542#106—534no—
543#106C22×D5314yes—
544C4⋊C8—534no—
545C4⋊C8—534no—
546C4⋊C8—534no—
547#103—534no—
548#103—534no—
549#103—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102C22×D5314yes—
556#102C22×D5314yes—
557#97—534no—
558#97C22×D5314yes—
559C4×C8—534no—
560C24—21no—
561C24—21no—
562C24—1061no—
563C2×Q8—534no—
564C2×Q8—532no—
565C2×Q8—1064no—
566C2×Q8—1064no—
567C2×Q8—1064no—
568C2×Q8—1061no—
569C2×Q8—1064no—
570C2×Q8—1062no—
571C2×Q8—1062no—
572C2×Q8—2124no—
573C2×Q8—2124no—
574C2×Q8—2124no—
575C2×Q8—21232no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—532no—
582C2×D4—1064no—
583C2×D4—1064no—
584C2×D4—1061no—
585C2×D4—1062no—
586C2×D4—1062no—
587C2×D4—4242no—
588C2×D4—2124no—
589C2×D4#1171994514yes—
590C2×D4C23×D5312yes—
591C2×D4C23×D5312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—531no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—4242no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4D4×D5311yescharacteristic
612C22×C4D4×D5311yescharacteristic
613C22×C4C23×D5311yescharacteristic
614SD16—1068no—
615D8—28no—
616D8—1068no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—532no—
620C2×C8—532no—
621C2×C8—1062no—
622C2×C8—1062no—
623C2×C8C23×D5312yes—
624C2×C8C23×D5312yes—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—534no—
630C4⋊C4—532no—
631C4⋊C4—532no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1061no—
636C4⋊C4—1061no—
637C4⋊C4—1064no—
638C4⋊C4C23×D5312yes—
639C4⋊C4C23×D5312yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C42—532no—
650C42—532no—
651C42—532no—
652C42—532no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—1068no—
670Q8—1062no—
671Q8—1062no—
672Q8—2128no—
673Q8—2128no—
674Q8—2128no—
675Q8—2122no—
676D4—24no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—1062no—
682D4—1062no—
683D4—4244no—
684D4—2128no—
685D4—2122no—
686D4C2×#1171994514yes—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4—534no—
696C2×C4—532no—
697C2×C4—532no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—4244no—
707C2×C4—2128no—
708C2×C4—2128no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×D4×D5312yes—
713C2×C4C2×D4×D5312yes—
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4C2×#1171994512yes—
716C2×C4#1313326412yes—
717C2×C4C24×D5311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1062no—
721C8—1062no—
722C22—24no—
723C22—48no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—4244no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22#1681128212yes—
735C22AGL(1,ℤ/8)×D5312yes—
736C22#1681143312yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—534no—
743C4—1062no—
744C4—1062no—
745C4—1062no—
746C4—2122no—
747C4—2122no—
748C4—2122no—
749C4#1681128212yes—
750C4C22×#1171994511yescharacteristic
751C4C2×#1313326411yescharacteristic
752C2—44no—
753C2—82no—
754C2—4242no—
755C2#2028750814yesdirect product factor
756C2C2×#1681128211yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
758C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
prime radicalC2×#16810816C2
hypercenterC2×#442D53
hypocenterC53C2×#3373
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811356C2semidirect
2. C2×D4×Dic106C2semidirect
3. #20287508C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810981C2semidirect
6. C2×#16810968C2semidirect
7. C2×#16810907C2semidirect
8. C2×#16810913C2semidirect
9. C2×#16810912C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810836C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810732C2semidirect
15. C2×#16810714C2semidirect
16. C2×C53×#442C2semidirect
21. #16811356C22semidirect
23. D4×Dic106C22semidirect
42. #16810983C22semidirect
43. #16810981C22semidirect
44. #16810968C22semidirect
45. #16810913C22semidirect
46. #16810912C22semidirect
47. #16810907C22semidirect
48. #16810838C22semidirect
49. #16810836C22semidirect
51. #16810751C22semidirect
52. #16810732C22semidirect
53. #16810714C22semidirect
72. C53×#442C22semidirect
387. C2×#442D53semidirect
391. C2×C53#3373semidirect
435. #442C2×D53semidirect
456. C53C2×#3373semidirect
755. C2#20287508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×D4×Dic1062
#202875082
C2×#168109832
C2×#168109812
C2×#168109682
C2×#168109072
C2×#168109132
C2×#168109122
C2×#168108382
C2×#168108362
C2×#168108162
C2×#168107512
C2×#168107322
C2×#168107142
C2×C53×#4422
C2×#337353