Finite Group Databasebeta

← C2×#20284964 #28252393

Subgroups — C2×#20284964 #28252393

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811231C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic
3#20284964C2116yesmaximal, direct product factor
4C2×#16810967C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810925C211yesmaximal, characteristic, complemented
7C2×#16810922C211yesmaximal, characteristic, complemented
8C2×#16810827C211yesmaximal, characteristic, complemented
9C2×#16810826C211yesmaximal, characteristic, complemented
10C2×#16810775C211yesmaximal, characteristic
11C2×#16810772C211yesmaximal, characteristic
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810721C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21#16811231—24no—
22#16811231C2218yescomplemented
23C2×#13133215C2211yescharacteristic, complemented
24C2×#13133212—21no—
25C2×#13133211—21no—
26C2×#13133209—21no—
27C2×#13133208C2211yescharacteristic, complemented
28C2×#13133207—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133193C2211yescharacteristic
31#16811095—24no—
32#16811095C2218yes—
33C2×C4×Dic106C2211yescharacteristic, complemented
34C2×C4×D212C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×#13133177—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174C2211yescharacteristic
41C22×#11719921—21no—
42C2×C22⋊C4×D53—21no—
43#16810967C2218yescomplemented
44#16810962C2218yescomplemented
45#16810925C2218yescomplemented
46#16810922C2218yescomplemented
47#16810827C2218yescomplemented
48#16810826C2218yescomplemented
49#16810775C2218yes—
50#16810772C2218yes—
51#16810723C2218yescomplemented
52#16810721C2218yescomplemented
53C4×#11719913C2218yescomplemented
54#16810682C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133149C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133141C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic, complemented
71C2×C4×D4×C53C2211yescharacteristic
72C4×SD16×C53C2218yescomplemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C2×D4×D53—24no—
82C2×D4×D53—24no—
83C2×D4×D53—22no—
84C2×D4×D53C2314yes—
85C23×Dic53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719913—24no—
90C2×#11719913C2314yes—
91C2×#11719923—24no—
92C2×#11719923C2314yes—
93C2×#11719924—24no—
94C2×#11719924C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133215—22no—
98#13133215C2314yescomplemented
99#13133212—28no—
100#13133211—28no—
101#13133209—28no—
102#13133208—22no—
103#13133208C2314yescomplemented
104#13133207—28no—
105#13133197—22no—
106#13133197C2314yes—
107#13133193—22no—
108#13133193C2314yes—
109C4×Dic106—22no—
110C4×Dic106C2314yescomplemented
111C4×D212—22no—
112C4×D212C2314yes—
113D4×Dic53—22no—
114D4×Dic53C2314yes—
115#13133179—22no—
116#13133179C2314yes—
117C4×C22⋊D53—28no—
118#13133177—28no—
119#13133175—22no—
120#13133175C2314yes—
121#13133174D414yes—
122#13133174C2314yes—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×C22⋊Dic53—21no—
135C2×#11719921—28no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×#11719921D411yescharacteristic
143C22⋊C4×D53—28no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yescomplemented
148#13133150C2314yescomplemented
149#13133149C2314yescomplemented
150#13133146C2314yescomplemented
151#13133146C2314yescomplemented
152#13133142C2314yescomplemented
153#13133141C2314yescomplemented
154#13133140C2314yescomplemented
155#13133139C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133128C2314yescomplemented
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yescomplemented
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#106×C53C2314yescomplemented
179#103×C53C2314yescomplemented
180#102×C53C2314yes—
181C4×C8×C53C2314yescomplemented
182C24×C53—21no—
183C23×D53—21no—
184C23×D53—28no—
185C23×D53—24no—
186C23×D53—82no—
187C23×D53—82no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—21no—
194C2×D4×C53—22no—
195C2×D4×C53#4114yes—
196C2×D4×C53C2412yes—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—24no—
201C22×C4×C53—82no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—28no—
206C2×C22⋊D53—24no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—82no—
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215D4×D53—216no—
216D4×D53—28no—
217D4×D53—28no—
218C2×D212—21no—
219C2×D212—22no—
220C2×D212#4114yes—
221C2×D212C2412yes—
222C2×C4×D53—22no—
223C2×C4×D53—22no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—82no—
227C2×C4×D53—82no—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2412yes—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106C2412yes—
234SD16×C53—28no—
235C2×C8×C53—22no—
236C2×C8×C53—22no—
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C42×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2412yes—
248C22⋊Dic53—24no—
249#11719924—28no—
250#11719923—28no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921C2×D414yes—
257#11719921C2×D414yes—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53—24no—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919C2×D414yes—
270#11719919C2×D414yes—
271C4×Dic53—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279#11719913—28no—
280C23×C53—24no—
281C23×C53—22no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—24no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—216no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—84no—
294C22×D53—84no—
295C22×D53—816no—
296C22×D53C22×D412yes—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—42no—
300D4×C53—24no—
301D4×C53—22no—
302D4×C53C2×#4114yes—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—84no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2×#4112yes—
317C2×C4×C53C2511yescharacteristic
318C22⋊D53—216no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—84no—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332D212—24no—
333D212—22no—
334D212C2×#4114yes—
335C4×D53—24no—
336C4×D53—22no—
337C4×D53—22no—
338C4×D53—84no—
339C4×D53—84no—
340Dic106—22no—
341Dic106—22no—
342Dic106—42no—
343C8×C53—22no—
344C8×C53—22no—
345#88322—22no—
346#88322—22no—
347C2×#3123—531nomaximal, Sylow
348C22×C53—24no—
349C22×C53—48no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53#52512yes—
353C22×C53#57712yes—
354C22×C53#57712yes—
355C22×C53C23×D411yescharacteristic
356C2×D53—22no—
357C2×D53—24no—
358C2×D53—22no—
359C2×D53—22no—
360C2×D53—44no—
361C2×D53—48no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—816no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#52512yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C22×#4111yescharacteristic
373Dic53—22no—
374Dic53—22no—
375Dic53—22no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379C2×#541—531no—
380C2×#518—531no—
381#3123—5316no—
382C2×#485—531no—
383C2×#485—531no—
384C2×#478—531no—
385C2×#478—531no—
386C2×#461—531no—
387C2×#461—531no—
388C2×#450—531no—
389C2×#450—531no—
390C2×#440—531no—
391C2×#440—531no—
392C2×C4×SD16—531no—
393C2×C4×SD16D5311yescharacteristic, complemented
394C2×#433—531no—
395C2×C53—44no—
396C2×C53#312314yescomplemented
397C2×C53C2×#52511yescharacteristic
398C2×C53C2×#57711yescharacteristic
399C2×C53C2×#57711yescharacteristic
400D53—42no—
401D53—44no—
402C23×D4—531no—
403C22×SD16—531no—
404C22×SD16—531no—
405C22×SD16—531no—
406C22×SD16C2×D5311yescharacteristic
407#541—538no—
408#541—1064no—
409C2×C4⋊Q8—531no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#125—531no—
413C2×#125—1061no—
414C2×#125—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8—531no—
417#518—538no—
418#518—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8C2×D5311yescharacteristic, complemented
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—1061no—
425C2×C4×D4—1061no—
426C2×C4×D4C2×D5311yescharacteristic
427C2×#117—531no—
428C2×#117—531no—
429C22×C22⋊C4—1061no—
430C22×C22⋊C4—1061no—
431#485—538no—
432#485—538no—
433#478—538no—
434#478—538no—
435#461—538no—
436#461—538no—
437#450—538no—
438#450—538no—
439#440—538no—
440#440—538no—
441C4×SD16—538no—
442C4×SD16C2×D5318yescomplemented
443#433—538no—
444C2×#107—531no—
445C2×#107—531no—
446C2×#106—531no—
447C2×#106C2×D5311yescharacteristic, complemented
448C2×C4⋊C8—531no—
449C2×C4⋊C8—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103C2×D5311yescharacteristic, complemented
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102C2×D5311yescharacteristic
458C2×C22⋊C8—531no—
459C2×C22⋊C8—531no—
460C2×#97—531no—
461C2×C4×C8C2×D5311yescharacteristic, complemented
462C53C2×#312311yescharacteristic, complemented, Sylow
463C25—1061no—
464C22×Q8—531no—
465C22×Q8C22×D5311yescharacteristic
466C22×D4—534no—
467C22×D4—531no—
468C22×D4—1062no—
469C22×D4—1061no—
470C22×D4—1064no—
471C22×D4—1064no—
472C22×D4C22×D5311yescharacteristic
473C23×C4—21no—
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C2×SD16—24no—
479C2×SD16—534no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16—1064no—
485C2×SD16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—1068no—
493#126—1068no—
494#125—534no—
495#125—1068no—
496#125—1062no—
497#125—1068no—
498C22⋊Q8—534no—
499C22⋊Q8—534no—
500C22⋊Q8—1062no—
501C22⋊Q8—1062no—
502C4×Q8—22no—
503C4×Q8—534no—
504C4×Q8—1062no—
505C4×Q8C22×D5314yescomplemented
506C4×D4—22no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1062no—
511C4×D4—1062no—
512C4×D4—1068no—
513C4×D4—1068no—
514C4×D4—1062no—
515C4×D4C22×D5314yes—
516#117—534no—
517#117—534no—
518#117—534no—
519#117—1062no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1068no—
538C2×C22⋊C4—1068no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C42—21no—
546C2×C42—531no—
547C2×C42—1061no—
548C2×C42—1061no—
549C2×C42C22×D5311yescharacteristic
550#107—534no—
551#107—534no—
552#106—534no—
553#106C22×D5314yescomplemented
554C4⋊C8—534no—
555C4⋊C8—534no—
556#103—534no—
557#103—534no—
558#103—534no—
559#103C22×D5314yescomplemented
560#102—534no—
561#102—534no—
562#102—534no—
563#102C22×D5314yes—
564C22⋊C8—534no—
565C22⋊C8—534no—
566#97—534no—
567C4×C8C22×D5314yescomplemented
568C24—21no—
569C24—531no—
570C24—1064no—
571C24—1068no—
572C24—1061no—
573C24—4242no—
574C24—4242no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—532no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8C23×D5312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—534no—
586C2×D4—532no—
587C2×D4—1064no—
588C2×D4—1068no—
589C2×D4—10616no—
590C2×D4—1068no—
591C2×D4—1068no—
592C2×D4—1061no—
593C2×D4—1062no—
594C2×D4#1171994514yes—
595C2×D4C23×D5312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—531no—
602C22×C4—531no—
603C22×C4—531no—
604C22×C4—532no—
605C22×C4—532no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1064no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4—4242no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620SD16—28no—
621SD16—1068no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—534no—
636C4⋊C4—534no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1064no—
648C4⋊C4C23×D5312yes—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—534no—
652C22⋊C4—534no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C42—24no—
660C42—532no—
661C42—532no—
662C42—1064no—
663C42—1064no—
664C42D4×D5312yes—
665C42C23×D5312yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—532no—
671C23—10616no—
672C23—1062no—
673C23—1064no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—4244no—
678C23—4244no—
679C23—42416no—
680C23—2122no—
681C23—2122no—
682C23C2×D4×D5311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—1062no—
687Q8—1062no—
688Q8—2122no—
689D4—24no—
690D4—22no—
691D4—534no—
692D4—10616no—
693D4—1064no—
694D4—1062no—
695D4C2×#1171994514yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—532no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—4244no—
718C2×C4—4244no—
719C2×C4—4244no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4C2×D4×D5312yes—
724C2×C4C2×D4×D5312yes—
725C2×C4C2×D4×D5311yescharacteristic
726C2×C4#41×D5312yes—
727C2×C4C2×#1171994512yes—
728C2×C4C24×D5311yescharacteristic
729C8—22no—
730C8—22no—
731C8—1062no—
732C8—1062no—
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—1062no—
738C22—1062no—
739C22—1062no—
740C22—1064no—
741C22—42416no—
742C22—2124no—
743C22—2128no—
744C22—2122no—
745C22—2122no—
746C22#1681113212yes—
747C22#1681142912yes—
748C22#1681143012yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1062no—
756C4—1062no—
757C4—1062no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4#1681113212yes—
762C4C2×#41×D5311yescharacteristic
763C4C22×#1171994511yescharacteristic
764C2—44no—
765C2—2122no—
766C2—2124no—
767C2#2028496414yesdirect product factor
768C2C2×#1681113211yescharacteristic
769C2C2×#1681142911yescharacteristic
770C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3123
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16811231C2semidirect
3. #20284964C2direct (N × H)
4. C2×#16810967C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810925C2semidirect
7. C2×#16810922C2semidirect
8. C2×#16810827C2semidirect
9. C2×#16810826C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810721C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×#16810682C2semidirect
16. C2×C4×SD16×C53C2semidirect
22. #16811231C22semidirect
23. C2×#13133215C22semidirect
27. C2×#13133208C22semidirect
33. C2×C4×Dic106C22semidirect
43. #16810967C22semidirect
44. #16810962C22semidirect
45. #16810925C22semidirect
46. #16810922C22semidirect
47. #16810827C22semidirect
48. #16810826C22semidirect
51. #16810723C22semidirect
52. #16810721C22semidirect
53. C4×#11719913C22semidirect
54. #16810682C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133149C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133141C22semidirect
62. C2×#13133140C22semidirect
68. C2×#13133128C22semidirect
70. C2×C4×Q8×C53C22semidirect
72. C4×SD16×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
98. #13133215C23semidirect
103. #13133208C23semidirect
110. C4×Dic106C23semidirect
147. #13133150C23semidirect
148. #13133150C23semidirect
149. #13133149C23semidirect
150. #13133146C23semidirect
151. #13133146C23semidirect
152. #13133142C23semidirect
153. #13133141C23semidirect
154. #13133140C23semidirect
160. #13133128C23semidirect
169. C4×Q8×C53C23semidirect
178. #106×C53C23semidirect
179. #103×C53C23semidirect
181. C4×C8×C53C23semidirect
393. C2×C4×SD16D53semidirect
396. C2×C53#3123semidirect
420. C2×C4×Q8C2×D53semidirect
442. C4×SD16C2×D53semidirect
447. C2×#106C2×D53semidirect
453. C2×#103C2×D53semidirect
461. C2×C4×C8C2×D53semidirect
462. C53C2×#3123semidirect
505. C4×Q8C22×D53semidirect
553. #106C22×D53semidirect
559. #103C22×D53semidirect
567. C4×C8C22×D53semidirect
767. C2#20284964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112312
C2×#168110952
#202849642
C2×#168109672
C2×#168109622
C2×#168109252
C2×#168109222
C2×#168108272
C2×#168108262
C2×#168107752
C2×#168107722
C2×#168107232
C2×#168107212
C2×C4×#117199132
C2×#168106822
C2×C4×SD16×C532
C2×#312353