Finite Group Databasebeta

← C2×#20287736 #28265049

Subgroups — C2×#20287736 #28265049

Order 13568.

2250 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811345C211yesmaximal, characteristic, complemented
2C2×#16811294C211yesmaximal, characteristic, complemented
3#20287736C2116yesmaximal, direct product factor
4C2×#16811012C211yesmaximal, characteristic, complemented
5C2×#16811009C211yesmaximal, characteristic, complemented
6C2×#16810994C211yesmaximal, characteristic, complemented
7C2×#16810823C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810841C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×#16810817C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×#16810705C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×D424C2211yescharacteristic
24C22×D424C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26#16811345—24no—
27#16811345C2218yescomplemented
28#16811294—24no—
29#16811294C2218yescomplemented
30C2×#13133215C2211yescharacteristic
31C2×#13133214C2211yescharacteristic
32C2×#13133213C2211yescharacteristic
33C2×#13133213C2211yescharacteristic
34C2×#13133212—21no—
35C2×#13133211—21no—
36C2×#13133206C2211yescharacteristic
37C2×#13133205C2211yescharacteristic
38C2×#13133195—21no—
39C2×#13133191—21no—
40C2×#13133190—21no—
41C2×#13133190—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133179C2211yescharacteristic
46C2×#13133179C2211yescharacteristic
47C2×#13133174—21no—
48#16811012C2218yescomplemented
49#16811009C2218yescomplemented
50#16810994C2218yescomplemented
51#16810841C2218yescomplemented
52#16810838C2218yescomplemented
53#16810827C2218yescomplemented
54#16810823C2218yescomplemented
55#16810822C2218yescomplemented
56#16810817C2218yescomplemented
57#16810751C2218yescomplemented
58#16810722C2218yescomplemented
59#16810705C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C2×#11719913—24no—
94C2×#11719913—42no—
95C2×#11719913C2314yes—
96C2×#11719913C2314yes—
97C2×#11719923—42no—
98C2×#11719923C2314yes—
99C2×#11719924—42no—
100C2×#11719924—42no—
101C2×#11719924C2314yes—
102C2×#11719924C2314yes—
103C2×D424—24no—
104C2×D424—42no—
105C2×D424C2314yes—
106C2×D424C2314yes—
107C2×#11719922—42no—
108C2×#11719922C2314yes—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111#13133215—22no—
112#13133215C2314yes—
113#13133214—22no—
114#13133214C2314yes—
115#13133213—22no—
116#13133213—22no—
117#13133213C2314yes—
118#13133213C2314yes—
119#13133212—28no—
120#13133211—28no—
121#13133206—22no—
122#13133206C2314yes—
123#13133205—22no—
124#13133205C2314yes—
125#13133195—28no—
126#13133191—28no—
127#13133190—28no—
128#13133190—28no—
129C4×Dic106D414yes—
130C4×Dic106C2314yes—
131#13133182—22no—
132#13133182C2314yes—
133#13133179—22no—
134#13133179—22no—
135#13133179—22no—
136#13133179C2314yes—
137#13133179C2314yes—
138#13133179C2314yes—
139#13133174—28no—
140C2×C4⋊Dic53D411yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919D411yescharacteristic
145C2×#11719919D411yescharacteristic
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×C4×Dic53—21no—
154C2×C4×Dic53C2311yescharacteristic
155C2×C4×Dic53C2311yescharacteristic
156C4⋊#88322C2314yes—
157#13133146C2314yes—
158#13133146C2314yes—
159#13133140C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133127C2314yes—
164C8×Dic53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C2×SD16×C53—24no—
169C2×SD16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C4×Q8×C53—22no—
173C4×Q8×C53C2314yes—
174C4×D4×C53—22no—
175C4×D4×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182#107×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185#97×C53C2314yes—
186C24×C53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—82no—
213C2×C22⋊D53—82no—
214C22×Dic53—21no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719945—432no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—21no—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—24no—
230C2×D212—24no—
231C2×D212—44no—
232C2×D212—82no—
233C2×D212C2412yes—
234C2×D212C2412yes—
235C2×D212C2412yes—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×Dic106—24no—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—21no—
246C2×Dic106C2×D414yes—
247C2×Dic106C2412yes—
248SD16×C53—28no—
249C2×C8×C53—22no—
250C2×C8×C53#4114yescomplemented
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C42×C53—24no—
260C42×C53C2×D412yes—
261C42×C53C2412yes—
262#11719924—44no—
263#11719924—44no—
264#11719923—44no—
265#11719922—44no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273C4⋊Dic53C2×D414yes—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919C2×D414yes—
278#11719919C2×D414yes—
279C4×Dic53—24no—
280C4×Dic53C2×D412yes—
281C4×Dic53C2×D412yes—
282C4×Dic53C2412yes—
283C4×Dic53C2412yes—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288D424—28no—
289D424—44no—
290#11719913—28no—
291#11719913—44no—
292C23×C53—22no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—42no—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—42no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—48no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4112yes—
328C2×C4×C53H(5,𝔽2)12yes—
329C2×C4×C53C2511yescharacteristic
330C22⋊D53—48no—
331C22⋊D53—48no—
332C22⋊D53—84no—
333C22⋊D53—84no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—42no—
339C2×Dic53AGL(1,ℤ/8)14yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343C2×Dic53C22×D412yes—
344D212—22no—
345D212—22no—
346D212—22no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—48no—
351D212—42no—
352D212—42no—
353D212—42no—
354D212—84no—
355C4×D53—48no—
356C4×D53—48no—
357C4×D53—48no—
358Dic106—28no—
359Dic106—22no—
360Dic106—22no—
361Dic106—42no—
362C8×C53—22no—
363C8×C53C2×#4114yescomplemented
364#88322—22no—
365#88322—22no—
366C2×#3397—531nomaximal, Sylow
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—84no—
371C22×C53#55012yes—
372C22×C53C2×AGL(1,ℤ/8)12yes—
373C22×C53#57712yes—
374C22×C53C23×D411yescharacteristic
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C2×D53—84no—
386C2×D53—84no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#55012yes—
393C4×C53C22×#4111yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—22no—
398Dic53—42no—
399Dic53C2×AGL(1,ℤ/8)14yes—
400C2×#556—531no—
401C2×#550—531no—
402#3397—5316no—
403C2×#496—531no—
404C2×#496—531no—
405C2×#492—531no—
406C2×#460—531no—
407C2×#460—531no—
408C2×#463—531no—
409C2×#463—531no—
410C2×#461—531no—
411C2×#459—531no—
412C2×#446—531no—
413C2×#440—531no—
414C2×#440D5311yescharacteristic, complemented
415C2×C4×D8—531no—
416C2×C53—82no—
417C2×C53#339714yescomplemented
418C2×C53C2×#55011yescharacteristic
419C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
420C2×C53C2×#57711yescharacteristic
421D53—82no—
422D53—82no—
423D53—82no—
424C22×#41—1061no—
425C22×SD16—531no—
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×SD16—531no—
430C22×SD16C2×D5311yescharacteristic
431C22×D8—531no—
432C22×D8—531no—
433C22×D8—531no—
434#556—538no—
435#556—1064no—
436#550—538no—
437#550—1064no—
438C2×C4⋊Q8—531no—
439C2×#127—531no—
440C2×#127—531no—
441C2×#127—531no—
442C2×#126—1061no—
443C2×#126—1061no—
444C2×#124—531no—
445C2×#124—531no—
446C2×C22⋊Q8—1061no—
447C2×#121—1061no—
448C2×#121—1061no—
449C2×#121—1061no—
450C2×C4×Q8—531no—
451C2×C4×Q8—531no—
452C2×C4×Q8C2×D5311yescharacteristic
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—531no—
456C2×C4×D4C2×D5311yescharacteristic
457C2×#117—1061no—
458#496—538no—
459#496—538no—
460#492—538no—
461#463—538no—
462#463—538no—
463#461—538no—
464#460—538no—
465#460—538no—
466#459—538no—
467#446—538no—
468#440—538no—
469#440C2×D5318yescomplemented
470C4×D8—538no—
471C2×#107C2×D5311yescharacteristic
472C2×C4⋊C8—531no—
473C2×C4⋊C8—531no—
474C2×C4⋊C8—531no—
475C2×#103—531no—
476C2×#103C2×D5311yescharacteristic
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102C2×D5311yescharacteristic
481C2×#97—531no—
482C2×#97C2×D5311yescharacteristic
483C2×C4×C8—531no—
484C53C2×#339711yescharacteristic, complemented, Sylow
485C2×#41—1068no—
486C2×#41—2128no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8C22×D5311yescharacteristic
490C22×D4—531no—
491C22×D4—531no—
492C22×D4—531no—
493C22×D4—1061no—
494C22×D4—1061no—
495C22×D4—1061no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C23×C4—21no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4—1061no—
504C2×SD16—24no—
505C2×SD16—534no—
506C2×SD16—534no—
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—534no—
510C2×SD16—1064no—
511C2×SD16—2122no—
512C2×SD16—2122no—
513C2×SD16—2122no—
514C2×SD16—2122no—
515C2×SD16C22×D5314yes—
516C2×D8—534no—
517C2×D8—534no—
518C2×D8—534no—
519C2×D8—1064no—
520C2×D8—2122no—
521C2×D8—2122no—
522C22×C8—531no—
523C22×C8—531no—
524C22×C8C22×D5311yescharacteristic
525C22×C8C22×D5311yescharacteristic
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528#127—534no—
529#127—534no—
530#127—534no—
531#127—1062no—
532#127—1062no—
533#127—1062no—
534#126—1068no—
535#126—1068no—
536#124—534no—
537#124—534no—
538#124—1062no—
539#124—1062no—
540C22⋊Q8—1068no—
541#121—1068no—
542#121—1068no—
543#121—1068no—
544C4×Q8—22no—
545C4×Q8—534no—
546C4×Q8—534no—
547C4×Q8—534no—
548C4×Q8—1062no—
549C4×Q8C22×D5314yes—
550C4×D4—22no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1062no—
555C4×D4—1062no—
556C4×D4—1062no—
557C4×D4C22×D5314yes—
558#117—1068no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C42—21no—
577C2×C42—531no—
578C2×C42—531no—
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581#107C22×D5314yes—
582C4⋊C8—534no—
583C4⋊C8—534no—
584C4⋊C8—534no—
585#103—534no—
586#103C22×D5314yes—
587#102—534no—
588#102—534no—
589#102—534no—
590#102C22×D5314yes—
591#97—534no—
592#97C22×D5314yes—
593C4×C8—534no—
594C24—21no—
595C24—1061no—
596C24—1061no—
597C24—1061no—
598#41—21232no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—534no—
603C2×Q8—532no—
604C2×Q8—1064no—
605C2×Q8—1061no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8C23×D5312yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—532no—
613C2×D4—532no—
614C2×D4—532no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1061no—
623C2×D4—1064no—
624C2×D4—1062no—
625C2×D4—1062no—
626C2×D4—1062no—
627C2×D4—1062no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—4242no—
631C2×D4—4242no—
632C2×D4—4242no—
633C2×D4—2124no—
634C2×D4—2124no—
635C2×D4—2124no—
636C2×D4C23×D5312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—531no—
643C22×C4—531no—
644C22×C4—531no—
645C22×C4—531no—
646C22×C4—1064no—
647C22×C4—1064no—
648C22×C4—1064no—
649C22×C4—1061no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656SD16—28no—
657SD16—1068no—
658SD16—2124no—
659SD16—2124no—
660SD16—2124no—
661SD16—2124no—
662D8—1068no—
663D8—2124no—
664D8—2124no—
665C2×C8—22no—
666C2×C8—532no—
667C2×C8—532no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8#1171994514yescomplemented
671C2×C8C23×D5312yes—
672C2×C8C23×D5312yes—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—534no—
677C4⋊C4—534no—
678C4⋊C4—534no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4C23×D5312yes—
683C4⋊C4C23×D5312yes—
684C22⋊C4—24no—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C42—24no—
693C42—532no—
694C42—532no—
695C42—532no—
696C42—532no—
697C42—1064no—
698C42D4×D5312yes—
699C42C23×D5312yes—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23—2122no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23C2×D4×D5311yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—1068no—
721Q8—1062no—
722Q8—1062no—
723Q8—2122no—
724D4—22no—
725D4—22no—
726D4—42no—
727D4—1062no—
728D4—1062no—
729D4—1062no—
730D4—1062no—
731D4—1062no—
732D4—1062no—
733D4—4244no—
734D4—4244no—
735D4—4244no—
736D4—2128no—
737D4—2128no—
738D4—2128no—
739D4—2122no—
740D4—2122no—
741D4—2122no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—534no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—532no—
755C2×C4—532no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—2128no—
761C2×C4—2128no—
762C2×C4—2128no—
763C2×C4—2122no—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5312yes—
766C2×C4C2×D4×D5311yescharacteristic
767C2×C4C2×#1171994512yes—
768C2×C4#1313326312yes—
769C2×C4C24×D5311yescharacteristic
770C8—22no—
771C8—1062no—
772C8—1062no—
773C8C2×#1171994514yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—4244no—
779C22—4244no—
780C22—4244no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22—2122no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22#1681129412yes—
791C22AGL(1,ℤ/8)×D5312yes—
792C22#1681143212yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—534no—
800C4—1062no—
801C4—1062no—
802C4—1062no—
803C4—2122no—
804C4#1681129412yes—
805C4C22×#1171994511yescharacteristic
806C4C2×#1313326311yescharacteristic
807C2—82no—
808C2—4242no—
809C2—4242no—
810C2—4242no—
811C2#2028773614yesdirect product factor
812C2C2×#1681129411yescharacteristic
813C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
814C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3397
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811345C2semidirect
2. C2×#16811294C2semidirect
3. #20287736C2direct (N × H)
4. C2×#16811012C2semidirect
5. C2×#16811009C2semidirect
6. C2×#16810994C2semidirect
7. C2×#16810823C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810841C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810827C2semidirect
12. C2×#16810817C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810722C2semidirect
15. C2×#16810705C2semidirect
16. C2×C53×#440C2semidirect
27. #16811345C22semidirect
29. #16811294C22semidirect
48. #16811012C22semidirect
49. #16811009C22semidirect
50. #16810994C22semidirect
51. #16810841C22semidirect
52. #16810838C22semidirect
53. #16810827C22semidirect
54. #16810823C22semidirect
55. #16810822C22semidirect
56. #16810817C22semidirect
57. #16810751C22semidirect
58. #16810722C22semidirect
59. #16810705C22semidirect
72. C53×#440C22semidirect
250. C2×C8×C53#41semidirect
363. C8×C53C2×#41semidirect
414. C2×#440D53semidirect
417. C2×C53#3397semidirect
469. #440C2×D53semidirect
484. C53C2×#3397semidirect
670. C2×C8#11719945semidirect
773. C8C2×#11719945semidirect
811. C2#20287736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113452
C2×#168112942
#202877362
C2×#168110122
C2×#168110092
C2×#168109942
C2×#168108232
C2×#168108222
C2×#168108412
C2×#168108382
C2×#168108272
C2×#168108172
C2×#168107512
C2×#168107222
C2×#168107052
C2×C53×#4402
C2×#339753