Finite Group Databasebeta

← C2×#20285784 #28255432

Subgroups — C2×#20285784 #28255432

Order 13568.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811231C211yesmaximal, characteristic, complemented
2C2×#16811191C211yesmaximal, characteristic
3#20285784C2116yesmaximal, direct product factor
4C2×#16811016C211yesmaximal, characteristic, complemented
5C2×#16810994C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810979C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810824C211yesmaximal, characteristic, complemented
10C2×#16810823C211yesmaximal, characteristic, complemented
11C2×#16810788C211yesmaximal, characteristic, complemented
12C2×#16810784C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810772C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24C22×#11719924C2211yescharacteristic, complemented
25#16811231—24no—
26#16811231C2218yescomplemented
27#16811191—24no—
28#16811191C2218yes—
29C2×#13133215C2211yescharacteristic, complemented
30C2×#13133214C2211yescharacteristic
31C2×#13133213C2211yescharacteristic
32C2×#13133212—21no—
33C2×#13133211—21no—
34C2×#13133209—21no—
35C2×#13133208C2211yescharacteristic, complemented
36C2×#13133207—21no—
37C2×#13133206C2211yescharacteristic
38C2×#13133197C2211yescharacteristic
39C2×#13133193C2211yescharacteristic
40C2×#13133190—21no—
41C2×#13133190—21no—
42C2×#13133187—21no—
43C2×#13133187—21no—
44C2×C4×Dic106C2211yescharacteristic, complemented
45C2×#13133174C2211yescharacteristic
46#16811016C2218yescomplemented
47#16810994C2218yescomplemented
48#16810986C2218yescomplemented
49#16810979C2218yescomplemented
50#16810842C2218yescomplemented
51#16810824C2218yescomplemented
52#16810823C2218yescomplemented
53#16810788C2218yescomplemented
54#16810784C2218yescomplemented
55#16810775C2218yescomplemented
56#16810772C2218yescomplemented
57#16810683C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×Q16×C53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic, complemented
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—42no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C2×D4×D53—22no—
92C2×D4×D53—42no—
93C2×D4×D53—42no—
94C2×D4×D53C2314yes—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719925—42no—
98C2×#11719925C2314yescomplemented
99C2×#11719913—42no—
100C2×#11719913—42no—
101C2×#11719913C2314yes—
102C2×#11719913C2314yescomplemented
103C2×#11719923—42no—
104C2×#11719923C2314yes—
105C2×#11719924—42no—
106C2×#11719924—42no—
107C2×#11719924C2314yes—
108C2×#11719924C2314yescomplemented
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111#13133215—22no—
112#13133215C2314yescomplemented
113#13133214—22no—
114#13133214C2314yes—
115#13133213—22no—
116#13133213C2314yes—
117#13133212—28no—
118#13133211—28no—
119#13133209—28no—
120#13133208—22no—
121#13133208C2314yescomplemented
122#13133207—28no—
123#13133206—22no—
124#13133206C2314yes—
125#13133197—22no—
126#13133197C2314yes—
127#13133193—22no—
128#13133193C2314yes—
129#13133190—28no—
130#13133190—28no—
131#13133187—28no—
132#13133187—28no—
133C4×Dic106—22no—
134C4×Dic106C2314yescomplemented
135#13133174D414yes—
136#13133174C2314yes—
137C2×C4⋊Dic53—21no—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919—21no—
145C2×#11719919D411yescharacteristic
146C2×#11719919D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921D411yescharacteristic
152C2×#11719921D411yescharacteristic
153C2×C4×Dic53—21no—
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yescomplemented
156#13133141C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yescomplemented
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164#13133127C2314yescomplemented
165C8×Dic53C2314yescomplemented
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C2×Q16×C53—42no—
170C2×Q16×C53C2314yescomplemented
171C2×SD16×C53—42no—
172C2×SD16×C53C2314yes—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175#124×C53—22no—
176#124×C53C2314yes—
177C4×Q8×C53—22no—
178C4×Q8×C53C2314yescomplemented
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C4⋊C8×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yes—
188C24×C53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—24no—
192C23×D53—44no—
193C23×D53—82no—
194C23×D53—82no—
195C23×D53C2×D411yescharacteristic
196C2×Q8×C53—21no—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C2×D4×C53—21no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53C2412yes—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53—82no—
219C2×C22⋊D53—82no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225#11719949—44no—
226#11719949—44no—
227#11719949—48no—
228D4×D53—44no—
229D4×D53—44no—
230D4×D53—48no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—24no—
236C2×D212—21no—
237C2×D212—21no—
238C2×D212—24no—
239C2×D212—24no—
240C2×D212—44no—
241C2×D212—82no—
242C2×D212—82no—
243C2×D212C2412yes—
244C2×D212C2412yes—
245C2×C4×D53—22no—
246C2×C4×D53—22no—
247C2×C4×D53—24no—
248C2×C4×D53—44no—
249C2×C4×D53C2×D412yes—
250C2×C4×D53C2412yes—
251C2×Dic106—22no—
252C2×Dic106—22no—
253C2×Dic106—21no—
254C2×Dic106C2412yes—
255Q16×C53—44no—
256SD16×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C22⋊C4×C53—24no—
265C22⋊C4×C53—24no—
266C42×C53—24no—
267C42×C53C2×D412yes—
268C42×C53C2412yes—
269#11719925—44no—
270#11719924—44no—
271#11719924—44no—
272#11719923—44no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921C2×D414yes—
278#11719921C2×D414yes—
279C4⋊Dic53—21no—
280C4⋊Dic53—24no—
281C4⋊Dic53—24no—
282C4⋊Dic53C2412yes—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287#11719919—24no—
288#11719919C2×D414yes—
289#11719919C2×D414yes—
290C4×Dic53—24no—
291C4×Dic53C2×D412yes—
292C4×Dic53C2412yes—
293C2×#88322—22no—
294C2×#88322—22no—
295C2×#88322C2412yes—
296C2×#88322C2412yes—
297#11719913—44no—
298#11719913—44no—
299C23×C53—22no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—48no—
310C22×D53—42no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—84no—
317C22×D53—84no—
318C22×D53—816no—
319C22×D53C22×D412yes—
320Q8×C53—22no—
321Q8×C53—22no—
322Q8×C53—22no—
323Q8×C53—22no—
324Q8×C53—42no—
325Q8×C53—42no—
326D4×C53—22no—
327D4×C53—22no—
328D4×C53—42no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—42no—
335C2×C4×C53—42no—
336C2×C4×C53—42no—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53H(5,𝔽2)12yes—
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53C2511yescharacteristic
343C22⋊D53—48no—
344C22⋊D53—84no—
345C22⋊D53—84no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356D212—22no—
357D212—22no—
358D212—22no—
359D212—22no—
360D212—48no—
361D212—42no—
362D212—42no—
363D212—84no—
364D212—84no—
365C4×D53—24no—
366C4×D53—22no—
367C4×D53—22no—
368C4×D53—48no—
369Dic106—22no—
370Dic106—22no—
371Dic106—42no—
372C8×C53—22no—
373C8×C53—22no—
374#88322—22no—
375#88322—22no—
376C2×#3222—531nomaximal, Sylow
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—84no—
381C22×C53#53512yes—
382C22×C53#57712yes—
383C22×C53#57712yes—
384C22×C53C23×D411yescharacteristic
385C2×D53—22no—
386C2×D53—22no—
387C2×D53—22no—
388C2×D53—44no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—816no—
396C2×D53—84no—
397C2×D53—84no—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53—42no—
403C4×C53#53512yes—
404C4×C53C2×H(5,𝔽2)11yescharacteristic
405C4×C53C2×H(5,𝔽2)11yescharacteristic
406Dic53—22no—
407Dic53—22no—
408Dic53—22no—
409Dic53—42no—
410Dic53—42no—
411C2×#541—531no—
412C2×#535—531no—
413#3222—5316no—
414C2×#497—531no—
415C2×#492—531no—
416C2×#490—531no—
417C2×#488—531no—
418C2×#464—531no—
419C2×#464D5311yescharacteristic, complemented
420C2×#460—531no—
421C2×#460—531no—
422C2×#452—531no—
423C2×#452—531no—
424C2×#450—531no—
425C2×#450—531no—
426C2×#433—531no—
427C2×C53—82no—
428C2×C53#322214yescomplemented
429C2×C53C2×#53511yescharacteristic
430C2×C53C2×#57711yescharacteristic
431C2×C53C2×#57711yescharacteristic
432D53—42no—
433D53—82no—
434D53—82no—
435C22×#41—531no—
436C23×D4—531no—
437C22×Q16—531no—
438C22×Q16C2×D5311yescharacteristic, complemented
439C22×SD16—531no—
440C22×SD16—531no—
441C22×SD16—531no—
442C22×SD16—531no—
443C22×SD16—531no—
444C22×SD16C2×D5311yescharacteristic
445#541—538no—
446#541—1064no—
447#535—538no—
448#535—1064no—
449C2×C4⋊Q8—531no—
450C2×#127—531no—
451C2×#127—531no—
452C2×#126—1061no—
453C2×#126—1061no—
454C2×#125—531no—
455C2×#125—1061no—
456C2×#125—1061no—
457C2×#124—531no—
458C2×#124C2×D5311yescharacteristic
459C2×C22⋊Q8—531no—
460C2×C22⋊Q8—531no—
461C2×#121—1061no—
462C2×#121—1061no—
463C2×#120—1061no—
464C2×#120—1061no—
465C2×C4×Q8—531no—
466C2×C4×Q8C2×D5311yescharacteristic, complemented
467C2×#117—531no—
468#497—538no—
469#492—538no—
470#490—538no—
471#488—538no—
472#464—538no—
473#464C2×D5318yescomplemented
474#460—538no—
475#460—538no—
476#452—538no—
477#452—538no—
478#450—538no—
479#450—538no—
480#433—538no—
481C2×C4⋊C8—531no—
482C2×C4⋊C8C2×D5311yescharacteristic, complemented
483C2×#103—531no—
484C2×#103C2×D5311yescharacteristic, complemented
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102C2×D5311yescharacteristic
491C2×C22⋊C8—531no—
492C2×C22⋊C8—531no—
493C2×#97—531no—
494C2×C4×C8—531no—
495C53C2×#322211yescharacteristic, complemented, Sylow
496C25—1061no—
497C2×#41—534no—
498C2×#41—1062no—
499C2×#41—2122no—
500C2×#41—2122no—
501C22×Q8—531no—
502C22×Q8C22×D5311yescharacteristic
503C22×Q8C22×D5311yescharacteristic
504C22×D4—534no—
505C22×D4—531no—
506C22×D4—531no—
507C22×D4—1061no—
508C22×D4—1062no—
509C22×D4—1061no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4—2122no—
515C22×D4—2122no—
516C22×D4C22×D5311yescharacteristic
517C23×C4—531no—
518C23×C4—1061no—
519C2×Q16—42no—
520C2×Q16—534no—
521C2×Q16—2122no—
522C2×Q16C22×D5314yescomplemented
523C2×SD16—42no—
524C2×SD16—534no—
525C2×SD16—534no—
526C2×SD16—534no—
527C2×SD16—534no—
528C2×SD16—534no—
529C2×SD16—2122no—
530C2×SD16—2122no—
531C2×SD16—2122no—
532C2×SD16—2122no—
533C2×SD16—2122no—
534C2×SD16C22×D5314yes—
535C22×C8—531no—
536C22×C8—531no—
537C22×C8C22×D5311yescharacteristic
538C22×C8C22×D5311yescharacteristic
539C4⋊Q8—534no—
540C4⋊Q8—1062no—
541#127—534no—
542#127—534no—
543#127—1062no—
544#127—1062no—
545#126—1068no—
546#126—1068no—
547#125—534no—
548#125—1068no—
549#125—1062no—
550#125—1068no—
551#124—22no—
552#124—534no—
553#124—1062no—
554#124C22×D5314yes—
555C22⋊Q8—534no—
556C22⋊Q8—534no—
557C22⋊Q8—1062no—
558C22⋊Q8—1062no—
559#121—1068no—
560#121—1068no—
561#120—1068no—
562#120—1068no—
563C4×Q8—22no—
564C4×Q8—534no—
565C4×Q8—1062no—
566C4×Q8C22×D5314yescomplemented
567#117—534no—
568#117—534no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—531no—
573C2×C4⋊C4—1061no—
574C2×C4⋊C4—1061no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1061no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4C22×D5311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—531no—
584C2×C22⋊C4—531no—
585C2×C22⋊C4—1061no—
586C2×C22⋊C4—1061no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C42—21no—
590C2×C42—531no—
591C2×C42—1061no—
592C2×C42C22×D5311yescharacteristic
593C4⋊C8—534no—
594C4⋊C8C22×D5314yescomplemented
595#103—534no—
596#103C22×D5314yescomplemented
597#102—534no—
598#102—534no—
599#102—534no—
600#102—534no—
601#102—534no—
602#102C22×D5314yes—
603C22⋊C8—534no—
604C22⋊C8—534no—
605#97—534no—
606C4×C8—534no—
607C24—21no—
608C24—531no—
609C24—1064no—
610C24—1061no—
611C24—1061no—
612C24—4242no—
613C24—4242no—
614C24—2124no—
615#41—2124no—
616#41—2124no—
617#41—2128no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—532no—
625C2×Q8—1061no—
626C2×Q8—1062no—
627C2×Q8—1062no—
628C2×Q8C23×D5312yes—
629C2×Q8C23×D5312yes—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—532no—
634C2×D4—532no—
635C2×D4—1064no—
636C2×D4—1064no—
637C2×D4—1064no—
638C2×D4—1064no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1062no—
644C2×D4—1062no—
645C2×D4—1062no—
646C2×D4—1062no—
647C2×D4—4242no—
648C2×D4—4242no—
649C2×D4—4242no—
650C2×D4—4242no—
651C2×D4—2124no—
652C2×D4—2124no—
653C2×D4—2124no—
654C2×D4—2128no—
655C2×D4—2124no—
656C2×D4C23×D5312yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—531no—
661C22×C4—531no—
662C22×C4—531no—
663C22×C4—532no—
664C22×C4—532no—
665C22×C4—1064no—
666C22×C4—1062no—
667C22×C4—1062no—
668C22×C4—1061no—
669C22×C4—1061no—
670C22×C4—2124no—
671C22×C4D4×D5311yescharacteristic
672C22×C4D4×D5311yescharacteristic
673C22×C4C23×D5311yescharacteristic
674Q16—44no—
675Q16—2124no—
676SD16—44no—
677SD16—2124no—
678SD16—2124no—
679SD16—2124no—
680SD16—2124no—
681SD16—2124no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—532no—
685C2×C8—532no—
686C2×C8—1062no—
687C2×C8—1062no—
688C2×C8C23×D5312yes—
689C2×C8C23×D5312yes—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—534no—
693C4⋊C4—534no—
694C4⋊C4—532no—
695C4⋊C4—1064no—
696C4⋊C4—1064no—
697C4⋊C4—1064no—
698C4⋊C4—1064no—
699C4⋊C4—1064no—
700C4⋊C4—1064no—
701C4⋊C4—1061no—
702C4⋊C4—1064no—
703C4⋊C4C23×D5312yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—534no—
707C22⋊C4—534no—
708C22⋊C4—1064no—
709C22⋊C4—1064no—
710C22⋊C4—1064no—
711C22⋊C4—1064no—
712C42—24no—
713C42—532no—
714C42—532no—
715C42—1064no—
716C42D4×D5312yes—
717C42C23×D5312yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—532no—
723C23—1062no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—4244no—
729C23—4244no—
730C23—42416no—
731C23—2128no—
732C23—2122no—
733C23—2122no—
734C23—2122no—
735C23—2122no—
736C23—2122no—
737C23—2122no—
738C23C2×D4×D5311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—1062no—
746Q8—1062no—
747Q8—2122no—
748D4—22no—
749D4—22no—
750D4—42no—
751D4—1062no—
752D4—1062no—
753D4—1062no—
754D4—1062no—
755D4—4244no—
756D4—4244no—
757D4—4244no—
758D4—4244no—
759D4—2128no—
760D4—2128no—
761D4—2122no—
762D4—2122no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—532no—
772C2×C4—532no—
773C2×C4—532no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1064no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—2128no—
783C2×C4—2122no—
784C2×C4—2122no—
785C2×C4C2×D4×D5312yes—
786C2×C4C2×D4×D5312yes—
787C2×C4C2×D4×D5311yescharacteristic
788C2×C4#1313326212yes—
789C2×C4#1313326312yes—
790C2×C4C24×D5311yescharacteristic
791C8—22no—
792C8—22no—
793C8—1062no—
794C8—1062no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—1062no—
800C22—1062no—
801C22—1062no—
802C22—42416no—
803C22—4244no—
804C22—4244no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2122no—
811C22—2124no—
812C22#1681118912yes—
813C22#1681143012yes—
814C22#1681143212yes—
815C22C22×D4×D5311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—1062no—
822C4—1062no—
823C4—1062no—
824C4—2122no—
825C4—2122no—
826C4#1681118912yes—
827C4C2×#1313326211yescharacteristic
828C4C2×#1313326311yescharacteristic
829C2—82no—
830C2—4242no—
831C2—4242no—
832C2—2122no—
833C2#2028578414yesdirect product factor
834C2C2×#1681118911yescharacteristic
835C2C2×#1681143011yescharacteristic
836C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#16811191C2
hypercenterC2×#464D53
hypocenterC53C2×#3222
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16811231C2semidirect
3. #20285784C2direct (N × H)
4. C2×#16811016C2semidirect
5. C2×#16810994C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810979C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810824C2semidirect
10. C2×#16810823C2semidirect
11. C2×#16810788C2semidirect
12. C2×#16810784C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810772C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#464C2semidirect
19. C22×#11719925C22semidirect
21. C22×#11719913C22semidirect
24. C22×#11719924C22semidirect
26. #16811231C22semidirect
29. C2×#13133215C22semidirect
35. C2×#13133208C22semidirect
44. C2×C4×Dic106C22semidirect
46. #16811016C22semidirect
47. #16810994C22semidirect
48. #16810986C22semidirect
49. #16810979C22semidirect
50. #16810842C22semidirect
51. #16810824C22semidirect
52. #16810823C22semidirect
53. #16810788C22semidirect
54. #16810784C22semidirect
55. #16810775C22semidirect
56. #16810772C22semidirect
57. #16810683C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133141C22semidirect
61. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
69. C22×Q16×C53C22semidirect
72. C2×C4×Q8×C53C22semidirect
73. C53×#464C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
98. C2×#11719925C23semidirect
102. C2×#11719913C23semidirect
108. C2×#11719924C23semidirect
112. #13133215C23semidirect
121. #13133208C23semidirect
134. C4×Dic106C23semidirect
155. C4⋊#88322C23semidirect
156. #13133141C23semidirect
158. #13133139C23semidirect
161. #13133137C23semidirect
164. #13133127C23semidirect
165. C8×Dic53C23semidirect
170. C2×Q16×C53C23semidirect
178. C4×Q8×C53C23semidirect
185. C4⋊C8×C53C23semidirect
186. #103×C53C23semidirect
419. C2×#464D53semidirect
428. C2×C53#3222semidirect
438. C22×Q16C2×D53semidirect
466. C2×C4×Q8C2×D53semidirect
473. #464C2×D53semidirect
482. C2×C4⋊C8C2×D53semidirect
484. C2×#103C2×D53semidirect
495. C53C2×#3222semidirect
522. C2×Q16C22×D53semidirect
566. C4×Q8C22×D53semidirect
594. C4⋊C8C22×D53semidirect
596. #103C22×D53semidirect
833. C2#20285784direct (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×#168111912
#202857842
C2×#168110162
C2×#168109942
C2×#168109862
C2×#168109792
C2×#168108422
C2×#168108242
C2×#168108232
C2×#168107882
C2×#168107842
C2×#168107752
C2×#168107722
C2×#168106832
C2×C53×#4642
C2×#322253