Finite Group Databasebeta

← C2×#20286754 #28260765

Subgroups — C2×#20286754 #28260765

Order 13568.

2254 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×#16811341C211yesmaximal, characteristic, complemented
2C2×#16811264C211yesmaximal, characteristic
3#20286754C2116yesmaximal, direct product factor
4C2×#16810984C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic, complemented
6C2×#16810912C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810848C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810776C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810697C211yesmaximal, characteristic, complemented
14C2×#16810627C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic, complemented
24#16811341—24no—
25#16811341C2218yescomplemented
26#16811264—24no—
27#16811264C2218yes—
28C2×#13133216C2211yescharacteristic, complemented
29C2×#13133211—21no—
30C2×#13133210—21no—
31C2×#13133206C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133202—21no—
34C2×#13133197C2211yescharacteristic, complemented
35C2×#13133196C2211yescharacteristic
36C2×#13133192—21no—
37C2×#13133192C2211yescharacteristic
38C2×#13133187—21no—
39C2×C4×Dic106—21no—
40C2×#13133182C2211yescharacteristic, complemented
41C2×#13133179C2211yescharacteristic
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133175C2211yescharacteristic, complemented
44C2×C22⋊C4×D53—21no—
45#16810984C2218yescomplemented
46#16810950C2218yescomplemented
47#16810912C2218yescomplemented
48#16810879C2218yescomplemented
49#16810853C2218yescomplemented
50#16810848C2218yescomplemented
51#16810788C2218yescomplemented
52#16810776C2218yescomplemented
53#16810722C2218yescomplemented
54#16810697C2218yescomplemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57#16810627C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133127C2211yescharacteristic, complemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×D212—24no—
85C22×D212—21no—
86C22×D212—22no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—42no—
90C22×D212C2311yescharacteristic
91C22×D212C2314yes—
92C22×D212C2311yescharacteristic
93C22×C22⋊D53D411yescharacteristic
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719925—42no—
98C2×#11719925C2314yescomplemented
99C2×#11719913—24no—
100C2×#11719913—42no—
101C2×#11719913C2314yes—
102C2×#11719913C2314yes—
103C2×#11719917—42no—
104C2×#11719917C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107C2×C8×D53—42no—
108C2×C8×D53C2314yescomplemented
109#13133216—22no—
110#13133216C2314yescomplemented
111#13133211—28no—
112#13133210—28no—
113#13133206—22no—
114#13133206C2314yes—
115#13133203—28no—
116#13133202—28no—
117#13133197—22no—
118#13133197C2314yescomplemented
119#13133196—22no—
120#13133196C2314yes—
121#13133192—28no—
122#13133192—22no—
123#13133192C2314yes—
124#13133187—28no—
125C4×Dic106—28no—
126#13133182—22no—
127#13133182C2314yescomplemented
128#13133179—22no—
129#13133179C2314yes—
130C4×C22⋊D53D414yes—
131C4×C22⋊D53C2314yes—
132#13133175—22no—
133#13133175C2314yescomplemented
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53D411yescharacteristic
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C22⋊C4×D53—28no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133148C2314yescomplemented
154#13133146C2314yescomplemented
155#13133141C2314yescomplemented
156#13133140C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yescomplemented
164#13133127C2314yescomplemented
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22⋊Q8×C53—22no—
170C22⋊Q8×C53C2314yes—
171#117×C53—22no—
172#117×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180#107×C53C2314yescomplemented
181#106×C53C2314yescomplemented
182#103×C53C2314yescomplemented
183#103×C53C2314yescomplemented
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—24no—
189C23×D53—44no—
190C23×D53—44no—
191C23×D53—82no—
192C23×D53C2×D411yescharacteristic
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—42no—
208C2×C22⋊D53C2×D414yes—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214#11719949—28no—
215#11719949—44no—
216#11719949—48no—
217C2×D212—21no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—28no—
222C2×D212—24no—
223C2×D212—24no—
224C2×D212—21no—
225C2×D212—24no—
226C2×D212—44no—
227C2×D212—48no—
228C2×D212—44no—
229C2×D212—44no—
230C2×D212—82no—
231C2×D212#4114yes—
232C2×D212C2412yes—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—44no—
239C2×C4×D53—82no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2412yes—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106—24no—
246C2×Dic106—44no—
247C2×Dic106C2412yes—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C22⋊C4×C53—24no—
260C22⋊C4×C53—24no—
261C42×C53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53C2×D414yes—
264#11719925—44no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919C2×D414yes—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53C2×D412yes—
282C4×Dic53C2412yes—
283#11719917—44no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288#11719913—28no—
289#11719913—44no—
290C8×D53—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53C22×D412yes—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—24no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—48no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—48no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—84no—
310C22×D53—816no—
311C22×D53C22×D412yes—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—42no—
315C2×C4×C53—22no—
316C2×C4×C53—24no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4112yes—
330C2×C4×C53H(5,𝔽2)12yes—
331C2×C4×C53C2511yescharacteristic
332C22⋊D53—44no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343D212—24no—
344D212—22no—
345D212—22no—
346D212—22no—
347D212—48no—
348D212—48no—
349D212—42no—
350D212—84no—
351D212C2×#4114yes—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—48no—
356C4×D53—84no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—42no—
361C8×C53—22no—
362C8×C53—22no—
363#88322—22no—
364#88322—22no—
365C2×#3311—531nomaximal, Sylow
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—44no—
370C22×C53#54612yes—
371C22×C53#57512yes—
372C22×C53#57712yes—
373C22×C53C23×D411yescharacteristic
374C2×D53—22no—
375C2×D53—24no—
376C2×D53—22no—
377C2×D53—22no—
378C2×D53—44no—
379C2×D53—48no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—816no—
386C2×D53—84no—
387C4×C53—22no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#54612yes—
393C4×C53C22×#4111yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—22no—
398Dic53—42no—
399Dic53—42no—
400C2×#556—531no—
401C2×#546—531no—
402#3311—5316no—
403C2×#489—531no—
404C2×#485D5311yescharacteristic, complemented
405C2×#482—531no—
406C2×#476—531no—
407C2×#470—531no—
408C2×#465—531no—
409C2×#464—531no—
410C2×#452—531no—
411C2×#450—531no—
412C2×#440—531no—
413C2×#435—531no—
414C2×#418—531no—
415C2×#416—531no—
416C2×C53—42no—
417C2×C53#331114yescomplemented
418C2×C53C2×#54611yescharacteristic
419C2×C53C2×#57511yescharacteristic
420C2×C53C2×#57711yescharacteristic
421D53—42no—
422D53—44no—
423D53—82no—
424C22×#41—531no—
425C23×D4—531no—
426C22×Q16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×M16—531no—
430C23×C8—531no—
431#556—538no—
432#556—1064no—
433#546—538no—
434#546—1064no—
435C2×C4⋊Q8—531no—
436C2×#126—1061no—
437C2×#126—1061no—
438C2×#124—531no—
439C2×#124—1061no—
440C2×#123—1061no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8C2×D5311yescharacteristic
444C2×#121—531no—
445C2×#121—1061no—
446C2×#120—1061no—
447C2×C4×Q8—531no—
448C2×C4×Q8—1061no—
449C2×C4×D4—531no—
450C2×C4×D4—531no—
451C2×#117—531no—
452C2×#117C2×D5311yescharacteristic
453C22×C22⋊C4—1061no—
454#489—538no—
455#485C2×D5318yescomplemented
456#482—538no—
457#476—538no—
458#470—538no—
459#465—538no—
460#464—538no—
461#452—538no—
462#450—538no—
463#440—538no—
464#435—538no—
465C2×#107C2×D5311yescharacteristic, complemented
466C2×#106—531no—
467C2×#106C2×D5311yescharacteristic, complemented
468C2×C4⋊C8—531no—
469#418—538no—
470#416—538no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103C2×D5311yescharacteristic, complemented
474C2×#103C2×D5311yescharacteristic, complemented
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×C22⋊C8—531no—
482C2×C22⋊C8C2×D5311yescharacteristic
483C2×#97—531no—
484C53C2×#331111yescharacteristic, complemented, Sylow
485C25—1061no—
486C2×#41—534no—
487C2×#41—1062no—
488C2×#41—1064no—
489C2×#41—2122no—
490C22×Q8—531no—
491C22×Q8—1061no—
492C22×Q8C22×D5311yescharacteristic
493C22×D4—531no—
494C22×D4—531no—
495C22×D4—531no—
496C22×D4—534no—
497C22×D4—1064no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4—1061no—
501C22×D4—1062no—
502C22×D4—2122no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×Q16—534no—
508C2×Q16—2122no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—1064no—
512C2×SD16—2122no—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521C4⋊Q8—534no—
522C4⋊Q8—1062no—
523#126—1068no—
524#126—1068no—
525#124—534no—
526#124—1062no—
527#124—1068no—
528#123—1068no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8C22×D5314yes—
535#121—534no—
536#121—1068no—
537#121—1062no—
538#120—1068no—
539C4×Q8—534no—
540C4×Q8—1068no—
541C4×Q8—1062no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1062no—
546#117—22no—
547#117—534no—
548#117—1062no—
549#117C22×D5314yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—531no—
563C2×C22⋊C4—531no—
564C2×C22⋊C4—1068no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C42—21no—
573C2×C42—531no—
574C2×C42—1061no—
575C2×C42—1061no—
576#107C22×D5314yescomplemented
577#106—534no—
578#106C22×D5314yescomplemented
579C4⋊C8—534no—
580#103—534no—
581#103—534no—
582#103C22×D5314yescomplemented
583#103C22×D5314yescomplemented
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102—534no—
590C22⋊C8—534no—
591C22⋊C8C22×D5314yes—
592#97—534no—
593C24—531no—
594C24—1061no—
595C24—1064no—
596C24—1061no—
597C24—4242no—
598C24—2124no—
599C24—2124no—
600C24D4×D5311yescharacteristic
601#41—1068no—
602#41—2124no—
603#41—2128no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—532no—
608C2×Q8—1064no—
609C2×Q8—1061no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×Q8—2124no—
613C2×Q8C23×D5312yes—
614C2×D4—534no—
615C2×D4—534no—
616C2×D4—532no—
617C2×D4—532no—
618C2×D4—1068no—
619C2×D4—1064no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1064no—
623C2×D4—1061no—
624C2×D4—1062no—
625C2×D4—1062no—
626C2×D4—1062no—
627C2×D4—4242no—
628C2×D4—2124no—
629C2×D4—2128no—
630C2×D4—2124no—
631C2×D4—2124no—
632C2×D4—2122no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—531no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—1064no—
645C22×C4—1064no—
646C22×C4—1062no—
647C22×C4—1062no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657SD16—1068no—
658SD16—2124no—
659M16—2124no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—534no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1061no—
679C4⋊C4—1064no—
680C4⋊C4C23×D5312yes—
681C4⋊C4C23×D5312yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—534no—
686C22⋊C4—534no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C42—24no—
695C42—532no—
696C42—532no—
697C42—1064no—
698C42—1064no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—532no—
703C23—1062no—
704C23—1064no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—4244no—
710C23—42416no—
711C23—2128no—
712C23—2128no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23C2×D4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1062no—
724Q8—1062no—
725Q8—2128no—
726Q8—2122no—
727D4—534no—
728D4—1064no—
729D4—1062no—
730D4—1062no—
731D4—1062no—
732D4—4244no—
733D4—2128no—
734D4—2128no—
735D4—2124no—
736D4—2122no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—532no—
750C2×C4—532no—
751C2×C4—532no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1064no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—4244no—
761C2×C4—2128no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4#41×D5312yes—
767C2×C4#1313326312yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—1062no—
778C22—1064no—
779C22—1062no—
780C22—1062no—
781C22—42416no—
782C22—4244no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22—2124no—
787C22—2128no—
788C22—2122no—
789C22—2122no—
790C22#1681126512yes—
791C22#1681142212yes—
792C22#1681143012yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1062no—
800C4—1062no—
801C4—1062no—
802C4—2122no—
803C4—2122no—
804C4#1681126512yes—
805C4C2×#41×D5311yescharacteristic
806C4C2×#1313326311yescharacteristic
807C2—42no—
808C2—4242no—
809C2—2122no—
810C2—2124no—
811C2#2028675414yesdirect product factor
812C2C2×#1681126511yescharacteristic
813C2C2×#1681142211yescharacteristic
814C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC2×#16811264C2
hypercenterC2×#485D53
hypocenterC53C2×#3311
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16811341C2semidirect
3. #20286754C2direct (N × H)
4. C2×#16810984C2semidirect
5. C2×#16810950C2semidirect
6. C2×#16810912C2semidirect
7. C2×#16810879C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810848C2semidirect
10. C2×#16810788C2semidirect
11. C2×#16810776C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810697C2semidirect
14. C2×#16810627C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#485C2semidirect
19. C22×#11719925C22semidirect
23. C22×C8×D53C22semidirect
25. #16811341C22semidirect
28. C2×#13133216C22semidirect
34. C2×#13133197C22semidirect
40. C2×#13133182C22semidirect
43. C2×#13133175C22semidirect
45. #16810984C22semidirect
46. #16810950C22semidirect
47. #16810912C22semidirect
48. #16810879C22semidirect
49. #16810853C22semidirect
50. #16810848C22semidirect
51. #16810788C22semidirect
52. #16810776C22semidirect
53. #16810722C22semidirect
54. #16810697C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133146C22semidirect
57. #16810627C22semidirect
58. #16810618C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133140C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133127C22semidirect
71. C53×#485C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
98. C2×#11719925C23semidirect
108. C2×C8×D53C23semidirect
110. #13133216C23semidirect
118. #13133197C23semidirect
127. #13133182C23semidirect
133. #13133175C23semidirect
153. #13133148C23semidirect
154. #13133146C23semidirect
155. #13133141C23semidirect
156. #13133140C23semidirect
163. #13133129C23semidirect
164. #13133127C23semidirect
180. #107×C53C23semidirect
181. #106×C53C23semidirect
182. #103×C53C23semidirect
183. #103×C53C23semidirect
404. C2×#485D53semidirect
417. C2×C53#3311semidirect
455. #485C2×D53semidirect
465. C2×#107C2×D53semidirect
467. C2×#106C2×D53semidirect
473. C2×#103C2×D53semidirect
474. C2×#103C2×D53semidirect
484. C53C2×#3311semidirect
576. #107C22×D53semidirect
578. #106C22×D53semidirect
582. #103C22×D53semidirect
583. #103C22×D53semidirect
811. C2#20286754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113412
C2×#168112642
#202867542
C2×#168109842
C2×#168109502
C2×#168109122
C2×#168108792
C2×#168108532
C2×#168108482
C2×#168107882
C2×#168107762
C2×#168107222
C2×#168106972
C2×#168106272
C2×#168106182
C2×C53×#4852
C2×#331153