Finite Group Databasebeta

← C2×#20286087 #28256947

Subgroups — C2×#20286087 #28256947

Order 13568.

1898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×#16811158C211yesmaximal, characteristic
3#20286087C2116yesmaximal, direct product factor
4C2×#16810927C211yesmaximal, characteristic, complemented
5C2×#16810917C211yesmaximal, characteristic, complemented
6C2×#16810912C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810872C211yesmaximal, characteristic
10C2×#16810870C211yesmaximal, characteristic
11C2×#16810846C211yesmaximal, characteristic, complemented
12C2×#16810845C211yesmaximal, characteristic, complemented
13C2×#16810832C211yesmaximal, characteristic, complemented
14C2×#16810827C211yesmaximal, characteristic, complemented
15C2×#16810645C211yesmaximal, characteristic, complemented
16C2×C53×#479C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23#16811177—24no—
24#16811177C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133215C2211yescharacteristic
27#16811158—24no—
28#16811158C2218yes—
29C2×#13133212—21no—
30C2×#13133207—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133197C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133193C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×C4×Dic106—21no—
39C2×C4×Dic106C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×#13133179—21no—
42C2×#13133179C2211yescharacteristic
43C2×#13133175—21no—
44C2×#13133174—21no—
45C2×C42×D53C2211yescharacteristic
46#16810927C2218yescomplemented
47#16810917C2218yescomplemented
48#16810912C2218yescomplemented
49#16810882C2218yescomplemented
50#16810880C2218yescomplemented
51#16810872C2218yes—
52#16810870C2218yes—
53#16810846C2218yescomplemented
54#16810845C2218yescomplemented
55#16810832C2218yescomplemented
56#16810827C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810645C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#479C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53D411yescharacteristic
84C22×C4×D53D411yescharacteristic
85C22×C4×D53C2311yescharacteristic
86C2×Dic212—42no—
87C2×Dic212C2314yes—
88C2×#11719925—42no—
89C2×#11719925C2314yes—
90C2×#11719913—42no—
91C2×#11719913C2314yes—
92C2×#11719924—42no—
93C2×#11719924C2314yes—
94C2×#11719912—42no—
95C2×#11719912—42no—
96C2×#11719912C2314yes—
97C2×#11719912C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100#13133216—22no—
101#13133216C2314yes—
102#13133215—22no—
103#13133215C2314yes—
104#13133212—28no—
105#13133207—28no—
106#13133205—22no—
107#13133205C2314yes—
108#13133202—28no—
109#13133197—22no—
110#13133197—22no—
111#13133197C2314yes—
112#13133197C2314yes—
113#13133195—28no—
114#13133193—22no—
115#13133193C2314yes—
116#13133192—22no—
117#13133192C2314yes—
118C4×Dic106—22no—
119C4×Dic106—28no—
120C4×Dic106C2314yes—
121#13133182—22no—
122#13133182C2314yes—
123#13133179—22no—
124#13133179—28no—
125#13133179C2314yes—
126#13133175—28no—
127#13133174—28no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53D411yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149C42×D53D414yes—
150C42×D53C2314yes—
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133139C2314yes—
161#13133137C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#125×C53—22no—
166#125×C53C2314yes—
167C4×Q8×C53—22no—
168C4×Q8×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—24no—
204C2×D212—21no—
205C2×D212—44no—
206C2×D212C2412yes—
207C2×C4×D53—22no—
208C2×C4×D53—22no—
209C2×C4×D53—24no—
210C2×C4×D53—24no—
211C2×C4×D53—42no—
212C2×C4×D53—44no—
213C2×C4×D53C2×D412yes—
214C2×C4×D53C2×D414yes—
215C2×C4×D53C2×D414yes—
216C2×C4×D53C2412yes—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—24no—
224C2×Dic106—44no—
225C2×Dic106C2412yes—
226C2×Dic106C2412yes—
227C2×C8×C53—22no—
228C2×C8×C53—22no—
229C2×C8×C53C2412yes—
230C2×C8×C53C2412yes—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C42×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243#11719925—44no—
244#11719924—44no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2×D414yes—
266C4×Dic53C2×D414yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272Dic212—44no—
273#11719913—44no—
274#11719912—44no—
275#11719912—44no—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53C22×D412yes—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—42no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53H(5,𝔽2)12yes—
302C2×C4×C532−1+412yes—
303C2×C4×C53C2511yescharacteristic
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53#13714yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316D212—22no—
317D212—22no—
318D212—48no—
319D212—42no—
320C4×D53—24no—
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—28no—
324C4×D53—44no—
325C4×D53—48no—
326Dic106—22no—
327Dic106—22no—
328Dic106—22no—
329Dic106—22no—
330Dic106—48no—
331Dic106—42no—
332Dic106—42no—
333C8×C53—22no—
334C8×C53—22no—
335#88322—22no—
336#88322—22no—
337C2×#3252—531nomaximal, Sylow
338C22×C53#53712yes—
339C22×C53C2×#13712yes—
340C22×C53#57512yes—
341C22×C53C23×D411yescharacteristic
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—44no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—84no—
350C4×C53—22no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53#53712yes—
357C4×C53C2×H(5,𝔽2)11yescharacteristic
358C4×C53C2×2−1+411yescharacteristic
359Dic53—22no—
360Dic53—22no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×#13714yes—
365C2×#533—531no—
366C2×#529—531no—
367#3252—5316no—
368C2×#479—531no—
369C2×#479D5311yescharacteristic, complemented
370C2×#477—531no—
371C2×#476—531no—
372C2×#470—531no—
373C2×#470—531no—
374C2×#468—531no—
375C2×#468—531no—
376C2×#464—531no—
377C2×#464—531no—
378C2×#462—531no—
379C2×#461—531no—
380C2×#423—531no—
381C2×C53#325214yescomplemented
382C2×C53C2×#53711yescharacteristic
383C2×C53C22×#13711yescharacteristic
384C2×C53C2×#57511yescharacteristic
385D53—42no—
386D53—82no—
387C22×Q16—531no—
388C22×Q16—531no—
389C22×SD16—531no—
390C22×SD16—531no—
391C22×M16—531no—
392C22×M16—531no—
393#533—538no—
394#533—1064no—
395C2×C4⋊Q8—531no—
396C2×C4⋊Q8—531no—
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—1061no—
401C2×#125C2×D5311yescharacteristic
402C2×#124—531no—
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—1061no—
412C2×C4×Q8C2×D5311yescharacteristic
413C2×C4×D4—531no—
414C2×C4×D4—1061no—
415C2×#117—1061no—
416C2×#117—1061no—
417C22×C42—531no—
418#479—538no—
419#479C2×D5318yescomplemented
420#477—538no—
421#476—538no—
422#470—538no—
423#470—538no—
424#468—538no—
425#468—538no—
426#464—538no—
427#464—538no—
428#462—538no—
429#461—538no—
430C2×#107—531no—
431C2×#107C2×D5311yescharacteristic
432C2×#106—531no—
433C2×#106C2×D5311yescharacteristic
434#423—538no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8—531no—
438C2×C4⋊C8C2×D5311yescharacteristic
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103C2×D5311yescharacteristic
444C2×#103C2×D5311yescharacteristic
445C2×#102—531no—
446C2×#102—531no—
447C53C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—531no—
449C22×Q8—531no—
450C22×Q8—1061no—
451C22×Q8C22×D5311yescharacteristic
452C22×D4—531no—
453C22×D4—1061no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—1061no—
458C2×Q16—534no—
459C2×Q16—534no—
460C2×Q16—2122no—
461C2×Q16—2122no—
462C2×SD16—534no—
463C2×SD16—534no—
464C2×SD16—2122no—
465C2×SD16—2122no—
466C2×M16—534no—
467C2×M16—534no—
468C2×M16—2122no—
469C2×M16—2122no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477C4⋊Q8—1062no—
478#126—1068no—
479#125—22no—
480#125—1068no—
481#125C22×D5314yes—
482#124—534no—
483#124—1062no—
484#123—1068no—
485C22⋊Q8—534no—
486C22⋊Q8—534no—
487C22⋊Q8—534no—
488C22⋊Q8—1062no—
489C22⋊Q8—1062no—
490C22⋊Q8—1068no—
491C22⋊Q8—1062no—
492#121—534no—
493#121—1062no—
494C4×Q8—22no—
495C4×Q8—534no—
496C4×Q8—534no—
497C4×Q8—1068no—
498C4×Q8—1062no—
499C4×Q8—1062no—
500C4×Q8C22×D5314yes—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1068no—
504#117—1068no—
505#117—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—534no—
533C2×C42—534no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42C22×D5311yescharacteristic
537#107—534no—
538#107C22×D5314yes—
539#106—534no—
540#106C22×D5314yes—
541C4⋊C8—534no—
542C4⋊C8—534no—
543C4⋊C8—534no—
544C4⋊C8C22×D5314yes—
545#103—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103C22×D5314yes—
550#103C22×D5314yes—
551#102—534no—
552#102—534no—
553C24—531no—
554C24—1061no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—532no—
559C2×Q8—532no—
560C2×Q8—1064no—
561C2×Q8—1061no—
562C2×Q8—1061no—
563C2×Q8—1062no—
564C2×Q8—1062no—
565C2×Q8—1062no—
566C2×Q8—1062no—
567C2×Q8—2124no—
568C2×Q8C23×D5312yes—
569C2×D4—532no—
570C2×D4—1064no—
571C2×D4—1061no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—2124no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—534no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—534no—
586C22×C4—1064no—
587C22×C4—1064no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—2122no—
594C22×C4—2124no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598Q16—2124no—
599Q16—2124no—
600SD16—2124no—
601SD16—2124no—
602M16—2124no—
603M16—2124no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1062no—
609C2×C8—1062no—
610C2×C8C23×D5312yes—
611C2×C8C23×D5312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—532no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C42—24no—
639C42—534no—
640C42—532no—
641C42—534no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42D4×D5312yes—
646C42C23×D5312yes—
647C23—532no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—1062no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1062no—
660Q8—1062no—
661Q8—1062no—
662Q8—1062no—
663Q8—2128no—
664Q8—2122no—
665Q8—2122no—
666D4—1062no—
667D4—1062no—
668D4—2128no—
669D4—2122no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—534no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—532no—
684C2×C4—1068no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1064no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2124no—
694C2×C4—2128no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4C2×D4×D5312yes—
699C2×C4C2×D4×D5312yes—
700C2×C4C2×D4×D5311yescharacteristic
701C2×C4#1313326312yes—
702C2×C4#1313326512yes—
703C2×C4C24×D5311yescharacteristic
704C8—22no—
705C8—22no—
706C8—1062no—
707C8—1062no—
708C22—1062no—
709C22—1062no—
710C22—1062no—
711C22—4244no—
712C22—2122no—
713C22—2122no—
714C22—2122no—
715C22—2124no—
716C22#1681120312yes—
717C22#137×D5312yes—
718C22#1681142012yes—
719C22C22×D4×D5311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—534no—
727C4—1062no—
728C4—1062no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4#1681120312yes—
733C4C2×#1313326311yescharacteristic
734C4C2×#1313326511yescharacteristic
735C2—4242no—
736C2—2122no—
737C2#2028608714yesdirect product factor
738C2C2×#1681120311yescharacteristic
739C2C2×#137×D5311yescharacteristic
740C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#479C2
socleC23×C53C22×D4
prime radicalC2×#13133192C22
hypercenterC2×#479D53
hypocenterC53C2×#3252
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16811177C2semidirect
3. #20286087C2direct (N × H)
4. C2×#16810927C2semidirect
5. C2×#16810917C2semidirect
6. C2×#16810912C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810880C2semidirect
11. C2×#16810846C2semidirect
12. C2×#16810845C2semidirect
13. C2×#16810832C2semidirect
14. C2×#16810827C2semidirect
15. C2×#16810645C2semidirect
16. C2×C53×#479C2semidirect
24. #16811177C22semidirect
46. #16810927C22semidirect
47. #16810917C22semidirect
48. #16810912C22semidirect
49. #16810882C22semidirect
50. #16810880C22semidirect
53. #16810846C22semidirect
54. #16810845C22semidirect
55. #16810832C22semidirect
56. #16810827C22semidirect
59. #16810645C22semidirect
71. C53×#479C22semidirect
369. C2×#479D53semidirect
381. C2×C53#3252semidirect
419. #479C2×D53semidirect
447. C53C2×#3252semidirect
737. C2#20286087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×#168111582
#202860872
C2×#168109272
C2×#168109172
C2×#168109122
C2×#168108822
C2×#168108802
C2×#168108722
C2×#168108702
C2×#168108462
C2×#168108452
C2×#168108322
C2×#168108272
C2×#168106452
C2×C53×#4792
C2×#325253