Finite Group Databasebeta

← C2×#20274947 #27384953

Subgroups — C2×#20274947 #27384953

Order 13568.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811104C211yesmaximal, characteristic
2C2×#16810663C211yesmaximal, characteristic, complemented
3C22×#13133145C211yesmaximal, characteristic
4C2×#16810622C211yesmaximal, characteristic
5#20274947C218yesmaximal, direct product factor
6C2×#16810392C211yesmaximal, characteristic, complemented
7C2×#16810383C211yesmaximal, characteristic, complemented
8C2×C53×#382C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10C22×#11719917C2211yescharacteristic
11C22×#11719917C2211yescharacteristic
12#16811104—22no—
13#16811104—22no—
14#16811104—22no—
15#16811104C2214yes—
16C2×#13133182—21no—
17C2×#13133179—21no—
18C2×C4×C22⋊D53—22no—
19C2×#13133176C2211yescharacteristic
20C2×#13133175—21no—
21C2×C4⋊C4×D53—21no—
22#16810663—22no—
23#16810663C2214yescomplemented
24C2×#13133150—21no—
25C2×#13133148—21no—
26C2×#13133145C418yescomplemented
27C2×#13133145C2214yes—
28#16810622—22no—
29#16810622C2214yes—
30C2×#13133140—21no—
31C2×#13133137—21no—
32#16810392C2214yescomplemented
33#16810383C2214yescomplemented
34C22×C4⋊C4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C53×#382—22no—
38C53×#382C2214yescomplemented
39C2×#95×C53—22no—
40C2×#11719945—21no—
41C2×#11719945—21no—
42C2×#11719945—22no—
43C2×#11719945—22no—
44C2×#11719945C2×C414yes—
45C2×#11719945D412yes—
46C2×#11719945Q814yes—
47C2×#11719945C2312yes—
48C22×Dic106D411yescharacteristic
49C22×D212D411yescharacteristic
50C22×C22⋊D53—21no—
51C22×C4×D53—21no—
52C22×C4×D53—22no—
53C2×#11719917—21no—
54C2×#11719917—21no—
55C2×#11719917—22no—
56C2×#11719917—22no—
57C2×#11719917—22no—
58C2×#11719917C2×C414yescomplemented
59C2×#11719917C2312yes—
60C2×#11719917C2312yes—
61C22×#88322—21no—
62C22×#88322—21no—
63#13133182—24no—
64#13133182—24no—
65#13133179—24no—
66#13133179—24no—
67C4×C22⋊D53—28no—
68C4×C22⋊D53—28no—
69#13133176—21no—
70#13133176—21no—
71#13133176D412yes—
72#13133176C2312yes—
73#13133175—24no—
74#13133175—24no—
75C2×C4⋊Dic53D411yescharacteristic
76C2×C4⋊Dic53D411yescharacteristic
77C2×#11719919—22no—
78C4⋊C4×D53—24no—
79C4⋊C4×D53—24no—
80C2×C22⋊Dic53—21no—
81C2×#11719921—22no—
82C2×C4×Dic53—22no—
83C2×C4×Dic53—21no—
84#13133150—24no—
85#13133148—24no—
86#13133145C2×C4116yescomplemented
87#13133140—24no—
88#13133137—24no—
89C23×C4×C53—21no—
90C23×C4×C53—21no—
91C23×C4×C53D412yes—
92C23×C4×C53C2311yescharacteristic
93C2×C4⋊C4×C53—21no—
94C2×C4⋊C4×C53—21no—
95C2×C4⋊C4×C53—21no—
96C2×C4⋊C4×C53—21no—
97C2×C4⋊C4×C53—21no—
98C2×C4⋊C4×C53—21no—
99C2×C4⋊C4×C53—21no—
100C2×C4⋊C4×C53—21no—
101C2×C4⋊C4×C53—21no—
102C2×C4⋊C4×C53D412yes—
103C2×C4⋊C4×C53C2312yes—
104C2×C4⋊C4×C53C2312yes—
105C2×C42×C53—21no—
106C2×C42×C53—22no—
107C2×C42×C53C2×C414yescomplemented
108C2×C42×C53C2312yes—
109#95×C53—28no—
110C24×C53C2×D411yescharacteristic
111C23×D53—21no—
112C22×C4×C53—24no—
113C22×C4×C53—22no—
114C22×C4×C53—22no—
115C22×C4×C53—22no—
116C22×C4×C53—22no—
117C22×C4×C53—42no—
118C22×C4×C53—42no—
119C22×C4×C53—44no—
120C22×C4×C53—44no—
121C22×C4×C53—41no—
122C22×C4×C53—41no—
123C22×C4×C53C22×C412yes—
124C22×C4×C53C2×D414yes—
125C22×C4×C53C2×D411yescharacteristic
126C22×C4×C53C2×D411yescharacteristic
127C22×C4×C53C2×D411yescharacteristic
128C22×C4×C53C2×D411yescharacteristic
129C22×C4×C53C2×D411yescharacteristic
130C22×C4×C53C2×Q812yes—
131C22×C4×C53#4112yes—
132C22×C4×C53#4112yes—
133C22×C4×C53C2411yescharacteristic
134C2×C22⋊D53—24no—
135C2×C22⋊D53—22no—
136C2×C22⋊D53—24no—
137C2×C22⋊D53—22no—
138C22×Dic53—21no—
139C22×Dic53—21no—
140C22×Dic53—21no—
141#11719945—24no—
142#11719945—24no—
143#11719945—24no—
144#11719945—24no—
145#11719945—24no—
146#11719945—22no—
147#11719945—22no—
148#11719945C4⋊C418yes—
149#11719945C22×C414yes—
150#11719945C2×Q814yes—
151C2×D212—21no—
152C2×D212—22no—
153C2×D212C4⋊C414yes—
154C2×D212C2×D412yes—
155C2×C4×D53—24no—
156C2×C4×D53—22no—
157C2×C4×D53—24no—
158C2×C4×D53—22no—
159C2×C4×D53—28no—
160C2×C4×D53—84no—
161C2×Dic106—21no—
162C2×Dic106—22no—
163C2×Dic106C4⋊C414yes—
164C2×Dic106C2×D412yes—
165C4⋊C4×C53—22no—
166C4⋊C4×C53—22no—
167C4⋊C4×C53—22no—
168C4⋊C4×C53—22no—
169C4⋊C4×C53—22no—
170C4⋊C4×C53—22no—
171C4⋊C4×C53—41no—
172C4⋊C4×C53—41no—
173C42×C53—24no—
174C42×C53—22no—
175C42×C53C22×C414yescomplemented
176C22⋊Dic53—22no—
177C22⋊Dic53—22no—
178#11719921—28no—
179C4⋊Dic53—21no—
180C4⋊Dic53—21no—
181C4⋊Dic53C2×D412yes—
182C4⋊Dic53C2×D412yes—
183#11719919—28no—
184C4×Dic53—28no—
185C4×Dic53—22no—
186C4×Dic53—22no—
187#11719917—24no—
188#11719917—22no—
189#11719917—22no—
190#11719917—22no—
191#11719917—42no—
192#11719917C22×C414yescomplemented
193C2×#88322—24no—
194C2×#88322—22no—
195C2×#88322—22no—
196C2×#88322—42no—
197C23×C53—22no—
198C23×C53—22no—
199C23×C53C4×D412yes—
200C23×C53#12011yescharacteristic
201C23×C53#12011yescharacteristic
202C23×C53C22⋊Q812yes—
203C23×C53C22×D411yescharacteristic
204C22×D53—22no—
205C22×D53—24no—
206C22×D53—42no—
207C22×D53—42no—
208C2×C4×C53—24no—
209C2×C4×C53—24no—
210C2×C4×C53—48no—
211C2×C4×C53—42no—
212C2×C4×C53—42no—
213C2×C4×C53—44no—
214C2×C4×C53—44no—
215C2×C4×C53—44no—
216C2×C4×C53—42no—
217C2×C4×C53—82no—
218C2×C4×C53—82no—
219C2×C4×C53—82no—
220C2×C4×C53C2×C4⋊C412yes—
221C2×C4×C53C2×C4⋊C412yes—
222C2×C4×C53C4×D412yes—
223C2×C4×C53C4×D412yes—
224C2×C4×C53C4×D412yes—
225C2×C4×C53#12011yescharacteristic
226C2×C4×C53#12011yescharacteristic
227C2×C4×C53C22⋊Q812yes—
228C2×C4×C53C22⋊Q812yes—
229C2×C4×C53C22⋊Q812yes—
230C2×C4×C53#12312yes—
231C2×C4×C53#12312yes—
232C2×C4×C53C23×C411yescharacteristic
233C2×C4×C53C22×D411yescharacteristic
234C2×C4×C53C22×D411yescharacteristic
235C2×C4×C53C22×Q811yescharacteristic
236C2×C4×C53C2×#4111yescharacteristic
237C2×C4×C53C2×#4111yescharacteristic
238C22⋊D53—24no—
239C22⋊D53—24no—
240C22⋊D53—28no—
241C2×Dic53—22no—
242C2×Dic53—24no—
243C2×Dic53—22no—
244C2×Dic53—22no—
245C2×Dic53—42no—
246C2×Dic53—42no—
247D212—22no—
248D212—24no—
249D212C2×C4⋊C414yes—
250C4×D53—24no—
251C4×D53—24no—
252C4×D53—28no—
253C4×D53—88no—
254Dic106—22no—
255Dic106—24no—
256Dic106C2×C4⋊C414yes—
257#88322—24no—
258#88322—42no—
259C2×#1860—531nomaximal, Sylow
260C22×C53—24no—
261C22×C53—24no—
262C22×C53—21no—
263C22×C53—21no—
264C22×C53—21no—
265C22×C53—21no—
266C22×C53#38512yes—
267C22×C53#38512yes—
268C22×C53#45412yes—
269C22×C53#45512yes—
270C22×C53C2×C4×D411yescharacteristic
271C22×C53C2×#12011yescharacteristic
272C22×C53C2×C22⋊Q811yescharacteristic
273C2×D53—24no—
274C2×D53—48no—
275C2×D53—42no—
276C2×D53—42no—
277C4×C53—44no—
278C4×C53—44no—
279C4×C53—82no—
280C4×C53#38512yes—
281C4×C53#38512yes—
282C4×C53C22×C4⋊C411yescharacteristic
283C4×C53C2×C4×D411yescharacteristic
284C4×C53C2×C22⋊Q811yescharacteristic
285C4×C53C2×#12311yescharacteristic
286Dic53—24no—
287Dic53—42no—
288Dic53—42no—
289C2×#520—531no—
290C2×#428—531no—
291C22×#104—531no—
292C2×#417—531no—
293C2×#382D5311yescharacteristic, complemented
294#1860—538no—
295C2×#343—531no—
296C2×#339—531no—
297C2×C53—21no—
298C2×C53—21no—
299C2×C53—22no—
300C2×C53#186014yescomplemented
301C2×C53C2×#38511yescharacteristic
302C2×C53C2×#45511yescharacteristic
303C2×C53C2×#45411yescharacteristic
304D53—44no—
305C22×#41—531no—
306C22×M16—531no—
307C22×M16—531no—
308#520—534no—
309#520—1062no—
310#520—1062no—
311#520—1062no—
312C2×C4×Q8—1061no—
313C2×C4×D4—1061no—
314C2×C4×D4—1062no—
315C2×#117—531no—
316C2×#117—1061no—
317C22×C4⋊C4—1061no—
318C22×C4⋊C4C2×D5311yescharacteristic
319C22×C4⋊C4C2×D5311yescharacteristic
320C22×C42C2×D5311yescharacteristic
321#428—534no—
322#428—1062no—
323C2×#107—1061no—
324C2×#106—1061no—
325C2×#104—538no—
326C2×#104—534no—
327#417—534no—
328#417—1062no—
329C2×#103—1061no—
330C2×#102—1061no—
331#382—22no—
332#382C2×D5314yescomplemented
333C2×#95—22no—
334#343—534no—
335#339—534no—
336C53C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—534no—
338C2×#41—532no—
339C2×#41—534no—
340C2×#41—532no—
341C2×#41—1062no—
342C2×#41—1061no—
343C2×#41—1062no—
344C2×#41—1061no—
345C22×Q8—531no—
346C22×D4—531no—
347C22×D4—1061no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—1062no—
351C23×C4—1061no—
352C23×C4C22⋊D5312yes—
353C23×C4C22×D5311yescharacteristic
354C2×M16—534no—
355C2×M16—532no—
356C2×M16—532no—
357C2×M16—1061no—
358C2×M16—1062no—
359C2×M16—1061no—
360C2×M16—1062no—
361C2×M16—1062no—
362C22×C8—1061no—
363C22×C8—1061no—
364C4×Q8—1064no—
365C4×Q8—1064no—
366C4×D4—1064no—
367C4×D4—1064no—
368C4×D4—1068no—
369C4×D4—1068no—
370#117—532no—
371#117—532no—
372#117—1064no—
373#117—1064no—
374#117—1061no—
375#117—1061no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—531no—
386C2×C4⋊C4—531no—
387C2×C4⋊C4—1064no—
388C2×C4⋊C4—1064no—
389C2×C4⋊C4—1062no—
390C2×C4⋊C4C22⋊D5312yes—
391C2×C4⋊C4C22×D5312yes—
392C2×C4⋊C4C22×D5312yes—
393C2×C22⋊C4—1062no—
394C2×C22⋊C4—1061no—
395C2×C42—22no—
396C2×C42—21no—
397C2×C42—1062no—
398C2×C42—1061no—
399C2×C42C4×D5314yescomplemented
400C2×C42C22×D5312yes—
401#107—1064no—
402#106—1064no—
403#104—5316no—
404#103—1064no—
405#102—1064no—
406#95—28no—
407C24—1061no—
408C24C2×C22⋊D5311yescharacteristic
409#41—538no—
410#41—534no—
411#41—534no—
412#41—1064no—
413#41—1064no—
414#41—1064no—
415#41—1064no—
416#41—1064no—
417#41—1062no—
418#41—1062no—
419C2×Q8—534no—
420C2×Q8—532no—
421C2×Q8—1061no—
422C2×Q8—1062no—
423C2×D4—534no—
424C2×D4—532no—
425C2×D4—1064no—
426C2×D4—1062no—
427C2×D4—1064no—
428C2×D4—1062no—
429C2×D4—1061no—
430C2×D4—1062no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—1068no—
443C22×C4—1061no—
444C22×C4—1064no—
445C22×C4—1062no—
446C22×C4—1064no—
447C22×C4—1062no—
448C22×C4—1061no—
449C22×C4—1061no—
450C22×C4—4244no—
451C22×C4C2×C4×D5312yes—
452C22×C4#1171994512yes—
453C22×C4D4×D5311yescharacteristic
454C22×C4D4×D5311yescharacteristic
455C22×C4D4×D5311yescharacteristic
456C22×C4D4×D5311yescharacteristic
457C22×C4Q8×D5312yes—
458C22×C4#1171994912yes—
459C22×C4C2×C22⋊D5314yes—
460C22×C4C2×C22⋊D5311yescharacteristic
461C22×C4C23×D5311yescharacteristic
462M16—534no—
463M16—1064no—
464M16—1062no—
465M16—1062no—
466M16—1062no—
467M16—2122no—
468C2×C8—1064no—
469C2×C8—1062no—
470C2×C8—1062no—
471C2×C8—2122no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—532no—
481C4⋊C4—532no—
482C4⋊C4—1068no—
483C4⋊C4—1061no—
484C4⋊C4—1061no—
485C22⋊C4—1068no—
486C22⋊C4—1062no—
487C22⋊C4—1062no—
488C42—24no—
489C42—22no—
490C42—1068no—
491C42—1062no—
492C42—1062no—
493C42C2×C4×D5314yescomplemented
494C23—22no—
495C23—22no—
496C23—1062no—
497C23—1064no—
498C23—2122no—
499C23—2122no—
500C23C4×C22⋊D5312yes—
501C23#1313318511yescharacteristic
502C23#1313318511yescharacteristic
503C23#1313319312yes—
504C23C22×C22⋊D5311yescharacteristic
505Q8—534no—
506Q8—1062no—
507Q8—1064no—
508D4—534no—
509D4—1064no—
510D4—1064no—
511D4—1068no—
512D4—1062no—
513D4—1064no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—48no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—1062no—
527C2×C4—1064no—
528C2×C4—1064no—
529C2×C4—1064no—
530C2×C4—1068no—
531C2×C4—1062no—
532C2×C4—1062no—
533C2×C4—4248no—
534C2×C4—2122no—
535C2×C4—2122no—
536C2×C4C4⋊C4×D5312yes—
537C2×C4C4⋊C4×D5312yes—
538C2×C4C4×C22⋊D5312yes—
539C2×C4#1313317912yes—
540C2×C4#1313317912yes—
541C2×C4#1313318511yescharacteristic
542C2×C4#1313318511yescharacteristic
543C2×C4#1313319312yes—
544C2×C4#1313319512yes—
545C2×C4#1313319512yes—
546C2×C4#1313320212yes—
547C2×C4#1313320212yes—
548C2×C4C22×C4×D5311yescharacteristic
549C2×C4C2×D4×D5311yescharacteristic
550C2×C4C2×D4×D5311yescharacteristic
551C2×C4C2×Q8×D5311yescharacteristic
552C2×C4C2×#1171994511yescharacteristic
553C2×C4C2×#1171994911yescharacteristic
554C8—1064no—
555C8—2122no—
556C22—24no—
557C22—24no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—1064no—
563C22—2128no—
564C22—2122no—
565C22—2122no—
566C22#1681049412yes—
567C22#1681049412yes—
568C22#1681079512yes—
569C22#1681080012yes—
570C22C2×C4×C22⋊D5311yescharacteristic
571C22C2×#1313318511yescharacteristic
572C22C2×#1313319311yescharacteristic
573C4—44no—
574C4—44no—
575C4—82no—
576C4—1064no—
577C4—2122no—
578C4—2122no—
579C4#1681049412yes—
580C4#1681049412yes—
581C4C2×C4⋊C4×D5311yescharacteristic
582C4C2×#1313317911yescharacteristic
583C4C2×#1313319511yescharacteristic
584C4C2×#1313320211yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—2124no—
589C2#2027494714yesdirect product factor
590C2C2×#1681049411yescharacteristic
591C2C2×#1681080011yescharacteristic
592C2C2×#1681079511yescharacteristic
subgroupG/H
centerC23#13133185
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#382C2
socleC23×C53#120
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenterC2×#382D53
hypocenterC53C2×#1860
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. C2×#16810663C2semidirect
5. #20274947C2direct (N × H)
6. C2×#16810392C2semidirect
7. C2×#16810383C2semidirect
8. C2×C53×#382C2semidirect
23. #16810663C22semidirect
26. C2×#13133145C4semidirect
32. #16810392C22semidirect
33. #16810383C22semidirect
38. C53×#382C22semidirect
58. C2×#11719917C2×C4semidirect
86. #13133145C2×C4semidirect
107. C2×C42×C53C2×C4semidirect
175. C42×C53C22×C4semidirect
192. #11719917C22×C4semidirect
293. C2×#382D53semidirect
300. C2×C53#1860semidirect
332. #382C2×D53semidirect
336. C53C2×#1860semidirect
399. C2×C42C4×D53semidirect
493. C42C2×C4×D53semidirect
589. C2#20274947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111042
C2×#168106632
C22×#131331452
C2×#168106222
#202749472
C2×#168103922
C2×#168103832
C2×C53×#3822
C2×#186053