Finite Group Databasebeta

← C2×#13078975 #15623014

Subgroups — C2×#13078975 #15623014

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2#13078975C2116yesmaximal, direct product factor
3C2×#10622680C212yesmaximal, complemented
4C2×#10622702C212yesmaximal, complemented
5C2×#10622681C212yesmaximal, complemented
6C2×#10622701C212yesmaximal, complemented
7C2×#10622579C211yesmaximal, characteristic, complemented
8C2×#10622614C211yesmaximal, characteristic, complemented
9C2×#10622615C211yesmaximal, characteristic, complemented
10C22×#66873C211yesmaximal, characteristic, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#544C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C11×#544—24no—
16C11×#544C2218yescomplemented
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2212yescomplemented
19C2×C11×#125—21no—
20C2×C11×#125C2212yescomplemented
21C2×C11×C22⋊Q8—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623056—24no—
28#10623056C2218yes—
29C2×#66948—21no—
30C2×#66948—21no—
31C2×#66935—22no—
32C2×#66928C2212yes—
33C2×#66927C2212yes—
34#10622702C22116yescomplemented
35#10622701C22116yescomplemented
36#10622681C22116yescomplemented
37#10622680C22116yescomplemented
38#10622615C2218yescomplemented
39#10622614C2218yescomplemented
40#10622610C2218yescomplemented
41C2×#66874C2211yescharacteristic, complemented
42C2×#66874C2211yescharacteristic, complemented
43C2×#66874C2212yescomplemented
44#10622579C2218yescomplemented
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66873C2218yescomplemented
50C2×#66873C2211yescharacteristic, complemented
51C2×#66873C2211yescharacteristic, complemented
52C2×#66873C2212yescomplemented
53C2×#66867C2212yescomplemented
54C2×C4×C11⋊C8C2212yescomplemented
55C24×D11—21no—
56C22×Q8×C11—22no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C2×#4339—22no—
61C2×#4339—24no—
62C2×#4339—24no—
63C2×#4339C2314yes—
64C22×D44—24no—
65C22×D44—24no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44C2311yescharacteristic
71C22×D44C2312yes—
72C22×D44C2314yes—
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×C4⋊Q8—28no—
76C11×C4⋊Q8—24no—
77C11×C4⋊Q8C2318yescomplemented
78C11×#125—28no—
79C11×#125—24no—
80C11×#125C2318yescomplemented
81C11×C22⋊Q8—216no—
82C11×#117—22no—
83C11×#117D414yes—
84C11×#117C2314yes—
85C11×#117C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11—21no—
100C2×C42×C11C2312yes—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×#4318—24no—
104C2×#4318C2314yes—
105C22×C11⋊C8—24no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66948—28no—
111#66948—28no—
112#66935—216no—
113#66928—24no—
114#66928C2318yes—
115#66927—24no—
116#66927C2318yes—
117#66874C2318yescomplemented
118#66874C2314yescomplemented
119#66874C2314yescomplemented
120#66873C2318yes—
121#66873C2318yes—
122#66873C2318yes—
123#66873C2318yes—
124#66873C2318yescomplemented
125#66873C2314yescomplemented
126#66873C2314yescomplemented
127#66867C2318yescomplemented
128C4×C11⋊C8C2318yescomplemented
129C2×#3136—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—82no—
136C23×D11—82no—
137C2×Q8×C11—28no—
138C2×Q8×C11—84no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—82no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4114yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2412yes—
152C2×C22⋊D11—24no—
153C2×C22⋊D11—44no—
154C22×Dic11—21no—
155#4339—28no—
156#4339—28no—
157#4339—48no—
158C2×D44—21no—
159C2×D44—22no—
160C2×D44—24no—
161C2×D44—28no—
162C2×D44—28no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—28no—
166C2×D44—28no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—44no—
170C2×D44—48no—
171C2×D44—84no—
172C2×D44—84no—
173C2×D44C2414yes—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—44no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22C2412yes—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—28no—
185C11×C4⋊C4—28no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2×D414yes—
189C11×C4⋊C4C2×D414yes—
190C11×C4⋊C4C2414yes—
191C11×C4⋊C4C2412yes—
192C11×C4⋊C4C2412yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4C2×D418yes—
195C42×C11—24no—
196C42×C11C2×D414yes—
197C42×C11C2414yes—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—28no—
200#4318—28no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—28no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×C11⋊C8C2412yes—
208C2×#544D1111yescharacteristic, complemented
209C2×#535—111no—
210#3136—1116no—
211C2×#490—112no—
212C2×#489—112no—
213C2×#488—112no—
214C2×#486—112no—
215C2×#417—111no—
216C2×#418—111no—
217C2×#416—111no—
218C22×#102—111no—
219C2×#405—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11#12414yes—
223C23×C11C22×D412yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—42no—
228C22×D11—48no—
229C22×D11—44no—
230C22×D11—42no—
231C22×D11—44no—
232C22×D11—42no—
233C22×D11—44no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—816no—
237Q8×C11—88no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—84no—
247C2×C4×C11#12414yes—
248C2×C4×C11#12418yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D414yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4112yes—
254C2×C4×C11C2×#4112yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—48no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261D44—24no—
262D44—24no—
263D44—22no—
264D44—22no—
265D44—44no—
266D44—48no—
267D44—42no—
268D44—88no—
269D44—88no—
270C4×D11—48no—
271Dic22—22no—
272Dic22—22no—
273Dic22—42no—
274C11⋊C8—22no—
275C11⋊C8—22no—
276C11⋊C8—24no—
277C22×#41—111no—
278C23×D4—111no—
279C22×M16—111no—
280C23×C8—111no—
281#544—24no—
282#544C2×D1118yescomplemented
283#535—118no—
284#535—224no—
285C2×C4⋊Q8—21no—
286C2×C4⋊Q8C2×D1112yescomplemented
287C2×#127—112no—
288C2×#125—21no—
289C2×#125C2×D1112yescomplemented
290C2×#124—112no—
291C2×C22⋊Q8—22no—
292C2×#121—221no—
293C2×#121—221no—
294C2×#120—222no—
295C2×#117C2×D1111yescharacteristic
296C2×#117C2×D1111yescharacteristic
297C22×C4⋊C4C2×D1111yescharacteristic
298#490—1116no—
299#489—1116no—
300#488—1116no—
301#486—1116no—
302#418—118no—
303#417—118no—
304#416—118no—
305C2×#103—111no—
306C2×#103—112no—
307C2×#103—111no—
308C2×#102—111no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×#102—118no—
316#405—118no—
317C2×#97—112no—
318C2×C4×C8—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11C2×#12414yes—
323C22×C11C2×#12412yes—
324C22×C11#57612yes—
325C22×C11#57712yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—44no—
328C2×D11—42no—
329C2×D11—44no—
330C2×D11—42no—
331C2×D11—44no—
332C2×D11—42no—
333C2×D11—816no—
334C2×D11—84no—
335C2×D11—88no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11C2×#12412yes—
342C4×C11C2×#12414yes—
343C4×C11C22×#4111yescharacteristic
344C4×C11C22×#4111yescharacteristic
345Dic11—42no—
346C25—221no—
347C2×#41—114no—
348C2×#41—222no—
349C2×#41—224no—
350C2×#41—224no—
351C22×Q8—22no—
352C22×Q8—111no—
353C22×D4—112no—
354C22×D4—111no—
355C22×D4—114no—
356C22×D4—221no—
357C22×D4—224no—
358C22×D4—224no—
359C22×D4—221no—
360C22×D4—222no—
361C22×D4—222no—
362C22×D4—222no—
363C23×C4—21no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—114no—
367C2×M16—224no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—114no—
371C22×C8—112no—
372C22×C8—224no—
373C4⋊Q8—28no—
374C4⋊Q8—24no—
375C4⋊Q8C22×D1118yescomplemented
376#127—118no—
377#127—224no—
378#125—28no—
379#125—24no—
380#125C22×D1118yescomplemented
381#124—118no—
382#124—224no—
383C22⋊Q8—216no—
384#121—228no—
385#121—228no—
386#120—2216no—
387#117—22no—
388#117C22⋊D1114yes—
389#117C22×D1114yes—
390#117C22×D1114yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4C22⋊D1111yescharacteristic
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C4⋊C4C22×D1112yes—
399C2×C4⋊C4C22×D1114yes—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4C22⋊D1112yes—
406C2×C42—21no—
407C2×C42C22×D1112yes—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—118no—
414#102—118no—
415#102—114no—
416#102—114no—
417#102—118no—
418#97—118no—
419C4×C8—118no—
420C2×C11—24no—
421C2×C11#313614yescomplemented
422C2×C11C22×#12411yescharacteristic
423C2×C11C2×#57611yescharacteristic
424C2×C11C2×#57711yescharacteristic
425D11—82no—
426D11—84no—
427C24—222no—
428C24—221no—
429C24—224no—
430C24—444no—
431C24—882no—
432C24—882no—
433C24C2×C22⋊D1111yescharacteristic
434#41—228no—
435#41—228no—
436#41—448no—
437C2×Q8—28no—
438C2×Q8—84no—
439C2×Q8—112no—
440C2×Q8—221no—
441C2×Q8—222no—
442C2×Q8—222no—
443C2×D4—114no—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—228no—
449C2×D4—228no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—224no—
453C2×D4—222no—
454C2×D4—221no—
455C2×D4—228no—
456C2×D4—228no—
457C2×D4—444no—
458C2×D4—444no—
459C2×D4—448no—
460C2×D4—884no—
461C2×D4—884no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—82no—
467C22×C4—221no—
468C22×C4—224no—
469C22×C4—444no—
470C22×C4#434314yes—
471C22×C4#434314yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—228no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—112no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—228no—
485C2×C8—224no—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—28no—
489C4⋊C4—28no—
490C4⋊C4—28no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4C2×C22⋊D1114yes—
494C4⋊C4C2×C22⋊D1114yes—
495C4⋊C4C23×D1114yes—
496C4⋊C4C23×D1112yes—
497C4⋊C4C23×D1112yes—
498C22⋊C4—24no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4C2×C22⋊D1118yes—
502C42—24no—
503C42C2×C22⋊D1114yes—
504C42C23×D1114yes—
505C11C2×#313611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—224no—
509C23—222no—
510C23—442no—
511C23—448no—
512C23—444no—
513C23—442no—
514C23—444no—
515C23—442no—
516C23—444no—
517C23—884no—
518C23—884no—
519C23—8816no—
520C23#6700014yes—
521C23C22×C22⋊D1112yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—88no—
524Q8—222no—
525Q8—222no—
526Q8—442no—
527D4—224no—
528D4—224no—
529D4—222no—
530D4—222no—
531D4—448no—
532D4—448no—
533D4—444no—
534D4—442no—
535D4—888no—
536D4—888no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—44no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—222no—
547C2×C4—442no—
548C2×C4—448no—
549C2×C4#6700014yes—
550C2×C4#6700018yes—
551C2×C4C2×#434312yes—
552C2×C4C2×#434312yes—
553C2×C4C2×#434314yes—
554C2×C4C2×#434314yes—
555C2×C4C22×C22⋊D1114yes—
556C2×C4C22×C22⋊D1114yes—
557C2×C4C22×C22⋊D1112yes—
558C2×C4C22×C22⋊D1111yescharacteristic
559C2×C4C24×D1111yescharacteristic
560C8—222no—
561C8—222no—
562C8—224no—
563C22—28no—
564C22—22no—
565C22—22no—
566C22—442no—
567C22—444no—
568C22—442no—
569C22—444no—
570C22—442no—
571C22—444no—
572C22—8816no—
573C22—888no—
574C22—884no—
575C22C2×#6700014yes—
576C22C2×#6700012yes—
577C22#1062336612yes—
578C22#1062336812yes—
579C22C23×C22⋊D1111yescharacteristic
580C4—24no—
581C4—24no—
582C4—44no—
583C4—42no—
584C4—42no—
585C4—442no—
586C4C2×#6700014yes—
587C4C2×#6700012yes—
588C4C22×#434311yescharacteristic
589C4C22×#434311yescharacteristic
590C2—24no—
591C2—884no—
592C2—882no—
593C2#1307897514yesdirect product factor
594C2C22×#6700011yescharacteristic
595C2C2×#1062336611yescharacteristic
596C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
hypercenterC2×#544D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13078975C2direct (N × H)
3. C2×#10622680C2semidirect
4. C2×#10622702C2semidirect
5. C2×#10622681C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622579C2semidirect
8. C2×#10622614C2semidirect
9. C2×#10622615C2semidirect
10. C22×#66873C2semidirect
11. C2×#10622610C2semidirect
12. C2×C11×#544C2semidirect
16. C11×#544C22semidirect
18. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×#125C22semidirect
34. #10622702C22semidirect
35. #10622701C22semidirect
36. #10622681C22semidirect
37. #10622680C22semidirect
38. #10622615C22semidirect
39. #10622614C22semidirect
40. #10622610C22semidirect
41. C2×#66874C22semidirect
42. C2×#66874C22semidirect
43. C2×#66874C22semidirect
44. #10622579C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
51. C2×#66873C22semidirect
52. C2×#66873C22semidirect
53. C2×#66867C22semidirect
54. C2×C4×C11⋊C8C22semidirect
77. C11×C4⋊Q8C23semidirect
80. C11×#125C23semidirect
117. #66874C23semidirect
118. #66874C23semidirect
119. #66874C23semidirect
124. #66873C23semidirect
125. #66873C23semidirect
126. #66873C23semidirect
127. #66867C23semidirect
128. C4×C11⋊C8C23semidirect
208. C2×#544D11semidirect
282. #544C2×D11semidirect
286. C2×C4⋊Q8C2×D11semidirect
289. C2×#125C2×D11semidirect
375. C4⋊Q8C22×D11semidirect
380. #125C22×D11semidirect
421. C2×C11#3136semidirect
505. C11C2×#3136semidirect
593. C2#13078975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230562
#130789752
C2×#106226802
C2×#106227022
C2×#106226812
C2×#106227012
C2×#106225792
C2×#106226142
C2×#106226152
C22×#668732
C2×#106226102
C2×C11×#5442
C2×#313611