Finite Group Databasebeta

← C2×#13078968 #15623007

Subgroups — C2×#13078968 #15623007

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×#10623031C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic
3#13078968C2116yesmaximal, direct product factor
4C2×#10622377C212yesmaximal, complemented
5C2×#10622378C212yesmaximal, complemented
6C2×#10622381C212yesmaximal, complemented
7C2×#10622373C212yesmaximal, complemented
8C2×#10622579C211yesmaximal, characteristic, complemented
9C2×#10622828C211yesmaximal, characteristic, complemented
10C2×#10622726C211yesmaximal, characteristic, complemented
11C2×#10622714C211yesmaximal, characteristic, complemented
12C22×C11×#102C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#67006—22no—
18#10623336—24no—
19#10623336C2218yes—
20C2×#66993C2212yes—
21C2×#66991—21no—
22C2×#66991—21no—
23C2×#66989C2212yes—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C2×#66977—22no—
27C22×#4318C2211yescharacteristic
28#10623031—24no—
29#10623031C2218yescomplemented
30C2×#66943—21no—
31C2×#66943C2212yescomplemented
32C2×#66941—21no—
33C2×#66941C2212yescomplemented
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2218yescomplemented
37#10622828C2218yescomplemented
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40#10622726C2218yescomplemented
41C2×#66885C2211yescharacteristic, complemented
42C2×#66885C2211yescharacteristic, complemented
43C2×#66880C2211yescharacteristic, complemented
44C2×#66880C2211yescharacteristic, complemented
45#10622714C2218yescomplemented
46C2×#66879C2212yescomplemented
47C2×C8×Dic11C2212yescomplemented
48C2×#66874C2212yescomplemented
49#10622579C2218yescomplemented
50C2×#66873C2212yescomplemented
51#10622381C22116yescomplemented
52#10622378C22116yescomplemented
53#10622377C22116yescomplemented
54#10622373C22116yescomplemented
55C25×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—24no—
59C22×D4×C11—24no—
60C22×D4×C11C2312yes—
61C22×D4×C11C2314yes—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C2×#4339—22no—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339C2314yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×Dic22—22no—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83#67006—216no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11D412yes—
88#66993—24no—
89#66993C2318yes—
90#66991—28no—
91#66991—28no—
92#66989—24no—
93#66989C2318yes—
94#66979—22no—
95#66979D414yes—
96#66979C2314yes—
97#66979C2314yes—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11D411yescharacteristic
100C2×C4⋊Dic11D411yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—216no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2312yes—
108C2×#4318—24no—
109C2×#4318C2314yes—
110C22×C11⋊C8C2312yes—
111#66943—28no—
112#66943—24no—
113#66943C2318yescomplemented
114#66941—28no—
115#66941—24no—
116#66941C2318yescomplemented
117C11×#102C2318yes—
118C11×#102C2318yes—
119#66896C2318yes—
120#66896C2318yes—
121#66885C2314yescomplemented
122#66885C2314yescomplemented
123#66880C2314yescomplemented
124#66880C2314yescomplemented
125#66879C2318yescomplemented
126C8×Dic11C2318yescomplemented
127#66874C2318yescomplemented
128#66873C2318yescomplemented
129C2×#3136—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—24no—
132C24×C11—44no—
133C24×C11—82no—
134C24×C11—82no—
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—28no—
143C2×D4×C11—44no—
144C2×D4×C11—48no—
145C2×D4×C11C2414yes—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—82no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11#4114yes—
152C22×C4×C11#4114yes—
153C22×C4×C11C2411yescharacteristic
154C22×C4×C11C2412yes—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—84no—
160C2×C22⋊D11—84no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166#4339—28no—
167#4339—28no—
168#4339—48no—
169C2×D44—21no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44C2412yes—
173C2×C4×D11—24no—
174C2×C4×D11—44no—
175C2×Dic22—28no—
176C2×Dic22—21no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—84no—
180C2×Dic22C2412yes—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—28no—
184C2×C8×C11C2412yes—
185C2×C8×C11C2412yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2414yes—
189C22⋊Dic11—28no—
190C22⋊Dic11—28no—
191C22⋊Dic11—24no—
192C22⋊Dic11C2×D418yes—
193C4⋊Dic11—28no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D414yes—
197C4⋊Dic11C2×D414yes—
198C4⋊Dic11C2412yes—
199C4⋊Dic11C2412yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202C4×Dic11—24no—
203C4×Dic11C2×D414yes—
204C4×Dic11C2414yes—
205#4318—28no—
206C2×C11⋊C8—24no—
207C2×C11⋊C8C2414yes—
208C2×#544—111no—
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×#102D1111yescharacteristic, complemented
219C2×#405—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—48no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—84no—
228C23×C11—84no—
229C23×C11—816no—
230C23×C11#12414yes—
231C23×C11C22×D412yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—44no—
240D4×C11—48no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11—84no—
244C2×C4×C11#12414yes—
245C2×C4×C11#12418yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4112yes—
249C2×C4×C11C2×#4114yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4114yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—48no—
254C22⋊D11—88no—
255C22⋊D11—88no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11C22×D414yes—
265C2×Dic11C22×D414yes—
266D44—22no—
267D44—22no—
268D44—42no—
269C4×D11—48no—
270Dic22—22no—
271Dic22—22no—
272Dic22—42no—
273Dic22—88no—
274C8×C11—22no—
275C8×C11—22no—
276C11⋊C8—24no—
277C22×#41—111no—
278C23×D4C2×D1111yescharacteristic
279C22×M16—111no—
280C23×C8C2×D1111yescharacteristic
281#544—118no—
282#544—224no—
283#535—118no—
284#535—224no—
285C2×C4⋊Q8—112no—
286C2×C4⋊Q8—221no—
287C2×#127—112no—
288C2×#125—112no—
289C2×#125—221no—
290C2×#124—112no—
291C2×C22⋊Q8—222no—
292C2×#121—221no—
293C2×#121—221no—
294C2×#120—222no—
295C2×#117—111no—
296C2×#117—111no—
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—111no—
307C2×#103—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—111no—
311C2×#102—111no—
312C2×#102—112no—
313C2×#102C2×D1112yes—
314C2×#102C2×D1112yes—
315C2×#102C2×D1118yescomplemented
316#405—118no—
317C2×#97—112no—
318C2×C4×C8—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—816no—
326C22×C11—88no—
327C22×C11C2×#12414yes—
328C22×C11C2×#12412yes—
329C22×C11#57612yes—
330C22×C11#57712yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—84no—
336C4×C11—44no—
337C4×C11C2×#12412yes—
338C4×C11C2×#12414yes—
339C4×C11C22×#4111yescharacteristic
340C4×C11C22×#4111yescharacteristic
341Dic11—24no—
342Dic11—24no—
343Dic11—42no—
344Dic11—42no—
345Dic11—42no—
346C25—21no—
347C2×#41—114no—
348C2×#41—222no—
349C2×#41—224no—
350C2×#41—224no—
351C22×Q8—111no—
352C22×Q8—222no—
353C22×D4—24no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—111no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—221no—
361C22×D4C22×D1112yes—
362C22×D4C22×D1114yes—
363C23×C4—21no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—114no—
367C2×M16—224no—
368C22×C8—24no—
369C22×C8—112no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1114yes—
373C4⋊Q8—118no—
374C4⋊Q8—224no—
375C4⋊Q8—228no—
376#127—118no—
377#127—224no—
378#125—118no—
379#125—224no—
380#125—228no—
381#124—118no—
382#124—224no—
383C22⋊Q8—2216no—
384#121—228no—
385#121—228no—
386#120—2216no—
387#117—114no—
388#117—114no—
389#117—114no—
390#117—222no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4C22×D1112yes—
401C2×C4⋊C4C22×D1114yes—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—221no—
406C2×C42—112no—
407C2×C42—221no—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—114no—
414#102—114no—
415#102—118no—
416#102C22×D1118yes—
417#102C22×D1118yes—
418#97—118no—
419C4×C8—118no—
420C2×C11—24no—
421C2×C11—84no—
422C2×C11#313614yescomplemented
423C2×C11C22×#12411yescharacteristic
424C2×C11C2×#57611yescharacteristic
425C2×C11C2×#57711yescharacteristic
426D11—82no—
427C24—22no—
428C24—24no—
429C24—44no—
430C24—82no—
431C24—82no—
432C24—221no—
433C24D4×D1111yescharacteristic
434#41—228no—
435#41—228no—
436#41—448no—
437C2×Q8—112no—
438C2×Q8—228no—
439C2×Q8—221no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—884no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—24no—
448C2×D4—28no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—112no—
452C2×D4—228no—
453C2×D4—228no—
454C2×D4—224no—
455C2×D4—222no—
456C2×D4—221no—
457C2×D4—222no—
458C2×D4—444no—
459C2×D4—884no—
460C2×D4—884no—
461C2×D4C23×D1114yes—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—82no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—224no—
471C22×C4—444no—
472C22×C4#433914yes—
473C22×C4D4×D1112yes—
474C22×C4D4×D1111yescharacteristic
475C22×C4#434114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—228no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—28no—
482C2×C8—114no—
483C2×C8—224no—
484C2×C8C23×D1112yes—
485C2×C8C23×D1112yes—
486C4⋊C4—22no—
487C4⋊C4—24no—
488C4⋊C4—114no—
489C4⋊C4—114no—
490C4⋊C4—112no—
491C4⋊C4—112no—
492C4⋊C4—228no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C23×D1114yes—
498C22⋊C4—118no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—224no—
502C42—114no—
503C42—114no—
504C42—224no—
505C11C2×#313611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—48no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—84no—
514C23—84no—
515C23—816no—
516C23—222no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23#6693814yes—
521C23C2×D4×D1112yes—
522C23C2×D4×D1111yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—442no—
526Q8—888no—
527D4—24no—
528D4—24no—
529D4—48no—
530D4—44no—
531D4—222no—
532D4—222no—
533D4—448no—
534D4—442no—
535D4—888no—
536D4—888no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—84no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—448no—
551C2×C4#6693814yes—
552C2×C4#6693818yes—
553C2×C4C2×#433912yes—
554C2×C4C2×#433914yes—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×D4×D1112yes—
557C2×C4C2×#434112yes—
558C2×C4C2×#434114yes—
559C2×C4C24×D1111yescharacteristic
560C8—22no—
561C8—22no—
562C8—224no—
563C22—28no—
564C22—22no—
565C22—22no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—816no—
570C22—88no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—884no—
575C22C2×#6693814yes—
576C22C2×#6693812yes—
577C22#1062328812yes—
578C22#1062329312yes—
579C22C22×D4×D1111yescharacteristic
580C4—44no—
581C4—224no—
582C4—224no—
583C4—442no—
584C4—442no—
585C4—442no—
586C4C2×#6693814yes—
587C4C2×#6693812yes—
588C4C22×#433911yescharacteristic
589C4C22×#434111yescharacteristic
590C2—24no—
591C2—84no—
592C2—882no—
593C2#1307896814yesdirect product factor
594C2C22×#6693811yescharacteristic
595C2C2×#1062328811yescharacteristic
596C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
hypercenterC22×#102D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13078968C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622378C2semidirect
6. C2×#10622381C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622579C2semidirect
9. C2×#10622828C2semidirect
10. C2×#10622726C2semidirect
11. C2×#10622714C2semidirect
12. C22×C11×#102C2semidirect
29. #10623031C22semidirect
31. C2×#66943C22semidirect
33. C2×#66941C22semidirect
36. C2×C11×#102C22semidirect
37. #10622828C22semidirect
40. #10622726C22semidirect
41. C2×#66885C22semidirect
42. C2×#66885C22semidirect
43. C2×#66880C22semidirect
44. C2×#66880C22semidirect
45. #10622714C22semidirect
46. C2×#66879C22semidirect
47. C2×C8×Dic11C22semidirect
48. C2×#66874C22semidirect
49. #10622579C22semidirect
50. C2×#66873C22semidirect
51. #10622381C22semidirect
52. #10622378C22semidirect
53. #10622377C22semidirect
54. #10622373C22semidirect
113. #66943C23semidirect
116. #66941C23semidirect
121. #66885C23semidirect
122. #66885C23semidirect
123. #66880C23semidirect
124. #66880C23semidirect
125. #66879C23semidirect
126. C8×Dic11C23semidirect
127. #66874C23semidirect
128. #66873C23semidirect
218. C22×#102D11semidirect
315. C2×#102C2×D11semidirect
422. C2×C11#3136semidirect
505. C11C2×#3136semidirect
593. C2#13078968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230312
C2×#106233362
#130789682
C2×#106223772
C2×#106223782
C2×#106223812
C2×#106223732
C2×#106225792
C2×#106228282
C2×#106227262
C2×#106227142
C22×C11×#1022
C2×#313611