Finite Group Databasebeta

← C2×#13078973 #15623012

Subgroups — C2×#13078973 #15623012

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×#10623361C211yesmaximal, characteristic
3#13078973C2116yesmaximal, direct product factor
4C2×#10622377C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622413C212yesmaximal, complemented
7C2×#10622373C212yesmaximal, complemented
8C2×#10622744C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic, complemented
10C22×#66873C211yesmaximal, characteristic, complemented
11C2×#10622735C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17#10623361—24no—
18#10623361C2218yes—
19C2×#67000C2212yes—
20C2×#66993C2212yes—
21C2×#66990—22no—
22C2×#66983—21no—
23C2×#66983—21no—
24C2×#66979C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C2×#66977—22no—
27C23×C11⋊C8C2211yescharacteristic
28#10623031—24no—
29#10623031C2218yescomplemented
30C2×#66943—21no—
31C2×#66943C2212yescomplemented
32C2×#66941—21no—
33C2×#66941C2212yescomplemented
34C11×#417C2218yescomplemented
35C2×C11×#103C2212yescomplemented
36C2×C11×#102C2212yescomplemented
37#10622846C2218yescomplemented
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42#10622744C2218yescomplemented
43#10622735C2218yescomplemented
44C2×#66885C2212yes—
45C2×#66885C2212yes—
46C2×#66879C2212yescomplemented
47C2×C8×Dic11C2212yescomplemented
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66873C2218yescomplemented
51#10622413C22116yescomplemented
52#10622408C22116yescomplemented
53#10622377C22116yescomplemented
54#10622373C22116yescomplemented
55C24×D11—21no—
56C2×C11×#41—22no—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41C2314yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×D44—24no—
69C22×D44—24no—
70C22×D44—21no—
71C22×D44—22no—
72C22×D44C2312yes—
73C22×D44C2314yes—
74C22×Dic22—22no—
75C2×C11×M16—24no—
76C2×C11×M16C2314yes—
77C22×C8×C11C2312yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D412yes—
84#67000—24no—
85#67000C2318yes—
86#66993—24no—
87#66993C2318yes—
88#66990—216no—
89#66983—28no—
90#66983—28no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93#66979—22no—
94#66979D414yes—
95#66979C2314yes—
96#66979C2314yes—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4⋊Dic11D411yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—216no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2312yes—
107C22×C11⋊C8—24no—
108C22×C11⋊C8C2314yes—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66943—28no—
112#66943—24no—
113#66943C2318yescomplemented
114#66941—28no—
115#66941—24no—
116#66941C2318yescomplemented
117C11×#103C2318yescomplemented
118C11×#102C2318yescomplemented
119#66899C2314yescomplemented
120#66899C2314yescomplemented
121#66896C2314yescomplemented
122#66896C2314yescomplemented
123#66885C2318yes—
124#66885C2318yes—
125#66879C2318yescomplemented
126C8×Dic11C2318yescomplemented
127#66873C2318yes—
128#66873C2318yes—
129C2×#3136—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C23×D11—22no—
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—82no—
136C23×D11—82no—
137C11×#41—28no—
138C11×#41—28no—
139C11×#41—48no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11C2412yes—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—44no—
149C2×D4×C11C2412yes—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—44no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4114yes—
159C22×C4×C11#4114yes—
160C22×C4×C11C2411yescharacteristic
161C22×C4×C11C2412yes—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—84no—
165C2×C22⋊D11—84no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170C2×D44—24no—
171C2×D44—22no—
172C2×D44—24no—
173C2×D44—28no—
174C2×D44—24no—
175C2×D44—28no—
176C2×D44—44no—
177C2×D44—48no—
178C2×D44C2414yes—
179C2×Dic22—28no—
180C2×Dic22—84no—
181C11×M16—28no—
182C2×C8×C11—24no—
183C2×C8×C11C2414yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2414yes—
187C22⋊Dic11—24no—
188C22⋊Dic11C2×D418yes—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191C4⋊Dic11—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D414yes—
195C4⋊Dic11C2×D414yes—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11—24no—
201C4×Dic11C2×D414yes—
202C4×Dic11C2414yes—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—28no—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2412yes—
208C2×#544—111no—
209C2×#535—111no—
210#3136—1116no—
211C2×#490—112no—
212C2×#489—112no—
213C2×#488—112no—
214C2×#486—112no—
215C2×#417D1111yescharacteristic, complemented
216C2×#418—111no—
217C2×#416—111no—
218C22×#102—111no—
219C2×#405—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11#12414yes—
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229C22×D11—24no—
230C22×D11—48no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—816no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—42no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—48no—
243D4×C11—42no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×C4×C11—84no—
250C2×C4×C11#12414yes—
251C2×C4×C11#12418yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—88no—
260C22⋊D11—88no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11C22×D414yes—
268C2×Dic11C22×D414yes—
269D44—24no—
270D44—24no—
271D44—48no—
272D44—44no—
273Dic22—88no—
274C8×C11—24no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C22×#41C2×D1111yescharacteristic
278C23×D4—111no—
279C22×M16C2×D1111yescharacteristic
280C23×C8—111no—
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#417C2×D1118yescomplemented
304#416—118no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1112yescomplemented
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—118no—
315C2×#102C2×D1112yescomplemented
316#405—118no—
317C2×#97—112no—
318C2×C4×C8—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—84no—
326C22×C11C2×#12414yes—
327C22×C11C2×#12412yes—
328C22×C11#57612yes—
329C22×C11#57712yes—
330C22×C11C23×D411yescharacteristic
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—816no—
335C2×D11—88no—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11C2×#12414yes—
339C4×C11C2×#12412yes—
340C4×C11C22×#4111yescharacteristic
341C4×C11C22×#4111yescharacteristic
342Dic11—24no—
343Dic11—24no—
344Dic11—42no—
345Dic11—42no—
346C25—221no—
347C2×#41—22no—
348C2×#41—24no—
349C2×#41—24no—
350C2×#41C22×D1114yes—
351C22×Q8—222no—
352C22×Q8C22×D1111yescharacteristic
353C22×D4—21no—
354C22×D4—112no—
355C22×D4—114no—
356C22×D4—222no—
357C22×D4—222no—
358C22×D4—224no—
359C22×D4—221no—
360C22×D4—222no—
361C22×D4—224no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—24no—
367C2×M16C22×D1114yes—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—114no—
371C22×C8—224no—
372C22×C8C22×D1112yes—
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#103C22×D1118yescomplemented
411#102—114no—
412#102—114no—
413#102—118no—
414#102—118no—
415#102—118no—
416#102—118no—
417#102C22×D1118yescomplemented
418#97—118no—
419C4×C8—118no—
420C2×C11—24no—
421C2×C11—82no—
422C2×C11#313614yescomplemented
423C2×C11C22×#12411yescharacteristic
424C2×C11C2×#57611yescharacteristic
425C2×C11C2×#57711yescharacteristic
426D11—84no—
427C24—21no—
428C24—222no—
429C24—224no—
430C24—444no—
431C24—882no—
432C24—882no—
433C24D4×D1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—48no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—228no—
441C2×Q8—884no—
442C2×Q8C23×D1112yes—
443C2×D4—24no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—44no—
448C2×D4—114no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—228no—
453C2×D4—224no—
454C2×D4—222no—
455C2×D4—224no—
456C2×D4—228no—
457C2×D4—444no—
458C2×D4—448no—
459C2×D4—884no—
460C2×D4—884no—
461C2×D4C23×D1112yes—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—44no—
467C22×C4—82no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4#433914yes—
473C22×C4D4×D1112yes—
474C22×C4D4×D1111yescharacteristic
475C22×C4#434114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—28no—
479C2×C8—24no—
480C2×C8—112no—
481C2×C8—112no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—228no—
485C2×C8C23×D1114yes—
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—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—224no—
513C23—448no—
514C23—444no—
515C23—444no—
516C23—444no—
517C23—884no—
518C23—884no—
519C23—8816no—
520C23#6693814yes—
521C23C2×D4×D1112yes—
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—42no—
526Q8—888no—
527D4—22no—
528D4—22no—
529D4—48no—
530D4—42no—
531D4—224no—
532D4—224no—
533D4—448no—
534D4—444no—
535D4—888no—
536D4—888no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—48no—
542C2×C4—84no—
543C2×C4—114no—
544C2×C4—114no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—442no—
550C2×C4—442no—
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—24no—
561C8—222no—
562C8—222no—
563C22—28no—
564C22—22no—
565C22—22no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—84no—
570C22—444no—
571C22—444no—
572C22—444no—
573C22—8816no—
574C22—888no—
575C22C2×#6693814yes—
576C22C2×#6693812yes—
577C22#1062330512yes—
578C22#1062330912yes—
579C22C22×D4×D1111yescharacteristic
580C4—42no—
581C4—44no—
582C4—224no—
583C4—224no—
584C4—442no—
585C4—442no—
586C4C2×#6693814yes—
587C4C2×#6693812yes—
588C4C22×#433911yescharacteristic
589C4C22×#434111yescharacteristic
590C2—24no—
591C2—82no—
592C2—884no—
593C2#1307897314yesdirect product factor
594C2C22×#6693811yescharacteristic
595C2C2×#1062330511yescharacteristic
596C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
hypercenterC2×#417D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13078973C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622744C2semidirect
9. C2×#10622846C2semidirect
10. C22×#66873C2semidirect
11. C2×#10622735C2semidirect
12. C2×C11×#417C2semidirect
29. #10623031C22semidirect
31. C2×#66943C22semidirect
33. C2×#66941C22semidirect
34. C11×#417C22semidirect
35. C2×C11×#103C22semidirect
36. C2×C11×#102C22semidirect
37. #10622846C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
42. #10622744C22semidirect
43. #10622735C22semidirect
46. C2×#66879C22semidirect
47. C2×C8×Dic11C22semidirect
50. C2×#66873C22semidirect
51. #10622413C22semidirect
52. #10622408C22semidirect
53. #10622377C22semidirect
54. #10622373C22semidirect
113. #66943C23semidirect
116. #66941C23semidirect
117. C11×#103C23semidirect
118. C11×#102C23semidirect
119. #66899C23semidirect
120. #66899C23semidirect
121. #66896C23semidirect
122. #66896C23semidirect
125. #66879C23semidirect
126. C8×Dic11C23semidirect
215. C2×#417D11semidirect
303. #417C2×D11semidirect
307. C2×#103C2×D11semidirect
315. C2×#102C2×D11semidirect
410. #103C22×D11semidirect
417. #102C22×D11semidirect
422. C2×C11#3136semidirect
505. C11C2×#3136semidirect
593. C2#13078973direct (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×#106233612
#130789732
C2×#106223772
C2×#106224082
C2×#106224132
C2×#106223732
C2×#106227442
C2×#106228462
C22×#668732
C2×#106227352
C2×C11×#4172
C2×#313611