Finite Group Databasebeta

← C2×#13080945 #15630708

Subgroups — C2×#13080945 #15630708

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080945C2116yesmaximal, direct product factor
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622476C212yesmaximal, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622395C212yesmaximal, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622785C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622416C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4339—21no—
15C22×C11×SD16C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66991C2212yes—
19C22×#4323C2212yes—
20C2×#66977—21no—
21C22×#4313C2212yes—
22#10623108—24no—
23#10623108C2218yescomplemented
24#10623082—24no—
25#10623082C2218yescomplemented
26C2×#66948—22no—
27C2×#66948C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66936—22no—
30C2×#66927—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C4×C11×SD16C2218yescomplemented
36C2×C11×#106C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C2×#66899C2212yes—
41#10622785C22116yescomplemented
42C2×#66885C2212yes—
43C2×#66885C2212yes—
44C2×(C2×D11)⋊C8C2212yes—
45#10622633C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622476C22116yescomplemented
51#10622416C22116yescomplemented
52#10622395C22116yescomplemented
53#10622307C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4343—24no—
60C2×#4343—28no—
61C2×#4343—44no—
62C2×#4343C2318yes—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—21no—
69C22×D44D411yescharacteristic
70C22×D44C2312yes—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11C2312yes—
74C22×Dic22—21no—
75C2×C11×SD16—24no—
76C2×C11×SD16C2314yes—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C4×D4×C11—22no—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90#66991—24no—
91#66991C2318yes—
92C2×#4323—44no—
93C2×#4323C2318yes—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4D412yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11C2312yes—
99#66977—28no—
100C2×Dic11⋊C4—22no—
101C22×C11⋊C8C2312yes—
102C2×#4313—44no—
103C2×#4313C2318yes—
104#66948—24no—
105#66948—216no—
106#66948C2318yes—
107C4⋊C4×D11—24no—
108C4⋊C4×D11C2318yes—
109#66936—216no—
110#66927—28no—
111#66927—22no—
112#66927C2314yes—
113C4×D44—28no—
114C4×D44D414yes—
115C4×D44C2314yes—
116#66922—22no—
117#66922C2314yes—
118C11×#106C2314yes—
119C11×#103C2314yes—
120C11×#102C2314yes—
121C4×C8×C11C2314yes—
122#66899C2318yes—
123#66885C2318yes—
124#66885C2318yes—
125(C2×D11)⋊C8C2318yes—
126#66873C2318yes—
127#66872C2318yes—
128C4⋊(C11⋊C8)C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—22no—
132C23×D11C2×D412yes—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11#4114yescomplemented
136C2×Q8×C11C2412yes—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11C2412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—28no—
150C2×C22⋊D11—48no—
151C22×Dic11—22no—
152C22×Dic11C2×D412yes—
153#4343—216no—
154#4343—48no—
155#4343—416no—
156#4339—432no—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—22no—
162C2×D44—24no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—48no—
166C2×D44—44no—
167C2×D44—82no—
168C2×D44—84no—
169C2×D44C2×D414yes—
170C2×D44C2414yes—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11—48no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2414yes—
179C2×Dic22—24no—
180C2×Dic22—44no—
181C11×SD16—28no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11C2412yes—
185C2×C8×C11C2412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C2412yes—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—24no—
192C42×C11—24no—
193C42×C11C2×D412yes—
194C42×C11C2412yes—
195C22⋊Dic11—28no—
196#4323—48no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4C2×D418yes—
199C4⋊Dic11—22no—
200C4⋊Dic11—24no—
201C4⋊Dic11C2×D414yes—
202C4⋊Dic11C2414yes—
203Dic11⋊C4—28no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8C2414yes—
206#4313—48no—
207C2×#550—111no—
208C2×#547—111no—
209#3332—1116no—
210C2×#486—111no—
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459—111no—
215C2×#449—112no—
216C2×C4×SD16D1111yescharacteristic, complemented
217C2×#436—111no—
218C2×#417—112no—
219C23×C11—22no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11C22×D414yes—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11C2×#4114yescomplemented
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—42no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—48no—
246C2×C4×C11AGL(1,ℤ/8)14yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—416no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—44no—
257C2×Dic11C22×D414yes—
258D44—28no—
259D44—24no—
260D44—24no—
261D44—416no—
262D44—44no—
263D44—48no—
264D44—84no—
265D44—88no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—416no—
270C4×D11—416no—
271Dic22—48no—
272C8×C11—22no—
273C8×C11—22no—
274C11⋊C8—24no—
275C22×#41—112no—
276C22×#41—221no—
277C22×SD16C2×D1111yescharacteristic
278C22×D8—112no—
279C22×M16—112no—
280#550—118no—
281#550—224no—
282#547—118no—
283#547—224no—
284C2×C4⋊Q8—111no—
285C2×#127—111no—
286C2×#127—221no—
287C2×#123—222no—
288C2×C22⋊Q8—221no—
289C2×#121—112no—
290C2×#121—112no—
291C2×#121—222no—
292C2×C4×Q8C2×D1111yescharacteristic
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4—112no—
297#486—118no—
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459—118no—
302#449—1116no—
303C4×SD16C2×D1118yescomplemented
304#436—118no—
305C2×#106—112no—
306C2×#106C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308#417—1116no—
309C2×#103—112no—
310C2×#103C2×D1111yescharacteristic
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102C2×D1111yescharacteristic
315C2×C22⋊C8—112no—
316C2×C4×C8C2×D1111yescharacteristic
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—84no—
321C22×C11#54612yes—
322C22×C11C2×AGL(1,ℤ/8)12yes—
323C22×C11#57712yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—24no—
328C2×D11—48no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—88no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11#54612yes—
338C4×C11C2×AGL(1,ℤ/8)14yes—
339C4×C11C22×#4111yescharacteristic
340C4×C11C2×H(5,𝔽2)11yescharacteristic
341Dic11—24no—
342Dic11—44no—
343C2×#41—118no—
344C2×#41—228no—
345C2×#41—224no—
346C2×#41—228no—
347C2×#41—448no—
348C2×#41—444no—
349C22×Q8—221no—
350C22×Q8C22×D1111yescharacteristic
351C22×D4—111no—
352C22×D4—112no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4C22×D1111yescharacteristic
359C23×C4—21no—
360C23×C4—112no—
361C23×C4—222no—
362C23×C4—222no—
363C2×SD16—24no—
364C2×SD16C22×D1114yes—
365C2×D8—118no—
366C2×D8—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—112no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—114no—
375#127—228no—
376#127—222no—
377#123—2216no—
378C22⋊Q8—228no—
379#121—118no—
380#121—118no—
381#121—2216no—
382#121—224no—
383#121—224no—
384C4×Q8—22no—
385C4×Q8C22×D1114yes—
386C4×D4—22no—
387C4×D4—114no—
388C4×D4—114no—
389C4×D4—228no—
390C4×D4C22×D1114yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—118no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—112no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C42—21no—
405C2×C42C22×D1111yescharacteristic
406#106—118no—
407#106C22×D1114yes—
408C4⋊C8—114no—
409#103—118no—
410#103C22×D1114yes—
411#102—118no—
412#102—118no—
413#102—118no—
414#102C22×D1114yes—
415C22⋊C8—118no—
416C4×C8C22×D1114yes—
417C2×C11—82no—
418C2×C11#333214yescomplemented
419C2×C11C2×#54611yescharacteristic
420C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C11C2×#57711yescharacteristic
422D11—44no—
423D11—84no—
424C24—21no—
425C24—112no—
426C24—222no—
427#41—2216no—
428#41—4432no—
429#41—448no—
430#41—4416no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—224no—
434C2×Q8—444no—
435C2×Q8#433914yescomplemented
436C2×Q8C23×D1112yes—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—114no—
441C2×D4—114no—
442C2×D4—228no—
443C2×D4—228no—
444C2×D4—228no—
445C2×D4—224no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—222no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—444no—
454C2×D4—882no—
455C2×D4—884no—
456C2×D4C23×D1112yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—44no—
462C22×C4—112no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—228no—
466C22×C4—228no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—222no—
470C22×C4—448no—
471C22×C4—448no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—28no—
476D8—448no—
477M16—448no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—114no—
481C2×C8—224no—
482C2×C8C23×D1112yes—
483C2×C8C23×D1112yes—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—114no—
488C4⋊C4—114no—
489C4⋊C4—228no—
490C4⋊C4—222no—
491C4⋊C4—224no—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—118no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—24no—
499C42D4×D1112yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—22no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—114no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—444no—
512C23—444no—
513C23—444no—
514C23C2×D4×D1111yescharacteristic
515Q8—24no—
516Q8—22no—
517Q8—448no—
518Q8C2×#433914yescomplemented
519D4—22no—
520D4—22no—
521D4—42no—
522D4—228no—
523D4—224no—
524D4—224no—
525D4—4416no—
526D4—4416no—
527D4—448no—
528D4—444no—
529D4—884no—
530D4—888no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—48no—
539C2×C4—114no—
540C2×C4—224no—
541C2×C4—228no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—4416no—
546C2×C4—4416no—
547C2×C4—444no—
548C2×C4#6696714yes—
549C2×C4C2×#433912yes—
550C2×C4C2×D4×D1112yes—
551C2×C4C2×D4×D1112yes—
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#6704212yes—
554C2×C4C24×D1111yescharacteristic
555C8—22no—
556C8—22no—
557C8—224no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—84no—
562C22—224no—
563C22—224no—
564C22—224no—
565C22—448no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—888no—
570C22#1062308112yes—
571C22C2×#6696712yes—
572C22#1062330112yes—
573C22C22×D4×D1111yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—224no—
579C4—444no—
580C4#1062308112yes—
581C4C2×#6696714yes—
582C4C22×#433911yescharacteristic
583C4C2×#6704211yescharacteristic
584C2—82no—
585C2—444no—
586C2—884no—
587C2#1308094514yesdirect product factor
588C2C2×#1062308111yescharacteristic
589C2C22×#6696711yescharacteristic
590C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623108C2semidirect
2. C2×#10623082C2semidirect
3. #13080945C2direct (N × H)
4. C2×#10622307C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622785C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622416C2semidirect
12. C2×C4×C11×SD16C2semidirect
23. #10623108C22semidirect
25. #10623082C22semidirect
35. C4×C11×SD16C22semidirect
41. #10622785C22semidirect
45. #10622633C22semidirect
46. #10622628C22semidirect
50. #10622476C22semidirect
51. #10622416C22semidirect
52. #10622395C22semidirect
53. #10622307C22semidirect
54. #10622301C22semidirect
135. C2×Q8×C11#41semidirect
216. C2×C4×SD16D11semidirect
234. Q8×C11C2×#41semidirect
303. C4×SD16C2×D11semidirect
418. C2×C11#3332semidirect
435. C2×Q8#4339semidirect
501. C11C2×#3332semidirect
518. Q8C2×#4339semidirect
587. C2#13080945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106230822
#130809452
C2×#106223072
C2×#106224762
C2×#106226332
C2×#106223952
C2×#106226282
C2×#106227852
C2×#106223012
C2×#106224162
C2×C4×C11×SD162
C2×#333211