Finite Group Databasebeta

← C2×#13069691 #14780813

Subgroups — C2×#13069691 #14780813

Order 2816.

2382 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4324C211yesmaximal, characteristic, complemented
2C22×#66989C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic, complemented
6#13069691C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C23×C11×D8C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×D8—24no—
13C22×C11×D8—24no—
14C22×C11×D8—24no—
15C22×C11×D8C2214yes—
16C23×C8×C11C2211yescharacteristic
17C22×C22⋊Dic11—22no—
18C22×C22⋊Dic11—22no—
19C2×#66989—24no—
20C2×#66989—24no—
21C2×#66989—22no—
22C2×#66989C2214yescomplemented
23C22×#4324—24no—
24C22×#4324—24no—
25C22×#4324—24no—
26C22×#4324C2214yescomplemented
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10622834—22no—
31#10622834C2214yescomplemented
32C2×#66896—24no—
33C2×#66896C2214yescomplemented
34C2×#66880—24no—
35C2×#66880C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C25×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11D414yes—
52C22×D4×C11D414yes—
53C22×D4×C11C2312yes—
54C22×D4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C23×Dic11D412yes—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22D414yes—
66C22×Dic22C2312yes—
67C2×C11×D8—232no—
68C2×C11×D8—28no—
69C2×C11×D8—28no—
70C2×C11×D8—28no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11D414yes—
74C22×C8×C11C2312yes—
75C2×C22⋊Dic11—216no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—48no—
79#66989—216no—
80#66989—28no—
81#66989—28no—
82C2×#4324—232no—
83C2×#4324—28no—
84C2×#4324—28no—
85C2×#4324—28no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2312yes—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11D412yes—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8D414yes—
97C22×C11⋊C8C2312yes—
98#66896—28no—
99#66880—28no—
100C2×#2012—111nomaximal, Sylow
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—44no—
110C24×C11—44no—
111C24×C11—44no—
112C24×C11—44no—
113C24×C11C2×D411yescharacteristic
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—44no—
158C22×Dic11C2×D414yes—
159C2×Dic22—28no—
160C2×Dic22—24no—
161C2×Dic22—28no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×Dic22C2×D414yes—
172C11×D8—232no—
173C2×C8×C11—28no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11C2×D414yes—
177C22⋊Dic11—232no—
178C22⋊Dic11—416no—
179#4324—232no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4×Dic11—24no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C2×C11⋊C8—28no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C2×D414yes—
190C23×SD16—111no—
191C23×D8D1111yescharacteristic
192C22×#124—111no—
193C22×#103—111no—
194C22×#102—111no—
195C2×#390—111no—
196#2012—118no—
197C2×#336—111no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—416no—
211C23×C11—416no—
212C23×C11—88no—
213C23×C11—88no—
214C23×C11—84no—
215C23×C11—84no—
216C23×C11—84no—
217C23×C11—84no—
218C23×C11#12012yes—
219C23×C11#12112yes—
220C23×C11#12712yes—
221C23×C11#13514yes—
222C23×C11AGL(1,ℤ/8)14yes—
223C23×C11C22×D411yescharacteristic
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—48no—
233D4×C11—48no—
234C2×C4×C11#12014yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12014yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12712yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—48no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—44no—
257C2×Dic11—84no—
258Dic22—24no—
259Dic22—24no—
260Dic22—42no—
261Dic22—42no—
262Dic22—48no—
263C8×C11—24no—
264C11⋊C8—24no—
265C23×Q8—111no—
266C23×D4C2×D1111yescharacteristic
267C23×D4C2×D1111yescharacteristic
268C22×SD16—114no—
269C22×SD16—224no—
270C22×SD16—224no—
271C22×SD16—224no—
272C22×D8—24no—
273C22×D8—24no—
274C22×D8—24no—
275C22×D8C2×D1114yes—
276C23×C8—111no—
277C23×C8C2×D1111yescharacteristic
278C2×#124—114no—
279C2×#124—222no—
280C2×#124—224no—
281C2×#124—224no—
282C22×C4⋊C4—111no—
283C22×C22⋊C4—222no—
284C22×C22⋊C4—222no—
285C22×C42—111no—
286C2×#103—114no—
287C2×#103—224no—
288C2×#102—114no—
289C2×#102—224no—
290#390—114no—
291#390—222no—
292#336—114no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—48no—
296C22×C11—48no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—84no—
302C22×C11—84no—
303C22×C11—816no—
304C22×C11—816no—
305C22×C11#39214yes—
306C22×C11#44918yes—
307C22×C11#46318yes—
308C22×C11#49514yes—
309C22×C11#49614yes—
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×#12711yescharacteristic
313C22×C11C2×#13512yes—
314C22×C11C2×AGL(1,ℤ/8)12yes—
315C4×C11#39214yes—
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12111yescharacteristic
319C4×C11C2×#12111yescharacteristic
320Dic11—44no—
321Dic11—44no—
322Dic11—82no—
323C25—21no—
324C25—21no—
325C22×Q8—114no—
326C22×Q8—112no—
327C22×Q8—221no—
328C22×Q8—222no—
329C22×Q8—222no—
330C22×Q8—222no—
331C22×Q8—222no—
332C22×Q8—222no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4C22⋊D1114yes—
346C22×D4C22⋊D1114yes—
347C22×D4C22×D1112yes—
348C22×D4C22×D1112yes—
349C23×C4—112no—
350C23×C4—221no—
351C23×C4—221no—
352C23×C4C22×D1111yescharacteristic
353C2×SD16—228no—
354C2×SD16—228no—
355C2×SD16—2232no—
356C2×SD16—228no—
357C2×D8—232no—
358C2×D8—28no—
359C2×D8—28no—
360C2×D8—28no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—114no—
364C22×C8—112no—
365C22×C8—222no—
366C22×C8—222no—
367C22×C8C22⋊D1114yes—
368C22×C8C22×D1112yes—
369#124—228no—
370#124—2216no—
371#124—228no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—2216no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—448no—
380C2×C42—112no—
381C2×C42—112no—
382C2×C42—222no—
383C2×C42—222no—
384#103—228no—
385#102—228no—
386C2×C11—84no—
387C2×C11—84no—
388C2×C11#201218yescomplemented
389C2×C11C2×#39211yescharacteristic
390C2×C11C2×#44912yes—
391C2×C11C2×#46312yes—
392C2×C11C2×#49511yescharacteristic
393C2×C11C2×#49611yescharacteristic
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—44no—
399C24—44no—
400C24—44no—
401C24—44no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24D4×D1111yescharacteristic
407C2×Q8—114no—
408C2×Q8—224no—
409C2×Q8—222no—
410C2×Q8—228no—
411C2×Q8—228no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—442no—
417C2×Q8—444no—
418C2×Q8—442no—
419C2×Q8—444no—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4C2×C22⋊D1114yes—
445C2×D4C2×C22⋊D1114yes—
446C22×C4—114no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—444no—
456C22×C4—442no—
457C22×C4D4×D1112yes—
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1112yes—
460C22×C4#434112yes—
461C22×C4C2×C22⋊D1112yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C23×D1111yescharacteristic
465SD16—2232no—
466D8—232no—
467C2×C8—28no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—114no—
471C2×C8—228no—
472C2×C8—222no—
473C2×C8—222no—
474C2×C8C2×C22⋊D1114yes—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—442no—
478C22⋊C4—2232no—
479C22⋊C4—4416no—
480C42—224no—
481C42—222no—
482C42—222no—
483C11C2×#201211yescharacteristic, complemented, Sylow
484C23—24no—
485C23—24no—
486C23—416no—
487C23—416no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—48no—
497C23—48no—
498C23—88no—
499C23—84no—
500C23—84no—
501C23—84no—
502C23—84no—
503C23—88no—
504C23#6696414yes—
505C23#6696514yes—
506C23#6699012yes—
507C23#6699212yes—
508C23#6699312yes—
509C23C2×D4×D1111yescharacteristic
510Q8—224no—
511Q8—224no—
512Q8—442no—
513Q8—448no—
514Q8—442no—
515D4—24no—
516D4—24no—
517D4—24no—
518D4—24no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—48no—
524D4—48no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—448no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—448no—
533C2×C4—444no—
534C2×C4—442no—
535C2×C4—884no—
536C2×C4#6699014yes—
537C2×C4#6699012yes—
538C2×C4#6699114yes—
539C2×C4#6699214yes—
540C2×C4#6699212yes—
541C2×C4#6699312yes—
542C2×C4#6700614yes—
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—24no—
550C8—224no—
551C22—48no—
552C22—48no—
553C22—44no—
554C22—44no—
555C22—82no—
556C22—82no—
557C22—84no—
558C22—84no—
559C22—816no—
560C22—816no—
561C22—82no—
562C22—82no—
563C22#1062276618yes—
564C22#1062276714yes—
565C22#1062276814yes—
566C22#1062277118yes—
567C22#1062283614yes—
568C22C2×#6696412yes—
569C22C2×#6696512yes—
570C22C2×#6699011yescharacteristic
571C22C2×#6699211yescharacteristic
572C22C2×#6699311yescharacteristic
573C4—444no—
574C4—444no—
575C4—882no—
576C4#1062283614yes—
577C4C2×#6699011yescharacteristic
578C4C2×#6699111yescharacteristic
579C4C2×#6699211yescharacteristic
580C4C2×#6700611yescharacteristic
581C2—84no—
582C2—84no—
583C2#1306969118yesdirect product factor
584C2C2×#1062283611yescharacteristic
585C2C2×#1062277112yes—
586C2C2×#1062276612yes—
587C2C2×#1062276811yescharacteristic
588C2C2×#1062276711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC23×C11×D8C2
socleC24×C11C2×D4
hypercenterC23×D8D11
hypocenterC11C2×#2012
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C23×#4324C2semidirect
2. C22×#66989C2semidirect
3. C22×#66880C2semidirect
4. C22×#66896C2semidirect
5. C2×#10622834C2semidirect
6. #13069691C2direct (N × H)
7. C2×#10622188C2semidirect
22. C2×#66989C22semidirect
26. C22×#4324C22semidirect
31. #10622834C22semidirect
33. C2×#66896C22semidirect
35. C2×#66880C22semidirect
36. #10622188C22semidirect
388. C2×C11#2012semidirect
483. C11C2×#2012semidirect
583. C2#13069691direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43242
C22×#669892
C22×#668802
C22×#668962
C2×#106228342
#130696912
C2×#106221882
C23×C11×D82
C2×#201211