Finite Group Databasebeta

← C2×#13069694 #14780816

Subgroups — C2×#13069694 #14780816

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×#4325C211yesmaximal, characteristic, complemented
2C23×D88C211yesmaximal, characteristic
3C22×#67000C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622601C211yesmaximal, characteristic, complemented
6#13069694C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#67000—24no—
15C2×#67000—24no—
16C2×#67000—22no—
17C2×#67000C2214yescomplemented
18C22×#4325—24no—
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325C2214yescomplemented
22C22×(C2×D11)⋊C4—22no—
23C22×(C2×D11)⋊C4—22no—
24C22×C4×Dic11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C22×D88—24no—
27C22×D88—24no—
28C22×D88—24no—
29C22×D88C2214yes—
30C2×C11×#103—24no—
31C2×C11×#103C2214yescomplemented
32#10622601—22no—
33#10622601C2214yescomplemented
34C2×#66873—24no—
35C2×#66873C2214yescomplemented
36#10622188C2214yescomplemented
37C24×D11—21no—
38C24×D11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11D414yes—
46C22×Q8×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11D412yes—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—22no—
63C22×D44D414yes—
64C22×D44D414yes—
65C22×D44C2312yes—
66C22×D44C2312yes—
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11D414yes—
70C22×C8×C11C2312yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75#67000—216no—
76#67000—28no—
77#67000—28no—
78C2×#4325—232no—
79C2×#4325—28no—
80C2×#4325—28no—
81C2×#4325—28no—
82C2×(C2×D11)⋊C4—216no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—48no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—22no—
92C22×C11⋊C8D414yes—
93C22×C11⋊C8C2312yes—
94C2×D88—232no—
95C2×D88—28no—
96C2×D88—28no—
97C2×D88—28no—
98C11×#103—28no—
99#66873—28no—
100C2×#2012—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—44no—
111C23×D11—44no—
112C23×D11—44no—
113C23×D11—44no—
114C2×Q8×C11—24no—
115C2×Q8×C11—22no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—44no—
123C2×Q8×C11—42no—
124C2×Q8×C11—44no—
125C2×Q8×C11—42no—
126C2×Q8×C11C2×D414yes—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11C2×D414yes—
146C2×D44—24no—
147C2×D44—28no—
148C2×D44—28no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—28no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—44no—
163C2×D44—42no—
164C2×D44—44no—
165C2×D44—42no—
166C2×D44—44no—
167C2×D44—44no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44C2×D414yes—
171C2×D44C2×D414yes—
172C2×C8×C11—28no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11C2×D414yes—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—42no—
179#4325—232no—
180(C2×D11)⋊C4—232no—
181(C2×D11)⋊C4—416no—
182C4×Dic11—24no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C2×C11⋊C8—28no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×D414yes—
189D88—232no—
190C23×SD16—111no—
191C23×D8—111no—
192C22×#124—111no—
193C22×#103D1111yescharacteristic, complemented
194C22×#102—111no—
195C2×#390—111no—
196#2012—118no—
197C2×#336—111no—
198C23×C11#12012yes—
199C23×C11#12112yes—
200C23×C11#12712yes—
201C23×C11#13514yes—
202C23×C11AGL(1,ℤ/8)14yes—
203C23×C11C22×D411yescharacteristic
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—48no—
215C22×D11—48no—
216C22×D11—416no—
217C22×D11—416no—
218C22×D11—88no—
219C22×D11—88no—
220C22×D11—84no—
221C22×D11—84no—
222C22×D11—84no—
223C22×D11—84no—
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—48no—
229C2×C4×C11—24no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—48no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—84no—
236C2×C4×C11#12014yes—
237C2×C4×C11#12012yes—
238C2×C4×C11#12014yes—
239C2×C4×C11#12114yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12712yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253D44—24no—
254D44—24no—
255D44—24no—
256D44—24no—
257D44—42no—
258D44—42no—
259D44—42no—
260D44—42no—
261D44—48no—
262D44—48no—
263C8×C11—24no—
264C11⋊C8—24no—
265C23×Q8C2×D1111yescharacteristic
266C23×D4—111no—
267C23×D4—111no—
268C22×SD16—114no—
269C22×SD16—224no—
270C22×SD16—224no—
271C22×SD16—224no—
272C22×D8—114no—
273C22×D8—224no—
274C22×D8—224no—
275C22×D8—224no—
276C23×C8—111no—
277C23×C8C2×D1111yescharacteristic
278C2×#124—114no—
279C2×#124—222no—
280C2×#124—224no—
281C2×#124—224no—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C22⋊C4—222no—
284C22×C22⋊C4—222no—
285C22×C42—111no—
286C2×#103—24no—
287C2×#103C2×D1114yescomplemented
288C2×#102—114no—
289C2×#102—224no—
290#390—114no—
291#390—222no—
292#336—114no—
293C22×C11#39214yes—
294C22×C11#44918yes—
295C22×C11#46318yes—
296C22×C11#49514yes—
297C22×C11#49614yes—
298C22×C11C2×#12011yescharacteristic
299C22×C11C2×#12111yescharacteristic
300C22×C11C2×#12711yescharacteristic
301C22×C11C2×#13512yes—
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—48no—
306C2×D11—48no—
307C2×D11—82no—
308C2×D11—82no—
309C2×D11—82no—
310C2×D11—82no—
311C2×D11—84no—
312C2×D11—84no—
313C2×D11—816no—
314C2×D11—816no—
315C4×C11—44no—
316C4×C11—82no—
317C4×C11#39214yes—
318C4×C11C2×#12011yescharacteristic
319C4×C11C2×#12011yescharacteristic
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×#12111yescharacteristic
322Dic11—44no—
323C25—221no—
324C25—221no—
325C22×Q8—22no—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8D4414yes—
332C22×Q8C22×D1112yes—
333C22×D4—114no—
334C22×D4—114no—
335C22×D4—112no—
336C22×D4—112no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—221no—
346C22×D4—221no—
347C22×D4—222no—
348C22×D4—222no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—112no—
352C23×C4C22×D1111yescharacteristic
353C2×SD16—228no—
354C2×SD16—228no—
355C2×SD16—2232no—
356C2×SD16—228no—
357C2×D8—228no—
358C2×D8—228no—
359C2×D8—2232no—
360C2×D8—228no—
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—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C22×D1112yes—
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—28no—
385#102—228no—
386C2×C11#201218yescomplemented
387C2×C11C2×#39211yescharacteristic
388C2×C11C2×#44912yes—
389C2×C11C2×#46312yes—
390C2×C11C2×#49511yescharacteristic
391C2×C11C2×#49611yescharacteristic
392D11—84no—
393D11—84no—
394C24—224no—
395C24—224no—
396C24—222no—
397C24—222no—
398C24—442no—
399C24—442no—
400C24—444no—
401C24—444no—
402C24—444no—
403C24—444no—
404C24—442no—
405C24—442no—
406C24D4×D1111yescharacteristic
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—42no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—42no—
419C2×Q8C2×D4414yes—
420C2×D4—114no—
421C2×D4—114no—
422C2×D4—228no—
423C2×D4—224no—
424C2×D4—228no—
425C2×D4—224no—
426C2×D4—228no—
427C2×D4—228no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—444no—
439C2×D4—442no—
440C2×D4—444no—
441C2×D4—442no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—442no—
445C2×D4—442no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—114no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4C2×D4412yes—
458C22×C4#433912yes—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1112yes—
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C23×D1111yescharacteristic
465SD16—2232no—
466D8—2232no—
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—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C22⋊C4—2232no—
479C22⋊C4—4416no—
480C42—224no—
481C42—222no—
482C42—222no—
483C11C2×#201211yescharacteristic, complemented, Sylow
484C23—224no—
485C23—224no—
486C23—442no—
487C23—442no—
488C23—444no—
489C23—444no—
490C23—444no—
491C23—444no—
492C23—442no—
493C23—442no—
494C23—448no—
495C23—448no—
496C23—4416no—
497C23—4416no—
498C23—884no—
499C23—884no—
500C23—884no—
501C23—884no—
502C23—888no—
503C23—888no—
504C23#6693512yes—
505C23#6693712yes—
506C23#6696714yes—
507C23#6697214yes—
508C23#6699312yes—
509C23C2×D4×D1111yescharacteristic
510Q8—24no—
511Q8—24no—
512Q8—42no—
513Q8—42no—
514Q8—48no—
515D4—224no—
516D4—224no—
517D4—224no—
518D4—224no—
519D4—442no—
520D4—442no—
521D4—442no—
522D4—442no—
523D4—448no—
524D4—448no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—84no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—448no—
536C2×C4#6693514yes—
537C2×C4#6693512yes—
538C2×C4#6693714yes—
539C2×C4#6693712yes—
540C2×C4#6698314yes—
541C2×C4#6699014yes—
542C2×C4#6699312yes—
543C2×C4C22×D4411yescharacteristic
544C2×C4C2×#433911yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—24no—
550C8—224no—
551C22—448no—
552C22—448no—
553C22—444no—
554C22—444no—
555C22—882no—
556C22—882no—
557C22—884no—
558C22—884no—
559C22—8816no—
560C22—8816no—
561C22—882no—
562C22—882no—
563C22#1062242418yes—
564C22#1062243218yes—
565C22#1062257314yes—
566C22#1062278914yes—
567C22#1062280414yes—
568C22C2×#6693511yescharacteristic
569C22C2×#6693711yescharacteristic
570C22C2×#6696712yes—
571C22C2×#6697212yes—
572C22C2×#6699311yescharacteristic
573C4—44no—
574C4—82no—
575C4—444no—
576C4#1062257314yes—
577C4C2×#6693511yescharacteristic
578C4C2×#6693711yescharacteristic
579C4C2×#6698311yescharacteristic
580C4C2×#6699011yescharacteristic
581C2—884no—
582C2—884no—
583C2#1306969418yesdirect product factor
584C2C2×#1062257311yescharacteristic
585C2C2×#1062242412yes—
586C2C2×#1062243212yes—
587C2C2×#1062280411yescharacteristic
588C2C2×#1062278911yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC23×D88C2
hypercenterC22×#103D11
hypocenterC11C2×#2012
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#4325C2semidirect
3. C22×#67000C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622601C2semidirect
6. #13069694C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#103C2semidirect
17. C2×#67000C22semidirect
21. C22×#4325C22semidirect
31. C2×C11×#103C22semidirect
33. #10622601C22semidirect
35. C2×#66873C22semidirect
36. #10622188C22semidirect
193. C22×#103D11semidirect
287. C2×#103C2×D11semidirect
386. C2×C11#2012semidirect
483. C11C2×#2012semidirect
583. C2#13069694direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43252
C23×D882
C22×#670002
C22×#668732
C2×#106226012
#130696942
C2×#106221882
C22×C11×#1032
C2×#201211