Finite Group Databasebeta

← C2×#13069853 #14781445

Subgroups — C2×#13069853 #14781445

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic
5C2×#10622586C211yesmaximal, characteristic, complemented
6#13069853C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#67000—24no—
14C2×#67000—24no—
15C2×#67000—22no—
16C2×#67000C2214yes—
17C22×(C2×D11)⋊C4—21no—
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×#103—24no—
24C2×C11×#103C2214yescomplemented
25C2×#66899—24no—
26C2×#66899C2214yescomplemented
27C2×C11⋊#95—21no—
28C2×#66885—24no—
29C2×#66885C2214yes—
30#10622586—22no—
31#10622586C2214yescomplemented
32C2×#66873—24no—
33C2×#66873C2214yes—
34#10622188C2214yescomplemented
35C24×D11—21no—
36C22×Q8×C11—22no—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11D414yes—
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66#67000—216no—
67#67000—28no—
68#67000—28no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11D414yes—
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—44no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D412yes—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8C2312yes—
87C11×#103—28no—
88#66899—28no—
89C11⋊#95—24no—
90#66885—28no—
91#66873—28no—
92C2×#2042—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—24no—
95C23×D11—22no—
96C23×D11—42no—
97C23×D11—42no—
98C23×D11—42no—
99C23×D11—42no—
100C23×D11—42no—
101C23×D11—42no—
102C2×Q8×C11—24no—
103C2×Q8×C11—22no—
104C2×Q8×C11—28no—
105C2×Q8×C11—28no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—42no—
111C2×Q8×C11—44no—
112C2×Q8×C11—44no—
113C2×Q8×C11—42no—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D412yes—
143C2×D44—24no—
144C2×D44—28no—
145C2×D44—28no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—42no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44—42no—
155C2×D44C2×D414yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—44no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—42no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—216no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D414yes—
168Dic11⋊C4—48no—
169C4×Dic11—24no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—44no—
176C22×#124—111no—
177C22×#103—111no—
178C22×#103D1111yescharacteristic, complemented
179C22×#102—111no—
180C22×#102—111no—
181C2×#389—111no—
182#2042—118no—
183C2×#336—111no—
184C23×C11#12012yes—
185C23×C11#12112yes—
186C23×C11#12412yes—
187C23×C11#13512yes—
188C23×C11#13512yes—
189C23×C11AGL(1,ℤ/8)12yes—
190C23×C11#13712yes—
191C23×C11C22×D411yescharacteristic
192C22×D11—24no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—48no—
200C22×D11—48no—
201C22×D11—48no—
202C22×D11—84no—
203C22×D11—84no—
204C22×D11—84no—
205C22×D11—84no—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—48no—
211C2×C4×C11—24no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—84no—
219C2×C4×C11#12012yes—
220C2×C4×C11#12114yes—
221C2×C4×C11#12112yes—
222C2×C4×C11#12114yes—
223C2×C4×C11#12314yes—
224C2×C4×C11#12314yes—
225C2×C4×C11#12412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11—48no—
244D44—24no—
245D44—24no—
246D44—42no—
247D44—42no—
248D44—48no—
249C8×C11—42no—
250C11⋊C8—42no—
251C23×Q8C2×D1111yescharacteristic
252C23×D4—111no—
253C23×C8—111no—
254C23×C8C2×D1111yescharacteristic
255C2×#124—114no—
256C2×#124—222no—
257C2×#124—224no—
258C2×#124—224no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—221no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—221no—
263C22×C22⋊C4—221no—
264C22×C42—111no—
265C2×#103—24no—
266C2×#103—114no—
267C2×#103—224no—
268C2×#103C2×D1114yescomplemented
269C2×#102—114no—
270C2×#102—114no—
271C2×#102—224no—
272C2×#102—224no—
273#389—114no—
274#389—222no—
275C2×#95—221no—
276#336—114no—
277C22×C11#39414yes—
278C22×C11#44914yes—
279C22×C11#45214yes—
280C22×C11#46314yes—
281C22×C11#46414yes—
282C22×C11#48814yes—
283C22×C11#48914yes—
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11C2×#12411yescharacteristic
287C22×C11C2×#13511yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C2×D11—816no—
299C4×C11—44no—
300C4×C11—82no—
301C4×C11#39414yes—
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12311yescharacteristic
306Dic11—42no—
307Dic11—42no—
308Dic11—44no—
309C25—221no—
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8C22⋊D1114yes—
317C22×Q8C22×D1112yes—
318C22×D4—114no—
319C22×D4—112no—
320C22×D4—222no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—221no—
324C22×D4—222no—
325C22×D4—222no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—112no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8—222no—
339C22×C8C22×D1112yes—
340#124—228no—
341#124—2216no—
342#124—228no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—444no—
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—224no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—228no—
356C2×C22⋊C4—228no—
357C2×C42—112no—
358C2×C42—112no—
359C2×C42—222no—
360C2×C42—222no—
361#103—28no—
362#103—228no—
363#102—228no—
364#102—228no—
365#95—224no—
366C2×C11#204218yescomplemented
367C2×C11C2×#39411yescharacteristic
368C2×C11C2×#44911yescharacteristic
369C2×C11C2×#45211yescharacteristic
370C2×C11C2×#46311yescharacteristic
371C2×C11C2×#46411yescharacteristic
372C2×C11C2×#48811yescharacteristic
373C2×C11C2×#48911yescharacteristic
374D11—84no—
375C24—224no—
376C24—222no—
377C24—442no—
378C24—442no—
379C24—442no—
380C24—442no—
381C24—442no—
382C24—442no—
383C24D4×D1111yescharacteristic
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—42no—
394C2×Q8—44no—
395C2×Q8—42no—
396C2×Q8C2×C22⋊D1114yes—
397C2×D4—114no—
398C2×D4—228no—
399C2×D4—228no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—442no—
407C2×D4—442no—
408C2×D4—444no—
409C2×D4—444no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4#433912yes—
431C22×C4#433912yes—
432C22×C4D4×D1112yes—
433C22×C4D4×D1112yes—
434C22×C4D4×D1111yescharacteristic
435C22×C4#434112yes—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C23×D1111yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—44no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—444no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—114no—
450C4⋊C4—224no—
451C4⋊C4—222no—
452C4⋊C4—448no—
453C22⋊C4—2216no—
454C22⋊C4—2216no—
455C42—224no—
456C42—222no—
457C42—222no—
458C11C2×#204211yescharacteristic, complemented, Sylow
459C23—224no—
460C23—442no—
461C23—442no—
462C23—442no—
463C23—442no—
464C23—442no—
465C23—442no—
466C23—448no—
467C23—448no—
468C23—448no—
469C23—884no—
470C23—884no—
471C23—884no—
472C23—884no—
473C23#6693712yes—
474C23#6693812yes—
475C23#6696712yes—
476C23#6696912yes—
477C23#6697112yes—
478C23#6697212yes—
479C23#6699012yes—
480C23C2×D4×D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486D4—224no—
487D4—224no—
488D4—442no—
489D4—442no—
490D4—448no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4—448no—
511C2×C4#6693614yes—
512C2×C4#6693714yes—
513C2×C4#6693712yes—
514C2×C4#6693812yes—
515C2×C4#6698214yes—
516C2×C4#6699012yes—
517C2×C4#6699214yes—
518C2×C4C2×#433911yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—42no—
525C8—442no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—882no—
530C22—8816no—
531C22—882no—
532C22—882no—
533C22—882no—
534C22#1062240814yes—
535C22#1062241114yes—
536C22#1062241314yes—
537C22#1062243214yes—
538C22#1062257214yes—
539C22#1062278514yes—
540C22#1062280014yes—
541C22C2×#6693711yescharacteristic
542C22C2×#6693811yescharacteristic
543C22C2×#6696711yescharacteristic
544C22C2×#6696911yescharacteristic
545C22C2×#6697111yescharacteristic
546C22C2×#6697211yescharacteristic
547C22C2×#6699011yescharacteristic
548C4—44no—
549C4—82no—
550C4—444no—
551C4—442no—
552C4—442no—
553C4#1062257214yes—
554C4C2×#6693611yescharacteristic
555C4C2×#6693711yescharacteristic
556C4C2×#6698211yescharacteristic
557C4C2×#6699211yescharacteristic
558C2—884no—
559C2#1306985318yesdirect product factor
560C2C2×#1062257211yescharacteristic
561C2C2×#1062278511yescharacteristic
562C2C2×#1062280011yescharacteristic
563C2C2×#1062243211yescharacteristic
564C2C2×#1062241111yescharacteristic
565C2C2×#1062241311yescharacteristic
566C2C2×#1062240811yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC22×#103D11
hypocenterC11C2×#2042
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
2. C22×#66899C2semidirect
5. C2×#10622586C2semidirect
6. #13069853C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#103C2semidirect
24. C2×C11×#103C22semidirect
26. C2×#66899C22semidirect
31. #10622586C22semidirect
34. #10622188C22semidirect
178. C22×#103D11semidirect
268. C2×#103C2×D11semidirect
366. C2×C11#2042semidirect
458. C11C2×#2042semidirect
559. C2#13069853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#668992
C22×#668852
C22×#668732
C2×#106225862
#130698532
C2×#106221882
C22×C11×#1032
C2×#204211