Finite Group Databasebeta

← C2×#13069858 #14781450

Subgroups — C2×#13069858 #14781450

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×#66928C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4C22×#66885C211yesmaximal, characteristic
5C22×#66885C211yesmaximal, characteristic
6C2×#10622541C211yesmaximal, characteristic, complemented
7#13069858C218yesmaximal, direct product factor
8C2×C11×#336C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C2×#66928—24no—
20C2×#66928—24no—
21C2×#66928—22no—
22C2×#66928C2214yes—
23C2×C11⋊#95—21no—
24C2×#66885—24no—
25C2×#66885—24no—
26C2×#66885C2214yes—
27C2×#66885C2214yes—
28C2×#66880—24no—
29C2×#66880—24no—
30C2×#66880C2214yescomplemented
31C2×#66880C2214yescomplemented
32#10622541—22no—
33#10622541C2214yescomplemented
34C11×#336C2214yescomplemented
35C24×D11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11—21no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44D414yes—
49C22×D44C2312yes—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—21no—
55C22×Dic22—22no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11D414yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—44no—
84#66928—216no—
85#66928—28no—
86#66928—28no—
87C11⋊#95—24no—
88#66885—28no—
89#66885—28no—
90#66880—28no—
91#66880—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—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—24no—
119C22×Dic11—24no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C2×D44—24no—
131C2×D44—28no—
132C2×D44—28no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—44no—
139C2×D44—42no—
140C2×D44—44no—
141C2×D44—42no—
142C2×D44C2×D414yes—
143C2×Dic22—24no—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—44no—
152C2×Dic22—42no—
153C2×Dic22—44no—
154C2×Dic22—42no—
155C2×Dic22C2×D414yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—44no—
163C2×C8×C11—44no—
164C42×C11—24no—
165C42×C11—22no—
166C42×C11—22no—
167(C2×D11)⋊C4—216no—
168(C2×D11)⋊C4—216no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11C2×D414yes—
175Dic11⋊C4—48no—
176C22×#124—111no—
177C22×#103—111no—
178C22×#103—111no—
179C22×#102—111no—
180C22×#102—111no—
181C2×#389—111no—
182#2042—118no—
183C2×#336D1111yescharacteristic, complemented
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—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12114yes—
216C2×C4×C11#12114yes—
217C2×C4×C11#12112yes—
218C2×C4×C11#12314yes—
219C2×C4×C11#12314yes—
220C2×C4×C11#12412yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—48no—
234C2×Dic11—48no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—84no—
239D44—24no—
240D44—24no—
241D44—42no—
242D44—42no—
243D44—48no—
244Dic22—24no—
245Dic22—24no—
246Dic22—42no—
247Dic22—42no—
248Dic22—48no—
249C8×C11—42no—
250C8×C11—42no—
251C23×Q8—111no—
252C23×D4—111no—
253C23×C8C2×D1111yescharacteristic
254C23×C8C2×D1111yescharacteristic
255C2×#124—114no—
256C2×#124—224no—
257C2×#124—224no—
258C2×#124—222no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—221no—
262C22×C22⋊C4—221no—
263C22×C22⋊C4—221no—
264C22×C42C2×D1111yescharacteristic
265C2×#103—114no—
266C2×#103—114no—
267C2×#103—224no—
268C2×#103—224no—
269C2×#102—114no—
270C2×#102—114no—
271C2×#102—224no—
272C2×#102—224no—
273#389—114no—
274#389—222no—
275C2×#95—221no—
276#336C2×D1114yescomplemented
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—42no—
300C4×C11—42no—
301C4×C11#39414yes—
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12311yescharacteristic
306Dic11—44no—
307Dic11—44no—
308Dic11—82no—
309C25—221no—
310C22×Q8—114no—
311C22×Q8—112no—
312C22×Q8—221no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×Q8—222no—
318C22×D4—114no—
319C22×D4—112no—
320C22×D4—221no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—222no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4—221no—
329C23×C4D4411yescharacteristic
330C23×C4D4411yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8C22×D1112yes—
339C22×C8C22×D1112yes—
340#124—228no—
341#124—228no—
342#124—2216no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—444no—
353C2×C22⋊C4—228no—
354C2×C22⋊C4—228no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—224no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42D4412yes—
360C2×C42C22×D1112yes—
361#103—228no—
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—
383C24C2×D4411yescharacteristic
384C2×Q8—114no—
385C2×Q8—224no—
386C2×Q8—222no—
387C2×Q8—228no—
388C2×Q8—228no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—442no—
394C2×Q8—444no—
395C2×Q8—444no—
396C2×Q8—442no—
397C2×D4—114no—
398C2×D4—224no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—442no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—442no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4C2×D4412yes—
429C22×C4C2×D4412yes—
430C22×C4C2×D4411yescharacteristic
431C22×C4#433912yes—
432C22×C4#433912yes—
433C22×C4D4×D1112yes—
434C22×C4D4×D1112yes—
435C22×C4D4×D1112yes—
436C22×C4#434312yes—
437C22×C4C23×D1111yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—44no—
445C2×C8—44no—
446C4⋊C4—114no—
447C4⋊C4—224no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—448no—
452C4⋊C4—442no—
453C22⋊C4—2216no—
454C22⋊C4—2216no—
455C42—24no—
456C42—22no—
457C42—22no—
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#6692812yes—
474C23#6693512yes—
475C23#6694812yes—
476C23#6695712yes—
477C23#6695712yes—
478C23#6696112yes—
479C23#6696212yes—
480C23C22×D4411yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485Q8—448no—
486D4—224no—
487D4—224no—
488D4—442no—
489D4—442no—
490D4—448no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—448no—
506C2×C4—448no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—884no—
511C2×C4#6692812yes—
512C2×C4#6693512yes—
513C2×C4#6693714yes—
514C2×C4#6693714yes—
515C2×C4#6694714yes—
516C2×C4#6694714yes—
517C2×C4#6694812yes—
518C2×C4C2×#433911yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434311yescharacteristic
524C8—42no—
525C8—42no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—882no—
530C22—8816no—
531C22—882no—
532C22—882no—
533C22—882no—
534C22#1062228514yes—
535C22#1062231014yes—
536C22#1062232714yes—
537C22#1062234614yes—
538C22#1062234714yes—
539C22#1062245714yes—
540C22#1062245814yes—
541C22C2×#6692811yescharacteristic
542C22C2×#6693511yescharacteristic
543C22C2×#6694811yescharacteristic
544C22C2×#6695711yescharacteristic
545C22C2×#6695711yescharacteristic
546C22C2×#6696111yescharacteristic
547C22C2×#6696211yescharacteristic
548C4—42no—
549C4—42no—
550C4—444no—
551C4—444no—
552C4—882no—
553C4#1062228514yes—
554C4C2×#6693711yescharacteristic
555C4C2×#6693711yescharacteristic
556C4C2×#6694711yescharacteristic
557C4C2×#6694711yescharacteristic
558C2—884no—
559C2#1306985818yesdirect product factor
560C2C2×#1062228511yescharacteristic
561C2C2×#1062234711yescharacteristic
562C2C2×#1062234611yescharacteristic
563C2C2×#1062245711yescharacteristic
564C2C2×#1062245811yescharacteristic
565C2C2×#1062231011yescharacteristic
566C2C2×#1062232711yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#336C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#336D11
hypocenterC11C2×#2042
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
3. C22×#66880C2semidirect
6. C2×#10622541C2semidirect
7. #13069858C2direct (N × H)
8. C2×C11×#336C2semidirect
30. C2×#66880C22semidirect
31. C2×#66880C22semidirect
33. #10622541C22semidirect
34. C11×#336C22semidirect
183. C2×#336D11semidirect
276. #336C2×D11semidirect
366. C2×C11#2042semidirect
458. C11C2×#2042semidirect
559. C2#13069858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669282
C22×#668802
C22×#668852
C2×#106225412
#130698582
C2×C11×#3362
C2×#204211