Finite Group Databasebeta

← C2×#13069856 #14781448

Subgroups — C2×#13069856 #14781448

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×#66989C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C22×#66874C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic
5C2×#10622598C211yesmaximal, characteristic, complemented
6#13069856C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C22×C22⋊Dic11—21no—
15C2×#66989—24no—
16C2×#66989—24no—
17C2×#66989—22no—
18C2×#66989C2214yes—
19C22×C4⋊Dic11—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×#102—24no—
24C2×C11×#102C2214yes—
25C2×#66896—24no—
26C2×#66896C2214yes—
27C2×C11⋊#95—21no—
28C2×#66880—24no—
29C2×#66880C2214yescomplemented
30#10622598—22no—
31#10622598C2214yescomplemented
32C2×#66874—24no—
33C2×#66874C2214yescomplemented
34#10622188C2214yescomplemented
35C25×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11D414yes—
43C22×D4×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—21no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—28no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70#66989—216no—
71#66989—28no—
72#66989—28no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—44no—
78C2×C4⋊Dic11C2312yes—
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×#102—28no—
88#66896—28no—
89C11⋊#95—24no—
90#66880—28no—
91#66874—28no—
92C2×#2042—111nomaximal, Sylow
93C24×C11—24no—
94C24×C11—22no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11C2×D411yescharacteristic
102C2×D4×C11—24no—
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—44no—
111C2×D4×C11—42no—
112C2×D4×C11—44no—
113C2×D4×C11—42no—
114C2×D4×C11C2×D414yes—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D412yes—
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—44no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D414yes—
163C22⋊Dic11—216no—
164C22⋊Dic11—216no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—48no—
168C4⋊Dic11—42no—
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×#103—111no—
179C22×#102—111no—
180C22×#102D1111yescharacteristic
181C2×#389—111no—
182#2042—118no—
183C2×#336—111no—
184C23×C11—24no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—48no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—84no—
195C23×C11—84no—
196C23×C11—84no—
197C23×C11—84no—
198C23×C11#12012yes—
199C23×C11#12112yes—
200C23×C11#12412yes—
201C23×C11#13512yes—
202C23×C11#13512yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206D4×C11—24no—
207D4×C11—24no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—48no—
211C2×C4×C11—24no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—48no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12114yes—
217C2×C4×C11#12114yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#12314yes—
220C2×C4×C11#12314yes—
221C2×C4×C11#12412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—48no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—84no—
244Dic22—24no—
245Dic22—24no—
246Dic22—42no—
247Dic22—42no—
248Dic22—48no—
249C8×C11—42no—
250C11⋊C8—42no—
251C23×Q8—111no—
252C23×D4C2×D1111yescharacteristic
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—114no—
266C2×#103—114no—
267C2×#103—224no—
268C2×#103—224no—
269C2×#102—24no—
270C2×#102—114no—
271C2×#102—224no—
272C2×#102C2×D1114yes—
273#389—114no—
274#389—222no—
275C2×#95—221no—
276#336—114no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11—816no—
285C22×C11#39414yes—
286C22×C11#44914yes—
287C22×C11#45214yes—
288C22×C11#46314yes—
289C22×C11#46414yes—
290C22×C11#48814yes—
291C22×C11#48914yes—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12411yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C4×C11—44no—
300C4×C11#39414yes—
301C4×C11C2×#12111yescharacteristic
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12311yescharacteristic
305Dic11—44no—
306Dic11—42no—
307Dic11—42no—
308Dic11—82no—
309C25—21no—
310C22×Q8—114no—
311C22×Q8—112no—
312C22×Q8—222no—
313C22×Q8—221no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×Q8—222no—
318C22×D4—22no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4D4414yes—
325C22×D4C22×D1112yes—
326C23×C4—21no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—221no—
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—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—444no—
351C2×C4⋊C4C22⋊D1114yes—
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—228no—
362#103—228no—
363#102—28no—
364#102—228no—
365#95—224no—
366C2×C11—84no—
367C2×C11#204218yescomplemented
368C2×C11C2×#39411yescharacteristic
369C2×C11C2×#44911yescharacteristic
370C2×C11C2×#45211yescharacteristic
371C2×C11C2×#46311yescharacteristic
372C2×C11C2×#46411yescharacteristic
373C2×C11C2×#48811yescharacteristic
374C2×C11C2×#48911yescharacteristic
375C24—24no—
376C24—22no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24D4×D1111yescharacteristic
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—24no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4C2×D4414yes—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4C2×D4412yes—
431C22×C4#433912yes—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1112yes—
434C22×C4#434112yes—
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—24no—
447C4⋊C4—22no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—448no—
451C4⋊C4—442no—
452C4⋊C4C2×C22⋊D1114yes—
453C22⋊C4—2216no—
454C22⋊C4—2216no—
455C42—224no—
456C42—222no—
457C42—222no—
458C11C2×#204211yescharacteristic, complemented, Sylow
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—48no—
467C23—48no—
468C23—48no—
469C23—84no—
470C23—84no—
471C23—84no—
472C23—84no—
473C23#6693512yes—
474C23#6693812yes—
475C23#6696412yes—
476C23#6696512yes—
477C23#6696812yes—
478C23#6696912yes—
479C23#6699212yes—
480C23C2×D4×D1111yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485Q8—448no—
486D4—24no—
487D4—24no—
488D4—42no—
489D4—42no—
490D4—48no—
491C2×C4—24no—
492C2×C4—48no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—448no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—884no—
511C2×C4#6693512yes—
512C2×C4#6693614yes—
513C2×C4#6693812yes—
514C2×C4#6693914yes—
515C2×C4#6698314yes—
516C2×C4#6699114yes—
517C2×C4#6699212yes—
518C2×C4C22×D4411yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—42no—
525C8—442no—
526C22—44no—
527C22—44no—
528C22—44no—
529C22—82no—
530C22—816no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22#1062237814yes—
535C22#1062238114yes—
536C22#1062239414yes—
537C22#1062239614yes—
538C22#1062257414yes—
539C22#1062276614yes—
540C22#1062277914yes—
541C22C2×#6693511yescharacteristic
542C22C2×#6693811yescharacteristic
543C22C2×#6696411yescharacteristic
544C22C2×#6696511yescharacteristic
545C22C2×#6696811yescharacteristic
546C22C2×#6696911yescharacteristic
547C22C2×#6699211yescharacteristic
548C4—44no—
549C4—442no—
550C4—442no—
551C4—444no—
552C4—882no—
553C4#1062257414yes—
554C4C2×#6693611yescharacteristic
555C4C2×#6693911yescharacteristic
556C4C2×#6698311yescharacteristic
557C4C2×#6699111yescharacteristic
558C2—84no—
559C2#1306985618yesdirect product factor
560C2C2×#1062257411yescharacteristic
561C2C2×#1062239411yescharacteristic
562C2C2×#1062239611yescharacteristic
563C2C2×#1062276611yescharacteristic
564C2C2×#1062277911yescharacteristic
565C2C2×#1062238111yescharacteristic
566C2C2×#1062237811yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2042
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
3. C22×#66874C2semidirect
5. C2×#10622598C2semidirect
6. #13069856C2direct (N × H)
7. C2×#10622188C2semidirect
29. C2×#66880C22semidirect
31. #10622598C22semidirect
33. C2×#66874C22semidirect
34. #10622188C22semidirect
367. C2×C11#2042semidirect
458. C11C2×#2042semidirect
559. C2#13069856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#668802
C22×#668742
C22×#668962
C2×#106225982
#130698562
C2×#106221882
C22×C11×#1022
C2×#204211