Finite Group Databasebeta

← C2×#13069820 #14781246

Subgroups — C2×#13069820 #14781246

Order 2816.

1662 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×#66977C211yesmaximal, characteristic
2C22×#66882C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4C22×#66880C211yesmaximal, characteristic, complemented
5C2×#10622825C211yesmaximal, characteristic
6#13069820C218yesmaximal, direct product factor
7C2×#10622189C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C8C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C22×C22⋊Dic11—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×#66977—22no—
19C2×#66977—24no—
20C2×#66977—24no—
21C2×#66977C2214yes—
22C22×Dic11⋊C4—21no—
23C2×C11×C22⋊C8—24no—
24C2×C11×C22⋊C8C2214yes—
25#10622825—22no—
26#10622825C2214yes—
27C2×C11⋊#95—21no—
28C2×#66882—24no—
29C2×#66882C2214yescomplemented
30C2×#66880—24no—
31C2×#66880—24no—
32C2×#66880C2214yescomplemented
33C2×#66880C2214yescomplemented
34#10622189C2214yescomplemented
35C25×C11D411yescharacteristic
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D412yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11—21no—
48C23×Dic11—21no—
49C23×Dic11—21no—
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×C11D414yes—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C2×C22⋊Dic11—28no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—44no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D414yes—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82#66977—216no—
83#66977—28no—
84#66977—28no—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—24no—
87C11×C22⋊C8—28no—
88C11⋊#95—24no—
89#66882—28no—
90#66880—28no—
91#66880—28no—
92C2×#2036—111nomaximal, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11Q1614yes—
100C24×C11C2×D412yes—
101C24×C11C2×D411yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11C2×D412yes—
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—24no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11—42no—
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—42no—
152C2×Dic22—44no—
153C2×Dic22—42no—
154C2×Dic22—44no—
155C2×Dic22C2×D414yes—
156C2×C8×C11—28no—
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×C11C2×D414yes—
164C22⋊Dic11—216no—
165C22⋊Dic11—48no—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—42no—
173C4⋊Dic11—42no—
174C4⋊Dic11C2×D414yes—
175Dic11⋊C4—216no—
176C22×C22⋊Q8—111no—
177C22×#107—111no—
178C22×#103—111no—
179C22×#103—111no—
180C22×C22⋊C8D1111yescharacteristic
181C2×#380—111no—
182#2036—118no—
183C2×#340—111no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11#12012yes—
198C23×C11#12112yes—
199C23×C11#12312yes—
200C23×C11C2×Q1614yes—
201C23×C11C2×Q1612yes—
202C23×C11#13512yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—48no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12114yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12314yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12414yes—
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—24no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—48no—
235C2×Dic11—48no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243C2×Dic11—84no—
244Dic22—24no—
245Dic22—24no—
246Dic22—42no—
247Dic22—42no—
248Dic22—48no—
249C8×C11—24no—
250C8×C11—42no—
251C23×Q8—111no—
252C24×C4C2×D1111yescharacteristic
253C23×C8C2×D1111yescharacteristic
254C23×C8C2×D1111yescharacteristic
255C2×C22⋊Q8—114no—
256C2×C22⋊Q8—224no—
257C2×C22⋊Q8—224no—
258C2×C22⋊Q8—222no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—221no—
263C22×C22⋊C4—221no—
264C22×C22⋊C4—221no—
265C2×#107—114no—
266C2×#107—224no—
267C2×#103—114no—
268C2×#103—114no—
269C2×#103—224no—
270C2×#103—224no—
271C2×C22⋊C8—24no—
272C2×C22⋊C8C2×D1114yes—
273#380—114no—
274#380—222no—
275C2×#95—221no—
276#340—114no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—416no—
285C22×C11#39414yes—
286C22×C11#44914yes—
287C22×C11#45114yes—
288C22×C11#46714yes—
289C22×C11#46814yes—
290C22×C11#48414yes—
291C22×C11#48514yes—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12311yescharacteristic
295C22×C11C22×Q1611yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C4×C11—42no—
300C4×C11#39414yes—
301C4×C11C2×#12111yescharacteristic
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12411yescharacteristic
305Dic11—44no—
306Dic11—44no—
307Dic11—82no—
308Dic11—82no—
309C25D4411yescharacteristic
310C22×Q8—114no—
311C22×Q8—112no—
312C22×Q8—221no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×Q8—222no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—221no—
325C23×C4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4D4412yes—
329C23×C4D4411yescharacteristic
330C23×C4C22×D1112yes—
331C23×C4C22×D1111yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8C22⋊D1114yes—
338C22×C8C22×D1112yes—
339C22×C8C22×D1112yes—
340C22⋊Q8—228no—
341C22⋊Q8—228no—
342C22⋊Q8—2216no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—444no—
361#107—228no—
362#103—228no—
363#103—228no—
364C22⋊C8—28no—
365#95—224no—
366C2×C11—44no—
367C2×C11#203618yescomplemented
368C2×C11C2×#39411yescharacteristic
369C2×C11C2×#45111yescharacteristic
370C2×C11C2×#44911yescharacteristic
371C2×C11C2×#46711yescharacteristic
372C2×C11C2×#46811yescharacteristic
373C2×C11C2×#48511yescharacteristic
374C2×C11C2×#48411yescharacteristic
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24Dic4414yes—
382C24C2×D4412yes—
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—444no—
394C2×Q8—442no—
395C2×Q8—442no—
396C2×Q8—444no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4C2×D4412yes—
430C22×C4C2×D4411yescharacteristic
431C22×C4#433912yes—
432C22×C4D4×D1112yes—
433C22×C4D4×D1112yes—
434C22×C4#434112yes—
435C22×C4#434112yes—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C23×D1111yescharacteristic
438C2×C8—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—44no—
445C2×C8C2×C22⋊D1114yes—
446C4⋊C4—114no—
447C4⋊C4—2216no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—222no—
454C4⋊C4—442no—
455C4⋊C4—442no—
456C22⋊C4—2216no—
457C22⋊C4—448no—
458C11C2×#203611yescharacteristic, complemented, Sylow
459C23—28no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—28no—
467C23—28no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#6693512yes—
473C23#6693912yes—
474C23#6695712yes—
475C23C2×Dic4414yes—
476C23C2×Dic4412yes—
477C23#6696112yes—
478C23#6696212yes—
479C23#6698312yes—
480C23C22×D4411yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485Q8—448no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—448no—
502C2×C4—448no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—884no—
510C2×C4—884no—
511C2×C4#6693512yes—
512C2×C4#6693614yes—
513C2×C4#6693814yes—
514C2×C4#6693912yes—
515C2×C4#6698312yes—
516C2×C4#6699114yes—
517C2×C4#6699214yes—
518C2×C4C2×#433911yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—24no—
525C8—42no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—416no—
534C22#1062233514yes—
535C22#1062233614yes—
536C22#1062234714yes—
537C22#1062235214yes—
538C22#1062257414yes—
539C22#1062272914yes—
540C22#1062274714yes—
541C22C2×#6693511yescharacteristic
542C22C2×#6693911yescharacteristic
543C22C2×#6695711yescharacteristic
544C22C22×Dic4411yescharacteristic
545C22C2×#6696111yescharacteristic
546C22C2×#6696211yescharacteristic
547C22C2×#6698311yescharacteristic
548C4—42no—
549C4—444no—
550C4—444no—
551C4—882no—
552C4—882no—
553C4#1062257414yes—
554C4C2×#6693611yescharacteristic
555C4C2×#6693811yescharacteristic
556C4C2×#6699111yescharacteristic
557C4C2×#6699211yescharacteristic
558C2—44no—
559C2#1306982018yesdirect product factor
560C2C2×#1062257411yescharacteristic
561C2C2×#1062235211yescharacteristic
562C2C2×#1062234711yescharacteristic
563C2C2×#1062272911yescharacteristic
564C2C2×#1062274711yescharacteristic
565C2C2×#1062233611yescharacteristic
566C2C2×#1062233511yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#2036
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66882C2semidirect
3. C22×#66880C2semidirect
4. C22×#66880C2semidirect
6. #13069820C2direct (N × H)
7. C2×#10622189C2semidirect
29. C2×#66882C22semidirect
32. C2×#66880C22semidirect
33. C2×#66880C22semidirect
34. #10622189C22semidirect
367. C2×C11#2036semidirect
458. C11C2×#2036semidirect
559. C2#13069820direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#668822
C22×#668802
C2×#106228252
#130698202
C2×#106221892
C22×C11×C22⋊C82
C2×#203611