Finite Group Databasebeta

← C2×#13069852 #14781444

Subgroups — C2×#13069852 #14781444

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×#66899C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic
4C22×#66896C211yesmaximal, characteristic
5C2×#10622541C211yesmaximal, characteristic, complemented
6#13069852C218yesmaximal, direct product factor
7C2×#10622162C211yesmaximal, characteristic, complemented
8C22×C11×#124C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C2×C11×#124—24no—
12C2×C11×#124—24no—
13C2×C11×#124—22no—
14C2×C11×#124C2214yes—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4—21no—
17C22×C42×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C23×C11⋊C8C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66899—24no—
24C2×#66899—24no—
25C2×#66899C2214yescomplemented
26C2×#66899C2214yescomplemented
27C2×#66896—24no—
28C2×#66896—24no—
29C2×#66896C2214yes—
30C2×#66896C2214yes—
31C2×C11⋊#95—21no—
32#10622541—22no—
33#10622541C2214yescomplemented
34#10622162C2214yescomplemented
35C25×C11—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—
44C22×D4×C11—22no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11D414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C11×#124—216no—
59C11×#124—28no—
60C11×#124—28no—
61C2×C11×C22⋊C4—28no—
62C2×C11×C22⋊C4—28no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11D412yes—
68C2×C42×C11C2312yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D414yes—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—44no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87#66899—28no—
88#66899—28no—
89#66896—28no—
90#66896—28no—
91C11⋊#95—24no—
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×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—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—42no—
127C2×D4×C11C2×D414yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C11×C22⋊C4—216no—
157C11×C22⋊C4—216no—
158C42×C11—24no—
159C42×C11—22no—
160C42×C11—22no—
161C4⋊Dic11—24no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4⋊Dic11C2×D414yes—
167Dic11⋊C4—48no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—44no—
175C2×C11⋊C8—44no—
176C22×#124D1111yescharacteristic
177C22×#103—111no—
178C22×#103—111no—
179C22×#102—111no—
180C22×#102—111no—
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
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—48no—
211D4×C11—24no—
212D4×C11—24no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—48no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—48no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12314yes—
233C2×C4×C11#12314yes—
234C2×C4×C11#12412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—48no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—84no—
249C11⋊C8—42no—
250C11⋊C8—42no—
251C23×Q8C2×D1111yescharacteristic
252C23×D4C2×D1111yescharacteristic
253C23×C8—111no—
254C23×C8—111no—
255C2×#124—24no—
256C2×#124—24no—
257C2×#124—22no—
258C2×#124C2×D1114yes—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—221no—
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
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#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—42no—
301C4×C11—42no—
302C4×C11#39414yes—
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12111yescharacteristic
305C4×C11C2×#12311yescharacteristic
306C4×C11C2×#12311yescharacteristic
307Dic11—44no—
308Dic11—82no—
309C25—21no—
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—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—21no—
324C22×D4C22⋊D1114yes—
325C22×D4C22×D1112yes—
326C23×C4—21no—
327C23×C4—221no—
328C23×C4—221no—
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22⋊D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C22×C8—112no—
333C22×C8—112no—
334C22×C8—222no—
335C22×C8—222no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8—222no—
339C22×C8—222no—
340#124—216no—
341#124—28no—
342#124—28no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—444no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42C22⋊D1112yes—
360C2×C42C22×D1112yes—
361#103—228no—
362#103—228no—
363#102—228no—
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—
383C24C2×C22⋊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—42no—
395C2×Q8—44no—
396C2×Q8C2×C22⋊D1114yes—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4C2×C22⋊D1114yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4D4×D1112yes—
429C22×C4#434112yes—
430C22×C4#434112yes—
431C22×C4#434112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C2×C8—444no—
446C4⋊C4—114no—
447C4⋊C4—224no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—448no—
452C4⋊C4—442no—
453C22⋊C4—216no—
454C22⋊C4—216no—
455C42—24no—
456C42—22no—
457C42—22no—
458C11C2×#204211yescharacteristic, complemented, Sylow
459C23—24no—
460C23—42no—
461C23—42no—
462C23—48no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—48no—
468C23—48no—
469C23—84no—
470C23—84no—
471C23—84no—
472C23—84no—
473C23#6698912yes—
474C23#6699112yes—
475C23#6700212yes—
476C23#6700312yes—
477C23#6700312yes—
478C23#6700412yes—
479C23#6700612yes—
480C23C22×C22⋊D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486D4—24no—
487D4—24no—
488D4—42no—
489D4—42no—
490D4—48no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—224no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—448no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—884no—
511C2×C4#6698814yes—
512C2×C4#6698814yes—
513C2×C4#6698912yes—
514C2×C4#6699112yes—
515C2×C4#6699214yes—
516C2×C4#6699214yes—
517C2×C4#6700612yes—
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×#434111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—442no—
525C8—442no—
526C22—44no—
527C22—44no—
528C22—44no—
529C22—82no—
530C22—816no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22#1062266714yes—
535C22#1062266814yes—
536C22#1062266914yes—
537C22#1062267014yes—
538C22#1062283514yes—
539C22#1062285114yes—
540C22#1062285214yes—
541C22C2×#6698911yescharacteristic
542C22C2×#6699111yescharacteristic
543C22C2×#6700211yescharacteristic
544C22C2×#6700311yescharacteristic
545C22C2×#6700311yescharacteristic
546C22C2×#6700411yescharacteristic
547C22C2×#6700611yescharacteristic
548C4—42no—
549C4—42no—
550C4—44no—
551C4—444no—
552C4—882no—
553C4#1062283514yes—
554C4C2×#6698811yescharacteristic
555C4C2×#6698811yescharacteristic
556C4C2×#6699211yescharacteristic
557C4C2×#6699211yescharacteristic
558C2—84no—
559C2#1306985218yesdirect product factor
560C2C2×#1062283511yescharacteristic
561C2C2×#1062285111yescharacteristic
562C2C2×#1062285211yescharacteristic
563C2C2×#1062267011yescharacteristic
564C2C2×#1062266711yescharacteristic
565C2C2×#1062266911yescharacteristic
566C2C2×#1062266811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#124C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#124D11
hypocenterC11C2×#2042
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#66899C2semidirect
2. C22×#66899C2semidirect
5. C2×#10622541C2semidirect
6. #13069852C2direct (N × H)
7. C2×#10622162C2semidirect
25. C2×#66899C22semidirect
26. C2×#66899C22semidirect
33. #10622541C22semidirect
34. #10622162C22semidirect
367. C2×C11#2042semidirect
458. C11C2×#2042semidirect
559. C2#13069852direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668992
C22×#668962
C2×#106225412
#130698522
C2×#106221622
C22×C11×#1242
C2×#204211