Finite Group Databasebeta

← C2×#13069809 #14781226

Subgroups — C2×#13069809 #14781226

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×#66872C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66899C211yesmaximal, characteristic, complemented
4C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
5C2×#10622825C211yesmaximal, characteristic
6#13069809C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊Q8C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C2×C11×C22⋊Q8—24no—
12C2×C11×C22⋊Q8—22no—
13C2×C11×C22⋊Q8—24no—
14C2×C11×C22⋊Q8C2214yes—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4—21no—
18C22×C22⋊Dic11—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66899—24no—
24C2×#66899—24no—
25C2×#66899C2214yescomplemented
26C2×#66899C2214yescomplemented
27#10622825—22no—
28#10622825C2214yes—
29C2×C11⋊#95—21no—
30C2×C22⋊(C11⋊C8)—24no—
31C2×C22⋊(C11⋊C8)C2214yes—
32C2×#66872—24no—
33C2×#66872C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11D411yescharacteristic
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×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D412yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C11×C22⋊Q8—216no—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—28no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D414yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—44no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8—22no—
84C22×C11⋊C8D414yes—
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87#66899—28no—
88#66899—28no—
89C11⋊#95—24no—
90C22⋊(C11⋊C8)—28no—
91#66872—28no—
92C2×#2035—111nomaximal, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11SD1614yes—
100C24×C11C2×D412yes—
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—42no—
113C2×Q8×C11—44no—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—44no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
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—22no—
149C22×Dic11—22no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C11×C4⋊C4—216no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—216no—
161C22⋊Dic11—48no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C2×C11⋊C8—28no—
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⋊C8C2×D414yes—
176C22×C22⋊Q8D1111yescharacteristic
177C22×#106—111no—
178C22×#103—111no—
179C22×#103—111no—
180C22×C22⋊C8—111no—
181C2×#380—111no—
182#2035—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×SD1614yes—
201C23×C11C2×SD1612yes—
202C23×C11#13512yes—
203C23×C11#13712yes—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—48no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—48no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12314yes—
233C2×C4×C11#12312yes—
234C2×C4×C11#12414yes—
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—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—84no—
248C2×Dic11—84no—
249C11⋊C8—24no—
250C11⋊C8—42no—
251C23×Q8C2×D1111yescharacteristic
252C24×C4C2×D1111yescharacteristic
253C23×C8—111no—
254C23×C8—111no—
255C2×C22⋊Q8—24no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—24no—
258C2×C22⋊Q8C2×D1114yes—
259C22×C4⋊C4—21no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4—221no—
265C2×#106—114no—
266C2×#106—224no—
267C2×#103—114no—
268C2×#103—114no—
269C2×#103—224no—
270C2×#103—224no—
271C2×C22⋊C8—114no—
272C2×C22⋊C8—224no—
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#44814yes—
287C22×C11#45214yes—
288C22×C11#46514yes—
289C22×C11#47014yes—
290C22×C11#48314yes—
291C22×C11#48514yes—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12311yescharacteristic
295C22×C11C22×SD1611yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C4×C11—42no—
300C4×C11—44no—
301C4×C11—44no—
302C4×C11#39414yes—
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12111yescharacteristic
305C4×C11C2×#12311yescharacteristic
306C4×C11C2×#12411yescharacteristic
307Dic11—82no—
308Dic11—82no—
309C25C22⋊D1111yescharacteristic
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8C22⋊D1114yes—
317C22×Q8C22×D1112yes—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22⋊D1112yes—
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22×D1112yes—
331C23×C4C22×D1111yescharacteristic
332C22×C8—114no—
333C22×C8—112no—
334C22×C8—112no—
335C22×C8—222no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8—222no—
339C22×C8—222no—
340C22⋊Q8—216no—
341C22⋊Q8—28no—
342C22⋊Q8—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22⋊D1114yes—
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—444no—
361#106—228no—
362#103—228no—
363#103—228no—
364C22⋊C8—228no—
365#95—224no—
366C2×C11—44no—
367C2×C11#203518yescomplemented
368C2×C11C2×#39411yescharacteristic
369C2×C11C2×#44811yescharacteristic
370C2×C11C2×#45211yescharacteristic
371C2×C11C2×#46511yescharacteristic
372C2×C11C2×#47011yescharacteristic
373C2×C11C2×#48311yescharacteristic
374C2×C11C2×#48511yescharacteristic
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24#432514yes—
382C24C2×C22⋊D1112yes—
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—42no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—42no—
396C2×Q8C2×C22⋊D1114yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4D4×D1112yes—
430C22×C4#434112yes—
431C22×C4#434112yes—
432C22×C4#434112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C23×D1111yescharacteristic
438C2×C8—114no—
439C2×C8—228no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—444no—
446C4⋊C4—216no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—442no—
454C4⋊C4—442no—
455C4⋊C4C2×C22⋊D1114yes—
456C22⋊C4—216no—
457C22⋊C4—448no—
458C11C2×#203511yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—28no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—28no—
467C23—28no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#6698812yes—
473C23#6699212yes—
474C23C2×#432514yes—
475C23C2×#432512yes—
476C23#6699512yes—
477C23#6700312yes—
478C23#6700412yes—
479C23#6700612yes—
480C23C22×C22⋊D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
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#6698814yes—
512C2×C4#6698812yes—
513C2×C4#6698914yes—
514C2×C4#6699114yes—
515C2×C4#6699214yes—
516C2×C4#6699212yes—
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—224no—
525C8—442no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—416no—
534C22#1062265614yes—
535C22#1062265814yes—
536C22#1062266114yes—
537C22#1062266514yes—
538C22#1062283514yes—
539C22#1062284014yes—
540C22#1062285214yes—
541C22C2×#6698811yescharacteristic
542C22C2×#6699211yescharacteristic
543C22C22×#432511yescharacteristic
544C22C2×#6699511yescharacteristic
545C22C2×#6700311yescharacteristic
546C22C2×#6700411yescharacteristic
547C22C2×#6700611yescharacteristic
548C4—44no—
549C4—42no—
550C4—44no—
551C4—882no—
552C4—882no—
553C4#1062283514yes—
554C4C2×#6698811yescharacteristic
555C4C2×#6698911yescharacteristic
556C4C2×#6699111yescharacteristic
557C4C2×#6699211yescharacteristic
558C2—44no—
559C2#1306980918yesdirect product factor
560C2C2×#1062283511yescharacteristic
561C2C2×#1062284011yescharacteristic
562C2C2×#1062285211yescharacteristic
563C2C2×#1062266111yescharacteristic
564C2C2×#1062266511yescharacteristic
565C2C2×#1062265611yescharacteristic
566C2C2×#1062265811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66872C2semidirect
2. C22×#66899C2semidirect
3. C22×#66899C2semidirect
6. #13069809C2direct (N × H)
7. C2×#10622167C2semidirect
25. C2×#66899C22semidirect
26. C2×#66899C22semidirect
33. C2×#66872C22semidirect
34. #10622167C22semidirect
367. C2×C11#2035semidirect
458. C11C2×#2035semidirect
559. C2#13069809direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668722
C22×#668992
C22×C22⋊(C11⋊C8)2
C2×#106228252
#130698092
C2×#106221672
C22×C11×C22⋊Q82
C2×#203511