Finite Group Databasebeta

← C2×#13069771 #14781132

Subgroups — C2×#13069771 #14781132

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C2×#10622744C211yesmaximal, characteristic
3C2×#10622614C211yesmaximal, characteristic
4C2×#10622552C211yesmaximal, characteristic
5#13069771C218yesmaximal, direct product factor
6C2×#10622192C211yesmaximal, characteristic, complemented
7C2×#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#339C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4—22no—
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623050—22no—
18#10623050—22no—
19#10623050—22no—
20#10623050C2214yescomplemented
21C2×#66943—21no—
22C2×#66941—21no—
23C2×#66931—22no—
24C2×#66923—21no—
25C2×#66922—21no—
26#10622744—22no—
27#10622744C2214yes—
28C2×#66885—21no—
29C2×#66885—21no—
30#10622614—22no—
31#10622614C2214yes—
32C2×#66873—21no—
33C2×#66873—21no—
34#10622552—22no—
35#10622552C2214yes—
36C11×#339C2214yescomplemented
37#10622192C2214yescomplemented
38#10622161C2214yescomplemented
39C24×D11—21no—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11D412yes—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44Q814yescomplemented
52C22×D44C2312yes—
53C22×Dic22—22no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16C2312yes—
58C22×C8×C11—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117D412yes—
62C11×#117C2312yes—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—21no—
70C2×C42×C11C2312yes—
71C2×C22⋊Dic11—21no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—48no—
74#66979—21no—
75#66979—21no—
76#66979D412yes—
77#66979C2312yes—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11D412yes—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×C4×Dic11—21no—
90C2×#4318—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2312yes—
94C22×C11⋊C8—21no—
95#66943—24no—
96#66943—24no—
97#66941—24no—
98#66941—24no—
99#66931—28no—
100#66931—28no—
101#66923—24no—
102#66923—24no—
103#66922—24no—
104#66922—24no—
105#66885—24no—
106#66885—24no—
107#66873—24no—
108#66873—24no—
109C2×#2027—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—24no—
112C23×D11—22no—
113C23×D11—44no—
114C23×D11—44no—
115C23×D11—41no—
116C23×D11—41no—
117C23×D11—42no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—44no—
139C22×Dic11C2×D414yes—
140C2×D44—24no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44C2×Q814yescomplemented
158C2×Dic22—28no—
159C2×Dic22—84no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—42no—
163C2×C8×C11—22no—
164C2×C8×C11—42no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—42no—
176C22⋊Dic11—22no—
177C22⋊Dic11—22no—
178(C2×D11)⋊C4—416no—
179C4⋊Dic11—28no—
180C4⋊Dic11—21no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11C2×D412yes—
187C4⋊Dic11C2×D412yes—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192#4318—22no—
193#4318—22no—
194#4318—42no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—42no—
197C2×#544—111no—
198C2×#418—111no—
199C2×#418—111no—
200C2×#390—111no—
201#2027—118no—
202C2×#343—111no—
203C2×#339—111no—
204C2×#339D1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11#12011yescharacteristic
208C23×C11#12011yescharacteristic
209C23×C11C22⋊Q812yes—
210C23×C11#12412yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—416no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—82no—
221C22×D11—82no—
222C22×D11—88no—
223C22×D11—82no—
224C22×D11—82no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11C22⋊Q812yes—
236C2×C4×C11C22⋊Q812yes—
237C2×C4×C11C22⋊Q812yes—
238C2×C4×C11C22⋊Q812yes—
239C2×C4×C11C22⋊Q812yes—
240C2×C4×C11#12412yes—
241C2×C4×C11#12412yes—
242C2×C4×C11#12412yes—
243C2×C4×C11#12412yes—
244C2×C4×C11#12412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—82no—
259D44—24no—
260D44—24no—
261D44—42no—
262D44—42no—
263D44—44no—
264D44—44no—
265Dic22—88no—
266C8×C11—42no—
267C11⋊C8—42no—
268C23×D4—111no—
269C22×M16—111no—
270C22×M16C2×D1111yescharacteristic
271#544—114no—
272#544—222no—
273#544—222no—
274#544—222no—
275C2×C4⋊Q8—221no—
276C2×C4⋊Q8—221no—
277C2×#125—221no—
278C2×#125—221no—
279C2×C22⋊Q8—222no—
280C2×#117—111no—
281C2×#117C2×D1111yescharacteristic
282C22×C4⋊C4—111no—
283C22×C22⋊C4—222no—
284C22×C42C2×D1111yescharacteristic
285#418—114no—
286#418—114no—
287#418—222no—
288#418—222no—
289C2×#102—221no—
290C2×#102—221no—
291C2×#102—221no—
292C2×#102—221no—
293#390—114no—
294#390—222no—
295#343—114no—
296#339—114no—
297#339C2×D1114yescomplemented
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11#39312yes—
305C22×C11#39312yes—
306C22×C11#45312yes—
307C22×C11#45412yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×C22⋊Q811yescharacteristic
310C22×C11C2×#12411yescharacteristic
311C2×D11—48no—
312C2×D11—44no—
313C2×D11—84no—
314C2×D11—88no—
315C2×D11—82no—
316C2×D11—82no—
317C2×D11—88no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11#39312yes—
322C4×C11#39312yes—
323C4×C11C2×C22⋊Q811yescharacteristic
324C4×C11C2×C22⋊Q811yescharacteristic
325C4×C11C2×#12411yescharacteristic
326C4×C11C2×#12411yescharacteristic
327Dic11—42no—
328Dic11—44no—
329Dic11—42no—
330C25—221no—
331C22×Q8—222no—
332C22×D4—114no—
333C22×D4—112no—
334C22×D4—221no—
335C22×D4—221no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4—222no—
342C23×C4—21no—
343C23×C4—112no—
344C23×C4C22×D1111yescharacteristic
345C2×M16—21no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—112no—
349C2×M16—221no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16C22×D1112yes—
353C22×C8—21no—
354C22×C8—221no—
355C4⋊Q8—224no—
356C4⋊Q8—224no—
357C4⋊Q8—224no—
358C4⋊Q8—224no—
359#125—224no—
360#125—224no—
361#125—224no—
362#125—224no—
363C22⋊Q8—228no—
364C22⋊Q8—228no—
365#117—21no—
366#117—21no—
367#117—112no—
368#117—112no—
369#117—221no—
370#117—221no—
371#117D4412yes—
372#117C22×D1112yes—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4D4411yescharacteristic
385C2×C4⋊C4D4411yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—448no—
390C2×C42—21no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—21no—
394C2×C42—221no—
395C2×C42C22×D1112yes—
396#102—224no—
397#102—224no—
398#102—224no—
399#102—224no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—22no—
403C2×C11#202714yescomplemented
404C2×C11C2×#39311yescharacteristic
405C2×C11C2×#45311yescharacteristic
406C2×C11C2×#45411yescharacteristic
407D11—84no—
408C24—224no—
409C24—222no—
410C24—444no—
411C24—444no—
412C24—441no—
413C24—441no—
414C24—442no—
415C24D4×D1111yescharacteristic
416C2×Q8—228no—
417C2×Q8—884no—
418C2×D4—114no—
419C2×D4—224no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—442no—
430C2×D4—442no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4—442no—
434C2×D4—442no—
435C2×D4—442no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—114no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—444no—
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4#433912yes—
451C22×C4#433912yes—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4#434112yes—
456C22×C4Q8×D1112yes—
457C22×C4C23×D1111yescharacteristic
458M16—22no—
459M16—22no—
460M16—42no—
461M16—222no—
462M16—222no—
463M16—442no—
464C2×C8—22no—
465C2×C8—42no—
466C2×C8—222no—
467C2×C8—442no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—228no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4C2×D4412yes—
482C4⋊C4C2×D4412yes—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—222no—
486C22⋊C4—222no—
487C22⋊C4—4416no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—42no—
493C42—222no—
494C42—222no—
495C11C2×#202711yescharacteristic, complemented, Sylow
496C23—22no—
497C23—22no—
498C23—224no—
499C23—444no—
500C23—444no—
501C23—4416no—
502C23—442no—
503C23—442no—
504C23—444no—
505C23—444no—
506C23—882no—
507C23—882no—
508C23—888no—
509C23—882no—
510C23—882no—
511C23#6693511yescharacteristic
512C23#6693511yescharacteristic
513C23#6693812yes—
514C23#6694912yes—
515C23C2×D4×D1111yescharacteristic
516Q8—888no—
517D4—224no—
518D4—224no—
519D4—442no—
520D4—442no—
521D4—444no—
522D4—444no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—444no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—444no—
538C2×C4—882no—
539C2×C4#6692812yes—
540C2×C4#6692812yes—
541C2×C4#6693511yescharacteristic
542C2×C4#6693511yescharacteristic
543C2×C4#6693812yes—
544C2×C4#6693812yes—
545C2×C4#6693812yes—
546C2×C4#6694912yes—
547C2×C4#6694912yes—
548C2×C4#6694912yes—
549C2×C4#6695012yes—
550C2×C4#6695012yes—
551C2×C4C22×D4411yescharacteristic
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×#433911yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4C2×Q8×D1111yescharacteristic
557C8—42no—
558C8—442no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—448no—
566C22—444no—
567C22—884no—
568C22—888no—
569C22—882no—
570C22—882no—
571C22—888no—
572C22#1062228612yes—
573C22#1062228612yes—
574C22#1062243512yes—
575C22#1062244012yes—
576C22C2×#6693511yescharacteristic
577C22C2×#6693811yescharacteristic
578C22C2×#6694911yescharacteristic
579C4—44no—
580C4—42no—
581C4—42no—
582C4—444no—
583C4—442no—
584C4—442no—
585C4#1062228612yes—
586C4#1062228612yes—
587C4C2×#6692811yescharacteristic
588C4C2×#6693811yescharacteristic
589C4C2×#6694911yescharacteristic
590C4C2×#6695011yescharacteristic
591C2—21no—
592C2—21no—
593C2—22no—
594C2—884no—
595C2#1306977114yesdirect product factor
596C2C2×#1062228611yescharacteristic
597C2C2×#1062243511yescharacteristic
598C2C2×#1062244011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC23×C11#120
prime radicalC23×D44C22
hypercenterC2×#339D11
hypocenterC11C2×#2027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
5. #13069771C2direct (N × H)
6. C2×#10622192C2semidirect
7. C2×#10622161C2semidirect
8. C2×C11×#339C2semidirect
20. #10623050C22semidirect
36. C11×#339C22semidirect
37. #10622192C22semidirect
38. #10622161C22semidirect
51. C22×D44Q8semidirect
157. C2×D44C2×Q8semidirect
204. C2×#339D11semidirect
297. #339C2×D11semidirect
403. C2×C11#2027semidirect
495. C11C2×#2027semidirect
595. C2#13069771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106227442
C2×#106226142
C2×#106225522
#130697712
C2×#106221922
C2×#106221612
C2×C11×#3392
C2×#202711