Finite Group Databasebeta

← C2×#13069688 #14780803

Subgroups — C2×#13069688 #14780803

Order 2816.

2942 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D88C211yesmaximal, characteristic, complemented
2C23×#4323C211yesmaximal, characteristic, complemented
3C22×#66993C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622601C211yesmaximal, characteristic, complemented
6#13069688C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11—22no—
11C23×D44C2211yescharacteristic
12C23×D44C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66993—24no—
16C2×#66993—24no—
17C2×#66993—22no—
18C2×#66993C2214yescomplemented
19C22×#4323—24no—
20C22×#4323—24no—
21C22×#4323—24no—
22C22×#4323C2214yescomplemented
23C22×(C2×D11)⋊C4—22no—
24C22×C4×Dic11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C22×D88—24no—
27C22×D88—24no—
28C22×D88—24no—
29C22×D88C2214yescomplemented
30C2×C11×#102—24no—
31C2×C11×#102C2214yescomplemented
32#10622601—22no—
33#10622601C2214yescomplemented
34C2×#66873—24no—
35C2×#66873C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C24×D11—21no—
39C24×D11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11D414yes—
47C22×D4×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—216no—
51C22×C22⋊D11—28no—
52C22×C22⋊D11—48no—
53C22×C22⋊D11—48no—
54C23×Dic11D412yes—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—22no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44D414yes—
68C22×D44D414yescomplemented
69C22×D44C2312yes—
70C22×D44C2312yes—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11D414yescomplemented
74C22×C8×C11C2312yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79#66993—216no—
80#66993—28no—
81#66993—28no—
82C2×#4323—232no—
83C2×#4323—28no—
84C2×#4323—28no—
85C2×#4323—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—48no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11D412yes—
91C2×C4×Dic11C2312yes—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8D414yescomplemented
95C22×C11⋊C8C2312yes—
96C2×D88—232no—
97C2×D88—28no—
98C2×D88—28no—
99C2×D88—28no—
100C11×#102—28no—
101#66873—28no—
102C2×#2011—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—44no—
108C24×C11—44no—
109C24×C11C2×D411yescharacteristic
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—42no—
115C23×D11—42no—
116C23×D11—42no—
117C23×D11—42no—
118C23×D11—44no—
119C23×D11—44no—
120C23×D11—44no—
121C23×D11—44no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—232no—
147C2×C22⋊D11—416no—
148C2×C22⋊D11—464no—
149C2×C22⋊D11—416no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11D818yescomplemented
153C22×Dic11C2×D414yes—
154C2×D44—24no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44—24no—
159C2×D44—28no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—44no—
171C2×D44—42no—
172C2×D44—44no—
173C2×D44—42no—
174C2×D44—44no—
175C2×D44—44no—
176C2×D44—42no—
177C2×D44—42no—
178C2×D44C2×D414yes—
179C2×D44C2×D414yescomplemented
180C2×C8×C11—28no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11C2×D414yescomplemented
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—42no—
187#4323—232no—
188(C2×D11)⋊C4—416no—
189C4×Dic11—24no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C2×D414yescomplemented
196D88—232no—
197C23×D8—111no—
198C23×D8—111no—
199C22×#127—111no—
200C22×#102—111no—
201C22×#102D1111yescharacteristic, complemented
202C2×#390—111no—
203#2011—118no—
204C2×#336—111no—
205C23×C11—24no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—416no—
212C23×C11—88no—
213C23×C11—84no—
214C23×C11—84no—
215C23×C11#12012yes—
216C23×C11#12112yes—
217C23×C11#12712yes—
218C23×C11C2×D814yes—
219C23×C11AGL(1,ℤ/8)14yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—48no—
232C22×D11—48no—
233C22×D11—416no—
234C22×D11—416no—
235C22×D11—88no—
236C22×D11—88no—
237C22×D11—84no—
238C22×D11—84no—
239C22×D11—84no—
240C22×D11—84no—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—84no—
249C2×C4×C11#12014yes—
250C2×C4×C11#12012yes—
251C2×C4×C11#12014yes—
252C2×C4×C11#12114yes—
253C2×C4×C11#12112yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12712yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C22⋊D11—464no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—216no—
266C2×Dic11C2×D818yescomplemented
267D44—24no—
268D44—24no—
269D44—24no—
270D44—24no—
271D44—42no—
272D44—42no—
273D44—42no—
274D44—42no—
275D44—48no—
276D44—48no—
277C8×C11—24no—
278C11⋊C8—24no—
279C23×D4—111no—
280C23×D4—111no—
281C23×D4—222no—
282C23×D4C2×D1111yescharacteristic
283C22×D8—114no—
284C22×D8—114no—
285C22×D8—224no—
286C22×D8—224no—
287C22×D8—224no—
288C22×D8—224no—
289C22×D8—224no—
290C22×D8—224no—
291C23×C8—111no—
292C23×C8C2×D1111yescharacteristic
293C2×#127—114no—
294C2×#127—222no—
295C2×#127—224no—
296C2×#127—224no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4—222no—
299C22×C42—111no—
300C2×#102—24no—
301C2×#102—114no—
302C2×#102—224no—
303C2×#102C2×D1114yescomplemented
304#390—114no—
305#390—222no—
306#336—114no—
307C22×C11—44no—
308C22×C11—48no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—84no—
312C22×C11—816no—
313C22×C11#39214yes—
314C22×C11#44718yes—
315C22×C11#45918yes—
316C22×C11#49314yes—
317C22×C11#49614yes—
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×#12711yescharacteristic
321C22×C11C22×D812yes—
322C22×C11C2×AGL(1,ℤ/8)12yes—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—48no—
326C2×D11—48no—
327C2×D11—82no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—84no—
332C2×D11—84no—
333C2×D11—816no—
334C2×D11—816no—
335C4×C11—82no—
336C4×C11#39214yes—
337C4×C11C2×#12011yescharacteristic
338C4×C11C2×#12011yescharacteristic
339C4×C11C2×#12111yescharacteristic
340C4×C11C2×#12111yescharacteristic
341Dic11—28no—
342C25—21no—
343C25—221no—
344C25—221no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—114no—
352C22×D4—114no—
353C22×D4—112no—
354C22×D4—112no—
355C22×D4—228no—
356C22×D4—2216no—
357C22×D4—222no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4—222no—
362C22×D4—222no—
363C22×D4—222no—
364C22×D4—222no—
365C22×D4—221no—
366C22×D4—221no—
367C22×D4—222no—
368C22×D4—222no—
369C22×D4—448no—
370C22×D4—448no—
371C22×D4D4414yes—
372C22×D4C22×D1112yes—
373C23×C4—21no—
374C23×C4—112no—
375C23×C4C22×D1111yescharacteristic
376C2×D8—228no—
377C2×D8—228no—
378C2×D8—2232no—
379C2×D8—228no—
380C2×D8—228no—
381C2×D8—2232no—
382C2×D8—228no—
383C2×D8—228no—
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—114no—
387C22×C8—112no—
388C22×C8—222no—
389C22×C8—222no—
390C22×C8C22⋊D1114yescomplemented
391C22×C8C22×D1112yes—
392#127—228no—
393#127—2216no—
394#127—228no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4C22×D1112yes—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—448no—
401C2×C42—112no—
402C2×C42—112no—
403C2×C42—222no—
404C2×C42—222no—
405#102—28no—
406#102—228no—
407C2×C11—84no—
408C2×C11#201118yescomplemented
409C2×C11C2×#39211yescharacteristic
410C2×C11C2×#44712yes—
411C2×C11C2×#45912yes—
412C2×C11C2×#49311yescharacteristic
413C2×C11C2×#49611yescharacteristic
414D11—84no—
415D11—84no—
416C24—24no—
417C24—22no—
418C24—42no—
419C24—44no—
420C24—44no—
421C24—42no—
422C24—224no—
423C24—224no—
424C24—222no—
425C24—222no—
426C24—442no—
427C24—442no—
428C24—444no—
429C24—444no—
430C24—444no—
431C24—444no—
432C24—442no—
433C24—442no—
434C24D4×D1111yescharacteristic
435C2×D4—28no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—44no—
444C2×D4—42no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—114no—
448C2×D4—114no—
449C2×D4—2232no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—228no—
453C2×D4—224no—
454C2×D4—228no—
455C2×D4—228no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C2×D4—222no—
462C2×D4—222no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—4416no—
467C2×D4—4416no—
468C2×D4—4464no—
469C2×D4—444no—
470C2×D4—442no—
471C2×D4—444no—
472C2×D4—442no—
473C2×D4—444no—
474C2×D4—444no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4C2×D4414yes—
478C22×C4—22no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4—118no—
482C22×C4—114no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4C2×D4412yes—
486C22×C4#433912yes—
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1112yes—
489C22×C4D4×D1112yes—
490C22×C4D4×D1112yes—
491C22×C4C2×C22⋊D1112yes—
492C22×C4C23×D1111yescharacteristic
493D8—2232no—
494D8—2232no—
495C2×C8—28no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—114no—
499C2×C8—228no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8C2×C22⋊D1114yescomplemented
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—42no—
506C22⋊C4—4416no—
507C42—224no—
508C42—222no—
509C42—222no—
510C11C2×#201111yescharacteristic, complemented, Sylow
511C23—24no—
512C23—42no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—48no—
517C23—416no—
518C23—84no—
519C23—84no—
520C23—88no—
521C23—224no—
522C23—224no—
523C23—442no—
524C23—442no—
525C23—444no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23—442no—
530C23—442no—
531C23—448no—
532C23—448no—
533C23—4416no—
534C23—4416no—
535C23—884no—
536C23—884no—
537C23—884no—
538C23—884no—
539C23—888no—
540C23—888no—
541C23#6693512yes—
542C23#6693712yes—
543C23D8×D1114yes—
544C23#6696714yes—
545C23#6699312yes—
546C23C2×D4×D1111yescharacteristic
547D4—24no—
548D4—24no—
549D4—42no—
550D4—42no—
551D4—48no—
552D4—224no—
553D4—224no—
554D4—224no—
555D4—224no—
556D4—4464no—
557D4—442no—
558D4—442no—
559D4—442no—
560D4—442no—
561D4—448no—
562D4—448no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4—118no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—2216no—
570C2×C4#6693514yes—
571C2×C4#6693512yes—
572C2×C4#6693714yes—
573C2×C4#6693712yes—
574C2×C4#6698314yes—
575C2×C4#6699014yes—
576C2×C4#6699312yes—
577C2×C4C22×D4411yescharacteristic
578C2×C4C2×#433911yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×D4×D1111yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C22×C22⋊D1111yescharacteristic
583C8—24no—
584C8—224no—
585C22—48no—
586C22—44no—
587C22—82no—
588C22—84no—
589C22—816no—
590C22—82no—
591C22—448no—
592C22—448no—
593C22—444no—
594C22—444no—
595C22—882no—
596C22—882no—
597C22—884no—
598C22—884no—
599C22—8816no—
600C22—8816no—
601C22—882no—
602C22—882no—
603C22#1062238618yes—
604C22#1062239918yes—
605C22#1062257314yes—
606C22#1062276414yes—
607C22#1062278914yes—
608C22C2×#6693511yescharacteristic
609C22C2×#6693711yescharacteristic
610C22C2×D8×D1112yes—
611C22C2×#6696712yes—
612C22C2×#6699311yescharacteristic
613C4—82no—
614C4—228no—
615C4#1062257314yes—
616C4C2×#6693511yescharacteristic
617C4C2×#6693711yescharacteristic
618C4C2×#6698311yescharacteristic
619C4C2×#6699011yescharacteristic
620C2—84no—
621C2—884no—
622C2—884no—
623C2#1306968818yesdirect product factor
624C2C2×#1062257311yescharacteristic
625C2C2×#1062238612yes—
626C2C2×#1062239912yes—
627C2C2×#1062276411yescharacteristic
628C2C2×#1062278911yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
hypercenterC22×#102D11
hypocenterC11C2×#2011
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
1. C23×D88C2semidirect
2. C23×#4323C2semidirect
3. C22×#66993C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622601C2semidirect
6. #13069688C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#102C2semidirect
18. C2×#66993C22semidirect
22. C22×#4323C22semidirect
29. C22×D88C22semidirect
31. C2×C11×#102C22semidirect
33. #10622601C22semidirect
35. C2×#66873C22semidirect
36. #10622188C22semidirect
68. C22×D44D4semidirect
73. C22×C8×C11D4semidirect
94. C22×C11⋊C8D4semidirect
152. C22×Dic11D8semidirect
179. C2×D44C2×D4semidirect
183. C2×C8×C11C2×D4semidirect
195. C2×C11⋊C8C2×D4semidirect
201. C22×#102D11semidirect
266. C2×Dic11C2×D8semidirect
303. C2×#102C2×D11semidirect
390. C22×C8C22⋊D11semidirect
408. C2×C11#2011semidirect
502. C2×C8C2×C22⋊D11semidirect
510. C11C2×#2011semidirect
623. C2#13069688direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D882
C23×#43232
C22×#669932
C22×#668732
C2×#106226012
#130696882
C2×#106221882
C22×C11×#1022
C2×#201111