Finite Group Databasebeta

← C2×#13069685 #14780800

Subgroups — C2×#13069685 #14780800

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×#4323C211yesmaximal, characteristic, complemented
2C22×#66993C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic, complemented
6#13069685C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C23×C11×D8C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×C22⋊D11—22no—
12C23×D44C2211yescharacteristic
13C22×C11×D8—24no—
14C22×C11×D8—24no—
15C22×C11×D8—24no—
16C22×C11×D8C2214yescomplemented
17C23×C8×C11C2211yescharacteristic
18C22×C22⋊Dic11—22no—
19C2×#66993—24no—
20C2×#66993—24no—
21C2×#66993—22no—
22C2×#66993C2214yescomplemented
23C22×#4323—24no—
24C22×#4323—24no—
25C22×#4323—24no—
26C22×#4323C2214yescomplemented
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10622834—22no—
31#10622834C2214yescomplemented
32C2×#66896—24no—
33C2×#66896C2214yescomplemented
34C2×#66885—24no—
35C2×#66885C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C25×C11—21no—
39C24×D11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11D414yes—
53C22×D4×C11D414yescomplemented
54C22×D4×C11C2312yes—
55C22×D4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—216no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—48no—
60C22×C22⋊D11—48no—
61C23×Dic11—21no—
62C23×Dic11D412yes—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44D414yes—
70C22×D44C2312yes—
71C2×C11×D8—232no—
72C2×C11×D8—28no—
73C2×C11×D8—28no—
74C2×C11×D8—28no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11D414yescomplemented
78C22×C8×C11C2312yes—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—48no—
81#66993—216no—
82#66993—28no—
83#66993—28no—
84C2×#4323—232no—
85C2×#4323—28no—
86C2×#4323—28no—
87C2×#4323—28no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11D412yes—
95C2×C4×Dic11C2312yes—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8D414yescomplemented
99C22×C11⋊C8C2312yes—
100#66896—28no—
101#66885—28no—
102C2×#2011—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11—42no—
111C24×C11—44no—
112C24×C11—44no—
113C24×C11—44no—
114C24×C11—44no—
115C24×C11C2×D411yescharacteristic
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—42no—
119C23×D11—42no—
120C23×D11—44no—
121C23×D11—44no—
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11—28no—
125C2×D4×C11—24no—
126C2×D4×C11—28no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—44no—
139C2×D4×C11—42no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11C2×D414yes—
147C2×D4×C11C2×D414yescomplemented
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—232no—
157C2×C22⋊D11—416no—
158C2×C22⋊D11—464no—
159C2×C22⋊D11—416no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—42no—
164C22×Dic11—44no—
165C22×Dic11D818yescomplemented
166C22×Dic11C2×D414yes—
167C2×D44—24no—
168C2×D44—28no—
169C2×D44—28no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—44no—
176C2×D44—44no—
177C2×D44—42no—
178C2×D44—42no—
179C2×D44C2×D414yes—
180C11×D8—232no—
181C2×C8×C11—28no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11C2×D414yescomplemented
185C22⋊Dic11—416no—
186#4323—232no—
187C4⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11—42no—
190C4×Dic11—24no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C2×C11⋊C8—28no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yescomplemented
197C23×D8—111no—
198C23×D8D1111yescharacteristic, complemented
199C22×#127—111no—
200C22×#102—111no—
201C22×#102—111no—
202C2×#390—111no—
203#2011—118no—
204C2×#336—111no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—416no—
218C23×C11—416no—
219C23×C11—88no—
220C23×C11—88no—
221C23×C11—84no—
222C23×C11—84no—
223C23×C11—84no—
224C23×C11—84no—
225C23×C11#12012yes—
226C23×C11#12112yes—
227C23×C11#12712yes—
228C23×C11C2×D814yes—
229C23×C11AGL(1,ℤ/8)14yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—24no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—416no—
238C22×D11—88no—
239C22×D11—84no—
240C22×D11—84no—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—24no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—48no—
250D4×C11—48no—
251C2×C4×C11#12014yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12014yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12114yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12712yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C22⋊D11—464no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—216no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270C2×Dic11—84no—
271C2×Dic11C2×D818yescomplemented
272D44—24no—
273D44—24no—
274D44—42no—
275D44—42no—
276D44—48no—
277C8×C11—24no—
278C11⋊C8—24no—
279C23×D4—111no—
280C23×D4—222no—
281C23×D4C2×D1111yescharacteristic
282C23×D4C2×D1111yescharacteristic
283C22×D8—24no—
284C22×D8—24no—
285C22×D8—24no—
286C22×D8—114no—
287C22×D8—224no—
288C22×D8—224no—
289C22×D8—224no—
290C22×D8C2×D1114yescomplemented
291C23×C8—111no—
292C23×C8C2×D1111yescharacteristic
293C2×#127—114no—
294C2×#127—222no—
295C2×#127—224no—
296C2×#127—224no—
297C22×C4⋊C4—111no—
298C22×C22⋊C4—222no—
299C22×C42—111no—
300C2×#102—114no—
301C2×#102—114no—
302C2×#102—224no—
303C2×#102—224no—
304#390—114no—
305#390—222no—
306#336—114no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—48no—
310C22×C11—48no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—84no—
316C22×C11—84no—
317C22×C11—816no—
318C22×C11—816no—
319C22×C11#39214yes—
320C22×C11#44718yes—
321C22×C11#45918yes—
322C22×C11#49314yes—
323C22×C11#49614yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C22×C11C2×#12711yescharacteristic
327C22×C11C22×D812yes—
328C22×C11C2×AGL(1,ℤ/8)12yes—
329C2×D11—44no—
330C2×D11—48no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—84no—
334C2×D11—816no—
335C4×C11#39214yes—
336C4×C11C2×#12011yescharacteristic
337C4×C11C2×#12011yescharacteristic
338C4×C11C2×#12111yescharacteristic
339C4×C11C2×#12111yescharacteristic
340Dic11—28no—
341Dic11—82no—
342C25—21no—
343C25—21no—
344C25—221no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—114no—
358C22×D4—112no—
359C22×D4—228no—
360C22×D4—2216no—
361C22×D4—222no—
362C22×D4—221no—
363C22×D4—222no—
364C22×D4—222no—
365C22×D4—222no—
366C22×D4—222no—
367C22×D4—448no—
368C22×D4—448no—
369C22×D4C22⋊D1114yes—
370C22×D4C22⋊D1114yescomplemented
371C22×D4C22×D1112yes—
372C22×D4C22×D1112yes—
373C23×C4—112no—
374C23×C4—221no—
375C23×C4C22×D1111yescharacteristic
376C2×D8—232no—
377C2×D8—28no—
378C2×D8—28no—
379C2×D8—28no—
380C2×D8—228no—
381C2×D8—228no—
382C2×D8—2232no—
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—112no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—448no—
401C2×C42—112no—
402C2×C42—112no—
403C2×C42—222no—
404C2×C42—222no—
405#102—228no—
406#102—228no—
407C2×C11—84no—
408C2×C11—84no—
409C2×C11#201118yescomplemented
410C2×C11C2×#39211yescharacteristic
411C2×C11C2×#44712yes—
412C2×C11C2×#45912yes—
413C2×C11C2×#49311yescharacteristic
414C2×C11C2×#49611yescharacteristic
415D11—84no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—44no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—224no—
429C24—222no—
430C24—444no—
431C24—444no—
432C24—442no—
433C24—442no—
434C24D4×D1111yescharacteristic
435C2×D4—28no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—24no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—114no—
460C2×D4—2232no—
461C2×D4—228no—
462C2×D4—224no—
463C2×D4—228no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—4416no—
470C2×D4—4464no—
471C2×D4—4416no—
472C2×D4—444no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4—444no—
476C2×D4C2×C22⋊D1114yes—
477C2×D4C2×C22⋊D1114yescomplemented
478C22×C4—118no—
479C22×C4—114no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—222no—
483C22×C4—444no—
484C22×C4—442no—
485C22×C4D4×D1112yes—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1112yes—
488C22×C4#434112yes—
489C22×C4C2×C22⋊D1112yes—
490C22×C4C2×C22⋊D1112yes—
491C22×C4C2×C22⋊D1112yes—
492C22×C4C23×D1111yescharacteristic
493D8—232no—
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—222no—
504C4⋊C4—222no—
505C4⋊C4—442no—
506C22⋊C4—4416no—
507C42—224no—
508C42—222no—
509C42—222no—
510C11C2×#201111yescharacteristic, complemented, Sylow
511C23—24no—
512C23—24no—
513C23—416no—
514C23—416no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—48no—
524C23—48no—
525C23—88no—
526C23—84no—
527C23—84no—
528C23—84no—
529C23—84no—
530C23—88no—
531C23—224no—
532C23—4416no—
533C23—444no—
534C23—444no—
535C23—442no—
536C23—442no—
537C23—448no—
538C23—888no—
539C23—884no—
540C23—884no—
541C23D8×D1114yes—
542C23#6696414yes—
543C23#6699012yes—
544C23#6699212yes—
545C23#6699312yes—
546C23C2×D4×D1111yescharacteristic
547D4—24no—
548D4—24no—
549D4—24no—
550D4—24no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—48no—
556D4—48no—
557D4—224no—
558D4—224no—
559D4—4464no—
560D4—442no—
561D4—448no—
562D4—442no—
563C2×C4—118no—
564C2×C4—2216no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—444no—
568C2×C4—442no—
569C2×C4—884no—
570C2×C4#6699014yes—
571C2×C4#6699012yes—
572C2×C4#6699114yes—
573C2×C4#6699214yes—
574C2×C4#6699212yes—
575C2×C4#6699312yes—
576C2×C4#6700614yes—
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×#434111yescharacteristic
580C2×C4C22×C22⋊D1111yescharacteristic
581C2×C4C22×C22⋊D1111yescharacteristic
582C2×C4C22×C22⋊D1111yescharacteristic
583C8—24no—
584C8—224no—
585C22—48no—
586C22—48no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—82no—
591C22—84no—
592C22—84no—
593C22—816no—
594C22—816no—
595C22—82no—
596C22—82no—
597C22—448no—
598C22—444no—
599C22—882no—
600C22—884no—
601C22—8816no—
602C22—882no—
603C22#1062276318yes—
604C22#1062276414yes—
605C22#1062276714yes—
606C22#1062276918yes—
607C22#1062283614yes—
608C22C2×D8×D1112yes—
609C22C2×#6696412yes—
610C22C2×#6699011yescharacteristic
611C22C2×#6699211yescharacteristic
612C22C2×#6699311yescharacteristic
613C4—228no—
614C4—882no—
615C4#1062283614yes—
616C4C2×#6699011yescharacteristic
617C4C2×#6699111yescharacteristic
618C4C2×#6699211yescharacteristic
619C4C2×#6700611yescharacteristic
620C2—84no—
621C2—84no—
622C2—884no—
623C2#1306968518yesdirect product factor
624C2C2×#1062283611yescharacteristic
625C2C2×#1062276912yes—
626C2C2×#1062276312yes—
627C2C2×#1062276411yescharacteristic
628C2C2×#1062276711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×D8C2
socleC24×C11C2×D4
hypercenterC23×D8D11
hypocenterC11C2×#2011
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C23×#4323C2semidirect
2. C22×#66993C2semidirect
3. C22×#66885C2semidirect
4. C22×#66896C2semidirect
5. C2×#10622834C2semidirect
6. #13069685C2direct (N × H)
7. C2×#10622188C2semidirect
8. C23×C11×D8C2semidirect
16. C22×C11×D8C22semidirect
22. C2×#66993C22semidirect
26. C22×#4323C22semidirect
31. #10622834C22semidirect
33. C2×#66896C22semidirect
35. C2×#66885C22semidirect
36. #10622188C22semidirect
53. C22×D4×C11D4semidirect
77. C22×C8×C11D4semidirect
98. C22×C11⋊C8D4semidirect
147. C2×D4×C11C2×D4semidirect
165. C22×Dic11D8semidirect
184. C2×C8×C11C2×D4semidirect
196. C2×C11⋊C8C2×D4semidirect
198. C23×D8D11semidirect
271. C2×Dic11C2×D8semidirect
290. C22×D8C2×D11semidirect
370. C22×D4C22⋊D11semidirect
390. C22×C8C22⋊D11semidirect
409. C2×C11#2011semidirect
477. C2×D4C2×C22⋊D11semidirect
502. C2×C8C2×C22⋊D11semidirect
510. C11C2×#2011semidirect
623. C2#13069685direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43232
C22×#669932
C22×#668852
C22×#668962
C2×#106228342
#130696852
C2×#106221882
C23×C11×D82
C2×#201111