Finite Group Databasebeta

← C2×#13069024 #14755386

Subgroups — C2×#13069024 #14755386

Order 2816.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66990C211yesmaximal, characteristic
2C22×#66898C211yesmaximal, characteristic, complemented
3C2×#10622568C212yesmaximal, complemented
4#13069024C218yesmaximal, direct product factor
5C2×#10622164C212yesmaximal, complemented
6C2×C11×#518C211yesmaximal, characteristic, complemented
7C25×D11C2211yescharacteristic
8C23×D4×C11C2211yescharacteristic
9C23×C22⋊D11—21no—
10C11×#518—22no—
11C11×#518—24no—
12C11×#518C2214yescomplemented
13C2×C4×D4×C11—24no—
14C2×C11×#117—21no—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C2×#66990—24no—
20C2×#66990—22no—
21C2×#66990C418yescomplemented
22C2×#66990C2214yes—
23C22×(C2×D11)⋊C4—21no—
24C22×(C2×D11)⋊C4—24no—
25C2×#66898—24no—
26C2×#66898C2214yescomplemented
27#10622568—24no—
28#10622568C2218yescomplemented
29#10622164C2218yescomplemented
30C25×C11D411yescharacteristic
31C25×C11C2311yescharacteristic
32C24×D11—22no—
33C24×D11—21no—
34C24×D11—22no—
35C24×D11—21no—
36C24×D11—22no—
37C24×D11—24no—
38C24×D11—48no—
39C24×D11C2×C414yescomplemented
40C24×D11C2312yes—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11C2×C414yes—
45C22×D4×C11D414yes—
46C22×D4×C11D412yes—
47C22×D4×C11C2312yes—
48C23×C4×C11—22no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D414yescomplemented
51C22×C22⋊D11—28no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—48no—
54C23×Dic11—21no—
55C23×Dic11—22no—
56C4×D4×C11—216no—
57C4×D4×C11—216no—
58C11×#117—24no—
59C11×#117—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D414yescomplemented
69C2×C11×C22⋊C4C2314yes—
70C2×C42×C11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11C2×C414yescomplemented
77C2×C22⋊Dic11C2314yes—
78C2×C22⋊Dic11C2312yes—
79#66990—216no—
80#66990—28no—
81#66990C2×C4116yescomplemented
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—216no—
85C2×(C2×D11)⋊C4—416no—
86#66898—28no—
87C2×#1889—111nomaximal, Sylow
88C24×C11—21no—
89C24×C11—21no—
90C24×C11—22no—
91C24×C11—44no—
92C24×C11—44no—
93C24×C11C22⋊C414yescomplemented
94C24×C11C22×C412yes—
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D412yes—
97C24×C11C2×D412yes—
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D412yes—
100C24×C11C2×D412yes—
101C24×C11#4114yes—
102C24×C11C2411yescharacteristic
103C23×D11—216no—
104C23×D11—28no—
105C23×D11—24no—
106C23×D11—28no—
107C23×D11—24no—
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—28no—
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—416no—
114C23×D11—48no—
115C23×D11—416no—
116C23×D11—416no—
117C23×D11—48no—
118C23×D11—432no—
119C23×D11—48no—
120C23×D11—44no—
121C23×D11—41no—
122C23×D11—42no—
123C23×D11—41no—
124C23×D11—44no—
125C23×D11—44no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11C22×C414yescomplemented
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—28no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11C22⋊C418yescomplemented
138C2×D4×C11C22×C414yes—
139C2×D4×C11C2×D414yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—48no—
147C22×C4×C11—84no—
148C22×C4×C11C22⋊C414yescomplemented
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D418yescomplemented
151C2×C22⋊D11—216no—
152C2×C22⋊D11—432no—
153C2×C22⋊D11—416no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—44no—
158C22×Dic11—48no—
159C22×Dic11—44no—
160C11×C4⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C42×C11—28no—
167C22⋊Dic11—24no—
168C22⋊Dic11—22no—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—44no—
172C22⋊Dic11C22×C414yescomplemented
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—432no—
175C22×#120—111no—
176C2×#518D1111yescharacteristic, complemented
177C22×#99—111no—
178C2×#379—112no—
179#1889—118no—
180C2×#342—112no—
181C23×C11—28no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—42no—
191C23×C11—48no—
192C23×C11—42no—
193C23×C11—48no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—84no—
197C23×C11—82no—
198C23×C11C2×C22⋊C412yes—
199C23×C11C2×C22⋊C412yes—
200C23×C11C2×C22⋊C414yescomplemented
201C23×C11C4×D414yes—
202C23×C11C4×D414yes—
203C23×C11#12011yescharacteristic
204C23×C11#12012yes—
205C23×C11#12011yescharacteristic
206C23×C11#12114yes—
207C23×C11#12114yes—
208C23×C11#12312yes—
209C23×C11#12312yes—
210C23×C11C23×C411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D412yes—
214C23×C11C2×#4112yes—
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—28no—
218C22×D11—232no—
219C22×D11—24no—
220C22×D11—28no—
221C22×D11—48no—
222C22×D11—432no—
223C22×D11—416no—
224C22×D11—416no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—416no—
228C22×D11—416no—
229C22×D11—432no—
230C22×D11—48no—
231C22×D11—416no—
232C22×D11—44no—
233C22×D11—48no—
234C22×D11—432no—
235C22×D11—416no—
236C22×D11—42no—
237C22×D11—44no—
238C22×D11—42no—
239C22×D11—44no—
240C22×D11—48no—
241C22×D11—44no—
242C22×D11—48no—
243D4×C11—28no—
244D4×C11—28no—
245D4×C11—216no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—28no—
251C2×C4×C11—48no—
252C2×C4×C11—48no—
253C2×C4×C11—84no—
254C2×C4×C11—88no—
255C2×C4×C11C2×C22⋊C414yescomplemented
256C22⋊D11—432no—
257C2×Dic11—24no—
258C2×Dic11—48no—
259C2×Dic11—44no—
260C2×Dic11—48no—
261C2×Dic11—44no—
262C2×Dic11—88no—
263C26—111no—
264C23×D4—221no—
265C23×D4C2×D1111yescharacteristic
266C2×#120—114no—
267C2×#120—118no—
268C2×#120—224no—
269C2×#120—222no—
270#518—22no—
271#518—24no—
272#518C2×D1114yescomplemented
273C2×C4×D4—24no—
274C2×#117—21no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—221no—
279C22×C22⋊C4—224no—
280C22×C22⋊C4C2×D1112yes—
281C2×#99—114no—
282C2×#99—224no—
283#379—118no—
284#379—224no—
285#342—118no—
286C22×C11—24no—
287C22×C11—28no—
288C22×C11—24no—
289C22×C11—28no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—48no—
304C22×C11—44no—
305C22×C11—82no—
306C22×C11—84no—
307C22×C11#38612yes—
308C22×C11#38614yes—
309C22×C11#38612yes—
310C22×C11B(4,𝔽2)14yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C2×C4×D412yes—
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×#12112yes—
315C22×C11C2×#12311yescharacteristic
316C2×D11—216no—
317C2×D11—28no—
318C2×D11—44no—
319C2×D11—416no—
320C2×D11—48no—
321C2×D11—48no—
322C2×D11—416no—
323C2×D11—432no—
324C2×D11—416no—
325C2×D11—48no—
326C2×D11—44no—
327C4×C11—24no—
328C4×C11—48no—
329Dic11—44no—
330Dic11—84no—
331C25—114no—
332C25—112no—
333C25—222no—
334C25—221no—
335C25—222no—
336C25—224no—
337C25—221no—
338C25—222no—
339C25—448no—
340C25C22⋊D1111yescharacteristic
341C25C22×D1111yescharacteristic
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—228no—
346C22×D4—224no—
347C22×D4—448no—
348C22×D4C4×D1114yes—
349C22×D4D4414yes—
350C22×D4C22⋊D1112yes—
351C22×D4C22×D1112yes—
352C23×C4—22no—
353C23×C4—221no—
354C23×C4—222no—
355C23×C4C22⋊D1111yescharacteristic
356C23×C4C22⋊D1114yescomplemented
357#120—1116no—
358#120—2216no—
359#120—228no—
360C4×D4—216no—
361C4×D4—216no—
362#117—24no—
363#117—24no—
364C2×C4⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—2216no—
383C2×C22⋊C4—4416no—
384C2×C22⋊C4C22⋊D1114yescomplemented
385C2×C22⋊C4C22×D1114yes—
386C2×C42—22no—
387#99—228no—
388C2×C11—21no—
389C2×C11—22no—
390C2×C11—22no—
391C2×C11—21no—
392C2×C11—22no—
393C2×C11—24no—
394C2×C11—44no—
395C2×C11#188914yescomplemented
396C2×C11C2×#38611yescharacteristic
397C2×C11C2×B(4,𝔽2)12yes—
398D11—48no—
399C24—21no—
400C24—22no—
401C24—21no—
402C24—44no—
403C24—44no—
404C24—114no—
405C24—2216no—
406C24—228no—
407C24—224no—
408C24—228no—
409C24—224no—
410C24—222no—
411C24—224no—
412C24—228no—
413C24—222no—
414C24—224no—
415C24—448no—
416C24—444no—
417C24—4416no—
418C24—448no—
419C24—4416no—
420C24—4432no—
421C24—4416no—
422C24—448no—
423C24—442no—
424C24—442no—
425C24—444no—
426C24—444no—
427C24—441no—
428C24—442no—
429C24—441no—
430C24(C2×D11)⋊C414yescomplemented
431C24C2×C4×D1112yes—
432C24C2×D4412yes—
433C24#433914yes—
434C24C2×C22⋊D1111yescharacteristic
435C24C2×C22⋊D1112yes—
436C24C2×C22⋊D1112yes—
437C24C2×C22⋊D1111yescharacteristic
438C24C2×C22⋊D1112yes—
439C24C23×D1111yescharacteristic
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—2216no—
449C2×D4—4432no—
450C2×D4—4416no—
451C2×D4(C2×D11)⋊C418yescomplemented
452C2×D4C2×C4×D1114yes—
453C2×D4C2×D4414yes—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—28no—
459C22×C4—24no—
460C22×C4—48no—
461C22×C4—84no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—444no—
466C22×C4—448no—
467C22×C4—444no—
468C22×C4(C2×D11)⋊C414yescomplemented
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1118yescomplemented
471C4⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—114no—
478C22⋊C4—224no—
479C22⋊C4—222no—
480C22⋊C4—2216no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C22⋊C4—4432no—
484C22⋊C4—444no—
485C42—28no—
486C11C2×#188911yescharacteristic, complemented, Sylow
487C23—28no—
488C23—24no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—44no—
495C23—48no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—48no—
500C23—44no—
501C23—44no—
502C23—84no—
503C23—82no—
504C23—2216no—
505C23—2216no—
506C23—228no—
507C23—2232no—
508C23—224no—
509C23—228no—
510C23—448no—
511C23—4432no—
512C23—4416no—
513C23—4416no—
514C23—448no—
515C23—4416no—
516C23—444no—
517C23—448no—
518C23—448no—
519C23—4416no—
520C23—4432no—
521C23—448no—
522C23—4416no—
523C23—4416no—
524C23—4432no—
525C23—442no—
526C23—444no—
527C23—444no—
528C23—448no—
529C23—444no—
530C23—448no—
531C23—442no—
532C23C2×(C2×D11)⋊C412yes—
533C23C2×(C2×D11)⋊C412yes—
534C23C2×(C2×D11)⋊C414yescomplemented
535C23C4×C22⋊D1114yes—
536C23C4×C22⋊D1114yes—
537C23#6698212yes—
538C23#6698212yes—
539C23#6698314yes—
540C23#6698314yes—
541C23#6700611yescharacteristic
542C23#6700612yes—
543C23#6700611yescharacteristic
544C23C22×C4×D1111yescharacteristic
545C23C22×D4411yescharacteristic
546C23C2×#433912yes—
547C23C22×C22⋊D1111yescharacteristic
548C23C22×C22⋊D1112yes—
549D4—28no—
550D4—28no—
551D4—216no—
552D4—4432no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—28no—
558C2×C4—48no—
559C2×C4—48no—
560C2×C4—84no—
561C2×C4—88no—
562C2×C4—224no—
563C2×C4—448no—
564C2×C4—444no—
565C2×C4—448no—
566C2×C4—444no—
567C2×C4—888no—
568C2×C4C2×(C2×D11)⋊C414yescomplemented
569C22—24no—
570C22—28no—
571C22—24no—
572C22—28no—
573C22—24no—
574C22—24no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—42no—
579C22—44no—
580C22—42no—
581C22—44no—
582C22—41no—
583C22—41no—
584C22—42no—
585C22—44no—
586C22—48no—
587C22—44no—
588C22—82no—
589C22—84no—
590C22—228no—
591C22—2216no—
592C22—444no—
593C22—4416no—
594C22—448no—
595C22—4416no—
596C22—448no—
597C22—4432no—
598C22—444no—
599C22—4416no—
600C22—448no—
601C22#1062282612yes—
602C22#1062282614yes—
603C22#1062282612yes—
604C22#1062285714yes—
605C22C22×(C2×D11)⋊C411yescharacteristic
606C22C2×C4×C22⋊D1112yes—
607C22C2×#6698211yescharacteristic
608C22C2×#6698312yes—
609C22C2×#6700611yescharacteristic
610C4—24no—
611C4—48no—
612C4—444no—
613C4—884no—
614C2—21no—
615C2—22no—
616C2—21no—
617C2—22no—
618C2—22no—
619C2—24no—
620C2—44no—
621C2—448no—
622C2#1306902414yesdirect product factor
623C2C2×#1062282611yescharacteristic
624C2C2×#1062285712yes—
subgroupG/H
centerC23#67006
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#518C2
socleC23×C11#120
prime radicalC22×#66990C2
cosocleC24×C11C24
hypercenterC2×#518D11
hypocenterC11C2×#1889
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C22×#66898C2semidirect
3. C2×#10622568C2semidirect
4. #13069024C2direct (N × H)
5. C2×#10622164C2semidirect
6. C2×C11×#518C2semidirect
12. C11×#518C22semidirect
21. C2×#66990C4semidirect
26. C2×#66898C22semidirect
28. #10622568C22semidirect
29. #10622164C22semidirect
39. C24×D11C2×C4semidirect
50. C23×C4×C11D4semidirect
68. C2×C11×C22⋊C4D4semidirect
76. C2×C22⋊Dic11C2×C4semidirect
81. #66990C2×C4semidirect
93. C24×C11C22⋊C4semidirect
128. C23×D11C22×C4semidirect
137. C2×D4×C11C22⋊C4semidirect
148. C22×C4×C11C22⋊C4semidirect
150. C22×C4×C11C2×D4semidirect
172. C22⋊Dic11C22×C4semidirect
176. C2×#518D11semidirect
200. C23×C11C2×C22⋊C4semidirect
255. C2×C4×C11C2×C22⋊C4semidirect
272. #518C2×D11semidirect
356. C23×C4C22⋊D11semidirect
384. C2×C22⋊C4C22⋊D11semidirect
395. C2×C11#1889semidirect
430. C24(C2×D11)⋊C4semidirect
451. C2×D4(C2×D11)⋊C4semidirect
468. C22×C4(C2×D11)⋊C4semidirect
470. C22×C4C2×C22⋊D11semidirect
486. C11C2×#1889semidirect
534. C23C2×(C2×D11)⋊C4semidirect
568. C2×C4C2×(C2×D11)⋊C4semidirect
622. C2#13069024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
C22×#668982
C2×#106225682
#130690242
C2×#106221642
C2×C11×#5182
C2×#188911