Finite Group Databasebeta

← C2×#13069022 #14755384

Subgroups — C2×#13069022 #14755384

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
2C2×#10623329C211yesmaximal, characteristic, complemented
3C2×#10622568C212yesmaximal, complemented
4#13069022C218yesmaximal, direct product factor
5C2×#10622165C212yesmaximal, complemented
6C22×C11×#99C211yesmaximal, characteristic, complemented
7C25×D11C2211yescharacteristic
8C23×D4×C11C2211yescharacteristic
9C23×C22⋊D11—21no—
10C22×C11×C22⋊C4C2212yes—
11C22×C22⋊Dic11—21no—
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2211yescharacteristic
14C2×#66990—22no—
15C2×#66990—24no—
16C2×#66990C418yescomplemented
17C2×#66990C2214yes—
18#10623329—22no—
19#10623329—24no—
20#10623329C2214yescomplemented
21C2×D4×Dic11—24no—
22C22×(C2×D11)⋊C4—21no—
23C22×(C2×D11)⋊C4—24no—
24C2×#66979—21no—
25C2×C11×#99—24no—
26C2×C11×#99C2214yescomplemented
27#10622568—24no—
28#10622568C2218yescomplemented
29#10622165C2218yescomplemented
30C25×C11D411yescharacteristic
31C25×C11C2311yescharacteristic
32C24×D11—22no—
33C24×D11—21no—
34C24×D11—21no—
35C24×D11—22no—
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×C11D412yes—
46C22×D4×C11D414yes—
47C22×D4×C11C2312yes—
48C23×C4×C11—22no—
49C23×C4×C11D411yescharacteristic
50C22×C22⋊D11—28no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—48no—
53C23×Dic11—21no—
54C23×Dic11—22no—
55C23×Dic11D414yescomplemented
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4C2314yes—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11C2×C414yescomplemented
70C2×C22⋊Dic11D414yescomplemented
71C2×C22⋊Dic11C2314yes—
72C2×C22⋊Dic11C2312yes—
73#66990—216no—
74#66990—28no—
75#66990C2×C4116yescomplemented
76D4×Dic11—216no—
77D4×Dic11—216no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—216no—
81C2×(C2×D11)⋊C4—416no—
82#66979—24no—
83#66979—24no—
84C2×C4⋊Dic11—22no—
85C2×C4×Dic11—22no—
86C11×#99—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—48no—
145C22×C4×C11—44no—
146C22×C4×C11C22⋊C414yescomplemented
147C22×C4×C11C2×D412yes—
148C2×C22⋊D11—216no—
149C2×C22⋊D11—432no—
150C2×C22⋊D11—416no—
151C22×Dic11—28no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—44no—
157C22×Dic11—48no—
158C22×Dic11—84no—
159C22×Dic11C2×D418yescomplemented
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—44no—
163C22⋊Dic11—28no—
164C22⋊Dic11—24no—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—22no—
170C22⋊Dic11C22×C414yescomplemented
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—432no—
173C4⋊Dic11—28no—
174C4×Dic11—28no—
175C22×#120—111no—
176C2×#518—111no—
177C22×#99D1111yescharacteristic, complemented
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—42no—
189C23×C11—44no—
190C23×C11—44no—
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×D412yes—
213C23×C11C22×D411yescharacteristic
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—432no—
227C22×D11—48no—
228C22×D11—416no—
229C22×D11—416no—
230C22×D11—48no—
231C22×D11—44no—
232C22×D11—48no—
233C22×D11—416no—
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—48no—
251C2×C4×C11—44no—
252C2×C4×C11—88no—
253C2×C4×C11C2×C22⋊C414yescomplemented
254C22⋊D11—432no—
255C2×Dic11—24no—
256C2×Dic11—28no—
257C2×Dic11—48no—
258C2×Dic11—44no—
259C2×Dic11—48no—
260C2×Dic11—48no—
261C2×Dic11—84no—
262C2×Dic11—88no—
263C26—111no—
264C23×D4—221no—
265C23×D4C2×D1111yescharacteristic
266C2×#120—114no—
267C2×#120—118no—
268C2×#120—222no—
269C2×#120—224no—
270#518—114no—
271#518—224no—
272#518—222no—
273C2×C4×D4—224no—
274C2×#117—221no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—221no—
278C22×C22⋊C4—221no—
279C22×C22⋊C4—224no—
280C22×C22⋊C4C2×D1112yes—
281C2×#99—24no—
282C2×#99C2×D1114yescomplemented
283#379—118no—
284#379—224no—
285#342—118no—
286C22×C11—28no—
287C22×C11—24no—
288C22×C11—28no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—24no—
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—84no—
329Dic11—44no—
330Dic11—48no—
331C25—114no—
332C25—112no—
333C25—221no—
334C25—222no—
335C25—221no—
336C25—222no—
337C25—224no—
338C25—222no—
339C25—448no—
340C25D4411yescharacteristic
341C25C22×D1111yescharacteristic
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—228no—
346C22×D4—224no—
347C22×D4—448no—
348C22×D4C4×D1114yes—
349C22×D4D4412yes—
350C22×D4C22⋊D1114yes—
351C22×D4C22×D1112yes—
352C23×C4—22no—
353C23×C4—114no—
354C23×C4—221no—
355C23×C4—222no—
356C23×C4D4411yescharacteristic
357#120—1116no—
358#120—2216no—
359#120—228no—
360C4×D4—2216no—
361C4×D4—2216no—
362#117—224no—
363#117—224no—
364C2×C4⋊C4—222no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—2216no—
384C2×C22⋊C4—4416no—
385C2×C22⋊C4C22×D1114yes—
386C2×C42—222no—
387#99—28no—
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—21no—
401C24—22no—
402C24—44no—
403C24—44no—
404C24—114no—
405C24—2216no—
406C24—228no—
407C24—228no—
408C24—224no—
409C24—222no—
410C24—224no—
411C24—228no—
412C24—224no—
413C24—224no—
414C24—222no—
415C24—448no—
416C24—444no—
417C24—4416no—
418C24—448no—
419C24—448no—
420C24—4416no—
421C24—4432no—
422C24—4416no—
423C24—441no—
424C24—442no—
425C24—441no—
426C24—442no—
427C24—442no—
428C24—444no—
429C24—444no—
430C24(C2×D11)⋊C414yescomplemented
431C24C2×C4×D1112yes—
432C24C2×D4411yescharacteristic
433C24C2×D4412yes—
434C24C2×D4411yescharacteristic
435C24D4×D1112yes—
436C24D4×D1112yes—
437C24#434114yes—
438C24C2×C22⋊D1112yes—
439C24C23×D1111yescharacteristic
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—28no—
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×C22⋊D1114yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—48no—
459C22×C4—44no—
460C22×C4—118no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—228no—
465C22×C4—224no—
466C22×C4—444no—
467C22×C4—448no—
468C22×C4—884no—
469C22×C4(C2×D11)⋊C414yescomplemented
470C22×C4C2×D4412yes—
471C4⋊C4—228no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—44no—
475C22⋊C4—114no—
476C22⋊C4—228no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—222no—
483C22⋊C4—2216no—
484C22⋊C4—4432no—
485C42—228no—
486C11C2×#188911yescharacteristic, complemented, Sylow
487C23—28no—
488C23—24no—
489C23—22no—
490C23—24no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—48no—
497C23—44no—
498C23—42no—
499C23—48no—
500C23—44no—
501C23—44no—
502C23—84no—
503C23—82no—
504C23—2216no—
505C23—2216no—
506C23—228no—
507C23—2232no—
508C23—228no—
509C23—224no—
510C23—4432no—
511C23—448no—
512C23—4416no—
513C23—4416no—
514C23—448no—
515C23—444no—
516C23—4416no—
517C23—448no—
518C23—448no—
519C23—4432no—
520C23—4416no—
521C23—4416no—
522C23—448no—
523C23—4416no—
524C23—4432no—
525C23—442no—
526C23—442no—
527C23—444no—
528C23—444no—
529C23—448no—
530C23—444no—
531C23—448no—
532C23(C22⋊D11)⋊C414yes—
533C23(C22⋊D11)⋊C414yes—
534C23#6693511yescharacteristic
535C23#6693512yes—
536C23#6693511yescharacteristic
537C23#6693912yes—
538C23#6693912yes—
539C23C2×(C2×D11)⋊C412yes—
540C23C2×(C2×D11)⋊C412yes—
541C23C2×(C2×D11)⋊C414yescomplemented
542C23#6699214yes—
543C23#6699214yes—
544C23C22×C4×D1111yescharacteristic
545C23C22×D4411yescharacteristic
546C23C2×D4×D1112yes—
547C23C2×#434112yes—
548C23C22×C22⋊D1111yescharacteristic
549D4—28no—
550D4—28no—
551D4—216no—
552D4—4432no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—48no—
558C2×C4—44no—
559C2×C4—88no—
560C2×C4—228no—
561C2×C4—224no—
562C2×C4—448no—
563C2×C4—444no—
564C2×C4—448no—
565C2×C4—448no—
566C2×C4—884no—
567C2×C4—888no—
568C2×C4C2×(C2×D11)⋊C414yescomplemented
569C22—28no—
570C22—24no—
571C22—24no—
572C22—28no—
573C22—24no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—24no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—44no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22—44no—
586C22—48no—
587C22—44no—
588C22—82no—
589C22—84no—
590C22—228no—
591C22—2216no—
592C22—4416no—
593C22—444no—
594C22—448no—
595C22—4416no—
596C22—448no—
597C22—4432no—
598C22—444no—
599C22—4416no—
600C22—448no—
601C22#1062235414yes—
602C22#1062257112yes—
603C22#1062257114yes—
604C22#1062257112yes—
605C22C2×(C22⋊D11)⋊C412yes—
606C22C2×#6693511yescharacteristic
607C22C2×#6693911yescharacteristic
608C22C22×(C2×D11)⋊C411yescharacteristic
609C22C2×#6699212yes—
610C4—24no—
611C4—84no—
612C4—444no—
613C4—448no—
614C2—22no—
615C2—21no—
616C2—21no—
617C2—22no—
618C2—22no—
619C2—24no—
620C2—44no—
621C2—448no—
622C2#1306902214yesdirect product factor
623C2C2×#1062257111yescharacteristic
624C2C2×#1062235412yes—
subgroupG/H
centerC23#66935
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C11×#99C2
socleC23×C11#120
prime radicalC22×#66990C2
cosocleC24×C11C24
hypercenterC22×#99D11
hypocenterC11C2×#1889
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10623329C2semidirect
3. C2×#10622568C2semidirect
4. #13069022C2direct (N × H)
5. C2×#10622165C2semidirect
6. C22×C11×#99C2semidirect
16. C2×#66990C4semidirect
20. #10623329C22semidirect
26. C2×C11×#99C22semidirect
28. #10622568C22semidirect
29. #10622165C22semidirect
39. C24×D11C2×C4semidirect
55. C23×Dic11D4semidirect
69. C2×C22⋊Dic11C2×C4semidirect
70. C2×C22⋊Dic11D4semidirect
75. #66990C2×C4semidirect
93. C24×C11C22⋊C4semidirect
128. C23×D11C22×C4semidirect
137. C2×D4×C11C22⋊C4semidirect
146. C22×C4×C11C22⋊C4semidirect
159. C22×Dic11C2×D4semidirect
170. C22⋊Dic11C22×C4semidirect
177. C22×#99D11semidirect
200. C23×C11C2×C22⋊C4semidirect
253. C2×C4×C11C2×C22⋊C4semidirect
282. C2×#99C2×D11semidirect
395. C2×C11#1889semidirect
430. C24(C2×D11)⋊C4semidirect
451. C2×D4(C2×D11)⋊C4semidirect
469. C22×C4(C2×D11)⋊C4semidirect
486. C11C2×#1889semidirect
541. C23C2×(C2×D11)⋊C4semidirect
568. C2×C4C2×(C2×D11)⋊C4semidirect
622. C2#13069022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
C2×#106233292
C2×#106225682
#130690222
C2×#106221652
C22×C11×#992
C2×#188911