Finite Group Databasebeta

← C2×#13076641 #14959896

Subgroups — C2×#13076641 #14959896

Order 2816.

3774 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C212yesmaximal, complemented
2#13076641C2116yesmaximal, direct product factor
3C2×#10622288C212yesmaximal, complemented
4C2×#10622565C212yesmaximal, complemented
5C2×#10622573C212yesmaximal, complemented
6C2×#10622573C211yesmaximal, characteristic, complemented
7C2×#10622836C212yesmaximal, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622556C211yesmaximal, characteristic, complemented
10C2×C11×#392C211yesmaximal, characteristic, complemented
11C23×D4×C11C2212yes—
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C24×Dic11C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C2×#66992—216no—
24C2×#66992C22116yescomplemented
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C11×#392C2218yescomplemented
30C2×C11×#95C2211yescharacteristic
31#10622836C22116yescomplemented
32#10622836C22116yescomplemented
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622573C22116yescomplemented
38#10622573C2218yescomplemented
39#10622565C22116yescomplemented
40#10622556C2218yescomplemented
41#10622288C22116yescomplemented
42C25×C11C2312yes—
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C22×D4×C11—28no—
46C22×D4×C11—44no—
47C22×D4×C11—44no—
48C22×D4×C11—44no—
49C22×D4×C11—42no—
50C22×D4×C11C2318yes—
51C22×D4×C11C2314yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—28no—
56C22×C22⋊D11—28no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11C2318yes—
65C22×C22⋊D11C2318yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11—42no—
68C23×Dic11—42no—
69C23×Dic11D418yescomplemented
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2314yes—
74C22×D44—42no—
75C22×D44—44no—
76C22×D44C2314yes—
77C2×C11×C22⋊C4—42no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2318yes—
87#66992—264no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4C2318yes—
96C11×#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2314yes—
101C2×#2815—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—24no—
105C24×C11—24no—
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11C2×D414yes—
114C24×C11C2414yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11C2414yes—
125C2×D4×C11—216no—
126C2×D4×C11—48no—
127C2×D4×C11—48no—
128C2×D4×C11—48no—
129C2×D4×C11—44no—
130C2×D4×C11—432no—
131C2×D4×C11—416no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—48no—
147C2×C22⋊D11—48no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—432no—
152C2×C22⋊D11—432no—
153C2×C22⋊D11—432no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—416no—
163C22×Dic11—44no—
164C22×Dic11—44no—
165C22×Dic11C2×D418yes—
166C22×Dic11C2×D4116yescomplemented
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C2×D44—44no—
171C2×D44—48no—
172C2×D44—416no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—48no—
175C22⋊Dic11—216no—
176C22⋊Dic11—44no—
177C22⋊Dic11—48no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181Dic11⋊C4—216no—
182C22×#121—112no—
183#2815—1116no—
184C2×#397—112no—
185C2×#397—112no—
186C2×#392—112no—
187C2×#392—112no—
188C2×#392—112no—
189C2×#392—111no—
190C2×#392D1111yescharacteristic, complemented
191C2×#381—111no—
192C23×C11—28no—
193C23×C11—216no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11C22×D414yes—
216C23×C11C22×D412yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11H(5,𝔽2)14yes—
220C23×C11H(5,𝔽2)12yes—
221C23×C11C2511yescharacteristic
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—48no—
230C22×D11—48no—
231C22×D11—48no—
232C22×D11—48no—
233C22×D11—48no—
234C22×D11—48no—
235C22×D11—48no—
236D4×C11—432no—
237D4×C11—416no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—48no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C22⋊D11—432no—
249C22⋊D11—432no—
250C22⋊D11—432no—
251C2×Dic11—216no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—416no—
261C2×Dic11—48no—
262C2×Dic11—48no—
263C2×Dic11C22×D418yes—
264D44—416no—
265C23×D4—112no—
266C23×D4—112no—
267C23×D4—112no—
268C23×D4—111no—
269C23×D4C2×D1112yes—
270C23×D4C2×D1111yescharacteristic
271C24×C4—111no—
272C2×#121—1116no—
273C2×#121—2216no—
274C22×C4⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C22⋊C4C2×D1111yescharacteristic
283#397—1116no—
284#397—1116no—
285#392—1116no—
286#392—1116no—
287#392—1116no—
288#392—118no—
289#392C2×D1118yescomplemented
290#381—118no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95C2×D1111yescharacteristic
296C22×C11—24no—
297C22×C11—28no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—416no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—816no—
310C22×C11#53414yes—
311C22×C11#53518yes—
312C22×C11#56014yes—
313C22×C11#56014yes—
314C22×C11#56018yes—
315C22×C11C23×D411yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C22×C11C2×H(5,𝔽2)12yes—
318C22×C11C2×H(5,𝔽2)12yes—
319C22×C11C2×H(5,𝔽2)11yescharacteristic
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—816no—
328C4×C11—44no—
329C4×C11—42no—
330C4×C11—42no—
331Dic11—28no—
332Dic11—44no—
333Dic11—44no—
334C25—112no—
335C25C22×D1112yes—
336C25C22×D1111yescharacteristic
337C22×D4—28no—
338C22×D4—44no—
339C22×D4—42no—
340C22×D4—44no—
341C22×D4—44no—
342C22×D4—118no—
343C22×D4—118no—
344C22×D4—118no—
345C22×D4—114no—
346C22×D4—228no—
347C22×D4—228no—
348C22×D4—444no—
349C22×D4—442no—
350C22×D4—444no—
351C22×D4—444no—
352C22×D4—444no—
353C22×D4—444no—
354C22×D4—444no—
355C22×D4—444no—
356C22×D4—444no—
357C22×D4C22×D1118yes—
358C22×D4C22×D1114yes—
359C23×C4—112no—
360C23×C4—118no—
361C23×C4—114no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—442no—
365C23×C4—442no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369#121—2264no—
370C2×C4⋊C4—118no—
371C2×C4⋊C4—228no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4—444no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1118yes—
388#95—118no—
389#95—118no—
390#95—118no—
391#95—114no—
392#95C22×D1114yes—
393C2×C11—44no—
394C2×C11—84no—
395C2×C11#281518yescomplemented
396C2×C11C2×#53411yescharacteristic
397C2×C11C2×#53512yes—
398C2×C11C2×#56011yescharacteristic
399C2×C11C2×#56012yes—
400C2×C11C2×#56011yescharacteristic
401D11—84no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—114no—
414C24—224no—
415C24—224no—
416C24—224no—
417C24—224no—
418C24—224no—
419C24—224no—
420C24—224no—
421C24D4×D1114yes—
422C24C23×D1114yes—
423C24C23×D1112yes—
424C24C23×D1111yescharacteristic
425C2×D4—216no—
426C2×D4—48no—
427C2×D4—44no—
428C2×D4—48no—
429C2×D4—48no—
430C2×D4—432no—
431C2×D4—416no—
432C2×D4—2216no—
433C2×D4—2216no—
434C2×D4—444no—
435C2×D4—448no—
436C2×D4—4416no—
437C2×D4—448no—
438C2×D4—448no—
439C2×D4—448no—
440C2×D4—448no—
441C2×D4—448no—
442C2×D4—448no—
443C2×D4—448no—
444C2×D4—4432no—
445C2×D4—4432no—
446C2×D4—4432no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—118no—
455C22×C4—114no—
456C22×C4—1116no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—4416no—
468C22×C4—444no—
469C22×C4—444no—
470C22×C4C23×D1112yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1114yes—
473C4⋊C4—2216no—
474C22⋊C4—44no—
475C22⋊C4—48no—
476C22⋊C4—2216no—
477C22⋊C4—2216no—
478C22⋊C4—448no—
479C22⋊C4—448no—
480C22⋊C4—448no—
481C22⋊C4—444no—
482C11C2×#281511yescharacteristic, complemented, Sylow
483C23—216no—
484C23—28no—
485C23—22no—
486C23—24no—
487C23—24no—
488C23—22no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—44no—
497C23—44no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—448no—
514C23—448no—
515C23—448no—
516C23—448no—
517C23—448no—
518C23—448no—
519C23—448no—
520C23C2×D4×D1114yes—
521C23C2×D4×D1112yes—
522C23#6703714yes—
523C23#6703712yes—
524C23#6703714yes—
525C23#6704212yes—
526C23C24×D1111yescharacteristic
527D4—432no—
528D4—416no—
529D4—4416no—
530D4—4432no—
531D4—4432no—
532D4—4432no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—44no—
541C2×C4—48no—
542C2×C4—44no—
543C2×C4—118no—
544C2×C4—2216no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—4416no—
554C2×C4—448no—
555C2×C4—448no—
556C22—24no—
557C22—28no—
558C22—42no—
559C22—44no—
560C22—42no—
561C22—416no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—816no—
570C22—444no—
571C22—444no—
572C22—444no—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—8816no—
578C22#1062312318yes—
579C22#1062312614yes—
580C22#1062313614yes—
581C22#1062315118yes—
582C22#1062325114yes—
583C22C22×D4×D1111yescharacteristic
584C22C2×#6703711yescharacteristic
585C22C2×#6703712yes—
586C22C2×#6703712yes—
587C22C2×#6704211yescharacteristic
588C4—44no—
589C4—42no—
590C4—42no—
591C4—228no—
592C4—444no—
593C4—444no—
594C2—44no—
595C2—84no—
596C2—884no—
597C2#1307664118yesdirect product factor
598C2C2×#1062313611yescharacteristic
599C2C2×#1062312312yes—
600C2C2×#1062325111yescharacteristic
601C2C2×#1062315112yes—
602C2C2×#1062312611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2815
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. #13076641C2direct (N × H)
3. C2×#10622288C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622573C2semidirect
6. C2×#10622573C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622556C2semidirect
10. C2×C11×#392C2semidirect
24. C2×#66992C22semidirect
29. C11×#392C22semidirect
31. #10622836C22semidirect
32. #10622836C22semidirect
37. #10622573C22semidirect
38. #10622573C22semidirect
39. #10622565C22semidirect
40. #10622556C22semidirect
41. #10622288C22semidirect
69. C23×Dic11D4semidirect
166. C22×Dic11C2×D4semidirect
190. C2×#392D11semidirect
289. #392C2×D11semidirect
395. C2×C11#2815semidirect
482. C11C2×#2815semidirect
597. C2#13076641direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
#130766412
C2×#106222882
C2×#106225652
C2×#106225732
C2×#106228362
C2×#106225562
C2×C11×#3922
C2×#281511