Finite Group Databasebeta

← C2×#13076645 #14959906

Subgroups — C2×#13076645 #14959906

Order 2816.

2998 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13076645C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622597C212yesmaximal, complemented
6C2×#10622604C212yesmaximal, complemented
7C2×#10622574C212yesmaximal, complemented
8C2×#10622572C212yesmaximal, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622560C211yesmaximal, characteristic, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C2×#66950—28no—
32C2×#66950C2218yescomplemented
33C2×#66937—28no—
34C2×#66937C2218yes—
35C11×#399C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622604C22116yescomplemented
43#10622597C22116yescomplemented
44#10622574C22116yescomplemented
45#10622572C22116yescomplemented
46#10622560C2218yescomplemented
47#10622286C2218yescomplemented
48#10622277C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C22×D44—24no—
67C22×D44—44no—
68C22×D44C2314yes—
69C22×C4×D11—44no—
70C22×C4×D11D418yes—
71C22×C4×D11C2314yes—
72C22×Dic22—24no—
73C22×Dic22—44no—
74C22×Dic22C2314yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2318yes—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×C4⋊Dic11—28no—
96C2×C4⋊Dic11C2318yes—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101#66950—232no—
102#66937—232no—
103C11×#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2816—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11C2×D414yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—416no—
147C2×C22⋊D11—416no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C2×D44—28no—
163C2×D44—48no—
164C2×D44—416no—
165C2×C4×D11—416no—
166C2×C4×D11—48no—
167C2×C4×D11C2×D4116yes—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—416no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—48no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—48no—
175C22⋊Dic11—48no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181C4⋊Dic11—216no—
182Dic11⋊C4—28no—
183Dic11⋊C4—48no—
184C22×C22⋊Q8—111no—
185C22×#121—111no—
186#2816—1116no—
187C2×#399—111no—
188C2×#399D1111yescharacteristic, complemented
189C2×#398—112no—
190C2×#394—112no—
191C2×#394—112no—
192C2×#394—112no—
193C2×#393—111no—
194C2×#393—111no—
195C2×#381—111no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11C22×D412yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11H(5,𝔽2)14yes—
209C23×C112−1+412yes—
210C23×C112−1+412yes—
211C23×C11C2511yescharacteristic
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—48no—
230C22×D11—48no—
231C22×D11C22×D414yes—
232C2×C4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—48no—
245C2×C4×C11C22×D414yes—
246C22⋊D11—416no—
247C22⋊D11—416no—
248C2×Dic11—28no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—48no—
259C2×Dic11—44no—
260C2×Dic11—48no—
261C2×Dic11C22×D414yes—
262D44—416no—
263C4×D11—416no—
264Dic22—416no—
265C23×Q8—111no—
266C23×D4—111no—
267C23×D4—111no—
268C23×D4—111no—
269C24×C4—111no—
270C2×C22⋊Q8—118no—
271C2×C22⋊Q8—228no—
272C2×#121—118no—
273C2×#121—228no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—112no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C4⋊C4C2×D1112yes—
279C22×C22⋊C4—111no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4C2×D1112yes—
287#399—118no—
288#399C2×D1118yescomplemented
289#398—1116no—
290#394—1116no—
291#394—1116no—
292#394—1116no—
293#393—118no—
294#393—118no—
295#381—118no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—111no—
299C2×#95—112no—
300C2×#95C2×D1111yescharacteristic
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—88no—
307C22×C11#53414yes—
308C22×C11#53514yes—
309C22×C11#53614yes—
310C22×C11#56218yes—
311C22×C11#56218yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C2×H(5,𝔽2)12yes—
314C22×C11C2×H(5,𝔽2)12yes—
315C22×C11C2×2−1+411yescharacteristic
316C22×C11C2×2−1+411yescharacteristic
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—416no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—88no—
329C4×C11—24no—
330C4×C11—44no—
331C4×C11—42no—
332C4×C11—44no—
333Dic11—24no—
334Dic11—44no—
335Dic11—42no—
336Dic11—44no—
337C25—111no—
338C25—111no—
339C25C22×D1111yescharacteristic
340C22×Q8—114no—
341C22×Q8—224no—
342C22×Q8—444no—
343C22×D4—114no—
344C22×D4—114no—
345C22×D4—114no—
346C22×D4—224no—
347C22×D4—224no—
348C22×D4—224no—
349C22×D4—444no—
350C22×D4—444no—
351C22×D4—444no—
352C23×C4—111no—
353C23×C4—118no—
354C23×C4—114no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—111no—
358C23×C4—444no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C22⋊Q8—2232no—
364#121—2232no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—228no—
372C2×C4⋊C4—444no—
373C2×C4⋊C4C22×D1114yes—
374C2×C4⋊C4C22×D1118yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—228no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4—444no—
387C2×C22⋊C4—444no—
388C2×C22⋊C4—444no—
389C2×C22⋊C4C22×D1114yes—
390C2×C22⋊C4C22×D1118yes—
391#95—114no—
392#95—118no—
393#95—118no—
394#95—118no—
395#95C22×D1114yes—
396C2×C11—82no—
397C2×C11#281618yescomplemented
398C2×C11C2×#53411yescharacteristic
399C2×C11C2×#53511yescharacteristic
400C2×C11C2×#53611yescharacteristic
401C2×C11C2×#56212yes—
402C2×C11C2×#56212yes—
403D11—44no—
404D11—82no—
405C24—22no—
406C24—24no—
407C24—22no—
408C24—24no—
409C24—22no—
410C24—114no—
411C24—112no—
412C24—112no—
413C24—224no—
414C24—222no—
415C24—224no—
416C24—222no—
417C24—222no—
418C24—224no—
419C24—222no—
420C24—224no—
421C24—222no—
422C24C23×D1112yes—
423C24C23×D1111yescharacteristic
424C2×Q8—228no—
425C2×Q8—448no—
426C2×Q8—4416no—
427C2×D4—228no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—448no—
431C2×D4—4416no—
432C2×D4—448no—
433C2×D4—448no—
434C2×D4—4416no—
435C2×D4—4416no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—1116no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—112no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—4416no—
461C22×C4—448no—
462C22×C4D4×D1114yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1112yes—
467C4⋊C4—28no—
468C4⋊C4—48no—
469C4⋊C4—228no—
470C4⋊C4—2216no—
471C4⋊C4—448no—
472C22⋊C4—28no—
473C22⋊C4—48no—
474C22⋊C4—2216no—
475C22⋊C4—228no—
476C22⋊C4—448no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C22⋊C4—448no—
480C11C2×#281611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—44no—
487C23—44no—
488C23—48no—
489C23—44no—
490C23—48no—
491C23—114no—
492C23—228no—
493C23—228no—
494C23—228no—
495C23—224no—
496C23—222no—
497C23—224no—
498C23—222no—
499C23—222no—
500C23—224no—
501C23—222no—
502C23—224no—
503C23—222no—
504C23—448no—
505C23—448no—
506C23—444no—
507C23—444no—
508C23—448no—
509C23—444no—
510C23—448no—
511C23C2×D4×D1112yes—
512C23#6703714yes—
513C23#6704012yes—
514C23#6704214yes—
515C23#6704312yes—
516C23C24×D1111yescharacteristic
517Q8—4416no—
518D4—4416no—
519D4—4416no—
520D4—4416no—
521C2×C4—28no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—48no—
532C2×C4—44no—
533C2×C4—48no—
534C2×C4—114no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—4416no—
546C2×C4—444no—
547C2×C4—448no—
548C2×C4—448no—
549C2×C4C2×D4×D1114yes—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—44no—
554C22—44no—
555C22—88no—
556C22—224no—
557C22—224no—
558C22—224no—
559C22—444no—
560C22—444no—
561C22—4416no—
562C22—442no—
563C22—442no—
564C22—442no—
565C22—444no—
566C22—444no—
567C22—888no—
568C22#1062315914yes—
569C22#1062317818yes—
570C22#1062318414yes—
571C22#1062319818yes—
572C22#1062324614yes—
573C22C22×D4×D1111yescharacteristic
574C22C2×#6703712yes—
575C22C2×#6704011yescharacteristic
576C22C2×#6704212yes—
577C22C2×#6704311yescharacteristic
578C4—24no—
579C4—42no—
580C4—44no—
581C4—44no—
582C4—224no—
583C4—444no—
584C4—442no—
585C4—444no—
586C2—82no—
587C2—444no—
588C2—882no—
589C2#1307664518yesdirect product factor
590C2C2×#1062318411yescharacteristic
591C2C2×#1062324611yescharacteristic
592C2C2×#1062315911yescharacteristic
593C2C2×#1062317812yes—
594C2C2×#1062319812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#399D11
hypocenterC11C2×#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
3. #13076645C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622597C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622560C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#399C2semidirect
32. C2×#66950C22semidirect
35. C11×#399C22semidirect
41. #10622605C22semidirect
42. #10622604C22semidirect
43. #10622597C22semidirect
44. #10622574C22semidirect
45. #10622572C22semidirect
46. #10622560C22semidirect
47. #10622286C22semidirect
48. #10622277C22semidirect
188. C2×#399D11semidirect
288. #399C2×D11semidirect
397. C2×C11#2816semidirect
480. C11C2×#2816semidirect
589. C2#13076645direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669372
#130766452
C2×#106226052
C2×#106225972
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222862
C2×#106225602
C2×#106222772
C2×C11×#3992
C2×#281611