Finite Group Databasebeta

← C2×#13076642 #14959900

Subgroups — C2×#13076642 #14959900

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×#66999C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13076642C2116yesmaximal, direct product factor
4C2×#10622290C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622270C212yesmaximal, complemented
7C2×#10622285C212yesmaximal, complemented
8C2×#10622574C212yesmaximal, complemented
9C2×#10622572C212yesmaximal, complemented
10C2×#10622844C211yesmaximal, characteristic, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C2×#66999—28no—
22C2×#66999C2218yescomplemented
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C2×#66937—28no—
34C2×#66937C2218yes—
35C11×#393C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38#10622844C2218yescomplemented
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622574C22116yescomplemented
43#10622572C22116yescomplemented
44#10622562C2218yescomplemented
45#10622290C2218yescomplemented
46#10622285C22116yescomplemented
47#10622277C2218yescomplemented
48#10622270C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—44no—
54C22×Q8×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11C2314yes—
64C22×C22⋊D11C2314yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C22×D44—24no—
70C22×D44—44no—
71C22×D44C2314yes—
72C22×C4×D11—44no—
73C22×C4×D11D418yes—
74C22×C4×D11C2314yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—44no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11C2318yes—
81#66999—232no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—44no—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2318yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102#66937—232no—
103C11×#95C2318yes—
104C11×#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
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—
128C2×Q8×C11—28no—
129C2×Q8×C11—48no—
130C2×Q8×C11—416no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—48no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—416no—
150C2×C22⋊D11—416no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11C2×D414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C2×D44—28no—
166C2×D44—48no—
167C2×D44—416no—
168C2×C4×D11—416no—
169C2×C4×D11—48no—
170C2×C4×D11C2×D4116yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—48no—
173C22⋊Dic11—48no—
174(C2×D11)⋊C4—216no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179C4⋊Dic11—28no—
180C4⋊Dic11—48no—
181Dic11⋊C4—28no—
182Dic11⋊C4—216no—
183Dic11⋊C4—48no—
184C22×C22⋊Q8—111no—
185C22×#121—111no—
186#2816—1116no—
187C2×#399—111no—
188C2×#399—111no—
189C2×#398—112no—
190C2×#394—112no—
191C2×#394—112no—
192C2×#394—112no—
193C2×#393—111no—
194C2×#393D1111yescharacteristic, complemented
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—
232Q8×C11—416no—
233C2×C4×C11—28no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—48no—
244C2×C4×C11—44no—
245C2×C4×C11—48no—
246C2×C4×C11C22×D414yes—
247C22⋊D11—416no—
248C22⋊D11—416no—
249C2×Dic11—28no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—48no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11C22×D414yes—
263D44—416no—
264C4×D11—416no—
265C23×Q8C2×D1111yescharacteristic
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—111no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—112no—
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#399—118no—
289#398—1116no—
290#394—1116no—
291#394—1116no—
292#394—1116no—
293#393—118no—
294#393C2×D1118yescomplemented
295#381—118no—
296C2×#95—112no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95C2×D1112yes—
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—24no—
341C22×Q8—44no—
342C22×Q8C22×D1114yes—
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—114no—
366C2×C4⋊C4—118no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—228no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—444no—
374C2×C4⋊C4—444no—
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#95C22×D1114yes—
395#95C22×D1118yes—
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—28no—
425C2×Q8—48no—
426C2×Q8—416no—
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—112no—
450C22×C4—114no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—222no—
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×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1112yes—
467C4⋊C4—228no—
468C4⋊C4—2216no—
469C4⋊C4—228no—
470C4⋊C4—448no—
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—224no—
495C23—222no—
496C23—224no—
497C23—222no—
498C23—228no—
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—416no—
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—224no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—4416no—
546C2×C4—448no—
547C2×C4—444no—
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#1062312014yes—
569C22#1062315914yes—
570C22#1062317818yes—
571C22#1062320514yes—
572C22#1062321518yes—
573C22C22×D4×D1111yescharacteristic
574C22C2×#6703712yes—
575C22C2×#6704011yescharacteristic
576C22C2×#6704212yes—
577C22C2×#6704311yescharacteristic
578C4—24no—
579C4—44no—
580C4—42no—
581C4—44no—
582C4—224no—
583C4—442no—
584C4—444no—
585C4—444no—
586C2—82no—
587C2—444no—
588C2—882no—
589C2#1307664218yesdirect product factor
590C2C2×#1062312011yescharacteristic
591C2C2×#1062320511yescharacteristic
592C2C2×#1062315911yescharacteristic
593C2C2×#1062321512yes—
594C2C2×#1062317812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#393D11
hypocenterC11C2×#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. #13076642C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622844C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#393C2semidirect
22. C2×#66999C22semidirect
35. C11×#393C22semidirect
38. #10622844C22semidirect
42. #10622574C22semidirect
43. #10622572C22semidirect
44. #10622562C22semidirect
45. #10622290C22semidirect
46. #10622285C22semidirect
47. #10622277C22semidirect
48. #10622270C22semidirect
194. C2×#393D11semidirect
294. #393C2×D11semidirect
397. C2×C11#2816semidirect
480. C11C2×#2816semidirect
589. C2#13076642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669372
#130766422
C2×#106222902
C2×#106225622
C2×#106222702
C2×#106222852
C2×#106225742
C2×#106225722
C2×#106228442
C2×#106222772
C2×C11×#3932
C2×#281611