Finite Group Databasebeta

← C2×#13072928 #14922944

Subgroups — C2×#13072928 #14922944

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13072928C2116yesmaximal, direct product factor
4C2×#10622599C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622605C211yesmaximal, characteristic, complemented
7C2×#10622260C212yesmaximal, complemented
8C2×#10622278C212yesmaximal
9C2×#10622281C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622280C212yesmaximal, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66946—28no—
31C2×#66946C2218yes—
32C2×C4⋊C4×D11—28no—
33C2×C4⋊C4×D11C2218yescomplemented
34C11×#400C2218yescomplemented
35C2×C11×#95C2212yes—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622599C2218yescomplemented
43#10622290C2218yescomplemented
44#10622281C22116yescomplemented
45#10622280C22116yescomplemented
46#10622280C2218yescomplemented
47#10622278C22116yes—
48#10622260C22116yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44Q818yes—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—24no—
67C22×C4×D11—28no—
68C22×C4×D11—44no—
69C22×C4×D11—44no—
70C22×C4×D11D418yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2318yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2314yes—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—44no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—44no—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2318yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11C2314yes—
100#66946—232no—
101C4⋊C4×D11—232no—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2314yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2487—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—22no—
113C23×D11—24no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11C2×D414yes—
117C23×D11C2×Q814yes—
118C23×D11C2×Q814yes—
119C23×D11#4114yes—
120C23×D11C2412yes—
121C23×D11C2412yes—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11C2×D414yes—
149C22×Dic11#4118yes—
150C22×Dic11C2414yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×D44—232no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44C2×Q8116yes—
158C2×C4×D11—232no—
159C2×C4×D11—216no—
160C2×C4×D11—28no—
161C2×C4×D11—216no—
162C2×C4×D11—216no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—432no—
166C2×C4×D11—416no—
167C2×C4×D11C2×D4116yes—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—28no—
176C4⋊Dic11—48no—
177Dic11⋊C4—216no—
178Dic11⋊C4—216no—
179Dic11⋊C4—48no—
180C4×Dic11—28no—
181C22×C4×D4—111no—
182C23×C4⋊C4—111no—
183#2487—1116no—
184C2×#400—111no—
185C2×#400D1111yescharacteristic, complemented
186C2×#399—111no—
187C2×#399—111no—
188C2×#389—112no—
189C2×#386—112no—
190C2×#385—112no—
191C2×#380—111no—
192C2×#380—112no—
193C23×C11C22×D412yes—
194C23×C11C22×Q812yes—
195C23×C11C2×#4112yes—
196C23×C11C2×#4114yes—
197C23×C11H(5,𝔽2)14yes—
198C23×C11C2511yescharacteristic
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—216no—
202C22×D11—216no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—28no—
206C22×D11—216no—
207C22×D11—22no—
208C22×D11—24no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—48no—
214C22×D11C22⋊Q8116yes—
215C22×D11C22×D414yes—
216C22×D11C22×Q814yes—
217C22×D11C22×Q814yes—
218C22×D11C2×#4114yes—
219C2×C4×C11—28no—
220C2×C4×C11—28no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—48no—
234C2×C4×C11—48no—
235C2×C4×C11C22×D414yes—
236C2×C4×C11C22×Q814yes—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—48no—
246C2×Dic11—44no—
247C2×Dic11—48no—
248C2×Dic11#123116yes—
249C2×Dic11C22×D414yes—
250C2×Dic11C2×#4118yes—
251D44—232no—
252C4×D11—232no—
253C4×D11—432no—
254C4×D11—416no—
255C23×D4—111no—
256C24×C4—111no—
257C24×C4—111no—
258C24×C4—112no—
259C2×C4×D4—118no—
260C2×C4×D4—228no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4—112no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—118no—
267C22×C4⋊C4—228no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C22⋊C4—111no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C42—111no—
276#400—118no—
277#400C2×D1118yescomplemented
278#399—118no—
279#399—118no—
280#389—1116no—
281#386—1116no—
282#385—1116no—
283#380—1116no—
284#380—118no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1112yes—
290C2×#95C2×D1112yes—
291C22×C11C2×C22⋊Q814yes—
292C22×C11C2×#12314yes—
293C22×C11#53514yes—
294C22×C11#55318yes—
295C22×C11#55418yes—
296C22×C11C23×D411yescharacteristic
297C22×C11C23×Q811yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C22×#4112yes—
300C22×C11C2×H(5,𝔽2)12yes—
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—28no—
304C2×D11—28no—
305C2×D11—232no—
306C2×D11—24no—
307C2×D11—28no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—44no—
311C2×D11—416no—
312C2×D11C2×C22⋊Q818yes—
313C4×C11—24no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11—44no—
318Dic11—44no—
319Dic11—42no—
320Dic11—44no—
321Dic11C2×#12318yes—
322C25—111no—
323C25—111no—
324C22×D4—118no—
325C22×D4—114no—
326C22×D4—224no—
327C22×D4—224no—
328C23×C4—111no—
329C23×C4—118no—
330C23×C4—114no—
331C23×C4—111no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4—114no—
335C23×C4—118no—
336C23×C4—228no—
337C23×C4—224no—
338C23×C4—228no—
339C23×C4—228no—
340C23×C4—444no—
341C23×C4—444no—
342C23×C4C22×D1112yes—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C4×D4—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—118no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—2232no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—228no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—444no—
360C2×C4⋊C4—444no—
361C2×C4⋊C4C22×D1114yes—
362C2×C4⋊C4C22×D1114yes—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—444no—
372C2×C22⋊C4—444no—
373C2×C42—114no—
374C2×C42—224no—
375#95—118no—
376#95—114no—
377#95—118no—
378#95C22×D1118yes—
379#95C22×D1114yes—
380#95C22×D1118yes—
381C2×C11#248718yescomplemented
382C2×C11C22×C22⋊Q811yescharacteristic
383C2×C11C22×#12311yescharacteristic
384C2×C11C2×#53511yescharacteristic
385C2×C11C2×#55312yes—
386C2×C11C2×#55412yes—
387D11—28no—
388D11—44no—
389C24—114no—
390C24—114no—
391C24—114no—
392C24—112no—
393C24—114no—
394C24—112no—
395C24—224no—
396C24—224no—
397C24—222no—
398C24—224no—
399C24—222no—
400C24—224no—
401C24C23×D1111yescharacteristic
402C2×D4—1116no—
403C2×D4—228no—
404C2×D4—2232no—
405C2×D4—228no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—114no—
418C22×C4—118no—
419C22×C4—112no—
420C22×C4—1116no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—2232no—
425C22×C4—2216no—
426C22×C4—228no—
427C22×C4—2216no—
428C22×C4—2216no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—448no—
438C22×C4—448no—
439C22×C4—4416no—
440C22×C4—4432no—
441C22×C4D4×D1114yes—
442C22×C4Q8×D1114yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1114yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1112yes—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—2216no—
451C4⋊C4—2216no—
452C4⋊C4—228no—
453C4⋊C4—448no—
454C4⋊C4—448no—
455C22⋊C4—228no—
456C22⋊C4—2216no—
457C22⋊C4—228no—
458C22⋊C4—448no—
459C22⋊C4—448no—
460C42—228no—
461C11C2×#248711yescharacteristic, complemented, Sylow
462C23—1116no—
463C23—114no—
464C23—114no—
465C23—114no—
466C23—114no—
467C23—2216no—
468C23—228no—
469C23—224no—
470C23—224no—
471C23—228no—
472C23—2216no—
473C23—228no—
474C23—222no—
475C23—224no—
476C23—222no—
477C23—224no—
478C23—2216no—
479C23—448no—
480C23—444no—
481C23—444no—
482C23C2×D4×D1112yes—
483C23C2×Q8×D1112yes—
484C23#41×D1112yes—
485C23#41×D1114yes—
486C23#6704214yes—
487C23C24×D1111yescharacteristic
488D4—2232no—
489C2×C4—28no—
490C2×C4—28no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—48no—
505C2×C4—1116no—
506C2×C4—114no—
507C2×C4—118no—
508C2×C4—2232no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—4416no—
518C2×C4—4432no—
519C2×C4—448no—
520C2×C4—448no—
521C2×C4—444no—
522C2×C4C2×D4×D1114yes—
523C2×C4C2×Q8×D1114yes—
524C22—118no—
525C22—228no—
526C22—2232no—
527C22—228no—
528C22—224no—
529C22—224no—
530C22—228no—
531C22—224no—
532C22—444no—
533C22—4416no—
534C22—442no—
535C22—442no—
536C22D11×C22⋊Q814yes—
537C22D11×#12314yes—
538C22#1062320514yes—
539C22#1062322118yes—
540C22#1062324018yes—
541C22C22×D4×D1111yescharacteristic
542C22C22×Q8×D1111yescharacteristic
543C22C2×#41×D1111yescharacteristic
544C22C2×#41×D1112yes—
545C22C2×#6704212yes—
546C4—24no—
547C4—24no—
548C4—44no—
549C4—44no—
550C4—42no—
551C4—118no—
552C4—444no—
553C4—444no—
554C4—442no—
555C2—228no—
556C2—444no—
557C2#1307292818yesdirect product factor
558C2C2×D11×C22⋊Q811yescharacteristic
559C2C2×D11×#12311yescharacteristic
560C2C2×#1062320511yescharacteristic
561C2C2×#1062324012yes—
562C2C2×#1062322112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#400D11
hypocenterC11C2×#2487
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13072928C2direct (N × H)
4. C2×#10622599C2semidirect
5. C2×#10622290C2semidirect
6. C2×#10622605C2semidirect
7. C2×#10622260C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#400C2semidirect
33. C2×C4⋊C4×D11C22semidirect
34. C11×#400C22semidirect
41. #10622605C22semidirect
42. #10622599C22semidirect
43. #10622290C22semidirect
44. #10622281C22semidirect
45. #10622280C22semidirect
46. #10622280C22semidirect
48. #10622260C22semidirect
185. C2×#400D11semidirect
277. #400C2×D11semidirect
381. C2×C11#2487semidirect
461. C11C2×#2487semidirect
557. C2#13072928direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
C22×C4⋊C4×D112
#130729282
C2×#106225992
C2×#106222902
C2×#106226052
C2×#106222602
C2×#106222782
C2×#106222812
C2×#106222802
C2×C11×#4002
C2×#248711