Finite Group Databasebeta

← C2×#13073971 #14924990

Subgroups — C2×#13073971 #14924990

Order 2816.

3222 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×#66940C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3#13073971C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622286C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic, complemented
7C2×#10622570C212yesmaximal
8C2×#10622585C212yesmaximal, complemented
9C2×#10622559C212yesmaximal, complemented
10C2×#10622602C212yesmaximal, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66940—28no—
32C2×#66940C2218yescomplemented
33C2×(C22⋊D11)⋊C4—28no—
34C2×(C22⋊D11)⋊C4C2218yes—
35C11×#399C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622602C22116yescomplemented
43#10622585C22116yescomplemented
44#10622570C22116yes—
45#10622560C2218yescomplemented
46#10622559C22116yescomplemented
47#10622286C2218yescomplemented
48#10622263C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—24no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11Q818yescomplemented
58C22×C22⋊D11C2314yes—
59C23×Dic11—24no—
60C23×Dic11—44no—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2314yes—
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—24no—
68C22×C4×D11—44no—
69C22×C4×D11C2314yes—
70C22×Dic22—24no—
71C22×Dic22—28no—
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—44no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11C2318yes—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—28no—
98C2×C4×Dic11D418yes—
99C2×C4×Dic11C2318yes—
100C2×C4×Dic11C2314yes—
101#66940—232no—
102(C22⋊D11)⋊C4—232no—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2580—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11C2×Q814yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—22no—
117C23×D11—24no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11C2×Q814yes—
121C23×D11C2412yes—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C2×C22⋊D11—232no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11C2×Q8116yescomplemented
140C22×Dic11—28no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—48no—
150C22×Dic11—416no—
151C22×Dic11C2×D414yes—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×Q814yes—
154C22×Dic11#4118yes—
155C22×Dic11#4114yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C2×C4×D11—28no—
162C2×C4×D11—48no—
163C2×C4×D11—416no—
164C2×Dic22—232no—
165C2×Dic22—216no—
166C2×Dic22—28no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—48no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—48no—
171C22⋊Dic11—216no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—48no—
175Dic11⋊C4—28no—
176Dic11⋊C4—216no—
177Dic11⋊C4—216no—
178Dic11⋊C4—48no—
179C4×Dic11—216no—
180C4×Dic11C2×D4116yes—
181C22×C4×Q8—111no—
182C22×C4×D4—111no—
183#2580—1116no—
184C2×#399—111no—
185C2×#399D1111yescharacteristic, complemented
186C2×#393—111no—
187C2×#393—111no—
188C2×#390—112no—
189C2×#389—112no—
190C2×#385—112no—
191C2×#385—112no—
192C2×#382—111no—
193C23×C11—28no—
194C23×C11—216no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—48no—
202C23×C11C22×D412yes—
203C23×C11C22×Q814yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4114yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11C2511yescharacteristic
209C22×D11—28no—
210C22×D11—216no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—48no—
218C22×D11C22×Q814yes—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11—48no—
232C2×C4×C11C22×D414yes—
233C22⋊D11—232no—
234C2×Dic11—216no—
235C2×Dic11—28no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—416no—
245C2×Dic11—44no—
246C2×Dic11—48no—
247C2×Dic11C22⋊Q8116yes—
248C2×Dic11C22×D414yes—
249C2×Dic11C22×D414yes—
250C2×Dic11C22×Q814yes—
251C2×Dic11C2×#4118yes—
252C2×Dic11C2×#4114yes—
253C4×D11—416no—
254Dic22—232no—
255C23×Q8—111no—
256C23×D4—111no—
257C24×C4—111no—
258C24×C4—111no—
259C2×C4×Q8—118no—
260C2×C4×Q8—228no—
261C2×C4×D4—118no—
262C2×C4×D4—228no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C4⋊C4C2×D1112yes—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—111no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4C2×D1112yes—
275C22×C42—111no—
276C22×C42—112no—
277#399—118no—
278#399C2×D1118yescomplemented
279#393—118no—
280#393—118no—
281#390—1116no—
282#389—1116no—
283#385—1116no—
284#385—1116no—
285#382—118no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95C2×D1111yescharacteristic
291C22×C11—24no—
292C22×C11—28no—
293C22×C11—416no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11C2×C22⋊Q814yes—
298C22×C11#52514yes—
299C22×C11#53514yes—
300C22×C11#55418yes—
301C22×C11#55918yes—
302C22×C11C23×D411yescharacteristic
303C22×C11C23×Q811yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4112yes—
306C22×C11C2×H(5,𝔽2)12yes—
307C2×D11—24no—
308C2×D11—28no—
309C2×D11—416no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—44no—
313C4×C11—24no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—44no—
317Dic11—28no—
318Dic11—24no—
319Dic11—42no—
320Dic11—44no—
321Dic11C2×C22⋊Q818yes—
322C25—111no—
323C25C22×D1111yescharacteristic
324C22×Q8—114no—
325C22×Q8—228no—
326C22×Q8—224no—
327C22×D4—118no—
328C22×D4—114no—
329C22×D4—224no—
330C22×D4—224no—
331C23×C4—111no—
332C23×C4—112no—
333C23×C4—111no—
334C23×C4—112no—
335C23×C4—111no—
336C23×C4—114no—
337C23×C4—114no—
338C23×C4—224no—
339C23×C4—224no—
340C23×C4—444no—
341C23×C4—444no—
342C23×C4C22×D1112yes—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C4×Q8—2232no—
347C4×D4—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—118no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—228no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—444no—
358C2×C4⋊C4C22×D1114yes—
359C2×C4⋊C4C22×D1118yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—118no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—228no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—444no—
370C2×C22⋊C4C22×D1114yes—
371C2×C22⋊C4C22×D1118yes—
372C2×C42—118no—
373C2×C42—114no—
374C2×C42—118no—
375C2×C42—228no—
376#95—118no—
377#95—114no—
378#95—118no—
379#95—118no—
380#95C22×D1114yes—
381C2×C11—44no—
382C2×C11#258018yescomplemented
383C2×C11C22×C22⋊Q811yescharacteristic
384C2×C11C2×#52511yescharacteristic
385C2×C11C2×#53511yescharacteristic
386C2×C11C2×#55412yes—
387C2×C11C2×#55912yes—
388D11—44no—
389C24—22no—
390C24—24no—
391C24—24no—
392C24—22no—
393C24—114no—
394C24—112no—
395C24—222no—
396C24—224no—
397C24—224no—
398C24—222no—
399C24Q8×D1114yes—
400C24C23×D1112yes—
401C24C23×D1111yescharacteristic
402C2×Q8—2216no—
403C2×Q8—2232no—
404C2×Q8—228no—
405C2×D4—1116no—
406C2×D4—228no—
407C2×D4—2232no—
408C2×D4—228no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—118no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—228no—
429C22×C4—228no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—448no—
439C22×C4—4416no—
440C22×C4—448no—
441C22×C4—4416no—
442C22×C4D4×D1114yes—
443C22×C4C23×D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—228no—
450C4⋊C4—2216no—
451C4⋊C4—2216no—
452C4⋊C4—448no—
453C22⋊C4—28no—
454C22⋊C4—48no—
455C22⋊C4—2216no—
456C22⋊C4—2216no—
457C22⋊C4—228no—
458C22⋊C4—448no—
459C42—1116no—
460C42—2216no—
461C11C2×#258011yescharacteristic, complemented, Sylow
462C23—28no—
463C23—216no—
464C23—22no—
465C23—24no—
466C23—24no—
467C23—22no—
468C23—44no—
469C23—44no—
470C23—48no—
471C23—114no—
472C23—228no—
473C23—2216no—
474C23—222no—
475C23—224no—
476C23—224no—
477C23—222no—
478C23—444no—
479C23—444no—
480C23—448no—
481C23C2×D4×D1112yes—
482C23#6703714yes—
483C23C2×Q8×D1114yes—
484C23C2×Q8×D1112yes—
485C23#41×D1112yes—
486C23#41×D1114yes—
487C23C24×D1111yescharacteristic
488Q8—2232no—
489D4—2232no—
490C2×C4—28no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—48no—
503C2×C4—1116no—
504C2×C4—114no—
505C2×C4—114no—
506C2×C4—114no—
507C2×C4—114no—
508C2×C4—118no—
509C2×C4—228no—
510C2×C4—2216no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—4416no—
520C2×C4—4416no—
521C2×C4—444no—
522C2×C4—448no—
523C2×C4C2×D4×D1114yes—
524C22—28no—
525C22—24no—
526C22—416no—
527C22—42no—
528C22—44no—
529C22—42no—
530C22—228no—
531C22—224no—
532C22—4416no—
533C22—442no—
534C22—444no—
535C22—442no—
536C22D11×C22⋊Q814yes—
537C22#1062316718yes—
538C22#1062318714yes—
539C22#1062319518yes—
540C22#1062324614yes—
541C22C22×D4×D1111yescharacteristic
542C22C2×#6703712yes—
543C22C22×Q8×D1111yescharacteristic
544C22C2×#41×D1112yes—
545C22C2×#41×D1111yescharacteristic
546C4—24no—
547C4—42no—
548C4—44no—
549C4—44no—
550C4—118no—
551C4—224no—
552C4—228no—
553C4—442no—
554C4—444no—
555C2—44no—
556C2—444no—
557C2#1307397118yesdirect product factor
558C2C2×D11×C22⋊Q811yescharacteristic
559C2C2×#1062318711yescharacteristic
560C2C2×#1062324611yescharacteristic
561C2C2×#1062316712yes—
562C2C2×#1062319512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66940C2semidirect
3. #13073971C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622286C2semidirect
6. C2×#10622560C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622559C2semidirect
10. C2×#10622602C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#399C2semidirect
32. C2×#66940C22semidirect
35. C11×#399C22semidirect
41. #10622605C22semidirect
42. #10622602C22semidirect
43. #10622585C22semidirect
45. #10622560C22semidirect
46. #10622559C22semidirect
47. #10622286C22semidirect
48. #10622263C22semidirect
57. C22×C22⋊D11Q8semidirect
139. C2×C22⋊D11C2×Q8semidirect
185. C2×#399D11semidirect
278. #399C2×D11semidirect
382. C2×C11#2580semidirect
461. C11C2×#2580semidirect
557. C2#13073971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669402
C22×(C22⋊D11)⋊C42
#130739712
C2×#106226052
C2×#106222862
C2×#106225602
C2×#106225702
C2×#106225852
C2×#106225592
C2×#106226022
C2×#106222632
C2×C11×#3992
C2×#258011