Finite Group Databasebeta

← C2×#13073791 #14923986

Subgroups — C2×#13073791 #14923986

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3#13073791C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622269C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic, complemented
7C2×#10622594C212yesmaximal, complemented
8C2×#10622569C212yesmaximal
9C2×#10622563C212yesmaximal, complemented
10C2×#10622600C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×#66950—28no—
30C2×#66950C2218yescomplemented
31C2×(C22⋊D11)⋊C4—28no—
32C2×(C22⋊D11)⋊C4C2218yes—
33C11×#399C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622600C22116yescomplemented
42#10622595C2218yescomplemented
43#10622594C22116yescomplemented
44#10622569C22116yes—
45#10622563C22116yescomplemented
46#10622560C2218yescomplemented
47D11×#95C2218yescomplemented
48#10622269C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
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×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2314yes—
67C22×C4×D11—28no—
68C22×C4×D11—28no—
69C22×C4×D11—44no—
70C22×C4×D11—44no—
71C22×C4×D11D418yes—
72C22×C4×D11C2318yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—44no—
76C22×Dic22C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2318yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2318yes—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×C4⋊Dic11—28no—
92C2×C4⋊Dic11—44no—
93C2×C4⋊Dic11C2318yes—
94C2×C4⋊Dic11C2318yes—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4C2314yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11C2314yes—
99#66950—232no—
100(C22⋊D11)⋊C4—232no—
101C11×#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2564—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11C2×Q814yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—24no—
118C23×D11C2×D414yes—
119C23×D11C2×Q814yes—
120C23×D11#4114yes—
121C23×D11C2412yes—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11C2×D414yes—
131C22×C4×C11#4118yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C2×C22⋊D11—232no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11C2×Q8116yescomplemented
140C22×Dic11—28no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—48no—
153C22×Dic11—416no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×Q814yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2412yes—
161C2×C4×D11—216no—
162C2×C4×D11—216no—
163C2×C4×D11—416no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—432no—
167C2×C4×D11C2×D4116yes—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—416no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—216no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—216no—
175C22⋊Dic11—48no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—216no—
178C4⋊Dic11—216no—
179C4⋊Dic11—48no—
180Dic11⋊C4—28no—
181C4×Dic11—28no—
182C22×C22⋊Q8—111no—
183C22×C4×D4—111no—
184#2564—1116no—
185C2×#400—111no—
186C2×#399D1111yescharacteristic, complemented
187C2×#395—111no—
188C2×#393—111no—
189C2×#387—112no—
190C2×#386—112no—
191C2×#385—112no—
192C2×#380—112no—
193C22×#95—111no—
194C23×C11—28no—
195C23×C11—216no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—48no—
203C23×C11C22×D412yes—
204C23×C11C22×Q814yes—
205C23×C11C22×Q812yes—
206C23×C11C2×#4114yes—
207C23×C11C2×#4112yes—
208C23×C11H(5,𝔽2)14yes—
209C23×C11C2511yescharacteristic
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—216no—
213C22×D11—216no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11C22⋊Q8116yes—
217C22×D11C22×D414yes—
218C22×D11C22×Q814yes—
219C22×D11C2×#4114yes—
220C2×C4×C11—28no—
221C2×C4×C11—216no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
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—44no—
231C2×C4×C11—48no—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C2×#4118yes—
234C22⋊D11—232no—
235C2×Dic11—28no—
236C2×Dic11—28no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—416no—
249C2×Dic11—48no—
250C2×Dic11—44no—
251C2×Dic11—48no—
252C2×Dic11C22×D414yes—
253C2×Dic11C22×Q814yes—
254C4×D11—416no—
255C4×D11—432no—
256Dic22—416no—
257C23×Q8—111no—
258C23×D4—111no—
259C24×C4—111no—
260C24×C4—111no—
261C24×C4—112no—
262C2×C22⋊Q8—118no—
263C2×C22⋊Q8—228no—
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1112yes—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4C2×D1112yes—
276C22×C42—111no—
277#400—118no—
278#399C2×D1118yescomplemented
279#395—118no—
280#393—118no—
281#387—1116no—
282#386—1116no—
283#385—1116no—
284#380—1116no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—118no—
292C2×#95C2×D1111yescharacteristic
293C22×C11—24no—
294C22×C11—28no—
295C22×C11—416no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11C2×C22⋊Q814yes—
300C22×C11#53214yes—
301C22×C11#53414yes—
302C22×C11#55118yes—
303C22×C11#55418yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4112yes—
307C22×C11C22×#4111yescharacteristic
308C22×C11C2×H(5,𝔽2)12yes—
309C2×D11—232no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—28no—
313C2×D11—28no—
314C2×D11C2×C22⋊Q818yes—
315C4×C11—24no—
316C4×C11—28no—
317C4×C11—42no—
318C4×C11—44no—
319Dic11—24no—
320Dic11—24no—
321Dic11—44no—
322Dic11—42no—
323Dic11—44no—
324C25—111no—
325C25C22×D1111yescharacteristic
326C22×Q8—114no—
327C22×Q8—224no—
328C22×Q8—444no—
329C22×D4—118no—
330C22×D4—114no—
331C22×D4—224no—
332C22×D4—224no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—118no—
336C23×C4—114no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—114no—
341C23×C4—118no—
342C23×C4—228no—
343C23×C4—224no—
344C23×C4—228no—
345C23×C4—444no—
346C23×C4—444no—
347C23×C4—444no—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C22⋊Q8—2232no—
353C4×D4—2232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—444no—
362C2×C4⋊C4C22×D1114yes—
363C2×C4⋊C4C22×D1118yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—444no—
372C2×C22⋊C4C22×D1114yes—
373C2×C22⋊C4C22×D1118yes—
374C2×C42—114no—
375C2×C42—224no—
376#95—118no—
377#95—114no—
378#95—118no—
379#95—118no—
380#95—118no—
381#95—118no—
382#95C22×D1114yes—
383C2×C11—44no—
384C2×C11#256418yescomplemented
385C2×C11C22×C22⋊Q811yescharacteristic
386C2×C11C2×#53211yescharacteristic
387C2×C11C2×#53411yescharacteristic
388C2×C11C2×#55112yes—
389C2×C11C2×#55412yes—
390D11—28no—
391C24—22no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—114no—
396C24—114no—
397C24—114no—
398C24—112no—
399C24—224no—
400C24—224no—
401C24Q8×D1114yes—
402C24C23×D1112yes—
403C24C23×D1111yescharacteristic
404C2×Q8—228no—
405C2×Q8—448no—
406C2×Q8—4416no—
407C2×D4—1116no—
408C2×D4—228no—
409C2×D4—2232no—
410C2×D4—228no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—1116no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—112no—
427C22×C4—2216no—
428C22×C4—228no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—2216no—
441C22×C4—4416no—
442C22×C4—448no—
443C22×C4—448no—
444C22×C4—4432no—
445C22×C4—448no—
446C22×C4—4416no—
447C22×C4D4×D1114yes—
448C22×C4#434118yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1114yes—
453C4⋊C4—28no—
454C4⋊C4—216no—
455C4⋊C4—2216no—
456C4⋊C4—228no—
457C4⋊C4—448no—
458C22⋊C4—28no—
459C22⋊C4—216no—
460C22⋊C4—228no—
461C22⋊C4—2216no—
462C22⋊C4—448no—
463C42—228no—
464C11C2×#256411yescharacteristic, complemented, Sylow
465C23—28no—
466C23—216no—
467C23—22no—
468C23—24no—
469C23—22no—
470C23—24no—
471C23—44no—
472C23—44no—
473C23—48no—
474C23—1116no—
475C23—114no—
476C23—114no—
477C23—114no—
478C23—228no—
479C23—2216no—
480C23—228no—
481C23—2216no—
482C23—224no—
483C23—224no—
484C23C2×D4×D1112yes—
485C23C2×#434114yes—
486C23C2×Q8×D1114yes—
487C23C2×Q8×D1112yes—
488C23#41×D1112yes—
489C23#6704214yes—
490C23C24×D1111yescharacteristic
491Q8—4416no—
492D4—2232no—
493C2×C4—28no—
494C2×C4—216no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—44no—
504C2×C4—48no—
505C2×C4—114no—
506C2×C4—114no—
507C2×C4—228no—
508C2×C4—228no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—4416no—
521C2×C4—4432no—
522C2×C4—4416no—
523C2×C4—444no—
524C2×C4—448no—
525C2×C4—448no—
526C2×C4C2×D4×D1114yes—
527C2×C4C2×#434118yes—
528C22—28no—
529C22—24no—
530C22—42no—
531C22—42no—
532C22—416no—
533C22—44no—
534C22—118no—
535C22—228no—
536C22—224no—
537C22—224no—
538C22—2232no—
539C22—228no—
540C22D11×C22⋊Q814yes—
541C22#1062316618yes—
542C22#1062318414yes—
543C22#1062318918yes—
544C22#1062324714yes—
545C22C22×D4×D1111yescharacteristic
546C22C22×#434112yes—
547C22C22×Q8×D1111yescharacteristic
548C22C2×#41×D1111yescharacteristic
549C22C2×#6704212yes—
550C4—24no—
551C4—28no—
552C4—42no—
553C4—44no—
554C4—224no—
555C4—224no—
556C4—442no—
557C4—444no—
558C4—444no—
559C2—44no—
560C2—228no—
561C2#1307379118yesdirect product factor
562C2C2×D11×C22⋊Q811yescharacteristic
563C2C2×#1062324711yescharacteristic
564C2C2×#1062318411yescharacteristic
565C2C2×#1062318912yes—
566C2C2×#1062316612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2564
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. #13073791C2direct (N × H)
4. C2×#10622595C2semidirect
5. C2×#10622269C2semidirect
6. C2×#10622560C2semidirect
7. C2×#10622594C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622600C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#399C2semidirect
30. C2×#66950C22semidirect
33. C11×#399C22semidirect
41. #10622600C22semidirect
42. #10622595C22semidirect
43. #10622594C22semidirect
45. #10622563C22semidirect
46. #10622560C22semidirect
47. D11×#95C22semidirect
48. #10622269C22semidirect
57. C22×C22⋊D11Q8semidirect
139. C2×C22⋊D11C2×Q8semidirect
186. C2×#399D11semidirect
278. #399C2×D11semidirect
384. C2×C11#2564semidirect
464. C11C2×#2564semidirect
561. C2#13073791direct (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×(C22⋊D11)⋊C42
#130737912
C2×#106225952
C2×#106222692
C2×#106225602
C2×#106225942
C2×#106225692
C2×#106225632
C2×#106226002
C2×D11×#952
C2×C11×#3992
C2×#256411