Finite Group Databasebeta

← C2×#13079325 #15623696

Subgroups — C2×#13079325 #15623696

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic
3#13079325C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622328C211yesmaximal, characteristic, complemented
6C2×#10622316C211yesmaximal, characteristic, complemented
7C2×#10622327C211yesmaximal, characteristic, complemented
8C2×#10622729C212yesmaximal, complemented
9C2×#10622727C212yesmaximal
10C2×#10622329C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C22×C11×#97C211yesmaximal, characteristic, complemented
13C23×C8×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66983C2211yescharacteristic
16C2×#66982—21no—
17C2×C4×C22⋊D11—21no—
18C2×#66979—21no—
19C2×#66977—21no—
20C2×#66977C2211yescharacteristic
21C2×#66977C2212yes—
22C22×Dic44C2212yes—
23C22×#4314C2212yes—
24#10623010—24no—
25#10623010C2218yes—
26C2×#66929—21no—
27C2×#66928C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C2×#66925—21no—
30#10623001—24no—
31#10623001C2218yescomplemented
32C2×#66923—21no—
33C2×#66923C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22—21no—
37C2×C4×Dic22C2211yescharacteristic
38C2×C4×Dic22C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2212yes—
41C2×C11×#97C2211yescharacteristic
42C2×C11×#97C2218yescomplemented
43#10622729C22116yescomplemented
44#10622727C22116yes—
45C2×#66885C2212yes—
46C2×#66882C2212yes—
47C2×#66881C2212yes—
48C2×#66880C2212yes—
49C2×#66880C2212yes—
50C2×#66880C2212yes—
51#10622329C22116yescomplemented
52#10622328C2218yescomplemented
53#10622327C2218yescomplemented
54#10622323C22116yescomplemented
55#10622316C2218yescomplemented
56#10622315C2218yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22C2312yes—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11—28no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2318yes—
69C22×C8×C11C2312yes—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11D414yes—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983C2314yes—
80#66982—28no—
81C4×C22⋊D11—28no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86#66979—28no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—24no—
94#66977—28no—
95#66977—22no—
96#66977C2318yes—
97#66977C2314yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—21no—
106C2×Dic44—28no—
107C2×Dic44C2318yes—
108C2×#4314—28no—
109C2×#4314C2318yes—
110#66929—28no—
111#66928—22no—
112#66928C2314yes—
113C4×D44—22no—
114C4×D44C2314yes—
115#66925—28no—
116#66923—28no—
117#66923—22no—
118#66923C2314yes—
119#66922—22no—
120#66922—22no—
121#66922C2314yes—
122#66922C2314yes—
123C4×Dic22—28no—
124C4×Dic22—24no—
125C4×Dic22—22no—
126C4×Dic22C2318yes—
127C4×Dic22C2314yes—
128C11×#97C2314yes—
129C11×#97C2314yes—
130C11×#97C2318yes—
131#66885C2318yes—
132#66882C2318yes—
133#66881C2318yes—
134#66880C2318yes—
135#66880C2318yes—
136#66880C2318yes—
137C2×#3181—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—44no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×D44—21no—
161C2×D44—24no—
162C2×D44C2412yes—
163C2×C4×D11—24no—
164C2×C4×D11—44no—
165C2×Dic22—22no—
166C2×Dic22—24no—
167C2×Dic22—21no—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—24no—
171C2×Dic22—44no—
172C2×Dic22C2414yes—
173C2×Dic22C2412yes—
174C2×C8×C11—216no—
175C2×C8×C11—24no—
176C2×C8×C11#4118yes—
177C2×C8×C11C2414yes—
178C2×C8×C11C2414yes—
179C42×C11C2×D412yes—
180C42×C11C2×D414yes—
181C42×C11C2×D412yes—
182C42×C11C2×D414yes—
183C42×C11C2412yes—
184C42×C11C2412yes—
185C22⋊Dic11—28no—
186C22⋊Dic11—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11—24no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2412yes—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206C4×Dic11—28no—
207C4×Dic11—24no—
208Dic44—216no—
209#4314—216no—
210C2×#533—111no—
211C2×#529—111no—
212#3181—1116no—
213C2×#501—111no—
214C2×#497—111no—
215C2×#491—111no—
216C2×#489—111no—
217C2×#467—112no—
218C2×#465—112no—
219C2×#441—112no—
220C2×#440—112no—
221C22×#97D1111yescharacteristic, complemented
222C23×C11—22no—
223C23×C11—22no—
224C23×C11#13714yes—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C2×C4×C11—22no—
232C2×C4×C11—28no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—44no—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4114yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—48no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—44no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259D44—24no—
260D44—42no—
261C4×D11—48no—
262Dic22—24no—
263Dic22—24no—
264Dic22—24no—
265Dic22—48no—
266Dic22—44no—
267Dic22—42no—
268C8×C11—24no—
269C8×C11C2×#4118yes—
270C22×Q16—112no—
271C22×SD16—112no—
272C23×C8C2×D1112yes—
273#533—118no—
274#533—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8—111no—
277#529—118no—
278#529—224no—
279C2×#126—221no—
280C2×#125—111no—
281C2×#125—221no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—111no—
285C2×C22⋊Q8—112no—
286C2×C22⋊Q8—221no—
287C2×#121—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8—112no—
290C2×C4×Q8—221no—
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C2×#117—221no—
294C2×#117—221no—
295C22×C42C2×D1111yescharacteristic
296#501—118no—
297#497—118no—
298#491—118no—
299#489—118no—
300#467—1116no—
301#465—1116no—
302#441—1116no—
303#440—1116no—
304C2×#107—112no—
305C2×#106—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#102—112no—
310C2×#97C2×D1111yescharacteristic
311C2×#97C2×D1111yescharacteristic
312C2×#97C2×D1112yes—
313C2×#97C2×D1118yescomplemented
314C22×C11—28no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11#53212yes—
318C22×C11C2×#13714yes—
319C22×C11C2×#13712yes—
320C22×C11#57512yes—
321C22×C11C23×D411yescharacteristic
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—84no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—22no—
331C4×C11#53212yes—
332C4×C11C22×#4112yes—
333Dic11—44no—
334Dic11—42no—
335Dic11—42no—
336Dic11—44no—
337Dic11—42no—
338C22×Q8—111no—
339C22×Q8—112no—
340C22×Q8—221no—
341C22×D4—111no—
342C22×D4—221no—
343C23×C4—221no—
344C23×C4D4411yescharacteristic
345C23×C4D4411yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C2×Q16—118no—
348C2×Q16—228no—
349C2×SD16—118no—
350C2×SD16—228no—
351C22×C8—28no—
352C22×C8C22×D1112yes—
353C22×C8C22×D1118yes—
354C22×C8C22×D1112yes—
355C4⋊Q8—114no—
356C4⋊Q8—114no—
357C4⋊Q8—222no—
358C4⋊Q8—222no—
359#126—228no—
360#125—114no—
361#125—222no—
362#125—228no—
363#124—114no—
364#124—222no—
365#123—228no—
366C22⋊Q8—114no—
367C22⋊Q8—118no—
368C22⋊Q8—222no—
369C22⋊Q8—224no—
370C22⋊Q8—228no—
371#121—114no—
372#121—222no—
373C4×Q8—114no—
374C4×Q8—118no—
375C4×Q8—222no—
376C4×Q8—224no—
377C4×Q8—228no—
378C4×D4—114no—
379C4×D4—228no—
380C4×D4—222no—
381#117—228no—
382#117—228no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—221no—
402C2×C42—222no—
403C2×C42D4411yescharacteristic
404C2×C42D4411yescharacteristic
405C2×C42D4414yes—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1114yes—
409#107—118no—
410#106—118no—
411#103—118no—
412#103—118no—
413#103—118no—
414#102—118no—
415#97C22×D1118yes—
416#97C22×D1114yes—
417#97C22×D1114yes—
418C2×C11—24no—
419C2×C11#318114yescomplemented
420C2×C11C2×#53211yescharacteristic
421C2×C11C22×#13711yescharacteristic
422C2×C11C2×#57511yescharacteristic
423D11—82no—
424C24—221no—
425C24C2×D4411yescharacteristic
426C2×Q8—112no—
427C2×Q8—114no—
428C2×Q8—221no—
429C2×Q8—224no—
430C2×Q8—222no—
431C2×Q8—224no—
432C2×Q8—224no—
433C2×Q8—224no—
434C2×Q8—444no—
435C2×D4—112no—
436C2×D4—224no—
437C2×D4—221no—
438C2×D4—224no—
439C2×D4—444no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—42no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—221no—
448C22×C4—224no—
449C22×C4—444no—
450C22×C4C2×D4414yes—
451C22×C4C2×D4412yes—
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4C2×D4411yescharacteristic
455C22×C4C2×D4411yescharacteristic
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4414yes—
458C22×C4C23×D1112yes—
459C22×C4C23×D1111yescharacteristic
460Q16—2216no—
461SD16—2216no—
462C2×C8—24no—
463C2×C8—216no—
464C2×C8#433918yes—
465C2×C8C23×D1114yes—
466C2×C8C23×D1114yes—
467C4⋊C4—114no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—222no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C4⋊C4—224no—
478C4⋊C4—228no—
479C4⋊C4—224no—
480C4⋊C4—228no—
481C4⋊C4—224no—
482C22⋊C4—228no—
483C22⋊C4—224no—
484C22⋊C4—224no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C42—224no—
489C42—228no—
490C42C2×D4414yes—
491C42C2×D4412yes—
492C42C2×D4414yes—
493C42C2×D4412yes—
494C42C23×D1112yes—
495C42C23×D1112yes—
496C11C2×#318111yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23—222no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23#6696214yes—
504C23C22×D4412yes—
505C23C22×D4411yescharacteristic
506Q8—224no—
507Q8—224no—
508Q8—224no—
509Q8—448no—
510Q8—442no—
511Q8—444no—
512D4—224no—
513D4—448no—
514D4—442no—
515C2×C4—22no—
516C2×C4—28no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—44no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—448no—
530C2×C4—442no—
531C2×C4—444no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—444no—
535C2×C4C22×D4412yes—
536C2×C4C22×D4412yes—
537C2×C4C22×D4412yes—
538C2×C4C22×D4412yes—
539C2×C4C22×D4412yes—
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433914yes—
542C2×C4C24×D1111yescharacteristic
543C8—24no—
544C8C2×#433918yes—
545C22—28no—
546C22—22no—
547C22—22no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—884no—
552C22#1062300812yes—
553C22C2×#6696214yes—
554C22C2×#6696212yes—
555C22#1062327912yes—
556C22C23×D4411yescharacteristic
557C4—22no—
558C4—22no—
559C4—22no—
560C4—22no—
561C4—22no—
562C4—442no—
563C4—444no—
564C4—442no—
565C4—442no—
566C4—444no—
567C4#1062300812yes—
568C4C22×#433912yes—
569C2—24no—
570C2—882no—
571C2#1307932514yesdirect product factor
572C2C2×#1062300811yescharacteristic
573C2C22×#6696211yescharacteristic
574C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#97C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×#97D11
hypocenterC11C2×#3181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
3. #13079325C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622328C2semidirect
6. C2×#10622316C2semidirect
7. C2×#10622327C2semidirect
8. C2×#10622729C2semidirect
10. C2×#10622329C2semidirect
11. C2×#10622323C2semidirect
12. C22×C11×#97C2semidirect
31. #10623001C22semidirect
42. C2×C11×#97C22semidirect
43. #10622729C22semidirect
51. #10622329C22semidirect
52. #10622328C22semidirect
53. #10622327C22semidirect
54. #10622323C22semidirect
55. #10622316C22semidirect
56. #10622315C22semidirect
221. C22×#97D11semidirect
313. C2×#97C2×D11semidirect
419. C2×C11#3181semidirect
496. C11C2×#3181semidirect
571. C2#13079325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106230102
#130793252
C2×#106223152
C2×#106223282
C2×#106223162
C2×#106223272
C2×#106227292
C2×#106227272
C2×#106223292
C2×#106223232
C22×C11×#972
C2×#318111