Finite Group Databasebeta

← C2×#13078789 #15621923

Subgroups — C2×#13078789 #15621923

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13078789C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic
6C2×#10622442C212yesmaximal, complemented
7C2×#10622458C212yesmaximal, complemented
8C2×#10622352C211yesmaximal, characteristic, complemented
9C2×#10622351C211yesmaximal, characteristic
10C2×#10622329C212yesmaximal, complemented
11C2×#10622323C212yesmaximal, complemented
12C2×C11×#432C211yesmaximal, characteristic, complemented
13C23×Dic22C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#66983C2211yescharacteristic
16C2×#66982—21no—
17C2×C4×C22⋊D11—21no—
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11—21no—
22C22×Dic44C2212yes—
23C22×#4314C2212yes—
24#10623010—24no—
25#10623010C2218yes—
26C2×#66929—21no—
27C2×#66928C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C2×#66925—21no—
30C2×#66923C2211yescharacteristic
31C2×C4×Dic22—24no—
32C2×C4×Dic22—21no—
33C2×C4×Dic22—21no—
34C2×C4×Dic22C2211yescharacteristic
35C2×C4×Dic22C2212yes—
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2218yescomplemented
38C11×#432C2218yescomplemented
39C2×C11×C4⋊C8C2212yes—
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×#97C2212yes—
43C2×#66885C2212yes—
44C2×#66882C2212yes—
45C2×#66881C2212yes—
46C2×#66880C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49#10622458C22116yescomplemented
50#10622442C22116yescomplemented
51#10622352C2218yescomplemented
52#10622351C2218yes—
53#10622348C2218yes—
54#10622335C2218yescomplemented
55#10622329C22116yescomplemented
56#10622323C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×Dic22—22no—
67C22×Dic22—28no—
68C22×Dic22C2311yescharacteristic
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C22×C8×C11C2312yes—
72C22×C8×C11C2312yes—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D414yes—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2314yes—
79C2×C22⋊Dic11—21no—
80#66983—22no—
81#66983C2314yes—
82#66982—28no—
83C4×C22⋊D11—28no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977C2314yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—28no—
106C2×C4×Dic11—21no—
107C2×Dic44—28no—
108C2×Dic44C2318yes—
109C2×#4314—28no—
110C2×#4314C2318yes—
111#66929—28no—
112#66928—22no—
113#66928C2314yes—
114C4×D44—22no—
115C4×D44C2314yes—
116#66925—28no—
117#66923—22no—
118#66923C2314yes—
119C4×Dic22—24no—
120C4×Dic22—24no—
121C4×Dic22—28no—
122C4×Dic22—28no—
123C4×Dic22—22no—
124C4×Dic22C2318yes—
125C4×Dic22C2318yes—
126C4×Dic22C2314yes—
127C11×C4⋊C8C2318yes—
128C11×C22⋊C8C2314yes—
129C11×C22⋊C8C2314yes—
130C11×#97C2318yes—
131#66885C2318yes—
132#66882C2318yes—
133#66881C2318yes—
134#66880C2318yes—
135#66880C2318yes—
136#66880C2318yes—
137C2×#3117—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×D414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—44no—
155C22×Dic11—28no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—44no—
164C2×D44—21no—
165C2×D44—24no—
166C2×D44C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×Dic22—28no—
170C2×Dic22—216no—
171C2×Dic22—216no—
172C2×Dic22—24no—
173C2×Dic22—22no—
174C2×Dic22—21no—
175C2×Dic22—24no—
176C2×Dic22—24no—
177C2×Dic22#4118yes—
178C2×Dic22C2412yes—
179C2×Dic22C2414yes—
180C2×C8×C11—24no—
181C2×C8×C11—24no—
182C2×C8×C11C2414yes—
183C2×C8×C11C2414yes—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186C42×C11C2×D414yes—
187C42×C11C2×D414yes—
188C42×C11C2412yes—
189C42×C11C2412yes—
190C22⋊Dic11—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—24no—
195C4⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C2412yes—
200C4⋊Dic11C2412yes—
201C4⋊Dic11C2414yes—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208C4×Dic11—28no—
209C4×Dic11—28no—
210C4×Dic11—24no—
211Dic44—216no—
212#4314—216no—
213C2×#529—111no—
214C22×C4×Q8—111no—
215#3117—1116no—
216C2×#484—111no—
217C2×#481—111no—
218C2×#479—112no—
219C2×#464—112no—
220C2×#451—111no—
221C2×#448—111no—
222C2×#441—112no—
223C2×#440—112no—
224C2×#432D1111yescharacteristic, complemented
225C23×C11—22no—
226C23×C11—22no—
227C23×C11#13714yes—
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C2×C4×C11—22no—
235C2×C4×C11—28no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4114yes—
250C2×C4×C11C2511yescharacteristic
251C22⋊D11—48no—
252C2×Dic11—216no—
253C2×Dic11—28no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—48no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—44no—
264D44—24no—
265D44—42no—
266C4×D11—48no—
267Dic22—216no—
268Dic22—28no—
269Dic22—24no—
270Dic22—24no—
271Dic22—42no—
272Dic22C2×#4118yes—
273C8×C11—24no—
274C8×C11—24no—
275C23×Q8—111no—
276C22×Q16—112no—
277C22×SD16—112no—
278#529—118no—
279#529—224no—
280C2×#126—221no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—111no—
285C2×#121—111no—
286C2×C4×Q8—112no—
287C2×C4×Q8—112no—
288C2×C4×Q8—111no—
289C2×C4×Q8—118no—
290C2×C4×Q8—221no—
291C2×C4×Q8—221no—
292C2×C4×Q8—224no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×#117—221no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—221no—
298C22×C42—221no—
299C22×C42C2×D1111yescharacteristic
300#484—118no—
301#481—118no—
302#479—1116no—
303#464—1116no—
304#451—118no—
305#448—118no—
306#441—1116no—
307#440—1116no—
308#432C2×D1118yescomplemented
309C2×#107—112no—
310C2×#106—112no—
311C2×C4⋊C8C2×D1112yes—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103—112no—
315C2×#102—112no—
316C2×C22⋊C8C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97C2×D1112yes—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11#52512yes—
323C22×C11C2×#13714yes—
324C22×C11C2×#13712yes—
325C22×C11#57512yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11#52512yes—
337C4×C11C22×#4112yes—
338Dic11—28no—
339Dic11—42no—
340Dic11—42no—
341Dic11—42no—
342Dic11—44no—
343C22×Q8—112no—
344C22×Q8—114no—
345C22×Q8—111no—
346C22×Q8—228no—
347C22×Q8—222no—
348C22×Q8—221no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4D4411yescharacteristic
355C23×C4D4411yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C2×Q16—118no—
358C2×Q16—228no—
359C2×SD16—118no—
360C2×SD16—228no—
361C22×C8C22×D1112yes—
362C22×C8C22×D1112yes—
363#126—228no—
364#125—114no—
365#125—222no—
366#124—114no—
367#124—222no—
368#123—228no—
369C22⋊Q8—114no—
370C22⋊Q8—222no—
371#121—114no—
372#121—222no—
373C4×Q8—118no—
374C4×Q8—118no—
375C4×Q8—114no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—224no—
379C4×Q8—228no—
380C4×Q8—222no—
381C4×D4—114no—
382C4×D4—228no—
383C4×D4—222no—
384#117—228no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—221no—
404C2×C42—228no—
405C2×C42—222no—
406C2×C42—222no—
407C2×C42D4411yescharacteristic
408C2×C42D4411yescharacteristic
409C2×C42D4414yes—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1114yes—
413#107—118no—
414#106—118no—
415C4⋊C8C22×D1118yes—
416#103—118no—
417#103—118no—
418#103—118no—
419#102—118no—
420C22⋊C8C22×D1114yes—
421C22⋊C8C22×D1114yes—
422#97C22×D1118yes—
423C2×C11—24no—
424C2×C11#311714yescomplemented
425C2×C11C2×#52511yescharacteristic
426C2×C11C22×#13711yescharacteristic
427C2×C11C2×#57511yescharacteristic
428D11—82no—
429C24—221no—
430C24C2×D4411yescharacteristic
431C2×Q8—118no—
432C2×Q8—114no—
433C2×Q8—112no—
434C2×Q8—2216no—
435C2×Q8—228no—
436C2×Q8—2216no—
437C2×Q8—224no—
438C2×Q8—222no—
439C2×Q8—221no—
440C2×Q8—224no—
441C2×Q8—224no—
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—221no—
445C2×D4—224no—
446C2×D4—444no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—42no—
450C22×C4—228no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—224no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4C2×D4414yes—
462C22×C4C2×D4412yes—
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4414yes—
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—2216no—
472SD16—2216no—
473C2×C8—24no—
474C2×C8—24no—
475C2×C8C23×D1114yes—
476C2×C8C23×D1114yes—
477C4⋊C4—114no—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—228no—
485C4⋊C4—228no—
486C4⋊C4—224no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C42—228no—
496C42—228no—
497C42—224no—
498C42C2×D4414yes—
499C42C2×D4412yes—
500C42C2×D4412yes—
501C42C2×D4414yes—
502C42C23×D1112yes—
503C42C23×D1112yes—
504C11C2×#311711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—222no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23#6696214yes—
512C23C22×D4412yes—
513C23C22×D4411yescharacteristic
514Q8—118no—
515Q8—2216no—
516Q8—228no—
517Q8—224no—
518Q8—224no—
519Q8—442no—
520D4—224no—
521D4—448no—
522D4—442no—
523C2×C4—28no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—44no—
532C2×C4—2216no—
533C2×C4—228no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—448no—
540C2×C4—448no—
541C2×C4—442no—
542C2×C4—444no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4C22×D4412yes—
546C2×C4C22×D4412yes—
547C2×C4C22×D4412yes—
548C2×C4C22×D4412yes—
549C2×C4C22×D4412yes—
550C2×C4C22×D4411yescharacteristic
551C2×C4#41×D1114yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—24no—
555C22—22no—
556C22—28no—
557C22—22no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062305512yes—
563C22C2×#6696214yes—
564C22C2×#6696212yes—
565C22#1062327912yes—
566C22C23×D4411yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—228no—
573C4—442no—
574C4—442no—
575C4—444no—
576C4—442no—
577C4#1062305512yes—
578C4C2×#41×D1112yes—
579C2—24no—
580C2—882no—
581C2#1307878914yesdirect product factor
582C2C2×#1062305511yescharacteristic
583C2C22×#6696211yescharacteristic
584C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#432D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13078789C2direct (N × H)
4. C2×#10622335C2semidirect
6. C2×#10622442C2semidirect
7. C2×#10622458C2semidirect
8. C2×#10622352C2semidirect
10. C2×#10622329C2semidirect
11. C2×#10622323C2semidirect
12. C2×C11×#432C2semidirect
37. C2×C4×Dic22C22semidirect
38. C11×#432C22semidirect
49. #10622458C22semidirect
50. #10622442C22semidirect
51. #10622352C22semidirect
54. #10622335C22semidirect
55. #10622329C22semidirect
56. #10622323C22semidirect
224. C2×#432D11semidirect
308. #432C2×D11semidirect
424. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
C22×C4×Dic222
#130787892
C2×#106223352
C2×#106223482
C2×#106224422
C2×#106224582
C2×#106223522
C2×#106223512
C2×#106223292
C2×#106223232
C2×C11×#4322
C2×#311711