Finite Group Databasebeta

← C2×#13079954 #15626579

Subgroups — C2×#13079954 #15626579

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic
3#13079954C2116yesmaximal, direct product factor
4C2×#10622442C212yesmaximal, complemented
5C2×#10622464C211yesmaximal, characteristic, complemented
6C2×#10622459C211yesmaximal, characteristic, complemented
7C2×#10622729C212yesmaximal, complemented
8C2×#10622727C212yesmaximal
9C2×#10622458C212yesmaximal, complemented
10C2×#10622462C211yesmaximal, characteristic, complemented
11C2×#10622454C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C8C211yesmaximal, 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×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C4⋊C8C2212yes—
42C2×C11×C4⋊C8C2218yescomplemented
43#10622729C22116yescomplemented
44#10622727C22116yes—
45C2×#66885C2212yes—
46C2×#66882C2212yes—
47C2×#66881C2212yes—
48C2×#66880C2212yes—
49C2×#66880C2212yes—
50C2×#66880C2212yes—
51#10622464C2218yescomplemented
52#10622462C2218yescomplemented
53#10622459C2218yescomplemented
54#10622458C22116yescomplemented
55#10622454C2218yescomplemented
56#10622442C22116yescomplemented
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—44no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C22×C8×C11C2318yes—
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—44no—
107C2×Dic44C2318yes—
108C2×#4314—44no—
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×Dic22C2314yes—
127C4×Dic22C2318yes—
128C11×C4⋊C8C2314yes—
129C11×C4⋊C8C2318yes—
130C11×C4⋊C8C2314yes—
131#66885C2318yes—
132#66882C2318yes—
133#66881C2318yes—
134#66880C2318yes—
135#66880C2318yes—
136#66880C2318yes—
137C2×#3248—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
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×C11C2×D411yescharacteristic
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—44no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44C2412yes—
165C2×C4×D11—24no—
166C2×C4×D11—44no—
167C2×Dic22—22no—
168C2×Dic22—24no—
169C2×Dic22—21no—
170C2×Dic22—24no—
171C2×Dic22—22no—
172C2×Dic22—24no—
173C2×Dic22—22no—
174C2×Dic22—44no—
175C2×Dic22C2414yes—
176C2×Dic22C2412yes—
177C2×C8×C11—24no—
178C2×C8×C11—24no—
179C2×C8×C11—48no—
180C2×C8×C11C2414yes—
181C2×C8×C11C2414yes—
182C42×C11C2×D412yes—
183C42×C11C2×D414yes—
184C42×C11C2×D412yes—
185C42×C11C2×D414yes—
186C42×C11C2412yes—
187C42×C11C2412yes—
188C22⋊Dic11—28no—
189C22⋊Dic11—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4⋊Dic11—22no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11—24no—
198C4⋊Dic11—24no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2412yes—
201C4⋊Dic11C2412yes—
202C4⋊Dic11C2414yes—
203Dic11⋊C4—28no—
204Dic11⋊C4—28no—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209C4×Dic11—28no—
210C4×Dic11—24no—
211Dic44—48no—
212#4314—48no—
213C2×#533—111no—
214C2×#529—111no—
215#3248—1116no—
216C2×#479—112no—
217C2×#475—111no—
218C2×#474—111no—
219C2×#467—112no—
220C2×#465—112no—
221C2×#464—112no—
222C2×#462—111no—
223C2×#461—111no—
224C22×C4⋊C8D1111yescharacteristic, 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—22no—
236C2×C4×C11—28no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11#13514yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C112−1+412yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—48no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—44no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264D44—22no—
265D44—22no—
266D44—42no—
267C4×D11—48no—
268Dic22—24no—
269Dic22—22no—
270Dic22—24no—
271Dic22—22no—
272Dic22—44no—
273Dic22—42no—
274Dic22—48no—
275C8×C11—24no—
276C8×C11—24no—
277C22×Q16—112no—
278C22×SD16—112no—
279C23×C8C2×D1112yes—
280#533—118no—
281#533—224no—
282C2×C4⋊Q8—111no—
283C2×C4⋊Q8—111no—
284#529—118no—
285#529—224no—
286C2×#126—221no—
287C2×#125—111no—
288C2×#125—221no—
289C2×#124—111no—
290C2×#123—221no—
291C2×C22⋊Q8—111no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—221no—
294C2×#121—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—112no—
297C2×C4×Q8—221no—
298C2×C4×D4—111no—
299C2×C4×D4—221no—
300C2×#117—221no—
301C2×#117—221no—
302C22×C42C2×D1111yescharacteristic
303#479—1116no—
304#475—118no—
305#474—118no—
306#467—1116no—
307#465—1116no—
308#464—1116no—
309#462—118no—
310#461—118no—
311C2×#107—112no—
312C2×#106—112no—
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×C4⋊C8C2×D1112yes—
315C2×C4⋊C8C2×D1111yescharacteristic
316C2×C4⋊C8C2×D1118yescomplemented
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C22×C11—22no—
322C22×C11—28no—
323C22×C11—22no—
324C22×C11#53712yes—
325C22×C11C2×#13512yes—
326C22×C11C2×#13714yes—
327C22×C11C2×#13712yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—84no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11#53712yes—
338C4×C11C2×#13514yes—
339C4×C11C2×H(5,𝔽2)11yescharacteristic
340C4×C11C2×2−1+411yescharacteristic
341Dic11—44no—
342Dic11—42no—
343Dic11—44no—
344Dic11—42no—
345Dic11—42no—
346C22×Q8—111no—
347C22×Q8—112no—
348C22×Q8—221no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4D4411yescharacteristic
353C23×C4D4411yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×Q16—118no—
356C2×Q16—444no—
357C2×SD16—118no—
358C2×SD16—444no—
359C22×C8—44no—
360C22×C8C22×D1112yes—
361C22×C8C22×D1112yes—
362C22×C8C22×D1118yes—
363C4⋊Q8—114no—
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366C4⋊Q8—222no—
367#126—228no—
368#125—114no—
369#125—222no—
370#125—228no—
371#124—114no—
372#124—222no—
373#123—228no—
374C22⋊Q8—114no—
375C22⋊Q8—118no—
376C22⋊Q8—222no—
377C22⋊Q8—224no—
378C22⋊Q8—228no—
379#121—114no—
380#121—222no—
381C4×Q8—114no—
382C4×Q8—118no—
383C4×Q8—222no—
384C4×Q8—224no—
385C4×Q8—228no—
386C4×D4—114no—
387C4×D4—228no—
388C4×D4—222no—
389#117—228no—
390#117—228no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—221no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—221no—
410C2×C42—222no—
411C2×C42D4411yescharacteristic
412C2×C42D4411yescharacteristic
413C2×C42D4414yes—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1114yes—
417#107—118no—
418#106—118no—
419C4⋊C8C22×D1114yes—
420C4⋊C8C22×D1114yes—
421C4⋊C8C22×D1118yes—
422#103—118no—
423#103—118no—
424#103—118no—
425#102—118no—
426C2×C11—24no—
427C2×C11#324814yescomplemented
428C2×C11C2×#53711yescharacteristic
429C2×C11C22×#13511yescharacteristic
430C2×C11C22×#13711yescharacteristic
431D11—82no—
432C24—221no—
433C24C2×D4411yescharacteristic
434C2×Q8—112no—
435C2×Q8—114no—
436C2×Q8—221no—
437C2×Q8—224no—
438C2×Q8—222no—
439C2×Q8—224no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—224no—
443C2×Q8—444no—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—221no—
447C2×D4—222no—
448C2×D4—222no—
449C2×D4—444no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—221no—
459C22×C4—224no—
460C22×C4—444no—
461C22×C4C2×D4414yes—
462C22×C4C2×D4414yes—
463C22×C4C2×D4412yes—
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—448no—
472SD16—448no—
473C2×C8—24no—
474C2×C8—24no—
475C2×C8—48no—
476C2×C8C23×D1114yes—
477C2×C8C23×D1114yes—
478C4⋊C4—114no—
479C4⋊C4—112no—
480C4⋊C4—112no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—222no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4—228no—
490C4⋊C4—224no—
491C4⋊C4—228no—
492C4⋊C4—224no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4—224no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—224no—
500C42—228no—
501C42C2×D4414yes—
502C42C2×D4412yes—
503C42C2×D4412yes—
504C42C2×D4414yes—
505C42C23×D1112yes—
506C42C23×D1112yes—
507C11C2×#324811yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—222no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23#6696214yes—
515C23C22×D4412yes—
516C23C22×D4411yescharacteristic
517Q8—224no—
518Q8—222no—
519Q8—222no—
520Q8—224no—
521Q8—448no—
522Q8—442no—
523Q8—444no—
524D4—222no—
525D4—222no—
526D4—448no—
527D4—442no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—442no—
543C2×C4—444no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—444no—
547C2×C4—448no—
548C2×C4#6695714yes—
549C2×C4C22×D4412yes—
550C2×C4C22×D4412yes—
551C2×C4C22×D4412yes—
552C2×C4C22×D4412yes—
553C2×C4C22×D4412yes—
554C2×C4C22×D4411yescharacteristic
555C2×C4#6703712yes—
556C2×C4#6704012yes—
557C2×C4C24×D1111yescharacteristic
558C8—24no—
559C8—24no—
560C22—22no—
561C22—28no—
562C22—22no—
563C22—442no—
564C22—442no—
565C22—442no—
566C22—884no—
567C22#1062304112yes—
568C22C2×#6695712yes—
569C22C2×#6696214yes—
570C22C2×#6696212yes—
571C22C23×D4411yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—442no—
577C4—444no—
578C4—442no—
579C4—444no—
580C4—442no—
581C4#1062304112yes—
582C4C2×#6695714yes—
583C4C2×#6703711yescharacteristic
584C4C2×#6704011yescharacteristic
585C2—24no—
586C2—882no—
587C2#1307995414yesdirect product factor
588C2C2×#1062304111yescharacteristic
589C2C22×#6695711yescharacteristic
590C2C22×#6696211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
3. #13079954C2direct (N × H)
4. C2×#10622442C2semidirect
5. C2×#10622464C2semidirect
6. C2×#10622459C2semidirect
7. C2×#10622729C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622462C2semidirect
11. C2×#10622454C2semidirect
12. C22×C11×C4⋊C8C2semidirect
31. #10623001C22semidirect
42. C2×C11×C4⋊C8C22semidirect
43. #10622729C22semidirect
51. #10622464C22semidirect
52. #10622462C22semidirect
53. #10622459C22semidirect
54. #10622458C22semidirect
55. #10622454C22semidirect
56. #10622442C22semidirect
224. C22×C4⋊C8D11semidirect
316. C2×C4⋊C8C2×D11semidirect
427. C2×C11#3248semidirect
507. C11C2×#3248semidirect
587. C2#13079954direct (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
#130799542
C2×#106224422
C2×#106224642
C2×#106224592
C2×#106227292
C2×#106227272
C2×#106224582
C2×#106224622
C2×#106224542
C22×C11×C4⋊C82
C2×#324811