Finite Group Databasebeta

← C2×#13079799 #15625855

Subgroups — C2×#13079799 #15625855

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic
3#13079799C2116yesmaximal, direct product factor
4C2×#10622471C212yesmaximal, complemented
5C2×#10622413C212yesmaximal, complemented
6C2×#10622428C212yesmaximal, complemented
7C2×#10622479C212yesmaximal
8C2×#10622634C211yesmaximal, characteristic, complemented
9C2×#10622455C211yesmaximal, characteristic, complemented
10C2×#10622700C211yesmaximal, characteristic, complemented
11C2×#10622446C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×#66999—21no—
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11—21no—
19#10623259—24no—
20#10623259C2218yescomplemented
21#10623111—24no—
22#10623111C2218yes—
23C2×#66951—21no—
24C2×#66950—21no—
25C2×#66948C2211yescharacteristic
26C2×#66947—21no—
27C2×#66945C2212yes—
28C2×#66943C2211yescharacteristic
29C2×#66943C2212yes—
30C2×#66940—21no—
31C2×C4×D44—21no—
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#475C2218yescomplemented
37C2×C11×#106C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66899C2212yes—
41C2×#66885C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×C8×Dic11C2212yes—
45#10622700C2218yescomplemented
46#10622634C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622479C22116yes—
52#10622471C22116yescomplemented
53#10622455C2218yescomplemented
54#10622446C2218yescomplemented
55#10622428C22116yescomplemented
56#10622413C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#67000—22no—
78#67000C2314yes—
79#66999—28no—
80#66999—22no—
81#66999C2314yes—
82Q8×Dic11—28no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2312yes—
102#66951—28no—
103#66950—28no—
104#66948—22no—
105#66948C2314yes—
106#66947—28no—
107#66945—24no—
108#66945C2318yes—
109#66943—24no—
110#66943—22no—
111#66943C2314yes—
112#66943C2318yes—
113#66940—28no—
114C4×D44—28no—
115C4×D44—22no—
116C4×D44C2314yes—
117#66925—28no—
118C42×D11D414yes—
119C42×D11C2314yes—
120#66922—22no—
121#66922C2314yes—
122C11×#106C2318yes—
123C11×C4⋊C8C2314yes—
124C11×#103C2318yes—
125#66899C2318yes—
126#66885C2318yes—
127(C2×D11)⋊C8C2318yes—
128#66881C2318yes—
129C8×Dic11C2318yes—
130#66873C2318yes—
131#66871C2318yes—
132#66871C2318yes—
133C4⋊(C11⋊C8)C2314yes—
134C2×#3233—111nomaximal, Sylow
135C23×D11—21no—
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—24no—
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—44no—
142C2×Q8×C11C2412yes—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—24no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—44no—
159C2×D44C2412yes—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—42no—
165C2×C4×D11—44no—
166C2×C4×D11C2×D412yes—
167C2×C4×D11C2×D414yes—
168C2×C4×D11C2×D414yes—
169C2×C4×D11C2412yes—
170C2×Dic22—24no—
171C2×Dic22—44no—
172C2×C8×C11—24no—
173C2×C8×C11C2414yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2414yes—
180C42×C11—24no—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11—28no—
191C4⋊Dic11—22no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2412yes—
195C4⋊Dic11C2414yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—28no—
199C4×Dic11—28no—
200C4×Dic11C2×D412yes—
201C4×Dic11C2×D414yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2412yes—
204C2×C11⋊C8—24no—
205C2×C11⋊C8C2414yes—
206C2×#533—111no—
207C2×#529—111no—
208#3233—1116no—
209C2×#499—112no—
210C2×#488—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#477—111no—
214C2×#475D1111yescharacteristic, complemented
215C2×#476—111no—
216C2×#474—111no—
217C2×#431—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11C22×D412yes—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—42no—
230Q8×C11—48no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11#13514yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D412yes—
242C2×C4×C112−1+412yes—
243C2×C4×C112−1+412yes—
244C2×C4×C11C2511yescharacteristic
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—42no—
251C2×Dic11—44no—
252C2×Dic11C22×D412yes—
253C2×Dic11C22×D412yes—
254C2×Dic11C22×D412yes—
255D44—22no—
256D44—22no—
257D44—48no—
258D44—42no—
259C4×D11—24no—
260C4×D11—28no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—44no—
264C4×D11—48no—
265Dic22—48no—
266C8×C11—24no—
267C11⋊C8—24no—
268#533—118no—
269#533—224no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8C2×D1111yescharacteristic
272#529—118no—
273#529—224no—
274C2×#126—221no—
275C2×#125—112no—
276C2×#125—111no—
277C2×#124—111no—
278C2×#123—221no—
279C2×C22⋊Q8—111no—
280C2×C22⋊Q8—221no—
281C2×C22⋊Q8—221no—
282C2×#121—111no—
283C2×C4×Q8—221no—
284C2×C4×Q8—221no—
285C2×C4×Q8C2×D1111yescharacteristic
286C2×C4×D4—111no—
287C2×C4×D4—221no—
288C2×#117—112no—
289C2×#117—221no—
290C22×C42—111no—
291#499—1116no—
292#488—1116no—
293#485—1116no—
294#482—1116no—
295#477—118no—
296#476—118no—
297#475C2×D1118yescomplemented
298#474—118no—
299#431—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#106—112no—
303C2×#106C2×D1112yes—
304C2×C4⋊C8—111no—
305C2×C4⋊C8C2×D1111yescharacteristic
306C2×#103—112no—
307C2×#103C2×D1112yes—
308C2×#102—112no—
309C2×#102—112no—
310C2×C22⋊C8—112no—
311C2×C4×C8—112no—
312C22×C11#53612yes—
313C22×C11C2×#13512yes—
314C22×C11#57512yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—22no—
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—44no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—84no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11#53612yes—
329C4×C11C2×#13514yes—
330C4×C11C2×2−1+411yescharacteristic
331C4×C11C2×2−1+411yescharacteristic
332Dic11—22no—
333Dic11—22no—
334Dic11—22no—
335Dic11—42no—
336Dic11—44no—
337C22×Q8—21no—
338C22×Q8—221no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—111no—
341C22×D4—221no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—221no—
346C22×C8—112no—
347C22×C8C22×D1112yes—
348C4⋊Q8—22no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8C22×D1114yes—
352#126—228no—
353#125—114no—
354#125—118no—
355#125—222no—
356#125—224no—
357#124—114no—
358#124—222no—
359#123—228no—
360C22⋊Q8—114no—
361C22⋊Q8—228no—
362C22⋊Q8—222no—
363C22⋊Q8—228no—
364#121—114no—
365#121—222no—
366C4×Q8—22no—
367C4×Q8—228no—
368C4×Q8—228no—
369C4×Q8C22×D1114yes—
370C4×D4—114no—
371C4×D4—228no—
372C4×D4—222no—
373#117—118no—
374#117—228no—
375#117—224no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—114no—
399C2×C42—114no—
400C2×C42—222no—
401C2×C42C22×D1111yescharacteristic
402#107—118no—
403#107—118no—
404#106—118no—
405#106C22×D1118yes—
406C4⋊C8—114no—
407C4⋊C8C22×D1114yes—
408#103—118no—
409#103C22×D1118yes—
410#102—118no—
411#102—118no—
412C22⋊C8—118no—
413C4×C8—118no—
414C2×C11#323314yescomplemented
415C2×C11C2×#53611yescharacteristic
416C2×C11C22×#13511yescharacteristic
417C2×C11C2×#57511yescharacteristic
418D11—42no—
419D11—82no—
420C24—111no—
421C24—221no—
422C2×Q8—21no—
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—44no—
427C2×Q8—224no—
428C2×Q8—444no—
429C2×Q8C23×D1112yes—
430C2×D4—112no—
431C2×D4—224no—
432C2×D4—221no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—444no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—224no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—442no—
453C22×C4—444no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457C2×C8—24no—
458C2×C8—114no—
459C2×C8—224no—
460C2×C8C23×D1114yes—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—114no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4—228no—
471C4⋊C4—228no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—224no—
475C4⋊C4C23×D1114yes—
476C4⋊C4C23×D1112yes—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—228no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—24no—
484C42—114no—
485C42—114no—
486C42—112no—
487C42—112no—
488C42—228no—
489C42D4×D1112yes—
490C42C23×D1112yes—
491C11C2×#323311yescharacteristic, complemented, Sylow
492C23—112no—
493C23—222no—
494C23—222no—
495C23—222no—
496C23—222no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23C2×D4×D1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—48no—
504Q8—42no—
505Q8—448no—
506D4—222no—
507D4—222no—
508D4—448no—
509D4—442no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—444no—
530C2×C4—442no—
531C2×C4—444no—
532C2×C4—448no—
533C2×C4#6696914yes—
534C2×C4C2×D4×D1112yes—
535C2×C4C2×D4×D1112yes—
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4#6704012yes—
538C2×C4#6704312yes—
539C2×C4C24×D1111yescharacteristic
540C8—24no—
541C8—224no—
542C22—222no—
543C22—222no—
544C22—222no—
545C22—444no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—884no—
550C22#1062315912yes—
551C22C2×#6696912yes—
552C22#1062330812yes—
553C22C22×D4×D1111yescharacteristic
554C4—22no—
555C4—42no—
556C4—44no—
557C4—42no—
558C4—222no—
559C4—222no—
560C4—222no—
561C4—442no—
562C4—444no—
563C4#1062315912yes—
564C4C2×#6696914yes—
565C4C2×#6704011yescharacteristic
566C4C2×#6704311yescharacteristic
567C2—442no—
568C2—882no—
569C2#1307979914yesdirect product factor
570C2C2×#1062315911yescharacteristic
571C2C22×#6696911yescharacteristic
572C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#475D11
hypocenterC11C2×#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079799C2direct (N × H)
4. C2×#10622471C2semidirect
5. C2×#10622413C2semidirect
6. C2×#10622428C2semidirect
8. C2×#10622634C2semidirect
9. C2×#10622455C2semidirect
10. C2×#10622700C2semidirect
11. C2×#10622446C2semidirect
12. C2×C11×#475C2semidirect
20. #10623259C22semidirect
36. C11×#475C22semidirect
45. #10622700C22semidirect
46. #10622634C22semidirect
52. #10622471C22semidirect
53. #10622455C22semidirect
54. #10622446C22semidirect
55. #10622428C22semidirect
56. #10622413C22semidirect
214. C2×#475D11semidirect
297. #475C2×D11semidirect
414. C2×C11#3233semidirect
491. C11C2×#3233semidirect
569. C2#13079799direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106231112
#130797992
C2×#106224712
C2×#106224132
C2×#106224282
C2×#106224792
C2×#106226342
C2×#106224552
C2×#106227002
C2×#106224462
C2×C11×#4752
C2×#323311