Finite Group Databasebeta

← C2×#13078466 #15621353

Subgroups — C2×#13078466 #15621353

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C2×#10623035C211yesmaximal, characteristic
3#13078466C2116yesmaximal, direct product factor
4C2×#10622470C212yesmaximal, complemented
5C2×#10622488C212yesmaximal, complemented
6C2×#10622484C212yesmaximal, complemented
7C2×#10622503C212yesmaximal, complemented
8C22×#66871C211yesmaximal, characteristic, complemented
9C2×#10622732C211yesmaximal, characteristic, complemented
10C2×#10622746C211yesmaximal, characteristic
11C2×#10622615C211yesmaximal, characteristic
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×C4×C22⋊D11—22no—
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21#10623050—24no—
22#10623050C2218yescomplemented
23#10623035—24no—
24#10623035C2218yes—
25C2×#66946C2212yes—
26C2×#66945—21no—
27C2×C4⋊C4×D11—21no—
28C2×#66943C2212yes—
29C2×#66941C2212yes—
30C2×#66940C2212yes—
31C2×#66931—22no—
32C2×#66923—21no—
33C2×#66922—21no—
34C11×#428C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×#106C2212yes—
37#10622746C2218yes—
38#10622732C2218yescomplemented
39C2×#66885C2212yes—
40C2×#66880C2212yes—
41C2×Dic11⋊C8C2212yes—
42C2×Dic11⋊C8C2212yes—
43#10622615C2218yes—
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2218yescomplemented
51#10622503C22116yescomplemented
52#10622488C22116yescomplemented
53#10622484C22116yescomplemented
54#10622470C22116yescomplemented
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C23×Dic11—21no—
59C2×#4339—22no—
60C2×#4339—24no—
61C2×#4339Q818yescomplemented
62C2×#4339C2314yes—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—22no—
66C22×Dic22—22no—
67C22×Dic22C2311yescharacteristic
68C2×C11×M16—24no—
69C2×C11×M16C2314yes—
70C22×C8×C11C2312yes—
71C11×#117—22no—
72C11×#117C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11D412yes—
82C4×C22⋊D11—216no—
83C2×(C2×D11)⋊C4—22no—
84#66979D414yes—
85#66979C2314yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11C2312yes—
98C22×C11⋊C8—24no—
99C22×C11⋊C8C2314yes—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—24no—
103#66946C2318yes—
104#66945—28no—
105C4⋊C4×D11—28no—
106#66943—24no—
107#66943C2318yes—
108#66941—24no—
109#66941C2318yes—
110#66940—24no—
111#66940C2318yes—
112#66931—216no—
113#66923—28no—
114#66922—28no—
115C11×#107C2318yes—
116C11×#106C2318yes—
117#66885C2318yes—
118#66880C2318yes—
119Dic11⋊C8C2318yes—
120Dic11⋊C8C2318yes—
121#66874C2314yes—
122#66874C2314yes—
123#66873C2314yes—
124#66873C2314yes—
125#66871C2318yes—
126#66871C2318yes—
127C2×#3083—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—82no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×Q814yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2412yes—
141C2×C22⋊D11—28no—
142C2×C22⋊D11—24no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—82no—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×D412yes—
149#4339—216no—
150#4339—28no—
151#4339C2×Q8116yescomplemented
152C2×D44—21no—
153C2×D44—22no—
154C2×D44C2×Q814yes—
155C2×D44C2412yes—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—84no—
160C2×Dic22—28no—
161C2×Dic22—21no—
162C2×Dic22—22no—
163C2×Dic22—84no—
164C2×Dic22C2×Q814yes—
165C2×Dic22C2412yes—
166C11×M16—28no—
167C2×C8×C11—24no—
168C2×C8×C11C2414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2414yes—
174C11×C4⋊C4C2412yes—
175C11×C4⋊C4C2412yes—
176C11×C22⋊C4—24no—
177C42×C11—24no—
178C22⋊Dic11C2×D418yes—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—28no—
181C4⋊Dic11—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11C2×D414yes—
184C4⋊Dic11C2×D414yes—
185C4⋊Dic11C2414yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189C4×Dic11—28no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2414yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—28no—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2412yes—
197C2×#544—111no—
198C2×#520—111no—
199#3083—1116no—
200C2×#479—112no—
201C2×#477—112no—
202C2×#478—112no—
203C2×#474—112no—
204C2×#428D1111yescharacteristic, complemented
205C22×#107—111no—
206C2×#424—111no—
207C2×#417—111no—
208C2×#416—111no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11C22⋊Q814yes—
212C23×C11C22×D412yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—22no—
216C22×D11—42no—
217C22×D11—42no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11C22⋊Q814yes—
226C2×C4×C11C22⋊Q818yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×Q812yes—
230C2×C4×C11C22×Q814yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11C2×#4114yes—
233C2×C4×C11C2511yescharacteristic
234C22⋊D11—216no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—44no—
241C2×Dic11—84no—
242C2×Dic11C22×D414yes—
243C2×Dic11C22×D414yes—
244D44—24no—
245D44—22no—
246D44C22×Q814yes—
247C4×D11—216no—
248C4×D11—88no—
249Dic22—24no—
250Dic22—22no—
251Dic22—88no—
252Dic22C22×Q814yes—
253C8×C11—24no—
254C11⋊C8—22no—
255C11⋊C8—22no—
256C22×#41—111no—
257C22×M16C2×D1111yescharacteristic
258C23×C8—111no—
259#544—118no—
260#544—224no—
261C2×C4⋊Q8—112no—
262C2×C4⋊Q8—221no—
263C2×#125—112no—
264C2×#125—221no—
265C2×C22⋊Q8—222no—
266#520—118no—
267#520—224no—
268C2×C4×Q8—112no—
269C2×C4×D4—112no—
270C2×C4×D4—222no—
271C2×#117—111no—
272C2×#117—221no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C4⋊C4—221no—
276C22×C4⋊C4C2×D1111yescharacteristic
277#479—1116no—
278#478—1116no—
279#477—1116no—
280#474—1116no—
281#428C2×D1118yescomplemented
282C2×#107—112no—
283C2×#107—112no—
284C2×#107—118no—
285C2×#107C2×D1112yes—
286C2×#106C2×D1112yes—
287#424—118no—
288C2×C4⋊C8—112no—
289C2×C4⋊C8—112no—
290#417—118no—
291#416—118no—
292C2×#103—112no—
293C2×#103—111no—
294C2×#103—111no—
295C2×#102—112no—
296C2×#102—111no—
297C2×#102—111no—
298C22×C11—28no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11C2×C22⋊Q814yes—
302C22×C11C2×C22⋊Q812yes—
303C22×C11#57612yes—
304C22×C11#57812yes—
305C22×C11C23×D411yescharacteristic
306C2×D11—24no—
307C2×D11—48no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11C2×C22⋊Q812yes—
314C4×C11C2×C22⋊Q814yes—
315C4×C11C23×Q811yescharacteristic
316C4×C11C22×#4111yescharacteristic
317Dic11—24no—
318Dic11—24no—
319Dic11—24no—
320Dic11—44no—
321C2×#41—118no—
322C2×#41—114no—
323C2×#41—224no—
324C2×#41—222no—
325C22×Q8—111no—
326C22×Q8—222no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—21no—
330C23×C4—222no—
331C23×C4—221no—
332C23×C4—221no—
333C23×C4C22×D1111yescharacteristic
334C2×M16—24no—
335C2×M16C22×D1114yes—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8—114no—
339C22×C8—224no—
340C22×C8C22×D1112yes—
341C4⋊Q8—118no—
342C4⋊Q8—228no—
343C4⋊Q8—224no—
344#125—118no—
345#125—228no—
346#125—224no—
347C22⋊Q8—2216no—
348C4×Q8—118no—
349C4×Q8—224no—
350C4×D4—118no—
351C4×D4—224no—
352C4×D4—2216no—
353#117—22no—
354#117—114no—
355#117—114no—
356#117—228no—
357#117C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4C22×D1112yes—
372C2×C4⋊C4C22×D1114yes—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—112no—
377C2×C22⋊C4—222no—
378C2×C42—21no—
379C2×C42—112no—
380C2×C42—222no—
381#107—118no—
382#107—118no—
383#107C22×D1118yes—
384#106C22×D1118yes—
385C4⋊C8—118no—
386C4⋊C8—118no—
387#103—118no—
388#103—114no—
389#103—114no—
390#102—118no—
391#102—114no—
392#102—114no—
393C2×C11—24no—
394C2×C11#308314yescomplemented
395C2×C11C22×C22⋊Q811yescharacteristic
396C2×C11C2×#57611yescharacteristic
397C2×C11C2×#57811yescharacteristic
398D11—44no—
399C24—221no—
400C24D4×D1111yescharacteristic
401#41—1116no—
402#41—2216no—
403#41—228no—
404C2×Q8—114no—
405C2×Q8—112no—
406C2×Q8—228no—
407C2×Q8—222no—
408C2×Q8—221no—
409C2×Q8—884no—
410C2×D4—114no—
411C2×D4—112no—
412C2×D4—228no—
413C2×D4—224no—
414C2×D4—222no—
415C2×D4—221no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—82no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—228no—
424C22×C4—221no—
425C22×C4—228no—
426C22×C4—224no—
427C22×C4—222no—
428C22×C4—224no—
429C22×C4—884no—
430C22×C4—882no—
431C22×C4#433914yes—
432C22×C4D4×D1112yes—
433C22×C4D4×D1111yescharacteristic
434C22×C4Q8×D1114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—28no—
438C2×C8—24no—
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—228no—
444C2×C8C23×D1114yes—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—114no—
450C4⋊C4—114no—
451C4⋊C4—114no—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—224no—
457C4⋊C4—222no—
458C4⋊C4C23×D1112yes—
459C4⋊C4C23×D1112yes—
460C4⋊C4C23×D1114yes—
461C22⋊C4—24no—
462C22⋊C4—118no—
463C22⋊C4—228no—
464C42—24no—
465C42—114no—
466C42—114no—
467C42—228no—
468C11C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—224no—
472C23—222no—
473C23—442no—
474C23—442no—
475C23#6694914yes—
476C23C2×D4×D1112yes—
477C23C2×D4×D1111yescharacteristic
478Q8—114no—
479Q8—224no—
480Q8—222no—
481Q8—888no—
482D4—114no—
483D4—2216no—
484D4—224no—
485D4—222no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—114no—
494C2×C4—114no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—2216no—
500C2×C4—224no—
501C2×C4—444no—
502C2×C4—888no—
503C2×C4—884no—
504C2×C4#6694914yes—
505C2×C4#6694918yes—
506C2×C4C2×#433912yes—
507C2×C4C2×#433914yes—
508C2×C4C2×D4×D1112yes—
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×Q8×D1112yes—
511C2×C4C2×Q8×D1114yes—
512C2×C4C24×D1111yescharacteristic
513C8—24no—
514C8—222no—
515C8—222no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—224no—
520C22—448no—
521C22—442no—
522C22—442no—
523C22C2×#6694914yes—
524C22C2×#6694912yes—
525C22#1062330512yes—
526C22#1062331012yes—
527C22C22×D4×D1111yescharacteristic
528C4—44no—
529C4—42no—
530C4—42no—
531C4—224no—
532C4—224no—
533C4—224no—
534C4—444no—
535C4C2×#6694914yes—
536C4C2×#6694912yes—
537C4C22×#433911yescharacteristic
538C4C22×Q8×D1111yescharacteristic
539C2—24no—
540C2—444no—
541C2#1307846614yesdirect product factor
542C2C22×#6694911yescharacteristic
543C2C2×#1062330511yescharacteristic
544C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#428D11
hypocenterC11C2×#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13078466C2direct (N × H)
4. C2×#10622470C2semidirect
5. C2×#10622488C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622503C2semidirect
8. C22×#66871C2semidirect
9. C2×#10622732C2semidirect
12. C2×C11×#428C2semidirect
22. #10623050C22semidirect
34. C11×#428C22semidirect
38. #10622732C22semidirect
50. C2×#66871C22semidirect
51. #10622503C22semidirect
52. #10622488C22semidirect
53. #10622484C22semidirect
54. #10622470C22semidirect
61. C2×#4339Q8semidirect
151. #4339C2×Q8semidirect
204. C2×#428D11semidirect
281. #428C2×D11semidirect
394. C2×C11#3083semidirect
468. C11C2×#3083semidirect
541. C2#13078466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106230352
#130784662
C2×#106224702
C2×#106224882
C2×#106224842
C2×#106225032
C22×#668712
C2×#106227322
C2×#106227462
C2×#106226152
C2×C11×#4282
C2×#308311