Finite Group Databasebeta

← C2×#13078469 #15621356

Subgroups — C2×#13078469 #15621356

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×#10623054C211yesmaximal, characteristic
3#13078469C2116yesmaximal, direct product factor
4C2×#10622442C212yesmaximal, complemented
5C2×#10622463C212yesmaximal, complemented
6C2×#10622460C212yesmaximal, complemented
7C2×#10622459C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C22×#66882C211yesmaximal, characteristic, complemented
10C2×#10622746C211yesmaximal, characteristic
11C2×#10622726C211yesmaximal, characteristic
12C2×C11×#424C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20#10623054—24no—
21#10623054C2218yes—
22#10623050—24no—
23#10623050C2218yescomplemented
24C2×#66945—21no—
25C2×C4⋊C4×D11—21no—
26C2×#66943—21no—
27C2×#66941—21no—
28C2×(C22⋊D11)⋊C4—22no—
29C2×#66931—22no—
30C2×C4×D44C2212yes—
31C2×#66923C2212yes—
32C2×#66922C2212yes—
33C2×C4×Dic22C2212yes—
34C11×#424C2218yescomplemented
35C2×C11×C4⋊C8C2212yes—
36C2×C11×C4⋊C8C2212yes—
37#10622746C2218yes—
38#10622734C2218yescomplemented
39#10622726C2218yes—
40C2×#66885C2211yescharacteristic
41C2×#66885C2212yes—
42C2×#66885C2211yescharacteristic
43C2×#66882C2212yes—
44C2×#66882C2212yes—
45C2×#66882C2212yes—
46C2×#66882C2218yescomplemented
47C2×#66881C2212yes—
48C2×#66880C2211yescharacteristic
49C2×#66880C2212yes—
50C2×#66880C2211yescharacteristic
51#10622463C22116yescomplemented
52#10622460C22116yescomplemented
53#10622459C22116yescomplemented
54#10622442C22116yescomplemented
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C23×Dic11—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×C11—24no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2312yes—
74C22×C8×C11C2314yes—
75C11×#117D414yes—
76C11×#117C2314yes—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D412yes—
80C2×C42×C11C2312yes—
81C2×C22⋊Dic11—21no—
82C2×(C2×D11)⋊C4—22no—
83#66979—22no—
84#66979C2314yes—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—21no—
101#66945—28no—
102C4⋊C4×D11—28no—
103#66943—28no—
104#66941—28no—
105(C22⋊D11)⋊C4—216no—
106#66931—216no—
107C4×D44—24no—
108C4×D44C2318yes—
109#66923—24no—
110#66923C2318yes—
111#66922—24no—
112#66922C2318yes—
113C4×Dic22—24no—
114C4×Dic22C2318yes—
115C11×C4⋊C8C2318yes—
116C11×C4⋊C8C2318yes—
117#66885C2314yes—
118#66885C2314yes—
119#66885C2318yes—
120#66882C2318yes—
121#66882C2318yes—
122#66882C2318yes—
123#66881C2318yes—
124#66880C2314yes—
125#66880C2314yes—
126#66880C2318yes—
127C2×#3083—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11#4114yes—
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2412yes—
138C2×C22⋊D11—28no—
139C2×C22⋊D11—24no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—82no—
148C22×Dic11—82no—
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—24no—
158C2×C4×D11—28no—
159C2×C4×D11—84no—
160C2×Dic22—21no—
161C2×Dic22—28no—
162C2×Dic22—22no—
163C2×Dic22—84no—
164C2×Dic22C2×Q814yes—
165C2×Dic22C2412yes—
166C11×M16—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—28no—
170C2×C8×C11—24no—
171C2×C8×C11C2414yes—
172C2×C8×C11C2412yes—
173C2×C8×C11C2412yes—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2×D414yes—
176C11×C22⋊C4C2×D418yes—
177C42×C11C2×D414yes—
178C42×C11C2414yes—
179C22⋊Dic11—24no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—22no—
184C4⋊Dic11—28no—
185C4⋊Dic11—21no—
186C4⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11C2412yes—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191C4⋊Dic11C2414yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195C4×Dic11—28no—
196C4×Dic11—24no—
197C2×#544—111no—
198C2×#520—111no—
199#3083—1116no—
200C2×#479—112no—
201C2×#477—112no—
202C2×#478—112no—
203C2×#474—112no—
204C2×#428—111no—
205C22×#107—111no—
206C2×#424D1111yescharacteristic, complemented
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—24no—
220C2×C4×C11C22⋊Q814yes—
221C2×C4×C11C22⋊Q818yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×Q812yes—
227C2×C4×C11C22×Q814yes—
228C2×C4×C11C2×#4112yes—
229C2×C4×C11C2×#4114yes—
230C2×C4×C11C2511yescharacteristic
231C22⋊D11—216no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243C2×Dic11—84no—
244D44—24no—
245D44—22no—
246D44C22×Q814yes—
247C4×D11—216no—
248C4×D11—88no—
249Dic22—24no—
250Dic22—22no—
251Dic22—88no—
252Dic22C22×Q814yes—
253C8×C11—22no—
254C8×C11—22no—
255C8×C11—24no—
256C22×#41—111no—
257C22×M16C2×D1111yescharacteristic
258C23×C8C2×D1111yescharacteristic
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—111no—
276C22×C4⋊C4—221no—
277#479—1116no—
278#478—1116no—
279#477—1116no—
280#474—1116no—
281#428—118no—
282C2×#107—112no—
283C2×#107—112no—
284C2×#107—112no—
285C2×#107—118no—
286C2×#106—112no—
287#424C2×D1118yescomplemented
288C2×C4⋊C8C2×D1112yes—
289C2×C4⋊C8C2×D1112yes—
290#417—118no—
291#416—118no—
292C2×#103—111no—
293C2×#103—112no—
294C2×#103—111no—
295C2×#102—111no—
296C2×#102—112no—
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—24no—
311C4×C11—24no—
312C4×C11C2×C22⋊Q812yes—
313C4×C11C2×C22⋊Q814yes—
314C4×C11C23×Q811yescharacteristic
315C4×C11C22×#4111yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—44no—
319Dic11—44no—
320Dic11—42no—
321C2×#41—118no—
322C2×#41—114no—
323C2×#41—222no—
324C2×#41—224no—
325C22×Q8—111no—
326C22×Q8—222no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—221no—
330C23×C4—221no—
331C23×C4—221no—
332C23×C4—222no—
333C23×C4C22×D1111yescharacteristic
334C2×M16—24no—
335C2×M16C22×D1114yes—
336C22×C8—24no—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339C22×C8C22×D1114yes—
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—2216no—
352C4×D4—224no—
353#117—114no—
354#117—222no—
355#117—228no—
356#117D4414yes—
357#117C22×D1114yes—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4D4411yescharacteristic
374C2×C4⋊C4D4411yescharacteristic
375C2×C22⋊C4—221no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4D4412yes—
378C2×C42—221no—
379C2×C42—222no—
380C2×C42C22×D1112yes—
381#107—118no—
382#107—118no—
383#107—118no—
384#106—118no—
385C4⋊C8C22×D1118yes—
386C4⋊C8C22×D1118yes—
387#103—114no—
388#103—114no—
389#103—118no—
390#102—114no—
391#102—114no—
392#102—118no—
393C2×C11—24no—
394C2×C11#308314yescomplemented
395C2×C11C22×C22⋊Q811yescharacteristic
396C2×C11C2×#57611yescharacteristic
397C2×C11C2×#57811yescharacteristic
398D11—44no—
399C24—221no—
400C24C2×D4411yescharacteristic
401#41—1116no—
402#41—2216no—
403#41—228no—
404C2×Q8—114no—
405C2×Q8—112no—
406C2×Q8—221no—
407C2×Q8—228no—
408C2×Q8—222no—
409C2×Q8—884no—
410C2×D4—114no—
411C2×D4—112no—
412C2×D4—228no—
413C2×D4—224no—
414C2×D4—221no—
415C2×D4—222no—
416C22×C4—221no—
417C22×C4—228no—
418C22×C4—224no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—228no—
426C22×C4—884no—
427C22×C4—882no—
428C22×C4—882no—
429C22×C4C2×D4412yes—
430C22×C4C2×D4412yes—
431C22×C4C2×D4412yes—
432C22×C4C2×D4411yescharacteristic
433C22×C4#434114yes—
434C22×C4Q8×D1114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—28no—
441C2×C8—24no—
442C2×C8C23×D1114yes—
443C2×C8C23×D1112yes—
444C2×C8C23×D1112yes—
445C4⋊C4—112no—
446C4⋊C4—114no—
447C4⋊C4—112no—
448C4⋊C4—114no—
449C4⋊C4—224no—
450C4⋊C4—222no—
451C4⋊C4—224no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4C2×D4414yes—
460C4⋊C4C2×D4414yes—
461C22⋊C4—224no—
462C22⋊C4—228no—
463C22⋊C4C2×D4418yes—
464C42—224no—
465C42—228no—
466C42C2×D4414yes—
467C42C23×D1114yes—
468C11C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—224no—
472C23—222no—
473C23—442no—
474C23—442no—
475C23#6695014yes—
476C23C22×D4412yes—
477C23C22×D4411yescharacteristic
478Q8—114no—
479Q8—224no—
480Q8—222no—
481Q8—888no—
482D4—114no—
483D4—2216no—
484D4—224no—
485D4—222no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—2216no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—888no—
500C2×C4—884no—
501C2×C4—884no—
502C2×C4#6695014yes—
503C2×C4#6695018yes—
504C2×C4C22×D4414yes—
505C2×C4C22×D4414yes—
506C2×C4C22×D4412yes—
507C2×C4C22×D4411yescharacteristic
508C2×C4C2×#434112yes—
509C2×C4C2×#434114yes—
510C2×C4C2×Q8×D1112yes—
511C2×C4C2×Q8×D1114yes—
512C2×C4C24×D1111yescharacteristic
513C8—22no—
514C8—22no—
515C8—24no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—224no—
520C22—448no—
521C22—442no—
522C22—442no—
523C22C2×#6695014yes—
524C22C2×#6695012yes—
525C22#1062328312yes—
526C22#1062328412yes—
527C22C23×D4411yescharacteristic
528C4—24no—
529C4—24no—
530C4—224no—
531C4—444no—
532C4—444no—
533C4—442no—
534C4—442no—
535C4C2×#6695014yes—
536C4C2×#6695012yes—
537C4C22×#434111yescharacteristic
538C4C22×Q8×D1111yescharacteristic
539C2—24no—
540C2—444no—
541C2#1307846914yesdirect product factor
542C2C22×#6695011yescharacteristic
543C2C2×#1062328311yescharacteristic
544C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#424C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#424D11
hypocenterC11C2×#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13078469C2direct (N × H)
4. C2×#10622442C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622460C2semidirect
7. C2×#10622459C2semidirect
8. C2×#10622734C2semidirect
9. C22×#66882C2semidirect
12. C2×C11×#424C2semidirect
23. #10623050C22semidirect
34. C11×#424C22semidirect
38. #10622734C22semidirect
46. C2×#66882C22semidirect
51. #10622463C22semidirect
52. #10622460C22semidirect
53. #10622459C22semidirect
54. #10622442C22semidirect
61. C2×#4339Q8semidirect
151. #4339C2×Q8semidirect
206. C2×#424D11semidirect
287. #424C2×D11semidirect
394. C2×C11#3083semidirect
468. C11C2×#3083semidirect
541. C2#13078469direct (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×#106230542
#130784692
C2×#106224422
C2×#106224632
C2×#106224602
C2×#106224592
C2×#106227342
C22×#668822
C2×#106227462
C2×#106227262
C2×C11×#4242
C2×#308311