Finite Group Databasebeta

← C2×#13078986 #15623026

Subgroups — C2×#13078986 #15623026

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2#13078986C2116yesmaximal, direct product factor
3C2×#10622682C212yesmaximal, complemented
4C2×#10622702C212yesmaximal, complemented
5C2×#10622681C212yesmaximal, complemented
6C2×#10622706C212yesmaximal, complemented
7C2×#10622579C211yesmaximal, characteristic
8C2×#10622617C211yesmaximal, characteristic, complemented
9C2×#10622615C211yesmaximal, characteristic
10C22×#66874C211yesmaximal, characteristic, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#544C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C11×#544—24no—
16C11×#544C2218yescomplemented
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#125—21no—
20C2×C11×#125C2212yes—
21C2×C11×C22⋊Q8—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623057—24no—
28#10623057C2218yes—
29C2×#66950—21no—
30C2×#66950—21no—
31C2×#66939—22no—
32C2×#66928C2212yes—
33C2×#66922C2212yes—
34#10622706C22116yescomplemented
35#10622702C22116yescomplemented
36#10622682C22116yescomplemented
37#10622681C22116yescomplemented
38#10622617C2218yescomplemented
39#10622615C2218yes—
40#10622610C2218yescomplemented
41C2×#66874C2212yes—
42C2×#66874C2212yes—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48C2×#66874C2218yescomplemented
49#10622579C2218yes—
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11—22no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C23×Dic11—21no—
60C2×#4339—22no—
61C2×#4339—24no—
62C2×#4339—24no—
63C2×#4339C2314yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22—24no—
67C22×Dic22—24no—
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×Dic22C2311yescharacteristic
71C22×Dic22C2312yes—
72C22×Dic22C2314yes—
73C11×C4⋊Q8—28no—
74C11×C4⋊Q8—24no—
75C11×C4⋊Q8C2318yes—
76C11×#125—28no—
77C11×#125—24no—
78C11×#125C2318yes—
79C11×C22⋊Q8—216no—
80C11×#117—22no—
81C11×#117D414yes—
82C11×#117C2314yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11—21no—
98C2×C42×C11C2312yes—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×#4318—24no—
104C2×#4318C2314yes—
105C22×C11⋊C8—24no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66950—28no—
111#66950—28no—
112#66939—216no—
113#66928—24no—
114#66928C2318yes—
115#66922—24no—
116#66922C2318yes—
117#66874C2318yes—
118#66874C2318yes—
119#66874C2318yes—
120#66874C2314yes—
121#66874C2314yes—
122#66874C2318yes—
123#66874C2318yes—
124#66873C2318yes—
125#66873C2314yes—
126#66873C2314yes—
127#66867C2318yes—
128C4×C11⋊C8C2318yes—
129C2×#3137—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—21no—
132C2×Q8×C11—28no—
133C2×Q8×C11—84no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—82no—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4114yes—
144C22×C4×C11#4114yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2412yes—
147C2×C22⋊D11—24no—
148C2×C22⋊D11—44no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—44no—
153#4339—28no—
154#4339—28no—
155#4339—48no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44C2412yes—
160C2×C4×D11—24no—
161C2×C4×D11—44no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—28no—
168C2×Dic22—28no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—44no—
172C2×Dic22—48no—
173C2×Dic22C2412yes—
174C2×Dic22C2414yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D414yes—
183C11×C4⋊C4C2×D414yes—
184C11×C4⋊C4C2414yes—
185C11×C4⋊C4C2412yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4C2×D418yes—
189C42×C11—24no—
190C42×C11C2×D414yes—
191C42×C11C2414yes—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—28no—
195C4⋊Dic11—28no—
196#4318—28no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—28no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×C11⋊C8C2412yes—
204C2×#544D1111yescharacteristic, complemented
205C2×#536—111no—
206#3137—1116no—
207C2×#491—112no—
208C2×#489—112no—
209C2×#488—112no—
210C2×#487—112no—
211C2×#417—111no—
212C2×#419—111no—
213C2×#416—111no—
214C22×#103—111no—
215C2×#405—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11#12414yes—
219C23×C11C22×D412yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225Q8×C11—88no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—84no—
235C2×C4×C11#12414yes—
236C2×C4×C11#12418yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4112yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2×#4114yes—
245C2×C4×C11C2511yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—48no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252D44—22no—
253D44—22no—
254D44—42no—
255C4×D11—48no—
256Dic22—24no—
257Dic22—24no—
258Dic22—22no—
259Dic22—22no—
260Dic22—44no—
261Dic22—48no—
262Dic22—42no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C11⋊C8—24no—
266C22×#41—111no—
267C23×Q8—111no—
268C22×M16—111no—
269C23×C8—111no—
270#544—24no—
271#544C2×D1118yescomplemented
272#536—118no—
273#536—224no—
274C2×C4⋊Q8—21no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8C2×D1112yes—
277C2×#125—21no—
278C2×#125C2×D1112yes—
279C2×#124—112no—
280C2×#123—222no—
281C2×C22⋊Q8—22no—
282C2×C22⋊Q8—221no—
283C2×C22⋊Q8—221no—
284C2×#117C2×D1111yescharacteristic
285C2×#117C2×D1111yescharacteristic
286C22×C4⋊C4C2×D1111yescharacteristic
287#491—1116no—
288#489—1116no—
289#488—1116no—
290#487—1116no—
291#419—118no—
292#417—118no—
293#416—118no—
294C2×#103—111no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—111no—
301C2×#103—118no—
302C2×#102—111no—
303C2×#102—112no—
304C2×#102—111no—
305#405—118no—
306C2×#97—112no—
307C2×C4×C8—112no—
308C22×C11—28no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11C2×#12414yes—
312C22×C11C2×#12412yes—
313C22×C11#57712yes—
314C22×C11#57812yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—84no—
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11C2×#12412yes—
326C4×C11C2×#12414yes—
327C4×C11C22×#4111yescharacteristic
328C4×C11C22×#4111yescharacteristic
329Dic11—44no—
330Dic11—42no—
331C2×#41—114no—
332C2×#41—222no—
333C2×#41—224no—
334C2×#41—224no—
335C22×Q8—22no—
336C22×Q8—112no—
337C22×Q8—111no—
338C22×Q8—114no—
339C22×Q8—221no—
340C22×Q8—222no—
341C22×Q8—224no—
342C22×Q8—224no—
343C22×D4—111no—
344C22×D4—221no—
345C23×C4—21no—
346C23×C4—221no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C2×M16—114no—
350C2×M16—224no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—114no—
354C22×C8—112no—
355C22×C8—224no—
356C4⋊Q8—28no—
357C4⋊Q8—24no—
358C4⋊Q8—118no—
359C4⋊Q8—224no—
360C4⋊Q8C22×D1118yes—
361#125—28no—
362#125—24no—
363#125C22×D1118yes—
364#124—118no—
365#124—224no—
366#123—2216no—
367C22⋊Q8—216no—
368C22⋊Q8—228no—
369C22⋊Q8—228no—
370#117—22no—
371#117C22⋊D1114yes—
372#117C22×D1114yes—
373#117C22×D1114yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1114yes—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4C22⋊D1112yes—
391C2×C42—21no—
392C2×C42C22×D1112yes—
393#103—118no—
394#103—118no—
395#103—114no—
396#103—114no—
397#103—118no—
398#103—118no—
399#103—118no—
400#102—114no—
401#102—114no—
402#102—118no—
403#97—118no—
404C4×C8—118no—
405C2×C11—24no—
406C2×C11#313714yescomplemented
407C2×C11C22×#12411yescharacteristic
408C2×C11C2×#57711yescharacteristic
409C2×C11C2×#57811yescharacteristic
410D11—82no—
411C24—221no—
412C24C2×C22⋊D1111yescharacteristic
413#41—228no—
414#41—228no—
415#41—448no—
416C2×Q8—28no—
417C2×Q8—84no—
418C2×Q8—114no—
419C2×Q8—112no—
420C2×Q8—224no—
421C2×Q8—222no—
422C2×Q8—221no—
423C2×Q8—224no—
424C2×Q8—224no—
425C2×Q8—228no—
426C2×Q8—228no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×Q8—444no—
430C2×Q8—448no—
431C2×D4—112no—
432C2×D4—224no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—221no—
436C2×D4—444no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—82no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—444no—
447C22×C4—444no—
448C22×C4#434314yes—
449C22×C4#434314yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1112yes—
455C22×C4C23×D1111yescharacteristic
456M16—228no—
457C2×C8—112no—
458C2×C8—114no—
459C2×C8—112no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—228no—
463C2×C8—224no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—28no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—228no—
472C4⋊C4—228no—
473C4⋊C4C2×C22⋊D1114yes—
474C4⋊C4C2×C22⋊D1114yes—
475C4⋊C4C23×D1114yes—
476C4⋊C4C23×D1112yes—
477C4⋊C4C23×D1112yes—
478C22⋊C4—24no—
479C22⋊C4—228no—
480C22⋊C4—228no—
481C22⋊C4C2×C22⋊D1118yes—
482C42—24no—
483C42C2×C22⋊D1114yes—
484C42C23×D1114yes—
485C11C2×#313711yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—222no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23#6700014yes—
493C23C22×C22⋊D1112yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—88no—
496Q8—224no—
497Q8—224no—
498Q8—222no—
499Q8—222no—
500Q8—448no—
501Q8—444no—
502Q8—442no—
503D4—222no—
504D4—222no—
505D4—448no—
506D4—442no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—442no—
519C2×C4—448no—
520C2×C4—444no—
521C2×C4—448no—
522C2×C4#6700014yes—
523C2×C4#6700018yes—
524C2×C4C2×#434312yes—
525C2×C4C2×#434312yes—
526C2×C4C2×#434314yes—
527C2×C4C2×#434314yes—
528C2×C4C22×C22⋊D1114yes—
529C2×C4C22×C22⋊D1114yes—
530C2×C4C22×C22⋊D1112yes—
531C2×C4C22×C22⋊D1111yescharacteristic
532C2×C4C24×D1111yescharacteristic
533C8—222no—
534C8—222no—
535C8—224no—
536C22—28no—
537C22—22no—
538C22—22no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—884no—
543C22C2×#6700014yes—
544C22C2×#6700012yes—
545C22#1062336712yes—
546C22#1062336912yes—
547C22C23×C22⋊D1111yescharacteristic
548C4—24no—
549C4—24no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—442no—
554C4—444no—
555C4C2×#6700014yes—
556C4C2×#6700012yes—
557C4C22×#434311yescharacteristic
558C4C22×#434311yescharacteristic
559C2—24no—
560C2—882no—
561C2#1307898614yesdirect product factor
562C2C22×#6700011yescharacteristic
563C2C2×#1062336711yescharacteristic
564C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#544D11
hypocenterC11C2×#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13078986C2direct (N × H)
3. C2×#10622682C2semidirect
4. C2×#10622702C2semidirect
5. C2×#10622681C2semidirect
6. C2×#10622706C2semidirect
8. C2×#10622617C2semidirect
10. C22×#66874C2semidirect
11. C2×#10622610C2semidirect
12. C2×C11×#544C2semidirect
16. C11×#544C22semidirect
34. #10622706C22semidirect
35. #10622702C22semidirect
36. #10622682C22semidirect
37. #10622681C22semidirect
38. #10622617C22semidirect
40. #10622610C22semidirect
48. C2×#66874C22semidirect
204. C2×#544D11semidirect
271. #544C2×D11semidirect
406. C2×C11#3137semidirect
485. C11C2×#3137semidirect
561. C2#13078986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230572
#130789862
C2×#106226822
C2×#106227022
C2×#106226812
C2×#106227062
C2×#106225792
C2×#106226172
C2×#106226152
C22×#668742
C2×#106226102
C2×C11×#5442
C2×#313711