Finite Group Databasebeta

← C2×#13081592 #15634669

Subgroups — C2×#13081592 #15634669

Order 2816.

2238 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×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081592C2116yesmaximal, direct product factor
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622788C212yesmaximal, complemented
6C2×#10622461C211yesmaximal, characteristic, complemented
7C2×#10622776C212yesmaximal, complemented
8C2×#10622431C212yesmaximal, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4324C211yesmaximal, characteristic, complemented
11C2×#10622401C212yesmaximal, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×Q8×Dic11C2212yes—
18C2×#66997C2212yes—
19C22×#4325C2212yes—
20C22×#4325C2212yes—
21C2×#66993C2212yes—
22C22×#4324C2211yescharacteristic
23C2×#66983—21no—
24C22×#4314C2212yes—
25#10623252—24no—
26#10623252C2218yescomplemented
27#10623084—24no—
28#10623084C2218yes—
29C2×#66946C2212yes—
30C2×#66943—21no—
31C2×#66942—22no—
32C2×#66940—21no—
33C2×#66937—22no—
34C2×#66927C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#461C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66896C2211yescharacteristic
41#10622788C22116yescomplemented
42#10622776C22116yescomplemented
43C2×#66885C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622698C2218yescomplemented
47C4×#4324C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622461C2218yescomplemented
52#10622443C2218yescomplemented
53#10622431C22116yescomplemented
54#10622401C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×C4×D11—22no—
66C22×Dic22D411yescharacteristic
67C22×Dic22C2311yescharacteristic
68C2×C11×SD16—44no—
69C2×C11×SD16C2318yes—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C4×D4×C11—22no—
74C4×D4×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80Q8×Dic11—24no—
81Q8×Dic11C2318yes—
82#66997—24no—
83#66997C2318yes—
84C2×#4325—28no—
85C2×#4325—44no—
86C2×#4325C2318yes—
87C2×#4325C2318yes—
88#66993—24no—
89#66993C2318yes—
90C2×#4324—24no—
91C2×#4324C2314yes—
92#66983—28no—
93C2×(C2×D11)⋊C4—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4D412yes—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2312yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4314—44no—
107C2×#4314C2318yes—
108#66946—24no—
109#66946C2318yes—
110#66943—28no—
111#66942—216no—
112#66940—28no—
113#66937—216no—
114#66927—22no—
115#66927C2314yes—
116C4×Dic22—22no—
117C4×Dic22D414yes—
118C4×Dic22C2314yes—
119C4×Dic22C2314yes—
120C11×C4⋊C8C2314yes—
121C11×#103C2318yes—
122#66896C2314yes—
123#66885C2318yes—
124Dic11⋊C8C2318yes—
125C8×Dic11C2318yes—
126#66874C2314yes—
127#66872C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3392—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11C2414yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2412yes—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—84no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155#4339—432no—
156C2×D44—22no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—44no—
162C2×D44—82no—
163C2×D44C2414yes—
164C2×C4×D11—28no—
165C2×C4×D11—48no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22SD1618yescomplemented
170C2×Dic22C2×D414yes—
171C2×Dic22C2412yes—
172C11×SD16—48no—
173C2×C8×C11—24no—
174C2×C8×C11C2414yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C22⋊C4—24no—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182#4325—216no—
183#4325—48no—
184#4324—28no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—28no—
187C4⋊Dic11—21no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2412yes—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192Dic11⋊C4—24no—
193Dic11⋊C4C2×D418yes—
194C4×Dic11—28no—
195C4×Dic11—24no—
196C4×Dic11C2×D414yes—
197C4×Dic11C2414yes—
198C2×C11⋊C8—22no—
199C2×C11⋊C8#4114yescomplemented
200C2×C11⋊C8C2412yes—
201C2×C11⋊C8C2412yes—
202#4314—48no—
203C2×#557—111no—
204C2×#550—111no—
205#3392—1116no—
206C2×#492—112no—
207C2×#492—111no—
208C2×#460—111no—
209C2×#460—112no—
210C2×#461—112no—
211C2×#461D1111yescharacteristic, complemented
212C2×C8×Q8—111no—
213C2×C4×SD16—112no—
214C2×C4×SD16—111no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—44no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—48no—
236C2×C4×C11C2×SD1614yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C11H(5,𝔽2)12yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—416no—
244C22⋊D11—88no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11C2×SD1618yes—
251C2×Dic11C22×D414yes—
252C2×Dic11C22×D414yes—
253D44—24no—
254D44—24no—
255D44—44no—
256D44—48no—
257D44—84no—
258C4×D11—416no—
259Dic22—22no—
260Dic22—22no—
261Dic22—42no—
262Dic22C2×SD16116yescomplemented
263C8×C11—24no—
264C11⋊C8—22no—
265C11⋊C8C2×#4114yescomplemented
266C22×#41—221no—
267C22×SD16—112no—
268C22×SD16—111no—
269C22×SD16—112no—
270C22×SD16—112no—
271C22×SD16C2×D1112yes—
272#557—118no—
273#557—224no—
274#550—118no—
275#550—224no—
276C2×C4⋊Q8—112no—
277C2×C4⋊Q8C2×D1111yescharacteristic
278C2×#127—112no—
279C2×#127—111no—
280C2×#125—222no—
281C2×#125—221no—
282C2×#121—222no—
283C2×#121—221no—
284C2×C4×Q8—111no—
285C2×C4×Q8—112no—
286C2×C4×Q8—111no—
287C2×C4×Q8—221no—
288C2×C4×D4—112no—
289C2×C4×D4C2×D1111yescharacteristic
290#492—1116no—
291#492—118no—
292#461—1116no—
293#461C2×D1118yescomplemented
294#460—1116no—
295#460—118no—
296C8×Q8—118no—
297C4×SD16—118no—
298C4×SD16—1116no—
299C2×#106—111no—
300C2×C4⋊C8—112no—
301C2×C4⋊C8C2×D1111yescharacteristic
302C2×#103—111no—
303C2×#103C2×D1112yes—
304C2×#102—111no—
305C2×#102—112no—
306C2×C4×C8—112no—
307C2×C4×C8—111no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—84no—
312C22×C11#55012yes—
313C22×C11C22×SD1612yes—
314C22×C11#57712yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—88no—
320C4×C11—22no—
321C4×C11—44no—
322C4×C11—42no—
323C4×C11#55012yes—
324C4×C11C22×SD1614yes—
325C4×C11C22×#4111yescharacteristic
326C4×C11C2×H(5,𝔽2)11yescharacteristic
327Dic11—24no—
328Dic11—42no—
329Dic11—42no—
330Dic11C22×SD1618yes—
331C2×#41—228no—
332C2×#41—448no—
333C22×Q8—111no—
334C22×Q8—111no—
335C22×Q8C22×D1112yes—
336C22×D4—112no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—222no—
344C2×SD16—44no—
345C2×SD16—118no—
346C2×SD16—114no—
347C2×SD16—118no—
348C2×SD16—118no—
349C2×SD16—224no—
350C2×SD16—228no—
351C2×SD16—444no—
352C2×SD16—444no—
353C2×SD16C22×D1118yes—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8C22×D1112yes—
357C4⋊Q8—22no—
358C4⋊Q8—118no—
359C4⋊Q8—224no—
360C4⋊Q8C22×D1114yes—
361#127—118no—
362#127—114no—
363#127—224no—
364#127—222no—
365#125—2216no—
366#125—228no—
367#121—2216no—
368#121—228no—
369C4×Q8—114no—
370C4×Q8—114no—
371C4×Q8—118no—
372C4×Q8—114no—
373C4×Q8—224no—
374C4×Q8—228no—
375C4×Q8—222no—
376C4×D4—22no—
377C4×D4—118no—
378C4×D4—224no—
379C4×D4C22×D1114yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—222no—
392C2×C42—112no—
393C2×C42—222no—
394C2×C42—221no—
395C2×C42C22×D1111yescharacteristic
396#106—114no—
397C4⋊C8—118no—
398C4⋊C8C22×D1114yes—
399#103—114no—
400#103C22×D1118yes—
401#102—114no—
402#102—118no—
403C4×C8—118no—
404C4×C8—114no—
405C2×C11—82no—
406C2×C11#339214yescomplemented
407C2×C11C2×#55011yescharacteristic
408C2×C11C23×SD1611yescharacteristic
409C2×C11C2×#57711yescharacteristic
410D11—84no—
411C24—21no—
412C24—222no—
413#41—4432no—
414C2×Q8—22no—
415C2×Q8—24no—
416C2×Q8—24no—
417C2×Q8—118no—
418C2×Q8—114no—
419C2×Q8—112no—
420C2×Q8—221no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8C23×D1114yes—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—222no—
431C2×D4—224no—
432C2×D4—224no—
433C2×D4—224no—
434C2×D4—224no—
435C2×D4—448no—
436C2×D4—444no—
437C2×D4—882no—
438C2×D4—884no—
439C2×D4C23×D1112yes—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—44no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—228no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—448no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453SD16—48no—
454SD16—228no—
455SD16—2216no—
456SD16—448no—
457SD16—448no—
458C2×C8—24no—
459C2×C8—114no—
460C2×C8—112no—
461C2×C8—112no—
462C2×C8—222no—
463C2×C8C23×D1114yes—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—118no—
468C4⋊C4—114no—
469C4⋊C4—112no—
470C4⋊C4—228no—
471C4⋊C4—228no—
472C4⋊C4—228no—
473C4⋊C4—221no—
474C4⋊C4—224no—
475C4⋊C4C23×D1112yes—
476C22⋊C4—24no—
477C22⋊C4—228no—
478C42—114no—
479C42—114no—
480C42—228no—
481C42—224no—
482C42D4×D1112yes—
483C42C23×D1112yes—
484C11C2×#339211yescharacteristic, complemented, Sylow
485C23—22no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—224no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23C2×D4×D1111yescharacteristic
494Q8—24no—
495Q8—24no—
496Q8—44no—
497Q8—1116no—
498Q8—222no—
499Q8—222no—
500Q8—442no—
501D4—22no—
502D4—22no—
503D4—42no—
504D4—224no—
505D4—224no—
506D4—4416no—
507D4—448no—
508D4—444no—
509D4—884no—
510D4—888no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—48no—
517C2×C4—118no—
518C2×C4—114no—
519C2×C4—114no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—4416no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4SD16×D1114yes—
527C2×C4C2×D4×D1112yes—
528C2×C4C2×D4×D1112yes—
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4#6703712yes—
531C2×C4#41×D1112yes—
532C2×C4C24×D1111yescharacteristic
533C8—24no—
534C8—114no—
535C8—222no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—84no—
540C22—444no—
541C22—444no—
542C22—444no—
543C22—888no—
544C22#1062313012yes—
545C22C2×SD16×D1112yes—
546C22#1062330912yes—
547C22C22×D4×D1111yescharacteristic
548C4—22no—
549C4—42no—
550C4—44no—
551C4—118no—
552C4—224no—
553C4—442no—
554C4—442no—
555C4#1062313012yes—
556C4C2×SD16×D1114yes—
557C4C2×#6703711yescharacteristic
558C4C2×#41×D1111yescharacteristic
559C2—82no—
560C2—884no—
561C2#1308159214yesdirect product factor
562C2C2×#1062313011yescharacteristic
563C2C22×SD16×D1111yescharacteristic
564C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#461D11
hypocenterC11C2×#3392
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081592C2direct (N × H)
4. C2×#10622698C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622461C2semidirect
7. C2×#10622776C2semidirect
8. C2×#10622431C2semidirect
9. C2×#10622443C2semidirect
10. C2×C4×#4324C2semidirect
11. C2×#10622401C2semidirect
12. C2×C11×#461C2semidirect
26. #10623252C22semidirect
37. C11×#461C22semidirect
41. #10622788C22semidirect
42. #10622776C22semidirect
46. #10622698C22semidirect
47. C4×#4324C22semidirect
51. #10622461C22semidirect
52. #10622443C22semidirect
53. #10622431C22semidirect
54. #10622401C22semidirect
169. C2×Dic22SD16semidirect
199. C2×C11⋊C8#41semidirect
211. C2×#461D11semidirect
262. Dic22C2×SD16semidirect
265. C11⋊C8C2×#41semidirect
293. #461C2×D11semidirect
406. C2×C11#3392semidirect
484. C11C2×#3392semidirect
561. C2#13081592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106230842
#130815922
C2×#106226982
C2×#106227882
C2×#106224612
C2×#106227762
C2×#106224312
C2×#106224432
C2×C4×#43242
C2×#106224012
C2×C11×#4612
C2×#339211