Finite Group Databasebeta

← C2×#13078977 #15623017

Subgroups — C2×#13078977 #15623017

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×#10623050C211yesmaximal, characteristic, complemented
2C2×#10623347C211yesmaximal, characteristic
3#13078977C2116yesmaximal, direct product factor
4C2×#10622410C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622413C212yesmaximal, complemented
7C2×#10622405C212yesmaximal, complemented
8C2×#10622746C211yesmaximal, characteristic
9C2×#10622615C211yesmaximal, characteristic
10C22×#66899C211yesmaximal, characteristic, complemented
11C2×#10622735C211yesmaximal, characteristic, complemented
12C2×C11×#419C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623347—24no—
18#10623347C2218yes—
19C2×#67000C2212yes—
20C2×#66999—21no—
21C2×#66999—21no—
22C2×#66997C2212yes—
23C2×#66982—22no—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623050—24no—
28#10623050C2218yescomplemented
29C2×#66943C2212yes—
30C2×#66941C2212yes—
31C2×#66931—22no—
32C2×#66923—21no—
33C2×#66922—21no—
34C11×#419C2218yescomplemented
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2218yescomplemented
40#10622746C2218yes—
41#10622735C2218yescomplemented
42C2×#66885C2212yes—
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45C2×C8×Dic11C2212yes—
46#10622615C2218yes—
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622413C22116yescomplemented
52#10622410C22116yescomplemented
53#10622408C22116yescomplemented
54#10622405C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—24no—
58C22×Q8×C11—24no—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2314yes—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C2×#4339—22no—
66C2×#4339—24no—
67C2×#4339—24no—
68C2×#4339C2314yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22—22no—
72C22×Dic22C2311yescharacteristic
73C2×C11×M16—24no—
74C2×C11×M16C2314yes—
75C22×C8×C11C2312yes—
76C11×#117—22no—
77C11×#117C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11D412yes—
83#67000—24no—
84#67000C2318yes—
85#66999—28no—
86#66999—28no—
87#66997—24no—
88#66997C2318yes—
89#66982—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92#66979D414yes—
93#66979C2314yes—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11C2312yes—
106C22×C11⋊C8—24no—
107C22×C11⋊C8C2314yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66943—24no—
111#66943C2318yes—
112#66941—24no—
113#66941C2318yes—
114#66931—216no—
115#66923—28no—
116#66922—28no—
117C11×#103C2318yes—
118C11×#103C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121#66885C2318yes—
122#66880C2318yes—
123#66879C2318yes—
124C8×Dic11C2318yes—
125#66874C2314yes—
126#66874C2314yes—
127#66873C2314yes—
128#66873C2314yes—
129C2×#3137—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11—28no—
136C2×Q8×C11—24no—
137C2×Q8×C11—28no—
138C2×Q8×C11—44no—
139C2×Q8×C11—48no—
140C2×Q8×C11C2414yes—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4114yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2412yes—
152C2×C22⋊D11—24no—
153C2×C22⋊D11—44no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—82no—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160#4339—28no—
161#4339—28no—
162#4339—48no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×Dic22—28no—
170C2×Dic22—21no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—84no—
174C2×Dic22C2412yes—
175C11×M16—28no—
176C2×C8×C11—24no—
177C2×C8×C11C2414yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2412yes—
181C11×C4⋊C4C2412yes—
182C11×C22⋊C4—24no—
183C42×C11—24no—
184C22⋊Dic11C2×D418yes—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187C4⋊Dic11—28no—
188C4⋊Dic11—24no—
189C4⋊Dic11—22no—
190C4⋊Dic11C2×D414yes—
191C4⋊Dic11C2×D414yes—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197C4×Dic11C2×D414yes—
198C4×Dic11C2414yes—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—28no—
202C2×C11⋊C8C2412yes—
203C2×C11⋊C8C2412yes—
204C2×#544—111no—
205C2×#536—111no—
206#3137—1116no—
207C2×#491—112no—
208C2×#489—112no—
209C2×#488—112no—
210C2×#487—112no—
211C2×#417—111no—
212C2×#419D1111yescharacteristic, complemented
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—24no—
226Q8×C11—24no—
227Q8×C11—44no—
228Q8×C11—48no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—48no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12414yes—
237C2×C4×C11#12418yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C11C2×#4114yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2511yescharacteristic
245C22⋊D11—48no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—42no—
251C2×Dic11—44no—
252C2×Dic11—84no—
253C2×Dic11C22×D414yes—
254C2×Dic11C22×D414yes—
255D44—22no—
256D44—22no—
257D44—42no—
258C4×D11—48no—
259Dic22—22no—
260Dic22—22no—
261Dic22—42no—
262Dic22—88no—
263C8×C11—24no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C22×#41—111no—
267C23×Q8C2×D1111yescharacteristic
268C22×M16C2×D1111yescharacteristic
269C23×C8—111no—
270#544—118no—
271#544—224no—
272#536—118no—
273#536—224no—
274C2×C4⋊Q8—112no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8—221no—
277C2×#125—112no—
278C2×#125—221no—
279C2×#124—112no—
280C2×#123—222no—
281C2×C22⋊Q8—222no—
282C2×C22⋊Q8—221no—
283C2×C22⋊Q8—221no—
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287#491—1116no—
288#489—1116no—
289#488—1116no—
290#487—1116no—
291#419C2×D1118yescomplemented
292#417—118no—
293#416—118no—
294C2×#103—112no—
295C2×#103—112no—
296C2×#103—118no—
297C2×#103—112no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103C2×D1112yes—
301C2×#103C2×D1112yes—
302C2×#102—112no—
303C2×#102—111no—
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—44no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11C2×#12412yes—
324C4×C11C2×#12414yes—
325C4×C11C22×#4111yescharacteristic
326C4×C11C22×#4111yescharacteristic
327Dic11—24no—
328Dic11—24no—
329Dic11—42no—
330Dic11—44no—
331C2×#41—114no—
332C2×#41—222no—
333C2×#41—224no—
334C2×#41—224no—
335C22×Q8—21no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8—111no—
340C22×Q8—222no—
341C22×Q8C22×D1112yes—
342C22×Q8C22×D1114yes—
343C22×D4—111no—
344C22×D4—221no—
345C23×C4—21no—
346C23×C4—221no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C2×M16—24no—
350C2×M16C22×D1114yes—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—114no—
354C22×C8—224no—
355C22×C8C22×D1112yes—
356C4⋊Q8—118no—
357C4⋊Q8—118no—
358C4⋊Q8—228no—
359C4⋊Q8—224no—
360C4⋊Q8—224no—
361#125—118no—
362#125—228no—
363#125—224no—
364#124—118no—
365#124—224no—
366#123—2216no—
367C22⋊Q8—2216no—
368C22⋊Q8—228no—
369C22⋊Q8—228no—
370#117—22no—
371#117—114no—
372#117—114no—
373#117C22×D1114yes—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C42—21no—
392C2×C42—112no—
393#103—118no—
394#103—118no—
395#103—118no—
396#103—114no—
397#103—114no—
398#103C22×D1118yes—
399#103C22×D1118yes—
400#102—118no—
401#102—114no—
402#102—114no—
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—
412C24D4×D1111yescharacteristic
413#41—228no—
414#41—228no—
415#41—448no—
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—24no—
419C2×Q8—28no—
420C2×Q8—24no—
421C2×Q8—28no—
422C2×Q8—44no—
423C2×Q8—48no—
424C2×Q8—112no—
425C2×Q8—228no—
426C2×Q8—221no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×Q8—884no—
430C2×Q8C23×D1114yes—
431C2×D4—112no—
432C2×D4—224no—
433C2×D4—222no—
434C2×D4—221no—
435C2×D4—222no—
436C2×D4—444no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—444no—
449C22×C4—882no—
450C22×C4#433914yes—
451C22×C4D4×D1112yes—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434114yes—
454C22×C4C23×D1112yes—
455C22×C4C23×D1111yescharacteristic
456M16—28no—
457C2×C8—24no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—228no—
463C2×C8C23×D1114yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—114no—
467C4⋊C4—114no—
468C4⋊C4—114no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C4⋊C4—228no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—224no—
475C4⋊C4—222no—
476C4⋊C4C23×D1112yes—
477C4⋊C4C23×D1112yes—
478C22⋊C4—24no—
479C22⋊C4—118no—
480C22⋊C4—228no—
481C22⋊C4—228no—
482C42—24no—
483C42—114no—
484C42—114no—
485C11C2×#313711yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—222no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23#6693814yes—
493C23C2×D4×D1112yes—
494C23C2×D4×D1111yescharacteristic
495Q8—24no—
496Q8—24no—
497Q8—48no—
498Q8—44no—
499Q8—222no—
500Q8—222no—
501Q8—442no—
502Q8—888no—
503D4—222no—
504D4—222no—
505D4—448no—
506D4—442no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—48no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—442no—
521C2×C4—444no—
522C2×C4—448no—
523C2×C4—884no—
524C2×C4#6693814yes—
525C2×C4#6693818yes—
526C2×C4C2×#433912yes—
527C2×C4C2×#433914yes—
528C2×C4C2×D4×D1112yes—
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434112yes—
531C2×C4C2×#434114yes—
532C2×C4C24×D1111yescharacteristic
533C8—24no—
534C8—222no—
535C8—222no—
536C22—28no—
537C22—22no—
538C22—22no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—884no—
543C22C2×#6693814yes—
544C22C2×#6693812yes—
545C22#1062330912yes—
546C22#1062331012yes—
547C22C22×D4×D1111yescharacteristic
548C4—44no—
549C4—42no—
550C4—42no—
551C4—224no—
552C4—224no—
553C4—442no—
554C4—444no—
555C4C2×#6693814yes—
556C4C2×#6693812yes—
557C4C22×#433911yescharacteristic
558C4C22×#434111yescharacteristic
559C2—24no—
560C2—882no—
561C2#1307897714yesdirect product factor
562C2C22×#6693811yescharacteristic
563C2C2×#1062330911yescharacteristic
564C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#419D11
hypocenterC11C2×#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13078977C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622405C2semidirect
10. C22×#66899C2semidirect
11. C2×#10622735C2semidirect
12. C2×C11×#419C2semidirect
28. #10623050C22semidirect
34. C11×#419C22semidirect
39. C2×#66899C22semidirect
41. #10622735C22semidirect
51. #10622413C22semidirect
52. #10622410C22semidirect
53. #10622408C22semidirect
54. #10622405C22semidirect
212. C2×#419D11semidirect
291. #419C2×D11semidirect
406. C2×C11#3137semidirect
485. C11C2×#3137semidirect
561. C2#13078977direct (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×#106233472
#130789772
C2×#106224102
C2×#106224082
C2×#106224132
C2×#106224052
C2×#106227462
C2×#106226152
C22×#668992
C2×#106227352
C2×C11×#4192
C2×#313711