Finite Group Databasebeta

← C2×#13080541 #15630221

Subgroups — C2×#13080541 #15630221

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic, complemented
3#13080541C2116yesmaximal, direct product factor
4C2×#10622706C211yesmaximal, characteristic, complemented
5C2×#10622480C212yesmaximal, complemented
6C2×#10622477C212yesmaximal, complemented
7C2×#10622454C211yesmaximal, characteristic, complemented
8C2×#10622394C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×#10622385C212yesmaximal, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×#4341C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000—22no—
17C22×#4323C2211yescharacteristic
18C2×#66983—21no—
19C22×C4⋊Dic11—21no—
20C22×#4314C2212yes—
21C22×C8×D11C2212yes—
22#10623265—24no—
23#10623265C2218yescomplemented
24#10623086—24no—
25#10623086C2218yescomplemented
26C2×#66950C2212yes—
27C2×#66948—21no—
28C2×#66948C2212yes—
29C2×#66945—21no—
30C2×#66945C2212yes—
31C2×#66939—22no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C11×#476C2218yescomplemented
36C2×C11×#106C2212yes—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102C2212yes—
39C2×#66896C2211yescharacteristic
40C2×(C2×D11)⋊C8C2212yes—
41C2×#66880C2212yes—
42#10622706C2218yescomplemented
43C4×#4323C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622480C22116yescomplemented
50#10622477C22116yescomplemented
51#10622454C2218yescomplemented
52#10622447C2218yescomplemented
53#10622394C22116yescomplemented
54#10622385C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C23×Dic11—22no—
60C2×#4341—28no—
61C2×#4341—24no—
62C2×#4341—44no—
63C2×#4341C2318yes—
64C22×D44—22no—
65C22×D44D411yescharacteristic
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11C2312yes—
69C22×Dic22C2312yes—
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⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80#67000—216no—
81C2×#4323—24no—
82C2×#4323C2314yes—
83#66983—28no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4D412yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—28no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4×Dic11—22no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×#4314—44no—
99C2×#4314C2318yes—
100C2×C8×D11—44no—
101C2×C8×D11C2318yes—
102#66950—24no—
103#66950C2318yes—
104#66948—28no—
105#66948—24no—
106#66948C2318yes—
107#66945—24no—
108#66945—28no—
109#66945C2318yes—
110#66939—216no—
111C4×D44—22no—
112C4×D44D414yes—
113C4×D44C2314yes—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117C11×#106C2318yes—
118C11×C4⋊C8C2314yes—
119C11×#102C2318yes—
120#66896C2314yes—
121(C2×D11)⋊C8C2318yes—
122#66880C2318yes—
123#66874C2318yes—
124#66874C2318yes—
125#66873C2314yes—
126#66871C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3303—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—21no—
131C23×D11C2×D412yes—
132C2×Q8×C11—24no—
133C2×Q8×C11—82no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11#4114yes—
137C2×D4×C11C2412yes—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C22×Dic11—28no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—48no—
151C22×Dic11C2×D412yes—
152#4341—216no—
153#4341—48no—
154#4341—416no—
155C2×D44—28no—
156C2×D44—24no—
157C2×D44—21no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—84no—
161C2×D44C2×D414yes—
162C2×D44C2412yes—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—24no—
166C2×C4×D11—44no—
167C2×C4×D11C2×D414yes—
168C2×C4×D11C2414yes—
169C2×Dic22—22no—
170C2×Dic22—24no—
171C2×Dic22—24no—
172C2×Dic22C2414yes—
173C2×C8×C11—24no—
174C2×C8×C11C2414yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2414yes—
180C11×C22⋊C4—24no—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183#4323—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4C2×D418yes—
189C4⋊Dic11—28no—
190C4⋊Dic11—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2×D414yes—
194C4⋊Dic11C2412yes—
195C4×Dic11—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4314—48no—
201C8×D11—48no—
202C2×#555—111no—
203C2×#547—111no—
204#3303—1116no—
205C2×#487—111no—
206C2×#485—112no—
207C2×#476D1111yescharacteristic, complemented
208C2×#465—112no—
209C2×#461—111no—
210C2×#449—112no—
211C2×C4×D8—111no—
212C2×C8×D4—111no—
213C2×#416—112no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11C22×D411yescharacteristic
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11C22×D414yes—
227Q8×C11—84no—
228D4×C11—24no—
229D4×C11—22no—
230D4×C11C2×#4114yes—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—48no—
237C2×C4×C11#13514yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C2×C4×C11C2511yescharacteristic
244C22⋊D11—416no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—416no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11C22×D414yes—
252D44—28no—
253D44—22no—
254D44—22no—
255D44—42no—
256D44—88no—
257C4×D11—28no—
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—48no—
261Dic22—24no—
262Dic22—24no—
263Dic22—44no—
264C8×C11—24no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×#41—112no—
268C22×SD16—112no—
269C22×D8—111no—
270C23×C8—112no—
271#555—118no—
272#555—224no—
273#547—118no—
274#547—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8C2×D1111yescharacteristic
277C2×#124—222no—
278C2×#123—222no—
279C2×C22⋊Q8—112no—
280C2×#121—112no—
281C2×#121—221no—
282C2×#121—221no—
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C2×#117—112no—
287C2×#117—221no—
288C22×C4⋊C4—221no—
289#487—118no—
290#485—1116no—
291#476C2×D1118yescomplemented
292#465—1116no—
293#461—118no—
294#449—1116no—
295C4×D8—118no—
296C8×D4—118no—
297C2×#107—111no—
298C2×#106C2×D1112yes—
299C2×C4⋊C8C2×D1111yescharacteristic
300#416—1116no—
301C2×#103—112no—
302C2×#103—112no—
303C2×#103—112no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102C2×D1112yes—
307C2×C22⋊C8—112no—
308C2×C4×C8—111no—
309C22×C11—24no—
310C22×C11—48no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11#54612yes—
314C22×C11C2×#13512yes—
315C22×C11#57712yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—48no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—84no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11#54612yes—
329C4×C11C2×#13514yes—
330C4×C11C22×#4111yescharacteristic
331C4×C11C2×H(5,𝔽2)11yescharacteristic
332Dic11—24no—
333Dic11—44no—
334Dic11—42no—
335C2×#41—118no—
336C2×#41—224no—
337C2×#41—228no—
338C2×#41—444no—
339C22×Q8—21no—
340C22×Q8—112no—
341C22×D4—111no—
342C22×D4—111no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C23×C4—112no—
348C23×C4—222no—
349C23×C4—221no—
350C2×SD16—118no—
351C2×SD16—444no—
352C2×D8—114no—
353C2×D8—224no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—118no—
357C22×C8—444no—
358C22×C8C22×D1112yes—
359C4⋊Q8—22no—
360C4⋊Q8—114no—
361C4⋊Q8—222no—
362C4⋊Q8C22×D1114yes—
363#124—2216no—
364#123—2216no—
365C22⋊Q8—118no—
366C22⋊Q8—224no—
367#121—118no—
368#121—224no—
369#121—228no—
370#121—228no—
371C4×D4—22no—
372C4×D4—114no—
373C4×D4—114no—
374C4×D4—114no—
375C4×D4—222no—
376C4×D4C22×D1114yes—
377#117—118no—
378#117—228no—
379#117—224no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—228no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22×D1112yes—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—221no—
395C2×C42—222no—
396C2×C42C22×D1111yescharacteristic
397#107—114no—
398#106C22×D1118yes—
399C4⋊C8C22×D1114yes—
400#103—118no—
401#103—118no—
402#103—118no—
403#102—114no—
404#102—114no—
405#102C22×D1118yes—
406C22⋊C8—118no—
407C4×C8—114no—
408C2×C11—44no—
409C2×C11#330314yescomplemented
410C2×C11C2×#54611yescharacteristic
411C2×C11C22×#13511yescharacteristic
412C2×C11C2×#57711yescharacteristic
413D11—44no—
414D11—82no—
415C24—21no—
416C24—112no—
417C24—221no—
418#41—2216no—
419#41—448no—
420#41—4416no—
421C2×Q8—24no—
422C2×Q8—82no—
423C2×Q8—114no—
424C2×Q8—222no—
425C2×Q8—224no—
426C2×Q8—224no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—114no—
430C2×D4—112no—
431C2×D4—228no—
432C2×D4—228no—
433C2×D4—224no—
434C2×D4—221no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—448no—
438C2×D4—884no—
439C2×D4#434314yes—
440C2×D4C23×D1112yes—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—44no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—228no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—448no—
455C22×C4—444no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459SD16—448no—
460D8—228no—
461C2×C8—24no—
462C2×C8—112no—
463C2×C8—112no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—448no—
467C2×C8C23×D1114yes—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—114no—
472C4⋊C4—112no—
473C4⋊C4—228no—
474C4⋊C4—221no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C4⋊C4C23×D1112yes—
478C4⋊C4C23×D1114yes—
479C22⋊C4—24no—
480C22⋊C4—118no—
481C22⋊C4—228no—
482C22⋊C4—228no—
483C22⋊C4—228no—
484C22⋊C4—224no—
485C42—228no—
486C42D4×D1112yes—
487C42C23×D1112yes—
488C11C2×#330311yescharacteristic, complemented, Sylow
489C23—24no—
490C23—22no—
491C23—42no—
492C23—42no—
493C23—114no—
494C23—224no—
495C23—224no—
496C23—224no—
497C23—222no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23C2×D4×D1111yescharacteristic
502Q8—84no—
503Q8—224no—
504Q8—224no—
505Q8—444no—
506D4—24no—
507D4—22no—
508D4—228no—
509D4—222no—
510D4—222no—
511D4—4416no—
512D4—442no—
513D4—888no—
514D4C2×#434314yes—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—114no—
522C2×C4—224no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—4416no—
529C2×C4—442no—
530C2×C4—444no—
531C2×C4—448no—
532C2×C4#6696914yes—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×D4×D1112yes—
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434312yes—
537C2×C4#6704212yes—
538C2×C4C24×D1111yescharacteristic
539C8—24no—
540C8—222no—
541C8—222no—
542C22—24no—
543C22—42no—
544C22—48no—
545C22—42no—
546C22—224no—
547C22—224no—
548C22—224no—
549C22—448no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—884no—
554C22#1062316112yes—
555C22C2×#6696912yes—
556C22#1062330612yes—
557C22C22×D4×D1111yescharacteristic
558C4—22no—
559C4—42no—
560C4—44no—
561C4—224no—
562C4—444no—
563C4—442no—
564C4#1062316112yes—
565C4C2×#6696914yes—
566C4C22×#434311yescharacteristic
567C4C2×#6704211yescharacteristic
568C2—44no—
569C2—444no—
570C2—882no—
571C2#1308054114yesdirect product factor
572C2C2×#1062316111yescharacteristic
573C2C22×#6696911yescharacteristic
574C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
hypercenterC2×#476D11
hypocenterC11C2×#3303
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10623086C2semidirect
3. #13080541C2direct (N × H)
4. C2×#10622706C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622477C2semidirect
7. C2×#10622454C2semidirect
8. C2×#10622394C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622447C2semidirect
11. C2×#10622385C2semidirect
12. C2×C11×#476C2semidirect
23. #10623265C22semidirect
25. #10623086C22semidirect
35. C11×#476C22semidirect
42. #10622706C22semidirect
43. C4×#4323C22semidirect
49. #10622480C22semidirect
50. #10622477C22semidirect
51. #10622454C22semidirect
52. #10622447C22semidirect
53. #10622394C22semidirect
54. #10622385C22semidirect
207. C2×#476D11semidirect
291. #476C2×D11semidirect
409. C2×C11#3303semidirect
488. C11C2×#3303semidirect
571. C2#13080541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106230862
#130805412
C2×#106227062
C2×#106224802
C2×#106224772
C2×#106224542
C2×#106223942
C2×C4×#43232
C2×#106224472
C2×#106223852
C2×C11×#4762
C2×#330311