Finite Group Databasebeta

← C2×#13078585 #15621612

Subgroups — C2×#13078585 #15621612

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2#13078585C2116yesmaximal, direct product factor
3C2×#10622583C212yesmaximal, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622609C212yesmaximal, complemented
6C2×#10622584C212yesmaximal, complemented
7C2×#10622577C211yesmaximal, characteristic, complemented
8C2×#10622611C211yesmaximal, characteristic, complemented
9C2×#10622617C211yesmaximal, characteristic, complemented
10C22×#66874C211yesmaximal, characteristic, complemented
11C2×#10622847C211yesmaximal, characteristic
12C2×C11×#520C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C11×#520—24no—
16C11×#520C2218yes—
17C2×C4×Q8×C11—21no—
18C2×C4×D4×C11—22no—
19C2×C4×D4×C11—21no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24#10623356—24no—
25#10623356C2218yes—
26C2×#66997—21no—
27C2×#66989—21no—
28C2×#66988—22no—
29C2×#66979C2211yescharacteristic
30C2×#66977C2212yes—
31C2×#66977C2212yes—
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34#10622847C2218yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622617C2218yescomplemented
38#10622611C2218yescomplemented
39#10622609C22116yescomplemented
40#10622609C22116yescomplemented
41#10622584C22116yescomplemented
42#10622583C22116yescomplemented
43C2×#66874C2212yes—
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66874C2218yescomplemented
48#10622577C2218yescomplemented
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66872C2212yes—
52C2×#66871C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2212yes—
55C2×C11×#41—24no—
56C2×C11×#41—24no—
57C2×C11×#41D414yes—
58C2×C11×#41C2314yes—
59C22×Q8×C11D411yescharacteristic
60C22×D4×C11D412yes—
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—21no—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C22×Dic22—24no—
68C22×Dic22—24no—
69C22×Dic22—21no—
70C22×Dic22—22no—
71C22×Dic22C2312yes—
72C22×Dic22C2314yes—
73C4×Q8×C11—28no—
74C4×D4×C11—216no—
75C4×D4×C11—28no—
76C11×#117—24no—
77C11×#117—22no—
78C11×#117C2318yes—
79C11×#117C2314yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2318yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—22no—
92C2×C42×C11—21no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—21no—
96#66997—28no—
97#66989—28no—
98#66988—216no—
99#66979—22no—
100#66979C2314yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—24no—
104#66977—24no—
105#66977C2318yes—
106#66977C2318yes—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×C4×Dic11—21no—
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8—24no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2314yes—
116C22×C11⋊C8C2312yes—
117C22⋊(C11⋊C8)C2318yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2318yes—
120#66874C2318yes—
121#66874C2318yes—
122#66874C2318yes—
123#66872C2318yes—
124#66872C2314yes—
125#66872C2314yes—
126#66871C2318yes—
127#66871C2314yes—
128#66871C2314yes—
129C2×#3097—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C24×C11C2×D411yescharacteristic
132C11×#41—216no—
133C11×#41—28no—
134C11×#41—28no—
135C2×Q8×C11—24no—
136C2×Q8×C11C2×D414yes—
137C2×D4×C11—28no—
138C2×D4×C11—24no—
139C2×D4×C11C2×D418yes—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—28no—
147C22×C4×C11—24no—
148C22×C4×C11—82no—
149C22×C4×C11—84no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4114yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2412yes—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—44no—
164C2×Dic22—22no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22—44no—
171C2×Dic22—48no—
172C2×Dic22C2414yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2414yes—
179C11×C4⋊C4C2412yes—
180C11×C4⋊C4C2412yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—24no—
183C42×C11—28no—
184C42×C11—24no—
185C22⋊Dic11—28no—
186C22⋊Dic11—28no—
187C22⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2412yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194C4×Dic11—24no—
195#4318—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—28no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8C2412yes—
201C2×C11⋊C8C2414yes—
202C2×C11⋊C8C2412yes—
203C2×#536—111no—
204C2×#520D1111yescharacteristic
205#3097—1116no—
206C2×#484—112no—
207C2×#485—112no—
208C2×#485—112no—
209C2×#483—112no—
210C2×#428—111no—
211C2×#427—111no—
212C2×#419—111no—
213C22×#103—111no—
214C2×#408—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11#12314yes—
221C23×C11C22×D414yes—
222C23×C11C22×D412yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—28no—
225D4×C11—216no—
226D4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—28no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—84no—
238C2×C4×C11—88no—
239C2×C4×C11#12314yes—
240C2×C4×C11#12318yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11C2×#4114yes—
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2511yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256Dic22—24no—
257Dic22—24no—
258Dic22—44no—
259Dic22—48no—
260C11⋊C8—22no—
261C11⋊C8—22no—
262C11⋊C8—24no—
263C22×#41C2×D1111yescharacteristic
264C23×Q8—111no—
265C22×M16—111no—
266C23×C8—111no—
267#536—118no—
268#536—224no—
269C2×C4⋊Q8—221no—
270C2×#124—221no—
271C2×#123—222no—
272C2×C22⋊Q8—112no—
273C2×C22⋊Q8—112no—
274#520—24no—
275#520C2×D1118yes—
276C2×C4×Q8—21no—
277C2×C4×D4—22no—
278C2×C4×D4—21no—
279C2×#117—111no—
280C2×#117C2×D1112yes—
281C2×#117C2×D1111yescharacteristic
282C22×C4⋊C4C2×D1112yes—
283C22×C4⋊C4C2×D1111yescharacteristic
284#485—1116no—
285#485—1116no—
286#484—1116no—
287#483—1116no—
288#428—118no—
289#427—118no—
290C2×#107—111no—
291C2×#107—112no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#106—112no—
295C2×#106—111no—
296#419—118no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—112no—
301C2×#103—118no—
302#408—118no—
303C2×C22⋊C8—112no—
304C2×C22⋊C8—112no—
305C22×C11—28no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—48no—
312C22×C11C2×#12314yes—
313C22×C11C2×#12312yes—
314C22×C11#57712yes—
315C22×C11#57812yes—
316C22×C11C23×D411yescharacteristic
317C4×C11—24no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11C2×#12312yes—
322C4×C11C2×#12314yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C22×#4111yescharacteristic
325Dic11—44no—
326Dic11—42no—
327Dic11—42no—
328C2×#41—24no—
329C2×#41—24no—
330C2×#41C22⋊D1114yes—
331C2×#41C22×D1114yes—
332C22×Q8—112no—
333C22×Q8—114no—
334C22×Q8—221no—
335C22×Q8—222no—
336C22×Q8—224no—
337C22×Q8—224no—
338C22×Q8C22⋊D1111yescharacteristic
339C22×D4C22⋊D1112yes—
340C22×D4C22⋊D1111yescharacteristic
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—221no—
344C23×C4C22×D1112yes—
345C23×C4C22×D1111yescharacteristic
346C2×M16—114no—
347C2×M16—224no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—114no—
351C22×C8—112no—
352C22×C8—224no—
353C4⋊Q8—228no—
354#124—228no—
355#123—2216no—
356C22⋊Q8—118no—
357C22⋊Q8—118no—
358C22⋊Q8—224no—
359C22⋊Q8—224no—
360C4×Q8—28no—
361C4×D4—216no—
362C4×D4—28no—
363#117—24no—
364#117—22no—
365#117—114no—
366#117—222no—
367#117C22×D1114yes—
368#117C22×D1118yes—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1112yes—
379C2×C4⋊C4C22×D1114yes—
380C2×C4⋊C4C22×D1118yes—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C42—22no—
388C2×C42—21no—
389C2×C42—221no—
390#107—114no—
391#107—114no—
392#107—118no—
393#106—114no—
394#106—114no—
395#106—118no—
396#103—118no—
397#103—118no—
398#103—118no—
399#103—118no—
400C22⋊C8—118no—
401C22⋊C8—118no—
402C2×C11—24no—
403C2×C11—44no—
404C2×C11#309714yescomplemented
405C2×C11C22×#12311yescharacteristic
406C2×C11C2×#57711yescharacteristic
407C2×C11C2×#57811yescharacteristic
408C24C2×C22⋊D1112yes—
409C24C2×C22⋊D1111yescharacteristic
410#41—216no—
411#41—28no—
412#41—28no—
413C2×Q8—24no—
414C2×Q8—114no—
415C2×Q8—222no—
416C2×Q8—224no—
417C2×Q8—224no—
418C2×Q8—224no—
419C2×Q8—228no—
420C2×Q8—228no—
421C2×Q8—444no—
422C2×Q8—448no—
423C2×Q8C2×C22⋊D1114yes—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4C2×C22⋊D1118yes—
427C2×D4C2×C22⋊D1114yes—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—28no—
434C22×C4—24no—
435C22×C4—82no—
436C22×C4—84no—
437C22×C4—224no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—222no—
441C22×C4—444no—
442C22×C4#433914yes—
443C22×C4#433914yes—
444C22×C4C2×C22⋊D1114yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C23×D1114yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1111yescharacteristic
451M16—228no—
452C2×C8—112no—
453C2×C8—114no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—228no—
458C2×C8—224no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—28no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4C23×D1114yes—
471C4⋊C4C23×D1112yes—
472C4⋊C4C23×D1112yes—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C22⋊C4—224no—
476C22⋊C4—228no—
477C22⋊C4—228no—
478C42—28no—
479C42—24no—
480C42—224no—
481C11C2×#309711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23#6698214yes—
488C23C22×C22⋊D1114yes—
489C23C22×C22⋊D1112yes—
490C23C22×C22⋊D1111yescharacteristic
491Q8—28no—
492Q8—224no—
493Q8—224no—
494Q8—444no—
495Q8—448no—
496D4—216no—
497D4—28no—
498C2×C4—24no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—88no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—448no—
514C2×C4—444no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4#6698214yes—
518C2×C4#6698218yes—
519C2×C4C2×#433912yes—
520C2×C4C2×#433912yes—
521C2×C4C2×#433914yes—
522C2×C4C2×#433914yes—
523C2×C4C22×C22⋊D1114yes—
524C2×C4C22×C22⋊D1112yes—
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C24×D1111yescharacteristic
527C8—222no—
528C8—222no—
529C8—224no—
530C22—28no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—24no—
535C22—24no—
536C22—48no—
537C22C2×#6698214yes—
538C22C2×#6698212yes—
539C22#1062336712yes—
540C22#1062336912yes—
541C22C23×C22⋊D1111yescharacteristic
542C4—24no—
543C4—44no—
544C4—42no—
545C4—42no—
546C4—442no—
547C4—442no—
548C4—444no—
549C4C2×#6698212yes—
550C4C2×#6698214yes—
551C4C22×#433911yescharacteristic
552C4C22×#433911yescharacteristic
553C2—24no—
554C2—44no—
555C2#1307858514yesdirect product factor
556C2C22×#6698211yescharacteristic
557C2C2×#1062336711yescharacteristic
558C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#520D11
hypocenterC11C2×#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. #13078585C2direct (N × H)
3. C2×#10622583C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622584C2semidirect
7. C2×#10622577C2semidirect
8. C2×#10622611C2semidirect
9. C2×#10622617C2semidirect
10. C22×#66874C2semidirect
37. #10622617C22semidirect
38. #10622611C22semidirect
39. #10622609C22semidirect
40. #10622609C22semidirect
41. #10622584C22semidirect
42. #10622583C22semidirect
47. C2×#66874C22semidirect
48. #10622577C22semidirect
404. C2×C11#3097semidirect
481. C11C2×#3097semidirect
555. C2#13078585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233562
#130785852
C2×#106225832
C2×#106226092
C2×#106225842
C2×#106225772
C2×#106226112
C2×#106226172
C22×#668742
C2×#106228472
C2×C11×#5202
C2×#309711