Finite Group Databasebeta

← C2×#13081205 #15632483

Subgroups — C2×#13081205 #15632483

Order 2816.

2146 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×#10623086C211yesmaximal, characteristic, complemented
2#13081205C2116yesmaximal, direct product factor
3C2×#10622692C211yesmaximal, characteristic, complemented
4C2×#10622647C212yesmaximal, complemented
5C2×#10622616C212yesmaximal, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622620C211yesmaximal, characteristic, complemented
8C2×#10622652C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622608C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C11×#555—24no—
15C11×#555C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#124—22no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2212yes—
24C22×#4323C2211yescharacteristic
25C2×#66983C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×#4318C2212yes—
28#10623086—24no—
29#10623086C2218yescomplemented
30C2×#66950—21no—
31C2×#66939—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622697C2218yescomplemented
38#10622692C2218yescomplemented
39#10622652C22116yescomplemented
40#10622647C22116yescomplemented
41C4×#4323C2218yescomplemented
42#10622625C2218yescomplemented
43#10622620C2218yescomplemented
44#10622616C22116yescomplemented
45#10622608C22116yescomplemented
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4341—28no—
64C2×#4341—48no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22—21no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C11×#124—216no—
71C11×#121—28no—
72C11×#121—24no—
73C11×#121C2318yes—
74C4×D4×C11—22no—
75C4×D4×C11D414yes—
76C4×D4×C11C2314yes—
77C4×D4×C11C2314yes—
78C11×#117—24no—
79C11×#117—28no—
80C11×#117C2318yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11C2311yescharacteristic
91C2×#4323—24no—
92C2×#4323C2314yes—
93#66983—24no—
94#66983C2318yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2318yes—
103C2×#4318—28no—
104C2×#4318C2318yes—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2311yescharacteristic
108#66950—28no—
109#66939—216no—
110C4×D44—22no—
111C4×D44C2314yes—
112#66922—22no—
113#66922C2314yes—
114#66896C2318yes—
115#66896C2314yes—
116C22⋊(C11⋊C8)C2318yes—
117#66873C2314yes—
118#66873C2318yes—
119#66872C2318yes—
120#66872C2318yes—
121#66872C2318yes—
122#66871C2314yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3354—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D412yes—
129C23×D11—21no—
130C2×Q8×C11—24no—
131C2×Q8×C11—82no—
132C2×D4×C11—28no—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—84no—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—28no—
153C2×C22⋊D11—48no—
154C22×Dic11—28no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—48no—
158#4341—432no—
159C2×D44—21no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44C2412yes—
163C2×C4×D11—24no—
164C2×C4×D11—44no—
165C2×Dic22—24no—
166C2×Dic22—44no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2412yes—
172C11×C4⋊C4C2414yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4C2×D418yes—
177C42×C11—28no—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180#4323—28no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—28no—
183C4⋊Dic11—22no—
184C4⋊Dic11—24no—
185C4⋊Dic11—21no—
186C4⋊Dic11—28no—
187C4⋊Dic11C2414yes—
188C4⋊Dic11C2412yes—
189#4318—216no—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8#4114yescomplemented
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2414yes—
195C2×C11⋊C8C2412yes—
196C2×#555D1111yescharacteristic, complemented
197C2×#547—111no—
198#3354—1116no—
199C2×#498—111no—
200C2×#481—112no—
201C2×#482—112no—
202C2×#476—111no—
203C2×#474—111no—
204C2×#469—112no—
205C2×C4×D8—111no—
206C2×#436—111no—
207C2×#428—112no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C22×D414yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221Q8×C11—84no—
222D4×C11—28no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226D4×C11—88no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—28no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—48no—
237C2×C4×C11AGL(1,ℤ/8)14yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C112−1+412yes—
244C2×C4×C11C2511yescharacteristic
245C22⋊D11—416no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—416no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251D44—22no—
252D44—22no—
253D44—42no—
254C4×D11—48no—
255Dic22—48no—
256C11⋊C8—24no—
257C11⋊C8—22no—
258C11⋊C8C2×#4114yescomplemented
259C22×#41—221no—
260C22×D8—111no—
261C22×M16—112no—
262#555—24no—
263#555C2×D1118yescomplemented
264#547—118no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#124—22no—
269C2×#123—222no—
270C2×C22⋊Q8—221no—
271C2×#121—21no—
272C2×#121—112no—
273C2×#121C2×D1112yes—
274C2×C4×D4—111no—
275C2×C4×D4C2×D1111yescharacteristic
276C2×C4×D4C2×D1111yescharacteristic
277C2×#117—21no—
278C2×#117C2×D1112yes—
279C22×C4⋊C4—112no—
280#498—118no—
281#482—1116no—
282#481—1116no—
283#476—118no—
284#474—118no—
285#469—1116no—
286C4×D8—118no—
287#436—118no—
288#428—1116no—
289C2×#107—112no—
290C2×#107—111no—
291C2×#106—112no—
292C2×#106—112no—
293C2×#106—112no—
294C2×C4⋊C8—111no—
295C2×#102—111no—
296C2×#102—112no—
297C2×#102—111no—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300C2×C4×C8—111no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—48no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—84no—
309C22×C11#54712yes—
310C22×C11C2×AGL(1,ℤ/8)12yes—
311C22×C11#57712yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—24no—
318C4×C11—22no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11#54712yes—
322C4×C11C2×AGL(1,ℤ/8)14yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C2×2−1+411yescharacteristic
325Dic11—44no—
326Dic11—42no—
327C2×#41—228no—
328C2×#41—448no—
329C22×Q8—21no—
330C22×Q8—221no—
331C22×D4—22no—
332C22×D4—111no—
333C22×D4—222no—
334C22×D4C22⋊D1111yescharacteristic
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—222no—
338C23×C4—221no—
339C23×C4C22×D1112yes—
340C2×D8—114no—
341C2×D8—224no—
342C2×M16—118no—
343C2×M16—228no—
344C22×C8—111no—
345C22×C8—112no—
346C22×C8—111no—
347C4⋊Q8—22no—
348C4⋊Q8—114no—
349C4⋊Q8—222no—
350C4⋊Q8C22×D1114yes—
351#124—216no—
352#123—2216no—
353C22⋊Q8—228no—
354#121—28no—
355#121—24no—
356#121—118no—
357#121—224no—
358#121C22×D1118yes—
359C4×D4—22no—
360C4×D4—114no—
361C4×D4—222no—
362C4×D4C22⋊D1114yes—
363C4×D4C22×D1114yes—
364C4×D4C22×D1114yes—
365#117—24no—
366#117—28no—
367#117C22×D1118yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4C22⋊D1112yes—
384C2×C42—22no—
385C2×C42C22×D1111yescharacteristic
386#107—114no—
387#107—118no—
388#106—118no—
389#106—118no—
390#106—118no—
391C4⋊C8—114no—
392#102—114no—
393#102—118no—
394#102—114no—
395#102—118no—
396C22⋊C8—118no—
397C4×C8—114no—
398C2×C11—44no—
399C2×C11—82no—
400C2×C11#335414yescomplemented
401C2×C11C2×#54711yescharacteristic
402C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
403C2×C11C2×#57711yescharacteristic
404D11—82no—
405C24—21no—
406C24—221no—
407C24C2×C22⋊D1112yes—
408#41—4432no—
409C2×Q8—24no—
410C2×Q8—82no—
411C2×Q8—224no—
412C2×Q8—444no—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—84no—
419C2×D4—112no—
420C2×D4—228no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—448no—
425C2×D4C2×C22⋊D1114yes—
426C2×D4C23×D1112yes—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—228no—
434C22×C4—221no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—448no—
438C22×C4—444no—
439C22×C4C2×C22⋊D1114yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1114yes—
444C22×C4C23×D1111yescharacteristic
445D8—228no—
446M16—2216no—
447C2×C8—114no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—114no—
451C2×C8—224no—
452C2×C8—222no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—112no—
457C4⋊C4—114no—
458C4⋊C4—221no—
459C4⋊C4—222no—
460C4⋊C4—228no—
461C4⋊C4—224no—
462C4⋊C4C2×C22⋊D1114yes—
463C4⋊C4C23×D1114yes—
464C4⋊C4C23×D1112yes—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—224no—
469C22⋊C4—228no—
470C22⋊C4C2×C22⋊D1118yes—
471C42—28no—
472C42C2×C22⋊D1112yes—
473C42C23×D1112yes—
474C11C2×#335411yescharacteristic, complemented, Sylow
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—222no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23C22×C22⋊D1114yes—
487C23C22×C22⋊D1111yescharacteristic
488Q8—84no—
489Q8—448no—
490D4—28no—
491D4—22no—
492D4—22no—
493D4—42no—
494D4—88no—
495D4—222no—
496D4—222no—
497D4—4416no—
498D4—442no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—28no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—48no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—4416no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4—448no—
515C2×C4#6700214yes—
516C2×C4#41×D1112yes—
517C2×C4#6704312yes—
518C2×C4C22×C22⋊D1114yes—
519C2×C4C22×C22⋊D1112yes—
520C2×C4C22×C22⋊D1112yes—
521C2×C4C22×C22⋊D1111yescharacteristic
522C2×C4C24×D1111yescharacteristic
523C8—114no—
524C8—224no—
525C8—222no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—48no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—884no—
538C22C2×#6700212yes—
539C22#1062335512yes—
540C22#1062336712yes—
541C22C23×C22⋊D1111yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—44no—
546C4—442no—
547C4—444no—
548C4C2×#6700214yes—
549C4#1062335512yes—
550C4C2×#41×D1111yescharacteristic
551C4C2×#6704311yescharacteristic
552C2—44no—
553C2—82no—
554C2—882no—
555C2#1308120514yesdirect product factor
556C2C2×#1062335511yescharacteristic
557C2C22×#6700211yescharacteristic
558C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3354
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. #13081205C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622620C2semidirect
8. C2×#10622652C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622608C2semidirect
12. C2×C11×#555C2semidirect
15. C11×#555C22semidirect
29. #10623086C22semidirect
37. #10622697C22semidirect
38. #10622692C22semidirect
39. #10622652C22semidirect
40. #10622647C22semidirect
41. C4×#4323C22semidirect
42. #10622625C22semidirect
43. #10622620C22semidirect
44. #10622616C22semidirect
45. #10622608C22semidirect
192. C2×C11⋊C8#41semidirect
196. C2×#555D11semidirect
258. C11⋊C8C2×#41semidirect
263. #555C2×D11semidirect
400. C2×C11#3354semidirect
474. C11C2×#3354semidirect
555. C2#13081205direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
#130812052
C2×#106226922
C2×#106226472
C2×#106226162
C2×#106226972
C2×#106226202
C2×#106226522
C2×C4×#43232
C2×#106226252
C2×#106226082
C2×C11×#5552
C2×#335411