Finite Group Databasebeta

← C2×#13079013 #15623067

Subgroups — C2×#13079013 #15623067

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623199C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic, complemented
3#13079013C2116yesmaximal, direct product factor
4C2×#10622410C212yesmaximal, complemented
5C2×#10622377C212yesmaximal, complemented
6C2×#10622681C211yesmaximal, characteristic, complemented
7C2×#10622310C211yesmaximal, characteristic, complemented
8C2×#10622669C211yesmaximal, characteristic, complemented
9C2×#10622416C212yesmaximal, complemented
10C2×#10622384C212yesmaximal, complemented
11C2×C4×#4313C211yesmaximal, characteristic, complemented
12C2×C11×#488C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×#4341C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C2×#66993C2211yescharacteristic
19C22×#4313C2212yes—
20D11×#125—24no—
21D11×#125C2218yescomplemented
22#10623199—24no—
23#10623199C2218yes—
24C2×C4⋊C4×D11—22no—
25C2×C4⋊C4×D11C2212yes—
26C2×#66943C2212yes—
27C2×#66942—22no—
28C2×#66937—22no—
29C2×(C22⋊D11)⋊C4—22no—
30C2×#66928C2211yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×#66923C2211yescharacteristic
33C11×#488C2218yescomplemented
34C2×C11×#103C2212yes—
35C2×C11×#102C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C2×#66899C2212yes—
38C2×#66896C2212yes—
39C2×#66885C2212yes—
40C2×#66880C2212yes—
41C2×#66879C2212yes—
42#10622681C2218yescomplemented
43#10622669C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66873C2212yes—
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622416C22116yescomplemented
48#10622410C22116yescomplemented
49#10622384C22116yescomplemented
50#10622377C22116yescomplemented
51#10622310C2218yescomplemented
52C4×#4313C2218yescomplemented
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C22×C22⋊D11—21no—
56C22×C22⋊D11—22no—
57C23×Dic11—21no—
58C2×#4343—22no—
59C2×#4343—28no—
60C2×#4343C2314yes—
61C2×#4341—22no—
62C2×#4341—28no—
63C2×#4341C2314yes—
64C22×D44—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—22no—
67C22×C4×D11—21no—
68C22×C4×D11D412yes—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C22×C8×C11C2312yes—
72C11×#125—22no—
73C11×#125C2314yes—
74C11×#124—22no—
75C11×#124C2314yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11C2311yescharacteristic
80#66997—22no—
81#66997C2314yes—
82#66993—22no—
83#66993C2314yes—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11D412yes—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94C2×#4313—28no—
95C2×#4313C2318yes—
96C4⋊C4×D11—216no—
97C4⋊C4×D11—24no—
98C4⋊C4×D11C2318yes—
99#66943—24no—
100#66943C2318yes—
101#66942—216no—
102#66937—216no—
103(C22⋊D11)⋊C4—216no—
104#66928—22no—
105#66928C2314yes—
106C42×D11D414yes—
107C42×D11C2314yes—
108#66923—22no—
109#66923C2314yes—
110C11×#103C2318yes—
111C11×#102C2318yes—
112C4×C8×C11C2314yes—
113#66899C2318yes—
114#66896C2318yes—
115#66885C2318yes—
116#66880C2318yes—
117#66879C2318yes—
118#66874C2318yes—
119#66873C2318yes—
120C4×C11⋊C8C2314yes—
121C2×#3142—111nomaximal, Sylow
122C24×C11—21no—
123C23×D11—21no—
124C23×D11C2×D411yescharacteristic
125C2×Q8×C11—21no—
126C2×Q8×C11—24no—
127C2×Q8×C11C2412yes—
128C2×D4×C11—21no—
129C2×D4×C11—24no—
130C2×D4×C11C2412yes—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—28no—
136C2×C22⋊D11—24no—
137C2×C22⋊D11—48no—
138C2×C22⋊D11—44no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—44no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D411yescharacteristic
145#4343—216no—
146#4343—48no—
147#4341—216no—
148#4341—48no—
149C2×D44—24no—
150C2×D44—21no—
151C2×D44—24no—
152C2×D44—44no—
153C2×D44C2412yes—
154C2×C4×D11—24no—
155C2×C4×D11—28no—
156C2×C4×D11—44no—
157C2×C4×D11—48no—
158C2×C4×D11—44no—
159C2×C4×D11C2×D418yes—
160C2×C4×D11C2×D412yes—
161C2×C4×D11#4118yes—
162C2×C4×D11C2412yes—
163C2×Dic22—21no—
164C2×Dic22—24no—
165C2×Dic22C2412yes—
166C2×C8×C11—24no—
167C2×C8×C11C2414yes—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4C2414yes—
171C11×C22⋊C4—28no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174(C2×D11)⋊C4—28no—
175C4⋊Dic11—28no—
176C4⋊Dic11—22no—
177C4⋊Dic11C2414yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182C4×Dic11C2×D412yes—
183C4×Dic11C2×D418yes—
184C4×Dic11C2412yes—
185C2×C11⋊C8—24no—
186C2×C11⋊C8C2414yes—
187#4313—216no—
188C2×#532—111no—
189C22×#125—111no—
190#3142—1116no—
191C2×#491—112no—
192C2×#490—112no—
193C2×#488—111no—
194C2×#488—111no—
195C2×#488—111no—
196C2×#488D1111yescharacteristic, complemented
197C2×#417—112no—
198C2×#417—112no—
199C2×C4×M16—111no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—44no—
203C23×C11C22×D411yescharacteristic
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—42no—
207C22×D11—44no—
208C22×D11#12414yes—
209C22×D11C22×D412yes—
210Q8×C11—24no—
211Q8×C11—42no—
212D4×C11—24no—
213D4×C11—42no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11C22×D414yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4114yes—
222C2×C4×C11C2511yescharacteristic
223C22⋊D11—416no—
224C22⋊D11—48no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230C2×Dic11—48no—
231C2×Dic11#12414yes—
232C2×Dic11C22×D414yes—
233C2×Dic11C22×D412yes—
234D44—24no—
235D44—48no—
236D44—42no—
237C4×D11—48no—
238C4×D11—416no—
239C4×D11—48no—
240C4×D11#12418yes—
241C4×D11C2×#4118yes—
242Dic22—24no—
243Dic22—42no—
244C8×C11—24no—
245C11⋊C8—24no—
246C22×#41—111no—
247C22×#41—111no—
248C22×M16—112no—
249#532—118no—
250#532—224no—
251C2×C4⋊Q8—111no—
252C2×#127—111no—
253C2×#125—118no—
254C2×#125—112no—
255C2×#125—111no—
256C2×#125—222no—
257C2×#125—224no—
258C2×#125C2×D1111yescharacteristic
259C2×#124—111no—
260C2×#124C2×D1111yescharacteristic
261C2×#121—222no—
262C2×C4×D4—222no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—222no—
265C22×C42—111no—
266#491—1116no—
267#490—1116no—
268#488—118no—
269#488—118no—
270#488—118no—
271#488C2×D1118yescomplemented
272#417—1116no—
273#417—1116no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103C2×D1112yes—
278C2×#102—112no—
279C2×#102—112no—
280C2×#102—112no—
281C2×#102C2×D1112yes—
282C4×M16—118no—
283C2×#97—112no—
284C2×C4×C8—111no—
285C2×C4×C8C2×D1111yescharacteristic
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—84no—
289C22×C11C2×#12412yes—
290C22×C11#57514yes—
291C22×C11C23×D411yescharacteristic
292C2×D11—28no—
293C2×D11—24no—
294C2×D11—42no—
295C2×D11—44no—
296C2×D11—84no—
297C2×D11C2×#12414yes—
298C4×C11—24no—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11C2×#12412yes—
302C4×C11C22×#4112yes—
303Dic11—24no—
304Dic11—42no—
305Dic11—44no—
306Dic11C2×#12414yes—
307C2×#41—114no—
308C2×#41—114no—
309C2×#41—222no—
310C2×#41—222no—
311C2×#41—228no—
312C2×#41—228no—
313C22×Q8—111no—
314C22×Q8C22×D1111yescharacteristic
315C22×D4—111no—
316C22×D4—221no—
317C22×D4—222no—
318C22×D4—221no—
319C22×D4C22×D1111yescharacteristic
320C23×C4—111no—
321C23×C4—112no—
322C23×C4—221no—
323C23×C4—222no—
324C23×C4—221no—
325C2×M16—118no—
326C2×M16—228no—
327C22×C8—112no—
328C22×C8C22×D1112yes—
329C4⋊Q8—114no—
330C4⋊Q8—222no—
331#127—114no—
332#127—222no—
333#125—22no—
334#125—118no—
335#125—114no—
336#125—2216no—
337#125—224no—
338#125—222no—
339#125C22×D1114yes—
340#124—22no—
341#124—114no—
342#124—222no—
343#124C22×D1114yes—
344#121—2216no—
345C4×D4—2216no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—2216no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—222no—
359C2×C42—112no—
360C2×C42—111no—
361C2×C42—114no—
362C2×C42—114no—
363C2×C42C22×D1111yescharacteristic
364#103—118no—
365#103—118no—
366#103—118no—
367#103C22×D1118yes—
368#102—118no—
369#102—118no—
370#102—118no—
371#102C22×D1118yes—
372#97—118no—
373C4×C8—114no—
374C4×C8C22×D1114yes—
375C2×C11—82no—
376C2×C11#314214yescomplemented
377C2×C11C22×#12411yescharacteristic
378C2×C11C2×#57512yes—
379D11—24no—
380D11—82no—
381C24—21no—
382C24—111no—
383C24—221no—
384#41—2216no—
385#41—2216no—
386#41—448no—
387#41—448no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8—112no—
391C2×Q8—221no—
392C2×Q8—224no—
393C2×Q8C23×D1112yes—
394C2×D4—21no—
395C2×D4—24no—
396C2×D4—112no—
397C2×D4—224no—
398C2×D4—228no—
399C2×D4—224no—
400C2×D4—221no—
401C2×D4—224no—
402C2×D4—444no—
403C2×D4—448no—
404C2×D4—444no—
405C2×D4C23×D1112yes—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—111no—
409C22×C4—112no—
410C22×C4—118no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—118no—
414C22×C4—224no—
415C22×C4—228no—
416C22×C4—224no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—448no—
422C22×C4—444no—
423C22×C4D4×D1112yes—
424C22×C4C23×D1111yescharacteristic
425M16—2216no—
426C2×C8—24no—
427C2×C8—114no—
428C2×C8—224no—
429C2×C8C23×D1114yes—
430C4⋊C4—28no—
431C4⋊C4—22no—
432C4⋊C4—114no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—222no—
438C4⋊C4—228no—
439C4⋊C4C23×D1114yes—
440C22⋊C4—28no—
441C22⋊C4—228no—
442C42—118no—
443C42—112no—
444C42—112no—
445C42D4×D1112yes—
446C42C23×D1112yes—
447C11C2×#314211yescharacteristic, complemented, Sylow
448C23—22no—
449C23—44no—
450C23—42no—
451C23—112no—
452C23—114no—
453C23—224no—
454C23—222no—
455C23—444no—
456C23—442no—
457C23C2×D4×D1111yescharacteristic
458Q8—24no—
459Q8—42no—
460Q8—224no—
461Q8—442no—
462D4—24no—
463D4—42no—
464D4—224no—
465D4—448no—
466D4—4416no—
467D4—448no—
468D4—442no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—112no—
475C2×C4—114no—
476C2×C4—118no—
477C2×C4—118no—
478C2×C4—114no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—448no—
483C2×C4—448no—
484C2×C4—4416no—
485C2×C4—448no—
486C2×C4—444no—
487C2×C4—442no—
488C2×C4C2×D4×D1114yes—
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4#41×D1114yes—
491C2×C4C24×D1111yescharacteristic
492C8—24no—
493C8—224no—
494C22—42no—
495C22—44no—
496C22—84no—
497C22—114no—
498C22—224no—
499C22—228no—
500C22—442no—
501C22—444no—
502C22—884no—
503C22D11×#12412yes—
504C22#1062329914yes—
505C22C22×D4×D1111yescharacteristic
506C4—24no—
507C4—42no—
508C4—44no—
509C4—114no—
510C4—224no—
511C4—442no—
512C4—444no—
513C4D11×#12412yes—
514C4C2×#41×D1112yes—
515C2—82no—
516C2—224no—
517C2—882no—
518C2#1307901314yesdirect product factor
519C2C2×D11×#12411yescharacteristic
520C2C2×#1062329912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#488C2
socleC23×C11C22×D4
prime radicalC2×#10623199C2
hypercenterC2×#488D11
hypocenterC11C2×#3142
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
2. C2×D11×#125C2semidirect
3. #13079013C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622681C2semidirect
7. C2×#10622310C2semidirect
8. C2×#10622669C2semidirect
9. C2×#10622416C2semidirect
10. C2×#10622384C2semidirect
11. C2×C4×#4313C2semidirect
12. C2×C11×#488C2semidirect
21. D11×#125C22semidirect
33. C11×#488C22semidirect
42. #10622681C22semidirect
43. #10622669C22semidirect
47. #10622416C22semidirect
48. #10622410C22semidirect
49. #10622384C22semidirect
50. #10622377C22semidirect
51. #10622310C22semidirect
52. C4×#4313C22semidirect
196. C2×#488D11semidirect
271. #488C2×D11semidirect
376. C2×C11#3142semidirect
447. C11C2×#3142semidirect
518. C2#13079013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231992
C2×D11×#1252
#130790132
C2×#106224102
C2×#106223772
C2×#106226812
C2×#106223102
C2×#106226692
C2×#106224162
C2×#106223842
C2×C4×#43132
C2×C11×#4882
C2×#314211