Finite Group Databasebeta

← C2×#13078465 #15621352

Subgroups — C2×#13078465 #15621352

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C2×#10623358C211yesmaximal, characteristic
3#13078465C2116yesmaximal, direct product factor
4C2×#10622409C212yesmaximal, complemented
5C2×#10622407C212yesmaximal, complemented
6C2×#10622379C212yesmaximal, complemented
7C2×#10622372C212yesmaximal, complemented
8C2×#10622608C211yesmaximal, characteristic, complemented
9C22×#66882C211yesmaximal, characteristic, complemented
10C2×#10622715C211yesmaximal, characteristic, complemented
11C2×#10622845C211yesmaximal, characteristic
12C2×C11×#416C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16#10623358—24no—
17#10623358C2218yes—
18C2×Q8×Dic11C2212yes—
19C2×D4×Dic11—22no—
20C2×D4×Dic11C2212yes—
21C2×#66979—21no—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11—21no—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27#10623050—24no—
28#10623050C2218yescomplemented
29C2×#66943C2212yes—
30C2×#66941C2212yes—
31C2×#66931—22no—
32C2×#66923—21no—
33C2×#66922—21no—
34C11×#416C2218yes—
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39#10622845C2218yes—
40C2×#66899C2212yes—
41C2×#66896C2212yes—
42C2×#66882C2212yes—
43C2×#66882C2212yes—
44C2×#66882C2218yescomplemented
45#10622715C2218yescomplemented
46C2×Dic11⋊C8C2212yes—
47C2×Dic11⋊C8C2212yes—
48#10622608C2218yescomplemented
49C2×#66872C2212yes—
50C2×#66871C2212yes—
51#10622409C22116yescomplemented
52#10622407C22116yescomplemented
53#10622379C22116yescomplemented
54#10622372C22116yescomplemented
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41Q818yescomplemented
58C2×C11×#41C2314yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C23×Dic11—22no—
67C22×Dic22—22no—
68C22×C8×C11—24no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2314yes—
72C11×#117—22no—
73C11×#117C2314yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11D412yes—
80Q8×Dic11—24no—
81Q8×Dic11C2318yes—
82D4×Dic11—216no—
83D4×Dic11—24no—
84D4×Dic11C2318yes—
85#66979—28no—
86#66979D414yes—
87#66979C2314yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—28no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11C2312yes—
105C2×#4318—24no—
106C2×#4318C2314yes—
107C22×C11⋊C8C2312yes—
108#66943—24no—
109#66943C2318yes—
110#66941—24no—
111#66941C2318yes—
112#66931—216no—
113#66923—28no—
114#66922—28no—
115C11×#103C2314yes—
116C11×#103C2314yes—
117C11×#102C2314yes—
118C11×#102C2314yes—
119#66899C2318yes—
120#66896C2318yes—
121#66882C2318yes—
122#66882C2318yes—
123Dic11⋊C8C2318yes—
124Dic11⋊C8C2318yes—
125#66872C2318yes—
126#66871C2318yes—
127C2×#3083—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C11×#41—216no—
131C11×#41—28no—
132C11×#41C2×Q8116yescomplemented
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2×Q814yes—
136C2×Q8×C11C2412yes—
137C2×D4×C11—28no—
138C2×D4×C11—24no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11C2×Q814yes—
142C2×D4×C11C2412yes—
143C22×C4×C11—21no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×Q814yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C22×Dic11—28no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—82no—
160C22×Dic11—82no—
161C22×Dic11—84no—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C2×Dic22—28no—
165C2×Dic22—84no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—28no—
169C2×C8×C11C2412yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2412yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—24no—
176C42×C11—24no—
177C22⋊Dic11—28no—
178C22⋊Dic11C2×D418yes—
179C4⋊Dic11—28no—
180C4⋊Dic11—28no—
181C4⋊Dic11—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11—24no—
184C4⋊Dic11—22no—
185C4⋊Dic11C2×D414yes—
186C4⋊Dic11C2×D414yes—
187C4⋊Dic11C2414yes—
188C4⋊Dic11C2414yes—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191C4×Dic11—28no—
192C4×Dic11C2×D414yes—
193C4×Dic11C2414yes—
194#4318—28no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2414yes—
197C2×#544—111no—
198C2×#520—111no—
199#3083—1116no—
200C2×#479—112no—
201C2×#477—112no—
202C2×#478—112no—
203C2×#474—112no—
204C2×#428—111no—
205C22×#107—111no—
206C2×#424—111no—
207C2×#417—111no—
208C2×#416D1111yescharacteristic
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C22⋊Q814yes—
216C23×C11C22×D412yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—24no—
219Q8×C11—22no—
220Q8×C11C22×Q814yes—
221D4×C11—216no—
222D4×C11—24no—
223D4×C11—22no—
224D4×C11C22×Q814yes—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—216no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11C22⋊Q814yes—
233C2×C4×C11C22⋊Q818yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×Q812yes—
237C2×C4×C11C22×Q814yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11C2×#4114yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—88no—
248C2×Dic11—84no—
249C2×Dic11—84no—
250C2×Dic11C22×D414yes—
251C2×Dic11C22×D414yes—
252Dic22—88no—
253C8×C11—22no—
254C8×C11—22no—
255C11⋊C8—24no—
256C22×#41C2×D1111yescharacteristic
257C22×M16—111no—
258C23×C8C2×D1111yescharacteristic
259#544—118no—
260#544—224no—
261C2×C4⋊Q8—112no—
262C2×C4⋊Q8—221no—
263C2×#125—112no—
264C2×#125—221no—
265C2×C22⋊Q8—222no—
266#520—118no—
267#520—224no—
268C2×C4×Q8—112no—
269C2×C4×D4—112no—
270C2×C4×D4—222no—
271C2×#117—111no—
272C2×#117—221no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—221no—
277#479—1116no—
278#478—1116no—
279#477—1116no—
280#474—1116no—
281#428—118no—
282C2×#107—112no—
283C2×#107—112no—
284C2×#107—118no—
285C2×#107—112no—
286C2×#106—112no—
287#424—118no—
288C2×C4⋊C8—112no—
289C2×C4⋊C8—112no—
290#417—118no—
291#416C2×D1118yes—
292C2×#103—112no—
293C2×#103C2×D1111yescharacteristic
294C2×#103C2×D1111yescharacteristic
295C2×#102—112no—
296C2×#102C2×D1111yescharacteristic
297C2×#102C2×D1111yescharacteristic
298C22×C11—28no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—24no—
302C22×C11—48no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C2×C22⋊Q814yes—
306C22×C11C2×C22⋊Q812yes—
307C22×C11#57612yes—
308C22×C11#57812yes—
309C22×C11C23×D411yescharacteristic
310C4×C11—24no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11C2×C22⋊Q814yes—
314C4×C11C2×C22⋊Q812yes—
315C4×C11C23×Q811yescharacteristic
316C4×C11C22×#4111yescharacteristic
317Dic11—24no—
318Dic11—24no—
319Dic11—44no—
320Dic11—44no—
321C2×#41—22no—
322C2×#41—24no—
323C2×#41Dic2218yescomplemented
324C2×#41C22×D1114yes—
325C22×Q8—222no—
326C22×Q8C22×D1111yescharacteristic
327C22×D4—21no—
328C22×D4C22×D1111yescharacteristic
329C23×C4—21no—
330C23×C4—222no—
331C23×C4—221no—
332C23×C4—221no—
333C23×C4C22×D1111yescharacteristic
334C2×M16—114no—
335C2×M16—224no—
336C22×C8—24no—
337C22×C8—112no—
338C22×C8C22×D1111yescharacteristic
339C22×C8C22×D1111yescharacteristic
340C22×C8C22×D1114yes—
341C4⋊Q8—118no—
342C4⋊Q8—228no—
343C4⋊Q8—224no—
344#125—118no—
345#125—228no—
346#125—224no—
347C22⋊Q8—2216no—
348C4×Q8—118no—
349C4×Q8—224no—
350C4×D4—118no—
351C4×D4—224no—
352C4×D4—2216no—
353#117—22no—
354#117—114no—
355#117—114no—
356#117—228no—
357#117C22×D1114yes—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—112no—
377C2×C22⋊C4—222no—
378C2×C42—21no—
379C2×C42—112no—
380C2×C42—222no—
381#107—118no—
382#107—118no—
383#107—118no—
384#106—118no—
385C4⋊C8—118no—
386C4⋊C8—118no—
387#103—118no—
388#103C22×D1114yes—
389#103C22×D1114yes—
390#102—118no—
391#102C22×D1114yes—
392#102C22×D1114yes—
393C2×C11—24no—
394C2×C11—44no—
395C2×C11#308314yescomplemented
396C2×C11C22×C22⋊Q811yescharacteristic
397C2×C11C2×#57611yescharacteristic
398C2×C11C2×#57811yescharacteristic
399C24—21no—
400C24D4×D1111yescharacteristic
401#41—216no—
402#41—28no—
403#41C2×Dic22116yescomplemented
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—228no—
407C2×Q8—884no—
408C2×Q8C2×Dic2214yes—
409C2×Q8C23×D1112yes—
410C2×D4—28no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4C2×Dic2214yes—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—228no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—884no—
429C22×C4—882no—
430C22×C4—882no—
431C22×C4C2×Dic2214yes—
432C22×C4D4×D1112yes—
433C22×C4D4×D1111yescharacteristic
434C22×C4#434114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—228no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—28no—
441C2×C8—114no—
442C2×C8—224no—
443C2×C8C23×D1112yes—
444C2×C8C23×D1112yes—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—114no—
448C4⋊C4—114no—
449C4⋊C4—114no—
450C4⋊C4—114no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—224no—
456C4⋊C4—222no—
457C4⋊C4—224no—
458C4⋊C4—222no—
459C4⋊C4C23×D1112yes—
460C4⋊C4C23×D1112yes—
461C22⋊C4—24no—
462C22⋊C4—118no—
463C22⋊C4—228no—
464C42—24no—
465C42—114no—
466C42—114no—
467C42—228no—
468C11C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—24no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23#6693114yes—
476C23C2×D4×D1112yes—
477C23C2×D4×D1111yescharacteristic
478Q8—24no—
479Q8—22no—
480Q8—888no—
481Q8C22×Dic2214yes—
482D4—216no—
483D4—24no—
484D4—22no—
485D4C22×Dic2214yes—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—216no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—114no—
494C2×C4—114no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—444no—
500C2×C4—444no—
501C2×C4—888no—
502C2×C4—884no—
503C2×C4—884no—
504C2×C4#6693114yes—
505C2×C4#6693118yes—
506C2×C4C22×Dic2212yes—
507C2×C4C22×Dic2214yes—
508C2×C4C2×D4×D1112yes—
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×#434112yes—
511C2×C4C2×#434114yes—
512C2×C4C24×D1111yescharacteristic
513C8—22no—
514C8—22no—
515C8—224no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#6693114yes—
524C22C2×#6693112yes—
525C22#1062330012yes—
526C22#1062330212yes—
527C22C22×D4×D1111yescharacteristic
528C4—24no—
529C4—42no—
530C4—42no—
531C4—224no—
532C4—224no—
533C4—444no—
534C4—444no—
535C4C2×#6693114yes—
536C4C2×#6693112yes—
537C4C23×Dic2211yescharacteristic
538C4C22×#434111yescharacteristic
539C2—24no—
540C2—44no—
541C2#1307846514yesdirect product factor
542C2C22×#6693111yescharacteristic
543C2C2×#1062330011yescharacteristic
544C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11C2×#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13078465C2direct (N × H)
4. C2×#10622409C2semidirect
5. C2×#10622407C2semidirect
6. C2×#10622379C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622608C2semidirect
9. C22×#66882C2semidirect
10. C2×#10622715C2semidirect
28. #10623050C22semidirect
44. C2×#66882C22semidirect
45. #10622715C22semidirect
48. #10622608C22semidirect
51. #10622409C22semidirect
52. #10622407C22semidirect
53. #10622379C22semidirect
54. #10622372C22semidirect
57. C2×C11×#41Q8semidirect
132. C11×#41C2×Q8semidirect
323. C2×#41Dic22semidirect
395. C2×C11#3083semidirect
403. #41C2×Dic22semidirect
468. C11C2×#3083semidirect
541. C2#13078465direct (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×#106233582
#130784652
C2×#106224092
C2×#106224072
C2×#106223792
C2×#106223722
C2×#106226082
C22×#668822
C2×#106227152
C2×#106228452
C2×C11×#4162
C2×#308311