Finite Group Databasebeta

← C2×#13078583 #15621610

Subgroups — C2×#13078583 #15621610

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×#10623347C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3#13078583C2116yesmaximal, direct product factor
4C2×#10622422C212yesmaximal, complemented
5C2×#10622427C212yesmaximal, complemented
6C2×#10622428C212yesmaximal, complemented
7C2×#10622418C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C2×#10622611C211yesmaximal, characteristic, complemented
10C22×#66899C211yesmaximal, characteristic, complemented
11C2×#10622742C211yesmaximal, characteristic
12C2×C11×#419C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623347—24no—
18#10623347C2218yes—
19C2×#67000—21no—
20C2×#66999C2212yes—
21C2×#66999C2212yes—
22C2×#66997—21no—
23C2×#66982—22no—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623054—24no—
28#10623054C2218yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×(C22⋊D11)⋊C4—22no—
32C2×C4×D44—21no—
33C2×C4×Dic22—21no—
34C11×#419C2218yescomplemented
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2218yescomplemented
40#10622742C2218yes—
41#10622734C2218yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66882C2212yes—
45C2×#66881C2212yes—
46#10622611C2218yescomplemented
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622428C22116yescomplemented
52#10622427C22116yescomplemented
53#10622422C22116yescomplemented
54#10622418C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—24no—
58C22×Q8×C11—24no—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2314yes—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D412yes—
64C23×Dic11—21no—
65C2×#4339—24no—
66C2×#4339—24no—
67C2×#4339D414yes—
68C2×#4339C2314yes—
69C22×D44D411yescharacteristic
70C22×C4×D11—22no—
71C22×C4×D11C2312yes—
72C22×Dic22D411yescharacteristic
73C2×C11×M16—24no—
74C2×C11×M16C2314yes—
75C22×C8×C11C2312yes—
76C11×#117—22no—
77C11×#117C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83#67000—28no—
84#66999—24no—
85#66999—24no—
86#66999C2318yes—
87#66999C2318yes—
88#66997—28no—
89#66982—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93#66979—22no—
94#66979C2314yes—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8—24no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66945—24no—
111#66945C2318yes—
112C4⋊C4×D11—24no—
113C4⋊C4×D11C2318yes—
114(C22⋊D11)⋊C4—216no—
115C4×D44—28no—
116C4×Dic22—28no—
117C11×#103C2318yes—
118C11×#103C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121(C2×D11)⋊C8C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66882C2318yes—
124#66881C2318yes—
125#66872C2314yes—
126#66872C2314yes—
127#66871C2314yes—
128#66871C2314yes—
129C2×#3097—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11C2×D412yes—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—28no—
136C2×Q8×C11—24no—
137C2×Q8×C11—28no—
138C2×Q8×C11—44no—
139C2×Q8×C11—48no—
140C2×Q8×C11C2414yes—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4114yes—
149C22×C4×C11#4114yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2412yes—
152C2×C22⋊D11—28no—
153C2×C22⋊D11C2×D418yes—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—82no—
159C22×Dic11C2×D412yes—
160#4339—216no—
161#4339—28no—
162#4339—28no—
163C2×D44—24no—
164C2×D44C2×D414yes—
165C2×C4×D11—28no—
166C2×C4×D11—24no—
167C2×C4×D11—24no—
168C2×C4×D11—84no—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2414yes—
171C2×Dic22—24no—
172C2×Dic22C2×D414yes—
173C11×M16—28no—
174C2×C8×C11—24no—
175C2×C8×C11C2414yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2412yes—
180C11×C22⋊C4—24no—
181C42×C11—24no—
182C22⋊Dic11—24no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2412yes—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196C4×Dic11—28no—
197C4×Dic11—24no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—28no—
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2412yes—
203C2×#536—111no—
204C2×#520—111no—
205#3097—1116no—
206C2×#484—112no—
207C2×#485—112no—
208C2×#485—112no—
209C2×#483—112no—
210C2×#428—111no—
211C2×#427—111no—
212C2×#419D1111yescharacteristic, complemented
213C22×#103—111no—
214C2×#408—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11#12314yes—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11C22×D414yes—
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—48no—
227Q8×C11—44no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11#12314yes—
236C2×C4×C11#12318yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4112yes—
240C2×C4×C11C2×#4114yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C11C2×#4114yes—
243C2×C4×C11C2511yescharacteristic
244C22⋊D11—216no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—84no—
253C2×Dic11C22×D414yes—
254D44—28no—
255C4×D11—28no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—88no—
259Dic22—28no—
260C8×C11—24no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C22×#41—111no—
264C23×Q8C2×D1111yescharacteristic
265C22×M16C2×D1111yescharacteristic
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—118no—
275#520—224no—
276C2×C4×Q8—221no—
277C2×C4×D4—221no—
278C2×C4×D4—222no—
279C2×#117—111no—
280C2×#117—112no—
281C2×#117C2×D1111yescharacteristic
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284#485—1116no—
285#485—1116no—
286#484—1116no—
287#483—1116no—
288#428—118no—
289#427—118no—
290C2×#107—112no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—112no—
294C2×#106—111no—
295C2×#106—111no—
296#419C2×D1118yescomplemented
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—118no—
300C2×#103C2×D1112yes—
301C2×#103C2×D1112yes—
302#408—118no—
303C2×C22⋊C8—112no—
304C2×C22⋊C8—112no—
305C22×C11—28no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11C2×#12314yes—
309C22×C11C2×#12312yes—
310C22×C11#57712yes—
311C22×C11#57812yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—48no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11C2×#12314yes—
321C4×C11C2×#12312yes—
322C4×C11C22×#4111yescharacteristic
323C4×C11C22×#4111yescharacteristic
324Dic11—24no—
325Dic11—44no—
326Dic11—42no—
327Dic11—42no—
328C2×#41—114no—
329C2×#41—114no—
330C2×#41—224no—
331C2×#41—224no—
332C22×Q8—21no—
333C22×Q8—22no—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—111no—
337C22×Q8C22×D1112yes—
338C22×Q8C22×D1114yes—
339C22×D4—112no—
340C22×D4—111no—
341C23×C4—21no—
342C23×C4—112no—
343C23×C4—222no—
344C23×C4—221no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—24no—
347C2×M16C22×D1114yes—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8—114no—
351C22×C8—224no—
352C22×C8C22×D1112yes—
353C4⋊Q8—228no—
354#124—228no—
355#123—2216no—
356C22⋊Q8—118no—
357C22⋊Q8—118no—
358C22⋊Q8—224no—
359C22⋊Q8—224no—
360C4×Q8—228no—
361C4×D4—228no—
362C4×D4—2216no—
363#117—22no—
364#117—114no—
365#117—118no—
366#117—224no—
367#117—222no—
368#117C22×D1114yes—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—221no—
387C2×C42—21no—
388C2×C42—222no—
389C2×C42—221no—
390#107—118no—
391#107—114no—
392#107—114no—
393#106—118no—
394#106—114no—
395#106—114no—
396#103—118no—
397#103—118no—
398#103C22×D1118yes—
399#103C22×D1118yes—
400C22⋊C8—118no—
401C22⋊C8—118no—
402C2×C11—24no—
403C2×C11#309714yescomplemented
404C2×C11C22×#12311yescharacteristic
405C2×C11C2×#57711yescharacteristic
406C2×C11C2×#57811yescharacteristic
407D11—44no—
408C24—112no—
409C24D4×D1111yescharacteristic
410#41—2216no—
411#41—228no—
412#41—228no—
413C2×Q8—22no—
414C2×Q8—24no—
415C2×Q8—24no—
416C2×Q8—28no—
417C2×Q8—24no—
418C2×Q8—28no—
419C2×Q8—44no—
420C2×Q8—48no—
421C2×Q8—114no—
422C2×Q8—224no—
423C2×Q8C23×D1114yes—
424C2×D4—118no—
425C2×D4—114no—
426C2×D4—228no—
427C2×D4—224no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—884no—
444C22×C4—882no—
445C22×C4#433914yes—
446C22×C4D4×D1112yes—
447C22×C4D4×D1111yescharacteristic
448C22×C4#434114yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1111yescharacteristic
451M16—28no—
452C2×C8—24no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—228no—
458C2×C8C23×D1114yes—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—114no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C23×D1112yes—
472C4⋊C4C23×D1112yes—
473C22⋊C4—24no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C22⋊C4—228no—
477C22⋊C4—224no—
478C42—24no—
479C42—228no—
480C42—224no—
481C11C2×#309711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—114no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23#6693614yes—
489C23C2×D4×D1112yes—
490C23C2×D4×D1111yescharacteristic
491Q8—24no—
492Q8—24no—
493Q8—44no—
494Q8—48no—
495Q8—228no—
496D4—2216no—
497D4—228no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—114no—
506C2×C4—224no—
507C2×C4—228no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—888no—
517C2×C4—884no—
518C2×C4#6693614yes—
519C2×C4#6693618yes—
520C2×C4C2×#433912yes—
521C2×C4C2×#433914yes—
522C2×C4C2×D4×D1112yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434112yes—
525C2×C4C2×#434114yes—
526C2×C4C24×D1111yescharacteristic
527C8—24no—
528C8—222no—
529C8—222no—
530C22—28no—
531C22—22no—
532C22—22no—
533C22—224no—
534C22—224no—
535C22—224no—
536C22—448no—
537C22C2×#6693614yes—
538C22C2×#6693612yes—
539C22#1062330912yes—
540C22#1062331012yes—
541C22C22×D4×D1111yescharacteristic
542C4—42no—
543C4—42no—
544C4—44no—
545C4—224no—
546C4—444no—
547C4—442no—
548C4—442no—
549C4C2×#6693612yes—
550C4C2×#6693614yes—
551C4C22×#433911yescharacteristic
552C4C22×#434111yescharacteristic
553C2—24no—
554C2—444no—
555C2#1307858314yesdirect product factor
556C2C22×#6693611yescharacteristic
557C2C2×#1062330911yescharacteristic
558C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#419D11
hypocenterC11C2×#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #13078583C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622734C2semidirect
9. C2×#10622611C2semidirect
10. C22×#66899C2semidirect
12. C2×C11×#419C2semidirect
34. C11×#419C22semidirect
39. C2×#66899C22semidirect
41. #10622734C22semidirect
46. #10622611C22semidirect
51. #10622428C22semidirect
52. #10622427C22semidirect
53. #10622422C22semidirect
54. #10622418C22semidirect
212. C2×#419D11semidirect
296. #419C2×D11semidirect
403. C2×C11#3097semidirect
481. C11C2×#3097semidirect
555. C2#13078583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233472
C2×#106230542
#130785832
C2×#106224222
C2×#106224272
C2×#106224282
C2×#106224182
C2×#106227342
C2×#106226112
C22×#668992
C2×#106227422
C2×C11×#4192
C2×#309711