Finite Group Databasebeta

← C2×#13078936 #15622973

Subgroups — C2×#13078936 #15622973

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10623363C211yesmaximal, characteristic
3#13078936C2116yesmaximal, direct product factor
4C2×#10622413C212yesmaximal, complemented
5C2×#10622381C212yesmaximal, complemented
6C2×#10622405C212yesmaximal, complemented
7C2×#10622373C212yesmaximal, complemented
8C2×#10622726C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C22×C8×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#416C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623363—24no—
18#10623363C2218yes—
19C2×#67000C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66992—22no—
23C2×#66989C2211yescharacteristic
24C2×C4×C22⋊D11—22no—
25C2×#66979C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28#10623048—24no—
29#10623048C2218yescomplemented
30C2×#66943C2212yes—
31C2×#66941C2212yes—
32C2×#66931—22no—
33C2×C4×Dic22—22no—
34C11×#416C2218yescomplemented
35C2×C11×#103C2212yes—
36C2×C11×#102C2212yes—
37#10622846C2218yescomplemented
38C2×#66899C2212yes—
39C2×#66896C2212yes—
40#10622726C2218yescomplemented
41C2×#66885C2212yes—
42C2×#66880C2212yes—
43C2×C8×Dic11C2212yes—
44C2×C8×Dic11C2212yes—
45C2×C8×Dic11C2218yescomplemented
46#10622615C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49#10622413C22116yescomplemented
50#10622405C22116yescomplemented
51#10622381C22116yescomplemented
52#10622373C22116yescomplemented
53C2×C11×#41—22no—
54C2×C11×#41—24no—
55C2×C11×#41—24no—
56C2×C11×#41C2314yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—22no—
64C23×Dic11D412yes—
65C2×#4339—22no—
66C2×#4339—24no—
67C2×#4339—24no—
68C2×#4339C2314yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22—22no—
72C22×Dic22C2311yescharacteristic
73C22×C8×C11—24no—
74C22×C8×C11C2312yes—
75C22×C8×C11C2314yes—
76C11×#117—22no—
77C11×#117C2314yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—22no—
83#67000—22no—
84#67000C2314yes—
85#66997—22no—
86#66997C2314yes—
87#66993—22no—
88#66993C2314yes—
89#66992—216no—
90#66989—22no—
91#66989C2314yes—
92C4×C22⋊D11—216no—
93C2×(C2×D11)⋊C4—22no—
94#66979—22no—
95#66979C2314yes—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2312yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D412yes—
103C2×C4×Dic11D414yes—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2314yes—
107C22×C11⋊C8—24no—
108C22×C11⋊C8C2312yes—
109C22×C11⋊C8C2314yes—
110#66943—24no—
111#66943C2318yes—
112#66941—24no—
113#66941C2318yes—
114#66931—216no—
115C4×Dic22—216no—
116C11×#103C2318yes—
117C11×#102C2318yes—
118#66899C2318yes—
119#66896C2318yes—
120#66885C2318yes—
121#66880C2318yes—
122C8×Dic11C2318yes—
123C8×Dic11C2318yes—
124#66874C2318yes—
125#66873C2318yes—
126C2×#3131—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C11×#41—28no—
131C11×#41—28no—
132C11×#41—48no—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11C2412yes—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—44no—
142C2×D4×C11C2412yes—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—44no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4114yes—
150C22×C4×C11#4114yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2412yes—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—44no—
157C22×Dic11—28no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11C2×D418yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163#4339—28no—
164#4339—28no—
165#4339—48no—
166C2×D44—21no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44C2412yes—
170C2×C4×D11—24no—
171C2×C4×D11—44no—
172C2×Dic22—28no—
173C2×Dic22—21no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—48no—
177C2×Dic22C2412yes—
178C2×C8×C11—24no—
179C2×C8×C11—28no—
180C2×C8×C11C2414yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C2414yes—
183C11×C22⋊C4—24no—
184C42×C11—24no—
185C22⋊Dic11—28no—
186C22⋊Dic11—24no—
187(C2×D11)⋊C4—28no—
188C4⋊Dic11—28no—
189C4⋊Dic11—22no—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194C4×Dic11—24no—
195C4×Dic11C2×D418yes—
196C4×Dic11C2×D412yes—
197C4×Dic11C2×D412yes—
198C4×Dic11C2412yes—
199C4×Dic11C2412yes—
200C2×C11⋊C8—24no—
201C2×C11⋊C8—28no—
202C2×C11⋊C8C2414yes—
203C2×#533—111no—
204C2×#532—111no—
205#3131—1116no—
206C2×#488—112no—
207C2×#488—112no—
208C2×#487—112no—
209C2×#486—112no—
210C2×#416—111no—
211C2×#416—111no—
212C2×#416—111no—
213C2×#416D1111yescharacteristic, complemented
214C22×C4×C8—111no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—44no—
219C23×C11#12414yes—
220C23×C11C22×D412yes—
221C23×C11C22×D411yescharacteristic
222C22×D11—22no—
223C22×D11—42no—
224C22×D11—44no—
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—42no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—48no—
231D4×C11—42no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—48no—
237C2×C4×C11#12414yes—
238C2×C4×C11#12418yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4112yes—
242C2×C4×C11C2×#4114yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4114yes—
245C2×C4×C11C2511yescharacteristic
246C22⋊D11—48no—
247C22⋊D11—416no—
248C2×Dic11—24no—
249C2×Dic11—216no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11#13518yes—
255C2×Dic11C22×D414yes—
256C2×Dic11C22×D414yes—
257D44—22no—
258D44—22no—
259D44—42no—
260C4×D11—48no—
261Dic22—22no—
262Dic22—22no—
263Dic22—42no—
264Dic22—416no—
265C8×C11—24no—
266C11⋊C8—24no—
267C22×#41—111no—
268C22×#41C2×D1111yescharacteristic
269C23×C8—111no—
270C23×C8C2×D1111yescharacteristic
271#533—118no—
272#533—224no—
273#532—118no—
274#532—224no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8—111no—
277C2×#127—111no—
278C2×#125—112no—
279C2×#124—111no—
280C2×#124—111no—
281C2×C22⋊Q8—222no—
282C2×#121—222no—
283C2×C4×Q8—222no—
284C2×C4×D4—222no—
285C2×#117—111no—
286C2×#117C2×D1111yescharacteristic
287C22×C42—111no—
288#488—1116no—
289#488—1116no—
290#487—1116no—
291#486—1116no—
292#416—118no—
293#416—118no—
294#416—118no—
295#416C2×D1118yescomplemented
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103C2×D1112yes—
300C2×#102—112no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102C2×D1112yes—
304C2×C4×C8—112no—
305C2×C4×C8—112no—
306C2×C4×C8—118no—
307C22×C11—28no—
308C22×C11—24no—
309C22×C11—42no—
310C22×C11—44no—
311C22×C11—84no—
312C22×C11C2×#12414yes—
313C22×C11C2×#12412yes—
314C22×C11C2×#13514yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—42no—
317C2×D11—44no—
318C2×D11—84no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11C2×#12414yes—
322C4×C11C2×#12412yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C22×#4111yescharacteristic
325Dic11—24no—
326Dic11—42no—
327Dic11—44no—
328Dic11C2×#13518yes—
329C2×#41—22no—
330C2×#41—24no—
331C2×#41—24no—
332C2×#41—114no—
333C2×#41—222no—
334C2×#41—224no—
335C2×#41—224no—
336C2×#41C22×D1114yes—
337C22×Q8—111no—
338C22×Q8—222no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—21no—
341C22×D4—111no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4C22×D1111yescharacteristic
345C23×C4—21no—
346C23×C4—112no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C22×C8—24no—
350C22×C8—112no—
351C22×C8—114no—
352C22×C8—224no—
353C22×C8C22×D1112yes—
354C22×C8C22×D1114yes—
355C4⋊Q8—118no—
356C4⋊Q8—114no—
357C4⋊Q8—224no—
358C4⋊Q8—222no—
359#127—114no—
360#127—222no—
361#125—118no—
362#125—224no—
363#124—114no—
364#124—114no—
365#124—222no—
366#124—222no—
367C22⋊Q8—2216no—
368#121—2216no—
369C4×Q8—2216no—
370C4×D4—2216no—
371#117—22no—
372#117—114no—
373#117—222no—
374#117C22×D1114yes—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4C22×D1112yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—221no—
385C2×C42—21no—
386C2×C42—114no—
387C2×C42—112no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—114no—
391C2×C42—221no—
392#103—118no—
393#103—118no—
394#103—118no—
395#103C22×D1118yes—
396#102—118no—
397#102—118no—
398#102—118no—
399#102C22×D1118yes—
400C4×C8—118no—
401C4×C8—118no—
402C2×C11—24no—
403C2×C11—82no—
404C2×C11#313114yescomplemented
405C2×C11C22×#12411yescharacteristic
406C2×C11C22×#13512yes—
407D11—82no—
408C24—21no—
409C24—221no—
410C24D4×D1111yescharacteristic
411#41—28no—
412#41—28no—
413#41—48no—
414#41—228no—
415#41—228no—
416#41—448no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—112no—
421C2×Q8—228no—
422C2×Q8—221no—
423C2×Q8—222no—
424C2×Q8—222no—
425C2×Q8—448no—
426C2×Q8C23×D1112yes—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—44no—
432C2×D4—112no—
433C2×D4—228no—
434C2×D4—224no—
435C2×D4—222no—
436C2×D4—221no—
437C2×D4—222no—
438C2×D4—448no—
439C2×D4—444no—
440C2×D4C23×D1112yes—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—44no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—118no—
448C22×C4—228no—
449C22×C4—222no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—444no—
453C22×C4#433914yes—
454C22×C4D4×D1112yes—
455C22×C4D4×D1111yescharacteristic
456C22×C4#434114yes—
457C22×C4C23×D1111yescharacteristic
458C22×C4C23×D1112yes—
459C2×C8—24no—
460C2×C8—28no—
461C2×C8—114no—
462C2×C8—224no—
463C2×C8—228no—
464C2×C8C23×D1114yes—
465C4⋊C4—22no—
466C4⋊C4—114no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C4⋊C4—222no—
472C4⋊C4C23×D1114yes—
473C22⋊C4—24no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C22⋊C4—224no—
477C42—24no—
478C42—118no—
479C42—112no—
480C42—112no—
481C42—112no—
482C42—112no—
483C42—224no—
484C11C2×#313111yescharacteristic, complemented, Sylow
485C23—24no—
486C23—22no—
487C23—42no—
488C23—44no—
489C23—222no—
490C23—442no—
491C23—444no—
492C23#6693814yes—
493C23C2×D4×D1112yes—
494C23C2×D4×D1111yescharacteristic
495Q8—22no—
496Q8—22no—
497Q8—42no—
498Q8—222no—
499Q8—222no—
500Q8—4416no—
501Q8—442no—
502D4—22no—
503D4—22no—
504D4—48no—
505D4—42no—
506D4—222no—
507D4—222no—
508D4—4416no—
509D4—448no—
510D4—442no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—118no—
517C2×C4—114no—
518C2×C4—114no—
519C2×C4—2216no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—442no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4#6693814yes—
527C2×C4#6693818yes—
528C2×C4C2×#433912yes—
529C2×C4C2×#433914yes—
530C2×C4C2×D4×D1112yes—
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×#434112yes—
533C2×C4C2×#434114yes—
534C2×C4C24×D1111yescharacteristic
535C8—24no—
536C8—224no—
537C22—28no—
538C22—24no—
539C22—42no—
540C22—44no—
541C22—84no—
542C22—442no—
543C22—444no—
544C22—884no—
545C22C2×#6693814yes—
546C22C2×#6693812yes—
547C22D11×#13514yes—
548C22C22×D4×D1111yescharacteristic
549C4—42no—
550C4—44no—
551C4—118no—
552C4—224no—
553C4—442no—
554C4—444no—
555C4C2×#6693814yes—
556C4C2×#6693812yes—
557C4C22×#433911yescharacteristic
558C4C22×#434111yescharacteristic
559C2—24no—
560C2—82no—
561C2—882no—
562C2#1307893614yesdirect product factor
563C2C22×#6693811yescharacteristic
564C2C2×D11×#13512yes—
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
hypercenterC2×#416D11
hypocenterC11C2×#3131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13078936C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622381C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622726C2semidirect
9. C2×#10622846C2semidirect
10. C2×#10622615C2semidirect
11. C22×C8×Dic11C2semidirect
12. C2×C11×#416C2semidirect
29. #10623048C22semidirect
34. C11×#416C22semidirect
37. #10622846C22semidirect
40. #10622726C22semidirect
45. C2×C8×Dic11C22semidirect
46. #10622615C22semidirect
49. #10622413C22semidirect
50. #10622405C22semidirect
51. #10622381C22semidirect
52. #10622373C22semidirect
213. C2×#416D11semidirect
295. #416C2×D11semidirect
404. C2×C11#3131semidirect
484. C11C2×#3131semidirect
562. C2#13078936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106233632
#130789362
C2×#106224132
C2×#106223812
C2×#106224052
C2×#106223732
C2×#106227262
C2×#106228462
C2×#106226152
C22×C8×Dic112
C2×C11×#4162
C2×#313111