Finite Group Databasebeta

← C2×#13080538 #15630218

Subgroups — C2×#13080538 #15630218

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2#13080538C2116yesmaximal, direct product factor
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622654C212yesmaximal, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622650C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622615C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
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—
24C2×#66991—21no—
25C22×#4324C2212yes—
26C22×#4323C2211yescharacteristic
27C2×#66977C2212yes—
28C23×C11⋊C8C2212yes—
29#10623082—24no—
30#10623082C2218yescomplemented
31C2×C4⋊C4×D11—21no—
32C2×#66936—22no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622706C2218yescomplemented
38#10622697C2218yescomplemented
39#10622654C22116yescomplemented
40#10622650C22116yescomplemented
41#10622632C2218yescomplemented
42C4×#4323C2218yescomplemented
43D4×C11⋊C8C2218yescomplemented
44#10622615C22116yescomplemented
45#10622609C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66873C2212yes—
50C2×#66873C2211yescharacteristic
51C2×#66872C2212yes—
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—
62C2×#4339—24no—
63C2×#4339—28no—
64C2×#4339—44no—
65C2×#4339C2318yes—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11—22no—
69C22×Dic22C2312yes—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C11×#124—216no—
73C11×#121—28no—
74C11×#121—24no—
75C11×#121C2318yes—
76C4×D4×C11—22no—
77C4×D4×C11D414yes—
78C4×D4×C11C2314yes—
79C4×D4×C11C2314yes—
80C11×#117—24no—
81C11×#117—28no—
82C11×#117C2318yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11—22no—
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—22no—
94#66991—28no—
95C2×#4324—44no—
96C2×#4324C2318yes—
97C2×#4323—24no—
98C2×#4323C2314yes—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—24no—
104#66977C2318yes—
105C2×Dic11⋊C4—22no—
106C22×C11⋊C8—44no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110C22×C11⋊C8C2318yes—
111C4⋊C4×D11—28no—
112#66936—216no—
113C4×D44—22no—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117#66896C2314yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2318yes—
120#66874C2318yes—
121#66874C2318yes—
122#66873C2314yes—
123#66873C2318yes—
124#66872C2318yes—
125#66871C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3303—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D412yes—
131C23×D11—21no—
132C2×Q8×C11—24no—
133C2×Q8×C11—82no—
134C2×D4×C11—28no—
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—84no—
140C2×D4×C11C2×D414yes—
141C2×D4×C11C2412yes—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2414yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—48no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158#4339—216no—
159#4339—48no—
160#4339—416no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44#4114yes—
164C2×D44C2412yes—
165C2×C4×D11—24no—
166C2×C4×D11—28no—
167C2×C4×D11—48no—
168C2×C4×D11—44no—
169C2×Dic22—22no—
170C2×Dic22—24no—
171C2×Dic22—24no—
172C2×Dic22C2414yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C2×D414yes—
177C11×C4⋊C4C2412yes—
178C11×C4⋊C4C2414yes—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4C2×D418yes—
183C42×C11—28no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186C22⋊Dic11—28no—
187#4324—48no—
188#4323—28no—
189(C2×D11)⋊C4—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—28no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—24no—
198C2×C11⋊C8—48no—
199C2×C11⋊C8C2412yes—
200C2×C11⋊C8C2412yes—
201C2×C11⋊C8C2414yes—
202C2×#555D1111yescharacteristic, complemented
203C2×#547—111no—
204#3303—1116no—
205C2×#487—111no—
206C2×#485—112no—
207C2×#476—111no—
208C2×#465—112no—
209C2×#461—111no—
210C2×#449—112no—
211C2×C4×D8—111no—
212C2×C8×D4—111no—
213C2×#416—112no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11C22×D414yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—22no—
225C22×D11—42no—
226C22×D11—42no—
227Q8×C11—84no—
228D4×C11—28no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—42no—
232D4×C11—88no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—28no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11#13514yes—
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×C4×C11C2511yescharacteristic
251C22⋊D11—416no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—44no—
255C2×Dic11—42no—
256D44—24no—
257D44—22no—
258D44C2×#4114yes—
259C4×D11—416no—
260C4×D11—48no—
261Dic22—24no—
262Dic22—24no—
263Dic22—44no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—24no—
267C22×#41—112no—
268C22×SD16—112no—
269C22×D8—111no—
270C23×C8—112no—
271#555—24no—
272#555C2×D1118yescomplemented
273#547—118no—
274#547—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8C2×D1111yescharacteristic
277C2×#124—22no—
278C2×#123—222no—
279C2×C22⋊Q8—112no—
280C2×#121—21no—
281C2×#121—221no—
282C2×#121C2×D1112yes—
283C2×C4×D4—111no—
284C2×C4×D4C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286C2×#117—21no—
287C2×#117C2×D1112yes—
288C22×C4⋊C4—221no—
289#487—118no—
290#485—1116no—
291#476—118no—
292#465—1116no—
293#461—118no—
294#449—1116no—
295C4×D8—118no—
296C8×D4—118no—
297C2×#107—111no—
298C2×#106—112no—
299C2×C4⋊C8—111no—
300#416—1116no—
301C2×#103—112no—
302C2×#103—112no—
303C2×#103—112no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—112no—
307C2×C22⋊C8—112no—
308C2×C4×C8—111no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—48no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—84no—
317C22×C11#54612yes—
318C22×C11C2×#13512yes—
319C22×C11#57712yes—
320C22×C11C23×D411yescharacteristic
321C2×D11—24no—
322C2×D11—48no—
323C2×D11—42no—
324C2×D11—42no—
325C4×C11—24no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—44no—
329C4×C11#54612yes—
330C4×C11C2×#13514yes—
331C4×C11C22×#4111yescharacteristic
332C4×C11C2×H(5,𝔽2)11yescharacteristic
333Dic11—44no—
334Dic11—42no—
335C2×#41—118no—
336C2×#41—228no—
337C2×#41—224no—
338C2×#41—444no—
339C22×Q8—21no—
340C22×Q8—112no—
341C22×D4—22no—
342C22×D4—111no—
343C22×D4—222no—
344C22×D4C22⋊D1111yescharacteristic
345C22×D4C22×D1111yescharacteristic
346C23×C4—21no—
347C23×C4—221no—
348C23×C4—222no—
349C23×C4C22×D1112yes—
350C2×SD16—118no—
351C2×SD16—444no—
352C2×D8—114no—
353C2×D8—224no—
354C22×C8—111no—
355C22×C8—112no—
356C22×C8—111no—
357C22×C8—118no—
358C22×C8—444no—
359C4⋊Q8—22no—
360C4⋊Q8—114no—
361C4⋊Q8—222no—
362C4⋊Q8C22×D1114yes—
363#124—216no—
364#123—2216no—
365C22⋊Q8—118no—
366C22⋊Q8—224no—
367#121—28no—
368#121—24no—
369#121—228no—
370#121C22×D1118yes—
371C4×D4—22no—
372C4×D4—114no—
373C4×D4—222no—
374C4×D4C22⋊D1114yes—
375C4×D4C22×D1114yes—
376C4×D4C22×D1114yes—
377#117—24no—
378#117—28no—
379#117C22×D1118yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—228no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1112yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C42—22no—
396C2×C42C22×D1111yescharacteristic
397#107—114no—
398#106—118no—
399C4⋊C8—114no—
400#103—118no—
401#103—118no—
402#103—118no—
403#102—114no—
404#102—114no—
405#102—118no—
406C22⋊C8—118no—
407C4×C8—114no—
408C2×C11—44no—
409C2×C11—82no—
410C2×C11#330314yescomplemented
411C2×C11C2×#54611yescharacteristic
412C2×C11C22×#13511yescharacteristic
413C2×C11C2×#57711yescharacteristic
414D11—44no—
415C24—21no—
416C24—221no—
417C24C2×C22⋊D1112yes—
418#41—2216no—
419#41—448no—
420#41—4416no—
421C2×Q8—24no—
422C2×Q8—82no—
423C2×Q8—114no—
424C2×Q8—222no—
425C2×Q8—224no—
426C2×Q8—224no—
427C2×D4—28no—
428C2×D4—24no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—84no—
433C2×D4—114no—
434C2×D4—112no—
435C2×D4—228no—
436C2×D4—222no—
437C2×D4—221no—
438C2×D4—448no—
439C2×D4C2×C22⋊D1114yes—
440C2×D4C23×D1112yes—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—44no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—228no—
451C22×C4—448no—
452C22×C4—444no—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C23×D1114yes—
458C22×C4C23×D1111yescharacteristic
459SD16—448no—
460D8—228no—
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—114no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—224no—
467C2×C8—448no—
468C4⋊C4—24no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—112no—
472C4⋊C4—221no—
473C4⋊C4—224no—
474C4⋊C4—228no—
475C4⋊C4—224no—
476C4⋊C4C2×C22⋊D1114yes—
477C4⋊C4C23×D1114yes—
478C4⋊C4C23×D1112yes—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—24no—
482C22⋊C4—228no—
483C22⋊C4—224no—
484C22⋊C4C2×C22⋊D1118yes—
485C42—28no—
486C42C2×C22⋊D1112yes—
487C42C23×D1112yes—
488C11C2×#330311yescharacteristic, complemented, Sylow
489C23—24no—
490C23—24no—
491C23—24no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—224no—
497C23—222no—
498C23—442no—
499C23—442no—
500C23C22×C22⋊D1114yes—
501C23C22×C22⋊D1111yescharacteristic
502Q8—84no—
503Q8—224no—
504Q8—224no—
505Q8—444no—
506D4—28no—
507D4—22no—
508D4—22no—
509D4—42no—
510D4—88no—
511D4—114no—
512D4—224no—
513D4—222no—
514D4—4416no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—28no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—4416no—
528C2×C4—442no—
529C2×C4—444no—
530C2×C4—448no—
531C2×C4#6700314yes—
532C2×C4#41×D1112yes—
533C2×C4#6704212yes—
534C2×C4C22×C22⋊D1114yes—
535C2×C4C22×C22⋊D1112yes—
536C2×C4C22×C22⋊D1112yes—
537C2×C4C22×C22⋊D1111yescharacteristic
538C2×C4C24×D1111yescharacteristic
539C8—222no—
540C8—222no—
541C8—224no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—48no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—84no—
550C22—224no—
551C22—442no—
552C22—448no—
553C22—442no—
554C22C2×#6700312yes—
555C22#1062336012yes—
556C22#1062336712yes—
557C22C23×C22⋊D1111yescharacteristic
558C4—24no—
559C4—22no—
560C4—42no—
561C4—44no—
562C4—444no—
563C4—442no—
564C4C2×#6700314yes—
565C4#1062336012yes—
566C4C2×#41×D1111yescharacteristic
567C4C2×#6704211yescharacteristic
568C2—44no—
569C2—82no—
570C2—444no—
571C2#1308053814yesdirect product factor
572C2C2×#1062336011yescharacteristic
573C2C22×#6700311yescharacteristic
574C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3303
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×#10623082C2semidirect
2. #13080538C2direct (N × H)
3. C2×#10622706C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622654C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622650C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C2×#10622615C2semidirect
12. C2×C11×#555C2semidirect
15. C11×#555C22semidirect
30. #10623082C22semidirect
37. #10622706C22semidirect
38. #10622697C22semidirect
39. #10622654C22semidirect
40. #10622650C22semidirect
41. #10622632C22semidirect
42. C4×#4323C22semidirect
43. D4×C11⋊C8C22semidirect
44. #10622615C22semidirect
45. #10622609C22semidirect
202. C2×#555D11semidirect
272. #555C2×D11semidirect
410. C2×C11#3303semidirect
488. C11C2×#3303semidirect
571. C2#13080538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230822
#130805382
C2×#106227062
C2×#106226092
C2×#106226972
C2×#106226542
C2×#106226322
C2×#106226502
C2×C4×#43232
C2×D4×C11⋊C82
C2×#106226152
C2×C11×#5552
C2×#330311