Finite Group Databasebeta

← C2×#13074416 #14920847

Subgroups — C2×#13074416 #14920847

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C22×#66925C211yesmaximal, characteristic
3#13074416C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622270C212yesmaximal, complemented
6C2×#10622288C212yesmaximal
7C2×#10622287C212yesmaximal
8C2×#10622843C211yesmaximal, characteristic, complemented
9C2×#10622598C211yesmaximal, characteristic, complemented
10C2×#10622541C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic
12C2×C11×#391C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×#66999—28no—
18C2×#66999C2218yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66925—28no—
32C2×#66925C2218yes—
33C11×#391C2218yescomplemented
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36#10622843C2218yescomplemented
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622600C2218yes—
43#10622598C2218yescomplemented
44#10622541C2218yescomplemented
45#10622288C22116yes—
46#10622287C22116yes—
47#10622271C22116yescomplemented
48#10622270C22116yescomplemented
49C24×D11C2311yescharacteristic
50C22×Q8×C11—24no—
51C22×Q8×C11—24no—
52C22×Q8×C11—24no—
53C22×Q8×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11D418yes—
67C22×C4×D11C2314yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2314yes—
70C2×C42×C11—24no—
71C2×C42×C11C2314yes—
72#66999—232no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—44no—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2318yes—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11C2314yes—
97#66925—232no—
98C11×#95C2318yes—
99C11×#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2625—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11C2×D414yes—
114C23×D11C2412yes—
115C2×Q8×C11—28no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—416no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11C2×D414yes—
154C22×Dic11C2412yes—
155C22×Dic11C2414yes—
156C22×Dic11C2412yes—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C2×C4×D11—232no—
160C2×C4×D11—28no—
161C2×C4×D11—28no—
162C2×C4×D11C2×D4116yes—
163C11×C4⋊C4—28no—
164C42×C11—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—216no—
168(C2×D11)⋊C4—48no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171C4⋊Dic11—48no—
172Dic11⋊C4—28no—
173Dic11⋊C4—28no—
174Dic11⋊C4—216no—
175Dic11⋊C4—48no—
176C4×Dic11—28no—
177C22×C22⋊Q8—111no—
178C22×#117—111no—
179#2625—1116no—
180C2×#400—112no—
181C2×#398—112no—
182C2×#397—112no—
183C2×#397—112no—
184C2×#391—111no—
185C2×#391D1111yescharacteristic, complemented
186C2×#389—111no—
187C2×#389—111no—
188C2×#380—111no—
189C23×C11C22×D412yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C112−1+412yes—
194C23×C112−1+412yes—
195C23×C112−1+412yes—
196C23×C11C2511yescharacteristic
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11C22×D414yes—
211Q8×C11—416no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—48no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11#123116yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C2×#4114yes—
231C2×C4×C11C2×#4114yes—
232C2×Dic11—28no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—48no—
251C2×Dic11C22×D414yes—
252C4×D11—232no—
253C23×Q8C2×D1111yescharacteristic
254C24×C4—111no—
255C2×C22⋊Q8—118no—
256C2×C22⋊Q8—228no—
257C2×#117—118no—
258C2×#117—228no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C22⋊C4—111no—
268C22×C22⋊C4—111no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C42—111no—
272C22×C42C2×D1111yescharacteristic
273#400—1116no—
274#398—1116no—
275#397—1116no—
276#397—1116no—
277#391—118no—
278#391C2×D1118yescomplemented
279#389—118no—
280#389—118no—
281#380—118no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95C2×D1112yes—
288C2×#95C2×D1112yes—
289C22×C11C2×#12314yes—
290C22×C11#53614yes—
291C22×C11#53714yes—
292C22×C11#54114yes—
293C22×C11#54114yes—
294C22×C11#54214yes—
295C22×C11#54214yes—
296C22×C11C23×D411yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C2×H(5,𝔽2)11yescharacteristic
300C22×C11C2×2−1+411yescharacteristic
301C22×C11C2×2−1+411yescharacteristic
302C22×C11C2×2−1+411yescharacteristic
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—416no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C4×C11—44no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11C2×#12318yes—
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—44no—
320Dic11—44no—
321C25—111no—
322C22×Q8—24no—
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8C22×D1114yes—
326C23×C4—111no—
327C23×C4—118no—
328C23×C4—114no—
329C23×C4—112no—
330C23×C4—111no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—224no—
334C23×C4—224no—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1112yes—
337C23×C4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C22⋊Q8—2232no—
341#117—2232no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—444no—
356C2×C4⋊C4—444no—
357C2×C4⋊C4C22×D1114yes—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—114no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—228no—
365C2×C22⋊C4—444no—
366C2×C42—24no—
367C2×C42—114no—
368C2×C42—224no—
369C2×C42C22×D1114yes—
370#95—118no—
371#95—118no—
372#95—118no—
373#95—118no—
374#95—118no—
375#95C22×D1118yes—
376#95C22×D1118yes—
377C2×C11#262518yescomplemented
378C2×C11C22×#12311yescharacteristic
379C2×C11C2×#53611yescharacteristic
380C2×C11C2×#53711yescharacteristic
381C2×C11C2×#54111yescharacteristic
382C2×C11C2×#54111yescharacteristic
383C2×C11C2×#54211yescharacteristic
384C2×C11C2×#54211yescharacteristic
385D11—44no—
386C24—114no—
387C24—112no—
388C24—222no—
389C24—222no—
390C24—222no—
391C24—222no—
392C24—222no—
393C24—222no—
394C24C23×D1111yescharacteristic
395C2×Q8—28no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—416no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—114no—
412C22×C4—112no—
413C22×C4—1116no—
414C22×C4—112no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—2232no—
421C22×C4—228no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4#433914yes—
436C22×C4D4×D1114yes—
437C22×C4#434114yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1114yes—
440C22×C4C23×D1114yes—
441C22×C4C23×D1112yes—
442C22×C4C23×D1112yes—
443C4⋊C4—28no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C4⋊C4—2216no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C4⋊C4—448no—
450C4⋊C4—448no—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—2216no—
454C22⋊C4—448no—
455C42—28no—
456C42—228no—
457C11C2×#262511yescharacteristic, complemented, Sylow
458C23—114no—
459C23—228no—
460C23—228no—
461C23—228no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—444no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23C2×#433912yes—
473C23C2×D4×D1112yes—
474C23C2×#434112yes—
475C23#6704012yes—
476C23#6704012yes—
477C23#6704212yes—
478C23#6704312yes—
479C23C24×D1111yescharacteristic
480Q8—416no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—48no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—48no—
497C2×C4—114no—
498C2×C4—228no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—2232no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—448no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4—448no—
518C2×C4#66936116yes—
519C2×C4C2×#433914yes—
520C2×C4C2×D4×D1114yes—
521C2×C4C2×#434114yes—
522C22—224no—
523C22—224no—
524C22—224no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—4416no—
530C22C2×#6693614yes—
531C22#1062311314yes—
532C22#1062311414yes—
533C22#1062315914yes—
534C22#1062316014yes—
535C22#1062321314yes—
536C22#1062326214yes—
537C22C22×#433911yescharacteristic
538C22C22×D4×D1111yescharacteristic
539C22C22×#434111yescharacteristic
540C22C2×#6704011yescharacteristic
541C22C2×#6704011yescharacteristic
542C22C2×#6704211yescharacteristic
543C22C2×#6704311yescharacteristic
544C4—42no—
545C4—42no—
546C4—44no—
547C4—44no—
548C4—224no—
549C4—442no—
550C4—442no—
551C4—444no—
552C4—444no—
553C4C2×#6693618yes—
554C2—444no—
555C2#1307441618yesdirect product factor
556C2C22×#6693611yescharacteristic
557C2C2×#1062315911yescharacteristic
558C2C2×#1062316011yescharacteristic
559C2C2×#1062311411yescharacteristic
560C2C2×#1062326211yescharacteristic
561C2C2×#1062321311yescharacteristic
562C2C2×#1062311311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#391C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#391D11
hypocenterC11C2×#2625
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13074416C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622270C2semidirect
8. C2×#10622843C2semidirect
9. C2×#10622598C2semidirect
10. C2×#10622541C2semidirect
12. C2×C11×#391C2semidirect
33. C11×#391C22semidirect
36. #10622843C22semidirect
43. #10622598C22semidirect
44. #10622541C22semidirect
47. #10622271C22semidirect
48. #10622270C22semidirect
185. C2×#391D11semidirect
278. #391C2×D11semidirect
377. C2×C11#2625semidirect
457. C11C2×#2625semidirect
555. C2#13074416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669252
#130744162
C2×#106222712
C2×#106222702
C2×#106222882
C2×#106222872
C2×#106228432
C2×#106225982
C2×#106225412
C2×#106226002
C2×C11×#3912
C2×#262511