Finite Group Databasebeta

← C2×#13074451 #14920839

Subgroups — C2×#13074451 #14920839

Order 2816.

2614 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×#66943C211yesmaximal, characteristic, complemented
2C22×#66925C211yesmaximal, characteristic
3#13074451C2116yesmaximal, direct product factor
4C2×#10622270C212yesmaximal, complemented
5C2×#10622593C212yesmaximal, complemented
6C2×#10622289C212yesmaximal
7C2×#10622607C212yesmaximal
8C2×#10622541C211yesmaximal, characteristic, complemented
9C2×#10622589C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic
11C2×#10622600C211yesmaximal, characteristic
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C2×#66943—28no—
33C2×#66943C2218yescomplemented
34C2×#66925—28no—
35C2×#66925C2218yes—
36C11×#389C2218yescomplemented
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yes—
42#10622600C2218yes—
43#10622600C2218yes—
44#10622593C22116yescomplemented
45#10622589C2218yescomplemented
46#10622541C2218yescomplemented
47#10622289C22116yes—
48#10622270C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11Q818yes—
63C22×C4×D11C2314yes—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—44no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C42×C11—24no—
71C2×C42×C11C2314yes—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—44no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2318yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11C2318yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4—44no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11D418yes—
99C2×C4×Dic11C2314yes—
100#66943—232no—
101#66925—232no—
102C11×#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2629—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11C2×Q814yes—
115C23×D11C2412yes—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×Q814yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D414yes—
150C22×Dic11C2×Q814yes—
151C22×Dic11C2414yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C2×C4×D11—232no—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11C2×Q8116yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—48no—
163C42×C11—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C4⋊Dic11—216no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171Dic11⋊C4—28no—
172Dic11⋊C4—28no—
173Dic11⋊C4—216no—
174Dic11⋊C4—48no—
175Dic11⋊C4—48no—
176Dic11⋊C4—48no—
177C4×Dic11C2×D4116yes—
178C22×#125—111no—
179C22×#117—111no—
180#2629—1116no—
181C2×#398—112no—
182C2×#398—112no—
183C2×#396—112no—
184C2×#396—112no—
185C2×#389—111no—
186C2×#389D1111yescharacteristic, complemented
187C2×#384—111no—
188C2×#380—111no—
189C2×#380—111no—
190C23×C11C22×D412yes—
191C23×C11C22×Q812yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C112−1+412yes—
196C23×C112−1+412yes—
197C23×C11C2511yescharacteristic
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11C22×Q814yes—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
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×C11C22⋊Q8116yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×Q814yes—
231C2×C4×C11C2×#4114yes—
232C2×Dic11—28no—
233C2×Dic11—28no—
234C2×Dic11—28no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—48no—
248C2×Dic11—48no—
249C2×Dic11C22×D414yes—
250C2×Dic11C22×D414yes—
251C2×Dic11C22×Q814yes—
252C4×D11—232no—
253C24×C4—111no—
254C2×#125—118no—
255C2×#125—228no—
256C2×#117—118no—
257C2×#117—228no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1112yes—
270C22×C22⋊C4—111no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C42—111no—
275C22×C42C2×D1111yescharacteristic
276#398—1116no—
277#398—1116no—
278#396—1116no—
279#396—1116no—
280#389—118no—
281#389C2×D1118yescomplemented
282#384—118no—
283#380—118no—
284#380—118no—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95C2×D1112yes—
289C22×C11C2×C22⋊Q814yes—
290C22×C11#53714yes—
291C22×C11#53714yes—
292C22×C11#54014yes—
293C22×C11#54114yes—
294C22×C11#54414yes—
295C22×C11#54414yes—
296C22×C11C23×D411yescharacteristic
297C22×C11C23×Q811yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C2×H(5,𝔽2)11yescharacteristic
300C22×C11C2×H(5,𝔽2)11yescharacteristic
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×C22⋊Q818yes—
316Dic11—24no—
317Dic11—24no—
318Dic11—24no—
319Dic11—44no—
320Dic11—44no—
321C25—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—118no—
326C23×C4—114no—
327C23×C4—112no—
328C23×C4—112no—
329C23×C4—224no—
330C23×C4—224no—
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1112yes—
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336#125—2232no—
337#117—2232no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—444no—
357C2×C4⋊C4—444no—
358C2×C4⋊C4—444no—
359C2×C4⋊C4C22×D1114yes—
360C2×C4⋊C4C22×D1114yes—
361C2×C4⋊C4C22×D1118yes—
362C2×C22⋊C4—114no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—118no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—444no—
369C2×C22⋊C4—444no—
370C2×C42—24no—
371C2×C42—118no—
372C2×C42—114no—
373C2×C42C22×D1114yes—
374#95—118no—
375#95—118no—
376#95—118no—
377#95C22×D1118yes—
378C2×C11#262918yescomplemented
379C2×C11C22×C22⋊Q811yescharacteristic
380C2×C11C2×#53711yescharacteristic
381C2×C11C2×#53711yescharacteristic
382C2×C11C2×#54011yescharacteristic
383C2×C11C2×#54111yescharacteristic
384C2×C11C2×#54411yescharacteristic
385C2×C11C2×#54411yescharacteristic
386D11—44no—
387C24—114no—
388C24—112no—
389C24—222no—
390C24—222no—
391C24—222no—
392C24—222no—
393C24—222no—
394C24—222no—
395C24C23×D1111yescharacteristic
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—1116no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—2232no—
424C22×C4—228no—
425C22×C4—228no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4#433914yes—
433C22×C4D4×D1114yes—
434C22×C4Q8×D1114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1114yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1112yes—
440C4⋊C4—28no—
441C4⋊C4—28no—
442C4⋊C4—48no—
443C4⋊C4—228no—
444C4⋊C4—228no—
445C4⋊C4—2216no—
446C4⋊C4—2216no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C4⋊C4—448no—
450C4⋊C4—448no—
451C4⋊C4—448no—
452C22⋊C4—228no—
453C22⋊C4—228no—
454C22⋊C4—448no—
455C22⋊C4—448no—
456C42—28no—
457C42—1116no—
458C11C2×#262911yescharacteristic, complemented, Sylow
459C23—114no—
460C23—228no—
461C23—228no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—228no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23—444no—
473C23C2×#433912yes—
474C23C2×D4×D1112yes—
475C23#6703712yes—
476C23C2×Q8×D1112yes—
477C23#6704012yes—
478C23#6704212yes—
479C23#6704312yes—
480C23C24×D1111yescharacteristic
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—48no—
494C2×C4—44no—
495C2×C4—48no—
496C2×C4—44no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—114no—
500C2×C4—228no—
501C2×C4—228no—
502C2×C4—228no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—2232no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—448no—
517C2×C4—448no—
518C2×C4#66949116yes—
519C2×C4C2×#433914yes—
520C2×C4C2×D4×D1114yes—
521C2×C4C2×Q8×D1114yes—
522C22—224no—
523C22—224no—
524C22—224no—
525C22—4416no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—442no—
530C22C2×#6694914yes—
531C22#1062309314yes—
532C22#1062311414yes—
533C22#1062313914yes—
534C22#1062316014yes—
535C22#1062322014yes—
536C22#1062326014yes—
537C22C22×#433911yescharacteristic
538C22C22×D4×D1111yescharacteristic
539C22C2×#6703711yescharacteristic
540C22C22×Q8×D1111yescharacteristic
541C22C2×#6704011yescharacteristic
542C22C2×#6704211yescharacteristic
543C22C2×#6704311yescharacteristic
544C4—42no—
545C4—44no—
546C4—42no—
547C4—44no—
548C4—224no—
549C4—224no—
550C4—224no—
551C4—444no—
552C4—444no—
553C4C2×#6694918yes—
554C2—444no—
555C2#1307445118yesdirect product factor
556C2C22×#6694911yescharacteristic
557C2C2×#1062313911yescharacteristic
558C2C2×#1062316011yescharacteristic
559C2C2×#1062309311yescharacteristic
560C2C2×#1062311411yescharacteristic
561C2C2×#1062326011yescharacteristic
562C2C2×#1062322011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11C2×#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13074451C2direct (N × H)
4. C2×#10622270C2semidirect
5. C2×#10622593C2semidirect
8. C2×#10622541C2semidirect
9. C2×#10622589C2semidirect
12. C2×C11×#389C2semidirect
33. C2×#66943C22semidirect
36. C11×#389C22semidirect
44. #10622593C22semidirect
45. #10622589C22semidirect
46. #10622541C22semidirect
48. #10622270C22semidirect
186. C2×#389D11semidirect
281. #389C2×D11semidirect
378. C2×C11#2629semidirect
458. C11C2×#2629semidirect
555. C2#13074451direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#669252
#130744512
C2×#106222702
C2×#106225932
C2×#106222892
C2×#106226072
C2×#106225412
C2×#106225892
C2×#106226002
C2×C11×#3892
C2×#262911