Finite Group Databasebeta

← C2×#13074767 #14920342

Subgroups — C2×#13074767 #14920342

Order 2816.

2786 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2#13074767C2116yesmaximal, direct product factor
3C2×#10622595C211yesmaximal, characteristic, complemented
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622565C212yesmaximal, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622572C212yesmaximal
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622585C212yesmaximal, complemented
10C2×#10622603C212yesmaximal, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C2×C11×C22⋊Q8—28no—
17C2×C11×C22⋊Q8C2218yescomplemented
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66982—28no—
24C2×#66982C2218yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×Dic11⋊C4C2212yes—
33C22×C4×Dic11C2212yes—
34#10622844C2218yescomplemented
35#10622842C2218yescomplemented
36C4×C22⋊Dic11C2218yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622605C2218yescomplemented
44#10622603C22116yescomplemented
45#10622595C2218yescomplemented
46#10622585C22116yescomplemented
47#10622572C22116yes—
48#10622565C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11—44no—
55C23×C4×C11D418yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11C2314yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C11×C22⋊Q8—232no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—28no—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4C2318yes—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11C2314yes—
79C2×C22⋊Dic11C2318yes—
80#66982—232no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—44no—
98C2×C4×Dic11C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C2×#2663—111nomaximal, Sylow
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C2×D414yes—
111C24×C11C2412yes—
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11C2412yes—
119C2×Q8×C11—28no—
120C2×Q8×C11—48no—
121C2×Q8×C11—416no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—416no—
131C22×C4×C11—48no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D4116yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—48no—
141C2×C22⋊D11—416no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11#4118yes—
155C22×Dic11C2414yes—
156C22×Dic11C2412yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—216no—
162C11×C22⋊C4—216no—
163C22⋊Dic11—216no—
164C22⋊Dic11—28no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—48no—
169Dic11⋊C4—216no—
170Dic11⋊C4—28no—
171Dic11⋊C4—28no—
172Dic11⋊C4—48no—
173C4×Dic11—48no—
174C22×#123—111no—
175C22×C22⋊Q8D1111yescharacteristic, complemented
176#2663—1116no—
177C2×#400—111no—
178C2×#399—111no—
179C2×#397—112no—
180C2×#395—111no—
181C2×#394—112no—
182C2×#393—111no—
183C2×#389—112no—
184C2×#388—112no—
185C2×C4×C22⋊C4—111no—
186C23×C11—28no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—48no—
194C23×C11—48no—
195C23×C11C22×D414yes—
196C23×C11C22×D412yes—
197C23×C11C2×#4114yes—
198C23×C11H(5,𝔽2)14yes—
199C23×C112−1+412yes—
200C23×C112−1+412yes—
201C23×C11C2511yescharacteristic
202C22×D11—22no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—48no—
211C22×D11—48no—
212Q8×C11—416no—
213C2×C4×C11—28no—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—416no—
224C2×C4×C11—48no—
225C2×C4×C11—48no—
226C2×C4×C11C22×D414yes—
227C2×C4×C11C22×D414yes—
228C22⋊D11—416no—
229C2×Dic11—216no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11—44no—
245C2×Dic11—48no—
246C2×Dic11C2×#4118yes—
247C23×Q8C2×D1111yescharacteristic
248C23×D4—111no—
249C24×C4C2×D1111yescharacteristic
250C2×#123—118no—
251C2×#123—228no—
252C2×C22⋊Q8—28no—
253C2×C22⋊Q8C2×D1118yescomplemented
254C22×C4⋊C4—111no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4C2×D1111yescharacteristic
259C22×C4⋊C4C2×D1112yes—
260C22×C22⋊C4—112no—
261C22×C22⋊C4—111no—
262C22×C22⋊C4—111no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—111no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4C2×D1112yes—
267C22×C42—112no—
268#400—118no—
269#399—118no—
270#397—1116no—
271#395—118no—
272#394—1116no—
273#393—118no—
274#389—1116no—
275#388—1116no—
276C4×C22⋊C4—118no—
277C2×#95—112no—
278C2×#95—111no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—112no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—416no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11#53214yes—
290C22×C11#53414yes—
291C22×C11#53614yes—
292C22×C11#53918yes—
293C22×C11#54218yes—
294C22×C11C23×D411yescharacteristic
295C22×C11C22×#4112yes—
296C22×C11C2×H(5,𝔽2)12yes—
297C22×C11C2×2−1+411yescharacteristic
298C22×C11C2×2−1+411yescharacteristic
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—88no—
305C4×C11—24no—
306C4×C11—24no—
307C4×C11—44no—
308C4×C11—44no—
309Dic11—28no—
310Dic11—42no—
311Dic11—42no—
312Dic11—42no—
313Dic11—44no—
314C25—111no—
315C25C22×D1111yescharacteristic
316C22×Q8—24no—
317C22×Q8—44no—
318C22×Q8C22×D1114yes—
319C22×D4—114no—
320C22×D4—224no—
321C22×D4—444no—
322C23×C4—44no—
323C23×C4—112no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4C22⋊D1118yes—
329C23×C4C22×D1112yes—
330C23×C4C22×D1112yes—
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1114yes—
334#123—2232no—
335C22⋊Q8—232no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—228no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—444no—
346C2×C4⋊C4C22×D1118yes—
347C2×C4⋊C4C22×D1114yes—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—118no—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—228no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—444no—
361C2×C22⋊C4C22×D1118yes—
362C2×C42—118no—
363C2×C42—444no—
364#95—114no—
365#95—114no—
366#95—118no—
367#95—118no—
368#95—118no—
369#95—118no—
370C2×C11—44no—
371C2×C11#266318yescomplemented
372C2×C11C2×#53211yescharacteristic
373C2×C11C2×#53411yescharacteristic
374C2×C11C2×#53611yescharacteristic
375C2×C11C2×#53912yes—
376C2×C11C2×#54212yes—
377D11—82no—
378C24—24no—
379C24—22no—
380C24—22no—
381C24—24no—
382C24—112no—
383C24—224no—
384C24—222no—
385C24—222no—
386C24—224no—
387C24—222no—
388C24C2×C22⋊D1114yes—
389C24C23×D1112yes—
390C24C23×D1111yescharacteristic
391C2×Q8—28no—
392C2×Q8—48no—
393C2×Q8—416no—
394C2×D4—228no—
395C2×D4—448no—
396C2×D4—4416no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—48no—
406C22×C4—416no—
407C22×C4—118no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4C2×C22⋊D1114yes—
426C22×C4C2×C22⋊D1114yes—
427C22×C4C2×C22⋊D11116yes—
428C22×C4C23×D1114yes—
429C22×C4C23×D1114yes—
430C22×C4C23×D1112yes—
431C22×C4C23×D1112yes—
432C4⋊C4—28no—
433C4⋊C4—216no—
434C4⋊C4—2216no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—448no—
438C22⋊C4—216no—
439C22⋊C4—2216no—
440C22⋊C4—2216no—
441C22⋊C4—228no—
442C22⋊C4—228no—
443C22⋊C4—228no—
444C22⋊C4—448no—
445C42—448no—
446C11C2×#266311yescharacteristic, complemented, Sylow
447C23—28no—
448C23—28no—
449C23—28no—
450C23—24no—
451C23—22no—
452C23—22no—
453C23—24no—
454C23—48no—
455C23—48no—
456C23—224no—
457C23—222no—
458C23—222no—
459C23—224no—
460C23—222no—
461C23—444no—
462C23—444no—
463C23—444no—
464C23—448no—
465C23—448no—
466C23#6703714yes—
467C23#6704012yes—
468C23#6704012yes—
469C23#41×D1114yes—
470C23C22×C22⋊D1114yes—
471C23C22×C22⋊D1112yes—
472C23C24×D1111yescharacteristic
473Q8—416no—
474D4—4416no—
475C2×C4—28no—
476C2×C4—28no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—416no—
486C2×C4—48no—
487C2×C4—48no—
488C2×C4—118no—
489C2×C4—2216no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—444no—
503C2×C4—444no—
504C2×C4—444no—
505C2×C4—448no—
506C2×C4C22×C22⋊D1114yes—
507C2×C4C22×C22⋊D1114yes—
508C22—24no—
509C22—24no—
510C22—24no—
511C22—416no—
512C22—44no—
513C22—44no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—444no—
518C22—444no—
519C22—888no—
520C22#1062316918yes—
521C22#1062317118yes—
522C22#1062333514yes—
523C22#1062334714yes—
524C22#1062336314yes—
525C22C2×#6703712yes—
526C22C2×#6704011yescharacteristic
527C22C2×#6704011yescharacteristic
528C22C2×#41×D1112yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—24no—
531C4—24no—
532C4—44no—
533C4—44no—
534C4—228no—
535C4—442no—
536C4—442no—
537C4—442no—
538C4—444no—
539C2—44no—
540C2—882no—
541C2#1307476718yesdirect product factor
542C2C2×#1062336311yescharacteristic
543C2C2×#1062333511yescharacteristic
544C2C2×#1062334711yescharacteristic
545C2C2×#1062316912yes—
546C2C2×#1062317112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2663
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13074767C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622605C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622842C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622585C2semidirect
10. C2×#10622603C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
12. C22×C11×C22⋊Q8C2semidirect
17. C2×C11×C22⋊Q8C22semidirect
34. #10622844C22semidirect
35. #10622842C22semidirect
36. C4×C22⋊Dic11C22semidirect
43. #10622605C22semidirect
44. #10622603C22semidirect
45. #10622595C22semidirect
46. #10622585C22semidirect
48. #10622565C22semidirect
175. C22×C22⋊Q8D11semidirect
253. C2×C22⋊Q8C2×D11semidirect
371. C2×C11#2663semidirect
446. C11C2×#2663semidirect
541. C2#13074767direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
#130747672
C2×#106225952
C2×#106226052
C2×#106225652
C2×#106228422
C2×#106225722
C2×#106228442
C2×#106225852
C2×#106226032
C2×C4×C22⋊Dic112
C22×C11×C22⋊Q82
C2×#266311