Finite Group Databasebeta

← C2×#13076670 #14960302

Subgroups — C2×#13076670 #14960302

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic
3#13076670C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622561C212yesmaximal, complemented
8C2×#10622607C212yesmaximal, complemented
9C2×#10622592C212yesmaximal, complemented
10C2×#10622572C212yesmaximal
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66943—28no—
32C2×#66943C2218yescomplemented
33C2×#66938—28no—
34C2×#66938C2218yes—
35C11×#399C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yescomplemented
42#10622605C2218yescomplemented
43#10622592C22116yescomplemented
44#10622572C22116yes—
45#10622566C2218yescomplemented
46#10622561C22116yescomplemented
47#10622287C2218yescomplemented
48#10622263C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—24no—
56C22×C22⋊D11—44no—
57C22×C22⋊D11C2314yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×Dic22—24no—
64C22×Dic22—44no—
65C22×Dic22C2314yes—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—44no—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—44no—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2318yes—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—44no—
76C2×C22⋊Dic11C2314yes—
77C2×C22⋊Dic11C2318yes—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—44no—
81C2×(C2×D11)⋊C4—44no—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—28no—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2318yes—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×C4×Dic11D418yes—
97C2×C4×Dic11C2314yes—
98#66943—232no—
99#66938—232no—
100C11×#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2820—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—22no—
111C24×C11C2412yes—
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—22no—
118C23×D11C2412yes—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
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×C11C2×D414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C2×C22⋊D11—28no—
134C2×C22⋊D11—48no—
135C2×C22⋊D11—416no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×Dic22—28no—
155C2×Dic22—48no—
156C2×Dic22—416no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—48no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—48no—
161C22⋊Dic11—28no—
162C22⋊Dic11—48no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—48no—
166(C2×D11)⋊C4—48no—
167C4⋊Dic11—216no—
168C4⋊Dic11—28no—
169Dic11⋊C4—216no—
170Dic11⋊C4—48no—
171Dic11⋊C4—48no—
172C4×Dic11C2×D4116yes—
173C22×#125—111no—
174C22×#124—111no—
175#2820—1116no—
176C2×#399—111no—
177C2×#399D1111yescharacteristic, complemented
178C2×#397—111no—
179C2×#397—111no—
180C2×#396—112no—
181C2×#396—112no—
182C2×#395—112no—
183C2×#394—112no—
184C2×#382—111no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—48no—
194C23×C11—48no—
195C23×C11C22×D412yes—
196C23×C11H(5,𝔽2)14yes—
197C23×C11H(5,𝔽2)12yes—
198C23×C112−1+412yes—
199C23×C112−1+414yes—
200C23×C11C2511yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—24no—
204C22×D11—22no—
205C22×D11—24no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—48no—
210C22×D11—48no—
211C2×C4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
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—44no—
222C2×C4×C11—48no—
223C2×C4×C11—48no—
224C2×C4×C11C22×D414yes—
225C22⋊D11—416no—
226C2×Dic11—28no—
227C2×Dic11—28no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—44no—
240C2×Dic11—48no—
241C2×Dic11—48no—
242C2×Dic11C22×D414yes—
243C2×Dic11C22×D414yes—
244Dic22—416no—
245C23×Q8—111no—
246C23×D4—111no—
247C2×#125—118no—
248C2×#125—228no—
249C2×#124—118no—
250C2×#124—228no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C4⋊C4C2×D1112yes—
258C22×C22⋊C4—111no—
259C22×C22⋊C4—111no—
260C22×C22⋊C4—111no—
261C22×C22⋊C4—112no—
262C22×C22⋊C4—112no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4C2×D1111yescharacteristic
265C22×C22⋊C4C2×D1112yes—
266C22×C42—111no—
267#399—118no—
268#399C2×D1118yescomplemented
269#397—118no—
270#397—118no—
271#396—1116no—
272#396—1116no—
273#395—1116no—
274#394—1116no—
275#382—118no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—111no—
280C2×#95C2×D1111yescharacteristic
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—88no—
287C22×C11#53514yes—
288C22×C11#53614yes—
289C22×C11#53714yes—
290C22×C11#56218yes—
291C22×C11#56318yes—
292C22×C11C23×D411yescharacteristic
293C22×C11C2×H(5,𝔽2)12yes—
294C22×C11C2×H(5,𝔽2)11yescharacteristic
295C22×C11C2×2−1+411yescharacteristic
296C22×C11C2×2−1+412yes—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—88no—
303C4×C11—24no—
304C4×C11—44no—
305C4×C11—42no—
306C4×C11—44no—
307Dic11—24no—
308Dic11—24no—
309Dic11—42no—
310Dic11—44no—
311Dic11—44no—
312C25—111no—
313C25C22×D1111yescharacteristic
314C22×Q8—114no—
315C22×Q8—224no—
316C22×Q8—444no—
317C22×D4—114no—
318C22×D4—224no—
319C22×D4—444no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—112no—
323C23×C4—111no—
324C23×C4—112no—
325C23×C4C22×D1112yes—
326C23×C4C22×D1112yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329#125—2232no—
330#124—2232no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—118no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—444no—
342C2×C4⋊C4—444no—
343C2×C4⋊C4C22×D1114yes—
344C2×C4⋊C4C22×D1118yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—114no—
348C2×C22⋊C4—114no—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—118no—
351C2×C22⋊C4—118no—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—224no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—444no—
357C2×C22⋊C4—444no—
358C2×C22⋊C4—444no—
359C2×C22⋊C4C22×D1114yes—
360C2×C22⋊C4C22×D1118yes—
361C2×C42—118no—
362C2×C42—114no—
363#95—118no—
364#95—114no—
365#95—118no—
366#95—118no—
367#95C22×D1114yes—
368C2×C11—82no—
369C2×C11#282018yescomplemented
370C2×C11C2×#53511yescharacteristic
371C2×C11C2×#53611yescharacteristic
372C2×C11C2×#53711yescharacteristic
373C2×C11C2×#56212yes—
374C2×C11C2×#56312yes—
375D11—82no—
376C24—22no—
377C24—24no—
378C24—22no—
379C24—22no—
380C24—24no—
381C24—112no—
382C24—222no—
383C24—224no—
384C24—222no—
385C24—222no—
386C24—224no—
387C24C23×D1112yes—
388C24C23×D1111yescharacteristic
389C2×Q8—228no—
390C2×Q8—448no—
391C2×Q8—4416no—
392C2×D4—228no—
393C2×D4—448no—
394C2×D4—4416no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—224no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4D4×D1114yes—
423C22×C4C23×D1114yes—
424C22×C4C23×D1112yes—
425C22×C4C23×D1114yes—
426C22×C4C23×D1112yes—
427C4⋊C4—28no—
428C4⋊C4—48no—
429C4⋊C4—2216no—
430C4⋊C4—2216no—
431C4⋊C4—228no—
432C4⋊C4—448no—
433C4⋊C4—448no—
434C22⋊C4—28no—
435C22⋊C4—48no—
436C22⋊C4—228no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C22⋊C4—448no—
440C22⋊C4—448no—
441C22⋊C4—448no—
442C42—1116no—
443C11C2×#282011yescharacteristic, complemented, Sylow
444C23—22no—
445C23—24no—
446C23—22no—
447C23—22no—
448C23—24no—
449C23—44no—
450C23—44no—
451C23—48no—
452C23—44no—
453C23—48no—
454C23—222no—
455C23—224no—
456C23—222no—
457C23—222no—
458C23—224no—
459C23—444no—
460C23—444no—
461C23—448no—
462C23—444no—
463C23—448no—
464C23C2×D4×D1112yes—
465C23#6703714yes—
466C23#6704012yes—
467C23#6704212yes—
468C23#6704314yes—
469C23C24×D1111yescharacteristic
470Q8—4416no—
471D4—4416no—
472C2×C4—28no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—48no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—114no—
486C2×C4—114no—
487C2×C4—228no—
488C2×C4—228no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—444no—
501C2×C4—448no—
502C2×C4—448no—
503C2×C4C2×D4×D1114yes—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—44no—
508C22—44no—
509C22—88no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—444no—
514C22—444no—
515C22—888no—
516C22#1062316014yes—
517C22#1062317718yes—
518C22#1062317914yes—
519C22#1062319818yes—
520C22#1062324614yes—
521C22C22×D4×D1111yescharacteristic
522C22C2×#6703712yes—
523C22C2×#6704011yescharacteristic
524C22C2×#6704211yescharacteristic
525C22C2×#6704312yes—
526C4—24no—
527C4—42no—
528C4—44no—
529C4—44no—
530C4—224no—
531C4—224no—
532C4—442no—
533C4—444no—
534C4—444no—
535C2—82no—
536C2—882no—
537C2#1307667018yesdirect product factor
538C2C2×#1062324611yescharacteristic
539C2C2×#1062317911yescharacteristic
540C2C2×#1062316011yescharacteristic
541C2C2×#1062319812yes—
542C2C2×#1062317712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13076670C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622607C2semidirect
9. C2×#10622592C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#399C2semidirect
32. C2×#66943C22semidirect
35. C11×#399C22semidirect
41. #10622607C22semidirect
42. #10622605C22semidirect
43. #10622592C22semidirect
45. #10622566C22semidirect
46. #10622561C22semidirect
47. #10622287C22semidirect
48. #10622263C22semidirect
177. C2×#399D11semidirect
268. #399C2×D11semidirect
369. C2×C11#2820semidirect
443. C11C2×#2820semidirect
537. C2#13076670direct (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×#669382
#130766702
C2×#106226052
C2×#106222872
C2×#106225662
C2×#106225612
C2×#106226072
C2×#106225922
C2×#106225722
C2×#106222632
C2×C11×#3992
C2×#282011