Finite Group Databasebeta

← C2×#13076691 #14960308

Subgroups — C2×#13076691 #14960308

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C212yesmaximal, complemented
2#13076691C2116yesmaximal, direct product factor
3C2×#10622270C212yesmaximal, complemented
4C2×#10622289C212yesmaximal, complemented
5C2×#10622607C212yesmaximal, complemented
6C2×#10622607C212yesmaximal, complemented
7C2×#10622285C212yesmaximal
8C2×#10622604C211yesmaximal, characteristic
9C2×#10622589C211yesmaximal, characteristic, complemented
10C2×C11×#398C211yesmaximal, characteristic, complemented
11C23×D44C2211yescharacteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×#66951—216no—
29C2×#66951C22116yescomplemented
30C11×#398C2218yescomplemented
31C2×C11×#95C2212yes—
32C2×C11×#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35#10622607C22116yescomplemented
36#10622607C22116yescomplemented
37#10622604C2218yes—
38#10622589C2218yescomplemented
39#10622289C22116yescomplemented
40#10622285C22116yes—
41#10622270C22116yescomplemented
42C24×D11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C22×D44—44no—
52C22×D44—42no—
53C22×D44C2314yes—
54C2×C11×C4⋊C4—28no—
55C2×C11×C4⋊C4—42no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4C2318yes—
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2314yes—
60C2×(C2×D11)⋊C4—28no—
61C2×(C2×D11)⋊C4—28no—
62C2×(C2×D11)⋊C4—28no—
63C2×(C2×D11)⋊C4—44no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4C2318yes—
67C2×(C2×D11)⋊C4C2318yes—
68C2×(C2×D11)⋊C4C2318yes—
69C2×(C2×D11)⋊C4C2318yes—
70C2×(C2×D11)⋊C4C2318yes—
71C2×(C2×D11)⋊C4C2318yes—
72C2×C4⋊Dic11—28no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11C2318yes—
75C2×C4⋊Dic11C2314yes—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—44no—
78C2×Dic11⋊C4—44no—
79C2×Dic11⋊C4—44no—
80C2×Dic11⋊C4C2318yes—
81C2×Dic11⋊C4C2318yes—
82C2×Dic11⋊C4C2318yes—
83C2×Dic11⋊C4C2318yes—
84C2×C4×Dic11D418yescomplemented
85C2×C4×Dic11C2314yes—
86#66951—264no—
87C11×#95C2318yes—
88C11×#95C2314yes—
89C11⋊#95C2314yes—
90C11⋊#95C2318yes—
91C2×#2823—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C23×D11—24no—
94C23×D11—24no—
95C23×D11—24no—
96C23×D11—24no—
97C23×D11—24no—
98C23×D11—24no—
99C23×D11—24no—
100C23×D11C2414yes—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2412yes—
115C22×C4×C11C2414yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2412yes—
118C22×C4×C11C2412yes—
119C22×Dic11—24no—
120C22×Dic11—24no—
121C22×Dic11—24no—
122C22×Dic11—24no—
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11C2×D418yes—
128C22×Dic11C2414yes—
129C22×Dic11C2414yes—
130C22×Dic11C2414yes—
131C2×D44—48no—
132C2×D44—44no—
133C2×D44—416no—
134C11×C4⋊C4—216no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—44no—
137(C2×D11)⋊C4—216no—
138(C2×D11)⋊C4—216no—
139(C2×D11)⋊C4—216no—
140(C2×D11)⋊C4—48no—
141(C2×D11)⋊C4—48no—
142(C2×D11)⋊C4—48no—
143C4⋊Dic11—216no—
144C4⋊Dic11—44no—
145Dic11⋊C4—216no—
146Dic11⋊C4—48no—
147Dic11⋊C4—48no—
148Dic11⋊C4—48no—
149C4×Dic11C2×D4116yescomplemented
150C22×#126—112no—
151#2823—1116no—
152C2×#398—112no—
153C2×#398D1111yescharacteristic, complemented
154C2×#396—112no—
155C2×#396—112no—
156C2×#396—112no—
157C2×#394—112no—
158C2×#394—111no—
159C2×#384—111no—
160C23×C11C22×D412yes—
161C23×C11H(5,𝔽2)12yes—
162C23×C11H(5,𝔽2)14yes—
163C23×C112−1+414yes—
164C23×C112−1+412yes—
165C23×C11C2511yescharacteristic
166C22×D11—24no—
167C22×D11—24no—
168C22×D11—24no—
169C22×D11—24no—
170C22×D11—24no—
171C22×D11—24no—
172C22×D11—24no—
173C22×D11—48no—
174C22×D11—48no—
175C22×D11—48no—
176C22×D11—48no—
177C22×D11—48no—
178C22×D11—48no—
179C22×D11—48no—
180C2×C4×C11—28no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—48no—
194C2×C4×C11—48no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11C22×D414yes—
198C2×Dic11—216no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—48no—
208C2×Dic11—48no—
209C2×Dic11C22×D418yes—
210D44—416no—
211C23×D4—111no—
212C2×#126—1116no—
213C2×#126—2216no—
214C22×C4⋊C4—112no—
215C22×C4⋊C4—112no—
216C22×C4⋊C4—112no—
217C22×C4⋊C4—112no—
218C22×C4⋊C4—112no—
219C22×C4⋊C4—111no—
220C22×C4⋊C4C2×D1112yes—
221C22×C4⋊C4C2×D1111yescharacteristic
222C22×C4⋊C4C2×D1111yescharacteristic
223C22×C22⋊C4—112no—
224C22×C22⋊C4—112no—
225C22×C22⋊C4—112no—
226C22×C22⋊C4—112no—
227C22×C22⋊C4—112no—
228C22×C22⋊C4—112no—
229C22×C42—111no—
230#398—1116no—
231#398C2×D1118yescomplemented
232#396—1116no—
233#396—1116no—
234#396—1116no—
235#394—118no—
236#394—1116no—
237#384—118no—
238C2×#95—111no—
239C2×#95—112no—
240C2×#95C2×D1112yes—
241C2×#95C2×D1111yescharacteristic
242C22×C11#53714yes—
243C22×C11#53718yes—
244C22×C11#56014yes—
245C22×C11#56314yes—
246C22×C11#56318yes—
247C22×C11C23×D411yescharacteristic
248C22×C11C2×H(5,𝔽2)11yescharacteristic
249C22×C11C2×H(5,𝔽2)12yes—
250C22×C11C2×2−1+412yes—
251C22×C11C2×2−1+411yescharacteristic
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—816no—
260C4×C11—24no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11—42no—
264C4×C11—42no—
265Dic11—28no—
266Dic11—44no—
267Dic11—44no—
268C25—112no—
269C22×D4—114no—
270C22×D4—442no—
271C22×D4—444no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4C22×D1111yescharacteristic
276C23×C4C22×D1112yes—
277C23×C4C22×D1112yes—
278C23×C4C22×D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280#126—2264no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—118no—
285C2×C4⋊C4—118no—
286C2×C4⋊C4—118no—
287C2×C4⋊C4—118no—
288C2×C4⋊C4—114no—
289C2×C4⋊C4—118no—
290C2×C4⋊C4—228no—
291C2×C4⋊C4—228no—
292C2×C4⋊C4—444no—
293C2×C4⋊C4—444no—
294C2×C4⋊C4—444no—
295C2×C4⋊C4—442no—
296C2×C4⋊C4C22×D1118yes—
297C2×C4⋊C4C22×D1114yes—
298C2×C4⋊C4C22×D1114yes—
299C2×C22⋊C4—118no—
300C2×C22⋊C4—118no—
301C2×C22⋊C4—118no—
302C2×C22⋊C4—118no—
303C2×C22⋊C4—118no—
304C2×C22⋊C4—118no—
305C2×C22⋊C4—228no—
306C2×C22⋊C4—228no—
307C2×C22⋊C4—228no—
308C2×C22⋊C4—444no—
309C2×C22⋊C4—444no—
310C2×C22⋊C4—444no—
311C2×C42—118no—
312C2×C42—114no—
313#95—114no—
314#95—118no—
315#95C22×D1118yes—
316#95C22×D1114yes—
317C2×C11#282318yescomplemented
318C2×C11C2×#53711yescharacteristic
319C2×C11C2×#53712yes—
320C2×C11C2×#56011yescharacteristic
321C2×C11C2×#56311yescharacteristic
322C2×C11C2×#56312yes—
323D11—84no—
324C24—114no—
325C24—224no—
326C24—224no—
327C24—224no—
328C24—224no—
329C24—224no—
330C24—224no—
331C24—224no—
332C24C23×D1111yescharacteristic
333C2×D4—444no—
334C2×D4—448no—
335C2×D4—4416no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—118no—
349C22×C4—114no—
350C22×C4—114no—
351C22×C4—114no—
352C22×C4—224no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—224no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4D4×D1114yes—
361C22×C4C23×D1112yes—
362C22×C4C23×D1114yes—
363C22×C4C23×D1114yes—
364C22×C4C23×D1112yes—
365C22×C4C23×D1112yes—
366C4⋊C4—216no—
367C4⋊C4—44no—
368C4⋊C4—44no—
369C4⋊C4—2216no—
370C4⋊C4—2216no—
371C4⋊C4—448no—
372C4⋊C4—448no—
373C4⋊C4—448no—
374C4⋊C4—444no—
375C22⋊C4—2216no—
376C22⋊C4—2216no—
377C22⋊C4—2216no—
378C22⋊C4—448no—
379C22⋊C4—448no—
380C22⋊C4—448no—
381C42—1116no—
382C11C2×#282311yescharacteristic, complemented, Sylow
383C23—224no—
384C23—224no—
385C23—224no—
386C23—224no—
387C23—224no—
388C23—224no—
389C23—224no—
390C23—448no—
391C23—448no—
392C23—448no—
393C23—448no—
394C23—448no—
395C23—448no—
396C23—448no—
397C23C2×D4×D1112yes—
398C23#6703712yes—
399C23#6704014yes—
400C23#6704214yes—
401C23#6704312yes—
402C23C24×D1111yescharacteristic
403D4—4416no—
404C2×C4—28no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—48no—
418C2×C4—48no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—118no—
422C2×C4—2216no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—448no—
432C2×C4—448no—
433C2×C4C2×D4×D1114yes—
434C22—444no—
435C22—444no—
436C22—444no—
437C22—444no—
438C22—444no—
439C22—444no—
440C22—444no—
441C22—8816no—
442C22#1062312814yes—
443C22#1062316018yes—
444C22#1062319714yes—
445C22#1062323018yes—
446C22#1062326614yes—
447C22C22×D4×D1111yescharacteristic
448C22C2×#6703711yescharacteristic
449C22C2×#6704012yes—
450C22C2×#6704212yes—
451C22C2×#6704311yescharacteristic
452C4—24no—
453C4—44no—
454C4—44no—
455C4—42no—
456C4—42no—
457C4—228no—
458C4—444no—
459C4—444no—
460C2—884no—
461C2#1307669118yesdirect product factor
462C2C2×#1062312811yescharacteristic
463C2C2×#1062316012yes—
464C2C2×#1062319711yescharacteristic
465C2C2×#1062326611yescharacteristic
466C2C2×#1062323012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#398D11
hypocenterC11C2×#2823
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66951C2semidirect
2. #13076691C2direct (N × H)
3. C2×#10622270C2semidirect
4. C2×#10622289C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622607C2semidirect
9. C2×#10622589C2semidirect
10. C2×C11×#398C2semidirect
29. C2×#66951C22semidirect
30. C11×#398C22semidirect
35. #10622607C22semidirect
36. #10622607C22semidirect
38. #10622589C22semidirect
39. #10622289C22semidirect
41. #10622270C22semidirect
84. C2×C4×Dic11D4semidirect
149. C4×Dic11C2×D4semidirect
153. C2×#398D11semidirect
231. #398C2×D11semidirect
317. C2×C11#2823semidirect
382. C11C2×#2823semidirect
461. C2#13076691direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
#130766912
C2×#106222702
C2×#106222892
C2×#106226072
C2×#106222852
C2×#106226042
C2×#106225892
C2×C11×#3982
C2×#282311