Finite Group Databasebeta

← C2×#13079768 #15625823

Subgroups — C2×#13079768 #15625823

Order 2816.

2006 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
1C2×#10623259C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079768C2116yesmaximal, direct product factor
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622294C211yesmaximal, characteristic, complemented
7C2×#10622497C214yesmaximal
8C2×#10622488C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic
10C2×C11×#500C211yesmaximal, characteristic, complemented
11C22×Q8×D11—21no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C2×Q8×Dic11—21no—
16C2×#66997—21no—
17#10623259—24no—
18#10623259C2218yes—
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8C2218yes—
21C2×#66950C2212yes—
22C2×#66945—21no—
23C2×C4⋊C4×D11—21no—
24C2×C4⋊C4×D11C2212yes—
25C2×#66943—21no—
26C2×#66941—21no—
27C2×#66941C2212yes—
28C2×#66940C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×#66922C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#500C2218yescomplemented
33C2×C11×#107C2214yes—
34C2×C4×C8×C11C2211yescharacteristic
35C2×(C2×D11)⋊C8C2212yes—
36C2×#66880C2214yes—
37C2×Dic11⋊C8C2212yes—
38#10622706C2218yescomplemented
39#10622691C2218yescomplemented
40C2×#66874C2214yes—
41C2×#66871C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622497C22132yes—
44#10622488C22132yescomplemented
45#10622298C2218yes—
46#10622294C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C2×Q8×D11—28no—
50C2×Q8×D11—48no—
51C22×C4×D11—22no—
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22—21no—
56C22×Dic22—22no—
57C22×Dic22C2312yes—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2314yes—
62C11×C4⋊Q8C2314yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66999—28no—
69Q8×Dic11—28no—
70#66997—28no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66950—24no—
86#66950C2318yes—
87#66945—28no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—28no—
90C4⋊C4×D11C2318yes—
91#66943—28no—
92#66941—24no—
93#66941—28no—
94#66941C2318yes—
95#66940—24no—
96#66940C2318yes—
97C42×D11D414yes—
98C42×D11C2314yes—
99#66922—22no—
100#66922—22no—
101#66922C2314yes—
102#66922C2314yes—
103C11×#107C23116yes—
104C4×C8×C11C2314yes—
105(C2×D11)⋊C8C2318yes—
106#66880C23116yes—
107Dic11⋊C8C2318yes—
108#66874C23116yes—
109#66871C23116yes—
110C4×C11⋊C8C2314yes—
111C2×#3230—111nomaximal, Sylow
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—24no—
115C2×Q8×C11—44no—
116C2×Q8×C11—44no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127Q8×D11—432no—
128C2×C4×D11—28no—
129C2×C4×D11—24no—
130C2×C4×D11—24no—
131C2×C4×D11—48no—
132C2×C4×D11Q1618yes—
133C2×C4×D11C2×D412yes—
134C2×C4×D11C2×D414yes—
135C2×C4×D11C2×D414yes—
136C2×C4×D11C2412yes—
137C2×Dic22—28no—
138C2×Dic22—22no—
139C2×Dic22—24no—
140C2×Dic22—28no—
141C2×Dic22—48no—
142C2×Dic22—44no—
143C2×Dic22C2414yes—
144C2×C8×C11—24no—
145C2×C8×C11C2414yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4C2414yes—
151C11×C4⋊C4C2414yes—
152C42×C11C2×D412yes—
153C42×C11C2412yes—
154(C2×D11)⋊C4—28no—
155C4⋊Dic11—28no—
156C4⋊Dic11—22no—
157C4⋊Dic11—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11C2414yes—
161Dic11⋊C4—28no—
162Dic11⋊C4—28no—
163Dic11⋊C4—28no—
164C4×Dic11—28no—
165C4×Dic11C2×D412yes—
166C4×Dic11C2×D414yes—
167C4×Dic11C2×D414yes—
168C4×Dic11C2412yes—
169C2×C11⋊C8—24no—
170C2×C11⋊C8C2414yes—
171C2×#533—111no—
172C22×C4⋊Q8—111no—
173#3230—1116no—
174C2×#500—111no—
175C2×#500D1111yescharacteristic, complemented
176C2×#487—111no—
177C2×#487—111no—
178C2×#484—114no—
179C2×#477—114no—
180C2×#431—111no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—22no—
184C22×D11C2×Q1614yes—
185C22×D11C22×D412yes—
186Q8×C11—48no—
187Q8×C11—48no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11C2×Q1614yes—
193C2×C4×C11AGL(1,ℤ/8)14yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D412yes—
196C2×C4×C11C22×D412yes—
197C2×C4×C112−1+414yes—
198C2×C4×C11C2511yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—44no—
204C2×Dic11—44no—
205C2×Dic11C2×Q1614yes—
206C2×Dic11C22×D412yes—
207C2×Dic11C22×D412yes—
208C2×Dic11C22×D412yes—
209C4×D11—24no—
210C4×D11—28no—
211C4×D11—24no—
212C4×D11—416no—
213C4×D11C2×Q16116yes—
214Dic22—28no—
215Dic22—416no—
216Dic22—44no—
217Dic22—48no—
218C8×C11—24no—
219C11⋊C8—24no—
220C23×Q8—221no—
221#533—118no—
222#533—224no—
223C2×C4⋊Q8—118no—
224C2×C4⋊Q8—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8—111no—
227C2×C4⋊Q8—221no—
228C2×C4⋊Q8—224no—
229C2×C4⋊Q8—221no—
230C2×C4⋊Q8C2×D1111yescharacteristic
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×#125—221no—
233C2×C22⋊Q8—112no—
234C2×C22⋊Q8—221no—
235C2×C4×Q8—112no—
236C2×C4×Q8—221no—
237C2×#117—221no—
238C22×C4⋊C4—112no—
239C22×C4⋊C4—221no—
240C22×C42—111no—
241#500—118no—
242#500C2×D1118yescomplemented
243#487—118no—
244#487—118no—
245#484—1132no—
246#477—1132no—
247#431—118no—
248C2×#107—114no—
249C2×#107C2×D1114yes—
250C2×C4⋊C8—112no—
251C2×#103—114no—
252C2×#103—114no—
253C2×C22⋊C8—112no—
254C2×C4×C8—111no—
255C2×C4×C8C2×D1111yescharacteristic
256C22×C11#53612yes—
257C22×C11C22×Q1612yes—
258C22×C11C2×AGL(1,ℤ/8)12yes—
259C22×C11C23×D411yescharacteristic
260C2×D11—22no—
261C2×D11—28no—
262C2×D11—22no—
263C2×D11C22×Q1614yes—
264C4×C11—44no—
265C4×C11—44no—
266C4×C11#53612yes—
267C4×C11C22×Q1614yes—
268C4×C11C2×AGL(1,ℤ/8)14yes—
269C4×C11C2×2−1+412yes—
270Dic11—22no—
271Dic11—22no—
272Dic11—44no—
273Dic11—44no—
274Dic11C22×Q1614yes—
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8—112no—
278C22×Q8—222no—
279C22×Q8—228no—
280C22×Q8—221no—
281C22×Q8—448no—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—222no—
286C22×C8—112no—
287C22×C8C22×D1112yes—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—118no—
291C4⋊Q8—114no—
292C4⋊Q8—114no—
293C4⋊Q8—224no—
294C4⋊Q8—228no—
295C4⋊Q8—228no—
296C4⋊Q8—222no—
297C4⋊Q8—222no—
298C4⋊Q8C22×D1114yes—
299C4⋊Q8C22×D1114yes—
300#125—228no—
301C22⋊Q8—118no—
302C22⋊Q8—224no—
303C22⋊Q8—228no—
304C4×Q8—118no—
305C4×Q8—224no—
306C4×Q8—228no—
307#117—228no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—118no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—228no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1112yes—
323C2×C22⋊C4—222no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—111no—
327C2×C42—114no—
328C2×C42—114no—
329C2×C42—222no—
330C2×C42C22×D1111yescharacteristic
331#107—1116no—
332#107C22×D11116yes—
333C4⋊C8—118no—
334#103—1116no—
335#103—1116no—
336C22⋊C8—118no—
337C4×C8—114no—
338C4×C8C22×D1114yes—
339C2×C11#323014yescomplemented
340C2×C11C2×#53611yescharacteristic
341C2×C11C23×Q1611yescharacteristic
342C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
343D11—24no—
344C24—111no—
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—44no—
348C2×Q8—44no—
349C2×Q8—114no—
350C2×Q8—228no—
351C2×Q8—222no—
352C2×Q8—224no—
353C2×Q8—228no—
354C2×Q8—448no—
355C2×Q8—4432no—
356C2×Q8—444no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—111no—
360C22×C4—118no—
361C22×C4—114no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—112no—
365C22×C4—114no—
366C22×C4—112no—
367C22×C4—228no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—448no—
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376C2×C8—24no—
377C2×C8—114no—
378C2×C8—224no—
379C2×C8C23×D1114yes—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—114no—
385C4⋊C4—228no—
386C4⋊C4—228no—
387C4⋊C4—228no—
388C4⋊C4—228no—
389C4⋊C4—222no—
390C4⋊C4—224no—
391C4⋊C4—224no—
392C4⋊C4—224no—
393C4⋊C4C23×D1114yes—
394C4⋊C4C23×D1114yes—
395C22⋊C4—228no—
396C42—114no—
397C42—112no—
398C42—114no—
399C42—112no—
400C42—228no—
401C42D4×D1112yes—
402C42C23×D1112yes—
403C11C2×#323011yescharacteristic, complemented, Sylow
404C23—114no—
405C23—112no—
406C23—222no—
407C23—222no—
408C23C2×D4×D1111yescharacteristic
409Q8—48no—
410Q8—48no—
411Q8—228no—
412Q8—4416no—
413Q8—444no—
414Q8—448no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—114no—
420C2×C4—112no—
421C2×C4—1116no—
422C2×C4—112no—
423C2×C4—112no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—224no—
427C2×C4—228no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—4416no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4#6696414yes—
435C2×C4Q16×D1114yes—
436C2×C4C2×D4×D1111yescharacteristic
437C2×C4C2×D4×D1112yes—
438C2×C4C2×D4×D1112yes—
439C2×C4#6704014yes—
440C2×C4C24×D1111yescharacteristic
441C8—24no—
442C8—224no—
443C22—114no—
444C22—222no—
445C22—222no—
446C22—228no—
447C22#1062325512yes—
448C22C2×#6696412yes—
449C22C2×Q16×D1112yes—
450C22C22×D4×D1111yescharacteristic
451C4—44no—
452C4—44no—
453C4—114no—
454C4—222no—
455C4—222no—
456C4—444no—
457C4—444no—
458C4#1062325512yes—
459C4C2×#6696414yes—
460C4C2×Q16×D1114yes—
461C4C2×#6704012yes—
462C2—224no—
463C2#1307976814yesdirect product factor
464C2C2×#1062325511yescharacteristic
465C2C22×Q16×D1111yescharacteristic
466C2C22×#6696411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#500D11
hypocenterC11C2×#3230
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13079768C2direct (N × H)
4. C2×#10622691C2semidirect
5. C2×#10622706C2semidirect
6. C2×#10622294C2semidirect
8. C2×#10622488C2semidirect
10. C2×C11×#500C2semidirect
32. C11×#500C22semidirect
38. #10622706C22semidirect
39. #10622691C22semidirect
44. #10622488C22semidirect
46. #10622294C22semidirect
175. C2×#500D11semidirect
242. #500C2×D11semidirect
339. C2×C11#3230semidirect
403. C11C2×#3230semidirect
463. C2#13079768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×D11×C4⋊Q82
#130797682
C2×#106226912
C2×#106227062
C2×#106222942
C2×#106224972
C2×#106224882
C2×#106222982
C2×C11×#5002
C2×#323011