Finite Group Databasebeta

← C2×#13079778 #15625844

Subgroups — C2×#13079778 #15625844

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10623259C211yesmaximal, characteristic
3#13079778C2116yesmaximal, direct product factor
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622294C211yesmaximal, characteristic, complemented
7C2×#10622480C214yesmaximal
8C2×#10622470C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic
10C2×C11×#498C211yesmaximal, characteristic, complemented
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66999—21no—
15C2×Q8×Dic11—21no—
16C2×Q8×Dic11—21no—
17#10623259—24no—
18#10623259—24no—
19#10623259C2218yes—
20#10623259C2218yes—
21C2×#66950—21no—
22C2×#66950C2212yes—
23C2×#66945—21no—
24C2×#66945C2212yes—
25C2×#66943—21no—
26C2×#66943C2212yes—
27C2×#66940—21no—
28C2×#66940C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×#66922C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#498C2218yescomplemented
33C2×C11×#106C2214yes—
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#10622480C22132yes—
44#10622470C22132yescomplemented
45#10622298C2218yes—
46#10622294C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×Dic22—21no—
53C22×Dic22C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8C2314yes—
58C11×C4⋊Q8C2314yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64#66999—28no—
65#66999—28no—
66Q8×Dic11—28no—
67Q8×Dic11—28no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84#66950—24no—
85#66950—28no—
86#66950C2318yes—
87#66945—24no—
88#66945—28no—
89#66945C2318yes—
90#66943—24no—
91#66943—28no—
92#66943C2318yes—
93#66940—24no—
94#66940—28no—
95#66940C2318yes—
96C42×D11D414yes—
97C42×D11C2314yes—
98#66922—22no—
99#66922—22no—
100#66922C2314yes—
101#66922C2314yes—
102C11×#106C23116yes—
103C4×C8×C11C2314yes—
104(C2×D11)⋊C8C2318yes—
105#66880C23116yes—
106Dic11⋊C8C2318yes—
107#66874C23116yes—
108#66871C23116yes—
109C4×C11⋊C8C2314yes—
110C2×#3231—111nomaximal, Sylow
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—44no—
115C2×Q8×C11—44no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C2×C4×D11—24no—
127C2×C4×D11—24no—
128C2×C4×D11—24no—
129C2×C4×D11C2×D412yes—
130C2×C4×D11C2×D414yes—
131C2×C4×D11C2×D414yes—
132C2×C4×D11C2412yes—
133C2×Dic22—22no—
134C2×Dic22—24no—
135C2×Dic22—28no—
136C2×Dic22—44no—
137C2×Dic22C2414yes—
138C2×C8×C11—24no—
139C2×C8×C11C2414yes—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2414yes—
145C11×C4⋊C4C2414yes—
146C42×C11C2×D412yes—
147C42×C11C2412yes—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—28no—
150C4⋊Dic11—28no—
151C4⋊Dic11—28no—
152C4⋊Dic11—22no—
153C4⋊Dic11—24no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156C4⋊Dic11C2414yes—
157Dic11⋊C4—28no—
158Dic11⋊C4—28no—
159C4×Dic11—28no—
160C4×Dic11—28no—
161C4×Dic11C2×D412yes—
162C4×Dic11C2×D414yes—
163C4×Dic11C2×D414yes—
164C4×Dic11C2412yes—
165C2×C11⋊C8—24no—
166C2×C11⋊C8C2414yes—
167C2×#533—111no—
168C2×#533—111no—
169#3231—1116no—
170C2×#500—111no—
171C2×#498D1111yescharacteristic, complemented
172C2×#487—111no—
173C2×#487—111no—
174C2×#485—114no—
175C2×#479—114no—
176C2×#431—111no—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11C22×D412yes—
182Q8×C11—48no—
183Q8×C11—48no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11#13514yes—
189C2×C4×C11#13714yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D412yes—
192C2×C4×C11C22×D412yes—
193C2×C4×C112−1+414yes—
194C2×C4×C11C2511yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11C22×D412yes—
203C2×Dic11C22×D412yes—
204C2×Dic11C22×D412yes—
205C4×D11—24no—
206C4×D11—28no—
207C4×D11—28no—
208C4×D11—24no—
209Dic22—28no—
210Dic22—44no—
211Dic22—48no—
212C8×C11—24no—
213C11⋊C8—24no—
214#533—118no—
215#533—118no—
216#533—224no—
217#533—224no—
218C2×C4⋊Q8—111no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×C4⋊Q8C2×D1111yescharacteristic
222C2×#125—112no—
223C2×#125—221no—
224C2×C22⋊Q8—112no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—221no—
227C2×C22⋊Q8—221no—
228C2×C4×Q8—112no—
229C2×C4×Q8—221no—
230C2×C4×Q8—221no—
231C2×C4×Q8—221no—
232C2×#117—112no—
233C2×#117—221no—
234C22×C42—111no—
235#500—118no—
236#498C2×D1118yescomplemented
237#487—118no—
238#487—118no—
239#485—1132no—
240#479—1132no—
241#431—118no—
242C2×#107—114no—
243C2×#106C2×D1114yes—
244C2×C4⋊C8—112no—
245C2×#103—114no—
246C2×#103—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8C2×D1111yescharacteristic
250C22×C11#53612yes—
251C22×C11C2×#13512yes—
252C22×C11C2×#13712yes—
253C22×C11C23×D411yescharacteristic
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—44no—
258C4×C11—44no—
259C4×C11—44no—
260C4×C11#53612yes—
261C4×C11C2×#13514yes—
262C4×C11C2×#13714yes—
263C4×C11C2×2−1+412yes—
264Dic11—22no—
265Dic11—22no—
266Dic11—22no—
267Dic11—44no—
268Dic11—44no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—112no—
272C22×Q8—221no—
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—111no—
276C22×C8—112no—
277C22×C8C22×D1112yes—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C4⋊Q8—114no—
281C4⋊Q8—114no—
282C4⋊Q8—222no—
283C4⋊Q8—222no—
284C4⋊Q8C22×D1114yes—
285C4⋊Q8C22×D1114yes—
286#125—118no—
287#125—224no—
288#125—228no—
289C22⋊Q8—118no—
290C22⋊Q8—224no—
291C22⋊Q8—228no—
292C22⋊Q8—228no—
293C22⋊Q8—228no—
294C4×Q8—118no—
295C4×Q8—224no—
296C4×Q8—228no—
297C4×Q8—228no—
298C4×Q8—228no—
299#117—118no—
300#117—224no—
301#117—228no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42—111no—
319C2×C42—114no—
320C2×C42—114no—
321C2×C42—222no—
322C2×C42—222no—
323C2×C42C22×D1111yescharacteristic
324#107—1116no—
325#106C22×D11116yes—
326C4⋊C8—118no—
327#103—1116no—
328#103—1116no—
329C22⋊C8—118no—
330C4×C8—114no—
331C4×C8C22×D1114yes—
332C2×C11#323114yescomplemented
333C2×C11C2×#53611yescharacteristic
334C2×C11C22×#13511yescharacteristic
335C2×C11C22×#13711yescharacteristic
336D11—42no—
337C24—111no—
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—114no—
343C2×Q8—224no—
344C2×Q8—222no—
345C2×Q8—228no—
346C2×Q8—444no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—112no—
353C22×C4—114no—
354C22×C4—114no—
355C22×C4—112no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364C2×C8—24no—
365C2×C8—114no—
366C2×C8—224no—
367C2×C8C23×D1114yes—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—114no—
373C4⋊C4—228no—
374C4⋊C4—228no—
375C4⋊C4—228no—
376C4⋊C4—228no—
377C4⋊C4—222no—
378C4⋊C4—224no—
379C4⋊C4—224no—
380C4⋊C4—224no—
381C4⋊C4C23×D1114yes—
382C4⋊C4C23×D1114yes—
383C22⋊C4—228no—
384C22⋊C4—228no—
385C42—114no—
386C42—112no—
387C42—114no—
388C42—112no—
389C42—228no—
390C42—228no—
391C42D4×D1112yes—
392C42C23×D1112yes—
393C11C2×#323111yescharacteristic, complemented, Sylow
394C23—112no—
395C23—222no—
396C23—222no—
397C23—222no—
398C23C2×D4×D1111yescharacteristic
399Q8—48no—
400Q8—48no—
401Q8—228no—
402Q8—444no—
403Q8—448no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—112no—
409C2×C4—112no—
410C2×C4—112no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—224no—
415C2×C4—228no—
416C2×C4—228no—
417C2×C4—224no—
418C2×C4—224no—
419C2×C4—224no—
420C2×C4—444no—
421C2×C4—444no—
422C2×C4#6696814yes—
423C2×C4#6696914yes—
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4C2×D4×D1112yes—
426C2×C4C2×D4×D1112yes—
427C2×C4#6704014yes—
428C2×C4C24×D1111yescharacteristic
429C8—24no—
430C8—224no—
431C22—222no—
432C22—222no—
433C22—222no—
434C22—444no—
435C22#1062325512yes—
436C22C2×#6696812yes—
437C22C2×#6696912yes—
438C22C22×D4×D1111yescharacteristic
439C4—44no—
440C4—44no—
441C4—222no—
442C4—222no—
443C4—222no—
444C4—444no—
445C4—444no—
446C4#1062325512yes—
447C4C2×#6696814yes—
448C4C2×#6696914yes—
449C4C2×#6704012yes—
450C2—442no—
451C2#1307977814yesdirect product factor
452C2C2×#1062325511yescharacteristic
453C2C22×#6696911yescharacteristic
454C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#498D11
hypocenterC11C2×#3231
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13079778C2direct (N × H)
4. C2×#10622691C2semidirect
5. C2×#10622706C2semidirect
6. C2×#10622294C2semidirect
8. C2×#10622470C2semidirect
10. C2×C11×#498C2semidirect
32. C11×#498C22semidirect
38. #10622706C22semidirect
39. #10622691C22semidirect
44. #10622470C22semidirect
46. #10622294C22semidirect
171. C2×#498D11semidirect
236. #498C2×D11semidirect
332. C2×C11#3231semidirect
393. C11C2×#3231semidirect
451. C2#13079778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
#130797782
C2×#106226912
C2×#106227062
C2×#106222942
C2×#106224802
C2×#106224702
C2×#106222982
C2×C11×#4982
C2×#323111