Finite Group Databasebeta

← C4×#10623251 #14916454

Subgroups — C4×#10623251 #14916454

Order 2816.

2568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623251C211yesmaximal, characteristic
2#13071809C212yesmaximal, complemented
3#13071793C211yesmaximal, characteristic, complemented
4#13071767C216yesmaximal, complemented
5#13071766C213yesmaximal, complemented
6#13071753C213yesmaximal, complemented
7C4×#66929C212yesmaximal, complemented
8C4×#66988C213yesmaximal, complemented
9C4×#66992C216yesmaximal, complemented
10C4×#66990C213yesmaximal, complemented
11C4×C11×#127C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×C4×D4×C11C2213yescomplemented
16C2×#66992C2216yes—
17C2×#66990C2213yes—
18C2×#66988C2213yes—
19C2×C4×C22⋊D11C2216yes—
20C22×C4×Dic11C2213yescomplemented
21#10623251C4116yesdirect product factor
22C2×#66929C2212yes—
23C11×#390C2213yes—
24C11×#390C2213yescomplemented
25C11×#384C2211yescharacteristic, complemented
26C43×C11C2211yescharacteristic, complemented
27#10622833C2213yes—
28#10622833C2213yes—
29#10622833C2216yescomplemented
30C4×C22⋊Dic11C2213yes—
31C4×C22⋊Dic11C2213yescomplemented
32#10622603C2216yes—
33#10622602C2216yes—
34#10622591C2216yescomplemented
35#10622585C2216yescomplemented
36#10622571C2216yes—
37#10622570C2216yes—
38#10622569C2216yes—
39#10622568C2213yes—
40#10622559C2213yes—
41#10622559C2213yescomplemented
42#10622558C2216yescomplemented
43#10622557C2216yes—
44#10622556C2213yescomplemented
45#10622555C2216yescomplemented
46#10622553C2216yes—
47C4×(C2×D11)⋊C4C2216yes—
48#10622550C2212yescomplemented
49#10622546C2216yescomplemented
50C4×Dic11⋊C4C2216yescomplemented
51C24×D11C2311yescharacteristic
52C22×D4×C11C2313yes—
53C22×D4×C11C2313yes—
54C23×C4×C11C2313yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11C2316yes—
57C23×Dic11C2313yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2313yes—
60C22×C4×D11—46no—
61C22×C4×D11C2312yes—
62C22×C4×D11C2312yes—
63C11×#127C2×C418yescomplemented
64C4×D4×C11—46no—
65C4×D4×C11—46no—
66C2×C11×C4⋊C4C2313yes—
67C2×C11×C4⋊C4C2313yes—
68C2×C11×C22⋊C4C2316yes—
69C2×C11×C22⋊C4C2313yes—
70C2×C11×C22⋊C4C2313yes—
71C2×C42×C11C2313yes—
72C2×C42×C11C2313yes—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2316yes—
75C2×C22⋊Dic11C2313yes—
76C2×C22⋊Dic11C2313yes—
77C2×C22⋊Dic11C2313yes—
78C2×C22⋊Dic11C2313yes—
79#66992C2×C4148yescomplemented
80#66990C2×C4124yescomplemented
81#66988C2×C4124yescomplemented
82C4×C22⋊D11—412no—
83C2×(C2×D11)⋊C4C2316yes—
84C2×(C2×D11)⋊C4C2316yes—
85C2×(C2×D11)⋊C4C2316yes—
86C2×Dic11⋊C4C2316yes—
87C2×Dic11⋊C4C2316yes—
88C2×Dic11⋊C4C2316yes—
89C2×C4×Dic11—46no—
90C2×C4×Dic11C2316yes—
91C2×C4×Dic11C2316yes—
92#66929C2×C4116yescomplemented
93C11⋊#95C2316yes—
94C11⋊#95C2316yes—
95C11⋊#95C2316yes—
96C11⋊#95C2316yes—
97C11⋊#95C2316yes—
98C11⋊#95C2316yes—
99C4×#560—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C24×C11C2413yes—
102C23×D11—43no—
103C23×D11—43no—
104C23×D11C22×C414yes—
105C23×D11C2412yes—
106C2×D4×C11—43no—
107C2×D4×C11—43no—
108C2×D4×C11—43no—
109C2×D4×C11—43no—
110C2×D4×C11C22×C4112yes—
111C2×D4×C11C22×C4112yescomplemented
112C22×C4×C11—26no—
113C22×C4×C11—212no—
114C22×C4×C11—26no—
115C22×C4×C11C2411yescharacteristic
116C22×C4×C11C2413yes—
117C22×C4×C11C2413yes—
118C22×C4×C11C2413yes—
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—46no—
121C2×C22⋊D11—46no—
122C2×C22⋊D11C22×C4124yes—
123C22×Dic11—43no—
124C22×Dic11—43no—
125C22×Dic11—43no—
126C22×Dic11—43no—
127C22×Dic11—46no—
128C22×Dic11C22×C4112yescomplemented
129C22×Dic11C2416yes—
130C22×Dic11C2412yes—
131C22×Dic11C2416yes—
132C2×C4×D11—212no—
133C2×C4×D11—46no—
134C2×C4×D11—416no—
135C11×C4⋊C4—43no—
136C11×C4⋊C4—43no—
137C11×C22⋊C4—43no—
138C11×C22⋊C4—46no—
139C11×C22⋊C4—43no—
140C42×C11—26no—
141C42×C11—43no—
142C42×C11C22×C414yescomplemented
143C22⋊Dic11—46no—
144C22⋊Dic11—43no—
145C22⋊Dic11—43no—
146C22⋊Dic11C22×C4112yes—
147C22⋊Dic11C22×C4112yescomplemented
148(C2×D11)⋊C4—46no—
149(C2×D11)⋊C4—46no—
150(C2×D11)⋊C4C22×C4124yes—
151Dic11⋊C4—46no—
152Dic11⋊C4—46no—
153Dic11⋊C4C22×C4124yescomplemented
154C4×Dic11—212no—
155C4×Dic11—46no—
156C2×#560—111no—
157#2383—112no—
158#2380—111no—
159#2377—116no—
160#2376—113no—
161#2375—113no—
162C4×#127D1111yescharacteristic, complemented
163C4×#126—112no—
164C4×#123—113no—
165C4×#121—116no—
166C4×#120—113no—
167C23×C11—26no—
168C23×C11—23no—
169C23×C11—23no—
170C23×C11—23no—
171C23×C11—23no—
172C23×C11—26no—
173C23×C11C23×C412yes—
174C23×C11C23×C416yes—
175C23×C11C2511yescharacteristic
176C22×D11—26no—
177C22×D11—26no—
178C22×D11—412no—
179C22×D11—44no—
180C22×D11—412no—
181C22×D11C23×C414yes—
182D4×C11—412no—
183D4×C11—412no—
184C2×C4×C11—23no—
185C2×C4×C11—23no—
186C2×C4×C11—23no—
187C2×C4×C11—26no—
188C2×C4×C11—23no—
189C2×C4×C11—23no—
190C2×C4×C11—26no—
191C2×C4×C11—44no—
192C2×C4×C11—412no—
193C2×C4×C11C23×C416yes—
194C2×C4×C11H(5,𝔽2)16yes—
195C22⋊D11—424no—
196C2×Dic11—26no—
197C2×Dic11—26no—
198C2×Dic11—26no—
199C2×Dic11—26no—
200C2×Dic11—26no—
201C2×Dic11—26no—
202C2×Dic11—412no—
203C2×Dic11—44no—
204C2×Dic11—412no—
205C2×Dic11C23×C4112yes—
206C4×D11—48no—
207C4×D11—48no—
208C24×C4—111no—
209#560—1116no—
210C2×#127C2×D1111yescharacteristic
211C2×#126—112no—
212C2×#123—113no—
213C2×#121—116no—
214C2×#120—113no—
215C2×C4×D4—116no—
216C2×C4×D4C2×D1113yes—
217C2×C4×D4C2×D1113yescomplemented
218C22×C42—113no—
219#390—116no—
220#390C2×D1113yes—
221#390C2×D1113yescomplemented
222#389—116no—
223#388—116no—
224#388—116no—
225#388—116no—
226#388—116no—
227#387—116no—
228#387—116no—
229#386—113no—
230#386—113no—
231#386—116no—
232#386—116no—
233#386—116no—
234#385—116no—
235#385—113no—
236#385—113no—
237#384C2×D1111yescharacteristic, complemented
238#383—112no—
239#381—113no—
240#380—116no—
241#379—113no—
242C4×C4⋊C4—116no—
243C4×C22⋊C4—113no—
244C4×C22⋊C4—113no—
245C4×C22⋊C4—116no—
246C43C2×D1111yescharacteristic, complemented
247C22×C11—26no—
248C22×C11—26no—
249C22×C11—212no—
250C22×C11—41no—
251C22×C11—43no—
252C22×C11—43no—
253C22×C11—46no—
254C22×C11—43no—
255C22×C11C24×C411yescharacteristic
256C22×C11C2×H(5,𝔽2)13yes—
257C22×C11#58513yes—
258C2×D11—212no—
259C2×D11—416no—
260C2×D11—42no—
261C2×D11—46no—
262C4×C11—26no—
263C4×C11—43no—
264C4×C11—41no—
265C4×C11—43no—
266C4×C11#56014yescomplemented
267Dic11—212no—
268Dic11—42no—
269Dic11—46no—
270C25—111no—
271C22×D4—116no—
272C22×D4C22×D1113yes—
273C22×D4C22×D1113yes—
274C23×C4—113no—
275C23×C4—111no—
276C23×C4—113no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—446no—
280C23×C4C22×D1113yes—
281C23×C4C22×D1111yescharacteristic
282#127C4×D1118yescomplemented
283#126—1116no—
284#123—1124no—
285#121—1148no—
286#120—1124no—
287C4×D4—46no—
288C4×D4—46no—
289C4×D4—4412no—
290C2×C4⋊C4—116no—
291C2×C4⋊C4—116no—
292C2×C4⋊C4—116no—
293C2×C4⋊C4C22×D1113yes—
294C2×C4⋊C4C22×D1113yes—
295C2×C22⋊C4—113no—
296C2×C22⋊C4—113no—
297C2×C22⋊C4—116no—
298C2×C22⋊C4—116no—
299C2×C22⋊C4—113no—
300C2×C22⋊C4—113no—
301C2×C22⋊C4—116no—
302C2×C22⋊C4—116no—
303C2×C22⋊C4C22×D1113yes—
304C2×C22⋊C4C22×D1113yes—
305C2×C22⋊C4C22×D1116yes—
306C2×C42—116no—
307C2×C42—116no—
308C2×C42—446no—
309C2×C42C22×D1113yes—
310C2×C42C22×D1113yes—
311C2×C42C22×D1111yescharacteristic
312#95—116no—
313#95—116no—
314#95—116no—
315#95—116no—
316#95—116no—
317#95—116no—
318C2×C11—42no—
319C2×C11—46no—
320C2×C11C4×H(5,𝔽2)13yes—
321C2×C11C2×#56011yescharacteristic
322C2×C11#352913yes—
323D11—44no—
324C24—112no—
325C24—114no—
326C24—443no—
327C24—443no—
328C24C23×D1111yescharacteristic
329C24C23×D1113yes—
330C2×D4—43no—
331C2×D4—43no—
332C2×D4—43no—
333C2×D4—43no—
334C2×D4—1124no—
335C2×D4—446no—
336C2×D4—446no—
337C2×D4C2×C4×D11112yes—
338C2×D4C2×C4×D11112yescomplemented
339C22×C4—26no—
340C22×C4—212no—
341C22×C4—26no—
342C22×C4—116no—
343C22×C4—1112no—
344C22×C4—116no—
345C22×C4—112no—
346C22×C4—2212no—
347C22×C4—446no—
348C22×C4—4416no—
349C22×C4—443no—
350C22×C4—443no—
351C22×C4—443no—
352C22×C4—443no—
353C22×C4—446no—
354C22×C4C23×D1111yescharacteristic
355C22×C4C23×D1113yes—
356C22×C4C23×D1113yes—
357C22×C4C23×D1113yes—
358C22×C4C23×D1111yescharacteristic
359C4⋊C4—43no—
360C4⋊C4—43no—
361C4⋊C4—1124no—
362C4⋊C4—446no—
363C4⋊C4—446no—
364C22⋊C4—43no—
365C22⋊C4—46no—
366C22⋊C4—43no—
367C22⋊C4—1112no—
368C22⋊C4—1112no—
369C22⋊C4—1124no—
370C22⋊C4—446no—
371C22⋊C4—446no—
372C22⋊C4—446no—
373C22⋊C4—443no—
374C22⋊C4—443no—
375C42—26no—
376C42—43no—
377C42—2212no—
378C42—446no—
379C42C2×C4×D1114yescomplemented
380C11C4×#56011yescharacteristic, complemented, Sylow
381C23—26no—
382C23—23no—
383C23—23no—
384C23—23no—
385C23—23no—
386C23—26no—
387C23—114no—
388C23—226no—
389C23—226no—
390C23—4412no—
391C23—444no—
392C23—4412no—
393C23C22×C4×D1112yes—
394C23C22×C4×D1116yes—
395C23C24×D1111yescharacteristic
396D4—412no—
397D4—412no—
398D4—4424no—
399C2×C4—23no—
400C2×C4—23no—
401C2×C4—23no—
402C2×C4—23no—
403C2×C4—26no—
404C2×C4—23no—
405C2×C4—26no—
406C2×C4—412no—
407C2×C4—44no—
408C2×C4—1112no—
409C2×C4—226no—
410C2×C4—226no—
411C2×C4—226no—
412C2×C4—226no—
413C2×C4—226no—
414C2×C4—226no—
415C2×C4—448no—
416C2×C4—4412no—
417C2×C4—444no—
418C2×C4—4412no—
419C2×C4—448no—
420C2×C4C22×C4×D1116yes—
421C2×C4#6703716yes—
422C22—26no—
423C22—212no—
424C22—26no—
425C22—41no—
426C22—43no—
427C22—43no—
428C22—43no—
429C22—46no—
430C22—2212no—
431C22—4416no—
432C22—442no—
433C22—446no—
434C22C23×C4×D1111yescharacteristic
435C22C2×#6703713yes—
436C22#1062345313yes—
437C4—26no—
438C4—41no—
439C4—43no—
440C4—43no—
441C4—2212no—
442C4—442no—
443C4—446no—
444C4#1062325114yesdirect product factor
445C2—42no—
446C2—46no—
447C2—444no—
448C2C4×#6703713yes—
449C2C2×#1062325111yescharacteristic
450C2#1308275213yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#127C2
socle, cosocleC23×C11C25
prime radicalC2×#10623251C2
hypercenterC4×#127D11
hypocenterC11C4×#560
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. #13071809C2semidirect
3. #13071793C2semidirect
4. #13071767C2semidirect
5. #13071766C2semidirect
6. #13071753C2semidirect
7. C4×#66929C2semidirect
8. C4×#66988C2semidirect
9. C4×#66992C2semidirect
10. C4×#66990C2semidirect
11. C4×C11×#127C2semidirect
15. C2×C4×D4×C11C22semidirect
20. C22×C4×Dic11C22semidirect
21. #10623251C4direct (N × H)
24. C11×#390C22semidirect
25. C11×#384C22semidirect
26. C43×C11C22semidirect
29. #10622833C22semidirect
31. C4×C22⋊Dic11C22semidirect
34. #10622591C22semidirect
35. #10622585C22semidirect
41. #10622559C22semidirect
42. #10622558C22semidirect
44. #10622556C22semidirect
45. #10622555C22semidirect
48. #10622550C22semidirect
49. #10622546C22semidirect
50. C4×Dic11⋊C4C22semidirect
63. C11×#127C2×C4semidirect
79. #66992C2×C4semidirect
80. #66990C2×C4semidirect
81. #66988C2×C4semidirect
92. #66929C2×C4semidirect
111. C2×D4×C11C22×C4semidirect
128. C22×Dic11C22×C4semidirect
142. C42×C11C22×C4semidirect
147. C22⋊Dic11C22×C4semidirect
153. Dic11⋊C4C22×C4semidirect
162. C4×#127D11semidirect
217. C2×C4×D4C2×D11semidirect
221. #390C2×D11semidirect
237. #384C2×D11semidirect
246. C43C2×D11semidirect
266. C4×C11#560semidirect
282. #127C4×D11semidirect
338. C2×D4C2×C4×D11semidirect
379. C42C2×C4×D11semidirect
380. C11C4×#560semidirect
444. C4#10623251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232512
#130718092
#130717932
#130717672
#130717662
#130717532
C4×#669292
C4×#669882
C4×#669922
C4×#669902
C4×C11×#1272
C4×#56011