Finite Group Databasebeta

← C4×#10623125 #14916478

Subgroups — C4×#10623125 #14916478

Order 2816.

2664 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623125C211yesmaximal, characteristic
2#13071789C216yesmaximal, complemented
3#13071786C213yesmaximal, complemented
4#13071757C211yesmaximal, characteristic, complemented
5#13071755C212yesmaximal, complemented
6#13071754C213yesmaximal, complemented
7C4×#66989C213yesmaximal, complemented
8C4×#66938C216yesmaximal, complemented
9C4×#67006C212yesmaximal, complemented
10C4×#66990C213yesmaximal, complemented
11C4×C11×#120C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic, complemented
14C2×C11×#120C2211yescharacteristic
15C2×C4×D4×C11C2213yes—
16C2×#67006C2212yes—
17C2×#66990C2213yes—
18C2×#66989C2213yes—
19C2×C4×C22⋊D11C2216yes—
20#10623125C4116yesdirect product factor
21C2×#66938C2216yes—
22C2×C4×Dic22C2213yescomplemented
23C11×#386C2213yes—
24C11×#385C2213yescomplemented
25C11×#379C2211yescharacteristic, complemented
26C4×C11×C22⋊C4C2213yescomplemented
27#10622860C2212yescomplemented
28#10622834C2213yes—
29#10622833C2213yes—
30#10622826C2216yes—
31#10622823C2216yescomplemented
32C4×C22⋊Dic11C2213yescomplemented
33C4×C22⋊Dic11C2216yescomplemented
34#10622602C2216yescomplemented
35#10622590C2213yescomplemented
36#10622587C2213yescomplemented
37#10622570C2216yes—
38#10622569C2216yes—
39#10622568C2213yescomplemented
40#10622564C2216yescomplemented
41#10622559C2213yescomplemented
42#10622558C2216yescomplemented
43#10622558C2216yescomplemented
44#10622557C2216yescomplemented
45C4×(C2×D11)⋊C4C2216yescomplemented
46C42×Dic11C2213yescomplemented
47#10622283C2216yescomplemented
48#10622282C2216yescomplemented
49#10622263C2216yescomplemented
50#10622259C2216yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C22×D4×C11C2313yes—
54C23×C4×C11—46no—
55C23×C4×C11C2313yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2313yes—
58C22×C22⋊D11C2316yes—
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—46no—
61C22×C4×D11C2312yes—
62C22×C4×D11C2312yes—
63C22×Dic22C2313yes—
64C11×#120C2×C418yescomplemented
65C4×D4×C11—46no—
66C2×C11×C4⋊C4C2313yes—
67C2×C11×C22⋊C4C2313yes—
68C2×C11×C22⋊C4C2313yes—
69C2×C11×C22⋊C4C2313yes—
70C2×C11×C22⋊C4C2313yes—
71C2×C42×C11C2313yes—
72#67006C2×C4116yescomplemented
73C2×C22⋊Dic11C2316yes—
74C2×C22⋊Dic11C2313yes—
75C2×C22⋊Dic11C2316yes—
76C2×C22⋊Dic11C2316yes—
77C2×C22⋊Dic11C2313yes—
78#66990C2×C4124yescomplemented
79#66989C2×C4124yescomplemented
80C4×C22⋊D11—412no—
81C2×(C2×D11)⋊C4C2316yes—
82C2×(C2×D11)⋊C4C2316yes—
83C2×(C2×D11)⋊C4C2316yes—
84C2×C4⋊Dic11C2313yes—
85C2×Dic11⋊C4C2316yes—
86C2×Dic11⋊C4C2316yes—
87C2×C4×Dic11C2316yes—
88C2×C4×Dic11C2316yes—
89C2×C4×Dic11C2313yes—
90C2×C4×Dic11C2313yes—
91#66938C2×C4148yescomplemented
92C4×Dic22—46no—
93C11×#95C2316yes—
94C11⋊#95C2316yes—
95C11⋊#95C2316yes—
96C11⋊#95C2316yes—
97C11⋊#95C2316yes—
98C11⋊#95C2316yes—
99C4×H(3,𝔽4)—111nomaximal, Sylow
100C24×C11—43no—
101C24×C11—43no—
102C24×C11C22×C414yescomplemented
103C24×C11C2411yescharacteristic
104C24×C11C2413yes—
105C23×D11—43no—
106C23×D11—43no—
107C23×D11C22×C414yescomplemented
108C23×D11C2412yes—
109C2×D4×C11—43no—
110C2×D4×C11—43no—
111C2×D4×C11C22×C4112yes—
112C22×C4×C11—212no—
113C22×C4×C11—26no—
114C22×C4×C11—26no—
115C22×C4×C11—43no—
116C22×C4×C11—46no—
117C22×C4×C11—416no—
118C22×C4×C11C2411yescharacteristic
119C22×C4×C11C2413yes—
120C22×C4×C11C2413yes—
121C22×C4×C11C2413yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—46no—
124C2×C22⋊D11—46no—
125C2×C22⋊D11C22×C4124yes—
126C22×Dic11—43no—
127C22×Dic11C2412yes—
128C22×Dic11C2416yes—
129C22×Dic11C2416yes—
130C2×C4×D11—212no—
131C2×C4×D11—46no—
132C2×C4×D11—416no—
133C2×Dic22—43no—
134C2×Dic22—43no—
135C2×Dic22C22×C4112yescomplemented
136C11×C4⋊C4—43no—
137C11×C22⋊C4—43no—
138C11×C22⋊C4—43no—
139C11×C22⋊C4—43no—
140C11×C22⋊C4C22×C4112yescomplemented
141C42×C11—26no—
142C22⋊Dic11—46no—
143C22⋊Dic11—46no—
144C22⋊Dic11—43no—
145C22⋊Dic11C22×C4124yescomplemented
146C22⋊Dic11C22×C4112yescomplemented
147(C2×D11)⋊C4—46no—
148(C2×D11)⋊C4—46no—
149(C2×D11)⋊C4C22×C4124yescomplemented
150C4⋊Dic11—43no—
151Dic11⋊C4—46no—
152Dic11⋊C4—46no—
153C4×Dic11—212no—
154C4×Dic11—43no—
155C4×Dic11—46no—
156C4×Dic11C22×C4112yescomplemented
157C2×H(3,𝔽4)—111no—
158#2379—113no—
159#2379—116no—
160#2375—113no—
161#2375—112no—
162#2375—111no—
163C4×#124—116no—
164C4×#124—113no—
165C4×#120—112no—
166C4×#120—113no—
167C4×#120D1111yescharacteristic, complemented
168C23×C11—26no—
169C23×C11—23no—
170C23×C11—23no—
171C23×C11—26no—
172C23×C11—23no—
173C23×C11—23no—
174C23×C11—412no—
175C23×C11—44no—
176C23×C11—412no—
177C23×C11C23×C412yes—
178C23×C11C23×C416yes—
179C23×C11C2511yescharacteristic
180C22×D11—26no—
181C22×D11—26no—
182C22×D11—412no—
183C22×D11—44no—
184C22×D11—412no—
185C22×D11C23×C414yes—
186D4×C11—412no—
187C2×C4×C11—23no—
188C2×C4×C11—23no—
189C2×C4×C11—23no—
190C2×C4×C11—26no—
191C2×C4×C11—23no—
192C2×C4×C11—23no—
193C2×C4×C11—26no—
194C2×C4×C11—412no—
195C2×C4×C11—44no—
196C2×C4×C11—412no—
197C2×C4×C11C23×C416yes—
198C2×C4×C11H(5,𝔽2)16yes—
199C22⋊D11—424no—
200C2×Dic11—26no—
201C2×Dic11—26no—
202C2×Dic11—26no—
203C2×Dic11—26no—
204C2×Dic11—26no—
205C2×Dic11—26no—
206C2×Dic11—44no—
207C2×Dic11C23×C4112yes—
208C4×D11—48no—
209C4×D11—48no—
210Dic22—412no—
211C24×C4—111no—
212C24×C4C2×D1111yescharacteristic, complemented
213H(3,𝔽4)—1116no—
214C2×#124—113no—
215C2×#124—116no—
216C2×#120—112no—
217C2×#120—113no—
218C2×#120C2×D1111yescharacteristic
219C2×C4×Q8—113no—
220C2×C4×D4—116no—
221C2×C4×D4C2×D1113yes—
222#391—113no—
223#391—116no—
224#390—113no—
225#390—116no—
226#388—116no—
227#388—116no—
228#388—116no—
229#388—116no—
230#388—116no—
231#388—116no—
232#386—113no—
233#386—116no—
234#386—116no—
235#386C2×D1113yes—
236#385—116no—
237#385—116no—
238#385—113no—
239#385C2×D1113yescomplemented
240#382—113no—
241#382—116no—
242#379—112no—
243#379—113no—
244#379C2×D1111yescharacteristic, complemented
245C4×C22⋊C4—116no—
246C4×C22⋊C4—113no—
247C4×C22⋊C4—116no—
248C4×C22⋊C4C2×D1113yescomplemented
249C43—113no—
250C22×C11—26no—
251C22×C11—26no—
252C22×C11—212no—
253C22×C11—416no—
254C22×C11—43no—
255C22×C11—41no—
256C22×C11—43no—
257C22×C11—46no—
258C22×C11—43no—
259C22×C11C24×C411yescharacteristic
260C22×C11C2×H(5,𝔽2)13yes—
261C22×C11#58513yes—
262C2×D11—212no—
263C2×D11—416no—
264C2×D11—42no—
265C2×D11—46no—
266C4×C11—26no—
267C4×C11—43no—
268C4×C11—41no—
269C4×C11—43no—
270C4×C11H(3,𝔽4)14yescomplemented
271Dic11—212no—
272Dic11—42no—
273Dic11—46no—
274C25—111no—
275C25C22×D1111yescharacteristic
276C22×Q8—113no—
277C22×D4—116no—
278C22×D4C22×D1113yes—
279C23×C4—46no—
280C23×C4—111no—
281C23×C4—112no—
282C23×C4—112no—
283C23×C4—446no—
284C23×C4C22×D1113yes—
285C23×C4C22×D1111yescharacteristic
286C23×C4C22×D1113yes—
287#124—1124no—
288#124—1148no—
289#120—1116no—
290#120—1124no—
291#120C4×D1118yescomplemented
292C4×Q8—446no—
293C4×D4—46no—
294C4×D4—4412no—
295C2×C4⋊C4—116no—
296C2×C4⋊C4—116no—
297C2×C4⋊C4—113no—
298C2×C4⋊C4C22×D1113yes—
299C2×C22⋊C4—113no—
300C2×C22⋊C4—116no—
301C2×C22⋊C4—116no—
302C2×C22⋊C4—116no—
303C2×C22⋊C4—113no—
304C2×C22⋊C4—116no—
305C2×C22⋊C4—116no—
306C2×C22⋊C4—116no—
307C2×C22⋊C4C22×D1113yes—
308C2×C22⋊C4C22×D1113yes—
309C2×C22⋊C4C22×D1113yes—
310C2×C22⋊C4C22×D1113yes—
311C2×C42—113no—
312C2×C42—116no—
313C2×C42—116no—
314C2×C42—113no—
315C2×C42C22×D1113yes—
316#95—116no—
317#95—116no—
318#95—116no—
319#95—116no—
320#95—116no—
321#95C22×D1116yes—
322C2×C11—42no—
323C2×C11—46no—
324C2×C11C4×H(5,𝔽2)13yes—
325C2×C11C2×H(3,𝔽4)11yescharacteristic
326C2×C11#352913yes—
327D11—44no—
328C24—43no—
329C24—43no—
330C24—112no—
331C24—114no—
332C24—443no—
333C24—443no—
334C24C2×C4×D1114yescomplemented
335C24C23×D1111yescharacteristic
336C24C23×D1113yes—
337C2×Q8—1112no—
338C2×Q8—443no—
339C2×Q8—443no—
340C2×D4—43no—
341C2×D4—43no—
342C2×D4—1124no—
343C2×D4—446no—
344C2×D4—446no—
345C2×D4C2×C4×D11112yes—
346C22×C4—26no—
347C22×C4—26no—
348C22×C4—212no—
349C22×C4—46no—
350C22×C4—43no—
351C22×C4—416no—
352C22×C4—116no—
353C22×C4—112no—
354C22×C4—116no—
355C22×C4—2212no—
356C22×C4—446no—
357C22×C4—4416no—
358C22×C4—443no—
359C22×C4C23×D1111yescharacteristic
360C22×C4C23×D1113yes—
361C22×C4C23×D1113yes—
362C22×C4C23×D1113yes—
363C22×C4C23×D1111yescharacteristic
364C4⋊C4—43no—
365C4⋊C4—446no—
366C4⋊C4—446no—
367C4⋊C4—443no—
368C22⋊C4—43no—
369C22⋊C4—43no—
370C22⋊C4—43no—
371C22⋊C4—1112no—
372C22⋊C4—1124no—
373C22⋊C4—1124no—
374C22⋊C4—446no—
375C22⋊C4—446no—
376C22⋊C4—446no—
377C22⋊C4—443no—
378C22⋊C4—446no—
379C22⋊C4C2×C4×D11112yescomplemented
380C42—26no—
381C42—1112no—
382C42—2212no—
383C42—443no—
384C42—446no—
385C11C4×H(3,𝔽4)11yescharacteristic, complemented, Sylow
386C23—23no—
387C23—23no—
388C23—26no—
389C23—23no—
390C23—23no—
391C23—26no—
392C23—412no—
393C23—44no—
394C23—412no—
395C23—114no—
396C23—226no—
397C23—226no—
398C23—4412no—
399C23—444no—
400C23—4412no—
401C23C22×C4×D1112yes—
402C23C22×C4×D1116yes—
403C23C24×D1111yescharacteristic
404Q8—4412no—
405D4—412no—
406D4—4424no—
407C2×C4—23no—
408C2×C4—23no—
409C2×C4—23no—
410C2×C4—23no—
411C2×C4—23no—
412C2×C4—26no—
413C2×C4—26no—
414C2×C4—412no—
415C2×C4—412no—
416C2×C4—44no—
417C2×C4—1112no—
418C2×C4—226no—
419C2×C4—226no—
420C2×C4—226no—
421C2×C4—226no—
422C2×C4—226no—
423C2×C4—226no—
424C2×C4—448no—
425C2×C4—444no—
426C2×C4—448no—
427C2×C4C22×C4×D1116yes—
428C2×C4#6703716yes—
429C22—26no—
430C22—26no—
431C22—212no—
432C22—416no—
433C22—43no—
434C22—41no—
435C22—43no—
436C22—46no—
437C22—43no—
438C22—2212no—
439C22—4416no—
440C22—442no—
441C22—446no—
442C22C23×C4×D1111yescharacteristic
443C22C2×#6703713yes—
444C22#1062345313yes—
445C4—26no—
446C4—43no—
447C4—41no—
448C4—43no—
449C4—2212no—
450C4—442no—
451C4—446no—
452C4#1062312514yesdirect product factor
453C2—46no—
454C2—42no—
455C2—444no—
456C2C4×#6703713yes—
457C2C2×#1062312511yescharacteristic
458C2#1308275413yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#120C2
socle, cosocleC23×C11C25
prime radicalC2×#10623125C2
hypercenterC4×#120D11
hypocenterC11C4×H(3,𝔽4)
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
2. #13071789C2semidirect
3. #13071786C2semidirect
4. #13071757C2semidirect
5. #13071755C2semidirect
6. #13071754C2semidirect
7. C4×#66989C2semidirect
8. C4×#66938C2semidirect
9. C4×#67006C2semidirect
10. C4×#66990C2semidirect
11. C4×C11×#120C2semidirect
12. C24×C4×C11C22semidirect
13. C23×C4×D11C22semidirect
20. #10623125C4direct (N × H)
22. C2×C4×Dic22C22semidirect
24. C11×#385C22semidirect
25. C11×#379C22semidirect
26. C4×C11×C22⋊C4C22semidirect
27. #10622860C22semidirect
31. #10622823C22semidirect
32. C4×C22⋊Dic11C22semidirect
33. C4×C22⋊Dic11C22semidirect
34. #10622602C22semidirect
35. #10622590C22semidirect
36. #10622587C22semidirect
39. #10622568C22semidirect
40. #10622564C22semidirect
41. #10622559C22semidirect
42. #10622558C22semidirect
43. #10622558C22semidirect
44. #10622557C22semidirect
45. C4×(C2×D11)⋊C4C22semidirect
46. C42×Dic11C22semidirect
47. #10622283C22semidirect
48. #10622282C22semidirect
49. #10622263C22semidirect
50. #10622259C22semidirect
64. C11×#120C2×C4semidirect
72. #67006C2×C4semidirect
78. #66990C2×C4semidirect
79. #66989C2×C4semidirect
91. #66938C2×C4semidirect
102. C24×C11C22×C4semidirect
107. C23×D11C22×C4semidirect
135. C2×Dic22C22×C4semidirect
140. C11×C22⋊C4C22×C4semidirect
145. C22⋊Dic11C22×C4semidirect
146. C22⋊Dic11C22×C4semidirect
149. (C2×D11)⋊C4C22×C4semidirect
156. C4×Dic11C22×C4semidirect
167. C4×#120D11semidirect
212. C24×C4C2×D11semidirect
239. #385C2×D11semidirect
244. #379C2×D11semidirect
248. C4×C22⋊C4C2×D11semidirect
270. C4×C11H(3,𝔽4)semidirect
291. #120C4×D11semidirect
334. C24C2×C4×D11semidirect
379. C22⋊C4C2×C4×D11semidirect
385. C11C4×H(3,𝔽4)semidirect
452. C4#10623125direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231252
#130717892
#130717862
#130717572
#130717552
#130717542
C4×#669892
C4×#669382
C4×#670062
C4×#669902
C4×C11×#1202
C4×H(3,𝔽4)11