Finite Group Databasebeta

← C4×C11⋊#564 #14916494

Subgroups — C4×C11⋊#564 #14916494

Order 2816.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11⋊#564C211yesmaximal, characteristic
2#13071802C211yesmaximal, characteristic
3#13071801C212yesmaximal
4#13071800C214yesmaximal
5#13071799C214yesmaximal
6#13071798C214yesmaximal
7C4×#66923C212yesmaximal
8C4×#66943C214yesmaximal
9C4×#66942C214yesmaximal
10C4×#66942C214yesmaximal
11C4×C11×#125C211yesmaximal, characteristic
12C2×C11×#125C2211yescharacteristic
13C11⋊#564C4116yesdirect product factor
14C2×#66943C2214yes—
15C2×#66942C2214yes—
16C2×#66942C2214yes—
17C2×#66923C2212yes—
18C11×#389C2212yes—
19C11×#387C2214yes—
20C11×#382C2211yescharacteristic
21C4×C11×C4⋊C4C2212yes—
22C4×C11×C4⋊C4C2214yes—
23C43×C11C2211yescharacteristic
24#10622598C2214yes—
25#10622594C2214yes—
26#10622594C2214yes—
27#10622591C2214yes—
28#10622591C2214yes—
29#10622590C2214yes—
30#10622586C2214yes—
31#10622585C2214yes—
32#10622585C2214yes—
33#10622549C2212yes—
34C4×C4⋊Dic11C2212yes—
35C4×C4⋊Dic11C2214yes—
36C4×C4⋊Dic11C2212yes—
37#10622546C2214yes—
38#10622546C2214yes—
39C4×Dic11⋊C4C2214yes—
40C4×Dic11⋊C4C2214yes—
41C4×Dic11⋊C4C2214yes—
42C4×Dic11⋊C4C2214yes—
43C42×Dic11C2214yes—
44#10622541C2212yes—
45#10622541C2212yes—
46#10622268C2214yes—
47#10622268C2214yes—
48#10622267C2214yes—
49#10622267C2214yes—
50#10622266C2214yes—
51#10622266C2214yes—
52#10622265C2214yes—
53#10622265C2214yes—
54#10622263C2214yes—
55#10622263C2214yes—
56#10622260C2214yes—
57#10622260C2214yes—
58C11×#125C2×C418yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2314yes—
63C2×C42×C11C2314yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2312yes—
66C2×C42×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2314yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2314yes—
75C2×Dic11⋊C4C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×Dic11⋊C4C2314yes—
82C2×Dic11⋊C4C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2314yes—
85C2×C4×Dic11C2314yes—
86C2×C4×Dic11C2314yes—
87C2×C4×Dic11C2314yes—
88C2×C4×Dic11C2314yes—
89#66943C2×C4132yes—
90#66942C2×C4132yes—
91#66942C2×C4132yes—
92#66923C2×C4116yes—
93C11×#95C2314yes—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C4×#564—111nomaximal, Sylow
109C22×C4×C11C2412yes—
110C22×C4×C11C2414yes—
111C22×C4×C11C2411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×C4×C11C2414yes—
114C22×C4×C11C2412yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11C2414yes—
117C22×Dic11C2414yes—
118C22×Dic11C2414yes—
119C22×Dic11C2414yes—
120C11×C4⋊C4—44no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4C22×C418yes—
123C11×C4⋊C4C22×C4116yes—
124C42×C11—22no—
125C42×C11—28no—
126C42×C11—24no—
127C42×C11—42no—
128C42×C11—41no—
129C42×C11C22×C414yes—
130C4⋊Dic11—44no—
131C4⋊Dic11—42no—
132C4⋊Dic11—42no—
133C4⋊Dic11C22×C418yes—
134C4⋊Dic11C22×C418yes—
135C4⋊Dic11C22×C4116yes—
136Dic11⋊C4—44no—
137Dic11⋊C4—44no—
138Dic11⋊C4—44no—
139Dic11⋊C4—44no—
140Dic11⋊C4C22×C4116yes—
141Dic11⋊C4C22×C4116yes—
142Dic11⋊C4C22×C4116yes—
143Dic11⋊C4C22×C4116yes—
144C4×Dic11—28no—
145C4×Dic11—28no—
146C4×Dic11—44no—
147C4×Dic11—44no—
148C4×Dic11—44no—
149C4×Dic11C22×C4116yes—
150C2×#564—111no—
151#2382—114no—
152#2382—114no—
153#2382—114no—
154#2382—112no—
155#2382—111no—
156C4×#125—114no—
157C4×#125—114no—
158C4×#125—114no—
159C4×#125—112no—
160C4×#125D1111yescharacteristic
161C23×C11C2511yescharacteristic
162C2×C4×C11—21no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11C23×C418yes—
177C2×C4×C11C23×C412yes—
178C2×C4×C11C23×C414yes—
179C2×C4×C112−1+412yes—
180C2×C4×C112−1+414yes—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11C23×C418yes—
192C2×Dic11C23×C418yes—
193#564—1116no—
194C2×#125—114no—
195C2×#125—114no—
196C2×#125—114no—
197C2×#125—112no—
198C2×#125C2×D1111yescharacteristic
199#389—114no—
200#389—114no—
201#389—114no—
202#389—114no—
203#389—112no—
204#389—112no—
205#389—114no—
206#389—114no—
207#389C2×D1112yes—
208#387—114no—
209#387—114no—
210#387—114no—
211#387—114no—
212#387—114no—
213#387—114no—
214#387—114no—
215#387—114no—
216#387—114no—
217#387—114no—
218#387—114no—
219#387—114no—
220#387—114no—
221#387—114no—
222#387C2×D1114yes—
223#382—114no—
224#382—112no—
225#382—114no—
226#382—114no—
227#382C2×D1111yescharacteristic
228C4×C4⋊C4—114no—
229C4×C4⋊C4—114no—
230C4×C4⋊C4—114no—
231C4×C4⋊C4—114no—
232C4×C4⋊C4—114no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4—112no—
235C4×C4⋊C4C2×D1114yes—
236C4×C4⋊C4C2×D1112yes—
237C43—114no—
238C43C2×D1111yescharacteristic
239C22×C11C24×C411yescharacteristic
240C22×C11C2×2−1+411yescharacteristic
241C22×C11C2×2−1+412yes—
242C22×C11#58511yescharacteristic
243C22×C11#58512yes—
244C4×C11—28no—
245C4×C11—24no—
246C4×C11—22no—
247C4×C11—44no—
248C4×C11—42no—
249C4×C11—41no—
250C4×C11#56414yescomplemented
251Dic11—28no—
252Dic11—28no—
253Dic11—44no—
254Dic11—44no—
255#125—1132no—
256#125—1132no—
257#125—1132no—
258#125—1116no—
259#125C4×D1118yes—
260C2×C4⋊C4—114no—
261C2×C4⋊C4—114no—
262C2×C4⋊C4—114no—
263C2×C4⋊C4—114no—
264C2×C4⋊C4—114no—
265C2×C4⋊C4—112no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—114no—
268C2×C4⋊C4—114no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4—114no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4C22×D1114yes—
275C2×C4⋊C4C22×D1112yes—
276C2×C4⋊C4C22×D1112yes—
277C2×C4⋊C4C22×D1114yes—
278C2×C42—114no—
279C2×C42—114no—
280C2×C42—114no—
281C2×C42—114no—
282C2×C42—114no—
283C2×C42—114no—
284C2×C42C22×D1114yes—
285C2×C42C22×D1111yescharacteristic
286C2×C42C22×D1112yes—
287C2×C42C22×D1111yescharacteristic
288C2×C42C22×D1112yes—
289C2×C42C22×D1111yescharacteristic
290#95—114no—
291#95—114no—
292#95—114no—
293#95—114no—
294#95—114no—
295#95—114no—
296#95—114no—
297#95—114no—
298#95—114no—
299#95—114no—
300#95—114no—
301#95—114no—
302#95C22×D1114yes—
303#95C22×D1114yes—
304#95C22×D1114yes—
305C2×C11C4×2−1+412yes—
306C2×C11C4×2−1+411yescharacteristic
307C2×C11C2×#56411yescharacteristic
308C2×C11#353112yes—
309C2×C11#353111yescharacteristic
310C22×C4—114no—
311C22×C4—114no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4C23×D1112yes—
315C22×C4C23×D1114yes—
316C22×C4C23×D1111yescharacteristic
317C22×C4C23×D1111yescharacteristic
318C22×C4C23×D1114yes—
319C22×C4C23×D1112yes—
320C22×C4C23×D1111yescharacteristic
321C4⋊C4—42no—
322C4⋊C4—44no—
323C4⋊C4—1116no—
324C4⋊C4—1116no—
325C4⋊C4—1116no—
326C4⋊C4—1116no—
327C4⋊C4—1116no—
328C4⋊C4—118no—
329C4⋊C4—118no—
330C4⋊C4—444no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C4⋊C4—444no—
334C4⋊C4—442no—
335C4⋊C4—442no—
336C4⋊C4—444no—
337C4⋊C4C2×C4×D1118yes—
338C4⋊C4C2×C4×D11116yes—
339C42—22no—
340C42—28no—
341C42—24no—
342C42—41no—
343C42—42no—
344C42—1116no—
345C42—228no—
346C42—228no—
347C42—444no—
348C42—444no—
349C42—444no—
350C42C2×C4×D1114yes—
351C11C4×#56411yescharacteristic, complemented, Sylow
352C23C24×D1111yescharacteristic
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—118no—
368C2×C4—118no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4—224no—
372C2×C4—224no—
373C2×C4—224no—
374C2×C4—224no—
375C2×C4—224no—
376C2×C4—224no—
377C2×C4—224no—
378C2×C4—224no—
379C2×C4C22×C4×D1118yes—
380C2×C4C22×C4×D1114yes—
381C2×C4C22×C4×D1112yes—
382C2×C4#6704012yes—
383C2×C4#6704314yes—
384C22C23×C4×D1111yescharacteristic
385C22C2×#6704011yescharacteristic
386C22C2×#6704312yes—
387C22#1062345311yescharacteristic
388C22#1062345312yes—
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—228no—
396C4—228no—
397C4—444no—
398C4—444no—
399C4C11⋊#56414yesdirect product factor
400C2C4×#6704312yes—
401C2C4×#6704011yescharacteristic
402C2C2×C11⋊#56411yescharacteristic
403C2#1308276112yes—
404C2#1308276311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#125C2
socle, prime radical, cosocleC23×C11C25
hypercenterC4×#125D11
hypocenterC11C4×#564
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
13. C11⋊#564C4direct (N × H)
250. C4×C11#564semidirect
351. C11C4×#564semidirect
399. C4C11⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11⋊#5642
#130718022
#130718012
#130718002
#130717992
#130717982
C4×#669232
C4×#669432
C4×#669422
C4×C11×#1252
C4×#56411