Finite Group Databasebeta

← #14645949

Subgroups — #14645949

Order 2816.

1014 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082260C211yesmaximal, characteristic
2#13068528C211yesmaximal, characteristic, complemented
3#13067170C214yesmaximal, complemented
4C11×#1782C211yesmaximal, characteristic, complemented
5C22×C11×#41C2211yescharacteristic
6C2×#67037C411yescharacteristic, complemented
7#10623360—24no—
8#10623355—24no—
9#10623347C412yescomplemented
10#10623335—22no—
11#10623329C411yescharacteristic, complemented
12#10623322C2212yes—
13C2×#66982—22no—
14C2×C11×#99—22no—
15C11×#381C2212yescomplemented
16C2×C22⋊(C11⋊C8)—22no—
17C2×C22⋊(C11⋊C8)C2212yescomplemented
18#10622090—24no—
19#10622089—24no—
20C2×C11×#41—24no—
21C2×C11×#41—44no—
22C22×Q8×C11C2×C411yescharacteristic
23C22×D4×C11C2×C411yescharacteristic
24C22×D4×C11D412yes—
25C23×C4×C11D412yes—
26C23×C4×C11C2311yescharacteristic
27C22×C22⋊D11—22no—
28#67037—44no—
29C2×#4341—22no—
30C2×D4×D11—22no—
31C2×#4339C2×C412yes—
32C2×C11×C22⋊C4—22no—
33#67006—22no—
34C2×C22⋊Dic11—22no—
35#67000—22no—
36#66999—24no—
37#66997—22no—
38#66992—28no—
39#66990—24no—
40#66988—24no—
41D4×Dic11—24no—
42#66983D414yes—
43#66982—28no—
44#66982—24no—
45#66982—22no—
46C4×C22⋊D11—24no—
47C2×(C2×D11)⋊C4—24no—
48#66979C2×C412yes—
49#66977D414yes—
50C2×Dic11⋊C4—24no—
51C22×C11⋊C8—22no—
52C11×#99—44no—
53C11×#95—24no—
54C22⋊(C11⋊C8)—24no—
55C22⋊(C11⋊C8)—44no—
56#8462—111nomaximal, Sylow
57C24×C11C22⋊C412yes—
58C24×C11C2×D411yescharacteristic
59C23×D11—22no—
60C11×#41—416no—
61C2×Q8×C11—22no—
62C2×Q8×C11—42no—
63C2×D4×C11—24no—
64C2×D4×C11—24no—
65C2×D4×C11—24no—
66C2×D4×C11—22no—
67C2×D4×C11—42no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—42no—
73C22×C4×C11C22⋊C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D414yes—
77C2×C22⋊D11—24no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—24no—
80C2×C22⋊D11—44no—
81C2×C22⋊D11—44no—
82C22×Dic11—22no—
83C22×Dic11—24no—
84#4341—48no—
85D4×D11—48no—
86#4339—44no—
87C2×D44C22⋊C412yes—
88C2×C4×D11—22no—
89C2×Dic22C22⋊C412yes—
90C11×C22⋊C4—44no—
91C22⋊Dic11—24no—
92C22⋊Dic11—22no—
93C22⋊Dic11—24no—
94(C2×D11)⋊C4—28no—
95(C2×D11)⋊C4—24no—
96C4⋊Dic11C22⋊C414yes—
97Dic11⋊C4—28no—
98Dic11⋊C4—24no—
99C4×Dic11—22no—
100C2×C11⋊C8—44no—
101C2×C11⋊C8—42no—
102#3485—111no—
103#1782D1111yescharacteristic, complemented
104#1780—111no—
105#1516—114no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—42no—
110C23×C11—44no—
111C23×C11#9914yes—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12012yes—
114C22×D11—22no—
115C22×D11—44no—
116C22×D11—84no—
117Q8×C11—44no—
118D4×C11—28no—
119D4×C11—48no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—44no—
126C2×C4×C11—48no—
127C2×C4×C11—82no—
128C2×C4×C11—84no—
129C2×C4×C11C2×C22⋊C412yes—
130C2×C4×C11#12012yes—
131C22⋊D11—48no—
132C22⋊D11—44no—
133C22⋊D11—84no—
134C2×Dic11—24no—
135C2×Dic11—22no—
136C2×Dic11—44no—
137C2×Dic11—84no—
138D44—42no—
139C4×D11—44no—
140Dic22—42no—
141C11⋊C8—82no—
142C2×H(5,𝔽2)—111no—
143C22×#41C2×D1111yescharacteristic
144#547—224no—
145#546—224no—
146#536—112no—
147#534—222no—
148#525—112no—
149C2×#123—222no—
150#518—111no—
151C2×#99—22no—
152C2×C22⋊C8—112no—
153C2×C22⋊C8—222no—
154#381C2×D1112yescomplemented
155#328—224no—
156#327—224no—
157C22×C11—22no—
158C22×C11—24no—
159C22×C11—22no—
160C22×C11—24no—
161C22×C11—44no—
162C22×C11—44no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11#37911yescharacteristic
166C22×C11C2×#9912yes—
167C2×D11—44no—
168C2×D11—42no—
169C2×D11—164no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—42no—
173C4×C11—162no—
174Dic11—44no—
175Dic11—42no—
176H(5,𝔽2)—444no—
177C2×#41—24no—
178C2×#41—44no—
179C2×#41—112no—
180C2×#41—222no—
181C22×Q8C4×D1111yescharacteristic
182C22×D4—222no—
183C22×D4—222no—
184C22×D4C4×D1111yescharacteristic
185C22×D4C22⋊D1112yes—
186C23×C4D4412yes—
187C23×C4C22×D1111yescharacteristic
188C22×C8—222no—
189C4⋊Q8—222no—
190#124—222no—
191#123—228no—
192#123—224no—
193#123—224no—
194#123—222no—
195C22⋊Q8—114no—
196C22⋊Q8—224no—
197#121—114no—
198#121—228no—
199#120—224no—
200#120—222no—
201C4×D4—224no—
202C4×D4—224no—
203#117—112no—
204C2×C4⋊C4—224no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—224no—
207C2×C22⋊C4—222no—
208#99—44no—
209C22⋊C8—224no—
210C22⋊C8—444no—
211#95—24no—
212C2×C11—22no—
213C2×C11—42no—
214C2×C11—44no—
215C2×C11#178111yescharacteristic
216C2×C11#179412yes—
217D11—82no—
218C24—222no—
219C24(C2×D11)⋊C412yes—
220C24C2×C22⋊D1111yescharacteristic
221#41—416no—
222#41—444no—
223#41—448no—
224C2×Q8—22no—
225C2×Q8—42no—
226C2×Q8—112no—
227C2×D4—24no—
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—42no—
232C2×D4—112no—
233C2×D4—224no—
234C2×D4—222no—
235C2×D4—224no—
236C2×D4—448no—
237C2×D4—444no—
238C2×D4—444no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—222no—
245C22×C4—224no—
246C22×C4—222no—
247C22×C4(C2×D11)⋊C412yes—
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4C2×D4411yescharacteristic
250C22×C4D4×D1114yes—
251C2×C8—444no—
252C2×C8—442no—
253C4⋊C4—114no—
254C4⋊C4—228no—
255C4⋊C4—224no—
256C22⋊C4—44no—
257C22⋊C4—228no—
258C22⋊C4—224no—
259C22⋊C4—222no—
260C22⋊C4—224no—
261C22⋊C4—224no—
262C42—222no—
263C11#846211yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23—22no—
267C23—42no—
268C23—44no—
269C23—222no—
270C23—444no—
271C23—884no—
272C23#6687014yes—
273C23C2×(C2×D11)⋊C411yescharacteristic
274C23#6699012yes—
275Q8—44no—
276Q8—442no—
277D4—28no—
278D4—48no—
279D4—442no—
280D4—448no—
281D4—444no—
282D4—884no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—44no—
289C2×C4—48no—
290C2×C4—82no—
291C2×C4—84no—
292C2×C4—224no—
293C2×C4—222no—
294C2×C4—444no—
295C2×C4—444no—
296C2×C4—884no—
297C2×C4C22⋊C4×D1112yes—
298C2×C4#6693512yes—
299C8—882no—
300C22—22no—
301C22—24no—
302C22—22no—
303C22—24no—
304C22—44no—
305C22—44no—
306C22—82no—
307C22—82no—
308C22—444no—
309C22—442no—
310C22—1764no—
311C22C2×#6687012yes—
312C22#1062256811yescharacteristic
313C4—22no—
314C4—22no—
315C4—42no—
316C4—162no—
317C4—444no—
318C4—442no—
319C2—22no—
320C2—42no—
321C2—44no—
322C2—882no—
323C2#1306853011yescharacteristic
324C2#1306858212yes—
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1782C2
socleC22×C11#379
prime radical#13082260C2
cosocleC23×C4×C11C23
hypercenter#1782D11
hypocenterC11#8462
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #13068528C2semidirect
3. #13067170C2semidirect
4. C11×#1782C2semidirect
6. C2×#67037C4semidirect
9. #10623347C4semidirect
11. #10623329C4semidirect
15. C11×#381C22semidirect
17. C2×C22⋊(C11⋊C8)C22semidirect
103. #1782D11semidirect
154. #381C2×D11semidirect
263. C11#8462semidirect

Maximal subgroups

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

subgroupindex
#130822602
#130685282
#130671702
C11×#17822
#846211