Finite Group Databasebeta

← #14648448

Subgroups — #14648448

Order 2816.

694 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C4×#66993C211yesmaximal, characteristic
2#13067006C212yesmaximal, complemented
3#13066937C211yesmaximal, characteristic, complemented
4#13066448C212yesmaximal, complemented
5C11×#2975C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C411yescharacteristic
8C2×C4×C22⋊D11—22no—
9C2×C4×D44C2211yescharacteristic
10C11×#436—24no—
11C11×#431C2212yes—
12C11×#407—22no—
13#10622834C411yescharacteristic
14#10622601C411yescharacteristic
15#10622589C411yescharacteristic
16#10622570—22no—
17C42×Dic11C2211yescharacteristic
18#10622538C2212yes—
19#10622163—22no—
20#10622121—24no—
21C22×D4×C11C2×C411yescharacteristic
22C23×C4×C11D412yes—
23C22×C22⋊D11—22no—
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C2×C11×M16—24no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D412yes—
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33#66993—22no—
34#66993—22no—
35C4×C22⋊D11—48no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C4×D44—22no—
45C4×D44—22no—
46C11×C4⋊C8D414yescomplemented
47C11×C22⋊C8—24no—
48C11×C22⋊C8—22no—
49C4×C8×C11—22no—
50C22⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)—22no—
52C4×C11⋊C8—22no—
53#8963—111nomaximal, Sylow
54C24×C11C22⋊C412yes—
55C23×D11—21no—
56C2×D4×C11—22no—
57C2×D4×C11—21no—
58C2×D4×C11—21no—
59C2×D4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—44no—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C2×C22⋊D11—28no—
68C2×C22⋊D11—44no—
69C2×C22⋊D11—44no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×D44—22no—
74C2×D44—21no—
75C2×D44—22no—
76C2×D44M1612yescomplemented
77C2×C4×D11—44no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C11×M16—84no—
81C2×C8×C11—24no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—24no—
84C42×C11C2×D412yes—
85C42×C11#4112yes—
86C22⋊Dic11—44no—
87(C2×D11)⋊C4—44no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90Dic11⋊C4—44no—
91C4×Dic11—24no—
92C4×Dic11—21no—
93C4×Dic11—22no—
94C4×Dic11—42no—
95C4×Dic11M1612yescomplemented
96C2×C11⋊C8—42no—
97#2975D1111yescharacteristic, complemented
98C4×#127—111no—
99#1478—112no—
100#1460—111no—
101#1276—112no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11C2×C22⋊C411yescharacteristic
108C22×D11—22no—
109C22×D11—42no—
110C22×D11—42no—
111C22×D11—41no—
112C22×D11—41no—
113D4×C11—42no—
114D4×C11—42no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11C4×D412yes—
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12112yes—
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11C2×M1611yescharacteristic
126C2×C4×C11C2×M1611yescharacteristic
127C2×C4×C11#13112yes—
128C22⋊D11—416no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136C2×Dic11—41no—
137D44—24no—
138D44—42no—
139C4×D11—82no—
140C4×D11—82no—
141C8×C11—44no—
142C11⋊C8—82no—
143C2×#127—111no—
144C2×C4×D4—111no—
145C2×C4×D4—222no—
146C2×C4×D4C2×D1111yescharacteristic
147#436—24no—
148#431—112no—
149#431C2×D1112yes—
150#407—22no—
151#390—111no—
152#390—111no—
153#390—222no—
154#384—111no—
155C43—111no—
156D4⋊C8—224no—
157#323—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—44no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—82no—
165C22×C11#38611yescharacteristic
166C22×C11#40711yescharacteristic
167C22×C11#40811yescharacteristic
168C2×D11—44no—
169C2×D11—42no—
170C2×D11—82no—
171C2×D11—81no—
172C2×D11—81no—
173C4×C11—22no—
174C4×C11—21no—
175C4×C11—42no—
176C4×C11#43512yes—
177C4×C11#43612yes—
178C4×C11#45312yes—
179Dic11—24no—
180Dic11—42no—
181Dic11—81no—
182C22×D4—111no—
183C22×D4—222no—
184C22×D4C4×D1111yescharacteristic
185C23×C4—221no—
186C23×C4C22⋊D1112yes—
187C2×M16—24no—
188#127—222no—
189#127—222no—
190C4×D4—22no—
191C4×D4—22no—
192C4×D4—222no—
193C4×D4—222no—
194C4×D4—448no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—222no—
197C2×C4⋊C4C4×D1111yescharacteristic
198C2×C22⋊C4—222no—
199C2×C22⋊C4—222no—
200C2×C22⋊C4—221no—
201C2×C22⋊C4D4412yes—
202C2×C42—111no—
203C2×C42—111no—
204C2×C42—221no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—222no—
208C4⋊C8C22⋊D1114yescomplemented
209C22⋊C8—24no—
210C22⋊C8—22no—
211C22⋊C8—222no—
212C4×C8—22no—
213C4×C8—222no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—82no—
217C2×C11#187011yescharacteristic
218C2×C11#188411yescharacteristic
219C2×C11#188711yescharacteristic
220D11—82no—
221C24—221no—
222C24(C2×D11)⋊C412yes—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—112no—
228C2×D4—228no—
229C2×D4—221no—
230C2×D4—222no—
231C2×D4—222no—
232C2×D4—444no—
233C2×D4—444no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—44no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—444no—
241C22×C4—441no—
242C22×C4—441no—
243C22×C4(C2×D11)⋊C412yes—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4C2×D4411yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—84no—
248C2×C8—24no—
249C2×C8—442no—
250C4⋊C4—22no—
251C4⋊C4—222no—
252C4⋊C4—444no—
253C22⋊C4—24no—
254C22⋊C4—444no—
255C22⋊C4—444no—
256C22⋊C4—442no—
257C42—112no—
258C42—224no—
259C42—221no—
260C42—222no—
261C42—442no—
262C42#433912yes—
263C42C2×C22⋊D1112yes—
264C11#896311yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—222no—
271C23—442no—
272C23—442no—
273C23—441no—
274C23—441no—
275C23C2×(C2×D11)⋊C411yescharacteristic
276D4—42no—
277D4—42no—
278D4—224no—
279D4—4416no—
280D4—442no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—82no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4—441no—
295C2×C4—882no—
296C2×C4—882no—
297C2×C4M16×D1111yescharacteristic
298C2×C4M16×D1111yescharacteristic
299C2×C4#6696012yes—
300C2×C4C4×C22⋊D1112yes—
301C2×C4#6698211yescharacteristic
302C2×C4#6698312yes—
303C2×C4#6700611yescharacteristic
304C8—44no—
305C8—882no—
306C22—21no—
307C22—21no—
308C22—44no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—82no—
313C22—444no—
314C22—442no—
315C22—882no—
316C22—881no—
317C22—881no—
318C22#1062273911yescharacteristic
319C22#1062274211yescharacteristic
320C22#1062282611yescharacteristic
321C4—22no—
322C4—21no—
323C4—42no—
324C4—224no—
325C4—442no—
326C4—881no—
327C4#1062274012yes—
328C4#1062274112yes—
329C4#1062285412yes—
330C2—21no—
331C2—21no—
332C2—82no—
333C2—882no—
334C2#1306891311yescharacteristic
335C2#1306899911yescharacteristic
336C2#1306901411yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2975C2
socleC22×C11#386
prime radicalC2×#66993C4
cosocleC2×C42×C11C23
hypercenter#2975D11
hypocenterC11#8963
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13067006C2semidirect
3. #13066937C2semidirect
4. #13066448C2semidirect
5. C11×#2975C2semidirect
46. C11×C4⋊C8D4semidirect
76. C2×D44M16semidirect
95. C4×Dic11M16semidirect
97. #2975D11semidirect
208. C4⋊C8C22⋊D11semidirect
264. C11#8963semidirect

Maximal subgroups

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

subgroupindex
C4×#669932
#130670062
#130669372
#130664482
C11×#29752
#896311