Finite Group Databasebeta

← #14651470

Subgroups — #14651470

Order 2816.

554 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077645C211yesmaximal, characteristic
2#13073569C211yesmaximal, characteristic
3#13067332C212yesmaximal, complemented
4#13066471C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×#66977—21no—
9C2×#66922C2211yescharacteristic
10C11×#432C2212yes—
11#10622834C412yes—
12#10622820—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622624—24no—
15#10622589C412yes—
16#10622562—21no—
17#10622562—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622539C2212yes—
20C11×#323—21no—
21C11×#323—21no—
22#10622124—24no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22—21no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38#66977—44no—
39#66977—44no—
40C2×Dic11⋊C4—22no—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11C2×C412yes—
43C2×#4318—22no—
44C22×C11⋊C8—22no—
45#66922—22no—
46#66922—22no—
47C11×C4⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×#97—22no—
50C11⋊#95—21no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)D414yes—
55#66867—22no—
56#9455—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22⋊C411yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C2×Dic22—42no—
76C2×Dic22—42no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×C8×C11—42no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C42×C11C2×D412yes—
84C42×C11#4112yes—
85C22⋊Dic11—44no—
86C22⋊Dic11—44no—
87C4⋊Dic11—24no—
88C4⋊Dic11—24no—
89C4⋊Dic11—42no—
90Dic11⋊C4—44no—
91Dic11⋊C4—44no—
92C4×Dic11—42no—
93#4318—82no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8—82no—
96#2973—111no—
97#2542—111no—
98#1556—112no—
99#1466D1111yescharacteristic
100#1285—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11#10112yes—
111C23×C11C2×C22⋊C411yescharacteristic
112D4×C11—44no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C4×D412yes—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12112yes—
128C2×C4×C11#12311yescharacteristic
129C2×Dic11—24no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135Dic22—82no—
136Dic22—82no—
137C8×C11—82no—
138C11⋊C8—44no—
139C2×C4⋊Q8—111no—
140C2×C22⋊Q8—221no—
141C2×C22⋊Q8—221no—
142C2×C4×D4C2×D1111yescharacteristic
143#435—224no—
144#432—112no—
145#432C2×D1112yes—
146#407—221no—
147C2×C22⋊C8—221no—
148#399—221no—
149#399—221no—
150#390—112no—
151#384—112no—
152C4×C4⋊C4—111no—
153#332—224no—
154#323—21no—
155#323—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—22no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#38611yescharacteristic
169C22×C11C2×#10111yescharacteristic
170C22×C11#41311yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11#45312yes—
177Dic11—44no—
178Dic11—82no—
179C22×Q8—221no—
180C22×D4C4×D1111yescharacteristic
181C23×C4D4411yescharacteristic
182C23×C4D4411yescharacteristic
183C2×M16—222no—
184C22×C8—222no—
185C4⋊Q8—222no—
186C4⋊Q8—222no—
187C22⋊Q8—444no—
188C22⋊Q8—444no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4C4×D1111yescharacteristic
197C2×C22⋊C4—222no—
198C2×C22⋊C4—222no—
199C2×C22⋊C4C22⋊D1111yescharacteristic
200C2×C22⋊C4C22⋊D1111yescharacteristic
201C2×C42—112no—
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—22no—
204C4⋊C8—114no—
205C22⋊C8—22no—
206C22⋊C8—222no—
207C22⋊C8—222no—
208C22⋊C8—222no—
209#97—22no—
210#97—222no—
211#95—221no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11—42no—
215C2×C11—81no—
216C2×C11#188711yescharacteristic
217C2×C11#190111yescharacteristic
218C2×C11#190911yescharacteristic
219C24(C2×D11)⋊C411yescharacteristic
220C24(C2×D11)⋊C411yescharacteristic
221C2×Q8—442no—
222C2×Q8—442no—
223C2×Q8—441no—
224C2×Q8—441no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—222no—
235C22×C4—222no—
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C2×D4411yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—882no—
242C2×C8—42no—
243C2×C8—224no—
244C2×C8—882no—
245C4⋊C4—22no—
246C4⋊C4—224no—
247C4⋊C4—224no—
248C4⋊C4—444no—
249C4⋊C4—444no—
250C4⋊C4—442no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—444no—
254C22⋊C4—444no—
255C42—442no—
256C42D4×D1112yes—
257C42#434112yes—
258C11#945511yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#6688812yes—
269C23C2×(C2×D11)⋊C411yescharacteristic
270Q8—882no—
271Q8—882no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—224no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4(C22⋊D11)⋊C412yes—
292C2×C4#6693511yescharacteristic
293C2×C4#6693911yescharacteristic
294C2×C4#6699212yes—
295C8—82no—
296C8—444no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1062257111yescharacteristic
310C22#1062274511yescharacteristic
311C22C2×#6688811yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—444no—
318C4—882no—
319C4#1062236012yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2#1306901211yescharacteristic
325C2#1306908211yescharacteristic
326C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1466C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1466D11
hypocenterC11#9455
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13067332C2semidirect
4. #13066471C2semidirect
258. C11#9455semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130735692
#130673322
#130664712
C11×#14662
#945511