Finite Group Databasebeta

← #14664927

Subgroups — #14664927

Order 2816.

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

normal subgroups only

This group has 372 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#13068612C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066646C212yesmaximal
4#13066643C212yesmaximal
5C11×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#400C411yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#395C411yescharacteristic
11C11×#395C2211yescharacteristic
12C11×#391—21no—
13C11×#389—21no—
14C11×#387—21no—
15C11×#387—21no—
16C11×#382C411yescharacteristic
17C2×#66900—21no—
18#10622538—21no—
19#10622537—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×#4318—22no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51#66900—42no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—41no—
54C4⋊(C11⋊C8)—41no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11905—111nomaximal, Sylow
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—42no—
61C2×Q8×C11—41no—
62C2×Q8×C11SD1612yes—
63C2×Q8×C11Q1612yes—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—42no—
91#4318—42no—
92#4318—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—42no—
95#2581D1111yescharacteristic
96#1801—111no—
97#1461—111no—
98#1354—112no—
99#1353—112no—
100C23×C11C2×C22⋊C411yescharacteristic
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—42no—
104Q8×C11—42no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10312yes—
132C2×C4×C11#10312yes—
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C11⋊C8—82no—
136C11⋊C8—82no—
137C2×C4×Q8Dic1111yescharacteristic
138C2×C4×Q8C2×D1111yescharacteristic
139#431—221no—
140#423—221no—
141C2×#101—221no—
142#400Dic1111yescharacteristic
143#400C2×D1111yescharacteristic
144#395Dic1111yescharacteristic
145#395C2×D1111yescharacteristic
146#391—21no—
147#389—21no—
148#387—21no—
149#387—21no—
150#382Dic1111yescharacteristic
151#343—112no—
152#324—112no—
153#324—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#9911yescharacteristic
157C22×C11C2×#10311yescharacteristic
158C22×C11#42111yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—42no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172C22×Q8C2×Dic1111yescharacteristic
173C22×Q8C22⋊D1111yescharacteristic
174C2×M16—222no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—41no—
178C4×Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1111yescharacteristic
184C2×C4⋊C4C2×Dic1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C42—21no—
188C2×C42C2×Dic1111yescharacteristic
189C2×C42C22⋊D1111yescharacteristic
190C2×C42C22⋊D1111yescharacteristic
191C4⋊C8—441no—
192C4⋊C8—441no—
193C4⋊C8—441no—
194#101—442no—
195C22⋊C8—222no—
196C4×C8—441no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95C2×Dic1111yescharacteristic
205#95C2×Dic1111yescharacteristic
206C2×C11—21no—
207C2×C11—21no—
208C2×C11#152011yescharacteristic
209C2×C11#212011yescharacteristic
210C2×C11#213311yescharacteristic
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—42no—
214C2×Q8—41no—
215C2×Q8#432512yes—
216C2×Q8#432612yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22×Dic1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—442no—
229M16—442no—
230C2×C8—442no—
231C2×C8—442no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—42no—
248C11#1190511yescharacteristic, complemented, Sylow
249C23C2×C22⋊Dic1111yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#6689811yescharacteristic
279C2×C4#6689811yescharacteristic
280C2×C4#6689912yes—
281C2×C4#6689912yes—
282C2×C4C2×#432511yescharacteristic
283C2×C4C2×#432611yescharacteristic
284C8—882no—
285C8—882no—
286C22—21no—
287C22—21no—
288C22C2×#6689811yescharacteristic
289C22C2×#6689911yescharacteristic
290C22#1062284911yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2#1306718811yescharacteristic
307C2#1307025711yescharacteristic
308C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2581C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2581D11
hypocenterC11#11905
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
248. C11#11905semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130669402
#130666462
#130666432
C11×#25812
#1190511