Finite Group Databasebeta

← #14664408

Subgroups — #14664408

Order 2816.

572 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071981C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic
3#13066647C214yesmaximal, complemented
4C11×#1465C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C11×#407—21no—
9#10622833—21no—
10C2×#66897—21no—
11#10622825C411yescharacteristic
12#10622592C2212yes—
13#10622560C412yes—
14#10622559—21no—
15#10622542—21no—
16C4×#4318—21no—
17C11×#324C2212yes—
18C11×#323—21no—
19#10622168C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C22×Dic22—21no—
25C22×Dic22—44no—
26C22×Dic22—41no—
27C22×Dic22—41no—
28C22×Dic22C2×C412yes—
29C2×C11×M16—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39#66977—44no—
40C2×Dic11⋊C4—22no—
41C2×#4318—22no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—41no—
44#66897—24no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95C2×C412yes—
48#66867—41no—
49C4×C11⋊C8—41no—
50#11791—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22⋊C411yescharacteristic
53C2×D4×C11—22no—
54C2×D4×C11—22no—
55C2×D4×C11—41no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—42no—
70C22×Dic11—44no—
71C2×Dic22—24no—
72C2×Dic22—42no—
73C2×Dic22—42no—
74C2×Dic22—48no—
75C2×Dic22—44no—
76C2×Dic22—44no—
77C2×Dic22—44no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C11×M16—82no—
81C2×C8×C11—42no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—21no—
86C42×C11—21no—
87C22⋊Dic11—44no—
88C22⋊Dic11—42no—
89C4⋊Dic11—42no—
90Dic11⋊C4—44no—
91#4318—24no—
92#4318—42no—
93C2×C11⋊C8—42no—
94#2409—111no—
95C4×#100—111no—
96#1465D1111yescharacteristic
97#1354—114no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10412yes—
108C23×C11C2×C22⋊C411yescharacteristic
109D4×C11—44no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11#9911yescharacteristic
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#13712yes—
126C2×Dic11—24no—
127C2×Dic11—42no—
128C2×Dic11—48no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133Dic22—44no—
134Dic22—44no—
135Dic22—44no—
136Dic22—44no—
137C8×C11—82no—
138C11⋊C8—44no—
139C23×Q8—111no—
140C2×C22⋊Q8—221no—
141C2×C4×D4C2×D1111yescharacteristic
142C2×#100—221no—
143#407—21no—
144C4×M16—221no—
145#395—112no—
146#393—112no—
147#391—221no—
148#386—221no—
149#385—221no—
150#380—111no—
151#343—112no—
152#324C2×D1112yes—
153#323—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41911yescharacteristic
168C22×C11C2×#10411yescharacteristic
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11AΣL(1,𝔽16)12yes—
175Dic11—44no—
176Dic11—82no—
177C22×Q8—112no—
178C22×Q8—221no—
179C22×Q8—441no—
180C22×Q8—441no—
181C22×Q8—444no—
182C22×D4D4411yescharacteristic
183C23×C4—221no—
184C23×C4C4×D1111yescharacteristic
185C23×C4C22⋊D1111yescharacteristic
186C2×M16—41no—
187C2×M16—222no—
188C22⋊Q8—444no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—222no—
193C2×C4⋊C4C22×D1111yescharacteristic
194C2×C22⋊C4—222no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4C4×D1111yescharacteristic
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C42D4411yescharacteristic
199#100—224no—
200C22⋊C8—22no—
201C22⋊C8—41no—
202#97—441no—
203C4×C8—441no—
204#95—112no—
205#95—222no—
206#95—222no—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—42no—
210C2×C11—81no—
211C2×C11#150811yescharacteristic
212C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C11#213511yescharacteristic
214C24(C2×D11)⋊C411yescharacteristic
215C24(C2×D11)⋊C411yescharacteristic
216C2×Q8—224no—
217C2×Q8—442no—
218C2×Q8—442no—
219C2×Q8—444no—
220C2×Q8—444no—
221C2×Q8—448no—
222C2×Q8—444no—
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—444no—
237C22×C4—442no—
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4C2×D4411yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243M16—82no—
244M16—224no—
245M16—442no—
246C2×C8—42no—
247C2×C8—442no—
248C4⋊C4—41no—
249C4⋊C4—442no—
250C4⋊C4—444no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—444no—
254C22⋊C4—442no—
255C42—21no—
256C42—21no—
257C11#1179111yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23#6688912yes—
268C23C2×(C2×D11)⋊C411yescharacteristic
269Q8—444no—
270Q8—444no—
271Q8—444no—
272Q8—444no—
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—224no—
288C2×C4—442no—
289C2×C4—448no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4#6687011yescharacteristic
295C2×C4#6687011yescharacteristic
296C2×C4#6696212yes—
297C8—82no—
298C8—444no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#6687011yescharacteristic
312C22#1062273311yescharacteristic
313C22C2×#6688911yescharacteristic
314C4—22no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—444no—
320C4—882no—
321C4#1062210912yes—
322C2—21no—
323C2—21no—
324C2—42no—
325C2—81no—
326C2#1306713711yescharacteristic
327C2C2×#1062210911yescharacteristic
328C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11791
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
257. C11#11791semidirect

Maximal subgroups

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

subgroupindex
#130719812
C4×#668972
#130666472
C11×#14652
#1179111