Finite Group Databasebeta

← #14664280

Subgroups — #14664280

Order 2816.

428 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074193C211yesmaximal, characteristic
2#13068355C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066623C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C22×#4318—21no—
8C2×C4×Dic22C411yescharacteristic
9C11×#432—21no—
10#10622823—21no—
11#10622596C2211yescharacteristic
12#10622592C2211yescharacteristic
13#10622591—21no—
14#10622566C411yescharacteristic
15#10622560C411yescharacteristic
16#10622557—21no—
17#10622550C411yescharacteristic
18#10622546—21no—
19C11×#324C2212yes—
20C11×#323—21no—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×#4318—24no—
41C2×#4318—22no—
42C2×#4318—41no—
43C2×#4318—42no—
44C22×C11⋊C8—41no—
45C4×Dic22—41no—
46C4×Dic22—41no—
47C11×C4⋊C8—41no—
48C11×C22⋊C8—22no—
49C11×#97—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11763—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—41no—
76C2×Dic22—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88C4⋊Dic11—41no—
89Dic11⋊C4—42no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94C4×Dic11—42no—
95#4318—24no—
96#4318—44no—
97#4318—42no—
98C2×C11⋊C8—44no—
99C2×C11⋊C8—42no—
100#2599—111no—
101#1742—111no—
102#1464D1111yescharacteristic
103#1354—112no—
104#1346—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11#10412yes—
110C23×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143Dic22—42no—
144Dic22—42no—
145C8×C11—82no—
146C11⋊C8—44no—
147C22×M16—221no—
148C2×C4×Q8—111no—
149C2×#117C2×D1111yescharacteristic
150#432—21no—
151#398—111no—
152#397—111no—
153#395—111no—
154#393—111no—
155#388—221no—
156#387—221no—
157#387—221no—
158#385—221no—
159#383—111no—
160#343—112no—
161#343—221no—
162#324C2×D1112yes—
163#323—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—81no—
171C22×C11C2×#9911yescharacteristic
172C22×C11#41711yescharacteristic
173C22×C11C2×#10411yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182Dic11—42no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—111no—
187C23×C4D4411yescharacteristic
188C2×M16—224no—
189C2×M16—222no—
190C2×M16—441no—
191C2×M16—442no—
192C22×C8—441no—
193C4×Q8—441no—
194C4×Q8—441no—
195#117—41no—
196#117—41no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4D4411yescharacteristic
202C2×C4⋊C4C22×D1111yescharacteristic
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4C4×D1111yescharacteristic
206C2×C22⋊C4C22⋊D1111yescharacteristic
207C2×C42—221no—
208C2×C42C4×D1111yescharacteristic
209C2×C42C22⋊D1111yescharacteristic
210C4⋊C8—41no—
211C22⋊C8—22no—
212#97—41no—
213#95—111no—
214#95—111no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—42no—
224C2×C11#150411yescharacteristic
225C2×C11#212011yescharacteristic
226C2×C11#213511yescharacteristic
227C24(C2×D11)⋊C411yescharacteristic
228C2×Q8—441no—
229C2×Q8—442no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4C2×C4×D1111yescharacteristic
243C22×C4C2×D4411yescharacteristic
244C22×C4C2×C22⋊D1111yescharacteristic
245M16—224no—
246M16—444no—
247M16—442no—
248C2×C8—42no—
249C2×C8—444no—
250C2×C8—442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—441no—
254C4⋊C4—442no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—442no—
262C22⋊C4—442no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—442no—
268C11#1176311yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#6688912yes—
274C23C2×(C2×D11)⋊C411yescharacteristic
275Q8—442no—
276Q8—442no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4#6687011yescharacteristic
306C2×C4#6687011yescharacteristic
307C2×C4#6696111yescharacteristic
308C2×C4#6696211yescharacteristic
309C8—82no—
310C8—444no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#6687011yescharacteristic
319C22#1062274611yescharacteristic
320C22C2×#6688911yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—442no—
330C4—881no—
331C4—881no—
332C4—881no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1306712111yescharacteristic
337C2#1307025511yescharacteristic
338C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11763
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066623C2semidirect
268. C11#11763semidirect

Maximal subgroups

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

subgroupindex
#130741932
#130683552
#130666472
#130666232
C11×#14642
#1176311