Finite Group Databasebeta

← #14664299

Subgroups — #14664299

Order 2816.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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#13068355C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066643C212yesmaximal, complemented
4#13066622C212yesmaximal, complemented
5C11×#2611C211yesmaximal, characteristic
6C2×C11×#125C411yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C22×#4318—21no—
9C11×#400C2211yescharacteristic
10C11×#399C411yescharacteristic
11C11×#398C2211yescharacteristic
12C11×#397C411yescharacteristic
13C11×#389—21no—
14C11×#388—21no—
15C11×#387—21no—
16C11×#385—21no—
17C11×#376C411yescharacteristic
18#10622539—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11D411yescharacteristic
24C11×#125—41no—
25C11×#125—41no—
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×#4318—24no—
44C2×#4318—22no—
45C2×#4318—41no—
46C2×#4318—42no—
47C22×C11⋊C8—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11×#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11767—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×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
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—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—42no—
94#4318—24no—
95#4318—44no—
96#4318—42no—
97C2×C11⋊C8—44no—
98C2×C11⋊C8—42no—
99C2×C11⋊C8—42no—
100#2611D1111yescharacteristic
101#1742—111no—
102#1464—111no—
103#1353—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—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11#9911yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C11⋊C8—44no—
144C11⋊C8—82no—
145C22×M16—221no—
146C2×#125Dic1111yescharacteristic
147C2×#117C2×D1111yescharacteristic
148#432—221no—
149#400C2×D1111yescharacteristic
150#399Dic1111yescharacteristic
151#398C2×D1111yescharacteristic
152#397Dic1111yescharacteristic
153#389—21no—
154#388—21no—
155#387—21no—
156#385—21no—
157#376Dic1111yescharacteristic
158#343—112no—
159#343—221no—
160#324—112no—
161#323—221no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—81no—
169C22×C11C2×#9911yescharacteristic
170C22×C11#41711yescharacteristic
171C22×C11C2×#10411yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11—81no—
184C23×C4C22⋊D1111yescharacteristic
185C2×M16—224no—
186C2×M16—222no—
187C2×M16—441no—
188C2×M16—442no—
189C22×C8—441no—
190#125—41no—
191#125—41no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×Dic1111yescharacteristic
199C2×C4⋊C4C2×Dic1111yescharacteristic
200C2×C4⋊C4C22⋊D1111yescharacteristic
201C2×C4⋊C4C22×D1111yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4C2×Dic1111yescharacteristic
205C2×C22⋊C4C22⋊D1111yescharacteristic
206C2×C42—21no—
207C2×C42C2×Dic1111yescharacteristic
208C2×C42C22⋊D1111yescharacteristic
209C4⋊C8—441no—
210C22⋊C8—222no—
211#97—441no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95C2×Dic1111yescharacteristic
218#95C2×Dic1111yescharacteristic
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—42no—
222C2×C11#150411yescharacteristic
223C2×C11#212311yescharacteristic
224C2×C11#213211yescharacteristic
225C24C22⋊Dic1111yescharacteristic
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22⋊Dic1111yescharacteristic
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—224no—
242M16—444no—
243M16—442no—
244C2×C8—444no—
245C2×C8—442no—
246C2×C8—442no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—42no—
266C11#1176711yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23#6690112yes—
272C23C2×C22⋊Dic1111yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4#6689811yescharacteristic
302C2×C4#6689811yescharacteristic
303C2×C4#6700211yescharacteristic
304C2×C4#6700411yescharacteristic
305C8—444no—
306C8—882no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—81no—
314C22C2×#6689811yescharacteristic
315C22#1062284511yescharacteristic
316C22C2×#6690111yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—81no—
329C2—21no—
330C2—21no—
331C2—42no—
332C2#1306712011yescharacteristic
333C2#1307027011yescharacteristic
334C2#1307030111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2611C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2611D11
hypocenterC11#11767
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2611

Complements

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

NH ≅ G/Ntype
3. #13066643C2semidirect
4. #13066622C2semidirect
266. C11#11767semidirect

Maximal subgroups

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

subgroupindex
#130683552
#130669502
#130666432
#130666222
C11×#26112
#1176711