Finite Group Databasebeta

← #14664590

Subgroups — #14664590

Order 2816.

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

normal subgroups only

This group has 384 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#13071907C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13066647C212yesmaximal
4#13066623C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic
8C11×#432—21no—
9#10622842—21no—
10C2×#66900—21no—
11#10622596C411yescharacteristic
12#10622596C2211yescharacteristic
13#10622593—21no—
14#10622592C411yescharacteristic
15#10622592C2211yescharacteristic
16#10622545C411yescharacteristic
17C4×Dic11⋊C4—21no—
18C4×Dic11⋊C4—21no—
19#10622537—21no—
20C11×#324—21no—
21C11×#324C2212yes—
22#10622168C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11—21no—
41C2×#4318—22no—
42C4×Dic22—41no—
43C4×Dic22—41no—
44C11×C4⋊C8—41no—
45C11×C22⋊C8—22no—
46C11×#97—41no—
47#66900—42no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C4⋊(C11⋊C8)—41no—
56C4⋊(C11⋊C8)—41no—
57#11831—111nomaximal, Sylow
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C4⋊Dic11—41no—
86Dic11⋊C4—42no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92C4×Dic11—24no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95#4318—42no—
96#4318—42no—
97C2×C11⋊C8—42no—
98#2399—111no—
99#1801—111no—
100#1467D1111yescharacteristic
101#1354—112no—
102#1346—112no—
103C23×C11C2×C22⋊C411yescharacteristic
104Q8×C11—42no—
105Q8×C11—42no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137Dic22—42no—
138Dic22—42no—
139C8×C11—82no—
140C11⋊C8—82no—
141C2×C4×Q8—111no—
142C2×C4×Q8C2×D1111yescharacteristic
143#432—21no—
144#423—221no—
145C2×#101—221no—
146#398—111no—
147#398—111no—
148#398—221no—
149#395—111no—
150#395—111no—
151#395—221no—
152C4×C4⋊C4—221no—
153C4×C4⋊C4—221no—
154#376—111no—
155#343—112no—
156#324—21no—
157#324C2×D1112yes—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C2×#9911yescharacteristic
161C22×C11#41711yescharacteristic
162C22×C11#42111yescharacteristic
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11#35612yes—
172Dic11—42no—
173Dic11—42no—
174Dic11—42no—
175Dic11—81no—
176C22×Q8—111no—
177C22×Q8D4411yescharacteristic
178C2×M16—222no—
179C4×Q8—41no—
180C4×Q8—41no—
181C4×Q8—441no—
182C4×Q8—441no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4C4×D1111yescharacteristic
190C2×C4⋊C4C22⋊D1111yescharacteristic
191C2×C4⋊C4C22×D1111yescharacteristic
192C2×C42—221no—
193C2×C42—221no—
194C2×C42C4×D1111yescharacteristic
195C2×C42D4411yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—441no—
199C4⋊C8—441no—
200#101—442no—
201C22⋊C8—22no—
202#97—41no—
203#95—111no—
204#95—111no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11#151311yescharacteristic
213C2×C11#212011yescharacteristic
214C2×C11C2×#35611yescharacteristic
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—441no—
220C2×Q8—442no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—442no—
233M16—442no—
234C2×C8—42no—
235C2×C8—442no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—441no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—224no—
253C42—441no—
254C42—441no—
255C11#1183111yescharacteristic, complemented, Sylow
256C23C2×(C2×D11)⋊C411yescharacteristic
257Q8—42no—
258Q8—42no—
259Q8—442no—
260Q8—442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4#6687011yescharacteristic
289C2×C4#6687011yescharacteristic
290C2×C4#6696111yescharacteristic
291C2×C4#6696211yescharacteristic
292C8—82no—
293C8—882no—
294C22—21no—
295C22—21no—
296C22C2×#6687011yescharacteristic
297C22#1062274611yescharacteristic
298C22#1062275211yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—442no—
308C4—442no—
309C4—442no—
310C4—881no—
311C4#1062211612yes—
312C2—21no—
313C2—21no—
314C2#1306716011yescharacteristic
315C2#1307025511yescharacteristic
316C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11831
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
255. C11#11831semidirect

Maximal subgroups

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

subgroupindex
#130719072
#130686122
#130666472
#130666232
C11×#14672
#1183111