Finite Group Databasebeta

← #14642356

Subgroups — #14642356

Order 2816.

372 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068733C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3#13066442C212yesmaximal
4#13066439C212yesmaximal
5C11×#2863C211yesmaximal, characteristic
6C11×#391C411yescharacteristic
7C11×#391C411yescharacteristic
8C11×#391C2211yescharacteristic
9C11×#389C411yescharacteristic
10C11×#389C411yescharacteristic
11C11×#389C2211yescharacteristic
12C11×#387—21no—
13C11×#387—21no—
14C11×#387—21no—
15C11×#383—21no—
16C43×C11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)—21no—
18C2×#66867—21no—
19#10622162—21no—
20#10622162—21no—
21#10622162C2212yes—
22#10622162C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C22×C11⋊C8—22no—
38C22×C11⋊C8—22no—
39C11×#95—21no—
40C11×#95—21no—
41C11×#95—21no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C4⋊(C11⋊C8)—42no—
49#66867—24no—
50#7709—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—22no—
77C42×C11—41no—
78C42×C11—41no—
79C42×C11—41no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86#2863D1111yescharacteristic
87#1831—111no—
88#1745—111no—
89#1272—112no—
90#1271—112no—
91C23×C11C2×C22⋊C411yescharacteristic
92Q8×C11—82no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
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#10412yes—
123C2×C4×C11#13112yes—
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13712yes—
126C2×C4×C11#13711yescharacteristic
127C11⋊C8—44no—
128C11⋊C8—82no—
129C2×C4⋊C8—221no—
130C2×#97—221no—
131#391Dic1111yescharacteristic
132#391Dic1111yescharacteristic
133#391C2×D1111yescharacteristic
134#389Dic1111yescharacteristic
135#389Dic1111yescharacteristic
136#389C2×D1111yescharacteristic
137#387—21no—
138#387—21no—
139#387—21no—
140#383—21no—
141C43C2×D1111yescharacteristic
142#336—112no—
143#336—112no—
144#336—221no—
145#336—221no—
146C22×C11#40811yescharacteristic
147C22×C11#41011yescharacteristic
148C22×C11#41311yescharacteristic
149C22×C11#41711yescharacteristic
150C22×C11#41911yescharacteristic
151C22×C11C2×#10411yescharacteristic
152C22×C11#42111yescharacteristic
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—81no—
162C4×C11—81no—
163C4×C11—81no—
164C4×C11—81no—
165C22×Q8C2×Dic1111yescharacteristic
166C22×C8—222no—
167C22×C8—222no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4C2×Dic1111yescharacteristic
172C2×C4⋊C4C2×Dic1111yescharacteristic
173C2×C4⋊C4C2×Dic1111yescharacteristic
174C2×C42C2×Dic1111yescharacteristic
175C2×C42C2×Dic1111yescharacteristic
176C2×C42C22⋊D1111yescharacteristic
177C2×C42C22⋊D1111yescharacteristic
178C2×C42C22⋊D1111yescharacteristic
179C2×C42C22⋊D1111yescharacteristic
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—442no—
182#97—224no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C2×C11#147311yescharacteristic
193C2×C11#148311yescharacteristic
194C2×C11#149711yescharacteristic
195C2×C11#150611yescharacteristic
196C2×C11#151211yescharacteristic
197C2×C11#152911yescharacteristic
198C2×C11#155911yescharacteristic
199C2×Q8—22no—
200C2×Q8—41no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C22⋊Dic1111yescharacteristic
209C22×C4C22⋊Dic1111yescharacteristic
210C22×C4C22×Dic1111yescharacteristic
211C22×C4C2×C22⋊D1111yescharacteristic
212C22×C4C2×C22⋊D1111yescharacteristic
213C2×C8—224no—
214C2×C8—442no—
215C2×C8—442no—
216C2×C8—442no—
217C2×C8—442no—
218C2×C8—442no—
219C4⋊C4—22no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C42—22no—
227C42—22no—
228C42—22no—
229C42—21no—
230C42—21no—
231C42—41no—
232C42—41no—
233C42—41no—
234C11#770911yescharacteristic, complemented, Sylow
235C23C2×C22⋊Dic1111yescharacteristic
236Q8—82no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4#6690112yes—
267C2×C4#6699512yes—
268C2×C4#6700112yes—
269C2×C4#6700211yescharacteristic
270C2×C4#6700411yescharacteristic
271C8—444no—
272C8—882no—
273C22#1062283811yescharacteristic
274C22#1062284511yescharacteristic
275C22#1062284711yescharacteristic
276C22C2×#6690111yescharacteristic
277C22#1062284911yescharacteristic
278C22#1062285011yescharacteristic
279C22#1062285311yescharacteristic
280C4—22no—
281C4—22no—
282C4—21no—
283C4—21no—
284C4—22no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—81no—
291C4—81no—
292C2#1306698511yescharacteristic
293C2#1306702911yescharacteristic
294C2#1306708911yescharacteristic
295C2#1306712811yescharacteristic
296C2#1306715411yescharacteristic
297C2#1306722311yescharacteristic
298C2#1306734611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2863C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2863D11
hypocenterC11#7709
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2863

Complements

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

NH ≅ G/Ntype
234. C11#7709semidirect

Maximal subgroups

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

subgroupindex
#130687332
#130683652
#130664422
#130664392
C11×#28632
#770911