Finite Group Databasebeta

← #14853472

Subgroups — #14853472

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic
2#13070173C212yesmaximal
3#13069859C212yesmaximal
4#13069295C214yesmaximal
5#13068631C212yesmaximal
6#13068631C212yesmaximal
7C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic
8C4×C11×C4⋊Q8C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2212yes—
11C11×#391C2212yes—
12C11×#389—22no—
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4—22no—
15C43×C11C2211yescharacteristic
16C2×#66899C2214yes—
17C2×#66899C2214yes—
18#10622549C2211yescharacteristic
19#10622549C2211yescharacteristic
20#10622546—22no—
21#10622546—22no—
22#10622541C2212yes—
23#10622541C2212yes—
24C2×C4⋊(C11⋊C8)C2212yes—
25C2×C4×C11⋊C8C2212yes—
26#10622167C2214yes—
27#10622167C2214yes—
28#10622162C2212yes—
29C22×Q8×C11C2312yes—
30C11×C4⋊Q8—24no—
31C4×Q8×C11—24no—
32C4×Q8×C11—24no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4C2312yes—
37C2×C42×C11—22no—
38C2×C42×C11D412yes—
39C2×C42×C11D412yes—
40C2×C42×C11C2311yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×C4⋊Dic11C2312yes—
44C2×C4⋊Dic11C2312yes—
45C2×Dic11⋊C4—22no—
46C2×Dic11⋊C4—22no—
47C22×C11⋊C8C2314yes—
48C11×#95—24no—
49#66899—28no—
50#66899—44no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C4⋊(C11⋊C8)—24no—
58C4×C11⋊C8—42no—
59#29126—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C2×Q8×C11—22no—
65C2×Q8×C11#4114yes—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C11×C4⋊C4—28no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4—44no—
80C42×C11—24no—
81C42×C11—24no—
82C42×C11—22no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—44no—
86C42×C11#4114yes—
87C4⋊Dic11—24no—
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90Dic11⋊C4—44no—
91Dic11⋊C4—44no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—24no—
95#2864—111no—
96C4×C4⋊Q8D1111yescharacteristic
97#2099—112no—
98#2043—112no—
99#1933—114no—
100#1805—112no—
101#1805—112no—
102C4×C4⋊C8—111no—
103C23×C11C22×D411yescharacteristic
104Q8×C11—24no—
105Q8×C11—24no—
106Q8×C11—42no—
107Q8×C11—42no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11#12412yes—
120C2×C4×C11#12412yes—
121C2×C4×C11#13514yes—
122C2×C4×C11#13714yes—
123C2×C4×C11C2×#4112yes—
124C2×C4×C11C2×#4112yes—
125C2×C4×C11H(5,𝔽2)11yescharacteristic
126C2×C4×C112−1+411yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C11⋊C8—44no—
134C2×C4⋊Q8C2×D1111yescharacteristic
135C2×C4×Q8C2×D1112yes—
136C2×C4⋊C8—112no—
137C2×#103—114no—
138C2×#103—114no—
139C2×C4×C8—112no—
140#391C2×D1112yes—
141#389—22no—
142#389—112no—
143#389—112no—
144#387—222no—
145#387—222no—
146#384C2×D1111yescharacteristic
147#382—111no—
148#382—111no—
149C4×C4⋊C4—22no—
150C43C2×D1111yescharacteristic
151#340—114no—
152#340—114no—
153#336—112no—
154C22×C11#52511yescharacteristic
155C22×C11C2×#12411yescharacteristic
156C22×C11#53711yescharacteristic
157C22×C11C2×#13512yes—
158C22×C11C2×#13712yes—
159C4×C11—24no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—44no—
164C4×C11—82no—
165C4×C11#55212yes—
166C4×C11#55312yes—
167Dic11—82no—
168Dic11—82no—
169C22×Q8C22×D1112yes—
170C22×C8—114no—
171C4⋊Q8—24no—
172C4×Q8—24no—
173C4×Q8—24no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4—222no—
180C2×C4⋊C4—222no—
181C2×C4⋊C4C22×D1112yes—
182C2×C42—22no—
183C2×C42C22⋊D1112yes—
184C2×C42C22⋊D1112yes—
185C2×C42C22×D1111yescharacteristic
186C2×C42C22×D1111yescharacteristic
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—224no—
189#103—228no—
190#103—444no—
191C4×C8—442no—
192#95—24no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197#95—222no—
198#95—222no—
199C2×C11#256211yescharacteristic
200C2×C11#310812yes—
201C2×C11#313111yescharacteristic
202C2×C11#313911yescharacteristic
203C2×C11#324812yes—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8#433914yes—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4C2×C22⋊D1111yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216C22×C4C2×C22⋊D1112yes—
217C22×C4C2×C22⋊D1112yes—
218C22×C4C23×D1111yescharacteristic
219C2×C8—224no—
220C2×C8—224no—
221C2×C8—224no—
222C4⋊C4—28no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—44no—
226C4⋊C4—44no—
227C4⋊C4—224no—
228C4⋊C4—222no—
229C4⋊C4—222no—
230C4⋊C4—444no—
231C4⋊C4—444no—
232C42—24no—
233C42—24no—
234C42—22no—
235C42—21no—
236C42—21no—
237C42—44no—
238C42#434114yes—
239C11#2912611yescharacteristic, complemented, Sylow
240C23C22×C22⋊D1111yescharacteristic
241Q8—24no—
242Q8—24no—
243Q8—42no—
244Q8—42no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4#6698912yes—
263C2×C4#6698912yes—
264C2×C4#6699514yes—
265C2×C4#6700314yes—
266C2×C4C2×#433912yes—
267C2×C4C2×#434112yes—
268C2×C4#6704211yescharacteristic
269C2×C4#6704311yescharacteristic
270C8—444no—
271C22#1062332211yescharacteristic
272C22C2×#6698911yescharacteristic
273C22C2×#6699512yes—
274C22C2×#6700312yes—
275C22#1062336411yescharacteristic
276C4—24no—
277C4—22no—
278C4—24no—
279C4—22no—
280C4—44no—
281C4—82no—
282C4—882no—
283C4—882no—
284C4#1062307212yes—
285C4#1062309612yes—
286C2#1307378211yescharacteristic
287C2#1307869612yes—
288C2#1307893811yescharacteristic
289C2#1307899611yescharacteristic
290C2#1307994712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socle, prime radicalC23×C11C22×D4
hypercenterC4×C4⋊Q8D11
hypocenterC11#29126
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
239. C11#29126semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130701732
#130698592
#130692952
#130686312
C4×C4⋊(C11⋊C8)2
C4×C11×C4⋊Q82
#2912611