Finite Group Databasebeta

← #14853494

Subgroups — #14853494

Order 2816.

674 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
2C4×#66922C211yesmaximal, characteristic
3#13070180C212yesmaximal
4#13069863C212yesmaximal
5#13069306C214yesmaximal
6#13068632C212yesmaximal
7#13068632C212yesmaximal
8C11×#1767C211yesmaximal, characteristic
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2212yes—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×#97C2212yes—
13C43×C11C2211yescharacteristic
14C2×#66880C2214yes—
15C2×#66880C2214yes—
16#10622549C2211yescharacteristic
17#10622549C2211yescharacteristic
18#10622548C2211yescharacteristic
19C4×C4⋊Dic11—22no—
20#10622546—22no—
21#10622546—22no—
22#10622542C2212yes—
23#10622541—22no—
24#10622541C2212yes—
25#10622541C2212yes—
26C11×#336C2212yes—
27#10622189C2214yes—
28#10622189C2214yes—
29C22×Dic22C2312yes—
30C22×C8×C11C2314yes—
31C2×C42×C11D412yes—
32C2×C42×C11D412yes—
33C2×C42×C11C2311yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11C2312yes—
39C2×C4⋊Dic11C2312yes—
40C2×C4⋊Dic11C2312yes—
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—22no—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45#66922—24no—
46C4×Dic22—24no—
47C4×Dic22—24no—
48C11×C4⋊C8—24no—
49C11×#97—42no—
50C11⋊#95—24no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66880—28no—
58#66880—44no—
59#29129—111nomaximal, Sylow
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×C4×C11C2411yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—22no—
73C2×Dic22—22no—
74C2×Dic22#4114yes—
75C2×C8×C11—24no—
76C2×C8×C11—24no—
77C2×C8×C11—24no—
78C42×C11—24no—
79C42×C11—22no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—42no—
83C42×C11#4114yes—
84C4⋊Dic11—28no—
85C4⋊Dic11—24no—
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90C4⋊Dic11—44no—
91Dic11⋊C4—44no—
92Dic11⋊C4—44no—
93Dic11⋊C4—44no—
94C4×Dic11—44no—
95#2864—111no—
96C4×C4⋊Q8—111no—
97#2100—112no—
98#2043—112no—
99#1935—114no—
100#1805—112no—
101#1805—112no—
102#1767D1111yescharacteristic
103C23×C11C22×D411yescharacteristic
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11#12412yes—
112C2×C4×C11#12412yes—
113C2×C4×C11#13714yes—
114C2×C4×C11C2×#4112yes—
115C2×C4×C11C2×#4112yes—
116C2×C4×C11H(5,𝔽2)11yescharacteristic
117C2×C4×C112−1+411yescharacteristic
118C2×Dic11—24no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—44no—
129Dic22—24no—
130Dic22—24no—
131Dic22—42no—
132Dic22—42no—
133C8×C11—44no—
134C2×C4⋊Q8—111no—
135C2×C4×Q8—112no—
136C2×C4⋊C8C2×D1112yes—
137C2×#103—114no—
138C2×#103—114no—
139C2×#97C2×D1112yes—
140#391—112no—
141#389—112no—
142#389—112no—
143#389—222no—
144#387—222no—
145#387—222no—
146#384—111no—
147#382—111no—
148#382—111no—
149C4×C4⋊C4—222no—
150C43C2×D1111yescharacteristic
151#340—114no—
152#340—114no—
153#336C2×D1112yes—
154C22×C11#52511yescharacteristic
155C22×C11C2×#12411yescharacteristic
156C22×C11#53711yescharacteristic
157C22×C11C2×#13712yes—
158C22×C11#57512yes—
159C4×C11—24no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—42no—
163C4×C11#55212yes—
164C4×C11#55312yes—
165Dic11—44no—
166Dic11—82no—
167Dic11—82no—
168Dic11—82no—
169C22×Q8—112no—
170C22×C8C22×D1114yes—
171C4⋊Q8—224no—
172C4×Q8—224no—
173C4×Q8—224no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—222no—
179C2×C4⋊C4—222no—
180C2×C4⋊C4—222no—
181C2×C4⋊C4—222no—
182C2×C42—222no—
183C2×C42D4412yes—
184C2×C42D4412yes—
185C2×C42C22×D1111yescharacteristic
186C2×C42C22×D1111yescharacteristic
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—24no—
189#103—228no—
190#103—444no—
191#97—42no—
192#95—224no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197#95—222no—
198#95—222no—
199C2×C11#256211yescharacteristic
200C2×C11#311712yes—
201C2×C11#313511yescharacteristic
202C2×C11#313911yescharacteristic
203C2×C11#325212yes—
204C2×Q8—114no—
205C2×Q8—222no—
206C2×Q8—222no—
207C2×Q8—222no—
208C2×Q8—222no—
209C2×Q8—222no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4C2×D4412yes—
215C22×C4C2×D4411yescharacteristic
216C22×C4C2×D4411yescharacteristic
217C22×C4C2×D4412yes—
218C22×C4C23×D1111yescharacteristic
219C2×C8—24no—
220C2×C8—24no—
221C2×C8—24no—
222C4⋊C4—228no—
223C4⋊C4—222no—
224C4⋊C4—222no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—224no—
228C4⋊C4—444no—
229C4⋊C4—444no—
230C4⋊C4—444no—
231C4⋊C4—444no—
232C42—24no—
233C42—21no—
234C42—21no—
235C42—22no—
236C42—42no—
237C42—444no—
238C42#433914yes—
239C11#2912911yescharacteristic, complemented, Sylow
240C23C22×D4411yescharacteristic
241Q8—224no—
242Q8—224no—
243Q8—442no—
244Q8—442no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—224no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—444no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4#6692812yes—
264C2×C4#6692812yes—
265C2×C4#6696214yes—
266C2×C4C2×#433912yes—
267C2×C4#6703711yescharacteristic
268C2×C4#6704011yescharacteristic
269C2×C4#41×D1112yes—
270C8—44no—
271C22C2×#6692811yescharacteristic
272C22#1062304111yescharacteristic
273C22#1062305511yescharacteristic
274C22C2×#6696212yes—
275C22#1062327912yes—
276C4—24no—
277C4—22no—
278C4—22no—
279C4—42no—
280C4—444no—
281C4—882no—
282C4—882no—
283C4—882no—
284C4#1062308912yes—
285C4#1062311212yes—
286C2#1307377711yescharacteristic
287C2#1307878912yes—
288C2#1307896211yescharacteristic
289C2#1307899711yescharacteristic
290C2#1307999012yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1767C2
socle, prime radicalC23×C11C22×D4
hypercenter#1767D11
hypocenterC11#29129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
239. C11#29129semidirect

Maximal subgroups

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

subgroupindex
#130770032
C4×#669222
#130701802
#130698632
#130693062
#130686322
C11×#17672
#2912911