Finite Group Databasebeta

← #14853500

Subgroups — #14853500

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
1C4×#66922C211yesmaximal, characteristic
2#13070179C212yesmaximal
3#13069862C212yesmaximal
4#13069305C214yesmaximal
5#13068628C212yesmaximal
6#13068628C212yesmaximal
7#13068469C211yesmaximal, characteristic
8C11×#2864C211yesmaximal, characteristic
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2212yes—
11C11×#389C2212yes—
12C11×#389C2212yes—
13C11×#387—22no—
14C11×#387—22no—
15C11×#382C2211yescharacteristic
16C11×#382C2211yescharacteristic
17C43×C11C2211yescharacteristic
18C2×#66874C2214yes—
19C2×#66874C2214yes—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11—22no—
22#10622542C2212yes—
23#10622541—22no—
24C2×C4⋊(C11⋊C8)C2212yes—
25C2×#66867C2212yes—
26#10622167C2214yes—
27#10622167C2214yes—
28#10622162C2212yes—
29C22×Dic22C2312yes—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2312yes—
33C2×C11×C4⋊C4C2312yes—
34C2×C42×C11D412yes—
35C2×C42×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11C2312yes—
42C2×Dic11⋊C4—22no—
43C2×C4×Dic11—22no—
44C22×C11⋊C8C2314yes—
45#66922—24no—
46C4×Dic22—24no—
47C4×Dic22—24no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—22no—
53C11×#95—22no—
54C11⋊#95—24no—
55#66874—28no—
56#66874—44no—
57C4⋊(C11⋊C8)—24no—
58#66867—42no—
59#29129—111nomaximal, Sylow
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2411yescharacteristic
67C22×Dic11—22no—
68C22×Dic11—22no—
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—22no—
72C2×Dic22—22no—
73C2×Dic22—22no—
74C2×Dic22#4114yes—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4—44no—
80C42×C11—24no—
81C42×C11—22no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—42no—
85C42×C11#4114yes—
86C4⋊Dic11—28no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—44no—
90Dic11⋊C4—44no—
91C4×Dic11—44no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—24no—
95#2864D1111yescharacteristic
96C4×C4⋊Q8—111no—
97#2100—112no—
98#2043—112no—
99#1935—114no—
100#1805—112no—
101#1805—112no—
102#1767—111no—
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—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11#12412yes—
118C2×C4×C11#12412yes—
119C2×C4×C11#13714yes—
120C2×C4×C11C2×#4112yes—
121C2×C4×C11C2×#4112yes—
122C2×C4×C11H(5,𝔽2)11yescharacteristic
123C2×C4×C112−1+411yescharacteristic
124C2×Dic11—24no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—44no—
129Dic22—24no—
130Dic22—24no—
131Dic22—42no—
132Dic22—42no—
133C11⋊C8—44no—
134C2×C4⋊Q8—111no—
135C2×C4×Q8—112no—
136C2×C4⋊C8—112no—
137C2×#103—114no—
138C2×#103—114no—
139C2×#97—112no—
140#391—112no—
141#389—222no—
142#389C2×D1112yes—
143#389C2×D1112yes—
144#387—22no—
145#387—22no—
146#384—111no—
147#382C2×D1111yescharacteristic
148#382C2×D1111yescharacteristic
149C4×C4⋊C4—222no—
150C43C2×D1111yescharacteristic
151#340—114no—
152#340—114no—
153#336—112no—
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—82no—
164C4×C11—82no—
165C4×C11#55212yes—
166C4×C11#55312yes—
167Dic11—44no—
168Dic11—82no—
169C22×Q8—112no—
170C22×C8—114no—
171C4⋊Q8—224no—
172C4×Q8—224no—
173C4×Q8—224no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—222no—
179C2×C4⋊C4—222no—
180C2×C4⋊C4C22×D1112yes—
181C2×C4⋊C4C22×D1112yes—
182C2×C42—222no—
183C2×C42C22⋊D1112yes—
184C2×C42C22⋊D1112yes—
185C2×C42C22×D1111yescharacteristic
186C2×C42C22×D1111yescharacteristic
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—224no—
189#103—228no—
190#103—444no—
191#97—442no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—22no—
197#95—22no—
198#95—224no—
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—22no—
211C22×C4—22no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4C2×C22⋊D1112yes—
215C22×C4C2×C22⋊D1111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217C22×C4C2×C22⋊D1112yes—
218C22×C4C23×D1111yescharacteristic
219C2×C8—224no—
220C2×C8—224no—
221C2×C8—224no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—44no—
226C4⋊C4—44no—
227C4⋊C4—228no—
228C4⋊C4—222no—
229C4⋊C4—222no—
230C4⋊C4—444no—
231C4⋊C4—444no—
232C42—24no—
233C42—22no—
234C42—21no—
235C42—21no—
236C42—42no—
237C42—444no—
238C42#434314yes—
239C11#2912911yescharacteristic, complemented, Sylow
240C23C22×C22⋊D1111yescharacteristic
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—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—224no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—444no—
263C2×C4#6700012yes—
264C2×C4#6700012yes—
265C2×C4#6700414yes—
266C2×C4C2×#434312yes—
267C2×C4#41×D1112yes—
268C2×C4#6704211yescharacteristic
269C2×C4#6704311yescharacteristic
270C8—444no—
271C22C2×#6700011yescharacteristic
272C22#1062335312yes—
273C22C2×#6700412yes—
274C22#1062335911yescharacteristic
275C22#1062336411yescharacteristic
276C4—22no—
277C4—22no—
278C4—24no—
279C4—42no—
280C4—82no—
281C4—82no—
282C4—444no—
283C4—882no—
284C4#1062322512yes—
285C4#1062322612yes—
286C2#1307378311yescharacteristic
287C2#1307878312yes—
288C2#1307896411yescharacteristic
289C2#1307899811yescharacteristic
290C2#1307998912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2864C2
socle, prime radicalC23×C11C22×D4
hypercenter#2864D11
hypocenterC11#29129
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2864

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
C4×#669222
#130701792
#130698622
#130693052
#130686282
#130684692
C11×#28642
#2912911