Finite Group Databasebeta

← #14909646

Subgroups — #14909646

Order 2816.

552 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 143 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#13078271C212yesmaximal
2#13070825C214yesmaximal, complemented
3#13070724C212yesmaximal, complemented
4#13070707C212yesmaximal, complemented
5#13070552C214yesmaximal, complemented
6C11×#2113C211yesmaximal, characteristic
7C2×C11×#131C2211yescharacteristic
8#10623356—22no—
9C22×Dic44C2212yes—
10C2×C11×M32C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12#10622750—22no—
13#10622750—22no—
14#10622733—22no—
15#10622729C2214yes—
16#10622729C2214yes—
17#10622719C2212yes—
18C2×Dic88C2212yes—
19C2×Dic88C2212yes—
20C11×C22⋊C16C2214yes—
21#10622143C2212yes—
22#10622142C2212yes—
23#10622141C2214yes—
24#10622141C2214yes—
25C2×C11×#41D411yescharacteristic
26C22×Dic22—22no—
27C11×#131—41no—
28C11×#131—41no—
29C2×C11×M16D412yes—
30C2×C11×M16D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C22×C8×C11C2312yes—
33#66997—42no—
34#66989—42no—
35#66988—42no—
36#66988—42no—
37#66979—22no—
38#66977—24no—
39#66977—24no—
40C2×Dic44—22no—
41C2×Dic44—42no—
42C2×Dic44—42no—
43C2×Dic44C2314yes—
44C11×M32—41no—
45C2×C11×C16—41no—
46C2×C11×C16C2312yes—
47C2×C11×C16C2312yes—
48#66882C2314yes—
49#66881—22no—
50#66880—24no—
51#66880—24no—
52Dic88—42no—
53Dic88—42no—
54#33768—111nomaximal, Sylow
55C11×#41—41no—
56C11×#41—41no—
57C2×Q8×C11D811yescharacteristic
58C2×D4×C11D811yescharacteristic
59C2×D4×C11D812yes—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C22×Dic11—42no—
63C2×Dic22—24no—
64C2×Dic22—44no—
65C2×Dic22—44no—
66C2×Dic22—42no—
67C11×M16—42no—
68C11×M16—41no—
69C2×C8×C11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D412yes—
75C2×C8×C11C2411yescharacteristic
76C22⋊Dic11—44no—
77C22⋊Dic11—44no—
78C22⋊Dic11—42no—
79C4⋊Dic11—24no—
80Dic11⋊C4—44no—
81Dic11⋊C4—44no—
82C4×Dic11—42no—
83Dic44—24no—
84Dic44—24no—
85Dic44—44no—
86C11×C16—22no—
87C11×C16—22no—
88#3059—112no—
89#2237—114no—
90#2219—112no—
91#2216—112no—
92#2188—114no—
93#2113D1111yescharacteristic
94C23×C11C2×D811yescharacteristic
95C23×C11C2×D812yes—
96Q8×C11—41no—
97D4×C11—41no—
98D4×C11—42no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11C2×D812yes—
104C2×C4×C11C2×D811yescharacteristic
105C2×C4×C11C22×D411yescharacteristic
106C2×Dic11—44no—
107C2×Dic11—44no—
108C2×Dic11—84no—
109Dic22—44no—
110Dic22—44no—
111Dic22—84no—
112C8×C11—22no—
113C8×C11—21no—
114C8×C11H(5,𝔽2)11yescharacteristic
115C8×C11H(5,𝔽2)11yescharacteristic
116C22×Q16—112no—
117C2×#131C2×D1111yescharacteristic
118#536—222no—
119C2×Q32—112no—
120C2×Q32—112no—
121C2×M32C2×D1111yescharacteristic
122C22×C16C2×D1111yescharacteristic
123#470—222no—
124#470—222no—
125#467—114no—
126#467—114no—
127#427—112no—
128#419—222no—
129#367—112no—
130#366—112no—
131#358—114no—
132#358—114no—
133C22⋊C16C2×D1114yes—
134C22×C11—22no—
135C22×C11—24no—
136C22×C11—21no—
137C22×C11—22no—
138C22×C11C22×D811yescharacteristic
139C4×C11—21no—
140C4×C11—22no—
141C4×C11#53411yescharacteristic
142C4×C11#57511yescharacteristic
143Dic11—84no—
144Dic11—84no—
145C2×#41D4411yescharacteristic
146C22×Q8—222no—
147C2×Q16—114no—
148C2×Q16—222no—
149C2×Q16—442no—
150C2×Q16—442no—
151#131—41no—
152#131—41no—
153C2×M16D4412yes—
154C2×M16D4411yescharacteristic
155C22×C8C22×D1112yes—
156C22×C8C22×D1111yescharacteristic
157C4⋊Q8—442no—
158#124—442no—
159#123—442no—
160#123—442no—
161C22⋊Q8—224no—
162C22⋊Q8—224no—
163#117—222no—
164Q32—442no—
165Q32—442no—
166M32—41no—
167C2×C16—41no—
168C2×C16C22×D1112yes—
169C2×C16C22×D1112yes—
170#107—114no—
171#106—222no—
172#103—224no—
173#103—224no—
174C2×C11—41no—
175C2×C11—42no—
176C2×C11#318611yescharacteristic
177C2×C11#341712yes—
178#41—41no—
179#41—41no—
180C2×Q8—224no—
181C2×Q8—444no—
182C2×Q8—444no—
183C2×Q8—442no—
184C2×Q8D8811yescharacteristic
185C2×D4D8811yescharacteristic
186C2×D4D8812yes—
187C22×C4—442no—
188C22×C4C2×D4412yes—
189C22×C4C2×D4411yescharacteristic
190Q16—224no—
191Q16—224no—
192Q16—444no—
193M16—41no—
194M16—42no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8C2×D4411yescharacteristic
200C2×C8C2×D4412yes—
201C2×C8C23×D1111yescharacteristic
202C4⋊C4—224no—
203C4⋊C4—444no—
204C4⋊C4—444no—
205C22⋊C4—442no—
206C22⋊C4—444no—
207C22⋊C4—444no—
208C42—442no—
209C16—22no—
210C16—22no—
211C11#3376811yescharacteristic, complemented, Sylow
212C23C2×D8811yescharacteristic
213C23C2×D8812yes—
214Q8—41no—
215Q8—444no—
216Q8—444no—
217Q8—884no—
218D4—42no—
219D4—41no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—444no—
225C2×C4—444no—
226C2×C4—884no—
227C2×C4C2×D8812yes—
228C2×C4C2×D8811yescharacteristic
229C2×C4C22×D4411yescharacteristic
230C8—22no—
231C8—21no—
232C8#6703711yescharacteristic
233C8#6703711yescharacteristic
234C22—22no—
235C22—21no—
236C22—22no—
237C22—24no—
238C22C22×D8811yescharacteristic
239C4—22no—
240C4—21no—
241C4—884no—
242C4—884no—
243C4#1062302411yescharacteristic
244C4#1062327911yescharacteristic
245C2—42no—
246C2—41no—
247C2#1307936711yescharacteristic
248C2#1308176912yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
prime radicalC2×C11×#41D4
hypercenter#2113D11
hypocenterC11#33768
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. #13070825C2semidirect
3. #13070724C2semidirect
4. #13070707C2semidirect
5. #13070552C2semidirect
211. C11#33768semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130708252
#130707242
#130707072
#130705522
C11×#21132
#3376811