Finite Group Databasebeta

← #14909575

Subgroups — #14909575

Order 2816.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#10622729C212yesmaximal
2#13070814C214yesmaximal, complemented
3#13070724C214yesmaximal, complemented
4#13070552C214yesmaximal, complemented
5C11×#2112C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C2×#66977—22no—
8C22×Dic44C2212yes—
9C2×C11×M32C2212yes—
10#10622729—22no—
11#10622729—22no—
12#10622729C2214yes—
13#10622729C2214yes—
14C2×#66882C2212yes—
15C2×#66880—22no—
16C2×Dic88C2214yescomplemented
17C11×C22⋊C16C2214yes—
18#10622143C2214yescomplemented
19#10622141C2218yescomplemented
20C23×C4×C11D411yescharacteristic
21C22×Dic22—22no—
22C22×C8×C11—42no—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11D412yes—
25C22×C8×C11C2311yescharacteristic
26C22×C8×C11C2312yes—
27C2×C22⋊Dic11—42no—
28C2×C4⋊Dic11—22no—
29#66977—24no—
30#66977—24no—
31#66977—42no—
32#66977—42no—
33C2×Dic11⋊C4—42no—
34C2×Dic44—22no—
35C2×Dic44—44no—
36C2×Dic44C2314yes—
37C11×M32—42no—
38C2×C11×C16C2314yes—
39#66882—22no—
40#66882C2314yes—
41#66880—24no—
42#66880—24no—
43Dic88—44no—
44#33761—111nomaximal, Sylow
45C24×C11D811yescharacteristic
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11D812yes—
49C22×C4×C11D811yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—42no—
53C22×Dic11—42no—
54C2×Dic22—24no—
55C2×Dic22—44no—
56C2×Dic22—44no—
57C2×Dic22—42no—
58C2×C8×C11—22no—
59C2×C8×C11—24no—
60C2×C8×C11—42no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D412yes—
64C2×C8×C11C2411yescharacteristic
65C22⋊Dic11—44no—
66C22⋊Dic11—44no—
67C4⋊Dic11—24no—
68C4⋊Dic11—42no—
69Dic11⋊C4—44no—
70Dic11⋊C4—44no—
71Dic44—28no—
72Dic44—44no—
73C11×C16—24no—
74C2×#467—112no—
75#2235—114no—
76#2219—114no—
77#2188—114no—
78#2112D1111yescharacteristic
79C23×C11—24no—
80C23×C11—41no—
81C23×C11C2×D811yescharacteristic
82C23×C11C2×D812yes—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11C2×D811yescharacteristic
90C2×C4×C11C2×D812yes—
91C2×C4×C11C22×D411yescharacteristic
92C2×Dic11—44no—
93C2×Dic11—44no—
94C2×Dic11—84no—
95C2×Dic11—84no—
96Dic22—44no—
97Dic22—44no—
98Dic22—84no—
99C8×C11—22no—
100C8×C11—21no—
101C8×C11H(5,𝔽2)12yes—
102C22×Q16—112no—
103C23×C8C2×D1111yescharacteristic
104C2×C22⋊Q8—222no—
105C2×Q32—114no—
106C2×M32C2×D1112yes—
107#467—114no—
108#467—114no—
109#467—222no—
110#467—222no—
111C2×#107—112no—
112C2×#103—222no—
113#367—114no—
114#358—118no—
115C22⋊C16C2×D1114yes—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—44no—
121C22×C11#51014yes—
122C22×C11C22×D811yescharacteristic
123C4×C11—21no—
124C4×C11—22no—
125C4×C11#53411yescharacteristic
126C4×C11#57511yescharacteristic
127Dic11—84no—
128Dic11—84no—
129C22×Q8—222no—
130C23×C4D4411yescharacteristic
131C2×Q16—114no—
132C2×Q16—222no—
133C2×Q16—444no—
134C22×C8—42no—
135C22×C8D4412yes—
136C22×C8D4411yescharacteristic
137C22×C8C22×D1112yes—
138C22×C8C22×D1111yescharacteristic
139C22⋊Q8—224no—
140C22⋊Q8—224no—
141C22⋊Q8—442no—
142C22⋊Q8—442no—
143C2×C4⋊C4—222no—
144C2×C4⋊C4—442no—
145C2×C22⋊C4—442no—
146Q32—444no—
147M32—42no—
148C2×C16C22×D1114yes—
149#107—114no—
150#107—222no—
151#103—224no—
152#103—224no—
153C2×C11—24no—
154C2×C11—41no—
155C2×C11#318611yescharacteristic
156C2×C11C2×#51012yes—
157C24D8811yescharacteristic
158C2×Q8—224no—
159C2×Q8—444no—
160C2×Q8—444no—
161C2×Q8—442no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—442no—
165C22×C4—442no—
166C22×C4D8812yes—
167C22×C4D8811yescharacteristic
168C22×C4C2×D4412yes—
169C22×C4C2×D4411yescharacteristic
170Q16—228no—
171Q16—444no—
172C2×C8—22no—
173C2×C8—24no—
174C2×C8—41no—
175C2×C8—42no—
176C2×C8C2×D4411yescharacteristic
177C2×C8C2×D4412yes—
178C2×C8C23×D1111yescharacteristic
179C4⋊C4—224no—
180C4⋊C4—442no—
181C4⋊C4—444no—
182C4⋊C4—444no—
183C22⋊C4—444no—
184C22⋊C4—444no—
185C16—24no—
186C11#3376111yescharacteristic, complemented, Sylow
187C23—24no—
188C23—41no—
189C23C2×D8811yescharacteristic
190C23C2×D8812yes—
191Q8—444no—
192Q8—444no—
193Q8—884no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—444no—
201C2×C4—444no—
202C2×C4—884no—
203C2×C4—884no—
204C2×C4C2×D8811yescharacteristic
205C2×C4C2×D8812yes—
206C2×C4C22×D4411yescharacteristic
207C8—22no—
208C8—21no—
209C8#6703712yes—
210C22—22no—
211C22—22no—
212C22—21no—
213C22—22no—
214C22—44no—
215C22#1062252214yes—
216C22C22×D8811yescharacteristic
217C4—22no—
218C4—21no—
219C4—884no—
220C4—884no—
221C4#1062302411yescharacteristic
222C4#1062327911yescharacteristic
223C2—24no—
224C2—41no—
225C2#1307936711yescharacteristic
226C2C2×#1062252212yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2112C2
socleC22×C11C22×D8
prime radicalC24×C11D8
hypercenter#2112D11
hypocenterC11#33761
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. #13070814C2semidirect
3. #13070724C2semidirect
4. #13070552C2semidirect
16. C2×Dic88C22semidirect
18. #10622143C22semidirect
19. #10622141C22semidirect
186. C11#33761semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
#130708142
#130707242
#130705522
C11×#21122
#3376111