Finite Group Databasebeta

← #14640451

Subgroups — #14640451

Order 2816.

286 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 49 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#13069626C211yesmaximal, characteristic
2#13066540C211yesmaximal, characteristic
3C11×#1289C211yesmaximal, characteristic
4C2×#66977—21no—
5C22×Dic44C411yescharacteristic, complemented
6C2×C11×C22⋊C8C2211yescharacteristic
7C11×#380—21no—
8C2×#66880—21no—
9#10622189C411yescharacteristic, complemented
10C22⋊(C11⋊C16)—21no—
11C23×C4×C11D411yescharacteristic
12C22×Dic22—21no—
13C22×C8×C11C2×C411yescharacteristic
14C22×C8×C11D411yescharacteristic
15C2×C11×C4⋊C4—41no—
16C2×C11×C22⋊C4—41no—
17C2×C22⋊Dic11—41no—
18C2×C4⋊Dic11—21no—
19#66977—42no—
20#66977—42no—
21C2×Dic11⋊C4—41no—
22C2×Dic44—41no—
23C2×Dic44—42no—
24C11×C22⋊C8—41no—
25C11×#95—22no—
26#66880—42no—
27C2×C11⋊C16—41no—
28#7078—111nomaximal, Sylow
29C24×C11D811yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11—41no—
33C22×C4×C11—41no—
34C22×C4×C11—42no—
35C22×C4×C11C22⋊C411yescharacteristic
36C22×C4×C11SD1611yescharacteristic
37C22×Dic11—41no—
38C22×Dic11—41no—
39C2×Dic22—22no—
40C2×Dic22—41no—
41C2×Dic22—41no—
42C2×Dic22—41no—
43C2×Dic22—41no—
44C2×Dic22—41no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—41no—
48C2×C8×C11—41no—
49C11×C4⋊C4—81no—
50C11×C4⋊C4—81no—
51C11×C22⋊C4—81no—
52C11×C22⋊C4—81no—
53C22⋊Dic11—44no—
54C4⋊Dic11—22no—
55C4⋊Dic11—41no—
56Dic11⋊C4—44no—
57Dic44—42no—
58Dic44—42no—
59C11⋊C16—81no—
60#2001—111no—
61#1314—111no—
62#1289D1111yescharacteristic
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11#10211yescharacteristic
68C23×C11SD3211yescharacteristic
69C23×C11Q3211yescharacteristic
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—41no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—81no—
77C2×C4×C11—82no—
78C2×C4×C11—82no—
79C2×C4×C11—82no—
80C2×C4×C11#9911yescharacteristic
81C2×C4×C11#10411yescharacteristic
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—81no—
85C2×Dic11—81no—
86C2×Dic11—81no—
87C2×Dic11—81no—
88Dic22—42no—
89Dic22—42no—
90Dic22—81no—
91Dic22—81no—
92C8×C11—41no—
93C8×C11—41no—
94C22×Q16—111no—
95C2×C22⋊Q8—221no—
96C2×#103—221no—
97C2×C22⋊C8C2×D1111yescharacteristic
98#380—21no—
99C22⋊C16—221no—
100#340—111no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—21no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11—41no—
108C22×C11—41no—
109C22×C11—81no—
110C22×C11#32711yescharacteristic
111C22×C11#35811yescharacteristic
112C22×C11#36011yescharacteristic
113C4×C11—21no—
114C4×C11—41no—
115C4×C11—162no—
116C4×C11AΣL(1,𝔽16)11yescharacteristic
117C4×C11#35311yescharacteristic
118Dic11—82no—
119Dic11—82no—
120C22×Q8—221no—
121C23×C4C22⋊D1111yescharacteristic
122C2×Q16—441no—
123C2×Q16—442no—
124C22×C8C4×D1111yescharacteristic
125C22×C8D4411yescharacteristic
126C22⋊Q8—442no—
127C22⋊Q8—442no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—221no—
130C2×C4⋊C4—441no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—441no—
133C2×C16—441no—
134#103—442no—
135C22⋊C8—41no—
136#95—22no—
137C2×C11—21no—
138C2×C11—21no—
139C2×C11—41no—
140C2×C11—41no—
141C2×C11#134011yescharacteristic
142C2×C11#134311yescharacteristic
143C2×C11#134811yescharacteristic
144C24#432311yescharacteristic
145C2×Q8—222no—
146C2×Q8—441no—
147C2×Q8—441no—
148C2×Q8—441no—
149C2×Q8—441no—
150C2×Q8—441no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—42no—
156C22×C4—441no—
157C22×C4—441no—
158C22×C4(C2×D11)⋊C411yescharacteristic
159C22×C4#432511yescharacteristic
160Q16—442no—
161Q16—442no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—41no—
166C4⋊C4—81no—
167C4⋊C4—81no—
168C4⋊C4—222no—
169C4⋊C4—441no—
170C4⋊C4—444no—
171C22⋊C4—81no—
172C22⋊C4—81no—
173C22⋊C4—444no—
174C16—881no—
175C11#707811yescharacteristic, complemented, Sylow
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#6687311yescharacteristic
181C23#6689111yescharacteristic
182C23#6689311yescharacteristic
183Q8—442no—
184Q8—442no—
185Q8—881no—
186Q8—881no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4—881no—
200C2×C4—881no—
201C2×C4—881no—
202C2×C4—881no—
203C2×C4#6686911yescharacteristic
204C2×C4#6687011yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22#1062208911yescharacteristic
217C22#1062212611yescharacteristic
218C22#1062213011yescharacteristic
219C4—21no—
220C4—41no—
221C4—162no—
222C4—882no—
223C4—882no—
224C4#1062210911yescharacteristic
225C4#1062211211yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#1306660311yescharacteristic
231C2#1306661211yescharacteristic
232C2#1306662711yescharacteristic
subgroupG/H
centerC22#10622089
commutatorC22×C8×C11C2×C4
FrattiniC2×C22⋊C8C2×D11
FittingC11×#1289C2
socleC22×C11#327
prime radicalC24×C11D8
cosocleC2×C11×C22⋊C8C22
hypercenter#1289D11
hypocenterC11#7078
LCSG ▷ C22×C8×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1289

Complements

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

NH ≅ G/Ntype
5. C22×Dic44C4semidirect
9. #10622189C4semidirect
175. C11#7078semidirect

Maximal subgroups

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

subgroupindex
#130696262
#130665402
C11×#12892
#707811