Finite Group Databasebeta

← #14663202

Subgroups — #14663202

Order 2816.

330 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 69 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#13077245C211yesmaximal, characteristic
2#13070425C212yesmaximal, complemented
3#13066566C212yesmaximal, complemented
4#13066552C211yesmaximal, characteristic
5C11×#1320C211yesmaximal, characteristic
6C22×C4×Dic11C411yescharacteristic
7C11×#407C2211yescharacteristic
8#10622820C411yescharacteristic
9#10622731C411yescharacteristic
10#10622731C2211yescharacteristic
11M16×Dic11C411yescharacteristic
12M16×Dic11C2211yescharacteristic
13#10622332—22no—
14#10622331—22no—
15C11×#349C2212yes—
16#10622191C2212yes—
17#10622150—22no—
18#10622149—22no—
19C23×C4×C11C2×C411yescharacteristic
20C23×Dic11—21no—
21C2×C11×M16C2×C411yescharacteristic
22C2×C11×M16C2311yescharacteristic
23C2×C4×Dic11—21no—
24C2×C4×Dic11—21no—
25C2×C4×Dic11—21no—
26C2×C4×Dic11—21no—
27C2×C4×Dic11—21no—
28C2×C4×Dic11C2×C411yescharacteristic
29C2×C4×Dic11C2×C411yescharacteristic
30C2×#4318C2×C411yescharacteristic
31C2×#4318C2×C411yescharacteristic
32C11×M32—22no—
33C11×C22⋊C8—22no—
34C22⋊(C11⋊C8)—22no—
35#66879—21no—
36#66879D412yes—
37Dic11⋊C8—22no—
38Dic11⋊C8—22no—
39C8×Dic11—21no—
40C8×Dic11D412yes—
41#66876—22no—
42#11521—111nomaximal, Sylow
43C24×C11M1611yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11M1611yescharacteristic
49C22×C4×C11C22×C411yescharacteristic
50C22×Dic11—21no—
51C22×Dic11—21no—
52C22×Dic11—21no—
53C22×Dic11—21no—
54C22×Dic11—21no—
55C22×Dic11—21no—
56C22×Dic11—44no—
57C11×M16—41no—
58C11×M16—41no—
59C2×C8×C11—21no—
60C2×C8×C11C2×D412yes—
61C4×Dic11—21no—
62C4×Dic11—21no—
63C4×Dic11—21no—
64C4×Dic11—21no—
65C4×Dic11—21no—
66C4×Dic11—21no—
67C4×Dic11C22⋊C411yescharacteristic
68C4×Dic11C22⋊C411yescharacteristic
69C4×Dic11M1611yescharacteristic
70C4×Dic11M1611yescharacteristic
71#4318—41no—
72#4318—41no—
73C2×C11⋊C8—21no—
74C2×C11⋊C8C22⋊C412yes—
75C11×C16—42no—
76C11⋊C16—42no—
77#2920—111no—
78#2165—112no—
79#1327—112no—
80#1320—111no—
81#1320D1111yescharacteristic
82C23×C11—21no—
83C23×C11—42no—
84C23×C11—41no—
85C23×C11C2×M1611yescharacteristic
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—42no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11C2×C22⋊C411yescharacteristic
94C2×C4×C11C2×M1611yescharacteristic
95C2×Dic11—24no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C8×C11—22no—
106C8×C11—41no—
107C11⋊C8—22no—
108C11⋊C8—41no—
109C22×C42—111no—
110#432—222no—
111#431—222no—
112#423—111no—
113#423—111no—
114#407—111no—
115#407C2×D1111yescharacteristic
116C4×M16—111no—
117C4×M16—111no—
118#364—222no—
119#349—112no—
120#349C2×D1112yes—
121#347—222no—
122C22×C11—22no—
123C22×C11—21no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—41no—
129C22×C11#40711yescharacteristic
130C4×C11—21no—
131C4×C11—41no—
132C4×C11#41011yescharacteristic
133C4×C11#41311yescharacteristic
134Dic11—22no—
135Dic11—22no—
136Dic11—41no—
137Dic11—41no—
138C23×C4—221no—
139C23×C4C4×D1111yescharacteristic
140C2×M16—111no—
141C2×M16—111no—
142C2×M16C4×D1111yescharacteristic
143C2×M16C22×D1111yescharacteristic
144C2×C42—111no—
145C2×C42—111no—
146C2×C42—221no—
147C2×C42—221no—
148C2×C42—221no—
149C2×C42—221no—
150C2×C42—221no—
151M32—22no—
152M32—222no—
153C4⋊C8—222no—
154C4⋊C8—222no—
155C22⋊C8—22no—
156C22⋊C8—222no—
157#97—112no—
158#97—221no—
159C4×C8—112no—
160C4×C8—221no—
161C2×C11—21no—
162C2×C11—42no—
163C2×C11—41no—
164C2×C11#146411yescharacteristic
165C24#431311yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—221no—
171C22×C4—221no—
172C22×C4—221no—
173C22×C4—221no—
174C22×C4—221no—
175C22×C4—221no—
176C22×C4—444no—
177C22×C4#431311yescharacteristic
178C22×C4C2×C4×D1111yescharacteristic
179M16—41no—
180M16—41no—
181M16—441no—
182M16—441no—
183C2×C8—21no—
184C2×C8—112no—
185C2×C8—221no—
186C2×C8D4×D1112yes—
187C42—111no—
188C42—111no—
189C42—111no—
190C42—111no—
191C42—221no—
192C42—221no—
193C42—221no—
194C42—221no—
195C42—221no—
196C42—221no—
197C16—42no—
198C16—442no—
199C11#1152111yescharacteristic, complemented, Sylow
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#431311yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—224no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4C22⋊C4×D1111yescharacteristic
222C2×C4M16×D1111yescharacteristic
223C8—22no—
224C8—41no—
225C8—222no—
226C8—441no—
227C22—22no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22#1062233911yescharacteristic
235C4—21no—
236C4—41no—
237C4—222no—
238C4—222no—
239C4—441no—
240C4—441no—
241C4#1062235311yescharacteristic
242C4#1062235811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#1306694711yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1320C2
socleC2×C11#1464
prime radicalC24×C11M16
cosocleC2×C11×M16C23
hypercenter#1320D11
hypocenterC11#11521
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13070425C2semidirect
3. #13066566C2semidirect
199. C11#11521semidirect

Maximal subgroups

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

subgroupindex
#130772452
#130704252
#130665662
#130665522
C11×#13202
#1152111