Finite Group Databasebeta

← #14663283

Subgroups — #14663283

Order 2816.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#13077554C211yesmaximal, characteristic
2#13070432C211yesmaximal, characteristic
3#13066568C212yesmaximal
4#13066566C212yesmaximal
5C11×#2166C211yesmaximal, characteristic
6#10623048C411yescharacteristic
7C11×#405C2211yescharacteristic
8#10622732C2211yescharacteristic
9#10622731C2211yescharacteristic
10#10622714C411yescharacteristic
11C2×#66879C411yescharacteristic
12#10622612C411yescharacteristic
13#10622314—21no—
14#10622314—21no—
15#10622292—21no—
16#10622292—21no—
17C11×#364—21no—
18C11×#349C2212yes—
19C11×#347—21no—
20#10622191C2212yes—
21#10622104—21no—
22#10622101—21no—
23C2×C11×M16C2311yescharacteristic
24C22×C8×C11C2×C411yescharacteristic
25C11×#117C2×C411yescharacteristic
26#66979C2×C411yescharacteristic
27C2×C4×Dic11C2×C411yescharacteristic
28C2×#4318C2×C411yescharacteristic
29C22×C11⋊C8C2×C411yescharacteristic
30#66943—21no—
31#66941—21no—
32#66931—21no—
33#66931—21no—
34C4×Dic22—21no—
35C4×Dic22—21no—
36C11×M32—22no—
37C11×#97D411yescharacteristic
38C11×#97D411yescharacteristic
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41#66879—21no—
42#66879—21no—
43#66879—21no—
44Dic11⋊C8—21no—
45Dic11⋊C8—21no—
46Dic11⋊C8—21no—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49#66876—22no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52#11540—111nomaximal, Sylow
53C22×C4×C11C22×C411yescharacteristic
54C22×Dic11—21no—
55C2×Dic22—21no—
56C2×Dic22—21no—
57C11×M16—41no—
58C2×C8×C11—22no—
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—21no—
64C11×C22⋊C4—21no—
65C42×C11C22⋊C411yescharacteristic
66C42×C11C22⋊C411yescharacteristic
67C22⋊Dic11M1611yescharacteristic
68C22⋊Dic11M1611yescharacteristic
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11M1611yescharacteristic
79C4×Dic11M1611yescharacteristic
80#4318—41no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—41no—
84C11×C16—42no—
85C11⋊C16—42no—
86#2961—111no—
87#2166—111no—
88#2166D1111yescharacteristic
89#1328—112no—
90#1327—112no—
91C23×C11C2×M1611yescharacteristic
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11C2×C22⋊C411yescharacteristic
97C2×C4×C11C2×M1611yescharacteristic
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—81no—
103Dic22—81no—
104Dic22—81no—
105C8×C11—21no—
106C8×C11—21no—
107C8×C11—21no—
108C8×C11#10112yes—
109C11⋊C8—41no—
110C11⋊C8—41no—
111#533—111no—
112#446—221no—
113#446—221no—
114#446—221no—
115#446—221no—
116#424—111no—
117#424—111no—
118#423—111no—
119#405—111no—
120#405C2×D1111yescharacteristic
121C2×#97—111no—
122#364—21no—
123#364—221no—
124#349—112no—
125#349C2×D1112yes—
126#347—21no—
127#347—221no—
128C22×C11—21no—
129C22×C11—41no—
130C22×C11#40711yescharacteristic
131C4×C11—21no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11#41011yescharacteristic
135C4×C11C2×#10111yescharacteristic
136Dic11—41no—
137Dic11—41no—
138Dic11—41no—
139Dic11—41no—
140C2×M16—111no—
141C2×M16C22×D1111yescharacteristic
142C22×C8—111no—
143C22×C8C4×D1111yescharacteristic
144C4⋊Q8—221no—
145#125—221no—
146C22⋊Q8—221no—
147C22⋊Q8—221no—
148C4×Q8—221no—
149C4×Q8—221no—
150#117—111no—
151#117C4×D1111yescharacteristic
152C2×C42—111no—
153M32—22no—
154M32—222no—
155C4⋊C8—221no—
156C4⋊C8—221no—
157C4⋊C8—221no—
158C4⋊C8—221no—
159C4⋊C8—221no—
160C4⋊C8—221no—
161#97—221no—
162#97—221no—
163#97—221no—
164#97D4411yescharacteristic
165#97C22⋊D1111yescharacteristic
166C4×C8—221no—
167C4×C8D4411yescharacteristic
168C4×C8C22⋊D1111yescharacteristic
169C2×C11—21no—
170C2×C11—41no—
171C2×C11#146711yescharacteristic
172C2×Q8—221no—
173C2×Q8—221no—
174C22×C4—221no—
175C22×C4C2×C4×D1111yescharacteristic
176M16—41no—
177M16—441no—
178C2×C8—22no—
179C2×C8—221no—
180C2×C8—221no—
181C2×C8—441no—
182C2×C8(C2×D11)⋊C411yescharacteristic
183C2×C8(C2×D11)⋊C411yescharacteristic
184C2×C8C2×D4411yescharacteristic
185C2×C8C2×C22⋊D1111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C22⋊C4—21no—
195C22⋊C4—111no—
196C22⋊C4—111no—
197C42—111no—
198C42—111no—
199C42—221no—
200C42—221no—
201C42(C2×D11)⋊C411yescharacteristic
202C42(C2×D11)⋊C411yescharacteristic
203C16—42no—
204C16—442no—
205C11#1154011yescharacteristic, complemented, Sylow
206C23M16×D1111yescharacteristic
207Q8—881no—
208Q8—881no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—221no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—881no—
218C2×C4M16×D1111yescharacteristic
219C2×C4C2×(C2×D11)⋊C411yescharacteristic
220C8—21no—
221C8—21no—
222C8—21no—
223C8—441no—
224C8—441no—
225C8#6688812yes—
226C22—21no—
227C22—41no—
228C22#1062273911yescharacteristic
229C4—21no—
230C4—41no—
231C4—41no—
232C4—441no—
233C4—441no—
234C4—441no—
235C4—441no—
236C4#1062261911yescharacteristic
237C4C2×#6688811yescharacteristic
238C2—21no—
239C2—41no—
240C2#1306695911yescharacteristic
subgroupG/H
centerC4#10622619
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2166C2
socleC2×C11#1467
prime radicalC23×C11C2×M16
cosocleC2×C11×M16C23
hypercenter#2166D11
hypocenterC11#11540
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
205. C11#11540semidirect

Maximal subgroups

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

subgroupindex
#130775542
#130704322
#130665682
#130665662
C11×#21662
#1154011