Finite Group Databasebeta

← #14645936

Subgroups — #14645936

Order 2816.

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

normal subgroups only

This group has 658 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#13069557C211yesmaximal, characteristic
2#13067316C212yesmaximal
3#13067231C212yesmaximal
4#13066960C211yesmaximal, characteristic
5C11×#3502C211yesmaximal, characteristic
6Q82×C11—22no—
7C11×#557—22no—
8C11×#557—24no—
9C11×#544—22no—
10C11×#544C412yes—
11C11×#533—22no—
12C11×#533C2212yes—
13C11×#519C412yes—
14C2×C4×Q8×C11C2211yescharacteristic
15#10622539C2212yes—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×#66867C2211yescharacteristic
18#10622185—22no—
19#10622185—22no—
20#10622181—24no—
21#10622166—22no—
22#10622162—22no—
23C22×Q8×C11C2×C411yescharacteristic
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—28no—
27C11×C4⋊Q8—24no—
28C11×C4⋊Q8D412yes—
29C11×C4⋊Q8D412yes—
30C11×#125—24no—
31C11×#125—28no—
32C11×#125—24no—
33C11×#125D414yes—
34C11×C22⋊Q8—24no—
35C11×C22⋊Q8—22no—
36C11×C22⋊Q8—22no—
37C4×Q8×C11—24no—
38C4×Q8×C11—24no—
39C4×Q8×C11—24no—
40C4×Q8×C11—24no—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C11×#117—24no—
46C11×#117C2×C414yes—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11D412yes—
50C2×C42×C11C2311yescharacteristic
51C22×C11⋊C8—21no—
52C22×C11⋊C8—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—22no—
56#66867—22no—
57#66867—22no—
58#8460—111nomaximal, Sylow
59C2×Q8×C11—24no—
60C2×Q8×C11—24no—
61C2×Q8×C11—22no—
62C2×Q8×C11—22no—
63C2×Q8×C11—22no—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C11×C4⋊C4—24no—
70C11×C4⋊C4—24no—
71C11×C4⋊C4—24no—
72C11×C4⋊C4—28no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4C22⋊C414yes—
80C11×C4⋊C4C22⋊C414yes—
81C11×C22⋊C4—24no—
82C42×C11—28no—
83C42×C11—24no—
84C42×C11—22no—
85C42×C11—22no—
86C42×C11C2×D412yes—
87C42×C11C2×D412yes—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—41no—
94#3502D1111yescharacteristic
95#1985—111no—
96#1552—112no—
97#1531—112no—
98#1467—111no—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—28no—
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—82no—
104Q8×C11—84no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—24no—
111C2×C4×C11—24no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11#10114yes—
116C2×C4×C11C2×C22⋊C412yes—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12012yes—
119C2×C4×C11#12011yescharacteristic
120C11⋊C8—42no—
121C11⋊C8—82no—
122C11⋊C8—81no—
123Q82—22no—
124#557—22no—
125#557—24no—
126#544—22no—
127#544Dic1112yes—
128#533—22no—
129#533C2×D1112yes—
130#519Dic1112yes—
131C2×C4×Q8C2×D1111yescharacteristic
132#432—112no—
133C2×C4⋊C8—111no—
134C2×#97—111no—
135#336—222no—
136#332—222no—
137#332—222no—
138#330—224no—
139#324—222no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11#37911yescharacteristic
143C22×C11C2×#10112yes—
144C4×C11—21no—
145C4×C11—22no—
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—44no—
149C4×C11—42no—
150C4×C11—44no—
151C4×C11#45411yescharacteristic
152C4×C11#45611yescharacteristic
153C22×Q8C2×Dic1111yescharacteristic
154C22×C8—221no—
155C22×C8—221no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—28no—
159C4⋊Q8—24no—
160C4⋊Q8C22⋊D1112yes—
161C4⋊Q8C22⋊D1112yes—
162#125—24no—
163#125—28no—
164#125—24no—
165#125C22⋊D1114yes—
166C22⋊Q8—24no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C4×Q8—24no—
170C4×Q8—24no—
171C4×Q8—24no—
172C4×Q8—24no—
173C4×Q8—22no—
174C4×Q8—22no—
175C4×Q8—22no—
176C4×Q8—22no—
177#117—24no—
178#117C2×Dic1114yes—
179C2×C4⋊C4C2×Dic1111yescharacteristic
180C2×C4⋊C4C22⋊D1112yes—
181C2×C42C22⋊D1112yes—
182C2×C42C22×D1111yescharacteristic
183C4⋊C8—222no—
184C4⋊C8—222no—
185C22⋊C8—222no—
186#97—222no—
187#97—222no—
188C2×C11—22no—
189C2×C11#178411yescharacteristic
190C2×C11#179311yescharacteristic
191C2×C11#179411yescharacteristic
192C2×Q8—24no—
193C2×Q8—24no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—22no—
197C22×C4C22⋊Dic1112yes—
198C22×C4C22⋊Dic1112yes—
199C22×C4C22×Dic1111yescharacteristic
200C22×C4C2×C22⋊D1111yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C2×C8—222no—
203C2×C8—441no—
204C2×C8—441no—
205C2×C8—442no—
206C2×C8—442no—
207C2×C8—441no—
208C4⋊C4—24no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—28no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4C22⋊Dic1114yes—
219C4⋊C4C22⋊Dic1114yes—
220C22⋊C4—24no—
221C42—28no—
222C42—24no—
223C42—22no—
224C42—22no—
225C42C2×C22⋊D1112yes—
226C42C2×C22⋊D1112yes—
227C11#846011yescharacteristic, complemented, Sylow
228C23C2×C22⋊Dic1111yescharacteristic
229Q8—28no—
230Q8—42no—
231Q8—42no—
232Q8—82no—
233Q8—84no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4#6690014yes—
245C2×C4C2×C22⋊Dic1112yes—
246C2×C4#6700611yescharacteristic
247C2×C4#6700612yes—
248C2×C4#6700611yescharacteristic
249C8—442no—
250C8—882no—
251C8—881no—
252C22—21no—
253C22—21no—
254C22C2×#6690012yes—
255C22#1062286011yescharacteristic
256C4—21no—
257C4—22no—
258C4—24no—
259C4—22no—
260C4—44no—
261C4—42no—
262C4—44no—
263C4#1062285811yescharacteristic
264C4#1062285911yescharacteristic
265C2—22no—
266C2#1306854011yescharacteristic
267C2#1306857511yescharacteristic
268C2#1306858011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3502C2
socleC22×C11#379
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#3502D11
hypocenterC11#8460
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
227. C11#8460semidirect

Maximal subgroups

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

subgroupindex
#130695572
#130673162
#130672312
#130669602
C11×#35022
#846011