Finite Group Databasebeta

← #14654468

Subgroups — #14654468

Order 2816.

698 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10622663C212yesmaximal
2#13068539C211yesmaximal, characteristic
3#13066980C212yesmaximal
4#13066503C211yesmaximal, characteristic
5C11×#3195C211yesmaximal, characteristic
6C23×Dic22C2211yescharacteristic
7C2×C11×C22⋊Q8C2212yes—
8C22×#4326—22no—
9C11×#483—22no—
10C11×#470—22no—
11C11×#451—22no—
12C11×#407C2211yescharacteristic
13#10622820C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15C2×#66888—22no—
16#10622663—24no—
17#10622663—24no—
18C2×#66874—22no—
19#10622166—24no—
20C22×Q8×C11D412yes—
21C23×C4×C11C2311yescharacteristic
22C23×Dic11—21no—
23C22×Dic22—22no—
24C22×Dic22—21no—
25C22×Dic22—22no—
26C22×Dic22—44no—
27C22×Dic22D412yes—
28C2×C11×Q16—22no—
29C2×C11×M16D412yes—
30C11×C22⋊Q8—22no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C22⋊C4—22no—
37C2×#4326—28no—
38C2×#4326—48no—
39C2×#4318—21no—
40C22×C11⋊C8—22no—
41C11×#106—22no—
42C11×#103—24no—
43C11×C22⋊C8—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)D414yes—
47#66888—44no—
48#66874—28no—
49#9991—111nomaximal, Sylow
50C24×C11#4111yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—44no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—42no—
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D412yes—
61C22×Dic11—22no—
62C22×Dic11—44no—
63C22×Dic11—42no—
64C2×Dic22—28no—
65C2×Dic22—24no—
66C2×Dic22—24no—
67C2×Dic22—44no—
68C2×Dic22—42no—
69C2×Dic22—44no—
70C2×Dic22—48no—
71C2×Dic22—41no—
72C2×Dic22—41no—
73C11×Q16—82no—
74C11×M16—42no—
75C2×C8×C11—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82#4326—416no—
83#4318—42no—
84C2×C11⋊C8—24no—
85C2×C11⋊C8—44no—
86C2×C11⋊C8—41no—
87#3195D1111yescharacteristic
88C2×#451—112no—
89#1784—111no—
90#1472—112no—
91#1298—111no—
92C23×C11—24no—
93C23×C11—41no—
94C23×C11#12111yescharacteristic
95C23×C11#12112yes—
96Q8×C11—44no—
97Q8×C11—44no—
98C2×C4×C11—24no—
99C2×C4×C11—22no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—44no—
105C2×C4×C11—82no—
106C2×C4×C11#12012yes—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12711yescharacteristic
109C2×Dic11—24no—
110C2×Dic11—48no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113Dic22—28no—
114Dic22—44no—
115Dic22—44no—
116Dic22—44no—
117C8×C11—42no—
118C11⋊C8—44no—
119C11⋊C8—81no—
120C23×Q8—111no—
121C22×Q16—222no—
122C2×C22⋊Q8C2×D1112yes—
123#483—22no—
124#470—22no—
125#451—22no—
126#451—224no—
127#451—224no—
128C2×#103—222no—
129C2×#101—222no—
130#407—111no—
131#407C2×D1111yescharacteristic
132C2×C22⋊C8—112no—
133#324—224no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—21no—
138C22×C11—44no—
139C22×C11#39211yescharacteristic
140C22×C11#47314yes—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—82no—
144C4×C11—82no—
145C4×C11B(4,𝔽2)12yes—
146Dic11—44no—
147C22×Q8—112no—
148C22×Q8—221no—
149C22×Q8—222no—
150C22×Q8—222no—
151C22×Q8—444no—
152C22×Q8C22⋊D1112yes—
153C23×C4—221no—
154C23×C4C22×D1111yescharacteristic
155C2×Q16—22no—
156C2×Q16—228no—
157C2×Q16—448no—
158C2×M16—221no—
159C2×M16C22⋊D1112yes—
160C22×C8—222no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C22⋊D1112yes—
167C2×C22⋊C4—22no—
168#106—22no—
169#103—24no—
170#103—228no—
171#101—444no—
172C22⋊C8—22no—
173C22⋊C8—114no—
174C22⋊C8—222no—
175C22⋊C8—222no—
176C2×C11—24no—
177C2×C11—41no—
178C2×C11#202012yes—
179C2×C11#202111yescharacteristic
180C24#434111yescharacteristic
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—44no—
184C2×Q8—224no—
185C2×Q8—228no—
186C2×Q8—224no—
187C2×Q8—444no—
188C2×Q8—442no—
189C2×Q8—444no—
190C2×Q8—448no—
191C2×Q8—441no—
192C2×Q8—441no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—222no—
197C22×C4—444no—
198C22×C4—442no—
199C22×C4D4×D1111yescharacteristic
200C22×C4D4×D1112yes—
201C22×C4C2×C22⋊D1112yes—
202C22×C4C2×C22⋊D1111yescharacteristic
203Q16—82no—
204Q16—4416no—
205M16—42no—
206M16—442no—
207C2×C8—22no—
208C2×C8—224no—
209C2×C8—444no—
210C2×C8—441no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C11#999111yescharacteristic, complemented, Sylow
218C23—24no—
219C23—41no—
220C23#6699111yescharacteristic
221C23#6699212yes—
222Q8—44no—
223Q8—44no—
224Q8—228no—
225Q8—444no—
226Q8—444no—
227Q8—444no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—224no—
237C2×C4—442no—
238C2×C4—448no—
239C2×C4—442no—
240C2×C4#6699012yes—
241C2×C4#6699311yescharacteristic
242C2×C4#6700611yescharacteristic
243C8—42no—
244C8—444no—
245C8—881no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22#1062281714yes—
252C22#1062283611yescharacteristic
253C4—22no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—444no—
258C4#1062285712yes—
259C2—24no—
260C2—41no—
261C2#1306973412yes—
262C2#1306974011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3195C2
socleC22×C11#392
prime radicalC24×C11#41
hypercenter#3195D11
hypocenterC11#9991
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
217. C11#9991semidirect

Maximal subgroups

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

subgroupindex
C2×#106226632
#130685392
#130669802
#130665032
C11×#31952
#999111