Finite Group Databasebeta

← #14654463

Subgroups — #14654463

Order 2816.

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

normal subgroups only

This group has 826 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×#10622659C212yesmaximal
2#13068536C211yesmaximal, characteristic
3#13066980C212yesmaximal, complemented
4#13066503C211yesmaximal, characteristic, complemented
5C11×#3195C211yesmaximal, characteristic, complemented
6C23×D44C2211yescharacteristic
7C2×C11×C22⋊Q8C2212yes—
8C22×#4325—22no—
9C11×#483—22no—
10C11×#470—22no—
11C11×#451—22no—
12C11×#407C2211yescharacteristic
13#10622820C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15C2×#66887—22no—
16#10622659—24no—
17#10622659—24no—
18C2×#66873—22no—
19#10622166—24no—
20C24×D11—21no—
21C22×Q8×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C22×D44—22no—
24C22×D44—21no—
25C22×D44—22no—
26C22×D44—44no—
27C22×D44D412yes—
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×#4325—28no—
38C2×#4325—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#66887—44no—
48#66873—28no—
49#9990—111nomaximal, Sylow
50C24×C11#4111yescharacteristic
51C23×D11—22no—
52C23×D11—44no—
53C23×D11—42no—
54C23×D11—84no—
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—44no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—42no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C2×D44—24no—
66C2×D44—28no—
67C2×D44—24no—
68C2×D44—44no—
69C2×D44—42no—
70C2×D44—44no—
71C2×D44—48no—
72C2×D44—41no—
73C2×D44—41no—
74C11×Q16—82no—
75C11×M16—42no—
76C2×C8×C11—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83#4325—416no—
84#4318—42no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—44no—
87C2×C11⋊C8—41no—
88#3195D1111yescharacteristic, complemented
89C2×#450—112no—
90#1783—111no—
91#1472—112no—
92#1298—111no—
93C23×C11—24no—
94C23×C11—41no—
95C23×C11#12111yescharacteristic
96C23×C11#12112yes—
97C22×D11—24no—
98C22×D11—48no—
99C22×D11—42no—
100C22×D11—42no—
101C22×D11—84no—
102C22×D11—816no—
103C22×D11—84no—
104C22×D11—84no—
105Q8×C11—44no—
106Q8×C11—44no—
107C2×C4×C11—24no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—44no—
114C2×C4×C11—82no—
115C2×C4×C11#12012yes—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12711yescharacteristic
118D44—28no—
119D44—44no—
120D44—44no—
121D44—44no—
122C8×C11—42no—
123C11⋊C8—44no—
124C11⋊C8—81no—
125C23×D4—111no—
126C22×SD16—222no—
127C2×C22⋊Q8C2×D1112yes—
128#483—22no—
129#470—22no—
130#451—22no—
131#450—224no—
132#450—224no—
133C2×#102—222no—
134C2×#100—222no—
135#407—111no—
136#407C2×D1111yescharacteristic
137C2×C22⋊C8—112no—
138#324—224no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—22no—
142C22×C11—21no—
143C22×C11—44no—
144C22×C11#39211yescharacteristic
145C22×C11#47114yes—
146C2×D11—44no—
147C2×D11—816no—
148C2×D11—84no—
149C2×D11—84no—
150C2×D11—84no—
151C4×C11—22no—
152C4×C11—21no—
153C4×C11—82no—
154C4×C11—82no—
155C4×C11B(4,𝔽2)12yes—
156C25—221no—
157C22×Q8C22⋊D1112yes—
158C22×D4—112no—
159C22×D4—222no—
160C22×D4—222no—
161C22×D4—221no—
162C22×D4—444no—
163C23×C4C22×D1111yescharacteristic
164C2×Q16—22no—
165C2×SD16—228no—
166C2×SD16—448no—
167C2×M16—221no—
168C2×M16C22⋊D1112yes—
169C22×C8—222no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C22⋊D1112yes—
176C2×C22⋊C4—22no—
177#106—22no—
178#103—24no—
179#102—228no—
180#100—444no—
181C22⋊C8—22no—
182C22⋊C8—114no—
183C22⋊C8—222no—
184C22⋊C8—222no—
185C2×C11—24no—
186C2×C11—41no—
187C2×C11#201912yes—
188C2×C11#202111yescharacteristic
189D11—84no—
190C24—222no—
191C24—444no—
192C24—442no—
193C24—884no—
194C24#434111yescharacteristic
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—44no—
198C2×D4—228no—
199C2×D4—224no—
200C2×D4—224no—
201C2×D4—444no—
202C2×D4—442no—
203C2×D4—444no—
204C2×D4—448no—
205C2×D4—441no—
206C2×D4—441no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4D4×D1111yescharacteristic
211C22×C4D4×D1112yes—
212C22×C4C2×C22⋊D1112yes—
213C22×C4C2×C22⋊D1111yescharacteristic
214Q16—82no—
215SD16—4416no—
216M16—42no—
217M16—442no—
218C2×C8—22no—
219C2×C8—224no—
220C2×C8—444no—
221C2×C8—441no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C11#999011yescharacteristic, complemented, Sylow
229C23—24no—
230C23—41no—
231C23—224no—
232C23—448no—
233C23—442no—
234C23—442no—
235C23—884no—
236C23—884no—
237C23—8816no—
238C23—884no—
239C23#6699111yescharacteristic
240C23#6699212yes—
241Q8—44no—
242Q8—44no—
243D4—228no—
244D4—444no—
245D4—444no—
246D4—444no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—44no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—82no—
255C2×C4#6699012yes—
256C2×C4#6699311yescharacteristic
257C2×C4#6700611yescharacteristic
258C8—42no—
259C8—444no—
260C8—881no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—21no—
265C22—44no—
266C22—444no—
267C22—8816no—
268C22—884no—
269C22—884no—
270C22—884no—
271C22#1062281614yes—
272C22#1062283611yescharacteristic
273C4—22no—
274C4—21no—
275C4—82no—
276C4—82no—
277C4#1062285712yes—
278C2—24no—
279C2—41no—
280C2—884no—
281C2#1306972712yes—
282C2#1306974011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3195C2
socleC22×C11#392
prime radicalC23×D44C22
hypercenter#3195D11
hypocenterC11#9990
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
3. #13066980C2semidirect
4. #13066503C2semidirect
5. C11×#3195C2semidirect
88. #3195D11semidirect
228. C11#9990semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
#130685362
#130669802
#130665032
C11×#31952
#999011