Finite Group Databasebeta

← #14654453

Subgroups — #14654453

Order 2816.

750 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 87 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#13079416C211yesmaximal, characteristic
2C2×#10622840C212yesmaximal, complemented
3#13066977C212yesmaximal, complemented
4#13066503C211yesmaximal, characteristic, complemented
5C11×#1784C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C22×#4325—22no—
8C2×#66983C2212yes—
9C2×C11×#101—22no—
10C11×#407C2211yescharacteristic
11C11×#407C2211yescharacteristic
12#10622840—24no—
13#10622840—24no—
14C2×#66899—22no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622748—22no—
17#10622348—22no—
18#10622345—22no—
19#10622106—24no—
20C22×Q8×C11—21no—
21C22×Q8×C11—22no—
22C22×Q8×C11—22no—
23C22×Q8×C11—44no—
24C22×Q8×C11D412yes—
25C23×C4×C11—21no—
26C23×C4×C11C2311yescharacteristic
27C22×C22⋊D11—22no—
28C22×D44D412yes—
29C2×C11×M16—21no—
30C2×C11×M16D412yes—
31C2×#4325—28no—
32C2×#4325—48no—
33#66983—22no—
34#66983—22no—
35#66983—22no—
36#66983—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×C4⋊Dic11D412yes—
39C22×C11⋊C8—22no—
40C2×D88—22no—
41C11×#101—44no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44#66899—28no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)D414yes—
47#66885—24no—
48#66881—22no—
49#9988—111nomaximal, Sylow
50C24×C11#4111yescharacteristic
51C23×D11—22no—
52C2×Q8×C11—24no—
53C2×Q8×C11—28no—
54C2×Q8×C11—24no—
55C2×Q8×C11—44no—
56C2×Q8×C11—44no—
57C2×Q8×C11—42no—
58C2×Q8×C11—48no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C22×C4×C11—22no—
62C22×C4×C11—42no—
63C22×C4×C11—44no—
64C22×C4×C11—42no—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C2×C22⋊D11—42no—
70C2×C22⋊D11—42no—
71C2×C22⋊D11—84no—
72C22×Dic11—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—44no—
76C11×M16—42no—
77C11×M16—42no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80#4325—416no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—42no—
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—44no—
87D88—82no—
88#3192—111no—
89C2×#448—112no—
90#1784D1111yescharacteristic, complemented
91#1471—112no—
92#1298—111no—
93C23×C11—24no—
94C23×C11—41no—
95C23×C11#12112yes—
96C23×C11#12111yescharacteristic
97C22×D11—42no—
98C22×D11—44no—
99C22×D11—82no—
100C22×D11—82no—
101Q8×C11—28no—
102Q8×C11—44no—
103Q8×C11—44no—
104Q8×C11—44no—
105C2×C4×C11—24no—
106C2×C4×C11—22no—
107C2×C4×C11—24no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—48no—
112C2×C4×C11—42no—
113C2×C4×C11#12012yes—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12711yescharacteristic
116C22⋊D11—84no—
117C22⋊D11—84no—
118C2×Dic11—42no—
119C2×Dic11—82no—
120D44—44no—
121D44—44no—
122C8×C11—42no—
123C8×C11—81no—
124C11⋊C8—44no—
125C23×Q8C2×D1111yescharacteristic
126C22×SD16—222no—
127C2×#121—112no—
128#481—222no—
129#469—222no—
130#448—224no—
131#448—224no—
132#447—222no—
133C2×#103—222no—
134C2×#101—22no—
135#407C2×D1111yescharacteristic
136#407C2×D1111yescharacteristic
137C2×C22⋊C8—112no—
138#323—224no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—22no—
142C22×C11—21no—
143C22×C11—44no—
144C22×C11#39211yescharacteristic
145C22×C11#47114yes—
146C2×D11—82no—
147C2×D11—82no—
148C2×D11—82no—
149C2×D11—164no—
150C4×C11—22no—
151C4×C11—21no—
152C4×C11—44no—
153C4×C11B(4,𝔽2)12yes—
154Dic11—82no—
155C22×Q8—21no—
156C22×Q8—22no—
157C22×Q8—22no—
158C22×Q8—44no—
159C22×Q8D4412yes—
160C22×D4—112no—
161C22×D4—222no—
162C23×C4—21no—
163C23×C4C22×D1111yescharacteristic
164C2×SD16—228no—
165C2×SD16—448no—
166C2×D8—222no—
167C2×M16—21no—
168C2×M16C22⋊D1112yes—
169C22×C8—222no—
170#121—222no—
171#121—222no—
172#121—222no—
173#121—222no—
174C2×C4⋊C4—112no—
175C2×C22⋊C4—222no—
176#106—222no—
177#103—228no—
178#102—224no—
179#101—44no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182C22⋊C8—114no—
183C22⋊C8—222no—
184C2×C11—24no—
185C2×C11—41no—
186C2×C11#201912yes—
187C2×C11#202111yescharacteristic
188D11—162no—
189C24—222no—
190C24#433911yescharacteristic
191C2×Q8—24no—
192C2×Q8—28no—
193C2×Q8—24no—
194C2×Q8—44no—
195C2×Q8—44no—
196C2×Q8—42no—
197C2×Q8—48no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×D4—222no—
201C2×D4—222no—
202C2×D4—444no—
203C2×D4—442no—
204C2×D4—442no—
205C2×D4—884no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—44no—
209C22×C4—42no—
210C22×C4—222no—
211C22×C4C2×D4411yescharacteristic
212C22×C4D4×D1112yes—
213C22×C4D4×D1112yes—
214C22×C4C2×C22⋊D1111yescharacteristic
215SD16—4416no—
216D8—882no—
217M16—42no—
218M16—42no—
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—224no—
222C2×C8—444no—
223C4⋊C4—222no—
224C4⋊C4—222no—
225C22⋊C4—442no—
226C22⋊C4—442no—
227C11#998811yescharacteristic, complemented, Sylow
228C23—24no—
229C23—41no—
230C23—442no—
231C23—444no—
232C23—882no—
233C23—882no—
234C23#6693712yes—
235C23#6698311yescharacteristic
236Q8—28no—
237Q8—44no—
238Q8—44no—
239Q8—44no—
240D4—444no—
241D4—444no—
242D4—884no—
243D4—884no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—48no—
251C2×C4—42no—
252C2×C4—442no—
253C2×C4—882no—
254C2×C4#6693512yes—
255C2×C4#6699011yescharacteristic
256C2×C4#6699311yescharacteristic
257C8—42no—
258C8—81no—
259C8—444no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—44no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22—1764no—
269C22#1062236714yes—
270C22#1062257311yescharacteristic
271C4—21no—
272C4—22no—
273C4—44no—
274C4—882no—
275C4#1062264512yes—
276C2—24no—
277C2—41no—
278C2—1762no—
279C2#1306972912yes—
280C2#1306974211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1784C2
socleC22×C11#392
prime radical#13079416C2
hypercenter#1784D11
hypocenterC11#9988
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. C2×#10622840C2semidirect
3. #13066977C2semidirect
4. #13066503C2semidirect
5. C11×#1784C2semidirect
90. #1784D11semidirect
227. C11#9988semidirect

Maximal subgroups

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

subgroupindex
#130794162
C2×#106228402
#130669772
#130665032
C11×#17842
#998811