Finite Group Databasebeta

← #14654451

Subgroups — #14654451

Order 2816.

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

normal subgroups only

This group has 750 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×#10622653C212yesmaximal, complemented
2#13068539C211yesmaximal, characteristic, complemented
3#13066976C212yesmaximal, complemented
4#13066503C211yesmaximal, characteristic, complemented
5C11×#3192C211yesmaximal, characteristic
6C23×Dic22C2211yescharacteristic
7C2×C11×#121C2212yes—
8C22×#4324—22no—
9C11×#481—22no—
10C11×#469—22no—
11C11×#447—22no—
12C11×#407C2211yescharacteristic
13#10622820C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15C2×#66888—22no—
16#10622653—24no—
17#10622653—24no—
18C2×#66874—22no—
19#10622163—24no—
20C22×D4×C11—22no—
21C22×D4×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C22×Dic22—22no—
25C22×Dic22—21no—
26C22×Dic22—22no—
27C22×Dic22—44no—
28C22×Dic22D412yes—
29C2×C11×D8—22no—
30C2×C11×M16D412yes—
31C11×#121—22no—
32C11×#121—22no—
33C11×#121—22no—
34C11×#121—22no—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C22⋊C4—22no—
37C2×#4324—28no—
38C2×#4324—48no—
39C2×#4318—21no—
40C22×C11⋊C8—22no—
41C11×#106—22no—
42C11×#102—24no—
43C11×C22⋊C8—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)D414yes—
47#66888—44no—
48#66874—28no—
49#9988—111nomaximal, Sylow
50C24×C11—22no—
51C24×C11#4111yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—44no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—84no—
58C22×C4×C11—22no—
59C22×C4×C11—42no—
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—44no—
66C22×Dic11—42no—
67C2×Dic22—28no—
68C2×Dic22—24no—
69C2×Dic22—24no—
70C2×Dic22—44no—
71C2×Dic22—42no—
72C2×Dic22—44no—
73C2×Dic22—48no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C11×D8—82no—
77C11×M16—42no—
78C2×C8×C11—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83#4324—416no—
84#4318—42no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—44no—
87C2×C11⋊C8—41no—
88#3192D1111yescharacteristic
89C2×#448—112no—
90#1784—111no—
91#1471—112no—
92#1298—111no—
93C23×C11—24no—
94C23×C11—41no—
95C23×C11—42no—
96C23×C11—44no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11#12111yescharacteristic
100C23×C11#12112yes—
101D4×C11—44no—
102D4×C11—44no—
103D4×C11—84no—
104D4×C11—84no—
105C2×C4×C11—24no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—82no—
111C2×C4×C11#12012yes—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12711yescharacteristic
114C2×Dic11—24no—
115C2×Dic11—48no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118Dic22—28no—
119Dic22—44no—
120Dic22—44no—
121Dic22—44no—
122C8×C11—42no—
123C11⋊C8—44no—
124C11⋊C8—81no—
125C23×Q8—111no—
126C22×SD16—222no—
127C2×#121C2×D1112yes—
128#481—22no—
129#469—22no—
130#448—224no—
131#448—224no—
132#447—22no—
133C2×#103—222no—
134C2×#101—222no—
135#407—111no—
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—82no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—164no—
148C22×C11#39211yescharacteristic
149C22×C11#47114yes—
150C4×C11—22no—
151C4×C11—21no—
152C4×C11—82no—
153C4×C11B(4,𝔽2)12yes—
154Dic11—44no—
155C22×Q8—112no—
156C22×Q8—221no—
157C22×Q8—222no—
158C22×Q8—222no—
159C22×Q8—444no—
160C22×D4—22no—
161C22×D4C22⋊D1112yes—
162C23×C4—221no—
163C23×C4C22×D1111yescharacteristic
164C2×SD16—228no—
165C2×SD16—448no—
166C2×D8—22no—
167C2×M16—221no—
168C2×M16C22⋊D1112yes—
169C22×C8—222no—
170#121—22no—
171#121—22no—
172#121—22no—
173#121—22no—
174C2×C4⋊C4C22⋊D1112yes—
175C2×C22⋊C4—22no—
176#106—22no—
177#103—228no—
178#102—24no—
179#101—444no—
180C22⋊C8—22no—
181C22⋊C8—114no—
182C22⋊C8—222no—
183C22⋊C8—222no—
184C2×C11—24no—
185C2×C11—41no—
186C2×C11—162no—
187C2×C11#201912yes—
188C2×C11#202111yescharacteristic
189C24—22no—
190C24#434111yescharacteristic
191C2×Q8—224no—
192C2×Q8—228no—
193C2×Q8—224no—
194C2×Q8—444no—
195C2×Q8—442no—
196C2×Q8—444no—
197C2×Q8—448no—
198C2×Q8—441no—
199C2×Q8—441no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—44no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—84no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—222no—
209C22×C4—444no—
210C22×C4—442no—
211C22×C4D4×D1111yescharacteristic
212C22×C4D4×D1112yes—
213C22×C4C2×C22⋊D1112yes—
214C22×C4C2×C22⋊D1111yescharacteristic
215SD16—4416no—
216D8—82no—
217M16—42no—
218M16—442no—
219C2×C8—22no—
220C2×C8—224no—
221C2×C8—444no—
222C2×C8—441no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C11#998811yescharacteristic, complemented, Sylow
228C23—24no—
229C23—41no—
230C23—42no—
231C23—44no—
232C23—82no—
233C23—82no—
234C23#6699111yescharacteristic
235C23#6699212yes—
236Q8—228no—
237Q8—444no—
238Q8—444no—
239Q8—444no—
240D4—44no—
241D4—44no—
242D4—84no—
243D4—84no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—224no—
251C2×C4—442no—
252C2×C4—448no—
253C2×C4—442no—
254C2×C4#6699012yes—
255C2×C4#6699311yescharacteristic
256C2×C4#6700611yescharacteristic
257C8—42no—
258C8—444no—
259C8—881no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—44no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22—164no—
269C22#1062281314yes—
270C22#1062283611yescharacteristic
271C4—22no—
272C4—21no—
273C4—82no—
274C4—444no—
275C4#1062285712yes—
276C2—24no—
277C2—41no—
278C2—162no—
279C2#1306973012yes—
280C2#1306974011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3192C2
socleC22×C11#392
hypercenter#3192D11
hypocenterC11#9988
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. C2×#10622653C2semidirect
2. #13068539C2semidirect
3. #13066976C2semidirect
4. #13066503C2semidirect
227. C11#9988semidirect

Maximal subgroups

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

subgroupindex
C2×#106226532
#130685392
#130669762
#130665032
C11×#31922
#998811