Finite Group Databasebeta

← #14646410

Subgroups — #14646410

Order 2816.

1154 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 147 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#13068540C212yesmaximal, complemented
2#13066943C214yesmaximal, complemented
3C22×C11×#124C211yesmaximal, characteristic
4C23×Q8×C11C2211yescharacteristic
5C23×D4×C11C411yescharacteristic
6C2×C11×#124—24no—
7C2×C11×#124—28no—
8C22×C11×C22⋊C4C412yes—
9C22×C11×C22⋊C4C2212yes—
10C22×C42×C11C411yescharacteristic
11C2×#66900—24no—
12#10622820C2214yes—
13#10622163—28no—
14C25×C11C2×C412yes—
15C22×Q8×C11—24no—
16C22×Q8×C11—44no—
17C22×Q8×C11D414yes—
18C22×D4×C11—24no—
19C22×D4×C11—22no—
20C22×D4×C11—44no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C412yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C11×#124—232no—
26C2×C11×C22⋊C4—24no—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—24no—
29C2×C11×C22⋊C4—24no—
30C2×C11×C22⋊C4—24no—
31C2×C11×C22⋊C4D418yes—
32C2×C42×C11—24no—
33C2×C42×C11—22no—
34C2×#4318—24no—
35#66900—48no—
36C22⋊(C11⋊C8)—28no—
37#8552—111nomaximal, Sylow
38C24×C11—22no—
39C24×C11—22no—
40C24×C11—44no—
41C24×C11—44no—
42C24×C11—44no—
43C24×C11C22⋊C414yes—
44C24×C11C22×C411yescharacteristic
45C2×Q8×C11—28no—
46C2×Q8×C11—28no—
47C2×Q8×C11—44no—
48C2×Q8×C11—416no—
49C2×D4×C11—28no—
50C2×D4×C11—416no—
51C2×D4×C11—44no—
52C2×D4×C11—44no—
53C22×C4×C11—22no—
54C22×C4×C11—24no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—44no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C414yes—
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D414yes—
66C11×C22⋊C4—216no—
67C11×C22⋊C4—216no—
68C42×C11—28no—
69#4318—48no—
70C2×C11⋊C8—44no—
71C22×#124D1111yescharacteristic
72#1784—112no—
73#1462—114no—
74C23×C11—22no—
75C23×C11—24no—
76C23×C11—24no—
77C23×C11—28no—
78C23×C11—44no—
79C23×C11—44no—
80C23×C11—44no—
81C23×C11—44no—
82C23×C11—44no—
83C23×C11—44no—
84C23×C11—44no—
85C23×C11—44no—
86C23×C11—816no—
87C23×C11C2×C22⋊C411yescharacteristic
88C23×C11C2×C22⋊C412yes—
89Q8×C11—416no—
90D4×C11—416no—
91C2×C4×C11—28no—
92C2×C4×C11—22no—
93C2×C4×C11—24no—
94C2×C4×C11—22no—
95C2×C4×C11—24no—
96C2×C4×C11—22no—
97C2×C4×C11—24no—
98C2×C4×C11—44no—
99C2×C4×C11—44no—
100C2×C4×C11—44no—
101C2×C4×C11—44no—
102C2×C4×C11—44no—
103C2×C4×C11#9914yes—
104C2×C4×C11#12014yes—
105C11⋊C8—84no—
106C23×Q8C2×D1111yescharacteristic
107C23×D4Dic1111yescharacteristic
108C2×#124—24no—
109C2×#124—28no—
110C22×C22⋊C4Dic1112yes—
111C22×C22⋊C4C2×D1112yes—
112C22×C42Dic1111yescharacteristic
113C2×#101—224no—
114#407—114no—
115#323—228no—
116C22×C11—28no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—44no—
121C22×C11—44no—
122C22×C11—44no—
123C22×C11—88no—
124C22×C11—88no—
125C22×C11—88no—
126C22×C11#37911yescharacteristic
127C22×C11C2×#9912yes—
128C22×C11#41314yes—
129C4×C11—24no—
130C4×C11—24no—
131C4×C11—42no—
132C4×C11—44no—
133C25C2×Dic1112yes—
134C22×Q8—24no—
135C22×Q8—44no—
136C22×Q8C22⋊D1114yes—
137C22×D4—24no—
138C22×D4—22no—
139C22×D4—44no—
140C23×C4C2×Dic1111yescharacteristic
141C23×C4C2×Dic1111yescharacteristic
142C23×C4C2×Dic1112yes—
143C23×C4C22×D1111yescharacteristic
144C2×M16—224no—
145#124—232no—
146C2×C22⋊C4—24no—
147C2×C22⋊C4—24no—
148C2×C22⋊C4—24no—
149C2×C22⋊C4—24no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4C22⋊D1118yes—
152C2×C42—24no—
153C2×C42—22no—
154#101—448no—
155C22⋊C8—228no—
156C2×C11—22no—
157C2×C11—24no—
158C2×C11—84no—
159C2×C11#178111yescharacteristic
160C2×C11#178512yes—
161C24—22no—
162C24—22no—
163C24—44no—
164C24—44no—
165C24—44no—
166C24C22⋊Dic1114yes—
167C24C22×Dic1111yescharacteristic
168C2×Q8—28no—
169C2×Q8—28no—
170C2×Q8—44no—
171C2×Q8—416no—
172C2×D4—28no—
173C2×D4—416no—
174C2×D4—44no—
175C2×D4—44no—
176C22×C4—22no—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4C22⋊Dic1112yes—
185C22×C4C22⋊Dic1112yes—
186C22×C4C22⋊Dic1114yes—
187C22×C4C2×C22⋊D1112yes—
188C22×C4C2×C22⋊D1114yes—
189M16—448no—
190C2×C8—444no—
191C22⋊C4—216no—
192C22⋊C4—216no—
193C42—28no—
194C11#855211yescharacteristic, complemented, Sylow
195C23—22no—
196C23—24no—
197C23—24no—
198C23—28no—
199C23—44no—
200C23—44no—
201C23—44no—
202C23—44no—
203C23—44no—
204C23—44no—
205C23—44no—
206C23—44no—
207C23—816no—
208C23C2×C22⋊Dic1111yescharacteristic
209C23C2×C22⋊Dic1112yes—
210Q8—416no—
211D4—416no—
212C2×C4—28no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—22no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4#6689814yes—
225C2×C4#6700614yes—
226C8—884no—
227C22—28no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—44no—
232C22—44no—
233C22—44no—
234C22—88no—
235C22—88no—
236C22—88no—
237C22C2×#6689812yes—
238C22#1062285014yes—
239C22#1062286011yescharacteristic
240C4—24no—
241C4—24no—
242C4—44no—
243C4—42no—
244C2—22no—
245C2—24no—
246C2—84no—
247C2#1306853111yescharacteristic
248C2#1306854412yes—
subgroupG/H
centerC22#10622860
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#124C2
socleC22×C11#379
prime radicalC23×D4×C11C4
cosocleC23×C4×C11C23
hypercenterC22×#124D11
hypocenterC11#8552
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #13068540C2semidirect
2. #13066943C2semidirect
194. C11#8552semidirect

Maximal subgroups

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

subgroupindex
#130685402
#130669432
C22×C11×#1242
#855211