Finite Group Databasebeta

← #14666830

Subgroups — #14666830

Order 2816.

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073645C211yesmaximal, characteristic
2#13069961C211yesmaximal, characteristic
3#13067592C212yesmaximal
4#13066647C212yesmaximal
5C11×#1325C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C2×#66941—22no—
8C11×#384C2211yescharacteristic
9#10622592—21no—
10#10622592C2212yes—
11#10622586—22no—
12#10622577—21no—
13C4×C4⋊Dic11—21no—
14#10622352—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×Dic22—21no—
20C22×Dic22D412yes—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C4⋊C4C2311yescharacteristic
24C2×C42×C11D411yescharacteristic
25#66979—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28#66977—22no—
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C2×C4×Dic11—22no—
32C2×#4318—21no—
33C2×Dic44—42no—
34#66943—41no—
35#66941—41no—
36#66941—48no—
37C11×C22⋊C8—22no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41#66880—42no—
42#66872—41no—
43#66871—41no—
44#12256—111nomaximal, Sylow
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C22×Dic11—22no—
50C22×Dic11—22no—
51C2×Dic22—22no—
52C2×Dic22—42no—
53C2×Dic22—44no—
54C2×Dic22—44no—
55C2×Dic22—81no—
56C2×C8×C11—42no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—44no—
59C11×C4⋊C4—41no—
60C42×C11—21no—
61C42×C11Q1612yescomplemented
62C22⋊Dic11—41no—
63C4⋊Dic11—24no—
64C4⋊Dic11—24no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—22no—
68Dic11⋊C4—42no—
69Dic11⋊C4—44no—
70Dic11⋊C4—44no—
71C4×Dic11—44no—
72C4×Dic11—41no—
73#4318—22no—
74#4318—41no—
75C2×C11⋊C8—41no—
76Dic44—84no—
77#2551—111no—
78#2060—111no—
79#1605—112no—
80#1354—112no—
81#1325D1111yescharacteristic
82C23×C11#12011yescharacteristic
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11C2×Q1611yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C2×Dic11—24no—
95C2×Dic11—24no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—41no—
101C2×Dic11—41no—
102Dic22—44no—
103Dic22—82no—
104Dic22—84no—
105Dic22—82no—
106C8×C11—82no—
107C11⋊C8—42no—
108#544—111no—
109C2×C4⋊Q8—222no—
110#451—222no—
111#428—221no—
112#395—112no—
113#395—221no—
114#389—222no—
115#384C2×D1111yescharacteristic
116C4×C4⋊C4—221no—
117#343—111no—
118#339—221no—
119#328—222no—
120#324C2×D1112yes—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#45111yescharacteristic
124C22×C11#45611yescharacteristic
125C22×C11B(4,𝔽2)11yescharacteristic
126C4×C11—24no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—42no—
130C4×C11—81no—
131Dic11—44no—
132Dic11—44no—
133Dic11—81no—
134Dic11—81no—
135C22×Q8—112no—
136C22×Q8—221no—
137C2×Q16—442no—
138C2×M16—221no—
139C4⋊Q8—441no—
140C4⋊Q8—448no—
141#125—441no—
142C22⋊Q8—222no—
143#117—221no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4D4411yescharacteristic
150C2×C4⋊C4C22×D1111yescharacteristic
151C2×C42—222no—
152C2×C42D4411yescharacteristic
153#107—441no—
154#106—441no—
155#103—442no—
156C22⋊C8—22no—
157#95—112no—
158#95—221no—
159#95—222no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11#160511yescharacteristic
163C2×C11#219611yescharacteristic
164C2×C11#220511yescharacteristic
165C2×Q8—222no—
166C2×Q8—442no—
167C2×Q8—444no—
168C2×Q8—444no—
169C2×Q8—881no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4C2×D4411yescharacteristic
175C22×C4D4×D1112yes—
176Q16—884no—
177M16—222no—
178M16—441no—
179C2×C8—42no—
180C2×C8—441no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—44no—
184C4⋊C4—224no—
185C4⋊C4—224no—
186C4⋊C4—222no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—442no—
190C4⋊C4—444no—
191C4⋊C4—444no—
192C22⋊C4—441no—
193C42—21no—
194C42—444no—
195C42—441no—
196C42Dic4412yescomplemented
197C11#1225611yescharacteristic, complemented, Sylow
198C23#6693511yescharacteristic
199Q8—444no—
200Q8—882no—
201Q8—882no—
202Q8—884no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—224no—
213C2×C4—224no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4C2×Dic4411yescharacteristic
221C2×C4#6696211yescharacteristic
222C8—82no—
223C8—442no—
224C22—21no—
225C22—21no—
226C22#1062235211yescharacteristic
227C22#1062235411yescharacteristic
228C22#1062236511yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—81no—
234C4—444no—
235C4—444no—
236C4—881no—
237C4—881no—
238C2—21no—
239C2—21no—
240C2#1306759211yescharacteristic
241C2#1307060211yescharacteristic
242C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1325D11
hypocenterC11#12256
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
61. C42×C11Q16semidirect
196. C42Dic44semidirect
197. C11#12256semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130699612
#130675922
#130666472
C11×#13252
#1225611