Finite Group Databasebeta

← #14666828

Subgroups — #14666828

Order 2816.

442 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069961C211yesmaximal, characteristic
2#13067589C212yesmaximal
3#13066646C212yesmaximal
4#13066562C211yesmaximal, characteristic
5C11×#2551C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—22no—
7#10623031C2211yescharacteristic
8C11×#395—21no—
9C11×#395C2212yes—
10C11×#389—22no—
11C11×#384C2211yescharacteristic
12C4×C11×C4⋊C4—21no—
13#10622841—22no—
14#10622577—21no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C22×Q8×C11D412yes—
21C11×C4⋊Q8—48no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11—22no—
30C2×C42×C11D411yescharacteristic
31C2×#4326—42no—
32#66979—21no—
33#66977—22no—
34C2×#4318—21no—
35#66943—41no—
36#66941—41no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95D412yes—
40#66899—42no—
41C22⋊(C11⋊C8)—22no—
42#66872—41no—
43#66871—41no—
44#12256—111nomaximal, Sylow
45C2×Q8×C11—44no—
46C2×Q8×C11—44no—
47C2×Q8×C11—42no—
48C2×Q8×C11—81no—
49C22×C4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C2×Dic22—22no—
56C11×C4⋊C4—24no—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—44no—
60C11×C4⋊C4—44no—
61C11×C4⋊C4—44no—
62C11×C4⋊C4—41no—
63C42×C11—21no—
64C42×C11—44no—
65C42×C11Q1612yescomplemented
66C22⋊Dic11—41no—
67#4326—84no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11—22no—
71Dic11⋊C4—42no—
72C4×Dic11—41no—
73#4318—22no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—42no—
77#2551D1111yescharacteristic
78#2060—111no—
79#1605—112no—
80#1354—112no—
81#1325—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—44no—
84Q8×C11—82no—
85Q8×C11—84no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—24no—
92C2×C4×C11—24no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11C2×Q1611yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C2×Dic11—41no—
104C2×Dic11—41no—
105Dic22—82no—
106C11⋊C8—42no—
107C11⋊C8—82no—
108#544—111no—
109C2×C4⋊Q8—22no—
110#451—222no—
111#428—221no—
112#395—21no—
113#395C2×D1112yes—
114#389—22no—
115#384C2×D1111yescharacteristic
116C4×C4⋊C4—21no—
117#343—111no—
118#339—221no—
119#328—222no—
120#324—112no—
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—44no—
130C4×C11—44no—
131C4×C11—42no—
132C4×C11—81no—
133Dic11—81no—
134Dic11—81no—
135C22×Q8—21no—
136C22×Q8C22⋊D1112yes—
137C2×Q16—442no—
138C2×M16—221no—
139C4⋊Q8—48no—
140C4⋊Q8—441no—
141#125—441no—
142C22⋊Q8—222no—
143#117—221no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4C22⋊D1111yescharacteristic
150C2×C4⋊C4C22×D1111yescharacteristic
151C2×C42—22no—
152C2×C42C22⋊D1111yescharacteristic
153#107—441no—
154#106—441no—
155#103—442no—
156C22⋊C8—222no—
157#95—21no—
158#95—22no—
159#95C22⋊D1112yes—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11#160511yescharacteristic
163C2×C11#219611yescharacteristic
164C2×C11#220511yescharacteristic
165C2×Q8—44no—
166C2×Q8—44no—
167C2×Q8—42no—
168C2×Q8—81no—
169C2×Q8—222no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4C2×C22⋊D1111yescharacteristic
175C22×C4C2×C22⋊D1112yes—
176Q16—884no—
177M16—222no—
178M16—441no—
179C2×C8—441no—
180C2×C8—442no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—44no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—442no—
192C22⋊C4—441no—
193C42—21no—
194C42—44no—
195C42—441no—
196C42#432612yescomplemented
197C11#1225611yescharacteristic, complemented, Sylow
198C23#6700611yescharacteristic
199Q8—44no—
200Q8—82no—
201Q8—84no—
202Q8—882no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4#6699511yescharacteristic
221C2×C4C2×#432611yescharacteristic
222C8—442no—
223C8—882no—
224C22—21no—
225C22—21no—
226C22#1062284111yescharacteristic
227C22#1062285711yescharacteristic
228C22#1062285911yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—44no—
235C4—81no—
236C4—881no—
237C4—881no—
238C2—21no—
239C2—21no—
240C2#1306759011yescharacteristic
241C2#1307060011yescharacteristic
242C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2551C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2551D11
hypocenterC11#12256
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
65. C42×C11Q16semidirect
196. C42#4326semidirect
197. C11#12256semidirect

Maximal subgroups

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

subgroupindex
#130699612
#130675892
#130666462
#130665622
C11×#25512
#1225611