Finite Group Databasebeta

← #14666564

Subgroups — #14666564

Order 2816.

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

normal subgroups only

This group has 400 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#13074281C211yesmaximal, characteristic
2#13067573C212yesmaximal
3#13066636C212yesmaximal
4#13066546C211yesmaximal, characteristic
5C11×#2030C211yesmaximal, characteristic
6C11×#543C2211yescharacteristic
7C11×#381—21no—
8C11×#381C2211yescharacteristic
9C4×C22⋊Dic11—21no—
10#10622663—22no—
11#10622562—21no—
12#10622560C2212yes—
13#10622268—22no—
14#10622259—22no—
15C11×#342—21no—
16C11×#342C2211yescharacteristic
17#10622176—22no—
18#10622163C2212yes—
19C23×C4×C11D411yescharacteristic
20C22×Dic22D412yes—
21C11×C22⋊Q8—22no—
22C11×C22⋊Q8—42no—
23C2×C11×C22⋊C4—21no—
24C2×C11×C22⋊C4—21no—
25C2×C11×C22⋊C4D411yescharacteristic
26C2×C11×C22⋊C4C2311yescharacteristic
27C2×C22⋊Dic11—22no—
28C2×#4326—42no—
29C2×C4⋊Dic11—21no—
30C2×Dic11⋊C4—22no—
31C2×C4×Dic11—21no—
32C2×C4×Dic11—21no—
33C11×#95—22no—
34C11×#95—42no—
35C11⋊#95—21no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95D412yes—
39C22⋊(C11⋊C8)—22no—
40#66874—42no—
41#12215—111nomaximal, Sylow
42C24×C11C2×D411yescharacteristic
43C2×Q8×C11—22no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—22no—
48C22×C4×C11—41no—
49C22×C4×C11—41no—
50C22×C4×C11—41no—
51C22×C4×C11Q1612yescomplemented
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C2×Dic22—42no—
56C2×Dic22—44no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59C11×C22⋊C4—41no—
60C11×C22⋊C4—41no—
61C11×C22⋊C4—41no—
62C11×C22⋊C4—41no—
63C11×C22⋊C4—41no—
64C11×C22⋊C4—41no—
65C22⋊Dic11—44no—
66#4326—84no—
67C4⋊Dic11—81no—
68Dic11⋊C4—44no—
69C4×Dic11—81no—
70C4×Dic11—81no—
71C2×C11⋊C8—42no—
72#2607—111no—
73#2030D1111yescharacteristic
74#1602—112no—
75#1351—112no—
76#1317—111no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—42no—
80C23×C11#12011yescharacteristic
81C23×C11C2×Q1611yescharacteristic
82C23×C11#13711yescharacteristic
83Q8×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—81no—
94C2×C4×C11—82no—
95C2×C4×C11—81no—
96C2×C4×C11—82no—
97C2×Dic11—24no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103Dic22—44no—
104Dic22—82no—
105C11⋊C8—82no—
106#543C2×D1111yescharacteristic
107#451—222no—
108#399—221no—
109#393—112no—
110#391—222no—
111#387—222no—
112#381—21no—
113#381C2×D1111yescharacteristic
114C4×C22⋊C4—221no—
115#342—21no—
116#342C2×D1111yescharacteristic
117#328—222no—
118#323—112no—
119C22×C11—22no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—42no—
125C22×C11—81no—
126C22×C11#45111yescharacteristic
127C22×C11#45511yescharacteristic
128C22×C11B(4,𝔽2)11yescharacteristic
129C4×C11—42no—
130C4×C11—42no—
131C4×C11—81no—
132C4×C11—82no—
133C4×C11—161no—
134Dic11—44no—
135Dic11—82no—
136C22×Q8—112no—
137C23×C4C22⋊D1111yescharacteristic
138C2×Q16—442no—
139C22⋊Q8—22no—
140C22⋊Q8—42no—
141C2×C4⋊C4—222no—
142C2×C4⋊C4—221no—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—222no—
146C2×C22⋊C4C22⋊D1111yescharacteristic
147C2×C22⋊C4C22×D1111yescharacteristic
148C2×C42—221no—
149C2×C42—221no—
150#103—442no—
151C22⋊C8—222no—
152#95—22no—
153#95—42no—
154#95—112no—
155#95—222no—
156#95—221no—
157#95—222no—
158C2×C11—21no—
159C2×C11—21no—
160C2×C11—41no—
161C2×C11—41no—
162C2×C11#160211yescharacteristic
163C2×C11#219712yes—
164C24C2×C22⋊D1111yescharacteristic
165C2×Q8—22no—
166C2×Q8—442no—
167C2×Q8—444no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—222no—
176C22×C4—222no—
177C22×C4#432612yescomplemented
178C22×C4D4×D1112yes—
179Q16—884no—
180C2×C8—442no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—444no—
184C4⋊C4—881no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—41no—
189C22⋊C4—41no—
190C22⋊C4—41no—
191C22⋊C4—444no—
192C42—881no—
193C42—881no—
194C11#1221511yescharacteristic, complemented, Sylow
195C23—21no—
196C23—21no—
197C23—42no—
198C23#6699011yescharacteristic
199C23C2×#432611yescharacteristic
200C23#6700411yescharacteristic
201Q8—82no—
202Q8—444no—
203Q8—882no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—81no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4—82no—
217C2×C4—224no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C8—882no—
224C22—22no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—81no—
231C22#1062264511yescharacteristic
232C22#1062266311yescharacteristic
233C22#1062267411yescharacteristic
234C4—42no—
235C4—42no—
236C4—81no—
237C4—82no—
238C4—161no—
239C4—444no—
240C4—882no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2#1306757211yescharacteristic
246C2#1307060312yes—
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2030C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#2030D11
hypocenterC11#12215
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
51. C22×C4×C11Q16semidirect
177. C22×C4#4326semidirect
194. C11#12215semidirect

Maximal subgroups

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

subgroupindex
#130742812
#130675732
#130666362
#130665462
C11×#20302
#1221511