Finite Group Databasebeta

← #14666618

Subgroups — #14666618

Order 2816.

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

normal subgroups only

This group has 380 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#13076609C211yesmaximal, characteristic
2#13069777C211yesmaximal, characteristic
3#13067592C212yesmaximal
4#13066647C212yesmaximal
5C11×#1319C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#391C2211yescharacteristic
8#10622843—21no—
9#10622838—21no—
10#10622592C2212yes—
11#10622542—21no—
12#10622352—22no—
13#10622269—22no—
14#10622259—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—21no—
21C22×Dic22D412yes—
22C2×C11×C4⋊C4C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66979—21no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×C4×Dic11—21no—
30C2×#4318—21no—
31C2×Dic44—42no—
32#66943—41no—
33#66941—41no—
34C11×C22⋊C8—22no—
35C11×#95—22no—
36#66899—41no—
37#66899—41no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95D412yes—
42#66880—42no—
43#12224—111nomaximal, Sylow
44C2×Q8×C11—21no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11Q1612yescomplemented
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C2×Dic22—24no—
55C2×Dic22—22no—
56C2×Dic22—42no—
57C2×Dic22—82no—
58C2×Dic22—81no—
59C2×Dic22—81no—
60C2×C8×C11—42no—
61C11×C4⋊C4—41no—
62C42×C11—41no—
63C22⋊Dic11—41no—
64C4⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—81no—
68C4⋊Dic11—81no—
69Dic11⋊C4—42no—
70Dic11⋊C4—82no—
71C4×Dic11—41no—
72C4×Dic11—81no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76Dic44—84no—
77#2811—111no—
78#2028—111no—
79#1605—112no—
80#1354—112no—
81#1319D1111yescharacteristic
82C23×C11#12011yescharacteristic
83Q8×C11—42no—
84Q8×C11—81no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13711yescharacteristic
97C2×Dic11—24no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105Dic22—44no—
106Dic22—84no—
107Dic22—82no—
108Dic22—82no—
109C8×C11—82no—
110C11⋊C8—81no—
111#544—111no—
112#451—222no—
113#419—221no—
114#395—112no—
115#395—222no—
116#391—222no—
117#391—221no—
118#391—221no—
119#391C2×D1111yescharacteristic
120#343—111no—
121#339—221no—
122#328—222no—
123#324C2×D1112yes—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11#45111yescharacteristic
127C22×C11#45511yescharacteristic
128C22×C11B(4,𝔽2)11yescharacteristic
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—42no—
132C4×C11—42no—
133C4×C11—42no—
134Dic11—44no—
135Dic11—82no—
136Dic11—81no—
137Dic11—81no—
138C22×Q8—112no—
139C22×Q8—221no—
140C22×Q8D4411yescharacteristic
141C2×Q16—442no—
142C2×M16—221no—
143C4⋊Q8—441no—
144#125—441no—
145C22⋊Q8—222no—
146#117—221no—
147C2×C4⋊C4—221no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4C22×D1111yescharacteristic
151C2×C42—221no—
152C2×C42D4411yescharacteristic
153#103—442no—
154#103—441no—
155#103—441no—
156C22⋊C8—22no—
157#95—22no—
158#95—112no—
159#95—222no—
160#95—222no—
161#95—222no—
162C2×C11—21no—
163C2×C11—21no—
164C2×C11#160211yescharacteristic
165C2×C11#219911yescharacteristic
166C2×C11#220511yescharacteristic
167C2×Q8—21no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—224no—
171C2×Q8—222no—
172C2×Q8—442no—
173C2×Q8—882no—
174C2×Q8—881no—
175C2×Q8—881no—
176C2×Q8Dic4412yescomplemented
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4C2×D4411yescharacteristic
182C22×C4D4×D1112yes—
183Q16—884no—
184M16—441no—
185M16—441no—
186C2×C8—42no—
187C2×C8—441no—
188C4⋊C4—41no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—222no—
192C4⋊C4—442no—
193C4⋊C4—882no—
194C4⋊C4—881no—
195C4⋊C4—881no—
196C22⋊C4—441no—
197C42—41no—
198C42—441no—
199C42—881no—
200C11#1222411yescharacteristic, complemented, Sylow
201C23#6693511yescharacteristic
202Q8—42no—
203Q8—81no—
204Q8—444no—
205Q8—884no—
206Q8—882no—
207Q8—882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—224no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4—441no—
225C2×C4—442no—
226C2×C4C2×Dic4411yescharacteristic
227C2×C4#6696211yescharacteristic
228C8—82no—
229C8—881no—
230C22—21no—
231C22—21no—
232C22#1062235211yescharacteristic
233C22#1062235411yescharacteristic
234C22#1062235911yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—444no—
241C4—882no—
242C4—881no—
243C4—881no—
244C2—21no—
245C2—21no—
246C2#1306757511yescharacteristic
247C2#1307061911yescharacteristic
248C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1319D11
hypocenterC11#12224
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C11Q16semidirect
176. C2×Q8Dic44semidirect
200. C11#12224semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130697772
#130675922
#130666472
C11×#13192
#1222411