Finite Group Databasebeta

← #14666553

Subgroups — #14666553

Order 2816.

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

normal subgroups only

This group has 380 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#13069777C211yesmaximal, characteristic
2#13067623C212yesmaximal
3#13066622C212yesmaximal
4#13066550C211yesmaximal, characteristic
5C11×#2734C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—21no—
7#10623031C2211yescharacteristic
8C11×#398C2212yes—
9C11×#395—22no—
10C11×#391C2211yescharacteristic
11C11×#389—21no—
12C11×#387—22no—
13#10622838—21no—
14#10622584—22no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C22×Q8×C11D411yescharacteristic
21C11×C4⋊Q8—42no—
22C11×C4⋊Q8—42no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D412yes—
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11—21no—
30C2×C42×C11D411yescharacteristic
31#66979—21no—
32#66977—22no—
33C2×#4318—21no—
34#66943—41no—
35#66941—41no—
36C11×#95—22no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95D412yes—
40#66899—41no—
41#66899—41no—
42C22⋊(C11⋊C8)—22no—
43#66874—42no—
44#66872—42no—
45#12213—111nomaximal, Sylow
46C2×Q8×C11—21no—
47C2×Q8×C11—42no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11—81no—
51C2×Q8×C11—81no—
52C2×Q8×C11SD1612yes—
53C22×C4×C11—21no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D412yes—
59C2×Dic22—22no—
60C11×C4⋊C4—24no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—44no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—81no—
67C42×C11—42no—
68C42×C11—41no—
69C22⋊Dic11—41no—
70C4⋊Dic11—22no—
71C4⋊Dic11—21no—
72C4⋊Dic11—21no—
73Dic11⋊C4—42no—
74C4×Dic11—41no—
75#4318—41no—
76#4318—41no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—41no—
79#2734D1111yescharacteristic
80#2028—111no—
81#1611—112no—
82#1346—112no—
83#1319—111no—
84C23×C11#12011yescharacteristic
85Q8×C11—42no—
86Q8×C11—81no—
87Q8×C11—84no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—24no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11C2×SD1611yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×Dic11—41no—
107C2×Dic11—41no—
108Dic22—82no—
109C11⋊C8—81no—
110C11⋊C8—82no—
111#544—111no—
112C2×C4⋊Q8—21no—
113#483—222no—
114#419—221no—
115#398C2×D1112yes—
116#395—22no—
117#391C2×D1111yescharacteristic
118#389—21no—
119#387—22no—
120#343—111no—
121#339—221no—
122#328—222no—
123#324—112no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11#45011yescharacteristic
127C22×C11#45511yescharacteristic
128C22×C11B(4,𝔽2)11yescharacteristic
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—44no—
132C4×C11—42no—
133C4×C11—42no—
134C4×C11—42no—
135C4×C11—82no—
136Dic11—81no—
137Dic11—81no—
138C22×Q8—21no—
139C22×Q8C22⋊D1111yescharacteristic
140C2×M16—221no—
141C4⋊Q8—42no—
142C4⋊Q8—42no—
143C4⋊Q8—441no—
144#125—441no—
145C22⋊Q8—222no—
146#117—221no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D1112yes—
152C2×C4⋊C4C22×D1111yescharacteristic
153C2×C42—21no—
154C2×C42C22⋊D1111yescharacteristic
155#106—442no—
156#103—442no—
157#103—441no—
158#103—441no—
159C22⋊C8—222no—
160#95—22no—
161#95—22no—
162#95—22no—
163#95C22⋊D1112yes—
164C2×C11—21no—
165C2×C11—21no—
166C2×C11#160111yescharacteristic
167C2×C11#220111yescharacteristic
168C2×C11#220511yescharacteristic
169C2×Q8—21no—
170C2×Q8—42no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—81no—
174C2×Q8—81no—
175C2×Q8—222no—
176C2×Q8#432412yes—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4C2×C22⋊D1111yescharacteristic
182C22×C4C2×C22⋊D1112yes—
183M16—441no—
184M16—441no—
185C2×C8—442no—
186C2×C8—441no—
187C4⋊C4—24no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—44no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—221no—
195C4⋊C4—221no—
196C4⋊C4—222no—
197C4⋊C4—442no—
198C22⋊C4—441no—
199C42—41no—
200C42—42no—
201C42—441no—
202C11#1221311yescharacteristic, complemented, Sylow
203C23#6700611yescharacteristic
204Q8—42no—
205Q8—81no—
206Q8—84no—
207Q8—882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—441no—
225C2×C4—441no—
226C2×C4#6698511yescharacteristic
227C2×C4C2×#432411yescharacteristic
228C8—881no—
229C8—882no—
230C22—21no—
231C22—21no—
232C22#1062283111yescharacteristic
233C22#1062285511yescharacteristic
234C22#1062285711yescharacteristic
235C4—21no—
236C4—21no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—42no—
241C4—82no—
242C4—881no—
243C4—881no—
244C2—21no—
245C2—21no—
246C2#1306756811yescharacteristic
247C2#1307062911yescharacteristic
248C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2734C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2734D11
hypocenterC11#12213
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2734

Complements

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

NH ≅ G/Ntype
202. C11#12213semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130676232
#130666222
#130665502
C11×#27342
#1221311