Finite Group Databasebeta

← #14666620

Subgroups — #14666620

Order 2816.

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

normal subgroups only

This group has 336 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#13076604C211yesmaximal, characteristic
2#13067658C212yesmaximal
3#13066642C212yesmaximal
4#13066550C211yesmaximal, characteristic
5C11×#2028C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C11×#419—21no—
8C11×#391C2211yescharacteristic
9#10622843—21no—
10#10622657—22no—
11#10622599C2212yes—
12#10622541—21no—
13#10622274—22no—
14#10622268—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×Q8×C11D411yescharacteristic
20C2×C11×M16—21no—
21C11×C4⋊Q8—41no—
22C11×#125—41no—
23C11×C22⋊Q8—22no—
24C11×#117—21no—
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11—21no—
33C11×#103—41no—
34C11×#103—41no—
35C11×#95—22no—
36#66899—42no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41C22⋊(C11⋊C8)—22no—
42#66871—42no—
43#12225—111nomaximal, Sylow
44C2×Q8×C11—21no—
45C2×Q8×C11—22no—
46C2×Q8×C11—41no—
47C2×Q8×C11—41no—
48C2×Q8×C11Q1612yes—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11—41no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C22⋊C4—41no—
64C42×C11—41no—
65C42×C11—41no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—81no—
69C4⋊Dic11—81no—
70Dic11⋊C4—44no—
71C4×Dic11—81no—
72C2×C11⋊C8—42no—
73#2809—111no—
74#2028D1111yescharacteristic
75#1617—112no—
76#1353—112no—
77#1319—111no—
78C23×C11#12011yescharacteristic
79Q8×C11—42no—
80Q8×C11—81no—
81Q8×C11—82no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11C2×Q1611yescharacteristic
95C2×C4×C11#13711yescharacteristic
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C8×C11—81no—
103C11⋊C8—82no—
104#544C2×D1111yescharacteristic
105#484—222no—
106#419—21no—
107#400—112no—
108#398—222no—
109#391—221no—
110#391C2×D1111yescharacteristic
111#389—221no—
112#387—222no—
113#343C2×D1111yescharacteristic
114#339—21no—
115#328—222no—
116#324—112no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11#45111yescharacteristic
120C22×C11#45511yescharacteristic
121C22×C11B(4,𝔽2)11yescharacteristic
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11—42no—
127C4×C11—81no—
128C4×C11—81no—
129Dic11—82no—
130Dic11—82no—
131C22×Q8C22⋊D1111yescharacteristic
132C2×M16—21no—
133C4⋊Q8—41no—
134#125—41no—
135C22⋊Q8—22no—
136#117—21no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—222no—
139C2×C4⋊C4—221no—
140C2×C4⋊C4—221no—
141C2×C4⋊C4—221no—
142C2×C4⋊C4C22×D1111yescharacteristic
143C2×C42—221no—
144C2×C42C22⋊D1111yescharacteristic
145#107—442no—
146#103—41no—
147#103—41no—
148#103—442no—
149C22⋊C8—222no—
150#95—22no—
151#95—112no—
152#95—222no—
153#95—222no—
154#95—222no—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#160211yescharacteristic
158C2×C11#220111yescharacteristic
159C2×C11#220411yescharacteristic
160C2×Q8—21no—
161C2×Q8—22no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8#432612yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—222no—
168C22×C4—222no—
169C22×C4D4×D1112yes—
170C22×C4C2×C22⋊D1111yescharacteristic
171M16—41no—
172M16—41no—
173C2×C8—41no—
174C2×C8—442no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—442no—
181C4⋊C4—444no—
182C4⋊C4—442no—
183C4⋊C4—881no—
184C4⋊C4—881no—
185C22⋊C4—41no—
186C42—41no—
187C42—41no—
188C42—881no—
189C11#1222511yescharacteristic, complemented, Sylow
190C23#6699011yescharacteristic
191Q8—42no—
192Q8—81no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4C2×#432611yescharacteristic
213C2×C4#6700411yescharacteristic
214C8—81no—
215C8—882no—
216C22—21no—
217C22—21no—
218C22#1062264511yescharacteristic
219C22#1062266311yescharacteristic
220C22#1062267411yescharacteristic
221C4—21no—
222C4—21no—
223C4—42no—
224C4—42no—
225C4—42no—
226C4—81no—
227C4—81no—
228C4—882no—
229C4—882no—
230C2—21no—
231C2—21no—
232C2#1306757211yescharacteristic
233C2#1307062811yescharacteristic
234C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2028C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2028D11
hypocenterC11#12225
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
189. C11#12225semidirect

Maximal subgroups

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

subgroupindex
#130766042
#130676582
#130666422
#130665502
C11×#20282
#1222511