Finite Group Databasebeta

← #14655063

Subgroups — #14655063

Order 2816.

552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622684C212yesmaximal
2#13076684C211yesmaximal, characteristic, complemented
3C2×#10622103C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×#66923C2212yes—
8C2×C11×#102—22no—
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66896—22no—
12C2×#66896—22no—
13#10622684—24no—
14#10622684—24no—
15#10622596—22no—
16C2×#66867C2212yes—
17#10622274—22no—
18#10622272—22no—
19#10622103—24no—
20C22×D4×C11—22no—
21C22×D4×C11—21no—
22C22×C8×C11—21no—
23C11×#127—22no—
24C11×#127—21no—
25C11×#127D412yes—
26C2×C11×C4⋊C4D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11D412yes—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C2×Dic11⋊C4—22no—
33C22×C11⋊C8—22no—
34#66923—22no—
35#66923—22no—
36#66923—22no—
37#66923—22no—
38C11×#102—44no—
39C11×#97—22no—
40C11×#95—22no—
41#66896—28no—
42#66896—28no—
43C11⋊#95—22no—
44C11⋊#95—24no—
45#66867—22no—
46#66867D414yes—
47#10080—111nomaximal, Sylow
48C24×C11—41no—
49C2×D4×C11—24no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C2×D4×C11—48no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—41no—
56C22×C4×C11—22no—
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×C8×C11—22no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C11×C4⋊C4—42no—
65C42×C11C2×D411yescharacteristic
66C42×C11C2×D412yes—
67C42×C11#4111yescharacteristic
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11—82no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—44no—
79C2×#490—112no—
80#2822—111no—
81#1961D1111yescharacteristic
82C2×#330—112no—
83#1295—111no—
84C23×C11—42no—
85C23×C11—81no—
86C23×C11—84no—
87C23×C11—81no—
88C23×C11#12011yescharacteristic
89D4×C11—48no—
90D4×C11—44no—
91D4×C11—84no—
92D4×C11—82no—
93C2×C4×C11—21no—
94C2×C4×C11—24no—
95C2×C4×C11—21no—
96C2×C4×C11—42no—
97C2×C4×C11—44no—
98C2×C4×C11#12012yes—
99C2×C4×C11#12112yes—
100C2×C4×C11#12111yescharacteristic
101C2×C4×C11#12711yescharacteristic
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—44no—
106C2×Dic11—42no—
107C8×C11—42no—
108C11⋊C8—44no—
109C2×#127C2×D1111yescharacteristic
110C2×#125—112no—
111#490—224no—
112#490—224no—
113C2×#102—22no—
114C2×#102—222no—
115C2×#102—222no—
116C2×#97—112no—
117C2×#97C2×D1111yescharacteristic
118#400—222no—
119#398—222no—
120#398—222no—
121#382C2×D1111yescharacteristic
122#330—224no—
123C22×C11—84no—
124C22×C11—82no—
125C22×C11—162no—
126C22×C11—162no—
127C22×C11#39211yescharacteristic
128C22×C11#45311yescharacteristic
129C22×C11#45414yes—
130C22×C11#45411yescharacteristic
131C4×C11—22no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—21no—
135C4×C11—82no—
136Dic11—82no—
137Dic11—82no—
138C22×D4—22no—
139C22×D4—21no—
140C22×C8—21no—
141C22×C8—222no—
142#127—21no—
143#127—22no—
144#127D4412yes—
145#125—222no—
146#125—222no—
147#125—222no—
148#125—222no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—222no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4C22⋊D1112yes—
155C2×C42C22×D1111yescharacteristic
156#102—44no—
157#102—228no—
158#102—228no—
159#97—22no—
160#97—114no—
161#97—222no—
162#95—22no—
163#95—224no—
164#95—222no—
165C2×C11—162no—
166C2×C11#165712yes—
167C2×C11#165812yes—
168C2×C11#200312yes—
169C2×C11#200611yescharacteristic
170C24—41no—
171C2×D4—24no—
172C2×D4—22no—
173C2×D4—42no—
174C2×D4—48no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—41no—
178C22×C4—22no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4D4×D1112yes—
182C22×C4C2×C22⋊D1111yescharacteristic
183C2×C8—22no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—224no—
187C2×C8—444no—
188C4⋊C4—42no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C4⋊C4—882no—
198C42C2×D4411yescharacteristic
199C42#433911yescharacteristic
200C42D4×D1112yes—
201C11#1008011yescharacteristic, complemented, Sylow
202C23—42no—
203C23—84no—
204C23—81no—
205C23—81no—
206C23#6699011yescharacteristic
207D4—48no—
208D4—44no—
209D4—84no—
210D4—82no—
211C2×C4—24no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—444no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4#6693512yes—
222C2×C4#6693712yes—
223C2×C4#6698311yescharacteristic
224C2×C4#6699311yescharacteristic
225C8—42no—
226C8—444no—
227C22—84no—
228C22—82no—
229C22—162no—
230C22—162no—
231C22#1062257311yescharacteristic
232C22#1062267511yescharacteristic
233C22#1062269011yescharacteristic
234C22#1062281414yes—
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—882no—
241C4—882no—
242C2—162no—
243C2#1306791212yes—
244C2#1306791712yes—
245C2#1306963912yes—
246C2#1306965711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1961C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenter#1961D11
hypocenterC11#10080
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #13076684C2semidirect
3. C2×#10622103C2semidirect
4. #13066497C2semidirect
201. C11#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
#130766842
C2×#106221032
#130664972
C11×#19612
#1008011