Finite Group Databasebeta

← #14643043

Subgroups — #14643043

Order 2816.

418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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#13075546C211yesmaximal, characteristic
2#13070180C212yesmaximal, complemented
3#13070149C211yesmaximal, characteristic
4#13066438C212yesmaximal, complemented
5C11×#1270C211yesmaximal, characteristic
6C2×#66988—21no—
7C11×#390C2211yescharacteristic
8C2×#66896—21no—
9#10622596—21no—
10C2×#66872—21no—
11#10622566—22no—
12#10622563—22no—
13#10622548C2211yescharacteristic
14#10622541C2212yes—
15C11×#336C2212yes—
16#10622189—22no—
17#10622189—22no—
18#10622162C2211yescharacteristic
19C22×D4×C11D411yescharacteristic
20C23×Dic11—21no—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C22⋊C4—22no—
24C2×C42×C11C2311yescharacteristic
25C2×C22⋊Dic11—22no—
26C2×C22⋊Dic11—21no—
27#66988—42no—
28#66988—42no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—22no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11D412yes—
33C2×C4⋊Dic11D412yes—
34C2×Dic11⋊C4—22no—
35C22×C11⋊C8—21no—
36#66896—42no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40#66872—42no—
41#7824—111nomaximal, Sylow
42C24×C11—21no—
43C2×D4×C11—21no—
44C2×D4×C11—41no—
45C2×D4×C11—41no—
46C2×D4×C11SD1612yes—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11—42no—
53C22×Dic11—41no—
54C22×Dic11—81no—
55C22×Dic11—81no—
56C2×C8×C11—42no—
57C2×C8×C11—42no—
58C2×C8×C11—42no—
59C11×C4⋊C4—41no—
60C11×C22⋊C4—42no—
61C11×C22⋊C4—42no—
62C42×C11—41no—
63C22⋊Dic11—42no—
64C22⋊Dic11—44no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67C4⋊Dic11—42no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—44no—
71C4⋊Dic11—81no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77#2724—111no—
78#2100—112no—
79#2094—111no—
80#1271—112no—
81#1270D1111yescharacteristic
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—41no—
85C23×C11—42no—
86C23×C11—41no—
87C23×C11#12011yescharacteristic
88D4×C11—42no—
89D4×C11—81no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11C2×SD1611yescharacteristic
97C2×C4×C11#13512yes—
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C11#13712yes—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—84no—
107C2×Dic11—81no—
108C2×Dic11—82no—
109C8×C11—82no—
110C11⋊C8—42no—
111C2×#123—221no—
112C2×#106—221no—
113C2×#102—221no—
114#398—221no—
115#397—222no—
116#390C2×D1111yescharacteristic
117#389—112no—
118#385—222no—
119#384—111no—
120#340—222no—
121#340—222no—
122#336—111no—
123#336C2×D1112yes—
124C22×C11—42no—
125C22×C11—44no—
126C22×C11—82no—
127C22×C11—81no—
128C22×C11—81no—
129C22×C11#45011yescharacteristic
130C22×C11#45212yes—
131C22×C11#45311yescharacteristic
132C22×C11#45412yes—
133C22×C11#45811yescharacteristic
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—81no—
139Dic11—82no—
140Dic11—82no—
141Dic11—161no—
142C22×D4D4411yescharacteristic
143C23×C4—221no—
144C22×C8—22no—
145C22×C8—221no—
146#123—442no—
147#123—442no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—222no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4D4411yescharacteristic
155C2×C22⋊C4—22no—
156C2×C22⋊C4—222no—
157C2×C22⋊C4—221no—
158C2×C42C22×D1111yescharacteristic
159#106—442no—
160#102—442no—
161#95—222no—
162#95—221no—
163#95—222no—
164C2×C11—82no—
165C2×C11#161311yescharacteristic
166C2×C11#161512yes—
167C2×C11#163011yescharacteristic
168C2×C11#163512yes—
169C2×C11#165711yescharacteristic
170C24—21no—
171C2×D4—21no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4#431412yes—
175C22×C4—21no—
176C22×C4—222no—
177C22×C4—222no—
178C22×C4—442no—
179C22×C4—441no—
180C22×C4—881no—
181C22×C4—881no—
182C22×C4C2×D4411yescharacteristic
183C22×C4D4×D1112yes—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—222no—
188C2×C8—441no—
189C2×C8—441no—
190C4⋊C4—41no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—444no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C4⋊C4—881no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—442no—
203C22⋊C4—444no—
204C42—41no—
205C11#782411yescharacteristic, complemented, Sylow
206C23—22no—
207C23—41no—
208C23—41no—
209C23—42no—
210C23—42no—
211C23#6693511yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—884no—
227C2×C4—881no—
228C2×C4—882no—
229C2×C4C2×#431411yescharacteristic
230C2×C4#6696111yescharacteristic
231C2×C4#6696512yes—
232C2×C4#6696812yes—
233C8—82no—
234C8—442no—
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#1062234411yescharacteristic
241C22#1062235511yescharacteristic
242C22#1062236011yescharacteristic
243C22#1062239612yes—
244C22#1062244012yes—
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—81no—
250C4—882no—
251C4—882no—
252C4—1761no—
253C2—82no—
254C2#1306763811yescharacteristic
255C2#1306764812yes—
256C2#1306773811yescharacteristic
257C2#1306776912yes—
258C2#1306791511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#1270D11
hypocenterC11#7824
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070180C2semidirect
4. #13066438C2semidirect
205. C11#7824semidirect

Maximal subgroups

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

subgroupindex
#130755462
#130701802
#130701492
#130664382
C11×#12702
#782411