Finite Group Databasebeta

← #14643015

Subgroups — #14643015

Order 2816.

434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070144C211yesmaximal, characteristic
2#13070092C212yesmaximal, complemented
3#13066439C212yesmaximal, complemented
4#13066437C211yesmaximal, characteristic
5C11×#2724C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C11×#398—21no—
8C11×#397—22no—
9C11×#390C2211yescharacteristic
10C11×#389C2212yes—
11C11×#385—22no—
12C2×#66896—21no—
13C2×#66872—22no—
14C2×#66871—21no—
15#10622548C2211yescharacteristic
16#10622167—22no—
17#10622162C2212yes—
18#10622162C2211yescharacteristic
19C22×D4×C11D411yescharacteristic
20C23×C4×C11—21no—
21C11×#123—42no—
22C11×#123—42no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4D412yes—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D412yes—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—22no—
34C22×C11⋊C8—21no—
35C22×C11⋊C8—22no—
36C11×#95—22no—
37C11×#95—21no—
38C11×#95—22no—
39#66896—42no—
40#66872—44no—
41#66871—42no—
42#7819—111nomaximal, Sylow
43C24×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11SD1612yes—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—42no—
52C22×C4×C11—81no—
53C22×C4×C11—81no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C22×Dic11—41no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—81no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—44no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C42×C11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—41no—
79#2724D1111yescharacteristic
80#2093—111no—
81#2084—112no—
82#1271—112no—
83#1270—111no—
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—41no—
87C23×C11—42no—
88C23×C11—41no—
89C23×C11#12011yescharacteristic
90D4×C11—42no—
91D4×C11—81no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—84no—
105C2×C4×C11C2×SD1611yescharacteristic
106C2×C4×C11#13512yes—
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×Dic11—82no—
110C2×Dic11—81no—
111C11⋊C8—44no—
112C11⋊C8—42no—
113C2×#123—21no—
114C2×#107—221no—
115C2×#106—222no—
116C2×#102—221no—
117#398—21no—
118#397—22no—
119#390C2×D1111yescharacteristic
120#389C2×D1112yes—
121#385—22no—
122#384—111no—
123#340—222no—
124#336—112no—
125#336—111no—
126C22×C11—42no—
127C22×C11—44no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#44912yes—
132C22×C11#45011yescharacteristic
133C22×C11#45311yescharacteristic
134C22×C11#45612yes—
135C22×C11#45811yescharacteristic
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11—82no—
143Dic11—161no—
144C22×D4C22⋊D1111yescharacteristic
145C23×C4—21no—
146C22×C8—222no—
147C22×C8—221no—
148#123—42no—
149#123—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4C22⋊D1112yes—
155C2×C4⋊C4C22⋊D1112yes—
156C2×C4⋊C4C22⋊D1111yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—22no—
160C2×C42C22×D1111yescharacteristic
161#107—442no—
162#106—444no—
163#102—442no—
164#95—22no—
165#95—21no—
166#95—22no—
167C2×C11—82no—
168C2×C11#160912yes—
169C2×C11#161311yescharacteristic
170C2×C11#162011yescharacteristic
171C2×C11#165412yes—
172C2×C11#166011yescharacteristic
173C24—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4#432412yes—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—441no—
185C22×C4C2×C22⋊D1111yescharacteristic
186C22×C4C2×C22⋊D1112yes—
187C2×C8—222no—
188C2×C8—224no—
189C2×C8—442no—
190C2×C8—441no—
191C2×C8—441no—
192C2×C8—442no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C22⋊C4—42no—
205C22⋊C4—44no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—41no—
209C11#781911yescharacteristic, complemented, Sylow
210C23—22no—
211C23—42no—
212C23—41no—
213C23—41no—
214C23—42no—
215C23#6700611yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—882no—
232C2×C4—881no—
233C2×C4#6698511yescharacteristic
234C2×C4C2×#432411yescharacteristic
235C2×C4#6700212yes—
236C2×C4#6700312yes—
237C8—444no—
238C8—442no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1062283111yescharacteristic
245C22#1062285112yes—
246C22#1062285411yescharacteristic
247C22#1062285611yescharacteristic
248C22#1062285912yes—
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—1761no—
257C2—82no—
258C2#1306761312yes—
259C2#1306763611yescharacteristic
260C2#1306767511yescharacteristic
261C2#1306790012yes—
262C2#1306792711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2724C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2724D11
hypocenterC11#7819
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

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

NH ≅ G/Ntype
2. #13070092C2semidirect
3. #13066439C2semidirect
209. C11#7819semidirect

Maximal subgroups

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

subgroupindex
#130701442
#130700922
#130664392
#130664372
C11×#27242
#781911