Finite Group Databasebeta

← #14643042

Subgroups — #14643042

Order 2816.

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

normal subgroups only

This group has 418 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#13070179C212yesmaximal, complemented
2#13070149C211yesmaximal, characteristic
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—21no—
14#10622548C2211yescharacteristic
15#10622167—22no—
16#10622167—22no—
17#10622162C2211yescharacteristic
18#10622162C2212yes—
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—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—22no—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—42no—
51C22×C4×C11—81no—
52C22×C4×C11—81no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C22×Dic11—41no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—81no—
63C11×C22⋊C4—42no—
64C11×C22⋊C4—44no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—42no—
67C42×C11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—44no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77#2724D1111yescharacteristic
78#2100—112no—
79#2094—111no—
80#1271—112no—
81#1270—111no—
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—22no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—84no—
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11#13512yes—
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C11#13712yes—
107C2×Dic11—81no—
108C2×Dic11—82no—
109C11⋊C8—42no—
110C11⋊C8—82no—
111C2×#123—21no—
112C2×#106—221no—
113C2×#102—221no—
114#398—21no—
115#397—22no—
116#390C2×D1111yescharacteristic
117#389C2×D1112yes—
118#385—22no—
119#384—111no—
120#340—222no—
121#340—222no—
122#336—111no—
123#336—112no—
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—82no—
139C4×C11—81no—
140C4×C11—82no—
141Dic11—161no—
142C22×D4C22⋊D1111yescharacteristic
143C23×C4—21no—
144C22×C8—221no—
145C22×C8—222no—
146#123—42no—
147#123—42no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—222no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4C22⋊D1112yes—
153C2×C4⋊C4C22⋊D1112yes—
154C2×C4⋊C4C22⋊D1111yescharacteristic
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—22no—
158C2×C42C22×D1111yescharacteristic
159#106—442no—
160#102—442no—
161#95—22no—
162#95—21no—
163#95—22no—
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#432412yes—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—441no—
182C22×C4C2×C22⋊D1111yescharacteristic
183C22×C4C2×C22⋊D1112yes—
184C2×C8—222no—
185C2×C8—441no—
186C2×C8—441no—
187C2×C8—442no—
188C2×C8—442no—
189C2×C8—442no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—441no—
198C4⋊C4—441no—
199C4⋊C4—444no—
200C22⋊C4—42no—
201C22⋊C4—44no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C42—41no—
205C11#782411yescharacteristic, complemented, Sylow
206C23—22no—
207C23—42no—
208C23—41no—
209C23—41no—
210C23—42no—
211C23#6700611yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—84no—
227C2×C4—881no—
228C2×C4—882no—
229C2×C4#6698511yescharacteristic
230C2×C4C2×#432411yescharacteristic
231C2×C4#6700312yes—
232C2×C4#6700412yes—
233C8—442no—
234C8—882no—
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#1062283111yescharacteristic
241C22#1062285212yes—
242C22#1062285411yescharacteristic
243C22#1062285611yescharacteristic
244C22#1062285812yes—
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—1761no—
253C2—82no—
254C2#1306763611yescharacteristic
255C2#1306764712yes—
256C2#1306773711yescharacteristic
257C2#1306776712yes—
258C2#1306791411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2724C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2724D11
hypocenterC11#7824
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
1. #13070179C2semidirect
3. #13066439C2semidirect
205. C11#7824semidirect

Maximal subgroups

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

subgroupindex
#130701792
#130701492
#130664392
#130664372
C11×#27242
#782411