Finite Group Databasebeta

← #14658509

Subgroups — #14658509

Order 2816.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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#13069410C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic, complemented
3#13068617C212yesmaximal
4#13066500C212yesmaximal, complemented
5C11×#1277C211yesmaximal, characteristic, complemented
6C2×C4×D44C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9C2×#66885—22no—
10C2×(C2×D11)⋊C8—22no—
11#10622548C2212yes—
12C2×C4⋊(C11⋊C8)C2211yescharacteristic
13#10622189—22no—
14#10622189—22no—
15C22×D44D411yescharacteristic
16C22×C4×D11—21no—
17C22×C8×C11—22no—
18C22×C8×C11D412yes—
19C2×C42×C11C2311yescharacteristic
20C2×(C2×D11)⋊C4—21no—
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11—22no—
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11D411yescharacteristic
25C22×C11⋊C8—21no—
26C4×D44—22no—
27C4×D44—22no—
28C11×C4⋊C8—22no—
29C11×C4⋊C8—22no—
30C4×C8×C11—22no—
31#66885—44no—
32(C2×D11)⋊C8—44no—
33C4⋊(C11⋊C8)—22no—
34#10621—111nomaximal, Sylow
35C23×D11—21no—
36C22×C4×C11C2×D411yescharacteristic
37C22×C4×C11C2×D411yescharacteristic
38C22×C4×C11#4111yescharacteristic
39C22×Dic11—21no—
40C22×Dic11—42no—
41C2×D44—22no—
42C2×D44—21no—
43C2×D44—22no—
44C2×D44D812yes—
45C2×C4×D11—41no—
46C2×C4×D11—41no—
47C2×C4×D11—42no—
48C2×C4×D11—42no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C2×C8×C11—22no—
52C2×C8×C11—42no—
53C2×C8×C11—42no—
54C2×C8×C11—42no—
55C42×C11#4112yes—
56C42×C11#4112yes—
57(C2×D11)⋊C4—42no—
58C4⋊Dic11—22no—
59C4⋊Dic11—42no—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63C4⋊Dic11—82no—
64C2×C11⋊C8—41no—
65C2×C11⋊C8—42no—
66#1954—111no—
67#1834—111no—
68#1802—112no—
69#1296—112no—
70#1277D1111yescharacteristic, complemented
71C23×C11#12111yescharacteristic
72C22×D11—22no—
73C22×D11—41no—
74C22×D11—42no—
75C22×D11—41no—
76C22×D11—42no—
77C2×C4×C11—22no—
78C2×C4×C11#12312yes—
79C2×C4×C11#12311yescharacteristic
80C2×C4×C11#12411yescharacteristic
81C2×C4×C11#12612yes—
82C2×C4×C11C2×D811yescharacteristic
83C2×C4×C11#13512yes—
84C2×C4×C11#13511yescharacteristic
85C2×C4×C11AGL(1,ℤ/8)12yes—
86C2×C4×C11#13712yes—
87C2×Dic11—41no—
88C2×Dic11—42no—
89C2×Dic11—82no—
90C2×Dic11—82no—
91C2×Dic11—82no—
92D44—24no—
93D44—42no—
94C4×D11—82no—
95C4×D11—81no—
96C4×D11—81no—
97C8×C11—42no—
98C8×C11—82no—
99C11⋊C8—81no—
100C2×C4×D4—111no—
101C2×C4⋊C8—111no—
102C2×C4⋊C8C2×D1112yes—
103C2×#102—222no—
104C2×C22⋊C8—222no—
105C2×C4×C8C2×D1111yescharacteristic
106#384—112no—
107#340—222no—
108#340—222no—
109C22×C11#39711yescharacteristic
110C22×C11#46312yes—
111C22×C11#46611yescharacteristic
112C22×C11#47011yescharacteristic
113C22×C11#47112yes—
114C2×D11—42no—
115C2×D11—44no—
116C2×D11—81no—
117C2×D11—81no—
118C2×D11—82no—
119C4×C11—22no—
120C4×C11#48012yes—
121C4×C11#48212yes—
122C4×C11#48512yes—
123C4×C11#48811yescharacteristic
124C4×C11#49011yescharacteristic
125Dic11—81no—
126Dic11—162no—
127C22×D4—111no—
128C23×C4—221no—
129C22×C8—22no—
130C22×C8—221no—
131C22×C8D4412yes—
132C4×D4—222no—
133C4×D4—222no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—222no—
136C2×C4⋊C4—222no—
137C2×C4⋊C4—222no—
138C2×C22⋊C4—221no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—222no—
143#102—444no—
144C22⋊C8—444no—
145C4×C8—22no—
146C2×C11#168112yes—
147C2×C11#170312yes—
148C2×C11#207311yescharacteristic
149C2×C11#207511yescharacteristic
150C2×C11#207911yescharacteristic
151D11—82no—
152C24—221no—
153C2×D4—112no—
154C2×D4—222no—
155C2×D4—222no—
156C2×D4—221no—
157C22×C4—221no—
158C22×C4—441no—
159C22×C4—441no—
160C22×C4—442no—
161C22×C4—442no—
162C22×C4—442no—
163C22×C4C2×D4411yescharacteristic
164C22×C4D4×D1111yescharacteristic
165C22×C4#434311yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—441no—
173C2×C8—442no—
174C4⋊C4—222no—
175C4⋊C4—442no—
176C4⋊C4—442no—
177C4⋊C4—442no—
178C4⋊C4—442no—
179C4⋊C4—882no—
180C22⋊C4—442no—
181C42#433912yes—
182C42#434112yes—
183C11#1062111yescharacteristic, complemented, Sylow
184C23—222no—
185C23—441no—
186C23—442no—
187C23—441no—
188C23—442no—
189C23#6694811yescharacteristic
190D4—224no—
191D4—442no—
192C2×C4—22no—
193C2×C4—441no—
194C2×C4—442no—
195C2×C4—881no—
196C2×C4—881no—
197C2×C4—882no—
198C2×C4—882no—
199C2×C4—882no—
200C2×C4—882no—
201C2×C4#6692811yescharacteristic
202C2×C4#6693612yes—
203C2×C4#6693911yescharacteristic
204C2×C4#6695112yes—
205C2×C4#6695712yes—
206C2×C4#6696112yes—
207C2×C4D8×D1111yescharacteristic
208C2×C4#6696812yes—
209C2×C4#6697211yescharacteristic
210C8—42no—
211C8—82no—
212C8—881no—
213C22—444no—
214C22—442no—
215C22—882no—
216C22—881no—
217C22—881no—
218C22#1062228711yescharacteristic
219C22#1062245712yes—
220C22#1062248111yescharacteristic
221C22#1062249611yescharacteristic
222C22#1062251112yes—
223C4—22no—
224C4—881no—
225C4—1762no—
226C4#1062231011yescharacteristic
227C4#1062232611yescharacteristic
228C4#1062235012yes—
229C4#1062238712yes—
230C4#1062242712yes—
231C2—882no—
232C2#1306805412yes—
233C2#1306819212yes—
234C2#1307003111yescharacteristic
235C2#1307004111yescharacteristic
236C2#1307006311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1277D11
hypocenterC11#10621
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #13068744C2semidirect
4. #13066500C2semidirect
5. C11×#1277C2semidirect
70. #1277D11semidirect
183. C11#10621semidirect

Maximal subgroups

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

subgroupindex
#130694102
#130687442
#130686172
#130665002
C11×#12772
#1062111