Finite Group Databasebeta

← #14658780

Subgroups — #14658780

Order 2816.

334 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 91 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#13068736C211yesmaximal, characteristic, complemented
2#13067392C211yesmaximal, characteristic, complemented
3#13067388C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic
5#13067015C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic, complemented
7C11×#1963C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C2×C11×#104—22no—
11C11×#376C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16D4⋊(C11⋊C8)—22no—
17D4⋊(C11⋊C8)—22no—
18#10622162—22no—
19#10622118—22no—
20#10622117—22no—
21C2×C11×#41—21no—
22C2×C11×M16—21no—
23C11×C4⋊Q8Q811yescharacteristic
24C11×#127Q811yescharacteristic
25C11×#124—21no—
26C11×#121—21no—
27C11×#121—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C2×C42×C11D412yes—
31C2×C42×C11C2311yescharacteristic
32C22×C11⋊C8—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×#104—44no—
37C11×#95—21no—
38C11×#95—21no—
39C22⋊(C11⋊C8)—21no—
40C22⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4×C11⋊C8D412yes—
48C4×C11⋊C8D412yes—
49#10665—111nomaximal, Sylow
50C11×#41—42no—
51C11×#41—42no—
52C2×Q8×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C11×M16—42no—
63C2×C8×C11—41no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—21no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×Q811yescharacteristic
73C42×C11#4111yescharacteristic
74C2×C11⋊C8—22no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#1963D1111yescharacteristic
81#1832—111no—
82#1571—111no—
83#1570—111no—
84#1480—111no—
85#1480—111no—
86#1274—111no—
87C23×C11—41no—
88C23×C11#12311yescharacteristic
89Q8×C11—42no—
90D4×C11—42no—
91D4×C11—42no—
92D4×C11—42no—
93D4×C11—82no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—81no—
101C2×C4×C11—81no—
102C2×C4×C11C22⋊Q811yescharacteristic
103C2×C4×C11C22⋊Q811yescharacteristic
104C2×C4×C11C22⋊Q811yescharacteristic
105C2×C4×C11#12311yescharacteristic
106C2×C4×C11#12311yescharacteristic
107C2×C4×C11#12711yescharacteristic
108C2×C4×C11#13512yes—
109C2×C4×C11AGL(1,ℤ/8)12yes—
110C8×C11—81no—
111C11⋊C8—42no—
112C11⋊C8—42no—
113C11⋊C8—81no—
114C11⋊C8—81no—
115#532C2×D1111yescharacteristic
116#431—111no—
117#431—111no—
118#423C2×D1111yescharacteristic
119C2×C4⋊C8—111no—
120C2×C4⋊C8—111no—
121C2×#104—22no—
122#376C2×D1111yescharacteristic
123#336—222no—
124#335—222no—
125#334—222no—
126D4⋊C8—222no—
127D4⋊C8—222no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11#39911yescharacteristic
134C22×C11#48212yes—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—82no—
140C4×C11—81no—
141C4×C11#47812yes—
142C4×C11#49511yescharacteristic
143C4×C11#49611yescharacteristic
144C2×#41—21no—
145C2×M16—21no—
146C22×C8—221no—
147C22×C8—221no—
148C4⋊Q8Dic2211yescharacteristic
149#127Dic2211yescharacteristic
150#124—21no—
151#121—21no—
152#121—21no—
153C4×D4—21no—
154C4×D4—21no—
155C2×C42C22⋊D1112yes—
156C2×C42C22×D1111yescharacteristic
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—221no—
160C4⋊C8—221no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#104—44no—
166C22⋊C8—221no—
167C22⋊C8—221no—
168C4×C8—112no—
169C4×C8—112no—
170#95—21no—
171#95—21no—
172C2×C11—22no—
173C2×C11—161no—
174C2×C11#209211yescharacteristic
175C2×C11#209811yescharacteristic
176C2×C11#209811yescharacteristic
177#41—42no—
178#41—42no—
179C2×Q8—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—41no—
184C22×C4—22no—
185C22×C4—41no—
186C22×C4#434111yescharacteristic
187C22×C4#434111yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189M16—42no—
190C2×C8—41no—
191C2×C8—222no—
192C2×C8—222no—
193C2×C8—442no—
194C2×C8—441no—
195C2×C8—441no—
196C2×C8—442no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C22⋊C4—41no—
200C22⋊C4—41no—
201C42—22no—
202C42—22no—
203C42C2×Dic2211yescharacteristic
204C42#433911yescharacteristic
205C42D4×D1111yescharacteristic
206C42D4×D1111yescharacteristic
207C11#1066511yescharacteristic, complemented, Sylow
208C23—41no—
209C23#6698811yescharacteristic
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—42no—
214D4—82no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4#6693111yescharacteristic
224C2×C4#6693111yescharacteristic
225C2×C4#6693611yescharacteristic
226C2×C4#6693611yescharacteristic
227C2×C4#6697711yescharacteristic
228C2×C4#6698512yes—
229C2×C4#6699311yescharacteristic
230C2×C4#6700312yes—
231C8—81no—
232C8—442no—
233C8—442no—
234C8—881no—
235C8—881no—
236C22—21no—
237C22—21no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22#1062256211yescharacteristic
242C22#1062264812yes—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—82no—
248C4—81no—
249C4#1062262212yes—
250C4#1062267211yescharacteristic
251C4#1062268711yescharacteristic
252C2—22no—
253C2—161no—
254C2#1307013711yescharacteristic
255C2#1307017111yescharacteristic
256C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#399
prime radicalC11×#532C22
hypercenter#1963D11
hypocenterC11#10665
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13068736C2semidirect
2. #13067392C2semidirect
3. #13067388C2semidirect
6. #13066445C2semidirect
207. C11#10665semidirect

Maximal subgroups

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

subgroupindex
#130687362
#130673922
#130673882
#130670152
#130664452
C11×#19632
#1066511