Finite Group Databasebeta

← #14658799

Subgroups — #14658799

Order 2816.

296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069597C211yesmaximal, characteristic
2#13068736C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067387C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13067020C211yesmaximal, characteristic
7C11×#1274C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622537C2211yescharacteristic
13C2×C4⋊(C11⋊C8)C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622162—22no—
16#10622161—22no—
17#10622096—22no—
18#10622095—22no—
19#10622094—22no—
20#10622094—22no—
21C2×C42×C11D412yes—
22C2×C42×C11C2311yescharacteristic
23#66979—21no—
24#66977—21no—
25#66977—21no—
26C2×#4318—21no—
27C22×C11⋊C8—21no—
28C22×C11⋊C8—21no—
29#66923—21no—
30#66922Q811yescharacteristic
31#66922Q811yescharacteristic
32C4×Dic22—21no—
33C4×Dic22—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C22⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C4×C8×C11D412yes—
40C11×#95—21no—
41C11×#95—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48#10669—111nomaximal, Sylow
49C22×C4×C11—22no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C2×Dic22—21no—
54C2×Dic22—21no—
55C2×C8×C11—22no—
56C2×C8×C11—22no—
57C42×C11—22no—
58C42×C11—22no—
59C42×C11C2×D411yescharacteristic
60C42×C11C2×D411yescharacteristic
61C42×C11C2×Q811yescharacteristic
62C42×C11#4111yescharacteristic
63C22⋊Dic11—41no—
64C4⋊Dic11—21no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—21no—
68Dic11⋊C4—41no—
69Dic11⋊C4—41no—
70C4×Dic11—41no—
71#4318—42no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77#1995—111no—
78#1832—111no—
79#1571—111no—
80#1570—111no—
81#1481—111no—
82#1481—111no—
83#1274D1111yescharacteristic
84C23×C11#12311yescharacteristic
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11C22⋊Q811yescharacteristic
91C2×C4×C11C22⋊Q811yescharacteristic
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11#12311yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11#12711yescharacteristic
96C2×C4×C11#13512yes—
97C2×C4×C11#13712yes—
98C2×Dic11—41no—
99C2×Dic11—41no—
100Dic22—42no—
101Dic22—42no—
102C8×C11—42no—
103C8×C11—42no—
104C11⋊C8—81no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107#533—111no—
108#431C2×D1111yescharacteristic
109#431C2×D1111yescharacteristic
110#423—111no—
111C2×C4⋊C8—111no—
112C2×C4⋊C8—111no—
113#376C2×D1111yescharacteristic
114#339—222no—
115#336—222no—
116#335—222no—
117#334—222no—
118Q8⋊C8—222no—
119Q8⋊C8—222no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#39911yescharacteristic
123C22×C11#48512yes—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—21no—
128C4×C11—82no—
129C4×C11#47912yes—
130C4×C11#49511yescharacteristic
131C4×C11#49711yescharacteristic
132Dic11—81no—
133Dic11—81no—
134C2×M16—221no—
135C22×C8—221no—
136C22×C8—221no—
137C4⋊Q8—111no—
138C4⋊Q8—111no—
139#125—221no—
140C22⋊Q8—221no—
141C22⋊Q8—221no—
142C4×Q8—221no—
143C4×Q8—221no—
144#117—221no—
145C2×C42D4412yes—
146C2×C42C22×D1111yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—221no—
150C4⋊C8—221no—
151C4⋊C8—221no—
152C4⋊C8—221no—
153C4⋊C8—221no—
154C4⋊C8—221no—
155C22⋊C8—21no—
156C22⋊C8—21no—
157C4×C8D4412yes—
158C4×C8D4412yes—
159#95—21no—
160#95—21no—
161C2×C11—22no—
162C2×C11#209711yescharacteristic
163C2×C11#209811yescharacteristic
164C2×C11#209811yescharacteristic
165C2×Q8—221no—
166C2×Q8—221no—
167C22×C4—22no—
168C22×C4C2×D4411yescharacteristic
169C22×C4#434111yescharacteristic
170C22×C4#434111yescharacteristic
171M16—442no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—441no—
175C2×C8—441no—
176C2×C8—441no—
177C2×C8—442no—
178C2×C8—442no—
179C4⋊C4—221no—
180C4⋊C4—221no—
181C4⋊C4—221no—
182C4⋊C4—221no—
183C4⋊C4—441no—
184C4⋊C4—441no—
185C22⋊C4—441no—
186C42—22no—
187C42—22no—
188C42—441no—
189C42C2×D4411yescharacteristic
190C42C2×D4411yescharacteristic
191C42#434111yescharacteristic
192C42Q8×D1111yescharacteristic
193C11#1066911yescharacteristic, complemented, Sylow
194C23#6693911yescharacteristic
195Q8—442no—
196Q8—442no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—441no—
203C2×C4—441no—
204C2×C4#6692711yescharacteristic
205C2×C4#6693911yescharacteristic
206C2×C4#6693911yescharacteristic
207C2×C4#6695011yescharacteristic
208C2×C4#6695011yescharacteristic
209C2×C4#6695011yescharacteristic
210C2×C4#6695712yes—
211C2×C4#6696212yes—
212C8—42no—
213C8—42no—
214C8—881no—
215C8—881no—
216C8—881no—
217C22—21no—
218C22—21no—
219C22#1062229011yescharacteristic
220C22#1062233612yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—881no—
227C4—881no—
228C4#1062230911yescharacteristic
229C4#1062232811yescharacteristic
230C4#1062244212yes—
231C2—22no—
232C2#1307016311yescharacteristic
233C2#1307017011yescharacteristic
234C2#1307017011yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#399
prime radicalC23×C11#123
hypercenter#1274D11
hypocenterC11#10669
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
193. C11#10669semidirect

Maximal subgroups

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

subgroupindex
#130695972
#130687362
#130673912
#130673872
#130670202
C11×#12742
#1066911