Finite Group Databasebeta

← #14647359

Subgroups — #14647359

Order 2816.

378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068612C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066519C212yesmaximal
4#13066474C212yesmaximal
5C11×#2356C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#391—21no—
8C11×#387—22no—
9C11×#383C412yes—
10C11×#382C2211yescharacteristic
11C4×C11×C4⋊C4—21no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C11×#376C412yes—
14C2×#66900—21no—
15#10622538C2212yes—
16#10622537C2212yes—
17#10622168—21no—
18#10622166—22no—
19C22×Q8×C11D411yescharacteristic
20C4×Q8×C11—22no—
21C4×Q8×C11—22no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11—22no—
27C2×C42×C11—21no—
28C2×C42×C11C2×C412yes—
29C2×C42×C11C2311yescharacteristic
30C2×#4318—22no—
31C11×#95—22no—
32C11×#95—22no—
33C11×#95—22no—
34C11×#95—21no—
35C11×#95C2×C411yescharacteristic
36C11×#95C2×C412yes—
37C11×#95C2×C411yescharacteristic
38#66900—42no—
39C22⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4×C11⋊C8—22no—
44#8768—111nomaximal, Sylow
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11—21no—
48C2×Q8×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—21no—
52C22×C4×C11C22⋊C412yes—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22×C411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C11×C4⋊C4—22no—
58C11×C4⋊C4—24no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C42×C11—22no—
62C42×C11—22no—
63C42×C11—44no—
64C42×C11—41no—
65C42×C11—41no—
66C42×C11#4112yes—
67C42×C11#4112yes—
68#4318—42no—
69#4318—42no—
70C2×C11⋊C8—42no—
71C2×C11⋊C8—42no—
72#2356D1111yescharacteristic
73#1801—111no—
74#1461—111no—
75#1303—112no—
76#1286—112no—
77C23×C11C2×C22⋊C411yescharacteristic
78Q8×C11—42no—
79Q8×C11—42no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11#11711yescharacteristic
97C2×C4×C11#11711yescharacteristic
98C2×C4×C11#12312yes—
99C2×C4×C11#12312yes—
100C2×C4×C11#13512yes—
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C11⋊C8—82no—
104C11⋊C8—82no—
105C2×C4×Q8C2×D1111yescharacteristic
106#431—112no—
107#423—112no—
108C2×#101—221no—
109#391—21no—
110#387—22no—
111#383Dic1112yes—
112#382C2×D1111yescharacteristic
113C4×C4⋊C4—21no—
114C4×C4⋊C4C2×D1111yescharacteristic
115#376Dic1112yes—
116#343—221no—
117#324—222no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11#38111yescharacteristic
121C22×C11#41611yescharacteristic
122C22×C11#41711yescharacteristic
123C4×C11—22no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—42no—
127C4×C11—42no—
128C4×C11—42no—
129C4×C11—81no—
130C4×C11—82no—
131C4×C11#48212yes—
132C4×C11#48512yes—
133C22×Q8C22⋊D1111yescharacteristic
134C2×M16—222no—
135C4×Q8—22no—
136C4×Q8—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C22⋊D1112yes—
140C2×C4⋊C4C22⋊D1111yescharacteristic
141C2×C42—22no—
142C2×C42—21no—
143C2×C42C2×Dic1112yes—
144C2×C42C22×D1111yescharacteristic
145C4⋊C8—222no—
146C4⋊C8—222no—
147C4⋊C8—222no—
148#101—442no—
149C22⋊C8—222no—
150C4×C8—222no—
151#95—22no—
152#95—22no—
153#95—22no—
154#95—21no—
155#95C2×Dic1111yescharacteristic
156#95C2×Dic1112yes—
157#95C2×Dic1111yescharacteristic
158C2×C11—21no—
159C2×C11—21no—
160C2×C11#182511yescharacteristic
161C2×C11#182711yescharacteristic
162C2×C11#183011yescharacteristic
163C2×Q8—22no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—21no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4C22⋊Dic1112yes—
171C22×C4C22⋊Dic1112yes—
172C22×C4C22×Dic1111yescharacteristic
173C22×C4C2×C22⋊D1111yescharacteristic
174C22×C4C2×C22⋊D1111yescharacteristic
175M16—442no—
176M16—442no—
177C2×C8—442no—
178C2×C8—442no—
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C42—22no—
184C42—22no—
185C42—44no—
186C42—41no—
187C42—41no—
188C42#433912yes—
189C42#433912yes—
190C11#876811yescharacteristic, complemented, Sylow
191C23C2×C22⋊Dic1111yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4#6697911yescharacteristic
211C2×C4#6697911yescharacteristic
212C2×C4#6698212yes—
213C2×C4#6698212yes—
214C2×C4#6700211yescharacteristic
215C2×C4#6700312yes—
216C2×C4#6700411yescharacteristic
217C8—882no—
218C8—882no—
219C22—21no—
220C22—21no—
221C22#1062282411yescharacteristic
222C22#1062284511yescharacteristic
223C22#1062284611yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4#1062260912yes—
233C4#1062261612yes—
234C2—21no—
235C2—21no—
236C2#1306871111yescharacteristic
237C2#1306872011yescharacteristic
238C2#1306873011yescharacteristic
subgroupG/H
centerC22#10622824
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2356C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2356D11
hypocenterC11#8768
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
190. C11#8768semidirect

Maximal subgroups

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

subgroupindex
#130686122
#130669402
#130665192
#130664742
C11×#23562
#876811