Finite Group Databasebeta

← #14651153

Subgroups — #14651153

Order 2816.

470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 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#13073828C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067300C212yesmaximal
4#13066518C212yesmaximal
5C11×#2982C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C8×Q8×C11—24no—
9C11×#431—22no—
10C11×#431C2212yes—
11#10622843—21no—
12C2×#66900—21no—
13#10622599C414yes—
14#10622590—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622542—22no—
17#10622537C2212yes—
18#10622168—21no—
19#10622120—24no—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22—21no—
22C4×Q8×C11—22no—
23C4×Q8×C11—22no—
24C2×C11×C4⋊C4C2×C412yes—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11C2×C412yes—
31C2×C4×Dic11—21no—
32C2×#4318—22no—
33#66922—22no—
34#66922—22no—
35C11×C4⋊C8—24no—
36C11×C4⋊C8D414yes—
37C11×C22⋊C8—22no—
38C4×C8×C11—24no—
39C4×C8×C11—22no—
40#66900—42no—
41C11⋊#95—24no—
42C11⋊#95—24no—
43C11⋊#95C2×C412yes—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—22no—
46#9396—111nomaximal, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—22no—
49C2×Q8×C11SD1612yes—
50C2×Q8×C11Q1612yes—
51C22×C4×C11C22⋊C412yes—
52C22×C4×C11C22⋊C412yes—
53C22×C4×C11C22×C411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×Dic11—22no—
57C22×Dic11—22no—
58C2×Dic22—44no—
59C2×Dic22—41no—
60C2×Dic22—41no—
61C2×C8×C11—24no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4—22no—
64C42×C11—22no—
65C42×C11—22no—
66C42×C11C2×D412yes—
67C42×C11#4112yes—
68C4⋊Dic11—24no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4×Dic11—42no—
72#4318—42no—
73#4318—42no—
74C2×C11⋊C8—42no—
75#2982D1111yescharacteristic
76#2568—111no—
77#1801—111no—
78#1549—112no—
79#1303—112no—
80C23×C11C2×C22⋊C411yescharacteristic
81Q8×C11—24no—
82Q8×C11—24no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11#10314yes—
90C2×C4×C11C4×D412yes—
91C2×C4×C11#12011yescharacteristic
92C2×C4×C11#12112yes—
93C2×C4×C11#12311yescharacteristic
94C2×C4×C11C2×SD1611yescharacteristic
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11#13512yes—
97C2×Dic11—42no—
98C2×Dic11—44no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102Dic22—82no—
103Dic22—82no—
104C8×C11—44no—
105C11⋊C8—82no—
106C2×C4⋊Q8—111no—
107C2×C4×Q8C2×D1111yescharacteristic
108C8×Q8—24no—
109#431—22no—
110#431C2×D1112yes—
111#423—112no—
112C2×#101—221no—
113#400—114no—
114#391—221no—
115#391—222no—
116#382—221no—
117C4×C4⋊C4—111no—
118#343—221no—
119#332—224no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#38611yescharacteristic
123C22×C11C2×#10311yescharacteristic
124C22×C11#41611yescharacteristic
125C4×C11—21no—
126C4×C11—24no—
127C4×C11—22no—
128C4×C11—42no—
129C4×C11#45412yes—
130C4×C11#46512yes—
131C4×C11#46712yes—
132Dic11—82no—
133Dic11—82no—
134C22×Q8—221no—
135C22×Q8D4411yescharacteristic
136C2×M16—222no—
137C4⋊Q8—222no—
138C4⋊Q8—222no—
139C4×Q8—22no—
140C4×Q8—22no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—221no—
143C2×C4⋊C4—221no—
144C2×C4⋊C4C4×D1112yes—
145C2×C4⋊C4D4411yescharacteristic
146C2×C42—221no—
147C2×C42C22⋊D1112yes—
148C2×C42C22×D1111yescharacteristic
149C4⋊C8—24no—
150C4⋊C8—222no—
151C4⋊C8—222no—
152C4⋊C8C22⋊D1114yes—
153#101—442no—
154C22⋊C8—22no—
155C4×C8—24no—
156C4×C8—22no—
157#95—112no—
158#95—224no—
159#95—224no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11#188811yescharacteristic
163C2×C11#189211yescharacteristic
164C2×C11#191511yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—444no—
168C2×Q8—441no—
169C2×Q8—441no—
170C2×Q8#431412yes—
171C2×Q8Dic4412yes—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4(C2×D11)⋊C412yes—
175C22×C4(C2×D11)⋊C412yes—
176C22×C4C2×C4×D1111yescharacteristic
177C22×C4C2×D4411yescharacteristic
178C22×C4C2×C22⋊D1111yescharacteristic
179M16—442no—
180M16—442no—
181C2×C8—24no—
182C2×C8—442no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—224no—
186C4⋊C4—442no—
187C4⋊C4—442no—
188C42—22no—
189C42—22no—
190C42—442no—
191C42#433912yes—
192C42C2×C22⋊D1112yes—
193C11#939611yescharacteristic, complemented, Sylow
194C23C2×(C2×D11)⋊C411yescharacteristic
195Q8—24no—
196Q8—24no—
197Q8—882no—
198Q8—882no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—442no—
206C2×C4—444no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—442no—
210C2×C4#6688014yes—
211C2×C4C2×#431411yescharacteristic
212C2×C4#6695712yes—
213C2×C4C2×Dic4411yescharacteristic
214C2×C4C4×C22⋊D1112yes—
215C2×C4#6698211yescharacteristic
216C2×C4#6698312yes—
217C2×C4#6700611yescharacteristic
218C8—44no—
219C8—882no—
220C22—21no—
221C22—21no—
222C22C2×#6688011yescharacteristic
223C22#1062272611yescharacteristic
224C22#1062282611yescharacteristic
225C4—22no—
226C4—21no—
227C4—24no—
228C4—42no—
229C4—882no—
230C4—882no—
231C4#1062272712yes—
232C4#1062272912yes—
233C4#1062285812yes—
234C2—21no—
235C2—21no—
236C2#1306901911yescharacteristic
237C2#1306903911yescharacteristic
238C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9396
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
193. C11#9396semidirect

Maximal subgroups

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

subgroupindex
#130738282
#130686122
#130673002
#130665182
C11×#29822
#939611