Finite Group Databasebeta

← #14647355

Subgroups — #14647355

Order 2816.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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#13071537C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13066518C212yesmaximal
4#13066475C212yesmaximal
5C11×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×Q8×Dic11—21no—
8C11×#431C2212yes—
9C2×#66900—21no—
10#10622598—21no—
11#10622598—22no—
12#10622549C412yes—
13#10622549C2211yescharacteristic
14C4×C4⋊Dic11C412yes—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622537C2212yes—
17C11×#324—22no—
18#10622168—21no—
19C22×Q8×C11D411yescharacteristic
20C4×Q8×C11—22no—
21C4×Q8×C11—22no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C4⋊C4D412yes—
24C2×C42×C11C2×C412yes—
25C2×C42×C11C2311yescharacteristic
26Q8×Dic11—44no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4×Dic11—22no—
32C2×C4×Dic11—21no—
33C2×#4318—22no—
34C11×C4⋊C8—22no—
35C11×C22⋊C8—22no—
36C4×C8×C11—22no—
37#66900—42no—
38C11⋊#95—22no—
39C11⋊#95—21no—
40C11⋊#95C2×C411yescharacteristic
41C11⋊#95C2×C412yes—
42C11⋊#95C2×C411yescharacteristic
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45#8767—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C2×Q8×C11—22no—
48C2×Q8×C11SD1612yes—
49C2×Q8×C11Q1612yes—
50C22×C4×C11C22⋊C412yes—
51C22×C4×C11C22⋊C412yes—
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—21no—
56C22×Dic11—21no—
57C22×Dic11—22no—
58C2×C8×C11—42no—
59C11×C4⋊C4—24no—
60C11×C4⋊C4—22no—
61C42×C11—22no—
62C42×C11—22no—
63C42×C11#4112yes—
64C42×C11#4112yes—
65C4⋊Dic11—44no—
66C4⋊Dic11—42no—
67C4⋊Dic11—44no—
68C4⋊Dic11—42no—
69C4×Dic11—44no—
70C4×Dic11—42no—
71#4318—42no—
72#4318—42no—
73C2×C11⋊C8—42no—
74#2351—111no—
75#1801—111no—
76#1461D1111yescharacteristic
77#1303—112no—
78#1286—112no—
79C23×C11C2×C22⋊C411yescharacteristic
80Q8×C11—24no—
81Q8×C11—24no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—42no—
88C2×C4×C11#10314yes—
89C2×C4×C11#11711yescharacteristic
90C2×C4×C11#11711yescharacteristic
91C2×C4×C11#12312yes—
92C2×C4×C11#12312yes—
93C2×C4×C11C2×SD1611yescharacteristic
94C2×C4×C11C2×Q1611yescharacteristic
95C2×C4×C11AGL(1,ℤ/8)12yes—
96C2×Dic11—22no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—41no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—41no—
105C8×C11—82no—
106C11⋊C8—82no—
107C2×C4×Q8—221no—
108C2×C4×Q8C2×D1111yescharacteristic
109#431C2×D1112yes—
110#423—112no—
111C2×#101—221no—
112#389—221no—
113#389—222no—
114#382—111no—
115#382—112no—
116C4×C4⋊C4—111no—
117C4×C4⋊C4—112no—
118#343—221no—
119#324—22no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#38111yescharacteristic
123C22×C11C2×#10311yescharacteristic
124C22×C11#41811yescharacteristic
125C4×C11—24no—
126C4×C11—22no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—42no—
130C4×C11#48112yes—
131C4×C11#48412yes—
132Dic11—42no—
133Dic11—82no—
134Dic11—81no—
135C22×Q8D4411yescharacteristic
136C2×M16—222no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—444no—
140C2×C4⋊C4—222no—
141C2×C4⋊C4—222no—
142C2×C4⋊C4—221no—
143C2×C4⋊C4—221no—
144C2×C4⋊C4D4411yescharacteristic
145C2×C4⋊C4C22⋊D1112yes—
146C2×C42—222no—
147C2×C42—221no—
148C2×C42C4×D1112yes—
149C2×C42C22×D1111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—222no—
152C4⋊C8—222no—
153#101—442no—
154C22⋊C8—22no—
155C4×C8—22no—
156#95—111no—
157#95—112no—
158#95—111no—
159#95—222no—
160#95—221no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11#182411yescharacteristic
164C2×C11#182711yescharacteristic
165C2×C11#183011yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8#431412yes—
169C2×Q8Dic4412yes—
170C22×C4—221no—
171C22×C4—221no—
172C22×C4—222no—
173C22×C4(C2×D11)⋊C412yes—
174C22×C4(C2×D11)⋊C412yes—
175C22×C4C2×C4×D1111yescharacteristic
176C22×C4C2×D4411yescharacteristic
177C22×C4C2×C22⋊D1111yescharacteristic
178M16—442no—
179M16—442no—
180C2×C8—42no—
181C2×C8—442no—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—444no—
185C4⋊C4—442no—
186C4⋊C4—444no—
187C4⋊C4—442no—
188C42—22no—
189C42—22no—
190C42—444no—
191C42—442no—
192C42#434112yes—
193C42#434112yes—
194C11#876711yescharacteristic, complemented, Sylow
195C23C2×(C2×D11)⋊C411yescharacteristic
196Q8—24no—
197Q8—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—222no—
205C2×C4—441no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4—442no—
209C2×C4—441no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4—441no—
213C2×C4#6688014yes—
214C2×C4#6693011yescharacteristic
215C2×C4#6693011yescharacteristic
216C2×C4#6693912yes—
217C2×C4C2×#431411yescharacteristic
218C2×C4C2×Dic4411yescharacteristic
219C2×C4#6696112yes—
220C2×C4#6698812yes—
221C8—82no—
222C8—882no—
223C22—21no—
224C22—21no—
225C22#1062255611yescharacteristic
226C22C2×#6688011yescharacteristic
227C22#1062274411yescharacteristic
228C4—24no—
229C4—22no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—442no—
234C4—882no—
235C4—881no—
236C4#1062233512yes—
237C4#1062234812yes—
238C2—21no—
239C2—21no—
240C2#1306870711yescharacteristic
241C2#1306871711yescharacteristic
242C2#1306872811yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#381
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1461D11
hypocenterC11#8767
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
194. C11#8767semidirect

Maximal subgroups

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

subgroupindex
#130715372
#130686122
#130665182
#130664752
C11×#14612
#876711