Finite Group Databasebeta

← #14642008

Subgroups — #14642008

Order 2816.

658 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 139 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#13068378C212yesmaximal
2#13066442C214yesmaximal, complemented
3C2×C11×#391C211yesmaximal, characteristic
4C23×Q8×C11C411yescharacteristic
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C42×C11C2211yescharacteristic
7C11×#391—22no—
8C11×#391C412yes—
9C11×#391C2212yes—
10C2×C11×#95—22no—
11C2×C22⋊(C11⋊C8)—22no—
12C2×#66867—22no—
13#10622162C2214yes—
14C22×Q8×C11—24no—
15C22×Q8×C11—21no—
16C22×Q8×C11—42no—
17C22×Q8×C11—42no—
18C22×Q8×C11C2×C412yes—
19C23×C4×C11—21no—
20C23×C4×C11—21no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D412yes—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—42no—
25C2×C11×C4⋊C4C2×C412yes—
26C2×C42×C11—42no—
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30C22×C11⋊C8—24no—
31C11×#95—24no—
32C11×#95—24no—
33C22⋊(C11⋊C8)—28no—
34#66867—44no—
35#7629—111nomaximal, Sylow
36C24×C11C22⋊C411yescharacteristic
37C2×Q8×C11—24no—
38C2×Q8×C11—22no—
39C2×Q8×C11—416no—
40C2×Q8×C11—42no—
41C2×Q8×C11—42no—
42C2×Q8×C11—42no—
43C2×Q8×C11—42no—
44C2×Q8×C11M1614yes—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—24no—
49C22×C4×C11—24no—
50C22×C4×C11—22no—
51C22×C4×C11—24no—
52C22×C4×C11—22no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11—44no—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D412yes—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C42×C11—24no—
65C42×C11—41no—
66C42×C11—41no—
67C2×C11⋊C8—28no—
68C2×C11⋊C8—44no—
69C2×C11⋊C8—44no—
70C2×#391D1111yescharacteristic
71#1749—112no—
72#1272—114no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11#10012yes—
77C23×C11#10414yes—
78C23×C11C2×C22⋊C411yescharacteristic
79Q8×C11—44no—
80Q8×C11—48no—
81Q8×C11—44no—
82C2×C4×C11—28no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—24no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—48no—
94C2×C4×C11—48no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—44no—
99C2×C4×C11—84no—
100C2×C4×C11#9912yes—
101C2×C4×C11C2×M1612yes—
102C2×C4×C11#13714yes—
103C11⋊C8—48no—
104C23×Q8Dic1111yescharacteristic
105C22×C4⋊C4Dic1111yescharacteristic
106C22×C42C2×D1111yescharacteristic
107C2×C22⋊C8—222no—
108C2×#97—222no—
109#391—22no—
110#391Dic1112yes—
111#391C2×D1112yes—
112C2×#95—22no—
113#336—114no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—24no—
117C22×C11—24no—
118C22×C11#32914yes—
119C22×C11#40711yescharacteristic
120C22×C11C2×#9911yescharacteristic
121C22×C11C2×#10011yescharacteristic
122C22×C11#41912yes—
123C22×C11C2×#10412yes—
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—24no—
127C4×C11—44no—
128C4×C11—42no—
129C4×C11—82no—
130C22×Q8—24no—
131C22×Q8—21no—
132C22×Q8—42no—
133C22×Q8—42no—
134C22×Q8C2×Dic1112yes—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4C2×Dic1111yescharacteristic
138C23×C4C22⋊D1112yes—
139C22×C8—224no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4C2×Dic1112yes—
143C2×C42—42no—
144C2×C42C2×Dic1111yescharacteristic
145C2×C42C22⋊D1112yes—
146C2×C42C22×D1111yescharacteristic
147C22⋊C8—228no—
148#97—444no—
149#95—24no—
150#95—24no—
151C2×C11—24no—
152C2×C11#146211yescharacteristic
153C2×C11#149112yes—
154C2×C11#150812yes—
155C2×C11C2×#32911yescharacteristic
156C2×C11#155811yescharacteristic
157C24C22⋊Dic1111yescharacteristic
158C2×Q8—24no—
159C2×Q8—22no—
160C2×Q8—416no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8#431814yes—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—22no—
172C22×C4—24no—
173C22×C4—22no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—44no—
179C22×C4C22⋊Dic1112yes—
180C22×C4C22⋊Dic1111yescharacteristic
181C22×C4C22×Dic1111yescharacteristic
182C22×C4C2×C22⋊D1112yes—
183C2×C8—228no—
184C2×C8—444no—
185C2×C8—444no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C42—24no—
189C42—41no—
190C42—41no—
191C11#762911yescharacteristic, complemented, Sylow
192C23—21no—
193C23—21no—
194C23—22no—
195C23#6689712yes—
196C23#6690114yes—
197C23C2×C22⋊Dic1111yescharacteristic
198Q8—44no—
199Q8—48no—
200Q8—44no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—48no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—84no—
219C2×C4#6689812yes—
220C2×C4C2×#431812yes—
221C2×C4#6699514yes—
222C8—448no—
223C22—24no—
224C22—22no—
225C22—24no—
226C22—22no—
227C22#1062217814yes—
228C22#1062282011yescharacteristic
229C22C2×#6689711yescharacteristic
230C22C2×#6689811yescharacteristic
231C22#1062283812yes—
232C22C2×#6690112yes—
233C4—24no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—44no—
238C4—82no—
239C2—24no—
240C2#1306694311yescharacteristic
241C2#1306706312yes—
242C2#1306713612yes—
243C2C2×#1062217811yescharacteristic
244C2#1306734211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#391C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#391D11
hypocenterC11#7629
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #13066442C2semidirect
191. C11#7629semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130664422
C2×C11×#3912
#762911