Finite Group Databasebeta

← #14641996

Subgroups — #14641996

Order 2816.

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

normal subgroups only

This group has 874 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, complemented
2#13066437C214yesmaximal, complemented
3C2×C11×#390C211yesmaximal, characteristic
4C23×D4×C11C411yescharacteristic
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C11×C22⋊C4—22no—
7C22×C42×C11C2211yescharacteristic
8C11×#390—22no—
9C11×#390C412yes—
10C11×#390C2212yes—
11C2×C22⋊(C11⋊C8)—22no—
12C2×#66867—22no—
13#10622162C2214yescomplemented
14C25×C11—21no—
15C22×D4×C11—24no—
16C22×D4×C11—21no—
17C22×D4×C11—42no—
18C22×D4×C11—42no—
19C22×D4×C11C2×C412yes—
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×C11×C22⋊C4—24no—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—48no—
29C2×C42×C11—42no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D412yes—
32C2×C42×C11C2311yescharacteristic
33C22×C11⋊C8—24no—
34C22⋊(C11⋊C8)—28no—
35#66867—44no—
36#7626—111nomaximal, Sylow
37C24×C11—24no—
38C24×C11—22no—
39C24×C11—44no—
40C24×C11—42no—
41C24×C11—42no—
42C24×C11—44no—
43C24×C11C22⋊C411yescharacteristic
44C2×D4×C11—24no—
45C2×D4×C11—22no—
46C2×D4×C11—416no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11M1614yes—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—22no—
58C22×C4×C11—42no—
59C22×C4×C11—44no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D412yes—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C22⋊C4—48no—
68C11×C22⋊C4—48no—
69C42×C11—24no—
70C42×C11—41no—
71C42×C11—41no—
72C2×C11⋊C8—28no—
73C2×C11⋊C8—44no—
74C2×C11⋊C8—44no—
75C2×#390D1111yescharacteristic
76#1749—112no—
77#1270—114no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—24no—
82C23×C11—48no—
83C23×C11—416no—
84C23×C11—42no—
85C23×C11—42no—
86C23×C11—44no—
87C23×C11—44no—
88C23×C11—84no—
89C23×C11—88no—
90C23×C11—84no—
91C23×C11#10012yes—
92C23×C11#10414yes—
93C23×C11C2×C22⋊C411yescharacteristic
94D4×C11—44no—
95D4×C11—48no—
96D4×C11—44no—
97C2×C4×C11—28no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—48no—
108C2×C4×C11—42no—
109C2×C4×C11—44no—
110C2×C4×C11—84no—
111C2×C4×C11#9912yes—
112C2×C4×C11C2×M1612yes—
113C2×C4×C11AGL(1,ℤ/8)14yes—
114C11⋊C8—48no—
115C23×D4Dic1111yescharacteristic
116C22×C4⋊C4Dic1111yescharacteristic
117C22×C22⋊C4—22no—
118C22×C42C2×D1111yescharacteristic
119C2×C22⋊C8—222no—
120C2×#97—222no—
121#390—22no—
122#390Dic1112yes—
123#390C2×D1112yes—
124#336—114no—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—24no—
128C22×C11—24no—
129C22×C11—44no—
130C22×C11—48no—
131C22×C11—816no—
132C22×C11—82no—
133C22×C11—84no—
134C22×C11—82no—
135C22×C11#32914yes—
136C22×C11#40711yescharacteristic
137C22×C11C2×#9911yescharacteristic
138C22×C11C2×#10011yescharacteristic
139C22×C11#41812yes—
140C22×C11C2×#10412yes—
141C4×C11—22no—
142C4×C11—22no—
143C4×C11—24no—
144C4×C11—42no—
145C4×C11—82no—
146C25—21no—
147C22×D4—24no—
148C22×D4—21no—
149C22×D4—42no—
150C22×D4—42no—
151C22×D4C2×Dic1112yes—
152C23×C4—21no—
153C23×C4C2×Dic1111yescharacteristic
154C23×C4C22⋊D1112yes—
155C22×C8—224no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4C2×Dic1112yes—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4—48no—
162C2×C42—42no—
163C2×C42C2×Dic1111yescharacteristic
164C2×C42C22⋊D1112yes—
165C2×C42C22×D1111yescharacteristic
166C22⋊C8—228no—
167#97—444no—
168C2×C11—24no—
169C2×C11—84no—
170C2×C11#146211yescharacteristic
171C2×C11#149012yes—
172C2×C11#150712yes—
173C2×C11C2×#32911yescharacteristic
174C2×C11#155511yescharacteristic
175C24—24no—
176C24—22no—
177C24—44no—
178C24—42no—
179C24—42no—
180C24—44no—
181C24C22⋊Dic1111yescharacteristic
182C2×D4—24no—
183C2×D4—22no—
184C2×D4—42no—
185C2×D4—42no—
186C2×D4—416no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4#431814yes—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—44no—
198C22×C4—42no—
199C22×C4C22⋊Dic1112yes—
200C22×C4C22⋊Dic1111yescharacteristic
201C22×C4C22×Dic1111yescharacteristic
202C22×C4C2×C22⋊D1112yes—
203C2×C8—228no—
204C2×C8—444no—
205C2×C8—444no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C22⋊C4—48no—
209C22⋊C4—48no—
210C42—24no—
211C42—41no—
212C42—41no—
213C11#762611yescharacteristic, complemented, Sylow
214C23—21no—
215C23—22no—
216C23—21no—
217C23—24no—
218C23—48no—
219C23—416no—
220C23—44no—
221C23—42no—
222C23—42no—
223C23—44no—
224C23—84no—
225C23—88no—
226C23—84no—
227C23#6689712yes—
228C23#6690114yes—
229C23C2×C22⋊Dic1111yescharacteristic
230D4—44no—
231D4—48no—
232D4—44no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—48no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4#6689812yes—
248C2×C4C2×#431812yes—
249C2×C4#6698514yes—
250C8—448no—
251C22—24no—
252C22—22no—
253C22—24no—
254C22—22no—
255C22—48no—
256C22—44no—
257C22—816no—
258C22—82no—
259C22—84no—
260C22—82no—
261C22#1062217814yes—
262C22#1062282011yescharacteristic
263C22#1062282812yes—
264C22C2×#6689711yescharacteristic
265C22C2×#6689811yescharacteristic
266C22C2×#6690112yes—
267C4—24no—
268C4—22no—
269C4—22no—
270C4—42no—
271C4—82no—
272C2—24no—
273C2—84no—
274C2#1306694311yescharacteristic
275C2#1306705912yes—
276C2#1306713212yes—
277C2C2×#1062217811yescharacteristic
278C2#1306733011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#390C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC2×C42×C11C23
hypercenterC2×#390D11
hypocenterC11#7626
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #13068378C2semidirect
2. #13066437C2semidirect
13. #10622162C22semidirect
213. C11#7626semidirect

Maximal subgroups

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

subgroupindex
#130683782
#130664372
C2×C11×#3902
#762611