Finite Group Databasebeta

← #14645257

Subgroups — #14645257

Order 2816.

1718 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1718 conjugacy classes of subgroups — too many to draw. Only its 227 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#13068596C212yesmaximal, complemented
2C2×#10622182C214yesmaximal, complemented
3C22×C11×#127C211yesmaximal, characteristic
4C23×D4×C11—22no—
5C23×D4×C11C412yes—
6C2×C11×#127—28no—
7C2×C11×#127—22no—
8C2×C11×#127C412yes—
9C2×C11×#127C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×C22⋊(C11⋊C8)—22no—
12C2×C4⋊(C11⋊C8)C2214yescomplemented
13#10622182—28no—
14#10622162—22no—
15C25×C11—22no—
16C22×D4×C11—216no—
17C22×D4×C11—28no—
18C22×D4×C11—22no—
19C22×D4×C11—24no—
20C22×D4×C11—24no—
21C22×D4×C11—44no—
22C22×D4×C11—48no—
23C22×D4×C11—44no—
24C22×D4×C11—44no—
25C22×D4×C11—44no—
26C22×D4×C11C2×C414yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D412yes—
29C11×#127—216no—
30C11×#127—28no—
31C11×#127—24no—
32C11×#127D418yes—
33C2×C42×C11—24no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C22×C11⋊C8—24no—
38C22⋊(C11⋊C8)—44no—
39C4⋊(C11⋊C8)—28no—
40#8339—111nomaximal, Sylow
41C24×C11—28no—
42C24×C11—24no—
43C24×C11—44no—
44C24×C11—48no—
45C24×C11—44no—
46C24×C11—48no—
47C24×C11C22⋊C411yescharacteristic
48C2×D4×C11—28no—
49C2×D4×C11—216no—
50C2×D4×C11—24no—
51C2×D4×C11—216no—
52C2×D4×C11—432no—
53C2×D4×C11—44no—
54C2×D4×C11—48no—
55C2×D4×C11—432no—
56C2×D4×C11—432no—
57C2×D4×C11—44no—
58C2×D4×C11—44no—
59C2×D4×C11—44no—
60C2×D4×C11—48no—
61C2×D4×C11—44no—
62C2×D4×C11—44no—
63C2×D4×C11—48no—
64C2×D4×C11C22⋊C418yes—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11D814yes—
73C22×C4×C11SD1614yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D412yes—
76C42×C11—22no—
77C42×C11—24no—
78C42×C11C2×D414yes—
79C2×C11⋊C8—44no—
80C2×C11⋊C8—44no—
81C2×C11⋊C8—44no—
82C22×#127D1111yescharacteristic
83#1797—112no—
84C2×#331—114no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—22no—
88C23×C11—28no—
89C23×C11—416no—
90C23×C11—432no—
91C23×C11—44no—
92C23×C11—44no—
93C23×C11—48no—
94C23×C11—48no—
95C23×C11—816no—
96C23×C11—88no—
97C23×C11—88no—
98C23×C11#10012yes—
99C23×C11#10214yes—
100C23×C11C2×C22⋊C411yescharacteristic
101D4×C11—48no—
102D4×C11—416no—
103D4×C11—48no—
104D4×C11—432no—
105D4×C11—416no—
106D4×C11—416no—
107C2×C4×C11—28no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—28no—
115C2×C4×C11—28no—
116C2×C4×C11#10012yes—
117C2×C4×C11#10214yes—
118C2×C4×C11C2×C22⋊C412yes—
119C2×C4×C11#12014yes—
120C2×C4×C11C2×D812yes—
121C2×C4×C11C2×SD1612yes—
122C2×C4×C11AGL(1,ℤ/8)14yes—
123C11⋊C8—84no—
124C23×D4—22no—
125C23×D4Dic1112yes—
126C2×#127—28no—
127C2×#127—22no—
128C2×#127Dic1112yes—
129C2×#127C2×D1112yes—
130C22×C42C2×D1111yescharacteristic
131C2×C4⋊C8—114no—
132C2×C22⋊C8—222no—
133#336—222no—
134#331—228no—
135C22×C11—24no—
136C22×C11—22no—
137C22×C11—22no—
138C22×C11—24no—
139C22×C11—48no—
140C22×C11—416no—
141C22×C11—832no—
142C22×C11—84no—
143C22×C11—88no—
144C22×C11—84no—
145C22×C11#33114yescomplemented
146C22×C11#37911yescharacteristic
147C22×C11C2×#10011yescharacteristic
148C22×C11C2×#10011yescharacteristic
149C22×C11C2×#10212yes—
150C22×C11#41812yes—
151C4×C11—22no—
152C4×C11—22no—
153C4×C11—24no—
154C4×C11#44714yes—
155C4×C11#45014yes—
156C25—22no—
157C22×D4—216no—
158C22×D4—28no—
159C22×D4—22no—
160C22×D4—24no—
161C22×D4—24no—
162C22×D4—44no—
163C22×D4—48no—
164C22×D4—44no—
165C22×D4—44no—
166C22×D4—44no—
167C22×D4C2×Dic1114yes—
168C23×C4C2×Dic1111yescharacteristic
169C23×C4C22⋊D1112yes—
170C22×C8—224no—
171#127—216no—
172#127—28no—
173#127—24no—
174#127C22⋊D1118yes—
175C2×C42—24no—
176C2×C42C2×Dic1111yescharacteristic
177C2×C42C22⋊D1112yes—
178C2×C42C22×D1111yescharacteristic
179C4⋊C8—228no—
180C22⋊C8—444no—
181C2×C11—24no—
182C2×C11—88no—
183C2×C11C2×#33111yescharacteristic
184C2×C11#154512yes—
185C2×C11#155511yescharacteristic
186C2×C11#178311yescharacteristic
187C2×C11#178612yes—
188C24—28no—
189C24—24no—
190C24—48no—
191C24—44no—
192C24—48no—
193C24—44no—
194C24C22⋊Dic1111yescharacteristic
195C2×D4—28no—
196C2×D4—216no—
197C2×D4—24no—
198C2×D4—216no—
199C2×D4—44no—
200C2×D4—44no—
201C2×D4—432no—
202C2×D4—48no—
203C2×D4—44no—
204C2×D4—432no—
205C2×D4—432no—
206C2×D4—48no—
207C2×D4—44no—
208C2×D4—44no—
209C2×D4—48no—
210C2×D4—44no—
211C2×D4C22⋊Dic1118yes—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4#432314yes—
218C22×C4#432414yes—
219C22×C4C22⋊Dic1112yes—
220C22×C4C22⋊Dic1111yescharacteristic
221C22×C4C22×Dic1111yescharacteristic
222C22×C4C2×C22⋊D1112yes—
223C2×C8—444no—
224C2×C8—444no—
225C2×C8—444no—
226C42—22no—
227C42—24no—
228C42C2×C22⋊D1114yes—
229C11#833911yescharacteristic, complemented, Sylow
230C23—22no—
231C23—21no—
232C23—21no—
233C23—28no—
234C23—432no—
235C23—416no—
236C23—48no—
237C23—48no—
238C23—44no—
239C23—44no—
240C23—816no—
241C23—88no—
242C23—88no—
243C23#6689614yes—
244C23#6689712yes—
245C23C2×C22⋊Dic1111yescharacteristic
246D4—48no—
247D4—432no—
248D4—416no—
249D4—48no—
250D4—416no—
251D4—416no—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—28no—
260C2×C4—28no—
261C2×C4#6689614yes—
262C2×C4#6689712yes—
263C2×C4C2×#432312yes—
264C2×C4#6698514yes—
265C2×C4C2×#432412yes—
266C2×C4C2×C22⋊Dic1112yes—
267C2×C4#6700614yes—
268C8—884no—
269C22—24no—
270C22—24no—
271C22—22no—
272C22—22no—
273C22—416no—
274C22—48no—
275C22—832no—
276C22—88no—
277C22—84no—
278C22—84no—
279C22#1062218214yescomplemented
280C22C2×#6689612yes—
281C22#1062282812yes—
282C22C2×#6689711yescharacteristic
283C22C2×#6689711yescharacteristic
284C22#1062286011yescharacteristic
285C4—24no—
286C4—22no—
287C4—22no—
288C4#1062283014yes—
289C4#1062283114yes—
290C2—24no—
291C2—88no—
292C2C2×#1062218211yescharacteristic
293C2#1306728412yes—
294C2#1306733011yescharacteristic
295C2#1306853711yescharacteristic
296C2#1306854712yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC22×C11×#127C2
socleC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC22×#127D11
hypocenterC11#8339
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C2×#10622182C2semidirect
12. C2×C4⋊(C11⋊C8)C22semidirect
145. C22×C11#331semidirect
229. C11#8339semidirect
279. C22#10622182semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221822
C22×C11×#1272
#833911