Finite Group Databasebeta

← #14657286

Subgroups — #14657286

Order 2816.

630 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 133 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#13068772C211yesmaximal, characteristic, complemented
2#13068616C212yesmaximal, complemented
3C2×D4⋊(C11⋊C8)C212yesmaximal, complemented
4#13066499C211yesmaximal, characteristic, complemented
5C11×#2537C211yesmaximal, characteristic
6C2×C11×#121—22no—
7C2×C4×D4×C11C2212yes—
8C11×#394—22no—
9C11×#384C2211yescharacteristic
10C11×#380—22no—
11C2×#66896—22no—
12C2×#66872—22no—
13#10622548C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16D4⋊(C11⋊C8)—24no—
17#10622167—22no—
18C22×D4×C11—22no—
19C22×D4×C11D412yes—
20C23×C4×C11—22no—
21C11×#121—44no—
22C11×#121—44no—
23C4×D4×C11—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C4×D4×C11—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—24no—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C22×C11⋊C8—21no—
36C22×C11⋊C8—22no—
37C11×#95—22no—
38#66896—44no—
39#66872—44no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4×C11⋊C8—21no—
43C4×C11⋊C8D412yescomplemented
44#10432—111nomaximal, Sylow
45C24×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11—48no—
52C2×D4×C11—82no—
53C2×D4×C11SD1614yes—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—41no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C22⋊C4—48no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—42no—
73C42×C11C2×D411yescharacteristic
74C42×C11#4111yescharacteristic
75C42×C11#4112yes—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C2×C11⋊C8—22no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85#2537D1111yescharacteristic
86#1844—111no—
87#1802—112no—
88C2×D4⋊C8—112no—
89#1296—111no—
90C23×C11—24no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11#12011yescharacteristic
98D4×C11—24no—
99D4×C11—24no—
100D4×C11—42no—
101D4×C11—42no—
102D4×C11—88no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—44no—
109C2×C4×C11—42no—
110C2×C4×C11—82no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×C4×C11#12111yescharacteristic
115C2×C4×C11#12112yes—
116C2×C4×C11#12312yes—
117C2×C4×C11#12411yescharacteristic
118C2×C4×C11C2×SD1612yes—
119C2×C4×C11#13512yes—
120C2×C4×C11AGL(1,ℤ/8)12yes—
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×Dic11—82no—
123C2×Dic11—81no—
124C11⋊C8—24no—
125C11⋊C8—82no—
126C2×#121—22no—
127C2×C4×D4C2×D1112yes—
128C2×#106—222no—
129C2×C4⋊C8—112no—
130C2×#102—222no—
131C2×C4×C8—111no—
132#394—22no—
133#384—111no—
134#384C2×D1111yescharacteristic
135#380—22no—
136#340—222no—
137D4⋊C8—224no—
138C22×C11—44no—
139C22×C11—44no—
140C22×C11—44no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11—82no—
144C22×C11—82no—
145C22×C11#39411yescharacteristic
146C22×C11#44912yes—
147C22×C11#45012yes—
148C22×C11#45311yescharacteristic
149C22×C11#45611yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—82no—
153C4×C11—82no—
154C4×C11#46512yes—
155C4×C11#46912yes—
156C4×C11#48112yes—
157C4×C11#48212yes—
158Dic11—161no—
159C22×D4—22no—
160C22×D4C22⋊D1112yes—
161C23×C4—22no—
162C22×C8—221no—
163C22×C8—222no—
164#121—44no—
165#121—44no—
166C4×D4—22no—
167C4×D4—22no—
168C4×D4—22no—
169C4×D4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4C22⋊D1112yes—
174C2×C4⋊C4C22⋊D1112yes—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—22no—
177C2×C42C22×D1111yescharacteristic
178#106—444no—
179C4⋊C8—222no—
180C4⋊C8—222no—
181#102—444no—
182C4×C8—112no—
183C4×C8—221no—
184#95—22no—
185C2×C11—84no—
186C2×C11#162411yescharacteristic
187C2×C11#162911yescharacteristic
188C2×C11#165412yes—
189C2×C11#203412yes—
190C2×C11#203911yescharacteristic
191C24—22no—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—48no—
198C2×D4—82no—
199C2×D4#432414yes—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—441no—
209C22×C4C2×C22⋊D1111yescharacteristic
210C22×C4C2×C22⋊D1112yes—
211C2×C8—222no—
212C2×C8—222no—
213C2×C8—222no—
214C2×C8—442no—
215C2×C8—442no—
216C2×C8—442no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—442no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C22⋊C4—48no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C42D4×D1111yescharacteristic
229C42#434111yescharacteristic
230C42#434112yes—
231C11#1043211yescharacteristic, complemented, Sylow
232C23—24no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23#6700611yescharacteristic
240D4—24no—
241D4—24no—
242D4—42no—
243D4—42no—
244D4—88no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—882no—
257C2×C4—881no—
258C2×C4#6698512yes—
259C2×C4C2×#432412yes—
260C2×C4#6698812yes—
261C2×C4#6698911yescharacteristic
262C2×C4#6699111yescharacteristic
263C2×C4#6699212yes—
264C2×C4#6700212yes—
265C2×C4#6700312yes—
266C8—224no—
267C8—882no—
268C22—44no—
269C22—44no—
270C22—44no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22#1062283112yes—
276C22#1062283511yescharacteristic
277C22#1062285112yes—
278C22#1062285411yescharacteristic
279C22#1062285911yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—82no—
284C4—1761no—
285C4#1062264712yes—
286C4#1062264812yes—
287C4#1062265212yes—
288C4#1062265412yes—
289C2—84no—
290C2#1306769911yescharacteristic
291C2#1306773211yescharacteristic
292C2#1306790012yes—
293C2#1306980212yes—
294C2#1306983711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11#120
hypercenter#2537D11
hypocenterC11#10432
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13068772C2semidirect
2. #13068616C2semidirect
3. C2×D4⋊(C11⋊C8)C2semidirect
4. #13066499C2semidirect
43. C4×C11⋊C8D4semidirect
231. C11#10432semidirect

Maximal subgroups

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

subgroupindex
#130687722
#130686162
C2×D4⋊(C11⋊C8)2
#130664992
C11×#25372
#1043211