Finite Group Databasebeta

← #14656308

Subgroups — #14656308

Order 2816.

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

normal subgroups only

This group has 574 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
1C2×#10622295C211yesmaximal, characteristic
2C2×#10622644C212yesmaximal
3C2×#10622124C212yesmaximal
4#13066451C211yesmaximal, characteristic
5C11×#1984C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C22×#4326—22no—
8C2×#66922C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66882—22no—
12#10622644—24no—
13#10622644—24no—
14C2×#66874—22no—
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622295—24no—
17C11×#336—22no—
18#10622124—24no—
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—22no—
21C22×C8×C11—21no—
22C22×C8×C11D412yes—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×#4326—28no—
30C2×#4326—44no—
31C2×#4326—44no—
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—22no—
34C22×C11⋊C8—22no—
35#66922—22no—
36#66922—22no—
37#66922—22no—
38#66922D414yes—
39C11×C4⋊C8—22no—
40C4×C8×C11—22no—
41#66882—28no—
42#66874—28no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45#10265—111nomaximal, Sylow
46C2×Q8×C11—21no—
47C2×Q8×C11—22no—
48C2×Q8×C11—22no—
49C2×Q8×C11D812yes—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—42no—
56C2×Dic22—24no—
57C2×Dic22—42no—
58C2×Dic22—42no—
59C2×Dic22—42no—
60C2×Dic22—42no—
61C2×Dic22—42no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—42no—
66C2×C8×C11Q1614yescomplemented
67C11×C4⋊C4—22no—
68C11×C4⋊C4—42no—
69C42×C11—41no—
70C42×C11—41no—
71C42×C11C2×D412yes—
72C42×C11C2×D412yes—
73#4326—416no—
74C4⋊Dic11—24no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81C2×#500—111no—
82C2×#462—112no—
83#1984D1111yescharacteristic
84C2×#332—112no—
85#1277—111no—
86C23×C11#12111yescharacteristic
87Q8×C11—24no—
88Q8×C11—42no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11#12012yes—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11#12112yes—
98C2×C4×C11#12711yescharacteristic
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11C2×Q1612yes—
101C2×C4×C11#13511yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)12yes—
103C2×C4×C11#13712yes—
104C2×Dic11—44no—
105C2×Dic11—82no—
106C2×Dic11—82no—
107Dic22—44no—
108Dic22—44no—
109Dic22—82no—
110Dic22—82no—
111C8×C11—24no—
112C8×C11—81no—
113C11⋊C8—44no—
114C22×Q16—222no—
115C2×C4⋊Q8—112no—
116C2×C4×Q8C2×D1111yescharacteristic
117#500—224no—
118#462—224no—
119#462—224no—
120C2×#107—222no—
121C2×C4⋊C8—112no—
122C2×C4⋊C8C2×D1111yescharacteristic
123C2×#103—222no—
124C2×C4×C8C2×D1111yescharacteristic
125#336—22no—
126#332—224no—
127C22×C11#39211yescharacteristic
128C22×C11#46212yes—
129C22×C11#46611yescharacteristic
130C22×C11#46911yescharacteristic
131C22×C11#47312yes—
132C4×C11—22no—
133C4×C11—42no—
134C4×C11—81no—
135C4×C11#44712yes—
136C4×C11#44912yes—
137C4×C11#45112yes—
138C4×C11#49411yescharacteristic
139C4×C11#49711yescharacteristic
140Dic11—84no—
141C22×Q8—222no—
142C22×Q8D4411yescharacteristic
143C2×Q16—228no—
144C2×Q16—444no—
145C2×Q16—444no—
146C22×C8—21no—
147C22×C8—222no—
148C22×C8C22⋊D1112yes—
149C4⋊Q8—114no—
150C4⋊Q8—222no—
151C4⋊Q8—222no—
152C4⋊Q8—222no—
153C4×Q8—22no—
154C4×Q8—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4D4411yescharacteristic
159C2×C42—21no—
160C2×C42C22×D1111yescharacteristic
161#107—228no—
162C4⋊C8—22no—
163C4⋊C8—114no—
164C4⋊C8—222no—
165#103—228no—
166C4×C8—22no—
167C2×C11#167412yes—
168C2×C11#169412yes—
169C2×C11#199911yescharacteristic
170C2×C11#201611yescharacteristic
171C2×C11#202011yescharacteristic
172C2×Q8—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—224no—
176C2×Q8—442no—
177C2×Q8—442no—
178C2×Q8—442no—
179C2×Q8—442no—
180C2×Q8—442no—
181C2×Q8D8812yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—442no—
185C22×C4C2×D4411yescharacteristic
186C22×C4#433911yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188Q16—4416no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—224no—
194C2×C8—442no—
195C2×C8—442no—
196C2×C8#432614yescomplemented
197C4⋊C4—22no—
198C4⋊C4—42no—
199C4⋊C4—224no—
200C4⋊C4—224no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C42—41no—
204C42—41no—
205C42D4×D1112yes—
206C42D4×D1112yes—
207C11#1026511yescharacteristic, complemented, Sylow
208C23#6698311yescharacteristic
209Q8—24no—
210Q8—42no—
211Q8—444no—
212Q8—444no—
213Q8—882no—
214Q8—882no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—444no—
222C2×C4—882no—
223C2×C4—882no—
224C2×C4#6693512yes—
225C2×C4#6693712yes—
226C2×C4C2×D8811yescharacteristic
227C2×C4#6695711yescharacteristic
228C2×C4#6696112yes—
229C2×C4#6699011yescharacteristic
230C2×C4#6699311yescharacteristic
231C2×C4C2×#432612yes—
232C2×C4#6700412yes—
233C8—24no—
234C8—81no—
235C8—444no—
236C22#1062257311yescharacteristic
237C22#1062264412yes—
238C22#1062272811yescharacteristic
239C22#1062274811yescharacteristic
240C22#1062275612yes—
241C4—22no—
242C4—42no—
243C4—81no—
244C4—884no—
245C4#1062234512yes—
246C4#1062234712yes—
247C4#1062266312yes—
248C4#1062267311yescharacteristic
249C4#1062270511yescharacteristic
250C2#1306801012yes—
251C2#1306813412yes—
252C2#1306961411yescharacteristic
253C2#1306971511yescharacteristic
254C2#1306973711yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socle, prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10265
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
66. C2×C8×C11Q16semidirect
196. C2×C8#4326semidirect
207. C11#10265semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106226442
C2×#106221242
#130664512
C11×#19842
#1026511