Finite Group Databasebeta

← #14656127

Subgroups — #14656127

Order 2816.

560 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10622634C212yesmaximal
2#13069417C211yesmaximal, characteristic
3C2×Q8⋊(C11⋊C8)C212yesmaximal
4#13066499C211yesmaximal, characteristic
5C11×#2582C211yesmaximal, characteristic
6C2×C4×Q8×C11C2212yes—
7C2×#66922C2211yescharacteristic
8C11×#398—22no—
9C11×#391—22no—
10C11×#389—22no—
11C11×#384C2211yescharacteristic
12C2×#66899—22no—
13#10622634—24no—
14#10622634—24no—
15C2×#66874—22no—
16C2×#66871—22no—
17C2×C4⋊(C11⋊C8)C2212yes—
18C2×C4×C11⋊C8C2211yescharacteristic
19Q8⋊(C11⋊C8)—24no—
20C22×Q8×C11D412yes—
21C22×Dic22—21no—
22C4×Q8×C11—22no—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C42×C11—22no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C22×C11⋊C8—21no—
35C22×C11⋊C8—22no—
36#66922—22no—
37#66922—21no—
38#66922D412yes—
39C11×#95—24no—
40C11×#95—22no—
41#66899—28no—
42#66874—44no—
43#66871—28no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46C4×C11⋊C8—22no—
47#10237—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11Q1614yes—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D412yes—
59C22×Dic11—41no—
60C2×Dic22—22no—
61C2×Dic22—42no—
62C2×Dic22—42no—
63C2×Dic22—41no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—82no—
72C42×C11—42no—
73C42×C11—42no—
74C42×C11C2×D411yescharacteristic
75C42×C11C2×D412yes—
76C42×C11#4111yescharacteristic
77C4⋊Dic11—24no—
78C4⋊Dic11—42no—
79C2×C11⋊C8—22no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85C2×#477—112no—
86#2582D1111yescharacteristic
87#1956—111no—
88C2×Q8⋊C8—112no—
89#1296—111no—
90C23×C11#12011yescharacteristic
91Q8×C11—24no—
92Q8×C11—24no—
93Q8×C11—42no—
94Q8×C11—42no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—24no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—44no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11#12012yes—
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11#12112yes—
108C2×C4×C11#12711yescharacteristic
109C2×C4×C11C2×Q1612yes—
110C2×C4×C11#13512yes—
111C2×C4×C11#13712yes—
112C2×C4×C11#13712yes—
113C2×Dic11—42no—
114C2×Dic11—81no—
115C2×Dic11—81no—
116Dic22—44no—
117Dic22—82no—
118C11⋊C8—42no—
119C11⋊C8—44no—
120C2×C4⋊Q8—111no—
121C2×C4×Q8C2×D1112yes—
122#477—224no—
123#477—224no—
124C2×#107—222no—
125C2×C4⋊C8—112no—
126C2×#103—222no—
127C2×#103—222no—
128C2×C4×C8—111no—
129#398—22no—
130#391—22no—
131#389—22no—
132#384C2×D1111yescharacteristic
133Q8⋊C8—224no—
134C22×C11#39211yescharacteristic
135C22×C11#45112yes—
136C22×C11#45212yes—
137C22×C11#45311yescharacteristic
138C22×C11#45411yescharacteristic
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—44no—
142C4×C11—82no—
143C4×C11—82no—
144C4×C11#45112yes—
145C4×C11#45212yes—
146C4×C11#46712yes—
147C4×C11#47012yes—
148Dic11—82no—
149C22×Q8—221no—
150C22×Q8C22⋊D1112yes—
151C22×C8—221no—
152C22×C8—222no—
153C4⋊Q8—112no—
154C4⋊Q8—222no—
155C4⋊Q8—221no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4C22⋊D1112yes—
165C2×C4⋊C4C22⋊D1112yes—
166C2×C42—22no—
167C2×C42C22×D1111yescharacteristic
168#107—228no—
169C4⋊C8—114no—
170C4⋊C8—222no—
171#103—228no—
172#103—444no—
173C4×C8—222no—
174#95—24no—
175#95—22no—
176C2×C11#163011yescharacteristic
177C2×C11#163311yescharacteristic
178C2×C11#163612yes—
179C2×C11#200112yes—
180C2×C11#200611yescharacteristic
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—222no—
187C2×Q8—442no—
188C2×Q8—442no—
189C2×Q8—441no—
190C2×Q8#432614yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—441no—
195C22×C4C2×C22⋊D1111yescharacteristic
196C22×C4C2×C22⋊D1112yes—
197C2×C8—222no—
198C2×C8—224no—
199C2×C8—441no—
200C2×C8—441no—
201C2×C8—442no—
202C2×C8—442no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—82no—
211C4⋊C4—224no—
212C4⋊C4—442no—
213C42—42no—
214C42—42no—
215C42D4×D1111yescharacteristic
216C42D4×D1112yes—
217C42#434111yescharacteristic
218C11#1023711yescharacteristic, complemented, Sylow
219C23#6700611yescharacteristic
220Q8—24no—
221Q8—24no—
222Q8—42no—
223Q8—42no—
224Q8—444no—
225Q8—882no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—442no—
237C2×C4—881no—
238C2×C4—881no—
239C2×C4#6699012yes—
240C2×C4#6699111yescharacteristic
241C2×C4#6699212yes—
242C2×C4#6699311yescharacteristic
243C2×C4#6699512yes—
244C2×C4C2×#432612yes—
245C2×C4#6700312yes—
246C2×C4#6700412yes—
247C8—442no—
248C8—444no—
249C22#1062283611yescharacteristic
250C22#1062284112yes—
251C22#1062285212yes—
252C22#1062285411yescharacteristic
253C22#1062285811yescharacteristic
254C4—21no—
255C4—21no—
256C4—44no—
257C4—82no—
258C4—82no—
259C4—882no—
260C4#1062266012yes—
261C4#1062266312yes—
262C4#1062266412yes—
263C4#1062266512yes—
264C2#1306773711yescharacteristic
265C2#1306775611yescharacteristic
266C2#1306777412yes—
267C2#1306962412yes—
268C2#1306965811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2582C2
socle, prime radicalC23×C11#120
hypercenter#2582D11
hypocenterC11#10237
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
218. C11#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#106226342
#130694172
C2×Q8⋊(C11⋊C8)2
#130664992
C11×#25822
#1023711