Finite Group Databasebeta

← #14648708

Subgroups — #14648708

Order 2816.

542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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#13071802C211yesmaximal, characteristic, complemented
2#13069441C212yesmaximal
3C2×#10622181C211yesmaximal, characteristic, complemented
4#13066498C212yesmaximal, complemented
5C2×C11×#490C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#125C2211yescharacteristic
8C11×#490—22no—
9C11×#490C414yescomplemented
10C2×C11×#102—22no—
11C2×C11×#97C2211yescharacteristic
12C2×#66896—22no—
13C2×#66896—22no—
14#10622598—22no—
15#10622594—22no—
16#10622594—22no—
17#10622549C2212yes—
18C2×#66867C2212yes—
19#10622181—22no—
20C22×D4×C11—22no—
21C22×D4×C11—21no—
22C22×C8×C11—21no—
23C11×#127—21no—
24C11×#127—22no—
25C11×#127C2×C412yes—
26C11×#125—22no—
27C11×#125C2×C412yes—
28C11×#125D412yes—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D412yes—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11D412yes—
34C2×C4⋊Dic11D412yes—
35C2×C4×Dic11—22no—
36C22×C11⋊C8—22no—
37C11×#102—28no—
38C11×#97—21no—
39C11×#97C2×C412yes—
40#66896—44no—
41#66896—44no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46#66867—22no—
47#66867—22no—
48#9002—111nomaximal, Sylow
49C24×C11—41no—
50C2×D4×C11—22no—
51C2×D4×C11—24no—
52C2×D4×C11—42no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—41no—
60C22×C4×C11—22no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D412yes—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C2×C8×C11—22no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—24no—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4C22⋊C414yes—
72C42×C11C22×C411yescharacteristic
73C42×C11C2×D411yescharacteristic
74C42×C11#4112yes—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—82no—
78C4×Dic11—82no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×#490D1111yescharacteristic
83#2382—111no—
84#1961—112no—
85C2×#330—111no—
86#1295—112no—
87C23×C11—42no—
88C23×C11—82no—
89C23×C11—82no—
90C23×C11—81no—
91C23×C11—81no—
92C23×C11#12011yescharacteristic
93D4×C11—44no—
94D4×C11—44no—
95D4×C11—44no—
96D4×C11—82no—
97D4×C11—82no—
98D4×C11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—24no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11C2×C22⋊C411yescharacteristic
107C2×C4×C11C4×D412yes—
108C2×C4×C11#12112yes—
109C2×C4×C11#12311yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C8×C11—42no—
117C11⋊C8—44no—
118C2×#127C2×D1111yescharacteristic
119C2×#125C2×D1111yescharacteristic
120#490—22no—
121#490Dic1114yescomplemented
122C2×#102—22no—
123C2×#102—222no—
124C2×#102—222no—
125C2×#97—112no—
126C2×#97C2×D1111yescharacteristic
127#389—222no—
128#387—222no—
129#387—222no—
130#382—112no—
131#330—222no—
132C22×C11—84no—
133C22×C11—82no—
134C22×C11—161no—
135C22×C11—162no—
136C22×C11—161no—
137C22×C11#38611yescharacteristic
138C22×C11#45312yes—
139C22×C11#45412yes—
140C22×C11#45411yescharacteristic
141C22×C11#45411yescharacteristic
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—44no—
147Dic11—82no—
148Dic11—82no—
149C22×D4—22no—
150C22×D4—21no—
151C22×C8—21no—
152C22×C8—222no—
153#127—22no—
154#127—21no—
155#127C2×Dic1112yes—
156#125—22no—
157#125C2×Dic1112yes—
158#125C22⋊D1112yes—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4—222no—
163C2×C4⋊C4C22⋊D1112yes—
164C2×C42—222no—
165C2×C42C22×D1111yescharacteristic
166#102—28no—
167#102—444no—
168#102—444no—
169#97—21no—
170#97—222no—
171#97—222no—
172#97C2×Dic1112yes—
173#95—222no—
174#95—222no—
175#95—222no—
176#95—222no—
177C2×C11—162no—
178C2×C11#165611yescharacteristic
179C2×C11#165712yes—
180C2×C11#165811yescharacteristic
181C2×C11#188312yes—
182C2×C11#188811yescharacteristic
183C24—41no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—41no—
193C2×D4—42no—
194C22×C4—22no—
195C22×C4—222no—
196C22×C4—222no—
197C22×C4D4×D1112yes—
198C22×C4C2×C22⋊D1111yescharacteristic
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—224no—
203C2×C8—442no—
204C2×C8—442no—
205C4⋊C4—24no—
206C4⋊C4—22no—
207C4⋊C4—24no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—882no—
211C4⋊C4C22⋊Dic1114yes—
212C42—882no—
213C42#434112yes—
214C42C22×Dic1111yescharacteristic
215C42C2×C22⋊D1111yescharacteristic
216C11#900211yescharacteristic, complemented, Sylow
217C23—42no—
218C23—82no—
219C23—82no—
220C23—81no—
221C23—81no—
222C23#6699011yescharacteristic
223D4—44no—
224D4—44no—
225D4—44no—
226D4—82no—
227D4—82no—
228D4—82no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—24no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4D4×Dic1112yes—
243C2×C4#6698811yescharacteristic
244C2×C4#6699212yes—
245C2×C4C2×C22⋊Dic1111yescharacteristic
246C8—42no—
247C8—444no—
248C22—84no—
249C22—82no—
250C22—161no—
251C22—162no—
252C22—161no—
253C22#1062267511yescharacteristic
254C22#1062267511yescharacteristic
255C22#1062281112yes—
256C22#1062281412yes—
257C22#1062283311yescharacteristic
258C4—22no—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—44no—
263C4—882no—
264C4—882no—
265C2—162no—
266C2#1306790811yescharacteristic
267C2#1306791312yes—
268C2#1306791711yescharacteristic
269C2#1306899412yes—
270C2#1306902011yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#490C2
socleC23×C11#120
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#490D11
hypocenterC11#9002
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. #13071802C2semidirect
3. C2×#10622181C2semidirect
4. #13066498C2semidirect
9. C11×#490C4semidirect
121. #490Dic11semidirect
216. C11#9002semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130694412
C2×#106221812
#130664982
C2×C11×#4902
#900211