Finite Group Databasebeta

← #14652211

Subgroups — #14652211

Order 2816.

338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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#13069592C211yesmaximal, characteristic
2C4⋊C8×Dic11C211yesmaximal, characteristic
3#13067271C211yesmaximal, characteristic
4#13067018C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic
6#13066448C211yesmaximal, characteristic
7C11×#1570C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C8×Dic11—21no—
13C42×Dic11C2211yescharacteristic
14#10622538C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×#334—22no—
17#10622193—21no—
18#10622193—21no—
19#10622188—21no—
20#10622122—22no—
21#10622120C412yescomplemented
22#10622119C412yescomplemented
23C2×C11×M16—21no—
24C22×C8×C11—21no—
25C2×C42×C11C2311yescharacteristic
26#66979—21no—
27#66977—21no—
28#66977—21no—
29C2×C4×Dic11—21no—
30C2×C4×Dic11—21no—
31C2×C4×Dic11D411yescharacteristic
32C2×C4×Dic11D411yescharacteristic
33C22×C11⋊C8—21no—
34#66923—21no—
35#66922C2×C411yescharacteristic
36#66922C2×C411yescharacteristic
37C4×Dic22—21no—
38C4×Dic22—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8C2×C412yes—
43C11×C4⋊C8D412yes—
44C11×C22⋊C8—21no—
45C4×C8×C11—21no—
46C22⋊(C11⋊C8)—21no—
47C8×Dic11—42no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)C2×C412yes—
51C4×C11⋊C8—21no—
52#9579—111nomaximal, Sylow
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C22×Dic11—21no—
58C2×Dic22—21no—
59C2×Dic22—21no—
60C11×M16—41no—
61C11×M16—41no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C42×C11C22×C411yescharacteristic
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C22⋊Dic11—41no—
72C4⋊Dic11—21no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76Dic11⋊C4—41no—
77Dic11⋊C4—41no—
78C4×Dic11—24no—
79C4×Dic11—21no—
80C4×Dic11—21no—
81C4×Dic11—21no—
82C4×Dic11—42no—
83C4×Dic11—41no—
84C4×Dic11SD1612yes—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89#1994—111no—
90C4×C4⋊C8—111no—
91#1570D1111yescharacteristic
92#1542—111no—
93#1481—111no—
94#1301—111no—
95#1276—111no—
96C23×C11#12311yescharacteristic
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11#11711yescharacteristic
100C2×C4×C11C4×D411yescharacteristic
101C2×C4×C11C4×D411yescharacteristic
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12411yescharacteristic
104C2×C4×C11#12611yescharacteristic
105C2×C4×C11C2×SD1611yescharacteristic
106C2×C4×C11#13511yescharacteristic
107C2×C4×C11#13711yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117Dic22—42no—
118Dic22—81no—
119C8×C11—42no—
120C8×C11—42no—
121C8×C11—81no—
122C11⋊C8—42no—
123C11⋊C8—81no—
124#533—111no—
125#431—111no—
126#431C2×D1111yescharacteristic
127#423C2×D1111yescharacteristic
128C2×C4⋊C8—111no—
129C2×C4⋊C8C2×D1111yescharacteristic
130C2×C4×C8—221no—
131C43—111no—
132#339—221no—
133#339—221no—
134#336—221no—
135#334—22no—
136#333—112no—
137#332—112no—
138Q8⋊C8—222no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#38811yescharacteristic
142C22×C11#48311yescharacteristic
143C22×C11#48511yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11C4×SD1611yescharacteristic
148C4×C11#44111yescharacteristic
149C4×C11#44312yes—
150C4×C11#46111yescharacteristic
151C4×C11#46411yescharacteristic
152Dic11—24no—
153Dic11—42no—
154Dic11—81no—
155Dic11—81no—
156C2×M16—21no—
157C22×C8—21no—
158C22×C8—221no—
159C4⋊Q8—111no—
160C4⋊Q8—111no—
161#125—221no—
162C22⋊Q8—221no—
163C22⋊Q8—221no—
164C4×Q8—221no—
165C4×Q8—221no—
166#117—221no—
167C2×C42—111no—
168C2×C42—111no—
169C2×C42—221no—
170C2×C42—221no—
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—112no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8C4×D1112yes—
179C4⋊C8C22⋊D1112yes—
180C22⋊C8—21no—
181C22⋊C8—221no—
182C4×C8—21no—
183C4×C8—221no—
184C4×C8—442no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#192711yescharacteristic
188C2×C11#193211yescharacteristic
189C2×C11#193711yescharacteristic
190C2×Q8—221no—
191C2×Q8—221no—
192C22×C4—221no—
193C22×C4—221no—
194C22×C4#433911yescharacteristic
195C22×C4D4×D1111yescharacteristic
196C22×C4#434311yescharacteristic
197M16—41no—
198M16—41no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—222no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C22⋊C4—441no—
215C42—112no—
216C42—224no—
217C42—221no—
218C42—221no—
219C42—221no—
220C42—442no—
221C42—441no—
222C42C2×C4×D1111yescharacteristic
223C42#434111yescharacteristic
224C42#434311yescharacteristic
225C42C2×C22⋊D1111yescharacteristic
226C11#957911yescharacteristic, complemented, Sylow
227C23#6694711yescharacteristic
228Q8—442no—
229Q8—881no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4#6694511yescharacteristic
241C2×C4#6694611yescharacteristic
242C2×C4#6695111yescharacteristic
243C2×C4SD16×D1111yescharacteristic
244C2×C4#6696811yescharacteristic
245C2×C4#6696811yescharacteristic
246C2×C4#6696911yescharacteristic
247C2×C4C4×C22⋊D1111yescharacteristic
248C2×C4#6699211yescharacteristic
249C2×C4#6700011yescharacteristic
250C8—42no—
251C8—42no—
252C8—81no—
253C8—442no—
254C8—881no—
255C22—21no—
256C22—21no—
257C22#1062247511yescharacteristic
258C22#1062248011yescharacteristic
259C22#1062260311yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—224no—
264C4—442no—
265C4—881no—
266C4—881no—
267C4#1062246511yescharacteristic
268C4#1062246611yescharacteristic
269C4#1062275712yes—
270C4#1062277511yescharacteristic
271C4#1062277911yescharacteristic
272C2—21no—
273C2—21no—
274C2#1306924911yescharacteristic
275C2#1306928411yescharacteristic
276C2#1306931911yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1570C2
socleC22×C11#388
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1570D11
hypocenterC11#9579
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
21. #10622120C4semidirect
22. #10622119C4semidirect
226. C11#9579semidirect

Maximal subgroups

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

subgroupindex
#130695922
C4⋊C8×Dic112
#130672712
#130670182
#130665112
#130664482
C11×#15702
#957911