Finite Group Databasebeta

← #14667786

Subgroups — #14667786

Order 2816.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081190C211yesmaximal, characteristic
2#13070902C211yesmaximal, characteristic, complemented
3#13070759C211yesmaximal, characteristic, complemented
4#13068139C211yesmaximal, characteristic
5#13066667C211yesmaximal, characteristic, complemented
6#13066587C211yesmaximal, characteristic, complemented
7C11×#1330C211yesmaximal, characteristic
8#10623072—21no—
9C11×#436C2211yescharacteristic
10#10622750—21no—
11#10622734—21no—
12#10622621—21no—
13#10622442—21no—
14#10622336—21no—
15#10622335—21no—
16C4×Dic44C2211yescharacteristic
17#10622296C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#346C2211yescharacteristic
21#10622143—21no—
22#10622143—21no—
23#10622142—21no—
24#10622141—21no—
25#10622119—21no—
26#10622095C2211yescharacteristic
27C2×C11×M16—21no—
28C4×D4×C11D411yescharacteristic
29#66988—41no—
30#66979—21no—
31C2×C4⋊Dic11—21no—
32#66977—21no—
33#66977—21no—
34C2×Dic44D411yescharacteristic
35#66942—41no—
36#66932—41no—
37#66930—41no—
38#66923—21no—
39#66922—21no—
40C4×Dic22—21no—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×C22⋊C8—21no—
45C4×C8×C11C2311yescharacteristic
46#66896—41no—
47#66882—21no—
48#66882—21no—
49#66882—21no—
50#66882D411yescharacteristic
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66881—21no—
54#66881—21no—
55#66880—21no—
56#66880—21no—
57#66880—21no—
58#66872—41no—
59C4⋊(C11⋊C8)—21no—
60#12401—111nomaximal, Sylow
61C2×D4×C11D811yescharacteristic
62C22×C4×C11—21no—
63C22×Dic11—41no—
64C2×Dic22—21no—
65C2×Dic22—41no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—21no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4D811yescharacteristic
72C11×C22⋊C4—21no—
73C42×C11C2×D411yescharacteristic
74C22⋊Dic11—41no—
75C22⋊Dic11—41no—
76C22⋊Dic11—41no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88C4×Dic11—41no—
89C4×Dic11—41no—
90C2×C11⋊C8—41no—
91Dic44—21no—
92Dic44—21no—
93C11×C16—22no—
94C11×C16—41no—
95#3352—111no—
96#2255—111no—
97#2225—111no—
98#1695—111no—
99#1363—111no—
100#1334—111no—
101#1330D1111yescharacteristic
102C23×C11—21no—
103D4×C11—41no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—82no—
115C2×Dic11—81no—
116Dic22—41no—
117Dic22—41no—
118Dic22—161no—
119C8×C11—21no—
120C8×C11—41no—
121C8×C11#13511yescharacteristic
122C8×C11#13711yescharacteristic
123C11⋊C8—81no—
124#552—221no—
125#500—111no—
126#499—111no—
127#485—221no—
128#484—221no—
129#479—221no—
130#476—221no—
131#470—221no—
132C4×Q16—111no—
133#436C2×D1111yescharacteristic
134#428—221no—
135#367—221no—
136#367—221no—
137#366—221no—
138C4⋊C16C2×D1111yescharacteristic
139#358—221no—
140#346C2×D1111yescharacteristic
141#334—111no—
142#333—221no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11#44711yescharacteristic
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11#45211yescharacteristic
151C4×C11#45611yescharacteristic
152Dic11—81no—
153Dic11—81no—
154Dic11—81no—
155Dic11—81no—
156Dic11—161no—
157C2×Q16—111no—
158C2×M16—21no—
159C4⋊Q8—221no—
160#126—441no—
161#125—221no—
162#125—441no—
163#123—441no—
164C22⋊Q8—221no—
165C22⋊Q8—221no—
166C4×Q8—221no—
167C4×D4D4411yescharacteristic
168#117—221no—
169#117—441no—
170C2×C4⋊C4—221no—
171C2×C16—21no—
172C2×C16—21no—
173#107—111no—
174#107—111no—
175#107—111no—
176#107—221no—
177#107—221no—
178#107—221no—
179#106—221no—
180#106—221no—
181#106—441no—
182C4⋊C8—221no—
183C4⋊C8D4411yescharacteristic
184#103—221no—
185#103—221no—
186#103—221no—
187#102—441no—
188C22⋊C8—21no—
189C4×C8C22×D1111yescharacteristic
190C2×C11—81no—
191C2×C11#164711yescharacteristic
192C2×C11#219111yescharacteristic
193C2×C11#219311yescharacteristic
194C2×Q8—221no—
195C2×Q8—441no—
196C2×D4D8811yescharacteristic
197C22×C4—21no—
198C22×C4—441no—
199Q16—221no—
200Q16—221no—
201M16—41no—
202M16—41no—
203C2×C8—21no—
204C2×C8—441no—
205C2×C8D4×D1111yescharacteristic
206C2×C8D4×D1111yescharacteristic
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—441no—
211C4⋊C4—441no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4D8811yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—441no—
221C22⋊C4—441no—
222C22⋊C4—441no—
223C42—441no—
224C42—441no—
225C42C2×D4411yescharacteristic
226C16—22no—
227C16—41no—
228C11#1240111yescharacteristic, complemented, Sylow
229C23—21no—
230Q8—441no—
231Q8—441no—
232Q8—1761no—
233D4—41no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—882no—
242C2×C4—881no—
243C2×C4#6693511yescharacteristic
244C2×C4C2×D8811yescharacteristic
245C2×C4#6696111yescharacteristic
246C8—21no—
247C8—41no—
248C8—881no—
249C8#6696511yescharacteristic
250C8#6696811yescharacteristic
251C22—41no—
252C22—41no—
253C22—41no—
254C22#1062234511yescharacteristic
255C4—21no—
256C4—21no—
257C4—41no—
258C4—881no—
259C4—881no—
260C4—881no—
261C4—881no—
262C4—1761no—
263C4#1062239611yescharacteristic
264C4#1062243911yescharacteristic
265C2—81no—
266C2#1306785311yescharacteristic
267C2#1307056911yescharacteristic
268C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1330C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenter#1330D11
hypocenterC11#12401
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #13070902C2semidirect
3. #13070759C2semidirect
5. #13066667C2semidirect
6. #13066587C2semidirect
228. C11#12401semidirect

Maximal subgroups

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

subgroupindex
#130811902
#130709022
#130707592
#130681392
#130666672
#130665872
C11×#13302
#1240111