Finite Group Databasebeta

← #14667524

Subgroups — #14667524

Order 2816.

278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081585C211yesmaximal, characteristic
2#13070861C211yesmaximal, characteristic
3#13070663C211yesmaximal, characteristic
4#13066669C211yesmaximal, characteristic
5#13066598C211yesmaximal, characteristic
6#13066585C211yesmaximal, characteristic
7C11×#1690C211yesmaximal, characteristic
8#10623098—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C11×#446C2211yescharacteristic
12C2×#66893—21no—
13#10622463—21no—
14#10622442—21no—
15#10622442—21no—
16#10622329—21no—
17#10622315—21no—
18C4×Dic44C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×#334C2211yescharacteristic
21C11×#332—21no—
22#10622202—21no—
23#10622202—21no—
24#10622202—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622099C2211yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C11×C4⋊Q8—21no—
30C4×Q8×C11D411yescharacteristic
31#66997—41no—
32C2×Dic44D411yescharacteristic
33#66942—41no—
34#66942—41no—
35#66940—41no—
36#66923—21no—
37#66923—21no—
38#66922—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×#106—41no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×#103—41no—
47C11×#97—21no—
48C4×C8×C11C2311yescharacteristic
49#66893—42no—
50#66882—21no—
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66881—21no—
56#66880—21no—
57#66880—21no—
58#66880—21no—
59C2×C11⋊C16—21no—
60C2×C11⋊C16—21no—
61#12363—111nomaximal, Sylow
62C2×Q8×C11—41no—
63C2×Q8×C11D811yescharacteristic
64C2×Dic22—21no—
65C2×Dic22—41no—
66C11×Q16—42no—
67C11×Q16—41no—
68C11×Q16—41no—
69C2×C8×C11—21no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4D811yescharacteristic
77C42×C11—21no—
78C42×C11C2×D411yescharacteristic
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—41no—
91C4×Dic11—41no—
92C4×Dic11—41no—
93Dic44—21no—
94Dic44SD1612yes—
95C11⋊C16—41no—
96C11⋊C16—41no—
97#3390—111no—
98#2245—111no—
99#2209—111no—
100#1690D1111yescharacteristic
101#1363—111no—
102#1338—111no—
103#1334—111no—
104Q8×C11—41no—
105Q8×C11—81no—
106Q8×C11—81no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—81no—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117Dic22—22no—
118Dic22—41no—
119Dic22—82no—
120C8×C11—21no—
121C8×C11—41no—
122C8×C11—81no—
123C8×C11C2×SD1611yescharacteristic
124C8×C11#13711yescharacteristic
125#557—221no—
126C2×Q32—221no—
127#501—221no—
128#499—111no—
129#494C2×D1111yescharacteristic
130#479—221no—
131#479—221no—
132#477—221no—
133#475—21no—
134#446C2×D1111yescharacteristic
135#441—221no—
136C4×Q16—111no—
137C4⋊C16—111no—
138#358—221no—
139#358—221no—
140#358—221no—
141#346—111no—
142#334C2×D1111yescharacteristic
143#332—21no—
144C22×C11#44711yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—161no—
150C4×C11#44811yescharacteristic
151C4×C11#45411yescharacteristic
152Dic11—42no—
153Dic11—81no—
154Dic11—81no—
155Dic11—81no—
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—111no—
159C4⋊Q8—21no—
160C4⋊Q8—221no—
161C4⋊Q8—441no—
162#125—221no—
163#125—221no—
164#125—441no—
165#125—441no—
166C4×Q8—221no—
167C4×Q8—221no—
168C4×Q8—221no—
169C4×Q8—441no—
170C4×Q8C22⋊D1111yescharacteristic
171Q32—442no—
172C2×C16—221no—
173C2×C16—221no—
174#107—111no—
175#107—111no—
176#107—111no—
177#107—221no—
178#106—41no—
179#106—221no—
180#106—221no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8C22⋊D1111yescharacteristic
184#103—41no—
185#103—221no—
186#103—221no—
187#103—221no—
188#97—21no—
189C4×C8C22×D1111yescharacteristic
190C2×C11#162711yescharacteristic
191C2×C11#219111yescharacteristic
192C2×C11#219511yescharacteristic
193C2×Q8—41no—
194C2×Q8—221no—
195C2×Q8—441no—
196C2×Q8#432311yescharacteristic
197Q16—42no—
198Q16—41no—
199Q16—41no—
200Q16—112no—
201Q16—221no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8D4×D1111yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4#432311yescharacteristic
221C42—21no—
222C42—441no—
223C42—441no—
224C42—441no—
225C42C2×C22⋊D1111yescharacteristic
226C16—441no—
227C16—441no—
228C11#1236311yescharacteristic, complemented, Sylow
229Q8—41no—
230Q8—81no—
231Q8—81no—
232Q8—222no—
233Q8—441no—
234Q8—882no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—81no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4C2×#432311yescharacteristic
243C2×C4#6699011yescharacteristic
244C2×C4#6700211yescharacteristic
245C8—21no—
246C8—41no—
247C8—81no—
248C8SD16×D1111yescharacteristic
249C8#6696811yescharacteristic
250C22#1062264911yescharacteristic
251C4—21no—
252C4—21no—
253C4—41no—
254C4—41no—
255C4—161no—
256C4—442no—
257C4—881no—
258C4—881no—
259C4—881no—
260C4#1062278311yescharacteristic
261C4#1062281411yescharacteristic
262C2#1306771711yescharacteristic
263C2#1307056611yescharacteristic
264C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1690C2
socle, prime radicalC22×C11#447
hypercenter#1690D11
hypocenterC11#12363
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1690

Complements

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

NH ≅ G/Ntype
228. C11#12363semidirect

Maximal subgroups

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

subgroupindex
#130815852
#130708612
#130706632
#130666692
#130665982
#130665852
C11×#16902
#1236311