Finite Group Databasebeta

← #14667482

Subgroups — #14667482

Order 2816.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081508C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic
3#13070663C211yesmaximal, characteristic
4#13066672C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic
6#13066579C211yesmaximal, characteristic
7C11×#1670C211yesmaximal, characteristic
8#10623098—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66893—21no—
13#10622464—21no—
14#10622442—22no—
15C4×Dic44—21no—
16C4×Dic44C2211yescharacteristic
17#10622296—21no—
18#10622295C2211yescharacteristic
19C11×#335C2211yescharacteristic
20C11×#332—21no—
21#10622202—21no—
22#10622202—22no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C4×Q8×C11D411yescharacteristic
29#66997—41no—
30C2×Dic44D411yescharacteristic
31#66942—42no—
32#66940—41no—
33#66923—22no—
34#66922—21no—
35C4×Dic22—22no—
36C4×Dic22—21no—
37C11×#106—41no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#103—41no—
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66893—42no—
45#66882—21no—
46#66882D412yes—
47#66882D411yescharacteristic
48#66881—22no—
49#66880—22no—
50#66880—21no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53#12357—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11D811yescharacteristic
56C2×Dic22—21no—
57C2×Dic22—41no—
58C11×Q16—42no—
59C11×Q16—41no—
60C11×Q16—41no—
61C2×C8×C11—21no—
62C2×C8×C11—41no—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—21no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4D811yescharacteristic
69C42×C11—21no—
70C42×C11C2×D411yescharacteristic
71C4⋊Dic11—21no—
72C4⋊Dic11—22no—
73C4⋊Dic11—41no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77Dic11⋊C4—41no—
78C4×Dic11—42no—
79C4×Dic11—41no—
80Dic44—21no—
81Dic44SD1612yes—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3383—111no—
85#2241—111no—
86#2209—111no—
87#1670D1111yescharacteristic
88#1364—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—21no—
92Q8×C11—21no—
93Q8×C11—81no—
94Q8×C11—81no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—81no—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
101C2×Dic11—41no—
102C2×Dic11—41no—
103C2×Dic11—42no—
104Dic22—22no—
105Dic22—41no—
106Dic22—81no—
107Dic22—81no—
108C8×C11—21no—
109C8×C11—41no—
110C8×C11—81no—
111C8×C11C2×SD1611yescharacteristic
112C8×C11#13711yescharacteristic
113#557—221no—
114C2×Q32—221no—
115#500—111no—
116#499—221no—
117#494C2×D1111yescharacteristic
118#479—222no—
119#475—21no—
120#475—221no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—111no—
123C4×Q16—221no—
124C4⋊C16—111no—
125#358—221no—
126#358—222no—
127C4×C16—111no—
128#335C2×D1111yescharacteristic
129#332—21no—
130C22×C11#44711yescharacteristic
131C4×C11—21no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11—161no—
135C4×C11#44811yescharacteristic
136C4×C11#45411yescharacteristic
137C4×C11#50811yescharacteristic
138C4×C11#51011yescharacteristic
139Dic11—42no—
140Dic11—82no—
141Dic11—81no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16—111no—
145C4⋊Q8—21no—
146C4⋊Q8—221no—
147C4⋊Q8—441no—
148#125—222no—
149#125—442no—
150C4×Q8—222no—
151C4×Q8—221no—
152C4×Q8—441no—
153C4×Q8C22⋊D1111yescharacteristic
154Q32—442no—
155C2×C16—221no—
156C2×C16—221no—
157#107—111no—
158#107—112no—
159#107—221no—
160#106—41no—
161#106—222no—
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8C22⋊D1111yescharacteristic
165#103—41no—
166#103—222no—
167#103—221no—
168C4×C8—21no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218911yescharacteristic
172C2×C11#219511yescharacteristic
173C2×Q8—41no—
174C2×Q8—221no—
175C2×Q8—441no—
176C2×Q8#432311yescharacteristic
177Q16—42no—
178Q16—41no—
179Q16—41no—
180Q16—112no—
181Q16—221no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8D4×D1111yescharacteristic
185C2×C8D4×D1111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—221no—
190C4⋊C4—222no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4#432311yescharacteristic
197C42—21no—
198C42—442no—
199C42—441no—
200C42C2×C22⋊D1111yescharacteristic
201C16—441no—
202C16—441no—
203C11#1235711yescharacteristic, complemented, Sylow
204Q8—21no—
205Q8—21no—
206Q8—81no—
207Q8—81no—
208Q8—222no—
209Q8—441no—
210Q8—881no—
211Q8—881no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—81no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—442no—
218C2×C4C2×#432311yescharacteristic
219C2×C4#6699011yescharacteristic
220C2×C4#6700211yescharacteristic
221C8—21no—
222C8—41no—
223C8—81no—
224C8SD16×D1111yescharacteristic
225C8#6696811yescharacteristic
226C22#1062264911yescharacteristic
227C4—21no—
228C4—41no—
229C4—41no—
230C4—161no—
231C4—442no—
232C4—881no—
233C4—882no—
234C4#1062278311yescharacteristic
235C4#1062279211yescharacteristic
236C4#1062280711yescharacteristic
237C4#1062281411yescharacteristic
238C2#1306771711yescharacteristic
239C2#1307055411yescharacteristic
240C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1670C2
socle, prime radicalC22×C11#447
hypercenter#1670D11
hypocenterC11#12357
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
203. C11#12357semidirect

Maximal subgroups

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

subgroupindex
#130815082
#130708432
#130706632
#130666722
Q8⋊(C11⋊C16)2
#130665792
C11×#16702
#1235711