Finite Group Databasebeta

← #14667484

Subgroups — #14667484

Order 2816.

282 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070845C211yesmaximal, characteristic
2#13070666C211yesmaximal, characteristic
3#13067986C211yesmaximal, characteristic
4#13066671C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic
6#13066580C211yesmaximal, characteristic
7C11×#3383C211yesmaximal, characteristic
8C11×#557—21no—
9C11×#500C2211yescharacteristic
10C11×#499—21no—
11C11×#479—22no—
12C11×#475—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×Q16C2211yescharacteristic
16C2×#66893—21no—
17#10622633—21no—
18#10622312C2211yescharacteristic
19#10622130—21no—
20#10622130—22no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—41no—
28C11×#125—22no—
29C11×#125—42no—
30C4×Q8×C11—22no—
31C4×Q8×C11—21no—
32C4×Q8×C11—41no—
33C4×Q8×C11D411yescharacteristic
34C2×Dic44—21no—
35C2×Dic44—21no—
36#66922—21no—
37C11×#107—21no—
38C11×#107D411yescharacteristic
39C11×#107D412yes—
40C11×#106—22no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×#103—22no—
44C11×#103—21no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—41no—
48#66893—42no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51#66872—41no—
52C4⋊(C11⋊C8)—21no—
53#12357—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Q8×C11D811yescharacteristic
57C2×Dic22—41no—
58C11×Q16—21no—
59C11×Q16SD1612yes—
60C2×C8×C11—21no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—21no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4D811yescharacteristic
72C42×C11—21no—
73C42×C11—42no—
74C42×C11—41no—
75C42×C11C2×D411yescharacteristic
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3383D1111yescharacteristic
85#2241—111no—
86#2209—111no—
87#1670—111no—
88#1364—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—22no—
92Q8×C11—21no—
93Q8×C11—21no—
94Q8×C11—41no—
95Q8×C11—81no—
96Q8×C11—81no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—81no—
106Dic22—81no—
107Dic22—81no—
108C8×C11—21no—
109C8×C11—41no—
110C8×C11C2×SD1611yescharacteristic
111C8×C11#13711yescharacteristic
112C11⋊C8—81no—
113#557—21no—
114C2×Q32—221no—
115#500C2×D1111yescharacteristic
116#499—21no—
117#494—111no—
118#479—22no—
119#475—21no—
120#475—221no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—21no—
123C4×Q16C2×D1111yescharacteristic
124C4⋊C16—111no—
125#358—221no—
126#358—222no—
127C4×C16—111no—
128#335—111no—
129#332—221no—
130C22×C11#44711yescharacteristic
131C4×C11—21no—
132C4×C11—42no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11—82no—
136C4×C11—81no—
137C4×C11#44811yescharacteristic
138C4×C11#45411yescharacteristic
139C4×C11#50811yescharacteristic
140C4×C11#51011yescharacteristic
141Dic11—161no—
142C2×Q16—221no—
143C2×Q16—221no—
144C2×Q16C22⋊D1111yescharacteristic
145C4⋊Q8—21no—
146C4⋊Q8—41no—
147C4⋊Q8—221no—
148#125—22no—
149#125—42no—
150C4×Q8—22no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8C22⋊D1111yescharacteristic
154Q32—442no—
155C2×C16—221no—
156C2×C16—221no—
157#107—21no—
158#107C22⋊D1111yescharacteristic
159#107C22⋊D1112yes—
160#106—22no—
161#106—441no—
162C4⋊C8—21no—
163C4⋊C8—221no—
164C4⋊C8C22⋊D1111yescharacteristic
165#103—22no—
166#103—21no—
167#103—441no—
168C4×C8—21no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218911yescharacteristic
172C2×C11#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—441no—
176C2×Q8#432311yescharacteristic
177Q16—21no—
178Q16—442no—
179Q16—441no—
180Q16—441no—
181Q16#432512yes—
182C2×C8—21no—
183C2×C8—441no—
184C2×C8C2×C22⋊D1111yescharacteristic
185C2×C8C2×C22⋊D1111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4#432311yescharacteristic
197C42—21no—
198C42—42no—
199C42—41no—
200C42C2×C22⋊D1111yescharacteristic
201C16—441no—
202C16—441no—
203C11#1235711yescharacteristic, complemented, Sylow
204Q8—21no—
205Q8—21no—
206Q8—22no—
207Q8—41no—
208Q8—81no—
209Q8—81no—
210Q8—881no—
211Q8—881no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—881no—
218C2×C4C2×#432311yescharacteristic
219C2×C4#6698511yescharacteristic
220C2×C4#6700611yescharacteristic
221C8—21no—
222C8—41no—
223C8—881no—
224C8C2×#432511yescharacteristic
225C8#6699511yescharacteristic
226C22#1062283011yescharacteristic
227C4—21no—
228C4—41no—
229C4—42no—
230C4—41no—
231C4—81no—
232C4—82no—
233C4—1761no—
234C4#1062280711yescharacteristic
235C4#1062280811yescharacteristic
236C4#1062284011yescharacteristic
237C4#1062285811yescharacteristic
238C2#1306771911yescharacteristic
239C2#1307055611yescharacteristic
240C2#1307059411yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3383C2
socle, prime radicalC22×C11#447
hypercenter#3383D11
hypocenterC11#12357
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3383

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
#130708452
#130706662
#130679862
#130666712
Q8⋊(C11⋊C16)2
#130665802
C11×#33832
#1235711