Finite Group Databasebeta

← #14667316

Subgroups — #14667316

Order 2816.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070871C211yesmaximal, characteristic
2#13070666C211yesmaximal, characteristic, complemented
3#13067986C211yesmaximal, characteristic, complemented
4#13066662C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066580C211yesmaximal, characteristic, complemented
7C11×#3396C211yesmaximal, characteristic
8C11×#559—21no—
9C11×#495—21no—
10C11×#493C2211yescharacteristic
11C11×#463—22no—
12C11×#460—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16C2211yescharacteristic
15C4×C11×D8—21no—
16C2×#66893—21no—
17C2×#66891—22no—
18#10622633—21no—
19#10622312C2211yescharacteristic
20#10622130—21no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C2×C11×SD16—22no—
27C2×C11×D8—21no—
28C2×C11×D8D412yes—
29C11×#127—21no—
30C11×#124—22no—
31C11×#124—41no—
32C11×#123—42no—
33C4×Q8×C11—21no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—22no—
36C4×D4×C11—41no—
37C2×Dic44—21no—
38C2×Dic44—21no—
39#66922—21no—
40C11×#107D411yescharacteristic
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×#103—21no—
44C11×#102—22no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—41no—
48#66893—42no—
49#66891—44no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66872—41no—
53C4⋊(C11⋊C8)—21no—
54#12333—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×Q8×C11D811yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C22×C4×C11—42no—
61C2×Dic22—41no—
62C11×Q16—21no—
63C11×Q16—21no—
64C11×SD16—82no—
65C11×D8—41no—
66C11×D8—41no—
67C11×D8—42no—
68C2×C8×C11—21no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4D811yescharacteristic
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—42no—
78C42×C11—21no—
79C42×C11—41no—
80C42×C11C2×D411yescharacteristic
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C2×C11⋊C8—41no—
84Dic44—42no—
85Dic44—41no—
86Dic44—41no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3396D1111yescharacteristic
90#2248—111no—
91#2209—111no—
92#1670—111no—
93#1361—111no—
94Q8⋊C16—111no—
95#1332—111no—
96C23×C11—42no—
97Q8×C11—21no—
98Q8×C11—21no—
99Q8×C11—41no—
100Q8×C11—41no—
101D4×C11—42no—
102D4×C11—42no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—161no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—162no—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C2×Dic11—81no—
115Dic22—81no—
116Dic22—81no—
117C8×C11—21no—
118C8×C11—41no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121C11⋊C8—81no—
122#559—21no—
123C2×Q32—221no—
124C2×SD32—222no—
125#495—21no—
126#494—111no—
127#493C2×D1111yescharacteristic
128#475—221no—
129#463—22no—
130#460—21no—
131C8×Q8C2×D1111yescharacteristic
132C4×Q16C2×D1111yescharacteristic
133C4×D8—21no—
134C4⋊C16—111no—
135#358—221no—
136C4×C16—111no—
137#335—111no—
138#332—221no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11#44711yescharacteristic
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—81no—
147C4×C11—81no—
148C4×C11#44911yescharacteristic
149C4×C11#45311yescharacteristic
150C4×C11#50811yescharacteristic
151C4×C11#51011yescharacteristic
152Dic11—161no—
153C2×Q16—221no—
154C2×Q16—221no—
155C2×Q16C22⋊D1111yescharacteristic
156C2×SD16—22no—
157C2×D8—21no—
158C2×D8C22⋊D1112yes—
159C4⋊Q8—221no—
160#127—21no—
161#124—22no—
162#124—41no—
163#123—42no—
164C4×Q8—21no—
165C4×Q8C22⋊D1111yescharacteristic
166C4×D4—22no—
167C4×D4—41no—
168Q32—442no—
169SD32—444no—
170C2×C16—221no—
171C2×C16—221no—
172#107C22⋊D1111yescharacteristic
173#106—441no—
174C4⋊C8—21no—
175C4⋊C8—221no—
176C4⋊C8C22⋊D1111yescharacteristic
177#103—21no—
178#103—441no—
179#102—22no—
180C4×C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—162no—
183C2×C11#162111yescharacteristic
184C2×C11#218911yescharacteristic
185C2×C11#219411yescharacteristic
186C2×Q8—21no—
187C2×Q8—441no—
188C2×Q8#432311yescharacteristic
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C22×C4—42no—
193Q16—21no—
194Q16—21no—
195Q16—442no—
196Q16—441no—
197Q16—441no—
198SD16—82no—
199D8—42no—
200D8—41no—
201D8—41no—
202C2×C8—21no—
203C2×C8—441no—
204C2×C8C2×C22⋊D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—441no—
210C4⋊C4—441no—
211C4⋊C4#432311yescharacteristic
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C42—21no—
216C42—41no—
217C42C2×C22⋊D1111yescharacteristic
218C16—222no—
219C16—441no—
220C11#1233311yescharacteristic, complemented, Sylow
221C23—42no—
222Q8—21no—
223Q8—21no—
224Q8—41no—
225Q8—41no—
226Q8—881no—
227Q8—881no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—162no—
238C2×C4—881no—
239C2×C4C2×#432311yescharacteristic
240C2×C4#6698511yescharacteristic
241C2×C4#6700611yescharacteristic
242C8—21no—
243C8—41no—
244C8—881no—
245C8#6700211yescharacteristic
246C8#6700311yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#1062283011yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—81no—
255C4—81no—
256C4—1761no—
257C4#1062280711yescharacteristic
258C4#1062280811yescharacteristic
259C4#1062285111yescharacteristic
260C4#1062285411yescharacteristic
261C2—162no—
262C2#1306768111yescharacteristic
263C2#1307055611yescharacteristic
264C2#1307058711yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3396C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#3396D11
hypocenterC11#12333
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
2. #13070666C2semidirect
3. #13067986C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066580C2semidirect
220. C11#12333semidirect

Maximal subgroups

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

subgroupindex
#130708712
#130706662
#130679862
#130666622
Q8⋊(C11⋊C16)2
#130665802
C11×#33962
#1233311