Finite Group Databasebeta

← #14667689

Subgroups — #14667689

Order 2816.

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

normal subgroups only

This group has 288 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#13081602C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070763C211yesmaximal, characteristic
4#13068021C211yesmaximal, characteristic, complemented
5#13066664C211yesmaximal, characteristic, complemented
6#13066596C211yesmaximal, characteristic, complemented
7C11×#1331C211yesmaximal, characteristic
8#10623073—21no—
9C4×C11×D8C2211yescharacteristic
10#10622768—21no—
11#10622632—21no—
12#10622486—21no—
13#10622463—21no—
14#10622380—22no—
15#10622312C2211yescharacteristic
16#10622295C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C4×C11×C16C2211yescharacteristic
19C11×#335C2211yescharacteristic
20#10622200—21no—
21#10622141—22no—
22#10622128—21no—
23#10622119—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×D8D411yescharacteristic
26C4×D4×C11—21no—
27#66989—22no—
28C2×#4324—22no—
29#66979—41no—
30#66977—41no—
31C2×Dic44—21no—
32C2×Dic44D412yes—
33#66940—22no—
34#66932—42no—
35#66922—21no—
36#66922—21no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×C4⋊C8—21no—
41C11×#102—21no—
42C4×C8×C11C2311yescharacteristic
43#66882—21no—
44#66882—21no—
45#66882—41no—
46#66880—41no—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50#66874—22no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12387—111nomaximal, Sylow
53C2×D4×C11—21no—
54C22×C4×C11—41no—
55C2×Dic22—22no—
56C2×Dic22—41no—
57C2×Dic22D811yescharacteristic
58C11×D8—21no—
59C11×D8—21no—
60C2×C8×C11—41no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—21no—
64C11×C22⋊C4—41no—
65C42×C11C2×D411yescharacteristic
66C22⋊Dic11—42no—
67C22⋊Dic11—42no—
68#4324—82no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C2×C11⋊C8—21no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3393—111no—
85#2241—111no—
86#2226—111no—
87#1676—111no—
88#1362—111no—
89Q8⋊C16—111no—
90#1331D1111yescharacteristic
91C23×C11—41no—
92D4×C11—41no—
93D4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—81no—
96C2×C4×C11—81no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—42no—
103C2×Dic11—81no—
104Dic22—21no—
105Dic22—21no—
106Dic22—42no—
107Dic22—42no—
108Dic22—161no—
109C8×C11—21no—
110C8×C11—81no—
111C8×C11#13511yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—41no—
114#556—221no—
115#500—111no—
116#495—221no—
117#494—111no—
118#477—221no—
119#464—222no—
120#461—221no—
121C8×Q8—111no—
122C4×Q16—221no—
123C4×D8C2×D1111yescharacteristic
124#367—221no—
125C4⋊C16—111no—
126#358—222no—
127#357—221no—
128C4×C16C2×D1111yescharacteristic
129#335C2×D1111yescharacteristic
130#333—221no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11—81no—
134C22×C11#44711yescharacteristic
135C4×C11—21no—
136C4×C11—81no—
137C4×C11#45211yescharacteristic
138C4×C11#45511yescharacteristic
139C4×C11#50811yescharacteristic
140C4×C11#51011yescharacteristic
141Dic11—41no—
142Dic11—41no—
143Dic11—82no—
144Dic11—161no—
145C2×Q16—112no—
146C2×Q16—221no—
147C2×SD16—222no—
148C2×D8D4411yescharacteristic
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151#126—442no—
152#124—222no—
153C22⋊Q8—441no—
154C4×Q8—111no—
155C4×Q8—222no—
156C4×D4—21no—
157#117—441no—
158C2×C16—21no—
159C2×C16—221no—
160#107—221no—
161#107—221no—
162#107—441no—
163#107D4411yescharacteristic
164C4⋊C8—21no—
165C4⋊C8—111no—
166C4⋊C8—221no—
167#103—222no—
168#103—441no—
169#102—21no—
170C4×C8—221no—
171C4×C8C22×D1111yescharacteristic
172C2×C11—161no—
173C2×C11#164111yescharacteristic
174C2×C11#218911yescharacteristic
175C2×C11#219311yescharacteristic
176C2×Q8—111no—
177C2×Q8—222no—
178C2×Q8—441no—
179C2×D4—21no—
180C22×C4—41no—
181Q16—442no—
182Q16—441no—
183Q16—441no—
184SD16—882no—
185D8—21no—
186D8—21no—
187C2×C8—41no—
188C2×C8—221no—
189C2×C8C2×D4411yescharacteristic
190C2×C8D4×D1111yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—111no—
193C4⋊C4—221no—
194C4⋊C4—442no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4—441no—
199C22⋊C4—41no—
200C22⋊C4—442no—
201C22⋊C4—442no—
202C42—221no—
203C42—442no—
204C42D4×D1111yescharacteristic
205C16—41no—
206C16—441no—
207C11#1238711yescharacteristic, complemented, Sylow
208C23—41no—
209Q8—221no—
210Q8—221no—
211Q8—442no—
212Q8—442no—
213Q8—1761no—
214D4—41no—
215D4—41no—
216C2×C4—41no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—442no—
222C2×C4—881no—
223C2×C4#6693511yescharacteristic
224C2×C4D8×D1111yescharacteristic
225C2×C4#6696711yescharacteristic
226C8—21no—
227C8—81no—
228C8—441no—
229C8#6695711yescharacteristic
230C8#6696211yescharacteristic
231C22—81no—
232C22—81no—
233C22—81no—
234C22#1062238611yescharacteristic
235C4—21no—
236C4—81no—
237C4—441no—
238C4—441no—
239C4—882no—
240C4—1761no—
241C4#1062234611yescharacteristic
242C4#1062243811yescharacteristic
243C4#1062252511yescharacteristic
244C4#1062252811yescharacteristic
245C2—161no—
246C2#1306781211yescharacteristic
247C2#1307055711yescharacteristic
248C2#1307058111yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1331C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#1331D11
hypocenterC11#12387
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
4. #13068021C2semidirect
5. #13066664C2semidirect
6. #13066596C2semidirect
207. C11#12387semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130708442
#130707632
#130680212
#130666642
#130665962
C11×#13312
#1238711