Finite Group Databasebeta

← #14667402

Subgroups — #14667402

Order 2816.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081047C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070667C211yesmaximal, characteristic, complemented
4#13067981C211yesmaximal, characteristic
5#13066670C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic
8#10623073—21no—
9C8×D4×C11C2211yescharacteristic
10#10622729—21no—
11#10622719—21no—
12#10622620—21no—
13C2×Dic88—21no—
14#10622464—21no—
15#10622336—22no—
16#10622312C2211yescharacteristic
17C4×Dic44C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622141—21no—
22#10622141—22no—
23#10622120—21no—
24#10622096C2211yescharacteristic
25C22×C8×C11—21no—
26C4×D4×C11D411yescharacteristic
27#66989—41no—
28#66979—22no—
29#66977—22no—
30C2×Dic44—21no—
31C2×Dic44—21no—
32C2×Dic44D411yescharacteristic
33#66940—41no—
34#66932—42no—
35#66922—21no—
36#66922—21no—
37C4×Dic22—21no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×C22⋊C8—21no—
42C4×C8×C11C2311yescharacteristic
43#66896—41no—
44#66882—21no—
45#66882D412yes—
46#66882D411yescharacteristic
47#66881—22no—
48#66880—22no—
49#66880—21no—
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52Dic88—42no—
53#12345—111nomaximal, Sylow
54C2×D4×C11D811yescharacteristic
55C22×C4×C11—21no—
56C2×Dic22—21no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4D811yescharacteristic
65C11×C22⋊C4—21no—
66C42×C11C2×D411yescharacteristic
67C22⋊Dic11—42no—
68C22⋊Dic11—42no—
69C4⋊Dic11—21no—
70C4⋊Dic11—22no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74Dic11⋊C4—42no—
75Dic11⋊C4—41no—
76C4×Dic11—42no—
77C4×Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—21no—
80Dic44—21no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84C11×C16—41no—
85C11×C16—41no—
86#3342—111no—
87#2241—111no—
88#2209—111no—
89#1669—111no—
90#1364—111no—
91#1332—111no—
92D4⋊C16D1111yescharacteristic
93C23×C11—21no—
94D4×C11—21no—
95D4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11#12011yescharacteristic
100C2×C4×C11C2×D811yescharacteristic
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11—81no—
106Dic22—41no—
107Dic22—41no—
108Dic22—81no—
109Dic22—81no—
110Dic22—81no—
111Dic22—81no—
112C8×C11—21no—
113C8×C11—41no—
114C8×C11#13511yescharacteristic
115C8×C11AGL(1,ℤ/8)11yescharacteristic
116C11⋊C8—81no—
117#556—221no—
118C2×Q32—221no—
119#500—111no—
120#494—111no—
121#485—222no—
122#475—221no—
123#474—221no—
124#467—221no—
125C4×Q16—111no—
126C8×D4C2×D1111yescharacteristic
127#427—221no—
128C4⋊C16C2×D1111yescharacteristic
129#358—221no—
130#358—222no—
131C4×C16C2×D1111yescharacteristic
132#335—111no—
133#332—221no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11#44711yescharacteristic
138C4×C11—21no—
139C4×C11—41no—
140C4×C11#44911yescharacteristic
141C4×C11#45411yescharacteristic
142C4×C11#50811yescharacteristic
143C4×C11#51011yescharacteristic
144Dic11—81no—
145Dic11—82no—
146Dic11—81no—
147Dic11—161no—
148C2×Q16—111no—
149C2×Q16—221no—
150C2×Q16—221no—
151C22×C8—21no—
152C4⋊Q8—221no—
153C4⋊Q8—221no—
154#126—442no—
155#124—441no—
156C22⋊Q8—222no—
157C4×Q8—221no—
158C4×Q8—441no—
159C4×D4D4411yescharacteristic
160#117—222no—
161Q32—442no—
162C2×C16—21no—
163C2×C16—21no—
164#107—111no—
165#107—112no—
166#107—221no—
167#107—441no—
168#106—222no—
169C4⋊C8—221no—
170C4⋊C8D4411yescharacteristic
171#103—222no—
172#103—221no—
173#102—441no—
174C22⋊C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11—81no—
177C2×C11#162511yescharacteristic
178C2×C11#218911yescharacteristic
179C2×C11#219511yescharacteristic
180C2×Q8—221no—
181C2×Q8—441no—
182C2×Q8—441no—
183C2×D4D8811yescharacteristic
184C22×C4—21no—
185Q16—221no—
186Q16—221no—
187Q16—442no—
188Q16—441no—
189Q16—441no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—441no—
194C2×C8D4×D1111yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—221no—
197C4⋊C4—222no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C4⋊C4—441no—
203C4⋊C4D8811yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C42—442no—
208C42—441no—
209C42C2×D4411yescharacteristic
210C16—41no—
211C16—41no—
212C11#1234511yescharacteristic, complemented, Sylow
213C23—21no—
214Q8—441no—
215Q8—441no—
216Q8—881no—
217Q8—881no—
218Q8—881no—
219Q8—881no—
220D4—21no—
221D4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—441no—
226C2×C4—442no—
227C2×C4—441no—
228C2×C4—881no—
229C2×C4#6693511yescharacteristic
230C2×C4C2×D8811yescharacteristic
231C2×C4#6696111yescharacteristic
232C8—21no—
233C8—41no—
234C8—881no—
235C8#6696411yescharacteristic
236C8#6696911yescharacteristic
237C22—41no—
238C22—41no—
239C22—41no—
240C22#1062234511yescharacteristic
241C4—21no—
242C4—41no—
243C4—881no—
244C4—881no—
245C4—882no—
246C4—1761no—
247C4#1062239411yescharacteristic
248C4#1062244011yescharacteristic
249C4#1062251711yescharacteristic
250C4#1062252211yescharacteristic
251C2—81no—
252C2#1306770711yescharacteristic
253C2#1307055811yescharacteristic
254C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenterD4⋊C16D11
hypocenterC11#12345
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
3. #13070667C2semidirect
5. #13066670C2semidirect
6. #13066581C2semidirect
212. C11#12345semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708442
#130706672
#130679812
#130666702
#130665812
C11×D4⋊C162
#1234511