Finite Group Databasebeta

← #14667398

Subgroups — #14667398

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#13070843C211yesmaximal, characteristic, complemented
3#13070663C211yesmaximal, characteristic, complemented
4#13066672C211yesmaximal, characteristic, complemented
5#13066579C211yesmaximal, characteristic, complemented
6D4⋊(C11⋊C16)C211yesmaximal, characteristic
7C11×#1669C211yesmaximal, characteristic
8#10623073—21no—
9C11×#494C2211yescharacteristic
10C11×#474—21no—
11C8×D4×C11C2211yescharacteristic
12C2×#66893—21no—
13#10622729—21no—
14#10622719—21no—
15#10622464—21no—
16#10622336—22no—
17C4×Dic44C2211yescharacteristic
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—
27C22×C8×C11—21no—
28C11×C4⋊Q8—21no—
29C4×D4×C11D411yescharacteristic
30#66989—41no—
31#66979—22no—
32#66977—22no—
33C2×Dic44D411yescharacteristic
34#66940—41no—
35#66932—42no—
36#66922—21no—
37C4×Dic22—21no—
38C11×#107—41no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#102—41no—
42C11×C22⋊C8—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#12345—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×D4×C11D811yescharacteristic
56C22×C4×C11—21no—
57C2×Dic22—21no—
58C2×Dic22—41no—
59C11×Q16—42no—
60C11×Q16—41no—
61C11×Q16—41no—
62C2×C8×C11—21no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4D811yescharacteristic
71C11×C22⋊C4—21no—
72C42×C11C2×D411yescharacteristic
73C22⋊Dic11—42no—
74C22⋊Dic11—42no—
75C4⋊Dic11—21no—
76C4⋊Dic11—22no—
77C4⋊Dic11—41no—
78Dic11⋊C4—42no—
79Dic11⋊C4—41no—
80C4×Dic11—42no—
81C4×Dic11—41no—
82Dic44—21no—
83Dic44—21no—
84C11⋊C16—41no—
85C11⋊C16—41no—
86#3342—111no—
87#2241—111no—
88#2209—111no—
89#1669D1111yescharacteristic
90#1364—111no—
91#1332—111no—
92D4⋊C16—111no—
93C23×C11—21no—
94Q8×C11—81no—
95Q8×C11—81no—
96D4×C11—21no—
97D4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—81no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—42no—
108Dic22—41no—
109Dic22—41no—
110Dic22—81no—
111Dic22—81no—
112C8×C11—21no—
113C8×C11—41no—
114C8×C11—81no—
115C8×C11#13511yescharacteristic
116C8×C11AGL(1,ℤ/8)11yescharacteristic
117#556—221no—
118C2×Q32—221no—
119#500—111no—
120#494C2×D1111yescharacteristic
121#485—222no—
122#475—221no—
123#474—21no—
124#467—221no—
125C4×Q16—111no—
126C8×D4C2×D1111yescharacteristic
127#427—221no—
128C4⋊C16—111no—
129#358—221no—
130#358—222no—
131C4×C16—111no—
132#335C2×D1111yescharacteristic
133#332—21no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11#44711yescharacteristic
138C4×C11—21no—
139C4×C11—41no—
140C4×C11—161no—
141C4×C11#44911yescharacteristic
142C4×C11#45411yescharacteristic
143C4×C11#50811yescharacteristic
144C4×C11#51011yescharacteristic
145Dic11—81no—
146Dic11—82no—
147Dic11—81no—
148C2×Q16—21no—
149C2×Q16—21no—
150C2×Q16—111no—
151C22×C8—21no—
152C4⋊Q8—21no—
153C4⋊Q8—221no—
154#126—442no—
155#124—441no—
156C22⋊Q8—222no—
157C4×Q8—221no—
158C4×Q8—441no—
159C4×D4C22⋊D1111yescharacteristic
160#117—222no—
161Q32—442no—
162C2×C16—221no—
163C2×C16—221no—
164#107—41no—
165#107—111no—
166#107—112no—
167#107—221no—
168#106—222no—
169C4⋊C8—21no—
170C4⋊C8C22⋊D1111yescharacteristic
171#103—222no—
172#103—221no—
173#102—41no—
174C22⋊C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11—81no—
177C2×C11#162511yescharacteristic
178C2×C11#218911yescharacteristic
179C2×C11#219511yescharacteristic
180C2×Q8—41no—
181C2×Q8—221no—
182C2×Q8—441no—
183C2×D4#432311yescharacteristic
184C22×C4—21no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188Q16—221no—
189Q16—221no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8D4×D1111yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—221no—
199C4⋊C4—222no—
200C4⋊C4—442no—
201C4⋊C4—441no—
202C4⋊C4—441no—
203C4⋊C4#432311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C42—442no—
208C42—441no—
209C42C2×C22⋊D1111yescharacteristic
210C16—441no—
211C16—441no—
212C11#1234511yescharacteristic, complemented, Sylow
213C23—21no—
214Q8—81no—
215Q8—81no—
216Q8—441no—
217Q8—441no—
218Q8—881no—
219Q8—881no—
220D4—21no—
221D4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—81no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4C2×#432311yescharacteristic
230C2×C4#6699011yescharacteristic
231C2×C4#6700211yescharacteristic
232C8—21no—
233C8—41no—
234C8—81no—
235C8#6696411yescharacteristic
236C8#6696511yescharacteristic
237C22—41no—
238C22—41no—
239C22—41no—
240C22#1062264911yescharacteristic
241C4—21no—
242C4—41no—
243C4—161no—
244C4—881no—
245C4—881no—
246C4—882no—
247C4#1062277111yescharacteristic
248C4#1062279211yescharacteristic
249C4#1062280711yescharacteristic
250C4#1062281411yescharacteristic
251C2—81no—
252C2#1306770311yescharacteristic
253C2#1307055411yescharacteristic
254C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1669C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenter#1669D11
hypocenterC11#12345
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1669

Complements

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

NH ≅ G/Ntype
2. #13070843C2semidirect
3. #13070663C2semidirect
4. #13066672C2semidirect
5. #13066579C2semidirect
212. C11#12345semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708432
#130706632
#130666722
#130665792
D4⋊(C11⋊C16)2
C11×#16692
#1234511