Finite Group Databasebeta

← #14656898

Subgroups — #14656898

Order 2816.

454 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 101 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#13069448C211yesmaximal, characteristic
2#13067110C212yesmaximal
3#13066519C212yesmaximal, complemented
4#13066445C211yesmaximal, characteristic, complemented
5C11×#2399C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11—21no—
7#10623008C2211yescharacteristic
8C11×#398—22no—
9C11×#395—22no—
10C4×C11×C4⋊C4—21no—
11C4×C11×C4⋊C4C2212yes—
12C11×#376C2211yescharacteristic
13C2×#66869—21no—
14C2×#66869—21no—
15#10622538C2212yes—
16#10622537C2211yescharacteristic
17#10622089—22no—
18#10622089—22no—
19C22×Q8×C11—21no—
20C2×#4339—21no—
21C4×Q8×C11—42no—
22C4×Q8×C11—42no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—22no—
27C2×C42×C11—22no—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66983—22no—
32C2×#4318—21no—
33#66928—21no—
34#66927Q811yescharacteristic, complemented
35C4×D44—22no—
36#66922Q811yescharacteristic, complemented
37C11×#95—21no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95D412yes—
41C11×#95D412yes—
42C22⋊(C11⋊C8)—22no—
43#66869—42no—
44#66869—42no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4×C11⋊C8—22no—
48#10370—111nomaximal, Sylow
49C2×Q8×C11—42no—
50C2×Q8×C11—44no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C2×C22⋊D11—41no—
58#4339—41no—
59#4339—41no—
60#4339—41no—
61#4339—41no—
62C2×D44—21no—
63C2×D44—22no—
64C2×C4×D11—41no—
65C2×Dic22—21no—
66C11×C4⋊C4—44no—
67C11×C4⋊C4—44no—
68C11×C4⋊C4—44no—
69C11×C4⋊C4—42no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—42no—
73C42×C11—42no—
74C42×C11D812yes—
75C42×C11SD1612yes—
76C42×C11C2×Q811yescharacteristic
77C42×C11#4112yes—
78C42×C11#4111yescharacteristic
79(C2×D11)⋊C4—42no—
80C4⋊Dic11—22no—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—41no—
85#2399D1111yescharacteristic, complemented
86#1963—111no—
87#1502—112no—
88#1303—112no—
89#1274—111no—
90C23×C11#12011yescharacteristic
91C22×D11—41no—
92Q8×C11—48no—
93C2×C4×C11—24no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11C22⋊Q812yes—
105C2×C4×C11C22⋊Q811yescharacteristic
106C2×C4×C11#12412yes—
107C2×C4×C11#12411yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11C2×SD1611yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C11#13711yescharacteristic
112C22⋊D11—81no—
113C22⋊D11—81no—
114C2×Dic11—41no—
115D44—41no—
116D44—41no—
117D44—82no—
118C4×D11—81no—
119C4×D11—81no—
120Dic22—41no—
121Dic22—41no—
122C11⋊C8—82no—
123C11⋊C8—81no—
124#532—111no—
125C2×C4×Q8—21no—
126#431—112no—
127#423—111no—
128C2×#104—221no—
129C2×#104—221no—
130#398—22no—
131#395—22no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4C2×D1112yes—
134#376C2×D1111yescharacteristic
135#327—222no—
136#327—222no—
137C22×C11—22no—
138C22×C11#39311yescharacteristic
139C22×C11#44711yescharacteristic
140C22×C11#44811yescharacteristic
141C2×D11—81no—
142C2×D11—82no—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—44no—
147C4×C11—42no—
148C4×C11—82no—
149C4×C11#47411yescharacteristic
150C4×C11#47611yescharacteristic
151C4×C11#48611yescharacteristic
152C4×C11#48911yescharacteristic
153Dic11—81no—
154C2×#41—221no—
155C22×Q8—21no—
156C2×M16—221no—
157C4⋊Q8—111no—
158#127—111no—
159#124—221no—
160#121—222no—
161C4×Q8—42no—
162C4×Q8—42no—
163C4×D4—222no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C42—22no—
169C2×C42C22⋊D1111yescharacteristic
170C2×C42C22⋊D1111yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—222no—
173C4⋊C8—222no—
174#104—442no—
175#104—442no—
176C22⋊C8—222no—
177C4×C8—222no—
178#95—21no—
179#95—21no—
180#95—22no—
181#95C22⋊D1112yes—
182#95C22⋊D1112yes—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#202311yescharacteristic
186C2×C11#203112yes—
187D11—161no—
188#41—441no—
189#41—441no—
190#41—441no—
191#41—441no—
192C2×Q8—42no—
193C2×Q8—44no—
194C2×Q8—221no—
195C2×D4—221no—
196C2×D4—222no—
197C2×D4—441no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—441no—
203C22×C4C2×C22⋊D1112yes—
204C22×C4C2×C22⋊D1111yescharacteristic
205M16—441no—
206M16—441no—
207C2×C8—442no—
208C2×C8—441no—
209C4⋊C4—44no—
210C4⋊C4—42no—
211C4⋊C4—44no—
212C4⋊C4—44no—
213C4⋊C4—222no—
214C22⋊C4—442no—
215C42—21no—
216C42—21no—
217C42—42no—
218C42—42no—
219C42#432312yes—
220C42#432512yes—
221C42Q8×D1111yescharacteristic
222C42#434311yescharacteristic
223C42#434312yes—
224C11#1037011yescharacteristic, complemented, Sylow
225C23—441no—
226C23#6700611yescharacteristic
227Q8—48no—
228Q8—441no—
229Q8—441no—
230D4—441no—
231D4—441no—
232D4—882no—
233D4—881no—
234D4—881no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—441no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4C2×#432311yescharacteristic
250C2×C4#6698511yescharacteristic
251C2×C4C2×#432511yescharacteristic
252C2×C4#6699511yescharacteristic
253C2×C4#6699912yes—
254C2×C4#6699911yescharacteristic
255C2×C4#6700012yes—
256C2×C4#6700011yescharacteristic
257C8—882no—
258C8—881no—
259C22—22no—
260C22—881no—
261C22—882no—
262C22#1062283011yescharacteristic
263C22#1062284011yescharacteristic
264C22#1062284411yescharacteristic
265C4—22no—
266C4—22no—
267C4—44no—
268C4—42no—
269C4—42no—
270C4—82no—
271C4—881no—
272C4#1062269711yescharacteristic
273C4#1062270011yescharacteristic
274C4#1062270111yescharacteristic
275C4#1062270211yescharacteristic
276C2—21no—
277C2—21no—
278C2—1761no—
279C2#1306974911yescharacteristic
280C2#1306978512yes—
subgroupG/H
centerC2×C4#67000
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2399C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#2399D11
hypocenterC11#10370
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
3. #13066519C2semidirect
4. #13066445C2semidirect
5. C11×#2399C2semidirect
34. #66927Q8semidirect
36. #66922Q8semidirect
85. #2399D11semidirect
224. C11#10370semidirect

Maximal subgroups

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

subgroupindex
#130694482
#130671102
#130665192
#130664452
C11×#23992
#1037011