Finite Group Databasebeta

← #14767663

Subgroups — #14767663

Order 2816.

810 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 211 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#13079044C211yesmaximal, characteristic
2#13077335C212yesmaximal, complemented
3#13069448C212yesmaximal, complemented
4#13068942C218yesmaximal, complemented
5#13068754C211yesmaximal, characteristic, complemented
6C11×#1746C211yesmaximal, characteristic, complemented
7C2×#66957C2214yes—
8C2×#66954C2214yes—
9#10623008C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622723C2214yes—
14C2×#66869C2218yes—
15#10622537C2212yes—
16#10622319—28no—
17#10622312C411yescharacteristic, complemented
18#10622309C414yescomplemented
19#10622308C411yescharacteristic, complemented
20#10622306C412yescomplemented
21C11×#336C2214yes—
22#10622190C2214yes—
23C2×#4339C2314yes—
24C22×C8×C11C2312yes—
25C22×C8×C11C2312yes—
26C2×C42×C11C2312yes—
27C2×C42×C11C2311yescharacteristic
28#66983—24no—
29C2×#4318C2314yes—
30C2×Dic44C2×C414yes—
31#66957—48no—
32C2×D88C2×C414yes—
33C2×#4314C2×C418yes—
34#66954—48no—
35C2×#4313—24no—
36C2×C8×D11—24no—
37#66928C2×C414yes—
38#66927C2×C412yes—
39C4×D44—24no—
40#66922C2×C412yes—
41C11×#97D414yes—
42C4×C8×C11C2×C411yescharacteristic
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11C2×C412yes—
45C11×#95—22no—
46(C2×D11)⋊C8—28no—
47#66869—48no—
48C4⋊(C11⋊C8)—24no—
49#22282—111nomaximal, Sylow
50C22×C4×C11—22no—
51C22×C4×C11#4112yes—
52C22×C4×C11C2411yescharacteristic
53C2×C22⋊D11—24no—
54#4339—28no—
55#4339—28no—
56C2×D44—24no—
57C2×D44C22×C414yes—
58C2×C4×D11—24no—
59C2×Dic22C22×C414yes—
60C2×C8×C11—24no—
61C2×C8×C11—24no—
62C2×C8×C11C22×C412yes—
63C2×C8×C11C22×C412yes—
64C2×C8×C11C2×D414yes—
65C42×C11—24no—
66C42×C11C22×C411yescharacteristic
67C42×C11C22×C411yescharacteristic
68C42×C11C2×D412yes—
69(C2×D11)⋊C4—28no—
70C4⋊Dic11—24no—
71#4318—28no—
72C2×C11⋊C8—24no—
73Dic44—44no—
74D88—44no—
75#4314—48no—
76#4313—48no—
77C8×D11—48no—
78#3147—111no—
79#2932—112no—
80#1963—112no—
81#1876—118no—
82#1837—111no—
83#1746D1111yescharacteristic, complemented
84C23×C11C2×#4111yescharacteristic
85C22×D11—24no—
86C2×C4×C11—42no—
87C2×C4×C11—44no—
88C2×C4×C11—42no—
89C2×C4×C11C4×D412yes—
90C2×C4×C11C4×D412yes—
91C2×C4×C11C23×C411yescharacteristic
92C2×C4×C11C22×D411yescharacteristic
93C2×C4×C11H(5,𝔽2)14yes—
94C22⋊D11—48no—
95C2×Dic11—24no—
96D44—28no—
97D44—84no—
98C4×D11—44no—
99C4×D11—44no—
100Dic22—28no—
101C8×C11—22no—
102C8×C11—22no—
103C8×C11—24no—
104C11⋊C8—44no—
105C2×#135—114no—
106C2×#131—114no—
107#532—112no—
108#495—114no—
109#494—111no—
110#493—111no—
111#492—112no—
112#435—228no—
113#423—112no—
114C2×#104—118no—
115#408—114no—
116C2×#97C2×D1111yescharacteristic
117C2×C4×C8C2×D1111yescharacteristic
118#376C2×D1111yescharacteristic
119#341—114no—
120#336C2×D1114yes—
121C22×C11—22no—
122C22×C11C2×C4×D411yescharacteristic
123C22×C11#54012yes—
124C2×D11—44no—
125C2×D11—48no—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—82no—
129C4×C11#51812yes—
130C4×C11#53512yes—
131Dic11—44no—
132C2×#41—114no—
133#135—448no—
134C2×Q16—114no—
135C2×SD16—118no—
136C2×D8—114no—
137#131—448no—
138C2×M16—114no—
139C2×M16—224no—
140C22×C8—224no—
141C22×C8C22×D1112yes—
142C22×C8C22×D1112yes—
143C4⋊Q8—112no—
144#127—112no—
145#124—114no—
146#121—224no—
147C4×D4—224no—
148C2×C42C22×D1112yes—
149C2×C42C22×D1111yescharacteristic
150C4⋊C8—224no—
151#104—448no—
152C22⋊C8—228no—
153#97D4414yes—
154C4×C8C4×D1111yescharacteristic
155C4×C8C4×D1111yescharacteristic
156C4×C8C4×D1112yes—
157#95—22no—
158C2×C11—22no—
159C2×C11#232811yescharacteristic
160C2×C11#295712yes—
161D11—84no—
162#41—228no—
163#41—228no—
164C2×Q8—114no—
165C2×D4—114no—
166C2×D4—224no—
167C2×D4—224no—
168C22×C4—22no—
169C22×C4—224no—
170C22×C4#433912yes—
171C22×C4C23×D1111yescharacteristic
172Q16—444no—
173SD16—448no—
174D8—444no—
175M16—228no—
176M16—448no—
177C2×C8—24no—
178C2×C8—24no—
179C2×C8—224no—
180C2×C8—448no—
181C2×C8C2×C4×D1112yes—
182C2×C8C2×C4×D1112yes—
183C2×C8C2×D4414yes—
184C4⋊C4—224no—
185C22⋊C4—228no—
186C42—24no—
187C42C2×C4×D1111yescharacteristic
188C42C2×C4×D1111yescharacteristic
189C42C2×D4412yes—
190C11#2228211yescharacteristic, complemented, Sylow
191C23—224no—
192C23C2×#433911yescharacteristic
193Q8—228no—
194D4—228no—
195D4—448no—
196D4—884no—
197C2×C4—42no—
198C2×C4—44no—
199C2×C4—42no—
200C2×C4—224no—
201C2×C4—444no—
202C2×C4—444no—
203C2×C4C4×D4412yes—
204C2×C4C4×D4412yes—
205C2×C4C22×C4×D1111yescharacteristic
206C2×C4C22×D4411yescharacteristic
207C2×C4#6704214yes—
208C8—22no—
209C8—22no—
210C8—24no—
211C8—444no—
212C22—22no—
213C22—448no—
214C22—444no—
215C22C2×C4×D4411yescharacteristic
216C22#1062306612yes—
217C4—22no—
218C4—22no—
219C4—82no—
220C4—444no—
221C4#1062305212yes—
222C4#1062305612yes—
223C2—22no—
224C2—884no—
225C2#1307134111yescharacteristic
226C2#1307753412yes—
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC22×C11C2×C4×D4
prime radical#13079044C2
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #13077335C2semidirect
3. #13069448C2semidirect
4. #13068942C2semidirect
5. #13068754C2semidirect
6. C11×#1746C2semidirect
17. #10622312C4semidirect
18. #10622309C4semidirect
19. #10622308C4semidirect
20. #10622306C4semidirect
83. #1746D11semidirect
190. C11#22282semidirect

Maximal subgroups

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

subgroupindex
#130790442
#130773352
#130694482
#130689422
#130687542
C11×#17462
#2228211