Finite Group Databasebeta

← #14651146

Subgroups — #14651146

Order 2816.

594 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 131 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#13077640C211yesmaximal, characteristic
2#13073569C211yesmaximal, characteristic
3#13067302C212yesmaximal, complemented
4#13066517C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—22no—
8C2×#66922C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#100—21no—
11#10622834—21no—
12C2×C22⋊(C11⋊C8)—22no—
13D4×C11⋊C8—24no—
14#10622589—21no—
15#10622562C414yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622538C2212yes—
18C11×#343—21no—
19#10622124—24no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D412yes—
22C22×Dic22—21no—
23C2×C11×M16—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—24no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33#66977—48no—
34C2×Dic11⋊C4—24no—
35C2×C4×Dic11—21no—
36C22×C11⋊C8—24no—
37#66922—22no—
38#66922—22no—
39C11×C4⋊C8—22no—
40C11×C4⋊C8—22no—
41C11×#100—42no—
42C11⋊#95C2×C412yes—
43C22⋊(C11⋊C8)—24no—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46C4×C11⋊C8—22no—
47#9395—111nomaximal, Sylow
48C24×C11C22⋊C412yes—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11SD1612yes—
52C2×D4×C11Q1612yes—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—44no—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—22no—
61C22×Dic11—22no—
62C2×Dic22—44no—
63C2×Dic22—41no—
64C2×Dic22—41no—
65C11×M16—42no—
66C11×M16—42no—
67C2×C8×C11—42no—
68C11×C4⋊C4—22no—
69C11×C22⋊C4—24no—
70C42×C11C2×D412yes—
71C42×C11#4112yes—
72C22⋊Dic11—48no—
73C4⋊Dic11—24no—
74C4⋊Dic11—24no—
75C4⋊Dic11—42no—
76Dic11⋊C4—48no—
77C4×Dic11—42no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—84no—
80#2972—111no—
81#2542—111no—
82#1800D1111yescharacteristic
83#1549—112no—
84#1303—112no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11#10314yes—
90C23×C11C2×C22⋊C411yescharacteristic
91D4×C11—24no—
92D4×C11—24no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—44no—
97C2×C4×C11—42no—
98C2×C4×C11—82no—
99C2×C4×C11C4×D412yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12311yescharacteristic
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11C2×Q1611yescharacteristic
105C2×C4×C11#13512yes—
106C2×Dic11—24no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—44no—
110C2×Dic11—42no—
111Dic22—82no—
112Dic22—82no—
113C8×C11—82no—
114C11⋊C8—44no—
115C2×C4⋊Q8—111no—
116C2×C22⋊Q8—222no—
117C2×C4×D4C2×D1111yescharacteristic
118C8×D4—224no—
119#431—112no—
120#423C2×D1112yes—
121C2×#100—21no—
122C2×C22⋊C8—222no—
123#399—114no—
124#390—221no—
125#384—221no—
126C4×C4⋊C4—111no—
127#343—21no—
128#332—224no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11—24no—
132C22×C11—44no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11—82no—
136C22×C11#38611yescharacteristic
137C22×C11C2×#10311yescharacteristic
138C22×C11#41611yescharacteristic
139C4×C11—21no—
140C4×C11—22no—
141C4×C11—42no—
142C4×C11#45312yes—
143C4×C11#46512yes—
144C4×C11#46712yes—
145Dic11—44no—
146Dic11—82no—
147C22×Q8—221no—
148C22×D4C22⋊D1111yescharacteristic
149C23×C4D4412yes—
150C2×M16—22no—
151C22×C8—224no—
152C4⋊Q8—222no—
153C4⋊Q8—222no—
154C22⋊Q8—448no—
155C4×D4—22no—
156C4×D4—22no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—221no—
159C2×C4⋊C4—224no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4C22⋊D1111yescharacteristic
162C2×C22⋊C4—224no—
163C2×C22⋊C4C4×D1112yes—
164C2×C42—221no—
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—114no—
169#100—42no—
170C22⋊C8—224no—
171C22⋊C8—222no—
172C4×C8—222no—
173#95—112no—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11—44no—
177C2×C11#188711yescharacteristic
178C2×C11#189211yescharacteristic
179C2×C11#191511yescharacteristic
180C24(C2×D11)⋊C412yes—
181C2×Q8—444no—
182C2×Q8—441no—
183C2×Q8—441no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4#432412yes—
187C2×D4#432612yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—44no—
191C22×C4—222no—
192C22×C4—222no—
193C22×C4(C2×D11)⋊C412yes—
194C22×C4C2×C4×D1111yescharacteristic
195C22×C4C2×D4411yescharacteristic
196C22×C4C2×C22⋊D1111yescharacteristic
197M16—42no—
198M16—42no—
199C2×C8—42no—
200C2×C8—224no—
201C2×C8—884no—
202C4⋊C4—22no—
203C4⋊C4—224no—
204C4⋊C4—224no—
205C4⋊C4—448no—
206C4⋊C4—442no—
207C22⋊C4—24no—
208C22⋊C4—448no—
209C42—442no—
210C42D4×D1112yes—
211C42#434112yes—
212C11#939511yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—42no—
216C23—42no—
217C23#6687414yes—
218C23C2×(C2×D11)⋊C411yescharacteristic
219Q8—882no—
220Q8—882no—
221D4—24no—
222D4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4—82no—
229C2×C4—224no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—444no—
233C2×C4—442no—
234C2×C4(C22⋊D11)⋊C412yes—
235C2×C4#6693511yescharacteristic
236C2×C4#6693911yescharacteristic
237C2×C4C2×#432411yescharacteristic
238C2×C4#6699212yes—
239C2×C4C2×#432611yescharacteristic
240C2×C4#6700312yes—
241C8—82no—
242C8—444no—
243C22—21no—
244C22—21no—
245C22—24no—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—82no—
250C22#1062257111yescharacteristic
251C22C2×#6687411yescharacteristic
252C22#1062261511yescharacteristic
253C4—22no—
254C4—21no—
255C4—42no—
256C4—444no—
257C4—882no—
258C4#1062236012yes—
259C4#1062265412yes—
260C4#1062266412yes—
261C2—21no—
262C2—21no—
263C2—44no—
264C2#1306901211yescharacteristic
265C2#1306903711yescharacteristic
266C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#9395
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13067302C2semidirect
4. #13066517C2semidirect
212. C11#9395semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130735692
#130673022
#130665172
C11×#18002
#939511