Finite Group Databasebeta

← #14674427

Subgroups — #14674427

Order 2816.

324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×D11×D16C211yesmaximal, characteristic
2C2×#10622159C211yesmaximal, characteristic, complemented
3#13070704C211yesmaximal, characteristic, complemented
4#13066795C211yesmaximal, characteristic, complemented
5#13066794C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic, complemented
7C2×C11×SD64C211yesmaximal, characteristic, complemented
8C2×D8×D11—21no—
9C2×C11×Q32C2211yescharacteristic, complemented
10C2×C11×D16C2211yescharacteristic
11#10622801—21no—
12C2×#66890—21no—
13D11×D16—22no—
14D11×D16—22no—
15C2×D176C2211yescharacteristic
16C2×C16×D11C2211yescharacteristic
17C11×SD64—22no—
18C2×C11×C32C2211yescharacteristic, complemented
19#10622202—21no—
20#10622159—22no—
21#10622142C2211yescharacteristic, complemented
22C2×C11⋊C32C2211yescharacteristic, complemented
23C2×D4×D11—41no—
24C2×C11×Q16—21no—
25C2×C11×D8—21no—
26#66999—41no—
27C2×#4323—41no—
28D8×D11—24no—
29D8×D11—42no—
30C2×D88—21no—
31C2×C8×D11D411yescharacteristic
32C11×Q32—21no—
33C11×Q32—21no—
34C11×D16—21no—
35C11×D16D412yes—
36C2×C11×C16C2311yescharacteristic
37#66899—41no—
38#66890—24no—
39#66882—21no—
40C2×C11⋊C16D411yescharacteristic
41D176—21no—
42D176D412yes—
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13664—111nomaximal, Sylow
48C23×D11—81no—
49C2×Q8×C11—41no—
50C2×D4×C11—41no—
51C2×C22⋊D11—81no—
52D4×D11—44no—
53D4×D11—82no—
54C2×D44—41no—
55C2×C4×D11D811yescharacteristic
56C11×Q16—41no—
57C11×Q16—41no—
58C11×D8—22no—
59C11×D8—41no—
60C2×C8×C11C2×D411yescharacteristic
61#4323—44no—
62(C2×D11)⋊C4—81no—
63C4⋊Dic11—41no—
64Dic11⋊C4—81no—
65C2×C11⋊C8D811yescharacteristic
66D88—22no—
67D88—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C22×D16—111no—
74C2×SD64—111no—
75C2×SD64D1111yescharacteristic, complemented
76#2216—111no—
77#1415—111no—
78#1415—111no—
79C22⋊C32—111no—
80C23×C11—81no—
81C22×D11—84no—
82C22×D11—81no—
83C22×D11—162no—
84C22×D11—162no—
85C22×D11D1611yescharacteristic
86Q8×C11—81no—
87Q8×C11—81no—
88D4×C11—42no—
89D4×C11—81no—
90C2×C4×C11—81no—
91C2×C4×C11C2×D811yescharacteristic
92C22⋊D11—84no—
93C2×Dic11—81no—
94C2×Dic11D1611yescharacteristic
95D44—42no—
96D44—81no—
97C4×D11—21no—
98C4×D11—21no—
99C8×C11#12011yescharacteristic
100C8×C11AGL(1,ℤ/8)11yescharacteristic
101C11⋊C8—21no—
102C22×D8—221no—
103C2×Q32C2×D1111yescharacteristic, complemented
104C2×D16—111no—
105C2×D16—221no—
106C2×D16—222no—
107C2×D16—222no—
108C2×D16C2×D1111yescharacteristic
109C22×C16—111no—
110#467—221no—
111SD64—22no—
112SD64—222no—
113C2×C32—111no—
114C2×C32C2×D1111yescharacteristic, complemented
115#366—111no—
116#358—221no—
117C22×C11—82no—
118C22×C11—161no—
119C22×C11—161no—
120C22×C11C2×D1611yescharacteristic
121C2×D11—21no—
122C2×D11—21no—
123C2×D11—82no—
124C2×D11—168no—
125C2×D11—161no—
126C2×D11—161no—
127C2×D11SD6412yescomplemented
128C4×C11—161no—
129C4×C11#44711yescharacteristic
130C4×C11#50911yescharacteristic
131Dic11—21no—
132Dic11—161no—
133C22×D4—441no—
134C2×Q16—21no—
135C2×D8—21no—
136C2×D8—224no—
137C2×D8—221no—
138C2×D8—441no—
139C2×D8—442no—
140C22×C8—111no—
141C22⋊Q8—441no—
142Q32—21no—
143Q32—21no—
144D16—21no—
145D16—112no—
146D16—224no—
147D16—221no—
148D16C22⋊D1112yes—
149C2×C16—111no—
150C2×C16—221no—
151C2×C16—221no—
152C2×C16C22×D1111yescharacteristic
153#107—221no—
154#103—441no—
155C32—21no—
156C32—221no—
157C2×C11—162no—
158C2×C11#218411yescharacteristic
159C2×C11C2×SD6411yescharacteristic
160C2×C11#226311yescharacteristic
161D11—22no—
162D11—162no—
163C24—881no—
164C2×Q8—41no—
165C2×D4—41no—
166C2×D4—444no—
167C2×D4—441no—
168C2×D4—881no—
169C2×D4—882no—
170C22×C4—111no—
171Q16—41no—
172Q16—41no—
173D8—22no—
174D8—41no—
175D8—222no—
176D8—444no—
177D8—441no—
178C2×C8—111no—
179C2×C8—221no—
180C2×C8—221no—
181C2×C8D4×D1111yescharacteristic
182C4⋊C4—441no—
183C4⋊C4—881no—
184C22⋊C4—881no—
185C16—221no—
186C16D4×D1111yescharacteristic
187C16C2×C22⋊D1111yescharacteristic
188C11#1366411yescharacteristic, complemented, Sylow
189C23—81no—
190C23—111no—
191C23—884no—
192C23—881no—
193C23—1762no—
194C23—1762no—
195Q8—81no—
196Q8—81no—
197D4—42no—
198D4—81no—
199D4—442no—
200D4—884no—
201D4—881no—
202C2×C4—81no—
203C2×C4—111no—
204C2×C4—221no—
205C2×C4—221no—
206C2×C4—881no—
207C2×C4D8×D1111yescharacteristic
208C8—221no—
209C8#6696411yescharacteristic
210C8#6699011yescharacteristic
211C22—82no—
212C22—112no—
213C22—161no—
214C22—161no—
215C22—221no—
216C22—221no—
217C22—882no—
218C22—1768no—
219C22—1761no—
220C22—1761no—
221C22D11×D1611yescharacteristic
222C4—161no—
223C4—221no—
224C4—1761no—
225C4#1062252411yescharacteristic
226C4#1062276911yescharacteristic
227C2—162no—
228C2—222no—
229C2—1762no—
230C2#1307052611yescharacteristic
231C2D11×SD6411yescharacteristic
232C2#1307093011yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×SD64C2
socleC22×C11C2×D16
prime radicalC2×D11×D16C2
hypercenterC2×SD64D11
hypocenterC11#13664
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
2. C2×#10622159C2semidirect
3. #13070704C2semidirect
4. #13066795C2semidirect
5. #13066794C2semidirect
6. (C2×D11)⋊C32C2semidirect
7. C2×C11×SD64C2semidirect
9. C2×C11×Q32C22semidirect
18. C2×C11×C32C22semidirect
21. #10622142C22semidirect
22. C2×C11⋊C32C22semidirect
75. C2×SD64D11semidirect
103. C2×Q32C2×D11semidirect
114. C2×C32C2×D11semidirect
127. C2×D11SD64semidirect
188. C11#13664semidirect

Maximal subgroups

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

subgroupindex
C2×D11×D162
C2×#106221592
#130707042
#130667952
#130667942
(C2×D11)⋊C322
C2×C11×SD642
#1366411