Finite Group Databasebeta

← #14674413

Subgroups — #14674413

Order 2816.

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

normal subgroups only

This group has 334 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, complemented
2C2×D352C211yesmaximal, characteristic, complemented
3C2×#10622157C211yesmaximal, characteristic, complemented
4#13070703C211yesmaximal, characteristic, complemented
5#13066793C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic, complemented
7C11×#1415C211yesmaximal, characteristic, complemented
8C2×D8×D11—21no—
9C2×C11×D16C2211yescharacteristic
10C2×#66890—21no—
11D11×D16—22no—
12D11×D16—22no—
13C2×D176C2211yescharacteristic
14C2×D176C2211yescharacteristic, complemented
15C2×C16×D11C2211yescharacteristic
16#10622496—21no—
17C2×C11×C32C2211yescharacteristic, complemented
18C11×#366C2211yescharacteristic, complemented
19#10622157—22no—
20C2×C11⋊C32C2211yescharacteristic, complemented
21#10622129—21no—
22D352—22no—
23C2×D4×D11—41no—
24C2×C11×D8—21no—
25C2×#4323—41no—
26D8×D11—24no—
27D8×D11—42no—
28C2×D88—21no—
29C2×D88—21no—
30C2×C8×D11D411yescharacteristic
31#66948—41no—
32C11×D16—21no—
33C11×D16D412yescomplemented
34C2×C11×C16C2311yescharacteristic
35C11×#107—21no—
36#66890—24no—
37C2×C11⋊C16D411yescharacteristic
38#66873—41no—
39D176—21no—
40D176—21no—
41D176—21no—
42D176D412yescomplemented
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13661—111nomaximal, Sylow
48C23×D11—81no—
49C2×D4×C11—41no—
50C2×C22⋊D11—81no—
51D4×D11—44no—
52D4×D11—82no—
53C2×D44—41no—
54C2×D44—41no—
55C2×D44—81no—
56C2×C4×D11D811yescharacteristic
57C11×D8—22no—
58C11×D8—41no—
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—41no—
61#4323—44no—
62(C2×D11)⋊C4—81no—
63C2×C11⋊C8D811yescharacteristic
64D88—22no—
65D88—41no—
66D88—41no—
67D88—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C22×D16—111no—
74C2×D32—111no—
75C2×D32—111no—
76#2215—111no—
77#1415—111no—
78#1415D1111yescharacteristic, complemented
79C22⋊C32—111no—
80C23×C11—81no—
81C22×D11—84no—
82C22×D11—81no—
83C22×D11—81no—
84C22×D11—162no—
85C22×D11—162no—
86C22×D11D1611yescharacteristic
87D4×C11—42no—
88D4×C11—81no—
89C2×C4×C11—81no—
90C2×C4×C11C2×D811yescharacteristic
91C22⋊D11—84no—
92C2×Dic11D1611yescharacteristic
93D44—42no—
94D44—81no—
95D44—81no—
96D44—81no—
97D44—162no—
98C4×D11—21no—
99C4×D11—21no—
100C8×C11#12011yescharacteristic
101C8×C11AGL(1,ℤ/8)11yescharacteristic
102C11⋊C8—21no—
103C22×D8—221no—
104C2×D16—111no—
105C2×D16—111no—
106C2×D16—221no—
107C2×D16—222no—
108C2×D16—222no—
109C2×D16C2×D1111yescharacteristic
110C22×C16—111no—
111#466—221no—
112D32—222no—
113D32—222no—
114C2×C32—111no—
115C2×C32C2×D1111yescharacteristic, complemented
116#366C2×D1111yescharacteristic, complemented
117#357—221no—
118C22×C11—82no—
119C22×C11—161no—
120C22×C11—161no—
121C22×C11C2×D1611yescharacteristic
122C2×D11—21no—
123C2×D11—21no—
124C2×D11—82no—
125C2×D11—168no—
126C2×D11—161no—
127C2×D11—161no—
128C2×D11—161no—
129C2×D11—161no—
130C2×D11—161no—
131C2×D11D3212yescomplemented
132C4×C11—161no—
133C4×C11#44711yescharacteristic
134C4×C11#50911yescharacteristic
135Dic11—21no—
136C22×D4—441no—
137C2×D8—21no—
138C2×D8—224no—
139C2×D8—221no—
140C2×D8—221no—
141C2×D8—441no—
142C2×D8—442no—
143C22×C8—111no—
144#121—441no—
145D16—21no—
146D16—112no—
147D16—224no—
148D16—221no—
149D16—221no—
150D16—221no—
151D16D4412yescomplemented
152C2×C16—111no—
153C2×C16—221no—
154C2×C16—221no—
155C2×C16C22×D1111yescharacteristic
156#107—21no—
157#102—441no—
158C32—21no—
159C32—221no—
160C2×C11—162no—
161C2×C11#218411yescharacteristic
162C2×C11C2×D3211yescharacteristic
163C2×C11#226311yescharacteristic
164D11—22no—
165D11—162no—
166D11—321no—
167C24—881no—
168C2×D4—41no—
169C2×D4—444no—
170C2×D4—441no—
171C2×D4—441no—
172C2×D4—881no—
173C2×D4—881no—
174C2×D4—882no—
175C22×C4—111no—
176D8—22no—
177D8—41no—
178D8—222no—
179D8—444no—
180D8—441no—
181D8—441no—
182D8—441no—
183C2×C8—111no—
184C2×C8—221no—
185C2×C8—221no—
186C2×C8D4×D1111yescharacteristic
187C4⋊C4—41no—
188C22⋊C4—881no—
189C16—221no—
190C16C2×D4411yescharacteristic
191C16D4×D1111yescharacteristic
192C11#1366111yescharacteristic, complemented, Sylow
193C23—81no—
194C23—111no—
195C23—884no—
196C23—881no—
197C23—881no—
198C23—1762no—
199C23—1762no—
200D4—42no—
201D4—81no—
202D4—442no—
203D4—884no—
204D4—881no—
205D4—881no—
206D4—881no—
207D4—1762no—
208C2×C4—81no—
209C2×C4—111no—
210C2×C4—221no—
211C2×C4—221no—
212C2×C4D8×D1111yescharacteristic
213C8—221no—
214C8#6693511yescharacteristic
215C8#6696711yescharacteristic
216C22—82no—
217C22—112no—
218C22—161no—
219C22—161no—
220C22—221no—
221C22—221no—
222C22—882no—
223C22—1768no—
224C22—1761no—
225C22—1761no—
226C22—1761no—
227C22—1761no—
228C22—1761no—
229C22D11×D1611yescharacteristic
230C4—161no—
231C4—221no—
232C4#1062238611yescharacteristic
233C4#1062252711yescharacteristic
234C2—162no—
235C2—222no—
236C2—3521no—
237C2—1762no—
238C2#1307052911yescharacteristic
239C2D11×D3211yescharacteristic
240C2#1307093011yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1415C2
socleC22×C11C2×D16
hypercenter#1415D11
hypocenterC11#13661
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×D11×D16C2semidirect
2. C2×D352C2semidirect
3. C2×#10622157C2semidirect
4. #13070703C2semidirect
5. #13066793C2semidirect
6. (C2×D11)⋊C32C2semidirect
7. C11×#1415C2semidirect
14. C2×D176C22semidirect
17. C2×C11×C32C22semidirect
18. C11×#366C22semidirect
20. C2×C11⋊C32C22semidirect
33. C11×D16D4semidirect
42. D176D4semidirect
78. #1415D11semidirect
115. C2×C32C2×D11semidirect
116. #366C2×D11semidirect
131. C2×D11D32semidirect
151. D16D44semidirect
192. C11#13661semidirect

Maximal subgroups

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

subgroupindex
C2×D11×D162
C2×D3522
C2×#106221572
#130707032
#130667932
(C2×D11)⋊C322
C11×#14152
#1366111