Finite Group Databasebeta

← #14909502

Subgroups — #14909502

Order 2816.

694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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×#10622728C212yesmaximal, complemented
2#13070797C214yesmaximal, complemented
3#13070702C214yesmaximal, complemented
4#13070530C214yesmaximal, complemented
5C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7C2×#66983—22no—
8C22×D88C2212yescomplemented
9C22×C11×C16C2212yescomplemented
10#10622728—22no—
11#10622728—22no—
12#10622728C2214yes—
13#10622728C2214yescomplemented
14C2×#66885—22no—
15C2×#66882C2212yescomplemented
16C2×D176C2214yescomplemented
17C11×C22⋊C16C2214yescomplemented
18#10622147C2218yescomplemented
19#10622142C2214yescomplemented
20C23×C4×C11D411yescharacteristic
21C22×C22⋊D11—42no—
22C22×D44—22no—
23C22×C8×C11—42no—
24C22×C8×C11D412yes—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11C2312yes—
27C22×C8×C11C2311yescharacteristic
28#66983—24no—
29#66983—24no—
30#66983—42no—
31#66983—42no—
32C2×(C2×D11)⋊C4—42no—
33C2×C4⋊Dic11—22no—
34C2×D88—22no—
35C2×D88—44no—
36C2×D88C2314yes—
37C2×C11×C16—42no—
38C2×C11×C16C2314yes—
39#66885—24no—
40#66885—24no—
41#66882—22no—
42#66882C2314yes—
43D176—44no—
44#33752—111nomaximal, Sylow
45C24×C11D811yescharacteristic
46C23×D11—42no—
47C22×C4×C11—41no—
48C22×C4×C11—41no—
49C22×C4×C11D812yes—
50C22×C4×C11D811yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×C4×C11C2×D411yescharacteristic
53C2×C22⋊D11—44no—
54C2×C22⋊D11—44no—
55C2×C22⋊D11—88no—
56C22×Dic11—42no—
57C2×D44—24no—
58C2×D44—44no—
59C2×D44—44no—
60C2×D44—42no—
61C2×C8×C11—22no—
62C2×C8×C11—24no—
63C2×C8×C11—42no—
64C2×C8×C11—41no—
65C2×C8×C11C2×D412yes—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2411yescharacteristic
68(C2×D11)⋊C4—44no—
69(C2×D11)⋊C4—44no—
70C4⋊Dic11—24no—
71C4⋊Dic11—42no—
72D88—28no—
73D88—44no—
74C11×C16—24no—
75C2×#466—112no—
76#2232—114no—
77#2215—114no—
78#2184—114no—
79C2×C22⋊C16D1111yescharacteristic, complemented
80C23×C11—41no—
81C23×C11—41no—
82C23×C11D1614yescomplemented
83C23×C11C2×D812yes—
84C23×C11C2×D811yescharacteristic
85C22×D11—44no—
86C22×D11—84no—
87C22×D11—84no—
88C22×D11—84no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11C2×D812yes—
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11C22×D411yescharacteristic
98C22⋊D11—88no—
99C22⋊D11—88no—
100C2×Dic11—44no—
101C2×Dic11—84no—
102D44—44no—
103D44—44no—
104D44—84no—
105C8×C11—22no—
106C8×C11—21no—
107C8×C11H(5,𝔽2)12yes—
108C22×D8—112no—
109C23×C8C2×D1111yescharacteristic
110C2×#121—222no—
111C2×D16—114no—
112C22×C16C2×D1112yescomplemented
113#466—114no—
114#466—114no—
115#466—222no—
116#466—222no—
117C2×#107—112no—
118C2×#102—222no—
119#366—114no—
120#357—118no—
121C22⋊C16C2×D1114yescomplemented
122C22×C11—22no—
123C22×C11—21no—
124C22×C11—22no—
125C22×C11—21no—
126C22×C11—44no—
127C22×C11C2×D1614yes—
128C22×C11C2×D1612yes—
129C22×C11C22×D811yescharacteristic
130C2×D11—84no—
131C2×D11—84no—
132C2×D11—84no—
133C2×D11—168no—
134C4×C11—21no—
135C4×C11—22no—
136C4×C11#53411yescharacteristic
137C4×C11#57511yescharacteristic
138Dic11—84no—
139C22×D4—222no—
140C22×D4—442no—
141C23×C4D4411yescharacteristic
142C2×D8—114no—
143C2×D8—222no—
144C2×D8—444no—
145C22×C8—42no—
146C22×C8D4412yes—
147C22×C8D4411yescharacteristic
148C22×C8C22×D1112yes—
149C22×C8C22×D1111yescharacteristic
150#121—224no—
151#121—224no—
152#121—442no—
153#121—442no—
154C2×C4⋊C4—222no—
155C2×C22⋊C4—442no—
156D16—444no—
157C2×C16—42no—
158C2×C16C22×D1114yes—
159#107—114no—
160#107—222no—
161#102—224no—
162#102—224no—
163C2×C11—24no—
164C2×C11—22no—
165C2×C11#318611yescharacteristic
166C2×C11C22×D1611yescharacteristic
167C2×C11#341411yescharacteristic
168D11—164no—
169C24—442no—
170C24D8811yescharacteristic
171C2×D4—224no—
172C2×D4—444no—
173C2×D4—444no—
174C2×D4—444no—
175C2×D4—444no—
176C2×D4—442no—
177C2×D4—888no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—442no—
181C22×C4D8812yes—
182C22×C4D8811yescharacteristic
183C22×C4C2×D4412yes—
184C22×C4C2×D4411yescharacteristic
185D8—228no—
186D8—444no—
187C2×C8—22no—
188C2×C8—24no—
189C2×C8—41no—
190C2×C8—42no—
191C2×C8C2×D4411yescharacteristic
192C2×C8C2×D4412yes—
193C2×C8C23×D1111yescharacteristic
194C4⋊C4—224no—
195C4⋊C4—442no—
196C22⋊C4—444no—
197C22⋊C4—444no—
198C16—24no—
199C11#3375211yescharacteristic, complemented, Sylow
200C23—41no—
201C23—41no—
202C23—444no—
203C23—884no—
204C23—884no—
205C23—884no—
206C23D17614yescomplemented
207C23C2×D8812yes—
208C23C2×D8811yescharacteristic
209D4—444no—
210D4—444no—
211D4—884no—
212D4—888no—
213D4—888no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—444no—
221C2×C4—884no—
222C2×C4C2×D8811yescharacteristic
223C2×C4C2×D8812yes—
224C2×C4C22×D4411yescharacteristic
225C8—22no—
226C8—21no—
227C8#6703712yes—
228C22—22no—
229C22—21no—
230C22—22no—
231C22—21no—
232C22—44no—
233C22—884no—
234C22—884no—
235C22—884no—
236C22—1768no—
237C22C2×D17614yes—
238C22C2×D17612yes—
239C22C22×D8811yescharacteristic
240C4—22no—
241C4—21no—
242C4—884no—
243C4#1062302411yescharacteristic
244C4#1062327911yescharacteristic
245C2—24no—
246C2—22no—
247C2—1764no—
248C2#1307936711yescharacteristic
249C2C22×D17611yescharacteristic
250C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11C22×D8
hypercenterC2×C22⋊C16D11
hypocenterC11#33752
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×#10622728C2semidirect
2. #13070797C2semidirect
3. #13070702C2semidirect
4. #13070530C2semidirect
5. C2×C11×C22⋊C16C2semidirect
8. C22×D88C22semidirect
9. C22×C11×C16C22semidirect
13. #10622728C22semidirect
15. C2×#66882C22semidirect
16. C2×D176C22semidirect
17. C11×C22⋊C16C22semidirect
18. #10622147C22semidirect
19. #10622142C22semidirect
79. C2×C22⋊C16D11semidirect
82. C23×C11D16semidirect
112. C22×C16C2×D11semidirect
121. C22⋊C16C2×D11semidirect
199. C11#33752semidirect
206. C23D176semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
#130707972
#130707022
#130705302
C2×C11×C22⋊C162
#3375211