Finite Group Databasebeta

← #14909526

Subgroups — #14909526

Order 2816.

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

normal subgroups only

This group has 590 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×#10622729C212yesmaximal
2#13070819C214yesmaximal, complemented
3#13070707C214yesmaximal, complemented
4#13070552C214yesmaximal, complemented
5C2×C11×C22⋊C16C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C2×#66977—22no—
8C22×Dic44C2212yes—
9C22×C11×C16C2212yes—
10#10622729—22no—
11#10622729—22no—
12#10622729C2214yes—
13#10622729C2214yes—
14C2×#66882C2212yes—
15C2×#66880—22no—
16C2×Dic88C2214yescomplemented
17C11×C22⋊C16C2214yes—
18#10622142C2214yescomplemented
19#10622141C2218yescomplemented
20C23×C4×C11D411yescharacteristic
21C22×Dic22—22no—
22C22×C8×C11—42no—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11D412yes—
25C22×C8×C11C2311yescharacteristic
26C22×C8×C11C2312yes—
27C2×C22⋊Dic11—42no—
28C2×C4⋊Dic11—22no—
29#66977—24no—
30#66977—24no—
31#66977—42no—
32#66977—42no—
33C2×Dic11⋊C4—42no—
34C2×Dic44—22no—
35C2×Dic44—44no—
36C2×Dic44C2314yes—
37C2×C11×C16—42no—
38C2×C11×C16C2314yes—
39#66882—22no—
40#66882C2314yes—
41#66880—24no—
42#66880—24no—
43Dic88—44no—
44#33755—111nomaximal, Sylow
45C24×C11D811yescharacteristic
46C22×C4×C11—41no—
47C22×C4×C11—41no—
48C22×C4×C11D812yes—
49C22×C4×C11D811yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—42no—
53C22×Dic11—42no—
54C2×Dic22—24no—
55C2×Dic22—44no—
56C2×Dic22—44no—
57C2×Dic22—42no—
58C2×C8×C11—22no—
59C2×C8×C11—24no—
60C2×C8×C11—42no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D412yes—
64C2×C8×C11C2411yescharacteristic
65C22⋊Dic11—44no—
66C22⋊Dic11—44no—
67C4⋊Dic11—24no—
68C4⋊Dic11—42no—
69Dic11⋊C4—44no—
70Dic11⋊C4—44no—
71Dic44—28no—
72Dic44—44no—
73C11×C16—24no—
74C2×#467—112no—
75#2236—114no—
76#2216—114no—
77#2188—114no—
78C2×C22⋊C16D1111yescharacteristic
79C23×C11—41no—
80C23×C11—41no—
81C23×C11Q3214yescomplemented
82C23×C11C2×D811yescharacteristic
83C23×C11C2×D812yes—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11—41no—
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11C2×D812yes—
92C2×C4×C11C22×D411yescharacteristic
93C2×Dic11—44no—
94C2×Dic11—44no—
95C2×Dic11—84no—
96C2×Dic11—84no—
97Dic22—44no—
98Dic22—44no—
99Dic22—84no—
100C8×C11—22no—
101C8×C11—21no—
102C8×C11H(5,𝔽2)12yes—
103C22×Q16—112no—
104C23×C8C2×D1111yescharacteristic
105C2×C22⋊Q8—222no—
106C2×Q32—114no—
107C22×C16C2×D1112yes—
108#467—114no—
109#467—114no—
110#467—222no—
111#467—222no—
112C2×#107—112no—
113C2×#103—222no—
114#366—114no—
115#358—118no—
116C22⋊C16C2×D1114yes—
117C22×C11—21no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—22no—
121C22×C11—44no—
122C22×C11C2×Q3212yes—
123C22×C11C2×Q3214yes—
124C22×C11C22×D811yescharacteristic
125C4×C11—21no—
126C4×C11—22no—
127C4×C11#53411yescharacteristic
128C4×C11#57511yescharacteristic
129Dic11—84no—
130Dic11—84no—
131C22×Q8—222no—
132C23×C4D4411yescharacteristic
133C2×Q16—114no—
134C2×Q16—222no—
135C2×Q16—444no—
136C22×C8—42no—
137C22×C8D4412yes—
138C22×C8D4411yescharacteristic
139C22×C8C22×D1112yes—
140C22×C8C22×D1111yescharacteristic
141C22⋊Q8—224no—
142C22⋊Q8—224no—
143C22⋊Q8—442no—
144C22⋊Q8—442no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—442no—
147C2×C22⋊C4—442no—
148Q32—444no—
149C2×C16—42no—
150C2×C16C22×D1114yes—
151#107—114no—
152#107—222no—
153#103—224no—
154#103—224no—
155C2×C11—22no—
156C2×C11—24no—
157C2×C11#318611yescharacteristic
158C2×C11C22×Q3211yescharacteristic
159C2×C11#341411yescharacteristic
160C24D8811yescharacteristic
161C2×Q8—224no—
162C2×Q8—444no—
163C2×Q8—444no—
164C2×Q8—442no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—442no—
168C22×C4—442no—
169C22×C4D8812yes—
170C22×C4D8811yescharacteristic
171C22×C4C2×D4412yes—
172C22×C4C2×D4411yescharacteristic
173Q16—228no—
174Q16—444no—
175C2×C8—22no—
176C2×C8—24no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8C2×D4411yescharacteristic
180C2×C8C2×D4412yes—
181C2×C8C23×D1111yescharacteristic
182C4⋊C4—224no—
183C4⋊C4—442no—
184C4⋊C4—444no—
185C4⋊C4—444no—
186C22⋊C4—444no—
187C22⋊C4—444no—
188C16—24no—
189C11#3375511yescharacteristic, complemented, Sylow
190C23—41no—
191C23—41no—
192C23Dic8814yescomplemented
193C23C2×D8811yescharacteristic
194C23C2×D8812yes—
195Q8—444no—
196Q8—444no—
197Q8—884no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—444no—
205C2×C4—444no—
206C2×C4—884no—
207C2×C4—884no—
208C2×C4C2×D8811yescharacteristic
209C2×C4C2×D8812yes—
210C2×C4C22×D4411yescharacteristic
211C8—22no—
212C8—21no—
213C8#6703712yes—
214C22—22no—
215C22—21no—
216C22—22no—
217C22—21no—
218C22—44no—
219C22C2×Dic8812yes—
220C22C2×Dic8814yes—
221C22C22×D8811yescharacteristic
222C4—22no—
223C4—21no—
224C4—884no—
225C4—884no—
226C4#1062302411yescharacteristic
227C4#1062327911yescharacteristic
228C2—24no—
229C2—22no—
230C2#1307936711yescharacteristic
231C2C22×Dic8811yescharacteristic
232C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11C22×D8
prime radicalC24×C11D8
hypercenterC2×C22⋊C16D11
hypocenterC11#33755
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
2. #13070819C2semidirect
3. #13070707C2semidirect
4. #13070552C2semidirect
16. C2×Dic88C22semidirect
18. #10622142C22semidirect
19. #10622141C22semidirect
81. C23×C11Q32semidirect
189. C11#33755semidirect
192. C23Dic88semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
#130708192
#130707072
#130705522
C2×C11×C22⋊C162
#3375511