Finite Group Databasebeta

← #14780338

Subgroups — #14780338

Order 2816.

882 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 239 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#13068914C213yesmaximal, complemented
2#13068914C216yesmaximal, complemented
3#13068909C213yesmaximal, complemented
4#13068761C212yesmaximal, complemented
5C11×#2397C211yesmaximal, characteristic
6C2×C4×D4×C11C2213yes—
7C2×C4×D4×C11C2213yes—
8C22×#4318C2213yes—
9C23×C11⋊C8C2211yescharacteristic
10C11×#399C413yes—
11C11×#399C411yescharacteristic
12C11×#392C413yes—
13C11×#392C411yescharacteristic
14C11×#376C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2216yes—
16C2×C22⋊(C11⋊C8)C2213yes—
17C2×C22⋊(C11⋊C8)C2213yes—
18#10622162C2216yes—
19#10622162C2216yes—
20C22×D4×C11C2×C413yes—
21C22×D4×C11C2×C413yes—
22C23×C4×C11C2311yescharacteristic
23C23×C4×C11C2313yes—
24C4×D4×C11—43no—
25C4×D4×C11—43no—
26C4×D4×C11—43no—
27C4×D4×C11—43no—
28C2×C11×C4⋊C4C2×C413yes—
29C2×C11×C4⋊C4C2×C413yes—
30C2×C11×C22⋊C4C2×C413yes—
31C2×C11×C22⋊C4C2×C416yes—
32C2×C11×C22⋊C4C2×C413yes—
33C2×C42×C11C2313yes—
34C2×#4318—43no—
35C2×#4318—46no—
36C22×C11⋊C8—43no—
37C22×C11⋊C8C2312yes—
38C22×C11⋊C8C2316yes—
39C11×#95C2×C413yes—
40C11×#95C2×C411yescharacteristic
41C22⋊(C11⋊C8)—46no—
42C22⋊(C11⋊C8)—43no—
43C22⋊(C11⋊C8)—43no—
44#23359—111nomaximal, Sylow
45C24×C11C22×C413yes—
46C24×C11C22×C411yescharacteristic
47C2×D4×C11—26no—
48C2×D4×C11—43no—
49C2×D4×C11—43no—
50C2×D4×C11—43no—
51C2×D4×C11—46no—
52C22×C4×C11—23no—
53C22×C4×C11—26no—
54C22×C4×C11—23no—
55C22×C4×C11—23no—
56C22×C4×C11—23no—
57C22×C4×C11—26no—
58C22×C4×C11C22×C413yes—
59C22×C4×C11C22×C413yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C22×C413yes—
62C22×C4×C11C2411yescharacteristic
63C11×C4⋊C4—43no—
64C11×C4⋊C4—43no—
65C11×C22⋊C4—43no—
66C11×C22⋊C4—46no—
67C11×C22⋊C4—43no—
68C42×C11—23no—
69C42×C11—23no—
70#4318—412no—
71C2×C11⋊C8—26no—
72C2×C11⋊C8—26no—
73C2×C11⋊C8—26no—
74C2×C11⋊C8—26no—
75C2×C11⋊C8—44no—
76#2397D1111yescharacteristic
77#1870—113no—
78#1870—116no—
79#1869—113no—
80#1840—112no—
81C23×C11—23no—
82C23×C11—23no—
83C23×C11—23no—
84C23×C11—26no—
85C23×C11—23no—
86C23×C11—23no—
87C23×C11—26no—
88C23×C11#13112yes—
89C23×C11C23×C411yescharacteristic
90D4×C11—412no—
91D4×C11—412no—
92C2×C4×C11—23no—
93C2×C4×C11—23no—
94C2×C4×C11—23no—
95C2×C4×C11—23no—
96C2×C4×C11—26no—
97C2×C4×C11—23no—
98C2×C4×C11—23no—
99C2×C4×C11—26no—
100C2×C4×C11—41no—
101C2×C4×C11—43no—
102C2×C4×C11—43no—
103C2×C4×C11—43no—
104C2×C4×C11—46no—
105C2×C4×C11H(5,𝔽2)13yes—
106C2×C4×C11H(5,𝔽2)13yes—
107C11⋊C8—42no—
108C11⋊C8—46no—
109C22×M16—113no—
110C23×C8—111no—
111C2×C4×D4C2×D1113yes—
112C2×C4×D4C2×D1113yes—
113C2×C22⋊C8—116no—
114C2×C22⋊C8—113no—
115C2×C22⋊C8—113no—
116#399Dic1113yes—
117#399Dic1111yescharacteristic
118#392Dic1113yes—
119#392Dic1111yescharacteristic
120#376C2×D1111yescharacteristic
121#336—116no—
122#336—116no—
123C22×C11—26no—
124C22×C11—41no—
125C22×C11—43no—
126C22×C11—43no—
127C22×C11—43no—
128C22×C11—46no—
129C22×C11—46no—
130C22×C11—43no—
131C22×C11#51813yes—
132C22×C11C2×#13111yescharacteristic
133C22×C11#56813yes—
134C4×C11—41no—
135C4×C11—43no—
136C4×C11—43no—
137C4×C11—43no—
138C4×C11#56011yescharacteristic
139C4×C11#56013yes—
140C22×D4C2×Dic1113yes—
141C22×D4C2×Dic1113yes—
142C23×C4C22×D1111yescharacteristic
143C23×C4C22×D1113yes—
144C2×M16—443no—
145C2×M16—446no—
146C22×C8—112no—
147C22×C8—116no—
148C22×C8—443no—
149C4×D4—43no—
150C4×D4—43no—
151C4×D4—43no—
152C4×D4—43no—
153C2×C4⋊C4C2×Dic1113yes—
154C2×C4⋊C4C2×Dic1113yes—
155C2×C22⋊C4C2×Dic1113yes—
156C2×C22⋊C4C2×Dic1116yes—
157C2×C22⋊C4C2×Dic1113yes—
158C2×C42C22×D1113yes—
159C22⋊C8—446no—
160C22⋊C8—443no—
161C22⋊C8—443no—
162#95C2×Dic1113yes—
163#95C2×Dic1111yescharacteristic
164C2×C11—42no—
165C2×C11—83no—
166C2×C11#238011yescharacteristic
167C2×C11#297613yes—
168C2×C11#297813yes—
169C24C22×Dic1113yes—
170C24C22×Dic1111yescharacteristic
171C2×D4—26no—
172C2×D4—43no—
173C2×D4—43no—
174C2×D4—43no—
175C2×D4—46no—
176C22×C4—23no—
177C22×C4—26no—
178C22×C4—23no—
179C22×C4—23no—
180C22×C4—23no—
181C22×C4—26no—
182C22×C4C22×Dic1113yes—
183C22×C4C22×Dic1113yes—
184C22×C4C22×Dic1111yescharacteristic
185C22×C4C22×Dic1113yes—
186C22×C4C23×D1111yescharacteristic
187M16—4412no—
188C2×C8—226no—
189C2×C8—226no—
190C2×C8—226no—
191C2×C8—226no—
192C2×C8—444no—
193C4⋊C4—43no—
194C4⋊C4—43no—
195C22⋊C4—43no—
196C22⋊C4—46no—
197C22⋊C4—43no—
198C42—23no—
199C42—23no—
200C11#2335911yescharacteristic, complemented, Sylow
201C23—23no—
202C23—23no—
203C23—23no—
204C23—26no—
205C23—23no—
206C23—23no—
207C23—26no—
208C23#6700112yes—
209C23C23×Dic1111yescharacteristic
210D4—412no—
211D4—412no—
212C2×C4—23no—
213C2×C4—23no—
214C2×C4—23no—
215C2×C4—23no—
216C2×C4—26no—
217C2×C4—23no—
218C2×C4—23no—
219C2×C4—26no—
220C2×C4—41no—
221C2×C4—43no—
222C2×C4—43no—
223C2×C4—43no—
224C2×C4—46no—
225C2×C4#6703713yes—
226C2×C4#6703713yes—
227C8—442no—
228C8—446no—
229C22—26no—
230C22—43no—
231C22—41no—
232C22—43no—
233C22—46no—
234C22—46no—
235C22—43no—
236C22—43no—
237C22#1062332913yes—
238C22C2×#6700111yescharacteristic
239C22#1062335013yes—
240C4—43no—
241C4—43no—
242C4—41no—
243C4—43no—
244C4#1062325111yescharacteristic
245C4#1062325113yes—
246C2—42no—
247C2—83no—
248C2#1307179311yescharacteristic
249C2#1307766413yes—
250C2#1307767813yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
Fitting, prime radicalC11×#2397C2
cosocleC22×C4×C11C24
hypercenter#2397D11
hypocenterC11#23359
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13068914C2semidirect
2. #13068914C2semidirect
3. #13068909C2semidirect
4. #13068761C2semidirect
200. C11#23359semidirect

Maximal subgroups

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

subgroupindex
#130689142
#130689092
#130687612
C11×#23972
#2335911