Finite Group Databasebeta

← #14684827

Subgroups — #14684827

Order 2816.

1530 conjugacy classes of subgroups; only the 371 normal subgroups are shown.

normal subgroups only

This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 371 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
1C22×#66929C211yesmaximal, characteristic
2C2×#10622550C211yesmaximal, characteristic, complemented
3#13066866C216yesmaximal, complemented
4#13066858C216yesmaximal
5C2×C11×#384C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2216yes—
7C22×C42×C11C2211yescharacteristic
8C22×(C2×D11)⋊C4C2213yes—
9C22×(C2×D11)⋊C4C2214yes—
10C22×Dic11⋊C4C2213yes—
11C2×#66929—24no—
12C2×#66929—24no—
13C2×#66929C418yescomplemented
14C11×#384—24no—
15C2×C11⋊#95C2216yes—
16C2×C11⋊#95C22112yes—
17#10622550—24no—
18C24×D11C2311yescharacteristic
19C23×C4×C11C2314yes—
20C23×C4×C11C2313yes—
21C23×Dic11C2314yes—
22C23×Dic11C2313yes—
23C2×C11×C4⋊C4—212no—
24C2×C11×C4⋊C4—412no—
25C2×C42×C11C2×C414yes—
26C2×C42×C11D414yes—
27C2×C42×C11D414yes—
28C2×(C2×D11)⋊C4—26no—
29C2×(C2×D11)⋊C4—26no—
30C2×(C2×D11)⋊C4—412no—
31C2×(C2×D11)⋊C4C2×C4112yes—
32C2×Dic11⋊C4—26no—
33C2×Dic11⋊C4—26no—
34C2×Dic11⋊C4C2×C4112yes—
35#66929—232no—
36C11⋊#95—212no—
37C11⋊#95—412no—
38#14665—111nomaximal, Sylow
39C24×C11C2411yescharacteristic
40C23×D11—21no—
41C23×D11—21no—
42C23×D11—26no—
43C23×D11—26no—
44C23×D11C22×C412yes—
45C22×C4×C11—26no—
46C22×C4×C11—26no—
47C22×C4×C11—24no—
48C22×C4×C11—212no—
49C22×C4×C11—212no—
50C22×C4×C11C22×C416yes—
51C22×C4×C11C2×D416yes—
52C22×C4×C11C2×D416yes—
53C22×Dic11—23no—
54C22×Dic11—23no—
55C22×Dic11—24no—
56C22×Dic11—26no—
57C22×Dic11—212no—
58C22×Dic11—26no—
59C22×Dic11—212no—
60C22×Dic11C22×C416yes—
61C11×C4⋊C4—424no—
62C42×C11C22⋊C4116yescomplemented
63(C2×D11)⋊C4—224no—
64(C2×D11)⋊C4—416no—
65Dic11⋊C4—224no—
66C22×#126—111no—
67C2×#384D1111yescharacteristic, complemented
68C2×#383—111no—
69#1441—116no—
70#1439—116no—
71C23×C11C23×C411yescharacteristic
72C23×C11C22×D411yescharacteristic
73C23×C11C22×D411yescharacteristic
74C23×C11H(5,𝔽2)16yes—
75C23×C112−1+416yes—
76C22×D11—22no—
77C22×D11—212no—
78C22×D11—43no—
79C22×D11—43no—
80C22×D11—46no—
81C22×D11—44no—
82C22×D11—412no—
83C2×C4×C11—212no—
84C2×C4×C11—26no—
85C2×C4×C11—26no—
86C2×C4×C11—212no—
87C2×C4×C11—412no—
88C2×C4×C11—44no—
89C2×C4×C11—412no—
90C2×C4×C11C2×C22⋊C4112yes—
91C2×Dic11—26no—
92C2×Dic11—212no—
93C2×Dic11—43no—
94C2×Dic11—43no—
95C2×Dic11—46no—
96C2×Dic11—412no—
97C2×Dic11—44no—
98C2×Dic11—412no—
99C2×#126—118no—
100C2×#126—224no—
101C2×#126—224no—
102C22×C4⋊C4—113no—
103C22×C4⋊C4C2×D1116yes—
104C22×C22⋊C4—113no—
105C22×C22⋊C4—114no—
106C22×C42C2×D1111yescharacteristic
107#384—24no—
108#383—224no—
109C2×#95—116no—
110C2×#95—1112no—
111C22×C11C22×C22⋊C411yescharacteristic
112C22×C11#52016yes—
113C22×C11#53513yes—
114C22×C11#53613yes—
115C22×C11#53716yes—
116C22×C11#56014yes—
117C22×C11#563112yes—
118C2×D11—46no—
119C2×D11—48no—
120C2×D11—81no—
121C2×D11—83no—
122C2×D11—84no—
123C4×C11—212no—
124C4×C11—84no—
125Dic11—46no—
126Dic11—84no—
127C25—111no—
128C23×C4—113no—
129C23×C4—114no—
130C23×C4C22×D1114yes—
131C23×C4C22×D1113yes—
132#126—2232no—
133C2×C4⋊C4—212no—
134C2×C4⋊C4—412no—
135C2×C4⋊C4—1112no—
136C2×C4⋊C4—226no—
137C2×C4⋊C4—226no—
138C2×C22⋊C4—1112no—
139C2×C22⋊C4—226no—
140C2×C22⋊C4—226no—
141C2×C22⋊C4—4412no—
142C2×C42C4×D1114yes—
143C2×C42D4414yes—
144C2×C42C22⋊D1114yes—
145#95—2212no—
146#95—4412no—
147C2×C11#231113yes—
148C2×C11#238314yes—
149C2×C11#281811yescharacteristic
150C2×C11#282113yes—
151C2×C11#282314yes—
152D11—82no—
153C24—112no—
154C24—221no—
155C24—226no—
156C24—226no—
157C24—221no—
158C24C23×D1111yescharacteristic
159C22×C4—26no—
160C22×C4—26no—
161C22×C4—212no—
162C22×C4—212no—
163C22×C4—24no—
164C22×C4—116no—
165C22×C4—223no—
166C22×C4—226no—
167C22×C4—226no—
168C22×C4—223no—
169C22×C4—224no—
170C22×C4—2212no—
171C22×C4—2212no—
172C22×C4C2×C4×D1116yes—
173C22×C4C2×D4416yes—
174C22×C4C2×C22⋊D1116yes—
175C4⋊C4—424no—
176C4⋊C4—2224no—
177C22⋊C4—2224no—
178C22⋊C4—4416no—
179C42(C2×D11)⋊C4116yescomplemented
180C11#1466511yescharacteristic, complemented, Sylow
181C23—2212no—
182C23—222no—
183C23—444no—
184C23—4412no—
185C23—446no—
186C23—443no—
187C23—443no—
188C23C22×C4×D1111yescharacteristic
189C23C22×D4411yescharacteristic
190C23#6703716yes—
191C23#6704016yes—
192C23C22×C22⋊D1111yescharacteristic
193C2×C4—212no—
194C2×C4—212no—
195C2×C4—26no—
196C2×C4—26no—
197C2×C4—44no—
198C2×C4—412no—
199C2×C4—412no—
200C2×C4—2212no—
201C2×C4—226no—
202C2×C4—446no—
203C2×C4—443no—
204C2×C4—443no—
205C2×C4—444no—
206C2×C4—4412no—
207C2×C4—4412no—
208C2×C4C2×(C2×D11)⋊C4112yes—
209C22—446no—
210C22—448no—
211C22—881no—
212C22—883no—
213C22—884no—
214C22#1062303516yes—
215C22#1062304116yes—
216C22#1062325114yes—
217C22#10623266112yes—
218C22C22×(C2×D11)⋊C411yescharacteristic
219C22#1062333613yes—
220C22#1062334713yes—
221C4—212no—
222C4—84no—
223C4—446no—
224C4—884no—
225C2—882no—
226C2#1307120913yes—
227C2#1307180914yes—
228C2#1307665711yescharacteristic
229C2#1307667513yes—
230C2#1307669014yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#384C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#384D11
hypocenterC11#14665
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. C2×#10622550C2semidirect
3. #13066866C2semidirect
5. C2×C11×#384C2semidirect
13. C2×#66929C4semidirect
62. C42×C11C22⋊C4semidirect
67. C2×#384D11semidirect
179. C42(C2×D11)⋊C4semidirect
180. C11#14665semidirect

Maximal subgroups

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

subgroupindex
C22×#669292
C2×#106225502
#130668662
#130668582
C2×C11×#3842
#1466511