Finite Group Databasebeta

← #14657022

Subgroups — #14657022

Order 2816.

762 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068530C213yesmaximal
2C11⋊#1304C213yesmaximal, complemented
3C11×#2840C211yesmaximal, characteristic, complemented
4C23×C22⋊D11C2211yescharacteristic
5C11×#393—26no—
6C11×#379C2213yes—
7#10622860C2213yes—
8C2×#66870—26no—
9C25×C11C2311yescharacteristic
10C24×D11Q811yescharacteristic, complemented
11C22×Q8×C11—22no—
12C22×C22⋊D11—23no—
13C22×C22⋊D11—23no—
14C22×C22⋊D11—44no—
15C23×Dic11Q811yescharacteristic, complemented
16C2×C11×C22⋊C4—26no—
17C2×C11×C22⋊C4D416yes—
18C2×C22⋊Dic11—23no—
19C2×C22⋊Dic11—26no—
20C11×#95—26no—
21#66870—412no—
22#10390—111nomaximal, Sylow
23C24×C11—42no—
24C24×C11—82no—
25C24×C11C2×D413yes—
26C24×C11C2×Q811yescharacteristic
27C24×C11#4113yes—
28C23×D11—23no—
29C23×D11—42no—
30C23×D11—82no—
31C2×Q8×C11—84no—
32C2×Q8×C11—82no—
33C22×C4×C11—26no—
34C2×C22⋊D11—212no—
35C2×C22⋊D11—46no—
36C2×C22⋊D11—46no—
37C2×C22⋊D11—46no—
38C2×C22⋊D11—41no—
39C2×C22⋊D11—43no—
40C22×Dic11—23no—
41C22×Dic11—42no—
42C22×Dic11—43no—
43C11×C22⋊C4—46no—
44C11×C22⋊C4—86no—
45C22⋊Dic11—46no—
46C22⋊Dic11—86no—
47#2840D1111yescharacteristic, complemented
48#1781—113no—
49#1304—113no—
50C23×C11—26no—
51C23×C11—41no—
52C23×C11—42no—
53C23×C11—46no—
54C23×C11—46no—
55C23×C11—43no—
56C23×C11—88no—
57C23×C11#12011yescharacteristic
58C23×C11C22⋊Q813yes—
59C23×C11#12413yes—
60C22×D11—26no—
61C22×D11—43no—
62C22×D11—41no—
63C22×D11—88no—
64C22×D11—86no—
65Q8×C11—88no—
66C2×C4×C11—412no—
67C2×C4×C11—46no—
68C22⋊D11—412no—
69C22⋊D11—44no—
70C2×Dic11—26no—
71C2×Dic11—43no—
72C2×Dic11—41no—
73C2×Dic11—83no—
74C2×Dic11—86no—
75C23×D4—111no—
76C2×#99—226no—
77#393—26no—
78#379—113no—
79#379C2×D1113yes—
80C22×C11—22no—
81C22×C11—23no—
82C22×C11—23no—
83C22×C11—26no—
84C22×C11—26no—
85C22×C11—44no—
86C22×C11—86no—
87C22×C11—86no—
88C22×C11#39311yescharacteristic
89C22×C11B(4,𝔽2)12yes—
90C2×D11—42no—
91C2×D11—86no—
92C2×D11—82no—
93C2×D11—86no—
94C4×C11—86no—
95Dic11—42no—
96Dic11—163no—
97C25—111no—
98C25C22×D1111yescharacteristic
99C22×Q8—22no—
100C22×D4—223no—
101C22×D4—223no—
102C22×D4—444no—
103C23×C4—111no—
104C2×C22⋊C4—26no—
105C2×C22⋊C4—223no—
106C2×C22⋊C4—226no—
107C2×C22⋊C4C22⋊D1116yes—
108#99—4412no—
109#95—26no—
110C2×C11—22no—
111C2×C11—43no—
112C2×C11—43no—
113C2×C11#202911yescharacteristic
114C2×C11#203212yes—
115D11—82no—
116C24—42no—
117C24—82no—
118C24—223no—
119C24—442no—
120C24—882no—
121C24Q8×D1111yescharacteristic
122C24#434313yes—
123C24C2×C22⋊D1113yes—
124C2×Q8—84no—
125C2×Q8—82no—
126C2×D4—2212no—
127C2×D4—446no—
128C2×D4—446no—
129C2×D4—446no—
130C2×D4—443no—
131C2×D4—441no—
132C22×C4—26no—
133C22×C4—223no—
134C22×C4—442no—
135C22×C4—443no—
136C22⋊C4—46no—
137C22⋊C4—86no—
138C22⋊C4—446no—
139C22⋊C4—886no—
140C11#1039011yescharacteristic, complemented, Sylow
141C23—26no—
142C23—41no—
143C23—42no—
144C23—46no—
145C23—46no—
146C23—43no—
147C23—88no—
148C23—226no—
149C23—443no—
150C23—441no—
151C23—886no—
152C23—888no—
153C23#6699913yes—
154C23#6700013yes—
155C23#6700611yescharacteristic
156Q8—88no—
157D4—4412no—
158D4—444no—
159C2×C4—412no—
160C2×C4—46no—
161C2×C4—226no—
162C2×C4—443no—
163C2×C4—441no—
164C2×C4—883no—
165C2×C4—886no—
166C22—22no—
167C22—23no—
168C22—23no—
169C22—26no—
170C22—26no—
171C22—44no—
172C22—86no—
173C22—86no—
174C22—442no—
175C22—886no—
176C22—886no—
177C22—882no—
178C22#1062284411yescharacteristic
179C22#1062285712yes—
180C4—86no—
181C4—442no—
182C4—1763no—
183C2—22no—
184C2—43no—
185C2—43no—
186C2—882no—
187C2#1306977911yescharacteristic
188C2#1306979212yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#2840C2
socleC22×C11#393
prime radicalC23×C22⋊D11C22
hypercenter#2840D11
hypocenterC11#10390
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2840

Complements

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

NH ≅ G/Ntype
2. C11⋊#1304C2semidirect
3. C11×#2840C2semidirect
10. C24×D11Q8semidirect
15. C23×Dic11Q8semidirect
47. #2840D11semidirect
140. C11#10390semidirect

Maximal subgroups

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

subgroupindex
#130685302
C11⋊#13042
C11×#28402
#1039011