Finite Group Databasebeta

← #14735851

Subgroups — #14735851

Order 2816.

876 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 145 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#13083110C211yesmaximal, characteristic, complemented
2#13078989C213yesmaximal
3#13067919C213yesmaximal, complemented
4#13067918C211yesmaximal, characteristic, complemented
5#13067917C213yesmaximal, complemented
6#13067209C213yesmaximal, complemented
7C11×#1658C211yesmaximal, characteristic, complemented
8C11×#564C2211yescharacteristic, complemented
9D11×#127C2211yescharacteristic
10#10623227—26no—
11#10623219C2213yes—
12C11⋊#564C2213yescomplemented
13#10623216—26no—
14C11×#490C2213yes—
15#10622684C2213yes—
16#10622680C2213yes—
17#10622383—26no—
18#10622373—26no—
19#10622326C2213yes—
20#10622320C2213yes—
21C11×#330C2213yescomplemented
22#10622181C2213yescomplemented
23#10622103C2216yescomplemented
24C2×D4×D11—23no—
25C11×#127C2311yescharacteristic
26C11×#125—26no—
27C11×#125C2313yes—
28#66993—23no—
29C2×#4313—23no—
30#66951—26no—
31#66949—26no—
32#66945D416yes—
33#66943—26no—
34#66942—26no—
35#66942—26no—
36#66942—26no—
37#66941—26no—
38#66941D416yes—
39#66940—26no—
40#66940—26no—
41#66929—22no—
42#66927C2311yescharacteristic
43C42×D11C2311yescharacteristic
44#66923C2313yes—
45C4×Dic22—26no—
46C11×#102—26no—
47C11×#97C2313yes—
48#66896—26no—
49#66885—26no—
50C8×Dic11—23no—
51#66873—26no—
52#66867C2313yes—
53#19083—111nomaximal, Sylow
54C23×D11—41no—
55C2×D4×C11—23no—
56C2×C22⋊D11—43no—
57D4×D11—412no—
58C2×D44—23no—
59C2×C4×D11C2×D413yes—
60C2×Dic22—26no—
61C2×C8×C11—23no—
62C11×C4⋊C4—26no—
63C11×C4⋊C4—26no—
64C11×C4⋊C4C2×D416yes—
65C42×C11—22no—
66C42×C11C2411yescharacteristic
67(C2×D11)⋊C4—26no—
68C4⋊Dic11—26no—
69C4⋊Dic11C2×D416yes—
70Dic11⋊C4—26no—
71Dic11⋊C4—26no—
72Dic11⋊C4—26no—
73Dic11⋊C4—26no—
74C4×Dic11—26no—
75C4×Dic11—26no—
76C4×Dic11C2×D413yes—
77C2×C11⋊C8—23no—
78#4313—46no—
79#3556—111no—
80#3138—113no—
81#1658—113no—
82#1658—113no—
83#1658—111no—
84#1658D1111yescharacteristic, complemented
85#1526—113no—
86C23×C11—41no—
87C22×D11—41no—
88C22×D11—86no—
89C22×D11#12011yescharacteristic
90D4×C11—46no—
91C2×C4×C11—26no—
92C2×C4×C11C22×D413yes—
93C22⋊D11—86no—
94C2×Dic11—26no—
95C2×Dic11#12013yes—
96D44—46no—
97C4×D11—26no—
98Dic22—412no—
99C8×C11—43no—
100C11⋊C8—43no—
101#564—113no—
102#564C2×D1111yescharacteristic, complemented
103#557—226no—
104#541—226no—
105#533—113no—
106C2×#127—111no—
107#490—113no—
108#490—113no—
109#490—113no—
110#490C2×D1113yes—
111#486—226no—
112#418—226no—
113C4×M16—113no—
114#330—113no—
115#330—116no—
116#330C2×D1113yescomplemented
117C22×C11—83no—
118C22×C11C2×#12011yescharacteristic
119C2×D11—23no—
120C2×D11—83no—
121C2×D11—164no—
122C4×C11—23no—
123C4×C11—46no—
124Dic11—46no—
125Dic11#45416yes—
126C22×D4—223no—
127C2×M16—223no—
128C4⋊Q8—116no—
129C4⋊Q8—226no—
130#127—111no—
131#127—223no—
132#127C22×D1111yescharacteristic
133#126—222no—
134#126—226no—
135#125—26no—
136#125—113no—
137#125—226no—
138#125—226no—
139#125—226no—
140#125—226no—
141#125C22×D1113yes—
142C22⋊Q8—226no—
143C4×Q8—226no—
144C4×Q8—226no—
145C4×Q8—226no—
146#117—116no—
147C2×C42—111no—
148#102—26no—
149#102—226no—
150#102—226no—
151#102—226no—
152#97—113no—
153#97C22×D1113yes—
154C4×C8—223no—
155C2×C11—161no—
156C2×C11C2×#45413yes—
157D11—41no—
158D11—161no—
159C24—441no—
160C2×Q8—226no—
161C2×D4—23no—
162C2×D4—223no—
163C2×D4—443no—
164C2×D4—4412no—
165C22×C4—113no—
166M16—446no—
167C2×C8—23no—
168C2×C8—223no—
169C4⋊C4—26no—
170C4⋊C4—26no—
171C4⋊C4—116no—
172C4⋊C4—226no—
173C4⋊C4—226no—
174C4⋊C4—226no—
175C4⋊C4—226no—
176C4⋊C4—226no—
177C4⋊C4D4×D1116yes—
178C22⋊C4—226no—
179C42—22no—
180C42—113no—
181C42—226no—
182C42—226no—
183C42C23×D1111yescharacteristic
184C11#1908311yescharacteristic, complemented, Sylow
185C23—41no—
186C23—111no—
187C23—441no—
188C23—886no—
189Q8—4412no—
190D4—46no—
191D4—446no—
192D4—886no—
193C2×C4—26no—
194C2×C4—113no—
195C2×C4—226no—
196C2×C4—226no—
197C2×C4C2×D4×D1113yes—
198C8—43no—
199C8—443no—
200C22—83no—
201C22—223no—
202C22—883no—
203C22—1764no—
204C22D11×#12011yescharacteristic
205C4—23no—
206C4—46no—
207C4—116no—
208C4—446no—
209C2—161no—
210C2—441no—
211C2—1761no—
212C2D11×#45413yes—
subgroupG/H
centerC22D11×#120
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1658C2
socleC22×C11C2×#120
prime radicalD11×#127C22
hypercenter#1658D11
hypocenterC11#19083
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1658

Complements

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

NH ≅ G/Ntype
1. #13083110C2semidirect
3. #13067919C2semidirect
4. #13067918C2semidirect
5. #13067917C2semidirect
6. #13067209C2semidirect
7. C11×#1658C2semidirect
8. C11×#564C22semidirect
12. C11⋊#564C22semidirect
21. C11×#330C22semidirect
22. #10622181C22semidirect
23. #10622103C22semidirect
84. #1658D11semidirect
102. #564C2×D11semidirect
116. #330C2×D11semidirect
184. C11#19083semidirect

Maximal subgroups

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

subgroupindex
#130831102
#130789892
#130679192
#130679182
#130679172
#130672092
C11×#16582
#1908311