Finite Group Databasebeta

← #14742989

Subgroups — #14742989

Order 2816.

814 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 151 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#13079544C213yesmaximal, complemented
2#13079530C213yesmaximal, complemented
3#13068281C213yesmaximal, complemented
4#13068254C213yesmaximal, complemented
5#13068228C211yesmaximal, characteristic, complemented
6#13066915C211yesmaximal, characteristic, complemented
7C11×#1712C211yesmaximal, characteristic, complemented
8#10623247C2213yes—
9D11×#127C2211yescharacteristic
10C11×#493C2213yes—
11C11×#493C2213yescomplemented
12#10622771—26no—
13#10622769—26no—
14#10622766—26no—
15#10622763—26no—
16#10622689C2213yescomplemented
17#10622686C2213yes—
18#10622683C2213yes—
19#10622683C2213yescomplemented
20#10622307C2213yes—
21#10622298C2213yes—
22#10622294C2213yescomplemented
23C82×C11C2211yescharacteristic, complemented
24#10622092C2213yescomplemented
25C2×#4341—23no—
26C2×D4×D11—23no—
27C2×C11×D8—26no—
28C2×C11×D8—26no—
29C11×#127C2311yescharacteristic
30C11×#127C2313yes—
31#66993—23no—
32#66991—23no—
33#66991—23no—
34#66989—23no—
35D4×Dic11—23no—
36D4×Dic11—23no—
37C2×#4324—26no—
38C2×#4323—26no—
39#66927C2311yescharacteristic
40C42×D11C2311yescharacteristic
41#66922C2313yes—
42C4×C8×C11C2313yes—
43#66896—26no—
44#66896—26no—
45#66885—26no—
46(C2×D11)⋊C8D416yes—
47#66880—26no—
48Dic11⋊C8D416yes—
49C4×C11⋊C8C2313yes—
50#19743—111nomaximal, Sylow
51C23×D11—41no—
52C2×D4×C11—23no—
53C2×D4×C11—23no—
54C2×D4×C11—23no—
55C2×D4×C11—23no—
56C2×C22⋊D11—43no—
57C2×C22⋊D11—43no—
58C22×Dic11—43no—
59#4341—86no—
60D4×D11—86no—
61C2×D44—23no—
62C2×C4×D11C2×D413yes—
63C2×Dic22—23no—
64C11×D8—86no—
65C11×D8—86no—
66C2×C8×C11C2×D416yes—
67C42×C11C2411yescharacteristic
68C22⋊Dic11—43no—
69C22⋊Dic11—43no—
70#4324—86no—
71#4323—86no—
72C4⋊Dic11—23no—
73C4⋊Dic11—23no—
74C4×Dic11C2×D413yes—
75C2×C11⋊C8C2×D416yes—
76#3207—113no—
77#3205—113no—
78#1721—113no—
79#1717—113no—
80#1712D1111yescharacteristic, complemented
81#1711—111no—
82#1454—111no—
83C23×C11—43no—
84C23×C11—41no—
85C22×D11—41no—
86C22×D11—86no—
87C22×D11#12711yescharacteristic
88D4×C11—46no—
89D4×C11—46no—
90D4×C11—46no—
91D4×C11—46no—
92C2×C4×C11C22×D413yes—
93C22⋊D11—86no—
94C22⋊D11—86no—
95C2×Dic11—43no—
96C2×Dic11—86no—
97C2×Dic11#12713yes—
98D44—46no—
99C4×D11—26no—
100Dic22—46no—
101C8×C11—26no—
102C11⋊C8—26no—
103#532—113no—
104C2×#127—111no—
105#493—113no—
106#493C2×D1113yes—
107#493C2×D1113yescomplemented
108#492—113no—
109#487—113no—
110#486—113no—
111#486—113no—
112#486—113no—
113#463—226no—
114#459—226no—
115#449—226no—
116#447—226no—
117#431—113no—
118#322—113no—
119C82C2×D1111yescharacteristic, complemented
120C22×C11—83no—
121C22×C11—83no—
122C22×C11—83no—
123C22×C11—83no—
124C22×C11C2×#12711yescharacteristic
125C2×D11—23no—
126C2×D11—83no—
127C2×D11—164no—
128C4×C11#57616yes—
129Dic11—23no—
130Dic11—83no—
131C2×#41—223no—
132C22×D4—223no—
133C2×SD16—226no—
134C2×D8—26no—
135C2×D8—26no—
136C2×D8—226no—
137C4⋊Q8—113no—
138#127—111no—
139#127—223no—
140#127C22×D1111yescharacteristic
141#127C22×D1113yes—
142#124—223no—
143#121—223no—
144#121—223no—
145C4×D4—223no—
146C4×D4—223no—
147C2×C42—111no—
148C4⋊C8—116no—
149#103—226no—
150#102—226no—
151#102—226no—
152#102—226no—
153C22⋊C8—116no—
154C4×C8—113no—
155C4×C8C22×D1113yes—
156C2×C11—161no—
157C2×C11—163no—
158C2×C11#315513yes—
159D11—41no—
160D11—161no—
161C24—441no—
162#41—886no—
163C2×Q8—223no—
164C2×D4—23no—
165C2×D4—23no—
166C2×D4—23no—
167C2×D4—23no—
168C2×D4—223no—
169C2×D4—443no—
170C2×D4—443no—
171C2×D4—886no—
172C22×C4—113no—
173C22×C4—443no—
174SD16—886no—
175D8—86no—
176D8—86no—
177D8—886no—
178C2×C8—116no—
179C2×C8D4×D1116yes—
180C4⋊C4—223no—
181C4⋊C4—223no—
182C22⋊C4—443no—
183C22⋊C4—443no—
184C42—113no—
185C42C23×D1111yescharacteristic
186C11#1974311yescharacteristic, complemented, Sylow
187C23—43no—
188C23—41no—
189C23—111no—
190C23—441no—
191C23—886no—
192Q8—446no—
193D4—46no—
194D4—46no—
195D4—46no—
196D4—46no—
197D4—446no—
198D4—886no—
199D4—886no—
200C2×C4—113no—
201C2×C4—226no—
202C2×C4—443no—
203C2×C4—886no—
204C2×C4C2×D4×D1113yes—
205C8—26no—
206C8—226no—
207C22—83no—
208C22—83no—
209C22—83no—
210C22—83no—
211C22—223no—
212C22—883no—
213C22—1764no—
214C22D11×#12711yescharacteristic
215C4—223no—
216C4—883no—
217C4#1062328816yes—
218C2—161no—
219C2—163no—
220C2—441no—
221C2—1761no—
222C2#1307909613yes—
subgroupG/H
centerC22D11×#127
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1712C2
socleC22×C11C2×#127
hypercenter#1712D11
hypocenterC11#19743
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1712

Complements

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

NH ≅ G/Ntype
1. #13079544C2semidirect
2. #13079530C2semidirect
3. #13068281C2semidirect
4. #13068254C2semidirect
5. #13068228C2semidirect
6. #13066915C2semidirect
7. C11×#1712C2semidirect
11. C11×#493C22semidirect
16. #10622689C22semidirect
19. #10622683C22semidirect
22. #10622294C22semidirect
23. C82×C11C22semidirect
24. #10622092C22semidirect
80. #1712D11semidirect
107. #493C2×D11semidirect
119. C82C2×D11semidirect
186. C11#19743semidirect

Maximal subgroups

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

subgroupindex
#130795442
#130795302
#130682812
#130682542
#130682282
#130669152
C11×#17122
#1974311