Finite Group Databasebeta

← #14742993

Subgroups — #14742993

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#13079552C213yesmaximal, complemented
2#13079535C213yesmaximal, complemented
3#13068284C213yesmaximal, complemented
4#13068258C213yesmaximal, complemented
5#13068231C211yesmaximal, characteristic, complemented
6#13066915C211yesmaximal, characteristic, complemented
7C11×#1711C211yesmaximal, characteristic, complemented
8#10623256C2213yes—
9D11×#127C2211yescharacteristic
10C11×#487C2213yescomplemented
11C11×#486C2213yes—
12#10622701C2213yes—
13#10622701C2213yescomplemented
14#10622698C2213yescomplemented
15#10622686C2213yes—
16#10622432—26no—
17#10622424—26no—
18#10622399—26no—
19#10622386—26no—
20#10622308C2213yes—
21#10622308C2213yescomplemented
22#10622298C2213yes—
23C82×C11C2211yescharacteristic, complemented
24#10622092C2213yescomplemented
25C2×#4343—23no—
26C2×D4×D11—23no—
27C11×C4⋊Q8C2313yes—
28C11×#127C2311yescharacteristic
29#67000—23no—
30C2×#4325—26no—
31#66993—23no—
32C2×#4323—26no—
33C2×D88—26no—
34C2×D88—26no—
35#66948—23no—
36#66948—23no—
37#66946—23no—
38#66946—23no—
39#66927C2311yescharacteristic
40#66927C2313yes—
41C42×D11C2311yescharacteristic
42C11×#103—26no—
43C11×#102—26no—
44C4×C8×C11C2313yes—
45(C2×D11)⋊C8D416yes—
46Dic11⋊C8D416yes—
47#66873—26no—
48#66873—26no—
49C4×C11⋊C8C2313yes—
50#19743—111nomaximal, Sylow
51C23×D11—41no—
52C2×Q8×C11—23no—
53C2×D4×C11—23no—
54C2×C22⋊D11—43no—
55#4343—86no—
56D4×D11—86no—
57C2×D44—23no—
58C2×D44—23no—
59C2×D44—23no—
60C2×D44—23no—
61C2×D44—43no—
62C2×C4×D11—43no—
63C2×C4×D11C2×D413yes—
64C2×C8×C11C2×D416yes—
65C11×C4⋊C4—23no—
66C11×C4⋊C4—23no—
67C42×C11C2411yescharacteristic
68#4325—86no—
69#4323—86no—
70(C2×D11)⋊C4—43no—
71(C2×D11)⋊C4—43no—
72C4×Dic11C2×D413yes—
73C2×C11⋊C8C2×D416yes—
74D88—86no—
75D88—86no—
76#3207—113no—
77#3205—113no—
78#1721—113no—
79#1717—113no—
80#1712—111no—
81#1711D1111yescharacteristic, complemented
82#1454—111no—
83C23×C11—41no—
84C22×D11—43no—
85C22×D11—41no—
86C22×D11—86no—
87C22×D11#12711yescharacteristic
88Q8×C11—46no—
89D4×C11—46no—
90C2×C4×C11—43no—
91C2×C4×C11C22×D413yes—
92C22⋊D11—86no—
93C2×Dic11#12713yes—
94D44—46no—
95D44—46no—
96D44—46no—
97D44—46no—
98D44—86no—
99C4×D11—26no—
100C4×D11—86no—
101C8×C11—26no—
102C11⋊C8—26no—
103#532—113no—
104C2×#127—111no—
105#493—113no—
106#493—113no—
107#493—113no—
108#492—113no—
109#487C2×D1113yescomplemented
110#486—113no—
111#486—113no—
112#486C2×D1113yes—
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×C11C2×#12711yescharacteristic
122C2×D11—23no—
123C2×D11—83no—
124C2×D11—83no—
125C2×D11—83no—
126C2×D11—83no—
127C2×D11—164no—
128C4×C11—83no—
129C4×C11#57616yes—
130Dic11—23no—
131C2×#41—223no—
132C22×D4—223no—
133C2×SD16—226no—
134C2×D8—226no—
135C2×D8—226no—
136C2×D8—226no—
137C4⋊Q8C22×D1113yes—
138#127—111no—
139#127—113no—
140#127—223no—
141#127C22×D1111yescharacteristic
142#124—223no—
143#121—223no—
144#121—223no—
145C4×D4—223no—
146C4×D4—223no—
147C2×C42—111no—
148C4⋊C8—116no—
149#103—26no—
150#102—26no—
151#102—226no—
152#102—226no—
153C22⋊C8—116no—
154C4×C8—113no—
155C4×C8C22×D1113yes—
156C2×C11—161no—
157C2×C11#315513yes—
158D11—41no—
159D11—163no—
160D11—161no—
161C24—441no—
162#41—886no—
163C2×Q8—23no—
164C2×D4—23no—
165C2×D4—223no—
166C2×D4—223no—
167C2×D4—223no—
168C2×D4—223no—
169C2×D4—443no—
170C2×D4—443no—
171C2×D4—886no—
172C22×C4—113no—
173C22×C4—443no—
174SD16—886no—
175D8—886no—
176D8—886no—
177D8—886no—
178C2×C8—116no—
179C2×C8D4×D1116yes—
180C4⋊C4—23no—
181C4⋊C4—23no—
182C22⋊C4—443no—
183C22⋊C4—443no—
184C42—113no—
185C42C23×D1111yescharacteristic
186C11#1974311yescharacteristic, complemented, Sylow
187C23—41no—
188C23—111no—
189C23—443no—
190C23—441no—
191C23—886no—
192Q8—46no—
193D4—46no—
194D4—446no—
195D4—446no—
196D4—446no—
197D4—446no—
198D4—886no—
199D4—886no—
200C2×C4—43no—
201C2×C4—113no—
202C2×C4—226no—
203C2×C4—886no—
204C2×C4C2×D4×D1113yes—
205C8—26no—
206C8—226no—
207C22—83no—
208C22—223no—
209C22—883no—
210C22—883no—
211C22—883no—
212C22—883no—
213C22—1764no—
214C22D11×#12711yescharacteristic
215C4—83no—
216C4—223no—
217C4#1062330016yes—
218C2—161no—
219C2—441no—
220C2—1761no—
221C2—1763no—
222C2#1307909813yes—
subgroupG/H
centerC22D11×#127
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1711C2
socleC22×C11C2×#127
hypercenter#1711D11
hypocenterC11#19743
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. #13079552C2semidirect
2. #13079535C2semidirect
3. #13068284C2semidirect
4. #13068258C2semidirect
5. #13068231C2semidirect
6. #13066915C2semidirect
7. C11×#1711C2semidirect
10. C11×#487C22semidirect
13. #10622701C22semidirect
14. #10622698C22semidirect
21. #10622308C22semidirect
23. C82×C11C22semidirect
24. #10622092C22semidirect
81. #1711D11semidirect
109. #487C2×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
#130795522
#130795352
#130682842
#130682582
#130682312
#130669152
C11×#17112
#1974311