Finite Group Databasebeta

← #14742992

Subgroups — #14742992

Order 2816.

814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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#13079551C213yesmaximal, complemented
2#13079536C213yesmaximal, complemented
3#13068282C213yesmaximal, complemented
4#13068255C213yesmaximal, complemented
5#13068231C211yesmaximal, characteristic, complemented
6#13068228C211yesmaximal, characteristic, complemented
7C11×#1454C211yesmaximal, characteristic, complemented
8#10623008C2213yes—
9C2×#66927C2211yescharacteristic
10C11×#431C2213yes—
11#10622457—26no—
12#10622456—26no—
13#10622347—26no—
14#10622345—26no—
15#10622308C2213yes—
16#10622308C2213yes—
17#10622308C2213yescomplemented
18#10622307C2213yes—
19#10622307C2213yes—
20#10622307C2213yescomplemented
21#10622306C2213yescomplemented
22#10622294C2213yescomplemented
23C11×#322C2213yescomplemented
24C82×C11C2211yescharacteristic, complemented
25C2×#4339—23no—
26C22×D44—23no—
27C2×C42×C11C2311yescharacteristic
28#66983—23no—
29#66983—23no—
30C2×D88—26no—
31C2×D88—26no—
32C2×D88—26no—
33C2×#4314—26no—
34#66928—23no—
35#66927—23no—
36#66927C2311yescharacteristic
37#66927C2311yescharacteristic
38#66927C2313yes—
39C4×D44—23no—
40C4×D44—23no—
41#66922C2313yes—
42C11×C4⋊C8D416yes—
43C11×C22⋊C8D416yes—
44C4×C8×C11C2313yes—
45C4×C8×C11C2313yes—
46#66885—26no—
47#66885—26no—
48#66885—26no—
49#66880—26no—
50#19743—111nomaximal, Sylow
51C23×D11—41no—
52C22×C4×C11C2×D413yes—
53C2×C22⋊D11—43no—
54#4339—86no—
55C2×D44—23no—
56C2×D44—23no—
57C2×D44—23no—
58C2×D44—23no—
59C2×D44—23no—
60C2×D44—43no—
61C2×D44—86no—
62C2×C4×D11—43no—
63C2×Dic22—23no—
64C2×C8×C11C2×D416yes—
65C2×C8×C11C2×D416yes—
66C42×C11C2×D413yes—
67C42×C11C2411yescharacteristic
68(C2×D11)⋊C4—43no—
69(C2×D11)⋊C4—43no—
70C4⋊Dic11—23no—
71C4⋊Dic11—23no—
72D88—86no—
73D88—86no—
74D88—86no—
75#4314—86no—
76#3207—113no—
77#3205—113no—
78#1721—113no—
79#1717—113no—
80#1712—111no—
81#1711—111no—
82#1454D1111yescharacteristic, complemented
83C23×C11#12711yescharacteristic
84C22×D11—43no—
85C22×D11—41no—
86C22×D11—41no—
87C22×D11—86no—
88C2×C4×C11—26no—
89C2×C4×C11#12713yes—
90C2×C4×C11C22×D413yes—
91C22⋊D11—86no—
92C2×Dic11—43no—
93D44—46no—
94D44—46no—
95D44—46no—
96D44—46no—
97D44—46no—
98D44—86no—
99C4×D11—86no—
100Dic22—46no—
101C8×C11—26no—
102C8×C11—26no—
103#532—113no—
104C2×#127—111no—
105#493—113no—
106#493—113no—
107#493—113no—
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#431C2×D1113yes—
118#322C2×D1113yescomplemented
119C82C2×D1111yescharacteristic, complemented
120C22×C11—23no—
121C22×C11C2×#12711yescharacteristic
122C2×D11—83no—
123C2×D11—83no—
124C2×D11—83no—
125C2×D11—83no—
126C2×D11—83no—
127C2×D11—164no—
128C4×C11—23no—
129C4×C11#57616yes—
130Dic11—83no—
131C2×#41—223no—
132C22×D4—223no—
133C2×SD16—226no—
134C2×D8—226no—
135C2×D8—226no—
136C2×D8—226no—
137C4⋊Q8—113no—
138#127—111no—
139#127—111no—
140#127—113no—
141#127—223no—
142#124—223no—
143#121—223no—
144#121—223no—
145C4×D4—223no—
146C4×D4—223no—
147C2×C42C22×D1111yescharacteristic
148C4⋊C8D4416yes—
149#103—226no—
150#102—226no—
151#102—226no—
152#102—226no—
153C22⋊C8D4416yes—
154C4×C8C22×D1113yes—
155C4×C8C22×D1113yes—
156C2×C11—41no—
157C2×C11#315513yes—
158D11—163no—
159D11—161no—
160D11—161no—
161C24—441no—
162#41—886no—
163C2×Q8—223no—
164C2×D4—223no—
165C2×D4—223no—
166C2×D4—223no—
167C2×D4—223no—
168C2×D4—223no—
169C2×D4—443no—
170C2×D4—443no—
171C2×D4—886no—
172C22×C4—443no—
173C22×C4C2×D4413yes—
174SD16—886no—
175D8—886no—
176D8—886no—
177D8—886no—
178C2×C8C2×D4416yes—
179C2×C8C2×D4416yes—
180C4⋊C4—223no—
181C4⋊C4—223no—
182C22⋊C4—443no—
183C22⋊C4—443no—
184C42C2×D4413yes—
185C42C23×D1111yescharacteristic
186C11#1974311yescharacteristic, complemented, Sylow
187C23—443no—
188C23—441no—
189C23—441no—
190C23—886no—
191C23#6692711yescharacteristic
192Q8—446no—
193D4—446no—
194D4—446no—
195D4—446no—
196D4—446no—
197D4—446no—
198D4—886no—
199D4—886no—
200C2×C4—26no—
201C2×C4—443no—
202C2×C4—886no—
203C2×C4#6692713yes—
204C2×C4C22×D4413yes—
205C8—26no—
206C8—26no—
207C22—23no—
208C22—883no—
209C22—883no—
210C22—883no—
211C22—883no—
212C22—883no—
213C22—1764no—
214C22C2×#6692711yescharacteristic
215C4—23no—
216C4—883no—
217C4#1062328316yes—
218C2—41no—
219C2—1761no—
220C2—1761no—
221C2—1763no—
222C2#1307910213yes—
subgroupG/H
centerC22C2×#66927
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1454C2
socleC22×C11C2×#127
hypercenter#1454D11
hypocenterC11#19743
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1454

Complements

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

NH ≅ G/Ntype
1. #13079551C2semidirect
2. #13079536C2semidirect
3. #13068282C2semidirect
4. #13068255C2semidirect
5. #13068231C2semidirect
6. #13068228C2semidirect
7. C11×#1454C2semidirect
17. #10622308C22semidirect
20. #10622307C22semidirect
21. #10622306C22semidirect
22. #10622294C22semidirect
23. C11×#322C22semidirect
24. C82×C11C22semidirect
82. #1454D11semidirect
118. #322C2×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
#130795512
#130795362
#130682822
#130682552
#130682312
#130682282
C11×#14542
#1974311