Finite Group Databasebeta

← D43×#1658 #25077780

Subgroups — D43×#1658 #25077780

Order 11008.

882 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 149 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#564×D43C211yesmaximal, characteristic, complemented
2#490×D43C213yesmaximal
3#19133898C213yesmaximal, complemented
4#19133897C211yesmaximal, characteristic, complemented
5#19133896C213yesmaximal, complemented
6#330×D43C213yesmaximal, complemented
7C43×#1658C211yesmaximal, characteristic, complemented
8C43⋊#564—26no—
9C43⋊#564C2213yescomplemented
10#127×D43C2211yescharacteristic
11#125×D43—26no—
12#125×D43C2213yes—
13#14583265C2213yes—
14#14583264C2213yes—
15#14583263C2213yes—
16#14583262—26no—
17#102×D43—26no—
18#97×D43C2213yes—
19#14582641C2213yescomplemented
20#14582640C2216yescomplemented
21C43×#564C2211yescharacteristic, complemented
22C43×#490C2213yes—
23C43×#330C2213yescomplemented
24C2×D4×D43—23no—
25C2×C8×D43—23no—
26#13063322C2311yescharacteristic
27#13063321—23no—
28#13063317—26no—
29#13063317C2313yes—
30#13063316—26no—
31#13063316—26no—
32#13063316D416yes—
33#13063315—26no—
34#13063315—26no—
35#13063315—26no—
36#13063315—26no—
37#13063315—26no—
38C4⋊C4×D43—26no—
39C4⋊C4×D43—26no—
40C4⋊C4×D43D416yes—
41C42×D43—22no—
42C42×D43C2311yescharacteristic
43#13063247—26no—
44#13063246—26no—
45#13063245—26no—
46#13063236C2313yes—
47#13063235—23no—
48#127×C43C2311yescharacteristic
49#125×C43—26no—
50#125×C43C2313yes—
51#102×C43—26no—
52#97×C43C2313yes—
53C23×D43—41no—
54C2×D4×C43—23no—
55C2×C22⋊D43—43no—
56D4×D43—412no—
57C2×D172—23no—
58C2×C4×D43—26no—
59C2×C4×D43C2×D413yes—
60C2×C8×C43—23no—
61C4⋊C4×C43—26no—
62C4⋊C4×C43—26no—
63C4⋊C4×C43C2×D416yes—
64C42×C43—22no—
65C42×C43C2411yescharacteristic
66C4⋊Dic43—26no—
67C4⋊Dic43—26no—
68C4⋊Dic43C2×D416yes—
69Dic43⋊C4—26no—
70Dic43⋊C4—26no—
71Dic43⋊C4—26no—
72Dic43⋊C4—26no—
73Dic43⋊C4—26no—
74C4×Dic43—26no—
75C4×Dic43C2×D413yes—
76C2×C43⋊C8—23no—
77C8×D43—46no—
78C23×C43—41no—
79C22×D43—41no—
80C22×D43—86no—
81C22×D43#12011yescharacteristic
82D4×C43—46no—
83C2×C4×C43—26no—
84C2×C4×C43C22×D413yes—
85C22⋊D43—86no—
86C2×Dic43—26no—
87C2×Dic43#12013yes—
88D172—46no—
89C4×D43—26no—
90C4×D43—412no—
91C8×C43—43no—
92C43⋊C8—43no—
93C2×#1658—431nomaximal, Sylow
94C22×C43—83no—
95C22×C43C2×#12011yescharacteristic
96C2×D43—83no—
97C2×D43—164no—
98C2×D43#45416yes—
99C4×C43—23no—
100C4×C43—46no—
101Dic43—23no—
102Dic43—46no—
103C2×#564—431no—
104C2×#490—433no—
105#1658—433no—
106#1658—433no—
107#1658—431no—
108#1658D4311yescharacteristic, direct product factor
109C2×#330—433no—
110C2×C43—161no—
111C2×C43C2×#45413yes—
112D43—161no—
113D43#165814yesdirect product factor
114#564—433no—
115#564—866no—
116#564C2×D4311yescharacteristic, complemented
117C2×#127—431no—
118C2×#125—433no—
119C2×#125—866no—
120#490—433no—
121#490—433no—
122#490—433no—
123#490—866no—
124#490C2×D4313yes—
125C2×#102—866no—
126C2×#97—433no—
127#330—433no—
128#330—436no—
129#330C2×D4313yescomplemented
130C43C2×#165811yescharacteristic, complemented, Sylow
131C22×D4—863no—
132C22×C8—863no—
133#127—431no—
134#127—863no—
135#127C22×D4311yescharacteristic
136#125—26no—
137#125—436no—
138#125—433no—
139#125—866no—
140#125—866no—
141#125—866no—
142#125—866no—
143#125—866no—
144#125—866no—
145#125—866no—
146#125—866no—
147#125C22×D4313yes—
148C2×C4⋊C4—436no—
149C2×C4⋊C4—866no—
150C2×C4⋊C4—866no—
151C2×C42—431no—
152C2×C42—862no—
153#102—26no—
154#102—866no—
155#102—866no—
156#102—866no—
157#97—433no—
158#97—863no—
159#97C22×D4313yes—
160C24—1721no—
161C2×D4—23no—
162C2×D4—863no—
163C2×D4—1723no—
164C2×D4—17212no—
165C22×C4—433no—
166C22×C4—866no—
167C2×C8—23no—
168C2×C8—863no—
169C2×C8—1726no—
170C4⋊C4—26no—
171C4⋊C4—26no—
172C4⋊C4—436no—
173C4⋊C4—866no—
174C4⋊C4—866no—
175C4⋊C4—866no—
176C4⋊C4—866no—
177C4⋊C4—866no—
178C4⋊C4—866no—
179C4⋊C4—866no—
180C4⋊C4D4×D4316yes—
181C42—22no—
182C42—433no—
183C42—866no—
184C42C23×D4311yescharacteristic
185C23—41no—
186C23—431no—
187C23—3446no—
188C23—1721no—
189D4—46no—
190D4—3446no—
191D4—1726no—
192C2×C4—26no—
193C2×C4—433no—
194C2×C4—866no—
195C2×C4—866no—
196C2×C4—17212no—
197C2×C4C2×D4×D4313yes—
198C8—43no—
199C8—1723no—
200C22—83no—
201C22—436no—
202C22—3443no—
203C22—6884no—
204C22#120×D4311yescharacteristic
205C4—23no—
206C4—46no—
207C4—863no—
208C4—1726no—
209C2—161no—
210C2—434no—
211C2—6881no—
212C2#454×D4313yes—
subgroupG/H
centerC22#120×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1658C2
socleC22×C43C2×#120
prime radical#127×D43C22
hypercenter#1658D43
hypocenterC43C2×#1658
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1658

Complements

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

NH ≅ G/Ntype
1. #564×D43C2semidirect
3. #19133898C2semidirect
4. #19133897C2semidirect
5. #19133896C2semidirect
6. #330×D43C2semidirect
7. C43×#1658C2semidirect
9. C43⋊#564C22semidirect
19. #14582641C22semidirect
20. #14582640C22semidirect
21. C43×#564C22semidirect
23. C43×#330C22semidirect
108. #1658D43direct (N × H)
113. D43#1658direct (N × H)
116. #564C2×D43semidirect
129. #330C2×D43semidirect
130. C43C2×#1658semidirect

Maximal subgroups

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

subgroupindex
#564×D432
#490×D432
#191338982
#191338972
#191338962
#330×D432
C43×#16582
C2×#165843