Finite Group Databasebeta

← D43×#1705 #25084232

Subgroups — D43×#1705 #25084232

Order 11008.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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#498×D43C213yesmaximal, complemented
2#492×D43C213yesmaximal
3#19134183C213yesmaximal, complemented
4#19134182C211yesmaximal, characteristic, complemented
5#19134181C213yesmaximal, complemented
6C82×D43C211yesmaximal, characteristic, complemented
7C43×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D43—26no—
9C4⋊Q8×D43C2213yes—
10#127×D43C2211yescharacteristic
11#14583297C2213yescomplemented
12#14583296—26no—
13#14583295C2216yescomplemented
14#14583273C2213yes—
15#14583272C2213yes—
16#14583271C2213yes—
17#14583270—26no—
18#106×D43—26no—
19C4×C8×D43C2213yes—
20C8×C43⋊C8C2213yescomplemented
21C43×#498C2213yescomplemented
22C43×#492C2213yes—
23C82×C43C2211yescharacteristic, complemented
24C2×Q8×D43—23no—
25C2×D4×D43—23no—
26C2×#10621873—26no—
27C2×#10621883—26no—
28C2×#10621884—26no—
29SD16×D43—424no—
30C2×C8×D43D416yes—
31#13063325C2313yes—
32#13063324—26no—
33#13063323—23no—
34#13063322C2311yescharacteristic
35#13063321—23no—
36C4⋊C4×D43—26no—
37C42×D43C2311yescharacteristic
38#13063257—26no—
39#13063256—212no—
40C4×C43⋊C8C2313yes—
41C8×Dic43D416yes—
42C2×SD16×C43—26no—
43C4⋊Q8×C43C2313yes—
44#127×C43C2311yescharacteristic
45#106×C43—26no—
46C4×C8×C43C2313yes—
47C23×D43—41no—
48C2×Q8×C43—23no—
49C2×D4×C43—23no—
50C2×C22⋊D43—43no—
51Q8×D43—412no—
52D4×D43—412no—
53C2×D172—23no—
54C2×C4×D43—43no—
55C2×C4×D43C2×D413yes—
56C2×Dic86—23no—
57C2×Dic86—43no—
58SD16×C43—412no—
59C2×C8×C43C2×D416yes—
60C4⋊C4×C43—26no—
61C42×C43C2411yescharacteristic
62#10621884—412no—
63#10621883—412no—
64C4⋊Dic43—26no—
65Dic43⋊C4—46no—
66C4×Dic43C2×D413yes—
67C2×C43⋊C8C2×D416yes—
68#10621873—412no—
69C8×D43SD16124yescomplemented
70C23×C43—41no—
71C22×D43—41no—
72C22×D43—86no—
73C22×D43#12711yescharacteristic
74Q8×C43—46no—
75D4×C43—46no—
76C2×C4×C43—43no—
77C2×C4×C43C22×D413yes—
78C22⋊D43—86no—
79C2×Dic43—43no—
80C2×Dic43#12713yes—
81D172—46no—
82C4×D43—86no—
83C4×D43C2×SD16112yes—
84Dic86—46no—
85Dic86—86no—
86C8×C43C2×SD16112yescomplemented
87C43⋊C8C2×SD16112yescomplemented
88C2×#1705—431nomaximal, Sylow
89C22×C43—83no—
90C22×C43C2×#12711yescharacteristic
91C2×D43—83no—
92C2×D43—164no—
93C2×D43#49216yes—
94C4×C43—83no—
95C4×C43C22×SD1616yes—
96Dic43—83no—
97Dic43#49216yes—
98C2×#498—433no—
99C2×#492—433no—
100#1705—433no—
101#1705—433no—
102#1705—431no—
103#1705D4311yescharacteristic, direct product factor
104C2×C82—431no—
105C2×C43—161no—
106C2×C43C2×#49213yes—
107D43—161no—
108D43#170514yesdirect product factor
109C22×SD16—866no—
110C2×C4⋊Q8—433no—
111C2×#127—431no—
112#498—436no—
113#498—433no—
114#498—866no—
115#498C2×D4313yescomplemented
116#492—433no—
117#492—433no—
118#492—433no—
119#492—866no—
120#492C2×D4313yes—
121C2×#106—866no—
122C2×C4×C8—433no—
123C82—433no—
124C82C2×D4311yescharacteristic, complemented
125C43C2×#170511yescharacteristic, complemented, Sylow
126C22×Q8—863no—
127C22×D4—863no—
128C2×SD16—26no—
129C2×SD16—866no—
130C2×SD16—866no—
131C2×SD16—866no—
132C2×SD16—17224no—
133C22×C8—436no—
134C4⋊Q8—433no—
135C4⋊Q8—866no—
136C4⋊Q8—863no—
137C4⋊Q8C22×D4313yes—
138#127—431no—
139#127—863no—
140#127C22×D4311yescharacteristic
141C2×C4⋊C4—866no—
142C2×C42—431no—
143#106—26no—
144#106—8612no—
145#106—866no—
146C4×C8—436no—
147C4×C8—433no—
148C4×C8C22×D4313yes—
149C24—1721no—
150C2×Q8—23no—
151C2×Q8—863no—
152C2×Q8—1723no—
153C2×Q8—17212no—
154C2×D4—23no—
155C2×D4—863no—
156C2×D4—17212no—
157C2×D4—1723no—
158C22×C4—433no—
159C22×C4—1723no—
160SD16—412no—
161SD16—17212no—
162SD16—17212no—
163SD16—17212no—
164C2×C8—436no—
165C2×C8—4324no—
166C2×C8D4×D4316yes—
167C4⋊C4—26no—
168C4⋊C4—866no—
169C4⋊C4—1726no—
170C42—433no—
171C42C23×D4311yescharacteristic
172C23—41no—
173C23—431no—
174C23—3446no—
175C23—1721no—
176Q8—46no—
177Q8—3446no—
178Q8—1726no—
179D4—46no—
180D4—3446no—
181D4—1726no—
182C2×C4—43no—
183C2×C4—433no—
184C2×C4—4312no—
185C2×C4—3446no—
186C2×C4—1723no—
187C2×C4C2×D4×D4313yes—
188C8—4312no—
189C8SD16×D43112yescomplemented
190C22—83no—
191C22—436no—
192C22—3443no—
193C22—6884no—
194C22#127×D4311yescharacteristic
195C4—83no—
196C4—436no—
197C4—3443no—
198C4C2×SD16×D4316yes—
199C2—161no—
200C2—434no—
201C2—6881no—
202C2#492×D4313yes—
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1705C2
socleC22×C43C2×#127
prime radical#127×D43C22
hypercenter#1705D43
hypocenterC43C2×#1705
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. #498×D43C2semidirect
3. #19134183C2semidirect
4. #19134182C2semidirect
5. #19134181C2semidirect
6. C82×D43C2semidirect
7. C43×#1705C2semidirect
11. #14583297C22semidirect
13. #14583295C22semidirect
20. C8×C43⋊C8C22semidirect
21. C43×#498C22semidirect
23. C82×C43C22semidirect
69. C8×D43SD16semidirect
86. C8×C43C2×SD16semidirect
87. C43⋊C8C2×SD16semidirect
103. #1705D43direct (N × H)
108. D43#1705direct (N × H)
115. #498C2×D43semidirect
124. C82C2×D43semidirect
125. C43C2×#1705semidirect
189. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#498×D432
#492×D432
#191341832
#191341822
#191341812
C82×D432
C43×#17052
C2×#170543