Finite Group Databasebeta

← D43×#1711 #25084271

Subgroups — D43×#1711 #25084271

Order 11008.

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

normal subgroups only

This group has 802 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#487×D43C213yesmaximal, complemented
2#486×D43C213yesmaximal
3#19134208C213yesmaximal, complemented
4#19134207C211yesmaximal, characteristic, complemented
5#19134206C213yesmaximal, complemented
6C82×D43C211yesmaximal, characteristic, complemented
7C43×#1711C211yesmaximal, characteristic, complemented
8C4⋊Q8×D43C2213yes—
9#127×D43C2211yescharacteristic
10#14583251C2213yescomplemented
11#14583250C2213yescomplemented
12#14583249C2213yescomplemented
13#14583248—26no—
14#14583247C2213yes—
15#14583246C2213yes—
16#14583245C2213yes—
17#14583244—26no—
18#103×D43—26no—
19#102×D43—26no—
20C4×C8×D43C2213yes—
21C8×C43⋊C8C2213yescomplemented
22C43×#487C2213yescomplemented
23C43×#486C2213yes—
24C82×C43C2211yescharacteristic, complemented
25C2×Q8×D43—23no—
26C2×D4×D43—23no—
27C2×C8×D43D416yes—
28#13063325C2313yes—
29#13063324—23no—
30#13063324—23no—
31#13063323—23no—
32#13063322C2311yescharacteristic
33#13063321—23no—
34C4⋊C4×D43—23no—
35C4⋊C4×D43—23no—
36C42×D43C2311yescharacteristic
37#13063250—26no—
38#13063249—26no—
39#13063248—26no—
40#13063247—26no—
41#13063246—26no—
42#13063245—26no—
43C4×C43⋊C8C2313yes—
44C8×Dic43D416yes—
45C4⋊Q8×C43C2313yes—
46#127×C43C2311yescharacteristic
47#103×C43—26no—
48#102×C43—26no—
49C4×C8×C43C2313yes—
50C23×D43—41no—
51C2×Q8×C43—23no—
52C2×D4×C43—23no—
53C2×C22⋊D43—43no—
54Q8×D43—412no—
55D4×D43—412no—
56C2×D172—23no—
57C2×C4×D43—43no—
58C2×C4×D43C2×D413yes—
59C2×Dic86—23no—
60C2×Dic86—43no—
61C2×C8×C43C2×D416yes—
62C4⋊C4×C43—23no—
63C4⋊C4×C43—23no—
64C42×C43C2411yescharacteristic
65C4⋊Dic43—23no—
66C4⋊Dic43—23no—
67Dic43⋊C4—43no—
68Dic43⋊C4—43no—
69C4×Dic43C2×D413yes—
70C2×C43⋊C8C2×D416yes—
71C8×D43—212no—
72C23×C43—41no—
73C22×D43—41no—
74C22×D43—86no—
75C22×D43#12711yescharacteristic
76Q8×C43—46no—
77D4×C43—46no—
78C2×C4×C43—43no—
79C2×C4×C43C22×D413yes—
80C22⋊D43—86no—
81C2×Dic43—43no—
82C2×Dic43#12713yes—
83D172—46no—
84C4×D43—86no—
85C4×D43#135112yes—
86Dic86—46no—
87Dic86—86no—
88C8×C43—26no—
89C43⋊C8—26no—
90C2×#1711—431nomaximal, Sylow
91C22×C43—83no—
92C22×C43C2×#12711yescharacteristic
93C2×D43—83no—
94C2×D43—164no—
95C2×D43#49516yes—
96C4×C43—83no—
97C4×C43C2×#13516yes—
98Dic43—83no—
99Dic43#49516yes—
100C2×#487—433no—
101C2×#486—433no—
102#1711—433no—
103#1711—433no—
104#1711—431no—
105#1711D4311yescharacteristic, direct product factor
106C2×C82—431no—
107C2×C43—161no—
108C2×C43C2×#49513yes—
109D43—161no—
110D43#171114yesdirect product factor
111C2×C4⋊Q8—433no—
112C2×#127—431no—
113#487—433no—
114#487—433no—
115#487—433no—
116#487—866no—
117#487C2×D4313yescomplemented
118#486—433no—
119#486—433no—
120#486—433no—
121#486—866no—
122#486C2×D4313yes—
123C2×#103—866no—
124C2×#102—866no—
125C2×C4×C8—433no—
126C82—433no—
127C82C2×D4311yescharacteristic, complemented
128C43C2×#171111yescharacteristic, complemented, Sylow
129C22×Q8—863no—
130C22×D4—863no—
131C22×C8—436no—
132C4⋊Q8—433no—
133C4⋊Q8—863no—
134C4⋊Q8—863no—
135C4⋊Q8—863no—
136C4⋊Q8C22×D4313yes—
137#127—431no—
138#127—863no—
139#127C22×D4311yescharacteristic
140C2×C4⋊C4—863no—
141C2×C4⋊C4—863no—
142C2×C42—431no—
143#103—26no—
144#103—866no—
145#103—866no—
146#103—866no—
147#102—26no—
148#102—866no—
149#102—866no—
150#102—866no—
151C4×C8—436no—
152C4×C8—433no—
153C4×C8C22×D4313yes—
154C24—1721no—
155C2×Q8—23no—
156C2×Q8—863no—
157C2×Q8—1723no—
158C2×Q8—17212no—
159C2×D4—23no—
160C2×D4—863no—
161C2×D4—17212no—
162C2×D4—1723no—
163C22×C4—433no—
164C22×C4—1723no—
165C2×C8—436no—
166C2×C8—8612no—
167C2×C8D4×D4316yes—
168C4⋊C4—23no—
169C4⋊C4—23no—
170C4⋊C4—863no—
171C4⋊C4—863no—
172C4⋊C4—1723no—
173C4⋊C4—1723no—
174C42—433no—
175C42C23×D4311yescharacteristic
176C23—41no—
177C23—431no—
178C23—3446no—
179C23—1721no—
180Q8—46no—
181Q8—3446no—
182Q8—1726no—
183D4—46no—
184D4—3446no—
185D4—1726no—
186C2×C4—43no—
187C2×C4—433no—
188C2×C4—4312no—
189C2×C4—3446no—
190C2×C4—1723no—
191C2×C4C2×D4×D4313yes—
192C8—26no—
193C8—866no—
194C22—83no—
195C22—436no—
196C22—3443no—
197C22—6884no—
198C22#127×D4311yescharacteristic
199C4—83no—
200C4—436no—
201C4—3443no—
202C4#135×D4316yes—
203C2—161no—
204C2—434no—
205C2—6881no—
206C2#495×D4313yes—
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1711C2
socleC22×C43C2×#127
prime radical#127×D43C22
hypercenter#1711D43
hypocenterC43C2×#1711
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. #487×D43C2semidirect
3. #19134208C2semidirect
4. #19134207C2semidirect
5. #19134206C2semidirect
6. C82×D43C2semidirect
7. C43×#1711C2semidirect
10. #14583251C22semidirect
11. #14583250C22semidirect
12. #14583249C22semidirect
21. C8×C43⋊C8C22semidirect
22. C43×#487C22semidirect
24. C82×C43C22semidirect
105. #1711D43direct (N × H)
110. D43#1711direct (N × H)
117. #487C2×D43semidirect
127. C82C2×D43semidirect
128. C43C2×#1711semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#486×D432
#191342082
#191342072
#191342062
C82×D432
C43×#17112
C2×#171143