Finite Group Databasebeta

← D43×#2845 #25303184

Subgroups — D43×#2845 #25303184

Order 11008.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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#19142870C213yesmaximal, complemented
2#19142869C2112yesmaximal, complemented
3#398×D43C2112yesmaximal
4#382×D43C213yesmaximal
5C43×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D43C22112yes—
7C2×C4⋊C4×D43C2216yes—
8C2×C42×D43C2211yescharacteristic
9#14582833C22112yes—
10#14582833C22112yes—
11#14582832C22112yes—
12#14582832C22112yes—
13#14582831C22112yes—
14#14582830C22112yes—
15#14582829C22112yes—
16#14582765C2213yes—
17#14582764C2216yes—
18#14582763C22112yes—
19#95×D43C2214yes—
20#95×D43C22112yes—
21C43×#398C22112yes—
22C43×#382C2213yes—
23C22×C4×D43C23112yes—
24C22×C4×D43C2313yes—
25C2×C4⋊Dic43C23112yes—
26C2×C4⋊Dic43C2316yes—
27C2×Dic43⋊C4C23112yes—
28C2×Dic43⋊C4C23112yes—
29C2×Dic43⋊C4C23112yes—
30C4⋊C4×D43—412no—
31C4⋊C4×D43—424no—
32C2×C4×Dic43C2313yes—
33C42×D43Q818yes—
34C43⋊#95C23112yes—
35C43⋊#95C23112yes—
36C43⋊#95C23112yes—
37C43⋊#95C23112yes—
38C2×C4⋊C4×C43C23112yes—
39C2×C4⋊C4×C43C2316yes—
40C2×C42×C43C2311yescharacteristic
41#95×C43C23112yes—
42#95×C43C2314yes—
43C23×D43C2411yescharacteristic
44C22×C4×C43C24112yes—
45C22×C4×C43C2413yes—
46C22×Dic43C24112yes—
47C22×Dic43C2413yes—
48C2×C4×D43—26no—
49C2×C4×D43—224no—
50C2×C4×D43—224no—
51C2×C4×D43—26no—
52C2×C4×D43—224no—
53C2×C4×D43C2×Q8112yes—
54C4⋊C4×C43—46no—
55C4⋊C4×C43—412no—
56C42×C43C2×Q814yes—
57C4⋊Dic43—412no—
58C4⋊Dic43—46no—
59Dic43⋊C4—412no—
60Dic43⋊C4—412no—
61Dic43⋊C4—412no—
62C4×Dic43C2×Q8112yes—
63C23×C43C2511yescharacteristic
64C22×D43C22×Q812yes—
65C22×D43H(5,𝔽2)16yes—
66C22×D432−1+416yes—
67C2×C4×C43—23no—
68C2×C4×C43—23no—
69C2×C4×C43—212no—
70C2×C4×C43—212no—
71C2×C4×C43—212no—
72C2×C4×C43C22×Q816yes—
73C2×Dic43—23no—
74C2×Dic43—23no—
75C2×Dic43—212no—
76C2×Dic43—212no—
77C2×Dic43—212no—
78C2×Dic43C22×Q816yes—
79C4×D43—224no—
80C4×D43—448no—
81C2×#2845—431nomaximal, Sylow
82C22×C43C23×Q811yescharacteristic
83C22×C43C2×H(5,𝔽2)13yes—
84C22×C43C2×2−1+413yes—
85C2×D43#544112yes—
86C2×D43#562112yes—
87C2×D43#56414yes—
88C4×C43—26no—
89C4×C43—412no—
90Dic43—26no—
91Dic43—412no—
92#2845—4312no—
93#2845—433no—
94#2845D4311yescharacteristic, direct product factor
95C2×#398—4312no—
96C2×#382—433no—
97C2×C43C2×#54413yes—
98C2×C43C2×#56213yes—
99C2×C43C2×#56411yescharacteristic
100D43#284518yesdirect product factor
101C22×C4⋊C4—4312no—
102C22×C4⋊C4—436no—
103C22×C42—431no—
104#398—4312no—
105#398—4312no—
106#398—4312no—
107#398—4312no—
108#398—4312no—
109#398—4312no—
110#398—4312no—
111#398C2×D43112yes—
112#382—436no—
113#382—433no—
114#382—4312no—
115#382C2×D4313yes—
116C2×#95—434no—
117C2×#95—4312no—
118C43C2×#284511yescharacteristic, complemented, Sylow
119C23×C4—433no—
120C23×C4—4312no—
121C2×C4⋊C4—4312no—
122C2×C4⋊C4—4312no—
123C2×C4⋊C4—4312no—
124C2×C4⋊C4—436no—
125C2×C4⋊C4—4312no—
126C2×C4⋊C4—17212no—
127C2×C4⋊C4—17224no—
128C2×C4⋊C4C22×D4316yes—
129C2×C4⋊C4C22×D43112yes—
130C2×C42—433no—
131C2×C42—438no—
132C2×C42C22×D4311yescharacteristic
133#95—4312no—
134#95—4312no—
135#95—4312no—
136#95—4312no—
137#95C22×D43112yes—
138#95C22×D4314yes—
139C24—431no—
140C22×C4—433no—
141C22×C4—4312no—
142C22×C4—4312no—
143C22×C4—866no—
144C22×C4—866no—
145C22×C4—8624no—
146C22×C4—8624no—
147C22×C4—8624no—
148C22×C4C23×D43112yes—
149C22×C4C23×D4313yes—
150C4⋊C4—46no—
151C4⋊C4—412no—
152C4⋊C4—17212no—
153C4⋊C4—17212no—
154C4⋊C4—17212no—
155C4⋊C4—1726no—
156C4⋊C4—17212no—
157C42—4312no—
158C42Q8×D4314yes—
159C23—432no—
160C23—436no—
161C23—436no—
162C23C24×D4311yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—436no—
169C2×C4—8624no—
170C2×C4—863no—
171C2×C4—863no—
172C2×C4—8612no—
173C2×C4—8612no—
174C2×C4—8612no—
175C2×C4—17248no—
176C2×C4C2×Q8×D4316yes—
177C22—4312no—
178C22—434no—
179C22—4312no—
180C22C22×Q8×D4311yescharacteristic
181C22H(5,𝔽2)×D4313yes—
182C222−1+4×D4313yes—
183C4—26no—
184C4—412no—
185C4—866no—
186C4—17212no—
187C2—438no—
188C2#544×D4313yes—
189C2#562×D4313yes—
190C2#564×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2845C2
prime radicalC23×D43C24
hypercenter#2845D43
hypocenterC43C2×#2845
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #19142870C2semidirect
2. #19142869C2semidirect
5. C43×#2845C2semidirect
94. #2845D43direct (N × H)
100. D43#2845direct (N × H)
118. C43C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#191428702
#191428692
#398×D432
#382×D432
C43×#28452
C2×#284543