Finite Group Databasebeta

← #393×D43 #19137793

Subgroups — #393×D43 #19137793

Order 5504.

1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C22×Q8×D43C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D43C213yesmaximal
3#14582812C213yesmaximal, complemented
4#14582811C213yesmaximal, complemented
5#14582810C211yesmaximal, characteristic, complemented
6#95×D43C213yesmaximal, complemented
7C43×#393C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C22×Dic86C2213yescomplemented
10C2×Q8×D43—212no—
11C22×C4×D43C2213yes—
12C22×C4×D43C2213yes—
13C2×C22⋊Dic43C2213yes—
14C2×(C2×D43)⋊C4C2213yes—
15C2×(C2×D43)⋊C4C2213yes—
16C22⋊C4×D43—212no—
17C43⋊#95C2213yescomplemented
18C43⋊#95C2216yescomplemented
19C22×Q8×C43C2211yescharacteristic, complemented
20C2×C22⋊C4×C43C2213yes—
21#95×C43C2213yescomplemented
22C24×C43C2311yescharacteristic
23C23×D43—26no—
24C23×D43—26no—
25C23×D43Q814yescomplemented
26C23×D43C2311yescharacteristic
27C23×D43C2311yescharacteristic
28C2×Q8×C43—26no—
29C22×C4×C43C2313yes—
30C22×C4×C43C2313yes—
31C22×Dic43C2313yes—
32C22×Dic43C2313yes—
33Q8×D43—232no—
34C2×C4×D43—212no—
35C2×C4×D43—26no—
36C2×C4×D43—212no—
37C2×C4×D43D4112yes—
38C2×Dic86—26no—
39C2×Dic86—212no—
40C22⋊C4×C43—26no—
41C22⋊Dic43—26no—
42(C2×D43)⋊C4—26no—
43(C2×D43)⋊C4—26no—
44C23×C43—23no—
45C23×C43—23no—
46C23×C43C2×Q812yescomplemented
47C23×C43C2411yescharacteristic
48C22×D43—23no—
49C22×D43—23no—
50C22×D43—224no—
51C22×D43—44no—
52C22×D43—412no—
53C22×D43C2×D416yes—
54C22×D43C2×Q812yes—
55C22×D43C2×Q812yescomplemented
56C22×D43#4116yes—
57Q8×C43—28no—
58C2×C4×C43—26no—
59C2×C4×C43—23no—
60C2×C4×C43—26no—
61C2×C4×C43C2×D416yes—
62C2×Dic43—26no—
63C2×Dic43—23no—
64C2×Dic43—26no—
65C2×Dic43C2×D416yes—
66C4×D43—224no—
67C4×D43—412no—
68Dic86—224no—
69C22×C43—26no—
70C22×C43—41no—
71C22×C43—43no—
72C22×C43C22×D413yes—
73C22×C43C22×Q811yescharacteristic
74C22×C43C2×#4113yes—
75C2×D43—26no—
76C2×D43—41no—
77C2×D43—43no—
78C2×D43—416no—
79C2×D43#12014yes—
80C2×D43C22⋊Q8112yes—
81C2×D43#124112yes—
82C4×C43—26no—
83C4×C43—43no—
84Dic43—26no—
85Dic43—43no—
86C2×#393—431nomaximal, Sylow
87C2×C43—42no—
88C2×C43C2×#12011yescharacteristic
89C2×C43C2×C22⋊Q813yes—
90C2×C43C2×#12413yes—
91D43—42no—
92D43#39318yesdirect product factor
93C23×Q8—431no—
94C22×C22⋊C4—433no—
95#393—431no—
96#393—433no—
97#393—433no—
98#393D4311yescharacteristic, direct product factor
99C2×#95—433no—
100C43C2×#39311yescharacteristic, complemented, Sylow
101C25—431no—
102C22×Q8—433no—
103C22×Q8—8612no—
104C22×Q8C2×D4311yescharacteristic, complemented
105C23×C4—433no—
106C23×C4—433no—
107C2×C22⋊C4—433no—
108C2×C22⋊C4—433no—
109C2×C22⋊C4—433no—
110C2×C22⋊C4—8612no—
111C2×C22⋊C4C2×D4313yes—
112#95—436no—
113#95—433no—
114#95C2×D4313yescomplemented
115C24—431no—
116C24—434no—
117C24—431no—
118C24—866no—
119C24—866no—
120C24C22×D4311yescharacteristic
121C2×Q8—26no—
122C2×Q8—8612no—
123C2×Q8—8632no—
124C2×Q8—866no—
125C22×C4—433no—
126C22×C4—4312no—
127C22×C4—433no—
128C22×C4—8612no—
129C22×C4—866no—
130C22×C4—8612no—
131C22×C4C22×D4313yes—
132C22×C4C22×D4313yes—
133C22⋊C4—26no—
134C22⋊C4—866no—
135C22⋊C4—866no—
136C22⋊C4—866no—
137C23—23no—
138C23—23no—
139C23—436no—
140C23—432no—
141C23—436no—
142C23—432no—
143C23—8624no—
144C23—863no—
145C23—863no—
146C23—1724no—
147C23—17212no—
148C23Q8×D4312yescomplemented
149C23C23×D4311yescharacteristic
150Q8—28no—
151Q8—8624no—
152C2×C4—26no—
153C2×C4—23no—
154C2×C4—26no—
155C2×C4—436no—
156C2×C4—8624no—
157C2×C4—866no—
158C2×C4—863no—
159C2×C4—866no—
160C2×C4—17212no—
161C2×C4D4×D4316yes—
162C22—26no—
163C22—41no—
164C22—43no—
165C22—434no—
166C22—4312no—
167C22—4312no—
168C22—866no—
169C22—17216no—
170C22—1721no—
171C22—1723no—
172C22C2×D4×D4313yes—
173C22C2×Q8×D4311yescharacteristic
174C22#41×D4313yes—
175C4—26no—
176C4—43no—
177C4—866no—
178C4—1723no—
179C2—42no—
180C2—438no—
181C2—1722no—
182C2#120×D4311yescharacteristic
183C2C22⋊Q8×D4313yes—
184C2#124×D4313yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43C2×#393
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D43C2semidirect
3. #14582812C2semidirect
4. #14582811C2semidirect
5. #14582810C2semidirect
6. #95×D43C2semidirect
7. C43×#393C2semidirect
9. C22×Dic86C22semidirect
17. C43⋊#95C22semidirect
18. C43⋊#95C22semidirect
19. C22×Q8×C43C22semidirect
21. #95×C43C22semidirect
25. C23×D43Q8semidirect
46. C23×C43C2×Q8semidirect
55. C22×D43C2×Q8semidirect
92. D43#393direct (N × H)
98. #393D43direct (N × H)
100. C43C2×#393semidirect
104. C22×Q8C2×D43semidirect
114. #95C2×D43semidirect
148. C23Q8×D43semidirect