Finite Group Databasebeta

← #399×D43 #19137841

Subgroups — #399×D43 #19137841

Order 5504.

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

normal subgroups only

This group has 908 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
1C2×C4⋊C4×D43C213yesmaximal, complemented
2C2×C22⋊C4×D43C213yesmaximal
3#14582836C211yesmaximal, characteristic, complemented
4#14582835C213yesmaximal, complemented
5#14582834C213yesmaximal, complemented
6#95×D43C211yesmaximal, characteristic, complemented
7C43×#399C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C22×C4×D43C2213yes—
10C22×C4×D43C2213yes—
11C2×C4⋊Dic43C2213yescomplemented
12C2×Dic43⋊C4C2216yescomplemented
13C4⋊C4×D43—212no—
14C2×C22⋊Dic43C2213yes—
15C2×(C2×D43)⋊C4C2213yes—
16C2×(C2×D43)⋊C4C2213yes—
17C22⋊C4×D43—212no—
18C43⋊#95C2213yescomplemented
19C2×C4⋊C4×C43C2213yescomplemented
20C2×C22⋊C4×C43C2213yes—
21#95×C43C2211yescharacteristic, complemented
22C24×C43C2311yescharacteristic
23C23×D43—26no—
24C23×D43—26no—
25C23×D43Q814yes—
26C23×D43C2311yescharacteristic
27C23×D43C2311yescharacteristic
28C22×C4×C43C2313yes—
29C22×C4×C43C2313yes—
30C22×Dic43C2313yes—
31C22×Dic43C2313yes—
32C2×C4×D43—26no—
33C2×C4×D43—212no—
34C2×C4×D43—212no—
35C2×C4×D43D4112yes—
36C4⋊C4×C43—26no—
37C22⋊C4×C43—26no—
38C22⋊Dic43—26no—
39(C2×D43)⋊C4—26no—
40(C2×D43)⋊C4—26no—
41C4⋊Dic43—26no—
42Dic43⋊C4—212no—
43C23×C43—23no—
44C23×C43—23no—
45C23×C43C2×Q812yes—
46C23×C43C2411yescharacteristic
47C22×D43—23no—
48C22×D43—23no—
49C22×D43—224no—
50C22×D43—412no—
51C22×D43—44no—
52C22×D43C2×D416yes—
53C22×D43C2×Q812yes—
54C22×D43C2×Q812yes—
55C22×D43#4116yes—
56C2×C4×C43—26no—
57C2×C4×C43—26no—
58C2×C4×C43—23no—
59C2×C4×C43C2×D416yes—
60C2×Dic43—26no—
61C2×Dic43—26no—
62C2×Dic43—23no—
63C2×Dic43C2×D416yes—
64C4×D43—224no—
65C4×D43—412no—
66C22×C43—26no—
67C22×C43—43no—
68C22×C43—41no—
69C22×C43C22×D413yes—
70C22×C43C22×Q811yescharacteristic
71C22×C43C2×#4113yes—
72C2×D43—26no—
73C2×D43—43no—
74C2×D43—41no—
75C2×D43—416no—
76C2×D43C22⋊Q8112yes—
77C2×D43#123112yes—
78C2×D43#12714yes—
79C4×C43—26no—
80C4×C43—43no—
81Dic43—26no—
82Dic43—43no—
83C2×#399—431nomaximal, Sylow
84C2×C43—42no—
85C2×C43C2×C22⋊Q813yes—
86C2×C43C2×#12313yes—
87C2×C43C2×#12711yescharacteristic
88D43—42no—
89D43#39918yesdirect product factor
90C22×C4⋊C4—433no—
91C22×C22⋊C4—433no—
92#399—433no—
93#399—433no—
94#399—431no—
95#399D4311yescharacteristic, direct product factor
96C2×#95—431no—
97C43C2×#39911yescharacteristic, complemented, Sylow
98C25—431no—
99C23×C4—433no—
100C23×C4—433no—
101C2×C4⋊C4—436no—
102C2×C4⋊C4—433no—
103C2×C4⋊C4—8612no—
104C2×C4⋊C4C2×D4313yescomplemented
105C2×C22⋊C4—433no—
106C2×C22⋊C4—433no—
107C2×C22⋊C4—433no—
108C2×C22⋊C4—8612no—
109C2×C22⋊C4C2×D4313yes—
110#95—433no—
111#95C2×D4311yescharacteristic, complemented
112C24—431no—
113C24—434no—
114C24—431no—
115C24—866no—
116C24—866no—
117C24C22×D4311yescharacteristic
118C22×C4—433no—
119C22×C4—4312no—
120C22×C4—433no—
121C22×C4—8612no—
122C22×C4—866no—
123C22×C4—8612no—
124C22×C4C22×D4313yes—
125C22×C4C22×D4313yes—
126C4⋊C4—26no—
127C4⋊C4—8612no—
128C4⋊C4—866no—
129C22⋊C4—26no—
130C22⋊C4—866no—
131C22⋊C4—866no—
132C22⋊C4—866no—
133C23—23no—
134C23—23no—
135C23—436no—
136C23—432no—
137C23—436no—
138C23—432no—
139C23—8624no—
140C23—863no—
141C23—863no—
142C23—17212no—
143C23—1724no—
144C23Q8×D4312yes—
145C23C23×D4311yescharacteristic
146C2×C4—26no—
147C2×C4—23no—
148C2×C4—26no—
149C2×C4—436no—
150C2×C4—8624no—
151C2×C4—866no—
152C2×C4—863no—
153C2×C4—866no—
154C2×C4—17212no—
155C2×C4D4×D4316yes—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—4312no—
160C22—4312no—
161C22—434no—
162C22—866no—
163C22—17216no—
164C22—1723no—
165C22—1721no—
166C22C2×D4×D4313yes—
167C22C2×Q8×D4311yescharacteristic
168C22#41×D4313yes—
169C4—26no—
170C4—43no—
171C4—866no—
172C4—1723no—
173C2—42no—
174C2—438no—
175C2—1722no—
176C2C22⋊Q8×D4313yes—
177C2#123×D4313yes—
178C2#127×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#399C2
hypercenter#399D43
hypocenterC43C2×#399
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D43C2semidirect
3. #14582836C2semidirect
4. #14582835C2semidirect
5. #14582834C2semidirect
6. #95×D43C2semidirect
7. C43×#399C2semidirect
11. C2×C4⋊Dic43C22semidirect
12. C2×Dic43⋊C4C22semidirect
18. C43⋊#95C22semidirect
19. C2×C4⋊C4×C43C22semidirect
21. #95×C43C22semidirect
89. D43#399direct (N × H)
95. #399D43direct (N × H)
97. C43C2×#399semidirect
104. C2×C4⋊C4C2×D43semidirect
111. #95C2×D43semidirect