Finite Group Databasebeta

← #396×D43 #19137814

Subgroups — #396×D43 #19137814

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#14582823C211yesmaximal, characteristic, complemented
4#14582822C213yesmaximal, complemented
5#14582821C213yesmaximal, complemented
6#95×D43C211yesmaximal, characteristic, complemented
7C43×#396C211yesmaximal, characteristic, complemented
8C24×D43C2211yescharacteristic
9C22×C4×D43C2213yes—
10C22×C4×D43C2213yes—
11C2×C4⋊Dic43C2213yescomplemented
12C2×Dic43⋊C4C2213yescomplemented
13C2×Dic43⋊C4C2213yescomplemented
14C4⋊C4×D43—212no—
15C2×C22⋊Dic43C2213yes—
16C2×(C2×D43)⋊C4C2213yes—
17C2×(C2×D43)⋊C4C2213yes—
18C22⋊C4×D43—212no—
19C43⋊#95C2213yescomplemented
20C2×C4⋊C4×C43C2213yescomplemented
21C2×C22⋊C4×C43C2213yes—
22#95×C43C2211yescharacteristic, complemented
23C24×C43C2311yescharacteristic
24C23×D43—26no—
25C23×D43—26no—
26C23×D43Q814yes—
27C23×D43C2311yescharacteristic
28C23×D43C2311yescharacteristic
29C22×C4×C43C2313yes—
30C22×C4×C43C2313yes—
31C22×Dic43C2313yes—
32C22×Dic43C2313yes—
33C2×C4×D43—26no—
34C2×C4×D43—26no—
35C2×C4×D43—26no—
36C2×C4×D43—26no—
37C2×C4×D43—26no—
38C2×C4×D43D4112yes—
39C4⋊C4×C43—26no—
40C22⋊C4×C43—26no—
41C22⋊Dic43—26no—
42(C2×D43)⋊C4—26no—
43(C2×D43)⋊C4—26no—
44C4⋊Dic43—26no—
45Dic43⋊C4—26no—
46Dic43⋊C4—26no—
47C23×C43—23no—
48C23×C43—23no—
49C23×C43C2×Q812yes—
50C23×C43C2411yescharacteristic
51C22×D43—23no—
52C22×D43—23no—
53C22×D43—224no—
54C22×D43—412no—
55C22×D43—44no—
56C22×D43C2×D416yes—
57C22×D43C2×Q812yes—
58C22×D43C2×Q812yes—
59C22×D43#4116yes—
60C2×C4×C43—23no—
61C2×C4×C43—23no—
62C2×C4×C43—23no—
63C2×C4×C43—23no—
64C2×C4×C43—23no—
65C2×C4×C43C2×D416yes—
66C2×Dic43—23no—
67C2×Dic43—23no—
68C2×Dic43—23no—
69C2×Dic43—23no—
70C2×Dic43—23no—
71C2×Dic43C2×D416yes—
72C4×D43—224no—
73C4×D43—412no—
74C22×C43—26no—
75C22×C43—43no—
76C22×C43—41no—
77C22×C43C22×D413yes—
78C22×C43C22×Q811yescharacteristic
79C22×C43C2×#4113yes—
80C2×D43—26no—
81C2×D43—43no—
82C2×D43—41no—
83C2×D43—416no—
84C2×D43#121112yes—
85C2×D43C22⋊Q8112yes—
86C2×D43#12614yes—
87C4×C43—26no—
88C4×C43—43no—
89Dic43—26no—
90Dic43—43no—
91C2×#396—431nomaximal, Sylow
92C2×C43—42no—
93C2×C43C2×#12113yes—
94C2×C43C2×C22⋊Q813yes—
95C2×C43C2×#12611yescharacteristic
96D43—42no—
97D43#39618yesdirect product factor
98C22×C4⋊C4—433no—
99C22×C22⋊C4—433no—
100#396—433no—
101#396—433no—
102#396—431no—
103#396D4311yescharacteristic, direct product factor
104C2×#95—431no—
105C43C2×#39611yescharacteristic, complemented, Sylow
106C25—431no—
107C23×C4—433no—
108C23×C4—433no—
109C2×C4⋊C4—433no—
110C2×C4⋊C4—433no—
111C2×C4⋊C4—433no—
112C2×C4⋊C4—8612no—
113C2×C4⋊C4C2×D4313yescomplemented
114C2×C22⋊C4—433no—
115C2×C22⋊C4—433no—
116C2×C22⋊C4—433no—
117C2×C22⋊C4—8612no—
118C2×C22⋊C4C2×D4313yes—
119#95—433no—
120#95C2×D4311yescharacteristic, complemented
121C24—431no—
122C24—434no—
123C24—431no—
124C24—866no—
125C24—866no—
126C24C22×D4311yescharacteristic
127C22×C4—433no—
128C22×C4—4312no—
129C22×C4—433no—
130C22×C4—866no—
131C22×C4—866no—
132C22×C4—866no—
133C22×C4—866no—
134C22×C4—866no—
135C22×C4C22×D4313yes—
136C22×C4C22×D4313yes—
137C4⋊C4—26no—
138C4⋊C4—866no—
139C4⋊C4—866no—
140C4⋊C4—866no—
141C22⋊C4—26no—
142C22⋊C4—866no—
143C22⋊C4—866no—
144C22⋊C4—866no—
145C23—23no—
146C23—23no—
147C23—436no—
148C23—432no—
149C23—436no—
150C23—432no—
151C23—8624no—
152C23—863no—
153C23—863no—
154C23—17212no—
155C23—1724no—
156C23Q8×D4312yes—
157C23C23×D4311yescharacteristic
158C2×C4—23no—
159C2×C4—23no—
160C2×C4—23no—
161C2×C4—23no—
162C2×C4—23no—
163C2×C4—436no—
164C2×C4—8624no—
165C2×C4—863no—
166C2×C4—863no—
167C2×C4—863no—
168C2×C4—863no—
169C2×C4—863no—
170C2×C4—17212no—
171C2×C4D4×D4316yes—
172C22—26no—
173C22—43no—
174C22—41no—
175C22—4312no—
176C22—4312no—
177C22—434no—
178C22—866no—
179C22—17216no—
180C22—1723no—
181C22—1721no—
182C22C2×D4×D4313yes—
183C22C2×Q8×D4311yescharacteristic
184C22#41×D4313yes—
185C4—26no—
186C4—43no—
187C4—866no—
188C4—1723no—
189C2—42no—
190C2—438no—
191C2—1722no—
192C2#121×D4313yes—
193C2C22⋊Q8×D4313yes—
194C2#126×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43C2×#396
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D43C2semidirect
3. #14582823C2semidirect
4. #14582822C2semidirect
5. #14582821C2semidirect
6. #95×D43C2semidirect
7. C43×#396C2semidirect
11. C2×C4⋊Dic43C22semidirect
12. C2×Dic43⋊C4C22semidirect
13. C2×Dic43⋊C4C22semidirect
19. C43⋊#95C22semidirect
20. C2×C4⋊C4×C43C22semidirect
22. #95×C43C22semidirect
97. D43#396direct (N × H)
103. #396D43direct (N × H)
105. C43C2×#396semidirect
113. C2×C4⋊C4C2×D43semidirect
120. #95C2×D43semidirect