Finite Group Databasebeta

← C8×Dic43⋊C4 #19134458

Subgroups — C8×Dic43⋊C4 #19134458

Order 5504.

296 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 157 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×Dic43⋊C8C211yesmaximal, characteristic
2C2×C8×Dic43C211yesmaximal, characteristic
3C2×C8×Dic43C211yesmaximal, characteristic
4C4×Dic43⋊C4C211yesmaximal, characteristic
5#14582654C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C2×C4×C8×C43C211yesmaximal, characteristic
8C22×C43⋊C8C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10C2×Dic43⋊C4C412yes—
11C2×C4×Dic43C2211yescharacteristic
12C2×C4×Dic43C2211yescharacteristic
13Dic43⋊C8C414yescomplemented
14C8×Dic43—22no—
15C8×Dic43C414yescomplemented
16C43⋊#95C412yes—
17C22×C8×C43C2211yescharacteristic
18C22×C8×C43C2211yescharacteristic
19C2×C42×C43C2211yescharacteristic
20C4×C8×C43—22no—
21C22×C4×C43C2×C412yes—
22C22×C4×C43C2311yescharacteristic
23C22×Dic43C2×C411yescharacteristic
24C22×Dic43C2×C412yes—
25C22×Dic43C2×C411yescharacteristic
26C2×C8×C43—21no—
27C2×C8×C43—21no—
28C2×C8×C43C2×C412yes—
29C2×C8×C43C2×C412yes—
30C2×C8×C43D412yes—
31C2×C8×C43Q812yes—
32C42×C43—21no—
33C42×C43—21no—
34Dic43⋊C4C818yesdirect product factor
35C4×Dic43—21no—
36C4×Dic43—21no—
37C4×Dic43C2×C412yes—
38C4×Dic43C2×C412yes—
39C2×C43⋊C8—21no—
40C2×C43⋊C8—21no—
41C2×C43⋊C8—21no—
42C2×C43⋊C8—21no—
43C2×C43⋊C8C2×C412yes—
44C2×C43⋊C8C2×C412yes—
45C23×C43C22×C411yescharacteristic
46C2×C4×C43—22no—
47C2×C4×C43—22no—
48C2×C4×C43C2×C814yes—
49C2×C4×C43C22×C411yescharacteristic
50C2×C4×C43C22×C411yescharacteristic
51C2×C4×C43C2×D411yescharacteristic
52C2×C4×C43C2×Q811yescharacteristic
53C2×C4×C43#4111yescharacteristic
54C2×C4×C43#4111yescharacteristic
55C2×Dic43—22no—
56C2×Dic43—22no—
57C2×Dic43—22no—
58C2×Dic43C4212yes—
59C2×Dic43C4212yes—
60C2×Dic43C2×C814yes—
61C2×Dic43C2×C814yes—
62C8×C43—22no—
63C8×C43C4⋊C414yescomplemented
64C43⋊C8—22no—
65C43⋊C8—22no—
66C22×C43C2×C4211yescharacteristic
67C22×C43C4×D411yescharacteristic
68C22×C43C4×Q811yescharacteristic
69C22×C43C22×C812yes—
70C22×C43#13112yes—
71C4×C43—24no—
72C4×C43C2×C4⋊C411yescharacteristic
73C4×C43#11711yescharacteristic
74C4×C43C4×D411yescharacteristic
75C4×C43C4×Q811yescharacteristic
76Dic43—22no—
77Dic43—24no—
78Dic43C4×C814yescomplemented
79C8×C4⋊C4—431nomaximal, Sylow
80C2×C43C4×C4⋊C411yescharacteristic
81C2×C43C2×C4×C811yescharacteristic
82C2×C43#40511yescharacteristic
83C2×C43C8×D412yes—
84C2×C43C8×Q812yes—
85C2×C4⋊C8—431no—
86C2×C4×C8—431no—
87C2×C4×C8—431no—
88C2×C4×C8D4311yescharacteristic
89C4×C4⋊C4—431no—
90#336—431no—
91#336—431no—
92C43C8×C4⋊C411yescharacteristic, complemented, Sylow
93C22×C8—431no—
94C22×C8—431no—
95C22×C8C2×D4311yescharacteristic
96C22×C8C2×D4311yescharacteristic
97C2×C4⋊C4—432no—
98C2×C42—431no—
99C2×C42—431no—
100C2×C42C2×D4311yescharacteristic
101C4⋊C8—434no—
102C4×C8—22no—
103C4×C8—434no—
104C4×C8—862no—
105#95—432no—
106C22×C4—431no—
107C22×C4—431no—
108C22×C4—432no—
109C22×C4C4×D4312yes—
110C22×C4C22×D4311yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—432no—
114C2×C8—432no—
115C2×C8—861no—
116C2×C8—861no—
117C2×C8—861no—
118C2×C8—861no—
119C2×C8Dic8612yes—
120C2×C8C4×D4312yes—
121C2×C8C4×D4312yes—
122C2×C8C22⋊D4312yes—
123C4⋊C4—438no—
124C42—21no—
125C42—21no—
126C42—432no—
127C42—432no—
128C42—861no—
129C42—861no—
130C23C2×C4×D4311yescharacteristic
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—432no—
134C2×C4—434no—
135C2×C4—432no—
136C2×C4—434no—
137C2×C4—862no—
138C2×C4—862no—
139C2×C4—862no—
140C2×C4C8×D4314yes—
141C2×C4C2×Dic8611yescharacteristic
142C2×C4C2×C4×D4311yescharacteristic
143C2×C4C2×C4×D4311yescharacteristic
144C2×C4#1062189811yescharacteristic
145C2×C4#1062189811yescharacteristic
146C2×C4C2×C22⋊D4311yescharacteristic
147C8—22no—
148C8—862no—
149C8—862no—
150C8Dic43⋊C414yesdirect product factor
151C22C42×D4311yescharacteristic
152C22C4×C22⋊D4311yescharacteristic
153C22C4×Dic8611yescharacteristic
154C22C2×C8×D4312yes—
155C22#1306333112yes—
156C4—24no—
157C4—434no—
158C4—862no—
159C4—864no—
160C4C2×Dic43⋊C411yescharacteristic
161C4#1306328211yescharacteristic
162C4C4×C22⋊D4311yescharacteristic
163C4C4×Dic8611yescharacteristic
164C2C4×Dic43⋊C411yescharacteristic
165C2C4×C8×D4311yescharacteristic
166C2#1458285311yescharacteristic
167C2C8×C22⋊D4312yes—
168C2C8×Dic8612yes—
subgroupG/H
centerC22×C8C2×D43
commutatorC2×C43C2×C4×C8
FrattiniC22×C4C22×D43
FittingC2×C4×C8×C43C2
socleC23×C43C22×C4
hypercenterC2×C4×C8D43
hypocenterC43C8×C4⋊C4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
13. Dic43⋊C8C4semidirect
15. C8×Dic43C4semidirect
34. Dic43⋊C4C8direct (N × H)
63. C8×C43C4⋊C4semidirect
78. Dic43C4×C8semidirect
92. C43C8×C4⋊C4semidirect
150. C8Dic43⋊C4direct (N × H)