Finite Group Databasebeta

← #1490×C241 #44503157

Subgroups — #1490×C241 #44503157

Order 30848.

316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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×D4×C241C211yesmaximal, characteristic
2#432×C241C211yesmaximal, characteristic, complemented
3C4×M16×C241C211yesmaximal, characteristic, complemented
4D4⋊C8×C241C214yesmaximal, complemented
5C22×D4×C241C411yescharacteristic
6C23×C4×C241—21no—
7C2×M16×C241—21no—
8C4×D4×C241—21no—
9C4×D4×C241—21no—
10C4×D4×C241C412yes—
11C4×D4×C241C2212yes—
12C2×C4⋊C4×C241C411yescharacteristic
13C2×C22⋊C4×C241—21no—
14C2×C42×C241C2211yescharacteristic
15C4⋊C8×C241C2212yescomplemented
16C22⋊C8×C241—21no—
17#97×C241—21no—
18#97×C241—21no—
19C4×C8×C241C2212yescomplemented
20C24×C241—21no—
21C2×D4×C241—24no—
22C2×D4×C241—21no—
23C2×D4×C241C2×C412yes—
24C22×C4×C241—21no—
25C22×C4×C241—22no—
26C22×C4×C241—22no—
27C22×C4×C241—44no—
28C22×C4×C241C2×C411yescharacteristic
29C22×C4×C241D411yescharacteristic
30C22×C4×C241D411yescharacteristic
31M16×C241—24no—
32C2×C8×C241—22no—
33C2×C8×C241—22no—
34C4⋊C4×C241—21no—
35C4⋊C4×C241C2×C412yes—
36C22⋊C4×C241—22no—
37C22⋊C4×C241—22no—
38C42×C241C2×C411yescharacteristic
39C42×C241D411yescharacteristic
40C42×C241D411yescharacteristic
41C42×C241C2311yescharacteristic
42C23×C241—24no—
43C23×C241—22no—
44C23×C241—42no—
45C23×C241—42no—
46C23×C241C22⋊C411yescharacteristic
47D4×C241—24no—
48D4×C241—22no—
49D4×C241M1614yescomplemented
50C2×C4×C241—22no—
51C2×C4×C241—22no—
52C2×C4×C241—22no—
53C2×C4×C241—22no—
54C2×C4×C241—44no—
55C2×C4×C241—42no—
56C2×C4×C241—44no—
57C2×C4×C241C22⋊C411yescharacteristic
58C2×C4×C241C22⋊C411yescharacteristic
59C2×C4×C241C22⋊C411yescharacteristic
60C2×C4×C241C22×C411yescharacteristic
61C2×C4×C241C2×D411yescharacteristic
62C2×C4×C241C2×D411yescharacteristic
63C8×C241—24no—
64C8×C241—42no—
65C22×C241—21no—
66C22×C241—21no—
67C22×C241—24no—
68C22×C241—48no—
69C22×C241—42no—
70C22×C241—42no—
71C22×C241#10412yes—
72C22×C241C2×C22⋊C411yescharacteristic
73C4×C241—21no—
74C4×C241—21no—
75C4×C241—21no—
76C4×C241—21no—
77C4×C241—42no—
78C4×C241C2×M1612yes—
79C4×C241AGL(1,ℤ/8)12yes—
80C2×C241—22no—
81C2×C241—44no—
82C2×C241#40711yescharacteristic
83C2×C241#41811yescharacteristic
84C2×C241C2×#10411yescharacteristic
85C241#149011yescharacteristic, direct product factor, Sylow
86#1490C24111yesmaximal, characteristic, direct product factor, Sylow
87C2×C4×D4C2×C24111yescharacteristic
88#432C2×C24111yescharacteristic, complemented
89C4×M16C2×C24111yescharacteristic, complemented
90D4⋊C8C2×C24114yescomplemented
91C22×D4C4×C24111yescharacteristic
92C23×C4—21no—
93C2×M16—21no—
94C4×D4—21no—
95C4×D4—21no—
96C4×D4C4×C24112yes—
97C4×D4C22×C24112yes—
98C2×C4⋊C4C4×C24111yescharacteristic
99C2×C22⋊C4—21no—
100C2×C42C22×C24111yescharacteristic
101C4⋊C8C22×C24112yescomplemented
102C22⋊C8—21no—
103#97—21no—
104#97—21no—
105C4×C8C22×C24112yescomplemented
106C24—21no—
107C2×D4—24no—
108C2×D4—21no—
109C2×D4C2×C4×C24112yes—
110C22×C4—21no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—44no—
114C22×C4C2×C4×C24111yescharacteristic
115C22×C4D4×C24111yescharacteristic
116C22×C4D4×C24111yescharacteristic
117M16—24no—
118C2×C8—22no—
119C2×C8—22no—
120C4⋊C4—21no—
121C4⋊C4C2×C4×C24112yes—
122C22⋊C4—22no—
123C22⋊C4—22no—
124C42C2×C4×C24111yescharacteristic
125C42D4×C24111yescharacteristic
126C42D4×C24111yescharacteristic
127C42C23×C24111yescharacteristic
128C23—24no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C22⋊C4×C24111yescharacteristic
133D4—24no—
134D4—22no—
135D4M16×C24114yescomplemented
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—44no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4C22⋊C4×C24111yescharacteristic
144C2×C4C22⋊C4×C24111yescharacteristic
145C2×C4C22⋊C4×C24111yescharacteristic
146C2×C4C22×C4×C24111yescharacteristic
147C2×C4C2×D4×C24111yescharacteristic
148C2×C4C2×D4×C24111yescharacteristic
149C8—24no—
150C8—42no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—48no—
155C22—42no—
156C22—42no—
157C22#104×C24112yes—
158C22C2×C22⋊C4×C24111yescharacteristic
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4C2×M16×C24112yes—
165C4AGL(1,ℤ/8)×C24112yes—
166C2—22no—
167C2—44no—
168C2#407×C24111yescharacteristic
169C2#418×C24111yescharacteristic
170C2C2×#104×C24111yescharacteristic
subgroupG/H
centerC2×C4×C241C2×D4
commutatorC2×C4C22×C4×C241
Frattini, cosocleC42C23×C241
socleC22×C241C2×C22⋊C4
prime radicalC22×D4×C241C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C241 ◁ C2×C42×C241 ◁ G

Complements

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

NH ≅ G/Ntype
2. #432×C241C2semidirect
3. C4×M16×C241C2semidirect
4. D4⋊C8×C241C2semidirect
15. C4⋊C8×C241C22semidirect
19. C4×C8×C241C22semidirect
49. D4×C241M16semidirect
85. C241#1490direct (N × H)
86. #1490C241direct (N × H)
88. #432C2×C241semidirect
89. C4×M16C2×C241semidirect
90. D4⋊C8C2×C241semidirect
101. C4⋊C8C22×C241semidirect
105. C4×C8C22×C241semidirect
135. D4M16×C241semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C2412
#432×C2412
C4×M16×C2412
D4⋊C8×C2412
#1490241