Finite Group Databasebeta

← C2×#442×C241 #44504609

Subgroups — C2×#442×C241 #44504609

Order 30848.

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

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 296 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×D8×C241C211yesmaximal, characteristic
2C2×C4×D4×C241C212yesmaximal, complemented
3#442×C241C218yesmaximal, direct product factor
4C2×#106×C241C211yesmaximal, characteristic, complemented
5C2×#102×C241C212yesmaximal, complemented
6C2×#97×C241C211yesmaximal, characteristic, complemented
7C22×D4×C241C2212yes—
8C23×C4×C241—22no—
9C2×D8×C241C418yescomplemented
10C2×D8×C241C2214yes—
11C22×C8×C241C2211yescharacteristic
12C22×C8×C241C2211yescharacteristic
13C4×D4×C241—24no—
14C4×D4×C241C2218yescomplemented
15C2×C4⋊C4×C241C2212yes—
16C2×C22⋊C4×C241—22no—
17C2×C42×C241C2211yescharacteristic
18#106×C241C2214yescomplemented
19#102×C241C2218yescomplemented
20#97×C241C2214yescomplemented
21C24×C241—22no—
22C2×D4×C241—22no—
23C2×D4×C241—24no—
24C2×D4×C241C2×C418yescomplemented
25C2×D4×C241C2314yes—
26C22×C4×C241—22no—
27C22×C4×C241—28no—
28C22×C4×C241—48no—
29C22×C4×C241D412yes—
30C22×C4×C241C2311yescharacteristic
31D8×C241C2×C4116yescomplemented
32C2×C8×C241—22no—
33C2×C8×C241C2×C414yescomplemented
34C2×C8×C241C2312yes—
35C2×C8×C241C2312yes—
36C4⋊C4×C241—22no—
37C4⋊C4×C241C2314yes—
38C22⋊C4×C241—28no—
39C42×C241D412yes—
40C42×C241C2312yes—
41C23×C241—28no—
42C23×C241—24no—
43C23×C241—44no—
44C23×C241—44no—
45C23×C241C2×D411yescharacteristic
46D4×C241—28no—
47D4×C241—24no—
48D4×C241C22×C418yescomplemented
49C2×C4×C241—24no—
50C2×C4×C241—24no—
51C2×C4×C241—416no—
52C2×C4×C241—44no—
53C2×C4×C241C22×C412yes—
54C2×C4×C241C2×D414yes—
55C2×C4×C241C2×D411yescharacteristic
56C2×C4×C241#4112yes—
57C2×C4×C241C2411yescharacteristic
58C8×C241—22no—
59C8×C241C22×C414yescomplemented
60C22×C241—28no—
61C22×C241—44no—
62C22×C241—44no—
63C22×C241—416no—
64C22×C241C4×D412yes—
65C22×C241AGL(1,ℤ/8)14yes—
66C22×C241C22×D411yescharacteristic
67C4×C241—24no—
68C4×C241—44no—
69C4×C241C4×D412yes—
70C4×C241C23×C411yescharacteristic
71C4×C241C2×#4111yescharacteristic
72C2×C241—48no—
73C2×C241#44214yesdirect product factor
74C2×C241C2×C4×D411yescharacteristic
75C2×C241C2×AGL(1,ℤ/8)12yes—
76C241C2×#44211yescharacteristic, direct product factor, Sylow
77C2×#442C24111yesmaximal, characteristic, direct product factor, Sylow
78C22×D8C2×C24111yescharacteristic
79C2×C4×D4C2×C24112yescomplemented
80#442C2×C24118yesdirect product factor
81C2×#106C2×C24111yescharacteristic, complemented
82C2×#102C2×C24112yescomplemented
83C2×#97C2×C24111yescharacteristic, complemented
84C22×D4C22×C24112yes—
85C23×C4—22no—
86C2×D8C4×C24118yescomplemented
87C2×D8C22×C24114yes—
88C22×C8C22×C24111yescharacteristic
89C22×C8C22×C24111yescharacteristic
90C4×D4—24no—
91C4×D4C22×C24118yescomplemented
92C2×C4⋊C4C22×C24112yes—
93C2×C22⋊C4—22no—
94C2×C42C22×C24111yescharacteristic
95#106C22×C24114yescomplemented
96#102C22×C24118yescomplemented
97#97C22×C24114yescomplemented
98C24—22no—
99C2×D4—22no—
100C2×D4—24no—
101C2×D4C2×C4×C24118yescomplemented
102C2×D4C23×C24114yes—
103C22×C4—22no—
104C22×C4—28no—
105C22×C4—48no—
106C22×C4D4×C24112yes—
107C22×C4C23×C24111yescharacteristic
108D8C2×C4×C241116yescomplemented
109C2×C8—22no—
110C2×C8C2×C4×C24114yescomplemented
111C2×C8C23×C24112yes—
112C2×C8C23×C24112yes—
113C4⋊C4—22no—
114C4⋊C4C23×C24114yes—
115C22⋊C4—28no—
116C42D4×C24112yes—
117C42C23×C24112yes—
118C23—28no—
119C23—24no—
120C23—44no—
121C23—44no—
122C23C2×D4×C24111yescharacteristic
123D4—28no—
124D4—24no—
125D4C22×C4×C24118yescomplemented
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—416no—
129C2×C4—44no—
130C2×C4C22×C4×C24112yes—
131C2×C4C2×D4×C24114yes—
132C2×C4C2×D4×C24111yescharacteristic
133C2×C4#41×C24112yes—
134C2×C4C24×C24111yescharacteristic
135C8—22no—
136C8C22×C4×C24114yescomplemented
137C22—28no—
138C22—44no—
139C22—44no—
140C22—416no—
141C22C4×D4×C24112yes—
142C22AGL(1,ℤ/8)×C24114yes—
143C22C22×D4×C24111yescharacteristic
144C4—24no—
145C4—44no—
146C4C4×D4×C24112yes—
147C4C23×C4×C24111yescharacteristic
148C4C2×#41×C24111yescharacteristic
149C2—48no—
150C2#442×C24114yesdirect product factor
151C2C2×C4×D4×C24111yescharacteristic
152C2C2×AGL(1,ℤ/8)×C24112yes—
subgroupG/H
center, socleC23×C241C2×D4
commutatorC4C23×C4×C241
Frattini, cosocleC2×C4C24×C241
prime radicalC22×D8×C241C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C241 ◁ C2×C42×C241 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×C241C2semidirect
3. #442×C241C2direct (N × H)
4. C2×#106×C241C2semidirect
5. C2×#102×C241C2semidirect
6. C2×#97×C241C2semidirect
9. C2×D8×C241C4semidirect
14. C4×D4×C241C22semidirect
18. #106×C241C22semidirect
19. #102×C241C22semidirect
20. #97×C241C22semidirect
24. C2×D4×C241C2×C4semidirect
31. D8×C241C2×C4semidirect
33. C2×C8×C241C2×C4semidirect
48. D4×C241C22×C4semidirect
59. C8×C241C22×C4semidirect
73. C2×C241#442direct (N × H)
76. C241C2×#442direct (N × H)
77. C2×#442C241direct (N × H)
79. C2×C4×D4C2×C241semidirect
80. #442C2×C241direct (N × H)
81. C2×#106C2×C241semidirect
82. C2×#102C2×C241semidirect
83. C2×#97C2×C241semidirect
86. C2×D8C4×C241semidirect
91. C4×D4C22×C241semidirect
95. #106C22×C241semidirect
96. #102C22×C241semidirect
97. #97C22×C241semidirect
101. C2×D4C2×C4×C241semidirect
108. D8C2×C4×C241semidirect
110. C2×C8C2×C4×C241semidirect
125. D4C22×C4×C241semidirect
136. C8C22×C4×C241semidirect
150. C2#442×C241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D8×C2412
C2×C4×D4×C2412
#442×C2412
C2×#106×C2412
C2×#102×C2412
C2×#97×C2412
C2×#442241