Finite Group Databasebeta

← C4×#41×C11⋊C5 #72248938

Subgroups — C4×#41×C11⋊C5 #72248938

Order 3520.

620 conjugacy classes of subgroups; only the 375 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 375 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×#41×C11⋊C5C211yesmaximal, characteristic
2C4×Q8×C11⋊C5C212yesmaximal, complemented
3C4×D4×C11⋊C5C216yesmaximal, complemented
4#117×C11⋊C5C213yesmaximal, complemented
5C2×C42×C11⋊C5C213yesmaximal, complemented
6#41×C11⋊C5C418yesdirect product factor
7C2×Q8×C11⋊C5C2211yescharacteristic
8C2×D4×C11⋊C5C2213yes—
9C22×C4×C11⋊C5C2216yes—
10C22×C4×C11⋊C5C2213yes—
11C4⋊C4×C11⋊C5C2216yes—
12C22⋊C4×C11⋊C5C2216yes—
13C42×C11⋊C5C2211yescharacteristic
14C42×C11⋊C5C2213yes—
15C42×C11⋊C5C2216yes—
16C4×C11×#41C511yesmaximal, characteristic, complemented, Hall
17C23×C11⋊C5C2313yes—
18Q8×C11⋊C5C2×C414yescomplemented
19D4×C11⋊C5C2×C4112yescomplemented
20C2×C4×C11⋊C5—212no—
21C2×C4×C11⋊C5C2×C4112yescomplemented
22C2×C4×C11⋊C5C2316yes—
23C2×C4×C11⋊C5C2311yescharacteristic
24C2×C4×C11⋊C5C2313yes—
25C2×C4×C11⋊C5C2312yes—
26C2×C11×#41C2×C511yescharacteristic
27C4×Q8×C11C2×C512yescomplemented
28C4×D4×C11C2×C516yescomplemented
29C11×#117C2×C513yescomplemented
30C2×C42×C11C2×C513yescomplemented
31C4×C5×#41—111nomaximal, Hall
32C22×C11⋊C5—26no—
33C22×C11⋊C5C22×C416yes—
34C22×C11⋊C5C2411yescharacteristic
35C4×C11⋊C5—26no—
36C4×C11⋊C5C22×C412yes—
37C4×C11⋊C5C22×C416yes—
38C4×C11⋊C5#4114yesdirect product factor
39C11×#41C4×C518yescomplemented
40C2×Q8×C11C22×C511yescharacteristic
41C2×D4×C11C22×C513yes—
42C22×C4×C11C22×C516yes—
43C22×C4×C11C22×C513yes—
44C11×C4⋊C4C22×C516yes—
45C11×C22⋊C4C22×C516yes—
46C42×C11C22×C513yes—
47C42×C11C22×C516yes—
48C42×C11C22×C511yescharacteristic
49C2×C5×#41—111no—
50C4×C5×Q8—112no—
51C4×C5×D4—116no—
52C5×#117—113no—
53C2×C42×C5—113no—
54C2×C11⋊C5—26no—
55C2×C11⋊C5C23×C411yescharacteristic
56C2×C11⋊C5C2×#4112yes—
57C23×C11C23×C513yes—
58Q8×C11C2×C4×C514yescomplemented
59D4×C11C2×C4×C5112yescomplemented
60C2×C4×C11—212no—
61C2×C4×C11C2×C4×C5112yescomplemented
62C2×C4×C11C23×C516yes—
63C2×C4×C11C23×C511yescharacteristic
64C2×C4×C11C23×C513yes—
65C2×C4×C11C23×C512yes—
66C5×#41—118no—
67C2×C5×Q8—111no—
68C2×C5×D4—113no—
69C22×C4×C5—113no—
70C22×C4×C5—116no—
71C5×C4⋊C4—116no—
72C5×C22⋊C4—116no—
73C42×C5—113no—
74C42×C5—116no—
75C42×C5—111no—
76C4×#41C11⋊C511yescharacteristic, direct product factor, Sylow
77C11⋊C5C4×#4111yescharacteristic, direct product factor, Hall
78C22×C11—26no—
79C22×C11C22×C4×C516yes—
80C22×C11C24×C511yescharacteristic
81C4×C11—26no—
82C4×C11C22×C4×C512yes—
83C4×C11C22×C4×C516yes—
84C4×C11C5×#4114yescomplemented
85C23×C5—113no—
86C5×Q8—114no—
87C5×D4—1112no—
88C2×C4×C5—1112no—
89C2×C4×C5—111no—
90C2×C4×C5—112no—
91C2×C4×C5—113no—
92C2×C4×C5—116no—
93C2×C4×C5—2212no—
94C2×#41C2×C11⋊C511yescharacteristic
95C4×Q8C2×C11⋊C512yescomplemented
96C4×D4C2×C11⋊C516yescomplemented
97#117C2×C11⋊C513yescomplemented
98C2×C42C2×C11⋊C513yescomplemented
99C2×C11—26no—
100C2×C11C23×C4×C511yescharacteristic
101C2×C11C2×C5×#4112yes—
102C22×C5—116no—
103C22×C5—111no—
104C22×C5—226no—
105C4×C5—112no—
106C4×C5—116no—
107C4×C5—114no—
108C4×C5—226no—
109#41C4×C11⋊C518yesdirect product factor
110C2×Q8C22×C11⋊C511yescharacteristic
111C2×D4C22×C11⋊C513yes—
112C22×C4C22×C11⋊C516yes—
113C22×C4C22×C11⋊C513yes—
114C4⋊C4C22×C11⋊C516yes—
115C22⋊C4C22×C11⋊C516yes—
116C42C22×C11⋊C513yes—
117C42C22×C11⋊C516yes—
118C42C22×C11⋊C511yescharacteristic
119C11C4×C5×#4111yescharacteristic, complemented, Sylow
120C2×C5—111no—
121C2×C5—112no—
122C2×C5—226no—
123C23C23×C11⋊C513yes—
124Q8C2×C4×C11⋊C514yescomplemented
125D4C2×C4×C11⋊C5112yescomplemented
126C2×C4—212no—
127C2×C4C2×C4×C11⋊C5112yescomplemented
128C2×C4C23×C11⋊C516yes—
129C2×C4C23×C11⋊C511yescharacteristic
130C2×C4C23×C11⋊C513yes—
131C2×C4C23×C11⋊C512yes—
132C5—111noSylow
133C22—26no—
134C22C22×C4×C11⋊C516yes—
135C22C24×C11⋊C511yescharacteristic
136C4—26no—
137C4C22×C4×C11⋊C512yes—
138C4C22×C4×C11⋊C516yes—
139C4#41×C11⋊C514yesdirect product factor
140C2—26no—
141C2C23×C4×C11⋊C511yescharacteristic
142C2C2×#41×C11⋊C512yes—
subgroupG/H
centerC42C22×C11⋊C5
commutatorC2×C11C23×C4×C5
FrattiniC22C24×C11⋊C5
FittingC4×C11×#41C5
socle, cosocleC22×C11C24×C5
prime radicalC2×#41×C11⋊C5C2
hypercenterC4×#41C11⋊C5
hypocenterC11C4×C5×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C11⋊C5C2semidirect
3. C4×D4×C11⋊C5C2semidirect
4. #117×C11⋊C5C2semidirect
5. C2×C42×C11⋊C5C2semidirect
6. #41×C11⋊C5C4direct (N × H)
16. C4×C11×#41C5semidirect
18. Q8×C11⋊C5C2×C4semidirect
19. D4×C11⋊C5C2×C4semidirect
21. C2×C4×C11⋊C5C2×C4semidirect
27. C4×Q8×C11C2×C5semidirect
28. C4×D4×C11C2×C5semidirect
29. C11×#117C2×C5semidirect
30. C2×C42×C11C2×C5semidirect
38. C4×C11⋊C5#41direct (N × H)
39. C11×#41C4×C5semidirect
58. Q8×C11C2×C4×C5semidirect
59. D4×C11C2×C4×C5semidirect
61. C2×C4×C11C2×C4×C5semidirect
76. C4×#41C11⋊C5direct (N × H)
77. C11⋊C5C4×#41direct (N × H)
84. C4×C11C5×#41semidirect
95. C4×Q8C2×C11⋊C5semidirect
96. C4×D4C2×C11⋊C5semidirect
97. #117C2×C11⋊C5semidirect
98. C2×C42C2×C11⋊C5semidirect
109. #41C4×C11⋊C5direct (N × H)
119. C11C4×C5×#41semidirect
124. Q8C2×C4×C11⋊C5semidirect
125. D4C2×C4×C11⋊C5semidirect
127. C2×C4C2×C4×C11⋊C5semidirect
139. C4#41×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×C11⋊C52
C4×Q8×C11⋊C52
C4×D4×C11⋊C52
#117×C11⋊C52
C2×C42×C11⋊C52
C4×C11×#415
C4×C5×#4111