Finite Group Databasebeta

← C41×#1660 #19105440

Subgroups — C41×#1660 #19105440

Order 5248.

196 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C41×#563C211yesmaximal, characteristic
2C41×#501C212yesmaximal, complemented
3C41×#497C211yesmaximal, characteristic
4C41×#330C212yesmaximal, complemented
5C41×#329C211yesmaximal, characteristic
6C2×Q16×C41—21no—
7C2×SD16×C41—21no—
8C4⋊Q8×C41—21no—
9C4⋊Q8×C41C2211yescharacteristic
10#126×C41—22no—
11#125×C41C2212yes—
12#124×C41C2211yescharacteristic
13#123×C41—21no—
14C22⋊Q8×C41—22no—
15#107×C41—22no—
16#106×C41—22no—
17#97×C41C2212yes—
18#97×C41C2211yescharacteristic
19C2×Q8×C41—21no—
20C2×Q8×C41—21no—
21C2×Q8×C41D411yescharacteristic
22C2×D4×C41D411yescharacteristic
23C22×C4×C41—21no—
24Q16×C41—42no—
25SD16×C41—42no—
26C2×C8×C41—22no—
27C2×C8×C41—21no—
28C4⋊C4×C41—22no—
29C4⋊C4×C41—22no—
30C4⋊C4×C41—22no—
31C4⋊C4×C41—22no—
32C4⋊C4×C41D412yes—
33C4⋊C4×C41D412yes—
34C22⋊C4×C41—22no—
35C22⋊C4×C41—21no—
36C22⋊C4×C41—22no—
37C42×C41—21no—
38C42×C41C2311yescharacteristic
39C23×C41—21no—
40Q8×C41—41no—
41Q8×C41—41no—
42Q8×C41—41no—
43Q8×C41—81no—
44D4×C41—41no—
45C2×C4×C41—22no—
46C2×C4×C41—21no—
47C2×C4×C41—22no—
48C2×C4×C41—41no—
49C2×C4×C41—81no—
50C2×C4×C41C2×D412yes—
51C2×C4×C41C2×D411yescharacteristic
52C8×C41—24no—
53C8×C41—22no—
54C22×C41—41no—
55C22×C41—42no—
56C22×C41#12011yescharacteristic
57C4×C41—21no—
58C4×C41—22no—
59C4×C41—42no—
60C4×C41—41no—
61C4×C41—42no—
62C4×C41—81no—
63#1660C4111yesmaximal, characteristic, direct product factor, Sylow
64C2×C41—81no—
65C2×C41#45311yescharacteristic
66C2×C41#45612yes—
67#563C2×C4111yescharacteristic
68#501C2×C4112yescomplemented
69#497C2×C4111yescharacteristic
70#330C2×C4112yescomplemented
71#329C2×C4111yescharacteristic
72C41#166011yescharacteristic, direct product factor, Sylow
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—21no—
76C4⋊Q8C22×C4111yescharacteristic
77#126—22no—
78#125C22×C4112yes—
79#124C22×C4111yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—22no—
83#106—22no—
84#97C22×C4112yes—
85#97C22×C4111yescharacteristic
86C2×Q8—21no—
87C2×Q8—21no—
88C2×Q8D4×C4111yescharacteristic
89C2×D4D4×C4111yescharacteristic
90C22×C4—21no—
91Q16—42no—
92SD16—42no—
93C2×C8—22no—
94C2×C8—21no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—22no—
99C4⋊C4D4×C4112yes—
100C4⋊C4D4×C4112yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C23×C4111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—81no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—41no—
116C2×C4—81no—
117C2×C4C2×D4×C4112yes—
118C2×C4C2×D4×C4111yescharacteristic
119C8—22no—
120C8—24no—
121C22—41no—
122C22—42no—
123C22#120×C4111yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—81no—
130C2—81no—
131C2C41×#45311yescharacteristic
132C2C41×#45612yes—
subgroupG/H
center, socleC22×C41#120
commutator, Frattini, cosocleC42C23×C41
prime radicalC2×D4×C41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#501C2semidirect
4. C41×#330C2semidirect
63. #1660C41direct (N × H)
68. #501C2×C41semidirect
70. #330C2×C41semidirect
72. C41#1660direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#5632
C41×#5012
C41×#4972
C41×#3302
C41×#3292
#166041