Finite Group Databasebeta

← C127×#7520 #44571193

Subgroups — C127×#7520 #44571193

Order 32512.

156 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C127×#1623C211yesmaximal, characteristic
2C127×#1409C211yesmaximal, characteristic
3C127×#1359C211yesmaximal, characteristic
4Q82×C127C411yescharacteristic, complemented
5#492×C127C2211yescharacteristic
6#460×C127—21no—
7#364×C127—21no—
8#353×C127—21no—
9#333×C127C411yescharacteristic, complemented
10Q8⋊C8×C127—21no—
11C2×SD16×C127—41no—
12C2×SD16×C127—41no—
13C4⋊Q8×C127—41no—
14C4⋊Q8×C127—41no—
15C4⋊Q8×C127C2×C411yescharacteristic
16#127×C127D411yescharacteristic
17C4×Q8×C127—21no—
18C4×Q8×C127—41no—
19M32×C127—41no—
20C4⋊C8×C127—21no—
21#102×C127—41no—
22#99×C127—41no—
23C4×C8×C127D411yescharacteristic
24C2×Q8×C127—21no—
25C2×Q8×C127—21no—
26C2×Q8×C127—41no—
27C2×D4×C127—21no—
28C2×D4×C127—41no—
29SD16×C127—81no—
30SD16×C127—81no—
31SD16×C127—82no—
32C2×C8×C127—21no—
33C2×C8×C127—41no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—41no—
36C4⋊C4×C127—42no—
37C4⋊C4×C127—41no—
38C22⋊C4×C127—81no—
39C42×C127—41no—
40C42×C127—41no—
41C42×C127C22⋊C411yescharacteristic
42C16×C127—81no—
43C23×C127—41no—
44Q8×C127—22no—
45Q8×C127—41no—
46Q8×C127—81no—
47Q8×C127—161no—
48D4×C127—81no—
49D4×C127—81no—
50D4×C127—81no—
51C2×C4×C127—21no—
52C2×C4×C127—41no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127—161no—
56C2×C4×C127#9911yescharacteristic
57C8×C127—21no—
58C8×C127—21no—
59C8×C127—81no—
60C22×C127—81no—
61C22×C127—161no—
62C22×C127AΣL(1,𝔽16)11yescharacteristic
63C4×C127—21no—
64C4×C127—21no—
65C4×C127—21no—
66C4×C127—42no—
67C4×C127—81no—
68C4×C127—81no—
69C4×C127—321no—
70#7520C12711yesmaximal, characteristic, direct product factor, Sylow
71C2×C127—21no—
72C2×C127—161no—
73C2×C127#140211yescharacteristic
74#1623C2×C12711yescharacteristic
75#1409C2×C12711yescharacteristic
76#1359C2×C12711yescharacteristic
77C127#752011yescharacteristic, direct product factor, Sylow
78Q82C4×C12711yescharacteristic, complemented
79#492C22×C12711yescharacteristic
80#460—21no—
81#364—21no—
82#353—21no—
83#333C4×C12711yescharacteristic, complemented
84Q8⋊C8—21no—
85C2×SD16—41no—
86C2×SD16—41no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8C2×C4×C12711yescharacteristic
90#127D4×C12711yescharacteristic
91C4×Q8—21no—
92C4×Q8—41no—
93M32—41no—
94C4⋊C8—21no—
95#102—41no—
96#99—41no—
97C4×C8D4×C12711yescharacteristic
98C2×Q8—21no—
99C2×Q8—21no—
100C2×Q8—41no—
101C2×D4—21no—
102C2×D4—41no—
103SD16—81no—
104SD16—81no—
105SD16—82no—
106C2×C8—21no—
107C2×C8—41no—
108C4⋊C4—21no—
109C4⋊C4—41no—
110C4⋊C4—42no—
111C4⋊C4—41no—
112C22⋊C4—81no—
113C42—41no—
114C42—41no—
115C42C22⋊C4×C12711yescharacteristic
116C16—81no—
117C23—41no—
118Q8—22no—
119Q8—41no—
120Q8—81no—
121Q8—161no—
122D4—81no—
123D4—81no—
124D4—81no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—161no—
130C2×C4#99×C12711yescharacteristic
131C8—21no—
132C8—21no—
133C8—81no—
134C22—81no—
135C22—161no—
136C22AΣL(1,𝔽16)×C12711yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—81no—
142C4—81no—
143C4—321no—
144C2—21no—
145C2—161no—
146C2C127×#140211yescharacteristic
subgroupG/H
center, socleC2×C127#1402
commutatorC4⋊Q8C2×C4×C127
Frattini, cosocle#492C22×C127
prime radical#127×C127D4
LCSG ▷ C4⋊Q8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C42×C127 ◁ #492×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. Q82×C127C4semidirect
9. #333×C127C4semidirect
70. #7520C127direct (N × H)
77. C127#7520direct (N × H)
78. Q82C4×C127semidirect
83. #333C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#16232
C127×#14092
C127×#13592
#7520127