Finite Group Databasebeta

← C127×#13693 #44577366

Subgroups — C127×#13693 #44577366

Order 32512.

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2264C212yesmaximal
2C127×#2247C211yesmaximal, characteristic, complemented
3C127×#2178C211yesmaximal, characteristic
4C127×#1422C211yesmaximal, characteristic, complemented
5C127×#1420C212yesmaximal, complemented
6#508×C127C2211yescharacteristic
7C2×Q32×C127—21no—
8C2×Q32×C127C2212yes—
9#494×C127—21no—
10#443×C127—21no—
11Q64×C127—22no—
12SD64×C127—22no—
13M64×C127C2212yes—
14#368×C127C2211yescharacteristic
15#359×C127—21no—
16C4×C16×C127C2211yescharacteristic
17#135×C127—21no—
18C2×Q16×C127—22no—
19C2×Q16×C127—41no—
20#131×C127—41no—
21C4⋊Q8×C127—41no—
22Q32×C127—22no—
23Q32×C127—22no—
24Q32×C127—42no—
25Q32×C127D411yescharacteristic
26SD32×C127—21no—
27D16×C127D411yescharacteristic
28C2×C16×C127D411yescharacteristic
29C2×C16×C127C2311yescharacteristic
30#108×C127—21no—
31#104×C127—41no—
32C4×C8×C127D411yescharacteristic
33C32×C127—22no—
34#41×C127—41no—
35C2×Q8×C127—42no—
36Q16×C127—21no—
37Q16×C127—42no—
38Q16×C127—42no—
39Q16×C127—81no—
40Q16×C127—81no—
41SD16×C127—41no—
42D8×C127—21no—
43M16×C127—41no—
44M16×C127—81no—
45C2×C8×C127—81no—
46C2×C8×C127D811yescharacteristic
47C2×C8×C127C2×D411yescharacteristic
48C4⋊C4×C127—82no—
49C42×C127D811yescharacteristic
50C16×C127—21no—
51C16×C127C2×D411yescharacteristic
52C16×C127#4111yescharacteristic
53Q8×C127—41no—
54Q8×C127—82no—
55Q8×C127—82no—
56D4×C127—41no—
57D4×C127—81no—
58C2×C4×C127—21no—
59C2×C4×C127—81no—
60C2×C4×C127—82no—
61C2×C4×C127C2×D811yescharacteristic
62C8×C127—81no—
63C8×C127D1611yescharacteristic
64C8×C127D1611yescharacteristic
65C8×C127#12111yescharacteristic
66C8×C127AGL(1,ℤ/8)11yescharacteristic
67C22×C127—81no—
68C22×C127#50911yescharacteristic
69C4×C127—22no—
70C4×C127—81no—
71C4×C127—162no—
72C4×C127#45911yescharacteristic
73C4×C127C2×D1611yescharacteristic
74#13693C12711yesmaximal, characteristic, direct product factor, Sylow
75C2×C127—21no—
76C2×C127—161no—
77C2×C127#220611yescharacteristic
78#2264C2×C12712yes—
79#2247C2×C12711yescharacteristic, complemented
80#2178C2×C12711yescharacteristic
81#1422C2×C12711yescharacteristic, complemented
82#1420C2×C12712yescomplemented
83C127#1369311yescharacteristic, direct product factor, Sylow
84#508C22×C12711yescharacteristic
85C2×Q32—21no—
86C2×Q32C22×C12712yes—
87#494—21no—
88#443—21no—
89Q64—22no—
90SD64—22no—
91M64C22×C12712yes—
92#368C22×C12711yescharacteristic
93#359—21no—
94C4×C16C22×C12711yescharacteristic
95#135—21no—
96C2×Q16—22no—
97C2×Q16—41no—
98#131—41no—
99C4⋊Q8—41no—
100Q32—22no—
101Q32—22no—
102Q32—42no—
103Q32D4×C12711yescharacteristic
104SD32—21no—
105D16D4×C12711yescharacteristic
106C2×C16D4×C12711yescharacteristic
107C2×C16C23×C12711yescharacteristic
108#108—21no—
109#104—41no—
110C4×C8D4×C12711yescharacteristic
111C32—22no—
112#41—41no—
113C2×Q8—42no—
114Q16—21no—
115Q16—42no—
116Q16—42no—
117Q16—81no—
118Q16—81no—
119SD16—41no—
120D8—21no—
121M16—41no—
122M16—81no—
123C2×C8—81no—
124C2×C8D8×C12711yescharacteristic
125C2×C8C2×D4×C12711yescharacteristic
126C4⋊C4—82no—
127C42D8×C12711yescharacteristic
128C16—21no—
129C16C2×D4×C12711yescharacteristic
130C16#41×C12711yescharacteristic
131Q8—41no—
132Q8—82no—
133Q8—82no—
134D4—41no—
135D4—81no—
136C2×C4—21no—
137C2×C4—81no—
138C2×C4—82no—
139C2×C4C2×D8×C12711yescharacteristic
140C8—81no—
141C8D16×C12711yescharacteristic
142C8D16×C12711yescharacteristic
143C8#121×C12711yescharacteristic
144C8AGL(1,ℤ/8)×C12711yescharacteristic
145C22—81no—
146C22#509×C12711yescharacteristic
147C4—22no—
148C4—81no—
149C4—162no—
150C4#459×C12711yescharacteristic
151C4C2×D16×C12711yescharacteristic
152C2—21no—
153C2—161no—
154C2C127×#220611yescharacteristic
subgroupG/H
center, socleC2×C127#2206
commutator, Frattini, cosocleC2×C16C23×C127
prime radical#508×C127C22
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ C4×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2247C2semidirect
4. C127×#1422C2semidirect
5. C127×#1420C2semidirect
74. #13693C127direct (N × H)
79. #2247C2×C127semidirect
81. #1422C2×C127semidirect
82. #1420C2×C127semidirect
83. C127#13693direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22642
C127×#22472
C127×#21782
C127×#14222
C127×#14202
#13693127