Finite Group Databasebeta

← C127×#12526 #44576199

Subgroups — C127×#12526 #44576199

Order 32512.

296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2248C212yesmaximal
2C127×#2241C212yesmaximal, complemented
3C127×#1713C211yesmaximal, characteristic, complemented
4C127×#1706C211yesmaximal, characteristic
5C127×#1312C211yesmaximal, characteristic, complemented
6C2×SD32×C127—24no—
7#500×C127—21no—
8#500×C127—21no—
9#500×C127C2211yescharacteristic
10#494×C127C2212yes—
11#493×C127C2211yescharacteristic
12#492×C127—21no—
13#486×C127—21no—
14#358×C127—24no—
15C4×C16×C127C2212yes—
16C82×C127C2211yescharacteristic
17C2×Q16×C127—22no—
18C2×Q16×C127—22no—
19C2×SD16×C127—42no—
20C2×D8×C127—22no—
21C4⋊Q8×C127—22no—
22C4⋊Q8×C127—21no—
23#127×C127—21no—
24SD32×C127—48no—
25C2×C16×C127D414yes—
26#107×C127—22no—
27#107×C127—42no—
28#107×C127—42no—
29#102×C127—42no—
30C4×C8×C127D411yescharacteristic
31C4×C8×C127D411yescharacteristic
32C4×C8×C127C2311yescharacteristic
33C2×Q8×C127—42no—
34C2×Q8×C127—41no—
35C2×D4×C127—41no—
36C2×D4×C127—41no—
37C2×D4×C127—41no—
38Q16×C127—44no—
39Q16×C127—44no—
40SD16×C127—84no—
41D8×C127—44no—
42C2×C8×C127D812yes—
43C2×C8×C127D812yes—
44C2×C8×C127C2×D412yes—
45C4⋊C4×C127—41no—
46C4⋊C4×C127—41no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127—42no—
49C42×C127C2×D411yescharacteristic
50C16×C127—24no—
51C23×C127—81no—
52Q8×C127—82no—
53Q8×C127—82no—
54Q8×C127—82no—
55D4×C127—82no—
56D4×C127—82no—
57D4×C127—82no—
58C2×C4×C127—82no—
59C2×C4×C127—81no—
60C2×C4×C127#12711yescharacteristic
61C2×C4×C127C2×D811yescharacteristic
62C2×C4×C127C2×D811yescharacteristic
63C8×C127—22no—
64C8×C127SD3214yescomplemented
65C8×C127AGL(1,ℤ/8)14yes—
66C22×C127—161no—
67C22×C127—161no—
68C22×C127—161no—
69C22×C127#49311yescharacteristic
70C4×C127—162no—
71C4×C127—161no—
72C4×C127#49612yes—
73C4×C127C2×SD3212yes—
74C4×C127#51012yes—
75#12526C12711yesmaximal, characteristic, direct product factor, Sylow
76C2×C127—321no—
77C2×C127#172111yescharacteristic
78C2×C127#224811yescharacteristic
79C2×C127#225111yescharacteristic
80#2248C2×C12712yes—
81#2241C2×C12712yescomplemented
82#1713C2×C12711yescharacteristic, complemented
83#1706C2×C12711yescharacteristic
84#1312C2×C12711yescharacteristic, complemented
85C127#1252611yescharacteristic, direct product factor, Sylow
86C2×SD32—24no—
87#500—21no—
88#500—21no—
89#500C22×C12711yescharacteristic
90#494C22×C12712yes—
91#493C22×C12711yescharacteristic
92#492—21no—
93#486—21no—
94#358—24no—
95C4×C16C22×C12712yes—
96C82C22×C12711yescharacteristic
97C2×Q16—22no—
98C2×Q16—22no—
99C2×SD16—42no—
100C2×D8—22no—
101C4⋊Q8—21no—
102C4⋊Q8—22no—
103#127—21no—
104SD32—48no—
105C2×C16D4×C12714yes—
106#107—22no—
107#107—42no—
108#107—42no—
109#102—42no—
110C4×C8D4×C12711yescharacteristic
111C4×C8D4×C12711yescharacteristic
112C4×C8C23×C12711yescharacteristic
113C2×Q8—42no—
114C2×Q8—41no—
115C2×D4—41no—
116C2×D4—41no—
117C2×D4—41no—
118Q16—44no—
119Q16—44no—
120SD16—84no—
121D8—44no—
122C2×C8D8×C12712yes—
123C2×C8D8×C12712yes—
124C2×C8C2×D4×C12712yes—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C42C2×D4×C12711yescharacteristic
130C16—24no—
131C23—81no—
132Q8—82no—
133Q8—82no—
134Q8—82no—
135D4—82no—
136D4—82no—
137D4—82no—
138C2×C4—82no—
139C2×C4—81no—
140C2×C4#127×C12711yescharacteristic
141C2×C4C2×D8×C12711yescharacteristic
142C2×C4C2×D8×C12711yescharacteristic
143C8—22no—
144C8SD32×C12714yescomplemented
145C8AGL(1,ℤ/8)×C12714yes—
146C22—161no—
147C22—161no—
148C22—161no—
149C22#493×C12711yescharacteristic
150C4—162no—
151C4—161no—
152C4#496×C12712yes—
153C4C2×SD32×C12712yes—
154C4#510×C12712yes—
155C2—321no—
156C2C127×#172111yescharacteristic
157C2C127×#224811yescharacteristic
158C2C127×#225111yescharacteristic
subgroupG/H
center, socleC22×C127#493
commutator, Frattini, cosocleC4×C8C23×C127
prime radical#493×C127C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2241C2semidirect
3. C127×#1713C2semidirect
5. C127×#1312C2semidirect
64. C8×C127SD32semidirect
75. #12526C127direct (N × H)
81. #2241C2×C127semidirect
82. #1713C2×C127semidirect
84. #1312C2×C127semidirect
85. C127#12526direct (N × H)
144. C8SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22482
C127×#22412
C127×#17132
C127×#17062
C127×#13122
#12526127