Finite Group Databasebeta

← C127×#12529 #44576202

Subgroups — C127×#12529 #44576202

Order 32512.

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

normal subgroups only

This group has 318 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, complemented
2C127×#2240C212yesmaximal, complemented
3C127×#1712C211yesmaximal, characteristic
4C127×#1707C211yesmaximal, characteristic, complemented
5C127×#1312C211yesmaximal, characteristic, complemented
6C2×SD32×C127—24no—
7#500×C127C2211yescharacteristic
8#498×C127—21no—
9#494×C127C2211yescharacteristic
10#493×C127—21no—
11#493×C127—21no—
12#493×C127C2212yes—
13#487×C127—21no—
14#357×C127—24no—
15C4×C16×C127C2212yes—
16C82×C127C2211yescharacteristic
17C2×Q16×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—42no—
21C2×D8×C127—42no—
22C4⋊Q8×C127—21no—
23C4⋊Q8×C127—21no—
24#127×C127—22no—
25SD32×C127—48no—
26C2×C16×C127D414yes—
27#107×C127—22no—
28#106×C127—42no—
29#103×C127—42no—
30C4×C8×C127D411yescharacteristic
31C4×C8×C127D411yescharacteristic
32C4×C8×C127C2311yescharacteristic
33C2×Q8×C127—41no—
34C2×Q8×C127—41no—
35C2×D4×C127—42no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38Q16×C127—44no—
39D8×C127—44no—
40D8×C127—44no—
41D8×C127—84no—
42D8×C127—84no—
43C2×C8×C127D812yes—
44C2×C8×C127D812yes—
45C2×C8×C127C2×D412yes—
46C4⋊C4×C127—41no—
47C4⋊C4×C127—41no—
48C4⋊C4×C127—41no—
49C4⋊C4×C127—41no—
50C42×C127C2×D411yescharacteristic
51C16×C127—24no—
52C23×C127—82no—
53Q8×C127—82no—
54Q8×C127—82no—
55D4×C127—82no—
56D4×C127—82no—
57D4×C127—84no—
58D4×C127—84no—
59C2×C4×C127—81no—
60C2×C4×C127—81no—
61C2×C4×C127#12711yescharacteristic
62C2×C4×C127C2×D811yescharacteristic
63C2×C4×C127C2×D811yescharacteristic
64C8×C127—22no—
65C8×C127SD3214yescomplemented
66C8×C127AGL(1,ℤ/8)14yes—
67C22×C127—162no—
68C22×C127—162no—
69C22×C127—162no—
70C22×C127#49311yescharacteristic
71C4×C127—161no—
72C4×C127—161no—
73C4×C127#49612yes—
74C4×C127C2×SD3212yes—
75C4×C127#50912yes—
76#12529C12711yesmaximal, characteristic, direct product factor, Sylow
77C2×C127—322no—
78C2×C127#172111yescharacteristic
79C2×C127#224811yescharacteristic
80C2×C127#225011yescharacteristic
81#2248C2×C12712yescomplemented
82#2240C2×C12712yescomplemented
83#1712C2×C12711yescharacteristic
84#1707C2×C12711yescharacteristic, complemented
85#1312C2×C12711yescharacteristic, complemented
86C127#1252911yescharacteristic, direct product factor, Sylow
87C2×SD32—24no—
88#500C22×C12711yescharacteristic
89#498—21no—
90#494C22×C12711yescharacteristic
91#493—21no—
92#493—21no—
93#493C22×C12712yes—
94#487—21no—
95#357—24no—
96C4×C16C22×C12712yes—
97C82C22×C12711yescharacteristic
98C2×Q16—22no—
99C2×D8—22no—
100C2×D8—22no—
101C2×D8—42no—
102C2×D8—42no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105#127—22no—
106SD32—48no—
107C2×C16D4×C12714yes—
108#107—22no—
109#106—42no—
110#103—42no—
111C4×C8D4×C12711yescharacteristic
112C4×C8D4×C12711yescharacteristic
113C4×C8C23×C12711yescharacteristic
114C2×Q8—41no—
115C2×Q8—41no—
116C2×D4—42no—
117C2×D4—42no—
118C2×D4—42no—
119Q16—44no—
120D8—44no—
121D8—44no—
122D8—84no—
123D8—84no—
124C2×C8D8×C12712yes—
125C2×C8D8×C12712yes—
126C2×C8C2×D4×C12712yes—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C42C2×D4×C12711yescharacteristic
132C16—24no—
133C23—82no—
134Q8—82no—
135Q8—82no—
136D4—82no—
137D4—82no—
138D4—84no—
139D4—84no—
140C2×C4—81no—
141C2×C4—81no—
142C2×C4#127×C12711yescharacteristic
143C2×C4C2×D8×C12711yescharacteristic
144C2×C4C2×D8×C12711yescharacteristic
145C8—22no—
146C8SD32×C12714yescomplemented
147C8AGL(1,ℤ/8)×C12714yes—
148C22—162no—
149C22—162no—
150C22—162no—
151C22#493×C12711yescharacteristic
152C4—161no—
153C4—161no—
154C4#496×C12712yes—
155C4C2×SD32×C12712yes—
156C4#509×C12712yes—
157C2—322no—
158C2C127×#172111yescharacteristic
159C2C127×#224811yescharacteristic
160C2C127×#225011yescharacteristic
subgroupG/H
center, socleC22×C127#493
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#1712C2
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
1. C127×#2248C2semidirect
2. C127×#2240C2semidirect
4. C127×#1707C2semidirect
5. C127×#1312C2semidirect
65. C8×C127SD32semidirect
76. #12529C127direct (N × H)
81. #2248C2×C127semidirect
82. #2240C2×C127semidirect
84. #1707C2×C127semidirect
85. #1312C2×C127semidirect
86. C127#12529direct (N × H)
146. 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×#22402
C127×#17122
C127×#17072
C127×#13122
#12529127