Finite Group Databasebeta

← C127×#12525 #44576198

Subgroups — C127×#12525 #44576198

Order 32512.

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

normal subgroups only

This group has 340 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×#2246C212yesmaximal, complemented
2C127×#2240C212yesmaximal, complemented
3C127×#1712C211yesmaximal, characteristic, complemented
4C127×#1706C211yesmaximal, characteristic, complemented
5C127×#1312C211yesmaximal, characteristic, complemented
6C2×D16×C127—24no—
7#500×C127C2211yescharacteristic
8#493×C127—21no—
9#493×C127—21no—
10#493×C127C2211yescharacteristic
11#493×C127C2212yes—
12#492×C127—21no—
13#486×C127—21no—
14#357×C127—24no—
15C4×C16×C127C2212yes—
16C82×C127C2211yescharacteristic
17C2×SD16×C127—42no—
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—22no—
21C2×D8×C127—42no—
22C2×D8×C127—42no—
23C4⋊Q8×C127—21no—
24#127×C127—21no—
25#127×C127—22no—
26D16×C127—48no—
27C2×C16×C127D414yes—
28#107×C127—22no—
29#102×C127—42no—
30C4×C8×C127D411yescharacteristic
31C4×C8×C127D411yescharacteristic
32C4×C8×C127C2311yescharacteristic
33C2×Q8×C127—41no—
34C2×D4×C127—41no—
35C2×D4×C127—42no—
36C2×D4×C127—41no—
37C2×D4×C127—42no—
38C2×D4×C127—42no—
39C2×D4×C127—41no—
40SD16×C127—84no—
41D8×C127—44no—
42D8×C127—44no—
43D8×C127—44no—
44D8×C127—84no—
45D8×C127—84no—
46C2×C8×C127D812yes—
47C2×C8×C127D812yes—
48C2×C8×C127C2×D412yes—
49C4⋊C4×C127—41no—
50C4⋊C4×C127—41no—
51C42×C127C2×D411yescharacteristic
52C16×C127—24no—
53C23×C127—81no—
54C23×C127—82no—
55Q8×C127—82no—
56D4×C127—82no—
57D4×C127—82no—
58D4×C127—82no—
59D4×C127—84no—
60D4×C127—82no—
61D4×C127—84no—
62D4×C127—82no—
63C2×C4×C127—81no—
64C2×C4×C127#12711yescharacteristic
65C2×C4×C127C2×D811yescharacteristic
66C2×C4×C127C2×D811yescharacteristic
67C8×C127—22no—
68C8×C127D1614yescomplemented
69C8×C127AGL(1,ℤ/8)14yes—
70C22×C127—161no—
71C22×C127—162no—
72C22×C127—162no—
73C22×C127—161no—
74C22×C127—162no—
75C22×C127—161no—
76C22×C127#49311yescharacteristic
77C4×C127—161no—
78C4×C127#49612yes—
79C4×C127C2×D1612yes—
80C4×C127#50912yes—
81#12525C12711yesmaximal, characteristic, direct product factor, Sylow
82C2×C127—322no—
83C2×C127—321no—
84C2×C127#172111yescharacteristic
85C2×C127#224611yescharacteristic
86C2×C127#225011yescharacteristic
87#2246C2×C12712yescomplemented
88#2240C2×C12712yescomplemented
89#1712C2×C12711yescharacteristic, complemented
90#1706C2×C12711yescharacteristic, complemented
91#1312C2×C12711yescharacteristic, complemented
92C127#1252511yescharacteristic, direct product factor, Sylow
93C2×D16—24no—
94#500C22×C12711yescharacteristic
95#493—21no—
96#493—21no—
97#493C22×C12711yescharacteristic
98#493C22×C12712yes—
99#492—21no—
100#486—21no—
101#357—24no—
102C4×C16C22×C12712yes—
103C82C22×C12711yescharacteristic
104C2×SD16—42no—
105C2×D8—22no—
106C2×D8—22no—
107C2×D8—22no—
108C2×D8—42no—
109C2×D8—42no—
110C4⋊Q8—21no—
111#127—21no—
112#127—22no—
113D16—48no—
114C2×C16D4×C12714yes—
115#107—22no—
116#102—42no—
117C4×C8D4×C12711yescharacteristic
118C4×C8D4×C12711yescharacteristic
119C4×C8C23×C12711yescharacteristic
120C2×Q8—41no—
121C2×D4—41no—
122C2×D4—42no—
123C2×D4—41no—
124C2×D4—42no—
125C2×D4—42no—
126C2×D4—41no—
127SD16—84no—
128D8—44no—
129D8—44no—
130D8—44no—
131D8—84no—
132D8—84no—
133C2×C8D8×C12712yes—
134C2×C8D8×C12712yes—
135C2×C8C2×D4×C12712yes—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C42C2×D4×C12711yescharacteristic
139C16—24no—
140C23—81no—
141C23—82no—
142Q8—82no—
143D4—82no—
144D4—82no—
145D4—82no—
146D4—84no—
147D4—82no—
148D4—84no—
149D4—82no—
150C2×C4—81no—
151C2×C4#127×C12711yescharacteristic
152C2×C4C2×D8×C12711yescharacteristic
153C2×C4C2×D8×C12711yescharacteristic
154C8—22no—
155C8D16×C12714yescomplemented
156C8AGL(1,ℤ/8)×C12714yes—
157C22—161no—
158C22—162no—
159C22—162no—
160C22—161no—
161C22—162no—
162C22—161no—
163C22#493×C12711yescharacteristic
164C4—161no—
165C4#496×C12712yes—
166C4C2×D16×C12712yes—
167C4#509×C12712yes—
168C2—322no—
169C2—321no—
170C2C127×#172111yescharacteristic
171C2C127×#224611yescharacteristic
172C2C127×#225011yescharacteristic
subgroupG/H
center, socleC22×C127#493
commutator, Frattini, cosocleC4×C8C23×C127
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×#2246C2semidirect
2. C127×#2240C2semidirect
3. C127×#1712C2semidirect
4. C127×#1706C2semidirect
5. C127×#1312C2semidirect
68. C8×C127D16semidirect
81. #12525C127direct (N × H)
87. #2246C2×C127semidirect
88. #2240C2×C127semidirect
89. #1712C2×C127semidirect
90. #1706C2×C127semidirect
91. #1312C2×C127semidirect
92. C127#12525direct (N × H)
155. C8D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22462
C127×#22402
C127×#17122
C127×#17062
C127×#13122
#12525127