Finite Group Databasebeta

← C127×#13729 #44577402

Subgroups — C127×#13729 #44577402

Order 32512.

252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×SD64×C127C212yesmaximal, complemented
2C2×D32×C127C212yesmaximal, complemented
3C127×#2249C211yesmaximal, characteristic, complemented
4C127×#2246C211yesmaximal, characteristic, complemented
5C127×#1397C211yesmaximal, characteristic, complemented
6C2×Q32×C127C2211yescharacteristic
7C2×SD32×C127—21no—
8C2×D16×C127—21no—
9C2×D16×C127C2212yes—
10C2×D16×C127C2211yescharacteristic
11#495×C127—21no—
12#493×C127—21no—
13SD64×C127—24no—
14D32×C127—24no—
15C2×C32×C127C2212yes—
16C4×C16×C127C2211yescharacteristic
17C2×Q16×C127—21no—
18C2×SD16×C127—41no—
19C2×D8×C127—22no—
20C2×D8×C127—21no—
21C2×D8×C127—41no—
22#127×C127—41no—
23#124×C127—41no—
24Q32×C127—22no—
25SD32×C127—42no—
26D16×C127—22no—
27D16×C127—22no—
28D16×C127—22no—
29D16×C127—42no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127C2311yescharacteristic
32C4×C8×C127D411yescharacteristic
33C32×C127D414yescomplemented
34C2×Q8×C127—41no—
35C2×D4×C127—41no—
36C2×D4×C127—42no—
37C2×D4×C127—82no—
38Q16×C127—41no—
39Q16×C127—41no—
40SD16×C127—82no—
41D8×C127—41no—
42D8×C127—42no—
43D8×C127—42no—
44D8×C127—41no—
45D8×C127—82no—
46C2×C8×C127D811yescharacteristic
47C2×C8×C127C2×D411yescharacteristic
48C22⋊C4×C127—82no—
49C42×C127D811yescharacteristic
50C16×C127D812yes—
51C16×C127C2×D412yes—
52C23×C127—81no—
53C23×C127—82no—
54Q8×C127—81no—
55Q8×C127—81no—
56D4×C127—82no—
57D4×C127—81no—
58D4×C127—82no—
59D4×C127—81no—
60D4×C127—164no—
61C2×C4×C127—81no—
62C2×C4×C127D1612yes—
63C2×C4×C127C2×D811yescharacteristic
64C8×C127D1612yes—
65C8×C127#12711yescharacteristic
66C8×C127C2×D811yescharacteristic
67C22×C127—162no—
68C22×C127—161no—
69C22×C127—164no—
70C22×C127—162no—
71C22×C127C2×D1611yescharacteristic
72C4×C127—22no—
73C4×C127—161no—
74C4×C127#49311yescharacteristic
75C4×C127C2×D1611yescharacteristic
76#13729C12711yesmaximal, characteristic, direct product factor, Sylow
77C2×C127—322no—
78C2×C127—321no—
79C2×C127#224611yescharacteristic
80C2×C127#226312yes—
81C2×SD64C2×C12712yescomplemented
82C2×D32C2×C12712yescomplemented
83#2249C2×C12711yescharacteristic, complemented
84#2246C2×C12711yescharacteristic, complemented
85#1397C2×C12711yescharacteristic, complemented
86C127#1372911yescharacteristic, direct product factor, Sylow
87C2×Q32C22×C12711yescharacteristic
88C2×SD32—21no—
89C2×D16—21no—
90C2×D16C22×C12712yes—
91C2×D16C22×C12711yescharacteristic
92#495—21no—
93#493—21no—
94SD64—24no—
95D32—24no—
96C2×C32C22×C12712yes—
97C4×C16C22×C12711yescharacteristic
98C2×Q16—21no—
99C2×SD16—41no—
100C2×D8—22no—
101C2×D8—21no—
102C2×D8—41no—
103#127—41no—
104#124—41no—
105Q32—22no—
106SD32—42no—
107D16—22no—
108D16—22no—
109D16—22no—
110D16—42no—
111C2×C16D4×C12711yescharacteristic
112C2×C16C23×C12711yescharacteristic
113C4×C8D4×C12711yescharacteristic
114C32D4×C12714yescomplemented
115C2×Q8—41no—
116C2×D4—41no—
117C2×D4—42no—
118C2×D4—82no—
119Q16—41no—
120Q16—41no—
121SD16—82no—
122D8—41no—
123D8—42no—
124D8—42no—
125D8—41no—
126D8—82no—
127C2×C8D8×C12711yescharacteristic
128C2×C8C2×D4×C12711yescharacteristic
129C22⋊C4—82no—
130C42D8×C12711yescharacteristic
131C16D8×C12712yes—
132C16C2×D4×C12712yes—
133C23—81no—
134C23—82no—
135Q8—81no—
136Q8—81no—
137D4—82no—
138D4—81no—
139D4—82no—
140D4—81no—
141D4—164no—
142C2×C4—81no—
143C2×C4D16×C12712yes—
144C2×C4C2×D8×C12711yescharacteristic
145C8D16×C12712yes—
146C8#127×C12711yescharacteristic
147C8C2×D8×C12711yescharacteristic
148C22—162no—
149C22—161no—
150C22—164no—
151C22—162no—
152C22C2×D16×C12711yescharacteristic
153C4—22no—
154C4—161no—
155C4#493×C12711yescharacteristic
156C4C2×D16×C12711yescharacteristic
157C2—322no—
158C2—321no—
159C2C127×#224611yescharacteristic
160C2C127×#226312yes—
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C4×C8×C127 ◁ C4×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×SD64×C127C2semidirect
2. C2×D32×C127C2semidirect
3. C127×#2249C2semidirect
4. C127×#2246C2semidirect
5. C127×#1397C2semidirect
33. C32×C127D4semidirect
76. #13729C127direct (N × H)
81. C2×SD64C2×C127semidirect
82. C2×D32C2×C127semidirect
83. #2249C2×C127semidirect
84. #2246C2×C127semidirect
85. #1397C2×C127semidirect
86. C127#13729direct (N × H)
114. C32D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×SD64×C1272
C2×D32×C1272
C127×#22492
C127×#22462
C127×#13972
#13729127