Finite Group Databasebeta

← C127×#13711 #44577384

Subgroups — C127×#13711 #44577384

Order 32512.

186 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2215C211yesmaximal, characteristic
2C2×#366×C127C211yesmaximal, characteristic, complemented
3C127×#1423C212yesmaximal, complemented
4C127×#1415C212yesmaximal, complemented
5C127×C22⋊C32C211yesmaximal, characteristic, complemented
6C2×D16×C127C2211yescharacteristic
7C22×C16×C127C2211yescharacteristic
8#466×C127—21no—
9C2×#107×C127—21no—
10C2×C32×C127C2212yes—
11#366×C127—21no—
12#366×C127C2212yes—
13#366×C127C2211yescharacteristic
14#357×C127—21no—
15C2×D8×C127—21no—
16C22×C8×C127D411yescharacteristic
17#121×C127—41no—
18C2×C4⋊C4×C127—41no—
19D16×C127—22no—
20C2×C16×C127—22no—
21C2×C16×C127D411yescharacteristic
22C2×C16×C127C2311yescharacteristic
23#107×C127—21no—
24#107×C127—22no—
25#107×C127—41no—
26#102×C127—41no—
27C32×C127—22no—
28C2×D4×C127—41no—
29C2×D4×C127—81no—
30C22×C4×C127—81no—
31C22×C4×C127D811yescharacteristic
32D8×C127—41no—
33D8×C127—41no—
34C2×C8×C127—21no—
35C2×C8×C127—21no—
36C2×C8×C127D811yescharacteristic
37C2×C8×C127C2×D411yescharacteristic
38C4⋊C4×C127—41no—
39C4⋊C4×C127—42no—
40C4⋊C4×C127—81no—
41C22⋊C4×C127—81no—
42C16×C127—21no—
43C16×C127#4112yes—
44C23×C127—81no—
45C23×C127D1611yescharacteristic
46D4×C127—81no—
47D4×C127—81no—
48D4×C127—162no—
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—81no—
52C2×C4×C127—82no—
53C2×C4×C127—162no—
54C2×C4×C127D1611yescharacteristic
55C2×C4×C127C2×D811yescharacteristic
56C8×C127—21no—
57C8×C127#12311yescharacteristic
58C8×C127#13711yescharacteristic
59C22×C127—21no—
60C22×C127—21no—
61C22×C127—161no—
62C22×C127—161no—
63C22×C127—161no—
64C22×C127D3212yes—
65C22×C127C2×D1611yescharacteristic
66C4×C127—21no—
67C4×C127—162no—
68C4×C127—161no—
69C4×C127#48011yescharacteristic
70C4×C127#51011yescharacteristic
71#13711C12711yesmaximal, characteristic, direct product factor, Sylow
72C2×C127—22no—
73C2×C127—321no—
74C2×C127#223211yescharacteristic
75C2×C127C2×D3211yescharacteristic
76C2×C127#226411yescharacteristic
77#2215C2×C12711yescharacteristic
78C2×#366C2×C12711yescharacteristic, complemented
79#1423C2×C12712yescomplemented
80#1415C2×C12712yescomplemented
81C22⋊C32C2×C12711yescharacteristic, complemented
82C127#1371111yescharacteristic, direct product factor, Sylow
83C2×D16C22×C12711yescharacteristic
84C22×C16C22×C12711yescharacteristic
85#466—21no—
86C2×#107—21no—
87C2×C32C22×C12712yes—
88#366—21no—
89#366C22×C12712yes—
90#366C22×C12711yescharacteristic
91#357—21no—
92C2×D8—21no—
93C22×C8D4×C12711yescharacteristic
94#121—41no—
95C2×C4⋊C4—41no—
96D16—22no—
97C2×C16—22no—
98C2×C16D4×C12711yescharacteristic
99C2×C16C23×C12711yescharacteristic
100#107—21no—
101#107—22no—
102#107—41no—
103#102—41no—
104C32—22no—
105C2×D4—41no—
106C2×D4—81no—
107C22×C4—81no—
108C22×C4D8×C12711yescharacteristic
109D8—41no—
110D8—41no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8D8×C12711yescharacteristic
114C2×C8C2×D4×C12711yescharacteristic
115C4⋊C4—41no—
116C4⋊C4—42no—
117C4⋊C4—81no—
118C22⋊C4—81no—
119C16—21no—
120C16#41×C12712yes—
121C23—81no—
122C23D16×C12711yescharacteristic
123D4—81no—
124D4—81no—
125D4—162no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—81no—
129C2×C4—82no—
130C2×C4—162no—
131C2×C4D16×C12711yescharacteristic
132C2×C4C2×D8×C12711yescharacteristic
133C8—21no—
134C8#123×C12711yescharacteristic
135C8#137×C12711yescharacteristic
136C22—21no—
137C22—21no—
138C22—161no—
139C22—161no—
140C22—161no—
141C22D32×C12712yes—
142C22C2×D16×C12711yescharacteristic
143C4—21no—
144C4—162no—
145C4—161no—
146C4#480×C12711yescharacteristic
147C4#510×C12711yescharacteristic
148C2—22no—
149C2—321no—
150C2C127×#223211yescharacteristic
151C2C2×D32×C12711yescharacteristic
152C2C127×#226411yescharacteristic
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#2215C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×C8×C127 ◁ C22×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#366×C127C2semidirect
3. C127×#1423C2semidirect
4. C127×#1415C2semidirect
5. C127×C22⋊C32C2semidirect
71. #13711C127direct (N × H)
78. C2×#366C2×C127semidirect
79. #1423C2×C127semidirect
80. #1415C2×C127semidirect
81. C22⋊C32C2×C127semidirect
82. C127#13711direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22152
C2×#366×C1272
C127×#14232
C127×#14152
C127×C22⋊C322
#13711127