Finite Group Databasebeta

← C127×#2020 #30634972

Subgroups — C127×#2020 #30634972

Order 16256.

342 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 92 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×#137×C127C212yesmaximal
2C22×Q16×C127C211yesmaximal, characteristic, complemented
3C2×#101×C127C212yesmaximal, complemented
4#408×C127C211yesmaximal, characteristic
5#341×C127C211yesmaximal, characteristic, complemented
6C2×#41×C127C2211yescharacteristic
7C22×Q8×C127C2212yes—
8#137×C127—24no—
9#137×C127—24no—
10C2×Q16×C127—24no—
11C2×Q16×C127—22no—
12C2×Q16×C127—22no—
13C2×SD16×C127—22no—
14C2×M16×C127C2211yescharacteristic
15C2×M16×C127C2212yes—
16C22×C8×C127C2211yescharacteristic
17#101×C127—24no—
18C22⋊C8×C127—22no—
19#41×C127—22no—
20#41×C127—22no—
21C2×Q8×C127—22no—
22C2×Q8×C127—22no—
23C2×Q8×C127—22no—
24C2×Q8×C127—22no—
25C2×Q8×C127—22no—
26C2×Q8×C127D411yescharacteristic
27C2×Q8×C127D414yes—
28C2×D4×C127—21no—
29C2×D4×C127D411yescharacteristic
30C22×C4×C127—22no—
31C22×C4×C127—21no—
32C22×C4×C127C2311yescharacteristic
33Q16×C127—28no—
34Q16×C127—28no—
35SD16×C127—28no—
36M16×C127—22no—
37M16×C127—22no—
38M16×C127D414yes—
39C2×C8×C127—22no—
40C2×C8×C127—22no—
41C2×C8×C127—21no—
42C2×C8×C127D412yes—
43C23×C127—21no—
44C23×C127#4111yescharacteristic
45Q8×C127—24no—
46Q8×C127—24no—
47Q8×C127—22no—
48Q8×C127—42no—
49Q8×C127—42no—
50D4×C127—22no—
51D4×C127—42no—
52C2×C4×C127—24no—
53C2×C4×C127—21no—
54C2×C4×C127—42no—
55C2×C4×C127—42no—
56C2×C4×C127—41no—
57C2×C4×C127—41no—
58C2×C4×C127C2×D412yes—
59C2×C4×C127C2×D411yescharacteristic
60C2×C4×C127C2×D412yes—
61C2×C4×C127C2×D411yescharacteristic
62C8×C127—22no—
63C8×C127—24no—
64C8×C127—41no—
65C22×C127—22no—
66C22×C127—41no—
67C22×C127—42no—
68C22×C127#12112yes—
69C22×C127#12111yescharacteristic
70C4×C127—41no—
71C4×C127—44no—
72C4×C127#12011yescharacteristic
73C4×C127#12012yes—
74C4×C127#12711yescharacteristic
75C2×C127—22no—
76C2×C127—81no—
77C2×C127#39211yescharacteristic
78C2×C127#47312yes—
79#2020C12711yesmaximal, characteristic, direct product factor, Sylow
80C127#202011yescharacteristic, direct product factor, Sylow
81C2×#137C2×C12712yes—
82C22×Q16C2×C12711yescharacteristic, complemented
83C2×#101C2×C12712yescomplemented
84#408C2×C12711yescharacteristic
85#341C2×C12711yescharacteristic, complemented
86C2×#41C22×C12711yescharacteristic
87C22×Q8C22×C12712yes—
88#137—24no—
89#137—24no—
90C2×Q16—24no—
91C2×Q16—22no—
92C2×Q16—22no—
93C2×SD16—22no—
94C2×M16C22×C12711yescharacteristic
95C2×M16C22×C12712yes—
96C22×C8C22×C12711yescharacteristic
97#101—24no—
98C22⋊C8—22no—
99#41—22no—
100#41—22no—
101C2×Q8—22no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—22no—
106C2×Q8D4×C12711yescharacteristic
107C2×Q8D4×C12714yes—
108C2×D4—21no—
109C2×D4D4×C12711yescharacteristic
110C22×C4—22no—
111C22×C4—21no—
112C22×C4C23×C12711yescharacteristic
113Q16—28no—
114Q16—28no—
115SD16—28no—
116M16—22no—
117M16—22no—
118M16D4×C12714yes—
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—21no—
122C2×C8D4×C12712yes—
123C23—21no—
124C23#41×C12711yescharacteristic
125Q8—24no—
126Q8—24no—
127Q8—22no—
128Q8—42no—
129Q8—42no—
130D4—22no—
131D4—42no—
132C2×C4—21no—
133C2×C4—24no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4C2×D4×C12711yescharacteristic
139C2×C4C2×D4×C12712yes—
140C2×C4C2×D4×C12711yescharacteristic
141C2×C4C2×D4×C12712yes—
142C8—22no—
143C8—24no—
144C8—41no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22#121×C12712yes—
149C22#121×C12711yescharacteristic
150C4—41no—
151C4—44no—
152C4#120×C12711yescharacteristic
153C4#120×C12712yes—
154C4#127×C12711yescharacteristic
155C2—22no—
156C2—81no—
157C2#392×C12711yescharacteristic
158C2#473×C12712yes—
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC2×#41×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×Q16×C127C2semidirect
3. C2×#101×C127C2semidirect
5. #341×C127C2semidirect
79. #2020C127direct (N × H)
80. C127#2020direct (N × H)
82. C22×Q16C2×C127semidirect
83. C2×#101C2×C127semidirect
85. #341C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#137×C1272
C22×Q16×C1272
C2×#101×C1272
#408×C1272
#341×C1272
#2020127