Finite Group Databasebeta

← C127×#2061 #30635013

Subgroups — C127×#2061 #30635013

Order 16256.

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

normal subgroups only

This group has 230 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
1#544×C127C211yesmaximal, characteristic
2#428×C127C212yesmaximal
3#382×C127C211yesmaximal, characteristic
4#343×C127C211yesmaximal, characteristic
5#339×C127C212yesmaximal
6C2×M16×C127C2212yes—
7C4⋊Q8×C127—22no—
8#125×C127—22no—
9C22⋊Q8×C127—22no—
10#117×C127C2212yes—
11C2×C4⋊C4×C127C2211yescharacteristic
12C2×C4⋊C4×C127C2211yescharacteristic
13C2×C42×C127C2211yescharacteristic
14#107×C127—22no—
15#106×C127—22no—
16#95×C127—22no—
17C2×Q8×C127—22no—
18C22×C4×C127—21no—
19C22×C4×C127—21no—
20C22×C4×C127D412yes—
21C22×C4×C127C2311yescharacteristic
22M16×C127—22no—
23M16×C127Q814yescomplemented
24C2×C8×C127—22no—
25C4⋊C4×C127—22no—
26C4⋊C4×C127—24no—
27C4⋊C4×C127—22no—
28C4⋊C4×C127—22no—
29C4⋊C4×C127D412yes—
30C4⋊C4×C127D412yes—
31C22⋊C4×C127—22no—
32C42×C127—22no—
33C42×C127—21no—
34C42×C127Q812yescomplemented
35C23×C127C2×D411yescharacteristic
36Q8×C127—82no—
37C2×C4×C127—22no—
38C2×C4×C127—22no—
39C2×C4×C127—22no—
40C2×C4×C127—22no—
41C2×C4×C127—41no—
42C2×C4×C127—41no—
43C2×C4×C127—42no—
44C2×C4×C127—42no—
45C2×C4×C127—41no—
46C2×C4×C127C2×D412yes—
47C2×C4×C127C2×Q812yes—
48C2×C4×C127C2×Q811yescharacteristic
49C2×C4×C127#4111yescharacteristic
50C8×C127—24no—
51C22×C127—21no—
52C22×C127—21no—
53C22×C127#12011yescharacteristic
54C22×C127C22⋊Q811yescharacteristic
55C22×C127C4⋊Q811yescharacteristic
56C4×C127—42no—
57C4×C127—42no—
58C4×C127—42no—
59C4×C127—42no—
60C4×C127—81no—
61C4×C127C22⋊Q812yes—
62C4×C127C4⋊Q812yes—
63C2×C127—21no—
64C2×C127—21no—
65C2×C127#39511yescharacteristic
66C2×C127#45411yescharacteristic
67C2×C127#45511yescharacteristic
68#2061C12711yesmaximal, characteristic, direct product factor, Sylow
69C127#206111yescharacteristic, direct product factor, Sylow
70#544C2×C12711yescharacteristic
71#428C2×C12712yes—
72#382C2×C12711yescharacteristic
73#343C2×C12711yescharacteristic
74#339C2×C12712yes—
75C2×M16C22×C12712yes—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C22×C12712yes—
80C2×C4⋊C4C22×C12711yescharacteristic
81C2×C4⋊C4C22×C12711yescharacteristic
82C2×C42C22×C12711yescharacteristic
83#107—22no—
84#106—22no—
85#95—22no—
86C2×Q8—22no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4D4×C12712yes—
90C22×C4C23×C12711yescharacteristic
91M16—22no—
92M16Q8×C12714yescomplemented
93C2×C8—22no—
94C4⋊C4—22no—
95C4⋊C4—24no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4D4×C12712yes—
99C4⋊C4D4×C12712yes—
100C22⋊C4—22no—
101C42—22no—
102C42—21no—
103C42Q8×C12712yescomplemented
104C23C2×D4×C12711yescharacteristic
105Q8—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—42no—
113C2×C4—42no—
114C2×C4—41no—
115C2×C4C2×D4×C12712yes—
116C2×C4C2×Q8×C12712yes—
117C2×C4C2×Q8×C12711yescharacteristic
118C2×C4#41×C12711yescharacteristic
119C8—24no—
120C22—21no—
121C22—21no—
122C22#120×C12711yescharacteristic
123C22C22⋊Q8×C12711yescharacteristic
124C22C4⋊Q8×C12711yescharacteristic
125C4—42no—
126C4—42no—
127C4—42no—
128C4—42no—
129C4—81no—
130C4C22⋊Q8×C12712yes—
131C4C4⋊Q8×C12712yes—
132C2—21no—
133C2—21no—
134C2#395×C12711yescharacteristic
135C2#454×C12711yescharacteristic
136C2#455×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#120
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC23×C127C2×D4
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
23. M16×C127Q8semidirect
34. C42×C127Q8semidirect
68. #2061C127direct (N × H)
69. C127#2061direct (N × H)
92. M16Q8×C127semidirect
103. C42Q8×C127semidirect

Maximal subgroups

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

subgroupindex
#544×C1272
#428×C1272
#382×C1272
#343×C1272
#339×C1272
#2061127