Finite Group Databasebeta

← C127×#1700 #30634652

Subgroups — C127×#1700 #30634652

Order 16256.

146 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 64 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#487×C127C211yesmaximal, characteristic
2#475×C127C211yesmaximal, characteristic
3#462×C127C211yesmaximal, characteristic
4#446×C127C211yesmaximal, characteristic
5#335×C127C211yesmaximal, characteristic
6#332×C127C211yesmaximal, characteristic
7#332×C127C211yesmaximal, characteristic
8C2×Q16×C127—21no—
9C4⋊Q8×C127C2211yescharacteristic
10C4⋊Q8×C127C2211yescharacteristic
11C4×Q8×C127C2211yescharacteristic
12#106×C127—21no—
13C4⋊C8×C127—21no—
14C4⋊C8×C127C2211yescharacteristic
15C4⋊C8×C127C2211yescharacteristic
16C4⋊C8×C127C2211yescharacteristic
17#103×C127—21no—
18#103×C127—21no—
19#103×C127—21no—
20#103×C127—21no—
21#97×C127—21no—
22C4×C8×C127C2211yescharacteristic
23C2×Q8×C127—21no—
24C2×Q8×C127—21no—
25C2×Q8×C127D411yescharacteristic
26Q16×C127—42no—
27C2×C8×C127—21no—
28C2×C8×C127—21no—
29C2×C8×C127—21no—
30C2×C8×C127D411yescharacteristic
31C2×C8×C127D411yescharacteristic
32C4⋊C4×C127—21no—
33C4⋊C4×C127—21no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—21no—
36C4⋊C4×C127—21no—
37C4⋊C4×C127D411yescharacteristic
38C42×C127—21no—
39C42×C127C2311yescharacteristic
40Q8×C127—21no—
41Q8×C127—21no—
42Q8×C127—41no—
43Q8×C127—41no—
44Q8×C127—41no—
45Q8×C127—41no—
46C2×C4×C127—21no—
47C2×C4×C127—21no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127C2×D411yescharacteristic
51C2×C4×C127C2×D411yescharacteristic
52C2×C4×C127#4111yescharacteristic
53C8×C127—21no—
54C8×C127—21no—
55C8×C127—41no—
56C8×C127—41no—
57C8×C127—41no—
58C22×C127#12111yescharacteristic
59C4×C127—21no—
60C4×C127—41no—
61C4×C127—41no—
62C4×C127—81no—
63C4×C127—81no—
64C4×C127#13511yescharacteristic
65C4×C127AGL(1,ℤ/8)11yescharacteristic
66C4×C127#13711yescharacteristic
67C4×C127#13711yescharacteristic
68C2×C127#46411yescharacteristic
69C2×C127#46811yescharacteristic
70C2×C127#47311yescharacteristic
71#1700C12711yesmaximal, characteristic, direct product factor, Sylow
72C127#170011yescharacteristic, direct product factor, Sylow
73#487C2×C12711yescharacteristic
74#475C2×C12711yescharacteristic
75#462C2×C12711yescharacteristic
76#446C2×C12711yescharacteristic
77#335C2×C12711yescharacteristic
78#332C2×C12711yescharacteristic
79#332C2×C12711yescharacteristic
80C2×Q16—21no—
81C4⋊Q8C22×C12711yescharacteristic
82C4⋊Q8C22×C12711yescharacteristic
83C4×Q8C22×C12711yescharacteristic
84#106—21no—
85C4⋊C8—21no—
86C4⋊C8C22×C12711yescharacteristic
87C4⋊C8C22×C12711yescharacteristic
88C4⋊C8C22×C12711yescharacteristic
89#103—21no—
90#103—21no—
91#103—21no—
92#103—21no—
93#97—21no—
94C4×C8C22×C12711yescharacteristic
95C2×Q8—21no—
96C2×Q8—21no—
97C2×Q8D4×C12711yescharacteristic
98Q16—42no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8D4×C12711yescharacteristic
103C2×C8D4×C12711yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4D4×C12711yescharacteristic
110C42—21no—
111C42C23×C12711yescharacteristic
112Q8—21no—
113Q8—21no—
114Q8—41no—
115Q8—41no—
116Q8—41no—
117Q8—41no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4C2×D4×C12711yescharacteristic
123C2×C4C2×D4×C12711yescharacteristic
124C2×C4#41×C12711yescharacteristic
125C8—21no—
126C8—21no—
127C8—41no—
128C8—41no—
129C8—41no—
130C22#121×C12711yescharacteristic
131C4—21no—
132C4—41no—
133C4—41no—
134C4—81no—
135C4—81no—
136C4#135×C12711yescharacteristic
137C4AGL(1,ℤ/8)×C12711yescharacteristic
138C4#137×C12711yescharacteristic
139C4#137×C12711yescharacteristic
140C2#464×C12711yescharacteristic
141C2#468×C12711yescharacteristic
142C2#473×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#121
commutator, Frattini, cosocleC42C23×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
71. #1700C127direct (N × H)
72. C127#1700direct (N × H)

Maximal subgroups

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

subgroupindex
#487×C1272
#475×C1272
#462×C1272
#446×C1272
#335×C1272
#332×C1272
#1700127