Finite Group Databasebeta

← C127×#1648 #30634600

Subgroups — C127×#1648 #30634600

Order 16256.

194 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 72 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#557×C127C211yesmaximal, characteristic
2#500×C127C211yesmaximal, characteristic
3#475×C127C211yesmaximal, characteristic
4#462×C127C211yesmaximal, characteristic
5#332×C127C211yesmaximal, characteristic
6Q8⋊C8×C127C211yesmaximal, characteristic
7Q8⋊C8×C127C211yesmaximal, characteristic
8C2×Q16×C127—21no—
9C4⋊Q8×C127—21no—
10C4⋊Q8×C127C2211yescharacteristic
11C4⋊Q8×C127C2211yescharacteristic
12#125×C127—22no—
13#125×C127—21no—
14C4×Q8×C127—21no—
15C4×Q8×C127—21no—
16C4×Q8×C127C2211yescharacteristic
17C4×Q8×C127C2211yescharacteristic
18#107×C127—22no—
19#106×C127—21no—
20C4⋊C8×C127C2211yescharacteristic
21C4⋊C8×C127C2211yescharacteristic
22#103×C127—21no—
23#103×C127—21no—
24C4×C8×C127C2211yescharacteristic
25C2×Q8×C127—21no—
26C2×Q8×C127—21no—
27C2×Q8×C127D411yescharacteristic
28C2×Q8×C127D411yescharacteristic
29Q16×C127—42no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—21no—
33C4⋊C4×C127—22no—
34C4⋊C4×C127—22no—
35C4⋊C4×C127—22no—
36C4⋊C4×C127—21no—
37C4⋊C4×C127—21no—
38C4⋊C4×C127—21no—
39C4⋊C4×C127—21no—
40C4⋊C4×C127—21no—
41C4⋊C4×C127D411yescharacteristic
42C4⋊C4×C127D411yescharacteristic
43C4⋊C4×C127D412yes—
44C42×C127—22no—
45C42×C127—21no—
46C42×C127—21no—
47C42×C127C2311yescharacteristic
48Q8×C127—21no—
49Q8×C127—21no—
50Q8×C127—21no—
51Q8×C127—41no—
52Q8×C127—41no—
53Q8×C127—41no—
54Q8×C127—41no—
55Q8×C127Q1612yescomplemented
56C2×C4×C127—21no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—22no—
61C2×C4×C127—41no—
62C2×C4×C127C2×D411yescharacteristic
63C2×C4×C127C2×D411yescharacteristic
64C2×C4×C127C2×D411yescharacteristic
65C8×C127—22no—
66C8×C127—41no—
67C8×C127—41no—
68C22×C127#12011yescharacteristic
69C4×C127—22no—
70C4×C127—21no—
71C4×C127—41no—
72C4×C127—42no—
73C4×C127—41no—
74C4×C127—41no—
75C4×C127—81no—
76C4×C127C2×Q1611yescharacteristic
77C4×C127#13511yescharacteristic
78C4×C127AGL(1,ℤ/8)11yescharacteristic
79C4×C127#13711yescharacteristic
80C2×C127#44911yescharacteristic
81C2×C127#45111yescharacteristic
82C2×C127#45611yescharacteristic
83#1648C12711yesmaximal, characteristic, direct product factor, Sylow
84C127#164811yescharacteristic, direct product factor, Sylow
85#557C2×C12711yescharacteristic
86#500C2×C12711yescharacteristic
87#475C2×C12711yescharacteristic
88#462C2×C12711yescharacteristic
89#332C2×C12711yescharacteristic
90Q8⋊C8C2×C12711yescharacteristic
91Q8⋊C8C2×C12711yescharacteristic
92C2×Q16—21no—
93C4⋊Q8—21no—
94C4⋊Q8C22×C12711yescharacteristic
95C4⋊Q8C22×C12711yescharacteristic
96#125—22no—
97#125—21no—
98C4×Q8—21no—
99C4×Q8—21no—
100C4×Q8C22×C12711yescharacteristic
101C4×Q8C22×C12711yescharacteristic
102#107—22no—
103#106—21no—
104C4⋊C8C22×C12711yescharacteristic
105C4⋊C8C22×C12711yescharacteristic
106#103—21no—
107#103—21no—
108C4×C8C22×C12711yescharacteristic
109C2×Q8—21no—
110C2×Q8—21no—
111C2×Q8D4×C12711yescharacteristic
112C2×Q8D4×C12711yescharacteristic
113Q16—42no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—21no—
117C4⋊C4—22no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4D4×C12711yescharacteristic
126C4⋊C4D4×C12711yescharacteristic
127C4⋊C4D4×C12712yes—
128C42—22no—
129C42—21no—
130C42—21no—
131C42C23×C12711yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—21no—
135Q8—41no—
136Q8—41no—
137Q8—41no—
138Q8—41no—
139Q8Q16×C12712yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4C2×D4×C12711yescharacteristic
147C2×C4C2×D4×C12711yescharacteristic
148C2×C4C2×D4×C12711yescharacteristic
149C8—22no—
150C8—41no—
151C8—41no—
152C22#120×C12711yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—42no—
157C4—41no—
158C4—41no—
159C4—81no—
160C4C2×Q16×C12711yescharacteristic
161C4#135×C12711yescharacteristic
162C4AGL(1,ℤ/8)×C12711yescharacteristic
163C4#137×C12711yescharacteristic
164C2#449×C12711yescharacteristic
165C2#451×C12711yescharacteristic
166C2#456×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#120
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
55. Q8×C127Q16semidirect
83. #1648C127direct (N × H)
84. C127#1648direct (N × H)
139. Q8Q16×C127semidirect

Maximal subgroups

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

subgroupindex
#557×C1272
#500×C1272
#475×C1272
#462×C1272
#332×C1272
Q8⋊C8×C1272
#1648127