Finite Group Databasebeta

← C127×#1692 #30634644

Subgroups — C127×#1692 #30634644

Order 16256.

146 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 68 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#498×C127C211yesmaximal, characteristic
2#477×C127C211yesmaximal, characteristic
3#462×C127C211yesmaximal, characteristic
4#446×C127C211yesmaximal, characteristic
5#335×C127C211yesmaximal, characteristic
6#333×C127C211yesmaximal, characteristic
7#332×C127C211yesmaximal, characteristic
8C2×Q16×C127—21no—
9C4⋊Q8×C127C2211yescharacteristic
10C4⋊Q8×C127C2211yescharacteristic
11C4×Q8×C127C2211yescharacteristic
12#107×C127—21no—
13#106×C127—21no—
14#106×C127—21no—
15C4⋊C8×C127—21no—
16C4⋊C8×C127C2211yescharacteristic
17C4⋊C8×C127C2211yescharacteristic
18C4⋊C8×C127C2211yescharacteristic
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—81no—
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—41no—
48C2×C4×C127—41no—
49C2×C4×C127C2×D411yescharacteristic
50C2×C4×C127C2×D411yescharacteristic
51C2×C4×C127#4111yescharacteristic
52C8×C127—21no—
53C8×C127—41no—
54C8×C127—41no—
55C8×C127—41no—
56C8×C127Q1612yescomplemented
57C22×C127#12111yescharacteristic
58C4×C127—21no—
59C4×C127—41no—
60C4×C127—41no—
61C4×C127—81no—
62C4×C127—81no—
63C4×C127C2×Q1611yescharacteristic
64C4×C127AGL(1,ℤ/8)11yescharacteristic
65C4×C127#13711yescharacteristic
66C4×C127#13711yescharacteristic
67C2×C127#46211yescharacteristic
68C2×C127#46811yescharacteristic
69C2×C127#47111yescharacteristic
70#1692C12711yesmaximal, characteristic, direct product factor, Sylow
71C127#169211yescharacteristic, direct product factor, Sylow
72#498C2×C12711yescharacteristic
73#477C2×C12711yescharacteristic
74#462C2×C12711yescharacteristic
75#446C2×C12711yescharacteristic
76#335C2×C12711yescharacteristic
77#333C2×C12711yescharacteristic
78#332C2×C12711yescharacteristic
79C2×Q16—21no—
80C4⋊Q8C22×C12711yescharacteristic
81C4⋊Q8C22×C12711yescharacteristic
82C4×Q8C22×C12711yescharacteristic
83#107—21no—
84#106—21no—
85#106—21no—
86C4⋊C8—21no—
87C4⋊C8C22×C12711yescharacteristic
88C4⋊C8C22×C12711yescharacteristic
89C4⋊C8C22×C12711yescharacteristic
90#103—21no—
91#103—21no—
92#97—21no—
93C4×C8C22×C12711yescharacteristic
94C2×Q8—21no—
95C2×Q8—21no—
96C2×Q8D4×C12711yescharacteristic
97Q16—42no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8D4×C12711yescharacteristic
102C2×C8D4×C12711yescharacteristic
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4D4×C12711yescharacteristic
109C42—21no—
110C42C23×C12711yescharacteristic
111Q8—21no—
112Q8—21no—
113Q8—41no—
114Q8—41no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4C2×D4×C12711yescharacteristic
121C2×C4C2×D4×C12711yescharacteristic
122C2×C4#41×C12711yescharacteristic
123C8—21no—
124C8—41no—
125C8—41no—
126C8—41no—
127C8Q16×C12712yescomplemented
128C22#121×C12711yescharacteristic
129C4—21no—
130C4—41no—
131C4—41no—
132C4—81no—
133C4—81no—
134C4C2×Q16×C12711yescharacteristic
135C4AGL(1,ℤ/8)×C12711yescharacteristic
136C4#137×C12711yescharacteristic
137C4#137×C12711yescharacteristic
138C2#462×C12711yescharacteristic
139C2#468×C12711yescharacteristic
140C2#471×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
56. C8×C127Q16semidirect
70. #1692C127direct (N × H)
71. C127#1692direct (N × H)
127. C8Q16×C127semidirect

Maximal subgroups

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

subgroupindex
#498×C1272
#477×C1272
#462×C1272
#446×C1272
#335×C1272
#333×C1272
#332×C1272
#1692127