Finite Group Databasebeta

← C127×#1497 #30634449

Subgroups — C127×#1497 #30634449

Order 16256.

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

normal subgroups only

This group has 202 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#533×C127C211yesmaximal, characteristic
2#432×C127C211yesmaximal, characteristic
3#431×C127C211yesmaximal, characteristic
4Q8⋊C8×C127C214yesmaximal, complemented
5C4⋊Q8×C127C411yescharacteristic
6C4⋊Q8×C127C411yescharacteristic
7#125×C127—21no—
8C22⋊Q8×C127—21no—
9C22⋊Q8×C127C412yes—
10C4×Q8×C127—21no—
11C4×Q8×C127C2212yes—
12#117×C127—21no—
13C2×C42×C127C2211yescharacteristic
14C4⋊C8×C127—21no—
15C4⋊C8×C127C2212yes—
16C22⋊C8×C127—21no—
17C22⋊C8×C127—21no—
18#97×C127—21no—
19C4×C8×C127C2212yes—
20C2×Q8×C127—21no—
21C2×Q8×C127C2×C412yes—
22C22×C4×C127C2×C411yescharacteristic
23C22×C4×C127D411yescharacteristic
24C22×C4×C127D411yescharacteristic
25C2×C8×C127—22no—
26C2×C8×C127—22no—
27C4⋊C4×C127—21no—
28C4⋊C4×C127—21no—
29C4⋊C4×C127—21no—
30C4⋊C4×C127—22no—
31C4⋊C4×C127—22no—
32C4⋊C4×C127C2×C412yes—
33C22⋊C4×C127—22no—
34C42×C127—22no—
35C42×C127C2×C411yescharacteristic
36C42×C127D411yescharacteristic
37C42×C127D411yescharacteristic
38C42×C127C2311yescharacteristic
39C23×C127C22⋊C411yescharacteristic
40Q8×C127—24no—
41Q8×C127—42no—
42C2×C4×C127—22no—
43C2×C4×C127—22no—
44C2×C4×C127—22no—
45C2×C4×C127—22no—
46C2×C4×C127—41no—
47C2×C4×C127C22⋊C411yescharacteristic
48C2×C4×C127C22⋊C411yescharacteristic
49C2×C4×C127C22⋊C411yescharacteristic
50C2×C4×C127C22×C411yescharacteristic
51C2×C4×C127C2×D411yescharacteristic
52C2×C4×C127C2×D411yescharacteristic
53C8×C127—42no—
54C8×C127—42no—
55C22×C127—21no—
56C22×C127—21no—
57C22×C127—21no—
58C22×C127C2×C22⋊C411yescharacteristic
59C4×C127—21no—
60C4×C127—21no—
61C4×C127—21no—
62C4×C127—21no—
63C4×C127—42no—
64C4×C127—42no—
65C4×C127#13112yes—
66C4×C127#13712yes—
67C2×C127—41no—
68C2×C127#40811yescharacteristic
69C2×C127#41911yescharacteristic
70C2×C127#42111yescharacteristic
71#1497C12711yesmaximal, characteristic, direct product factor, Sylow
72C127#149711yescharacteristic, direct product factor, Sylow
73#533C2×C12711yescharacteristic
74#432C2×C12711yescharacteristic
75#431C2×C12711yescharacteristic
76Q8⋊C8C2×C12714yescomplemented
77C4⋊Q8C4×C12711yescharacteristic
78C4⋊Q8C4×C12711yescharacteristic
79#125—21no—
80C22⋊Q8—21no—
81C22⋊Q8C4×C12712yes—
82C4×Q8—21no—
83C4×Q8C22×C12712yes—
84#117—21no—
85C2×C42C22×C12711yescharacteristic
86C4⋊C8—21no—
87C4⋊C8C22×C12712yes—
88C22⋊C8—21no—
89C22⋊C8—21no—
90#97—21no—
91C4×C8C22×C12712yes—
92C2×Q8—21no—
93C2×Q8C2×C4×C12712yes—
94C22×C4C2×C4×C12711yescharacteristic
95C22×C4D4×C12711yescharacteristic
96C22×C4D4×C12711yescharacteristic
97C2×C8—22no—
98C2×C8—22no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4C2×C4×C12712yes—
105C22⋊C4—22no—
106C42—22no—
107C42C2×C4×C12711yescharacteristic
108C42D4×C12711yescharacteristic
109C42D4×C12711yescharacteristic
110C42C23×C12711yescharacteristic
111C23C22⋊C4×C12711yescharacteristic
112Q8—24no—
113Q8—42no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4C22⋊C4×C12711yescharacteristic
120C2×C4C22⋊C4×C12711yescharacteristic
121C2×C4C22⋊C4×C12711yescharacteristic
122C2×C4C22×C4×C12711yescharacteristic
123C2×C4C2×D4×C12711yescharacteristic
124C2×C4C2×D4×C12711yescharacteristic
125C8—42no—
126C8—42no—
127C22—21no—
128C22—21no—
129C22—21no—
130C22C2×C22⋊C4×C12711yescharacteristic
131C4—21no—
132C4—21no—
133C4—21no—
134C4—21no—
135C4—42no—
136C4—42no—
137C4#131×C12712yes—
138C4#137×C12712yes—
139C2—41no—
140C2#408×C12711yescharacteristic
141C2#419×C12711yescharacteristic
142C2#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC42C23×C127
socleC22×C127C2×C22⋊C4
prime radicalC23×C127C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. Q8⋊C8×C127C2semidirect
71. #1497C127direct (N × H)
72. C127#1497direct (N × H)
76. Q8⋊C8C2×C127semidirect

Maximal subgroups

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

subgroupindex
#533×C1272
#432×C1272
#431×C1272
Q8⋊C8×C1272
#1497127