Finite Group Databasebeta

← C127×#7061 #44570734

Subgroups — C127×#7061 #44570734

Order 32512.

188 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C127×#1985C211yesmaximal, characteristic
2C127×#1322C212yesmaximal
3C2×C4×Q8×C127C411yescharacteristic
4C2×C4⋊C8×C127C2211yescharacteristic
5C2×#97×C127C411yescharacteristic
6C22⋊C16×C127—22no—
7#336×C127—22no—
8C22×Q8×C127C811yescharacteristic
9C22×C8×C127—21no—
10C22×C8×C127D412yes—
11C4×Q8×C127—41no—
12C4×Q8×C127—41no—
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127C811yescharacteristic
15C2×C42×C127—21no—
16C2×C42×C127C2×C411yescharacteristic
17C2×C16×C127—42no—
18C4⋊C8×C127—41no—
19#97×C127—41no—
20C2×Q8×C127—42no—
21C2×Q8×C127—41no—
22C22×C4×C127—21no—
23C22×C4×C127—21no—
24C22×C4×C127C22⋊C411yescharacteristic
25C22×C4×C127C2×C811yescharacteristic
26C22×C4×C127M1611yescharacteristic
27C2×C8×C127—22no—
28C2×C8×C127—22no—
29C2×C8×C127—41no—
30C2×C8×C127—41no—
31C2×C8×C127—42no—
32C4⋊C4×C127—41no—
33C4⋊C4×C127—42no—
34C42×C127—21no—
35C42×C127—21no—
36C42×C127—41no—
37C42×C127—41no—
38C16×C127—82no—
39C23×C127C22⋊C811yescharacteristic
40Q8×C127—42no—
41Q8×C127—42no—
42C2×C4×C127—21no—
43C2×C4×C127—21no—
44C2×C4×C127—22no—
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—22no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127—41no—
52C2×C4×C127—42no—
53C2×C4×C127#9911yescharacteristic
54C2×C4×C127#10011yescharacteristic
55C8×C127—42no—
56C8×C127—42no—
57C22×C127—21no—
58C22×C127—21no—
59C22×C127#32311yescharacteristic
60C22×C127#35012yes—
61C4×C127—21no—
62C4×C127—41no—
63C4×C127—42no—
64C4×C127—41no—
65C4×C127—81no—
66C4×C127#35411yescharacteristic
67C4×C127#35611yescharacteristic
68#7061C12711yesmaximal, characteristic, direct product factor, Sylow
69C2×C127—22no—
70C2×C127#131511yescharacteristic
71C2×C127#131911yescharacteristic
72C2×C127#132011yescharacteristic
73#1985C2×C12711yescharacteristic
74#1322C2×C12712yes—
75C127#706111yescharacteristic, direct product factor, Sylow
76C2×C4×Q8C4×C12711yescharacteristic
77C2×C4⋊C8C22×C12711yescharacteristic
78C2×#97C4×C12711yescharacteristic
79C22⋊C16—22no—
80#336—22no—
81C22×Q8C8×C12711yescharacteristic
82C22×C8—21no—
83C22×C8D4×C12712yes—
84C4×Q8—41no—
85C4×Q8—41no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4C8×C12711yescharacteristic
88C2×C42—21no—
89C2×C42C2×C4×C12711yescharacteristic
90C2×C16—42no—
91C4⋊C8—41no—
92#97—41no—
93C2×Q8—42no—
94C2×Q8—41no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4C22⋊C4×C12711yescharacteristic
98C22×C4C2×C8×C12711yescharacteristic
99C22×C4M16×C12711yescharacteristic
100C2×C8—22no—
101C2×C8—22no—
102C2×C8—41no—
103C2×C8—41no—
104C2×C8—42no—
105C4⋊C4—41no—
106C4⋊C4—42no—
107C42—21no—
108C42—21no—
109C42—41no—
110C42—41no—
111C16—82no—
112C23C22⋊C8×C12711yescharacteristic
113Q8—42no—
114Q8—42no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—42no—
126C2×C4#99×C12711yescharacteristic
127C2×C4#100×C12711yescharacteristic
128C8—42no—
129C8—42no—
130C22—21no—
131C22—21no—
132C22#323×C12711yescharacteristic
133C22#350×C12712yes—
134C4—21no—
135C4—41no—
136C4—42no—
137C4—41no—
138C4—81no—
139C4#354×C12711yescharacteristic
140C4#356×C12711yescharacteristic
141C2—22no—
142C2C127×#131511yescharacteristic
143C2C127×#131911yescharacteristic
144C2C127×#132011yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C2×C8×C127
Frattini, cosocleC2×C4⋊C8C22×C127
socleC22×C127#323
prime radicalC23×C127C22⋊C8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
68. #7061C127direct (N × H)
75. C127#7061direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19852
C127×#13222
#7061127