Finite Group Databasebeta

← C127×#11494 #44575167

Subgroups — C127×#11494 #44575167

Order 32512.

330 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C2×C8×Q8×C127C211yesmaximal, characteristic
2C127×#2163C212yesmaximal
3C127×#1322C214yesmaximal
4C2×C4×Q8×C127C411yescharacteristic
5C8×Q8×C127—22no—
6C8×Q8×C127—22no—
7C2×C4⋊C8×C127C411yescharacteristic
8C2×C4⋊C8×C127C2212yes—
9C2×C4×C8×C127C412yes—
10C2×C4×C8×C127C2211yescharacteristic
11C4⋊C16×C127—22no—
12C22⋊C16×C127C2214yes—
13#346×C127—22no—
14C22×Q8×C127C811yescharacteristic
15C22×C8×C127C2×C411yescharacteristic
16C22×C8×C127C2×C412yes—
17C22×C8×C127C2311yescharacteristic
18C4×Q8×C127—22no—
19C4×Q8×C127—22no—
20C2×C4⋊C4×C127C811yescharacteristic
21C2×C4⋊C4×C127C812yes—
22C2×C42×C127C2×C412yes—
23C2×C42×C127C2×C411yescharacteristic
24C2×C16×C127—24no—
25C4⋊C8×C127—24no—
26C4⋊C8×C127—22no—
27C4×C8×C127—22no—
28C4×C8×C127—22no—
29C4×C8×C127D412yes—
30C4×C8×C127D412yes—
31C2×Q8×C127—22no—
32C2×Q8×C127—24no—
33C22×C4×C127C2×C811yescharacteristic
34C22×C4×C127C2×C812yes—
35C22×C4×C127C2×C812yes—
36C22×C4×C127C2×C811yescharacteristic
37C22×C4×C127C22×C411yescharacteristic
38C2×C8×C127—22no—
39C2×C8×C127—22no—
40C2×C8×C127—41no—
41C2×C8×C127—42no—
42C2×C8×C127C22⋊C411yescharacteristic
43C2×C8×C127C22⋊C411yescharacteristic
44C2×C8×C127C2×D412yes—
45C4⋊C4×C127—24no—
46C4⋊C4×C127—22no—
47C42×C127—22no—
48C42×C127—22no—
49C42×C127C22⋊C412yes—
50C42×C127M1612yes—
51C16×C127—44no—
52C23×C127C22×C811yescharacteristic
53Q8×C127—28no—
54C2×C4×C127—22no—
55C2×C4×C127—22no—
56C2×C4×C127—22no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—22no—
60C2×C4×C127—41no—
61C2×C4×C127—42no—
62C2×C4×C127C22⋊C812yes—
63C2×C4×C127C22⋊C812yes—
64C2×C4×C127M3214yes—
65C2×C4×C127C2×C22⋊C411yescharacteristic
66C2×C4×C127C2×M1611yescharacteristic
67C8×C127—22no—
68C8×C127—21no—
69C8×C127—42no—
70C8×C127#10112yes—
71C22×C127—21no—
72C22×C127—21no—
73C22×C127C2×C22⋊C811yescharacteristic
74C22×C127C2×M3212yes—
75C4×C127—22no—
76C4×C127—24no—
77C4×C127—22no—
78C4×C127—21no—
79C4×C127—42no—
80C4×C127#41011yescharacteristic
81C4×C127C2×#10111yescharacteristic
82#11494C12711yesmaximal, characteristic, direct product factor, Sylow
83C2×C127—22no—
84C2×C127#146111yescharacteristic
85C2×C127#211211yescharacteristic
86C2×C127#211511yescharacteristic
87C2×C8×Q8C2×C12711yescharacteristic
88#2163C2×C12712yes—
89#1322C2×C12714yes—
90C127#1149411yescharacteristic, direct product factor, Sylow
91C2×C4×Q8C4×C12711yescharacteristic
92C8×Q8—22no—
93C8×Q8—22no—
94C2×C4⋊C8C4×C12711yescharacteristic
95C2×C4⋊C8C22×C12712yes—
96C2×C4×C8C4×C12712yes—
97C2×C4×C8C22×C12711yescharacteristic
98C4⋊C16—22no—
99C22⋊C16C22×C12714yes—
100#346—22no—
101C22×Q8C8×C12711yescharacteristic
102C22×C8C2×C4×C12711yescharacteristic
103C22×C8C2×C4×C12712yes—
104C22×C8C23×C12711yescharacteristic
105C4×Q8—22no—
106C4×Q8—22no—
107C2×C4⋊C4C8×C12711yescharacteristic
108C2×C4⋊C4C8×C12712yes—
109C2×C42C2×C4×C12712yes—
110C2×C42C2×C4×C12711yescharacteristic
111C2×C16—24no—
112C4⋊C8—24no—
113C4⋊C8—22no—
114C4×C8—22no—
115C4×C8—22no—
116C4×C8D4×C12712yes—
117C4×C8D4×C12712yes—
118C2×Q8—22no—
119C2×Q8—24no—
120C22×C4C2×C8×C12711yescharacteristic
121C22×C4C2×C8×C12712yes—
122C22×C4C2×C8×C12712yes—
123C22×C4C2×C8×C12711yescharacteristic
124C22×C4C22×C4×C12711yescharacteristic
125C2×C8—22no—
126C2×C8—22no—
127C2×C8—41no—
128C2×C8—42no—
129C2×C8C22⋊C4×C12711yescharacteristic
130C2×C8C22⋊C4×C12711yescharacteristic
131C2×C8C2×D4×C12712yes—
132C4⋊C4—24no—
133C4⋊C4—22no—
134C42—22no—
135C42—22no—
136C42C22⋊C4×C12712yes—
137C42M16×C12712yes—
138C16—44no—
139C23C22×C8×C12711yescharacteristic
140Q8—28no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4C22⋊C8×C12712yes—
150C2×C4C22⋊C8×C12712yes—
151C2×C4M32×C12714yes—
152C2×C4C2×C22⋊C4×C12711yescharacteristic
153C2×C4C2×M16×C12711yescharacteristic
154C8—22no—
155C8—21no—
156C8—42no—
157C8#101×C12712yes—
158C22—21no—
159C22—21no—
160C22C2×C22⋊C8×C12711yescharacteristic
161C22C2×M32×C12712yes—
162C4—22no—
163C4—24no—
164C4—22no—
165C4—21no—
166C4—42no—
167C4#410×C12711yescharacteristic
168C4C2×#101×C12711yescharacteristic
169C2—22no—
170C2C127×#146111yescharacteristic
171C2C127×#211211yescharacteristic
172C2C127×#211511yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radicalC23×C127C22×C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
82. #11494C127direct (N × H)
90. C127#11494direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×Q8×C1272
C127×#21632
C127×#13222
#11494127