Finite Group Databasebeta

← C127×#7287 #44570960

Subgroups — C127×#7287 #44570960

Order 32512.

322 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1955C211yesmaximal, characteristic
2C127×#1459C212yesmaximal
3C2×C4×D4×C127C2211yescharacteristic
4C2×C4⋊C8×C127C411yescharacteristic
5C2×C22⋊C8×C127—22no—
6C2×C22⋊C8×C127—22no—
7C2×#97×C127C411yescharacteristic
8#324×C127—22no—
9#323×C127C414yes—
10C22×D4×C127Q811yescharacteristic
11C23×C4×C127D412yes—
12C22×C8×C127—21no—
13C22×C8×C127—21no—
14C22×C8×C127—42no—
15C4×D4×C127—41no—
16C4×D4×C127—41no—
17C2×C4⋊C4×C127D411yescharacteristic
18C2×C22⋊C4×C127C2×C412yes—
19C2×C42×C127C2×C411yescharacteristic
20C4⋊C8×C127—41no—
21C22⋊C8×C127—24no—
22C22⋊C8×C127—44no—
23C22⋊C8×C127—42no—
24#97×C127—41no—
25C24×C127C4⋊C412yes—
26C2×D4×C127—24no—
27C2×D4×C127—41no—
28C22×C4×C127—22no—
29C22×C4×C127—22no—
30C22×C4×C127—42no—
31C22×C4×C127—42no—
32C22×C4×C127C4211yescharacteristic
33C22×C4×C127C22⋊C412yes—
34C22×C4×C127C22⋊C411yescharacteristic
35C22×C4×C127C4⋊C411yescharacteristic
36C2×C8×C127—22no—
37C2×C8×C127—41no—
38C2×C8×C127—41no—
39C2×C8×C127—44no—
40C2×C8×C127—42no—
41C2×C8×C127—41no—
42C2×C8×C127—82no—
43C2×C8×C127—82no—
44C4⋊C4×C127—41no—
45C22⋊C4×C127—42no—
46C42×C127—21no—
47C42×C127—21no—
48C23×C127—22no—
49C23×C127—22no—
50C23×C127—42no—
51C23×C127—42no—
52C23×C127#9511yescharacteristic
53C23×C127#10814yes—
54D4×C127—44no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—22no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—22no—
61C2×C4×C127—42no—
62C2×C4×C127—42no—
63C2×C4×C127—42no—
64C2×C4×C127—41no—
65C2×C4×C127—82no—
66C2×C4×C127#9911yescharacteristic
67C2×C4×C127#9911yescharacteristic
68C8×C127—42no—
69C8×C127—84no—
70C8×C127—81no—
71C22×C127—21no—
72C22×C127—21no—
73C22×C127—24no—
74C22×C127—44no—
75C22×C127—42no—
76C22×C127—42no—
77C22×C127—82no—
78C22×C127#34112yes—
79C22×C127#34211yescharacteristic
80C4×C127—21no—
81C4×C127—41no—
82C4×C127—41no—
83C4×C127—42no—
84C4×C127#35311yescharacteristic
85C4×C127#35411yescharacteristic
86#7287C12711yesmaximal, characteristic, direct product factor, Sylow
87C2×C127—22no—
88C2×C127—44no—
89C2×C127#129811yescharacteristic
90C2×C127#139211yescharacteristic
91C2×C127#139311yescharacteristic
92#1955C2×C12711yescharacteristic
93#1459C2×C12712yes—
94C127#728711yescharacteristic, direct product factor, Sylow
95C2×C4×D4C22×C12711yescharacteristic
96C2×C4⋊C8C4×C12711yescharacteristic
97C2×C22⋊C8—22no—
98C2×C22⋊C8—22no—
99C2×#97C4×C12711yescharacteristic
100#324—22no—
101#323C4×C12714yes—
102C22×D4Q8×C12711yescharacteristic
103C23×C4D4×C12712yes—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—42no—
107C4×D4—41no—
108C4×D4—41no—
109C2×C4⋊C4D4×C12711yescharacteristic
110C2×C22⋊C4C2×C4×C12712yes—
111C2×C42C2×C4×C12711yescharacteristic
112C4⋊C8—41no—
113C22⋊C8—24no—
114C22⋊C8—44no—
115C22⋊C8—42no—
116#97—41no—
117C24C4⋊C4×C12712yes—
118C2×D4—24no—
119C2×D4—41no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4C42×C12711yescharacteristic
125C22×C4C22⋊C4×C12711yescharacteristic
126C22×C4C22⋊C4×C12712yes—
127C22×C4C4⋊C4×C12711yescharacteristic
128C2×C8—22no—
129C2×C8—41no—
130C2×C8—41no—
131C2×C8—44no—
132C2×C8—42no—
133C2×C8—41no—
134C2×C8—82no—
135C2×C8—82no—
136C4⋊C4—41no—
137C22⋊C4—42no—
138C42—21no—
139C42—21no—
140C23—22no—
141C23—22no—
142C23—42no—
143C23—42no—
144C23#95×C12711yescharacteristic
145C23#108×C12714yes—
146D4—44no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—82no—
158C2×C4#99×C12711yescharacteristic
159C2×C4#99×C12711yescharacteristic
160C8—42no—
161C8—84no—
162C8—81no—
163C22—21no—
164C22—21no—
165C22—24no—
166C22—44no—
167C22—42no—
168C22—42no—
169C22—82no—
170C22#341×C12712yes—
171C22#342×C12711yescharacteristic
172C4—21no—
173C4—41no—
174C4—41no—
175C4—42no—
176C4#353×C12711yescharacteristic
177C4#354×C12711yescharacteristic
178C2—22no—
179C2—44no—
180C2C127×#129811yescharacteristic
181C2C127×#139211yescharacteristic
182C2C127×#139311yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C42×C127
Frattini, cosocleC2×C4×D4C22×C127
socleC22×C127#342
prime radicalC22×D4×C127Q8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
86. #7287C127direct (N × H)
94. C127#7287direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19552
C127×#14592
#7287127