Finite Group Databasebeta

← C127×#7087 #44570760

Subgroups — C127×#7087 #44570760

Order 32512.

196 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 50 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×#2075C211yesmaximal, characteristic
2C127×#1314C211yesmaximal, characteristic
3C127×#1293C211yesmaximal, characteristic
4C2×#107×C127C411yescharacteristic
5#407×C127—21no—
6C2×C22⋊C8×C127C2211yescharacteristic
7#380×C127—21no—
8C22⋊C16×C127—21no—
9#340×C127—21no—
10#340×C127C411yescharacteristic
11C23×C4×C127D411yescharacteristic
12C2×M16×C127—41no—
13C22×C8×C127C2×C411yescharacteristic
14C22×C8×C127D411yescharacteristic
15C2×C4⋊C4×C127—21no—
16C2×C4⋊C4×C127—21no—
17C2×C22⋊C4×C127—41no—
18C2×C16×C127—41no—
19#107×C127—41no—
20C22⋊C8×C127—22no—
21C22⋊C8×C127—41no—
22C22⋊C8×C127—41no—
23#95×C127—41no—
24C24×C127SD1611yescharacteristic
25C22×C4×C127—21no—
26C22×C4×C127—21no—
27C22×C4×C127—41no—
28C22×C4×C127—41no—
29C22×C4×C127—41no—
30C22×C4×C127—41no—
31C22×C4×C127C22⋊C411yescharacteristic
32C22×C4×C127D811yescharacteristic
33M16×C127—81no—
34M16×C127—81no—
35C2×C8×C127—21no—
36C2×C8×C127—21no—
37C2×C8×C127—41no—
38C2×C8×C127—41no—
39C2×C8×C127—42no—
40C4⋊C4×C127—41no—
41C4⋊C4×C127—41no—
42C4⋊C4×C127—41no—
43C4⋊C4×C127—41no—
44C22⋊C4×C127—82no—
45C16×C127—81no—
46C23×C127—21no—
47C23×C127—21no—
48C23×C127—21no—
49C23×C127—41no—
50C23×C127—41no—
51C23×C127#10211yescharacteristic
52C2×C4×C127—21no—
53C2×C4×C127—21no—
54C2×C4×C127—21no—
55C2×C4×C127—41no—
56C2×C4×C127—41no—
57C2×C4×C127—41no—
58C2×C4×C127—81no—
59C2×C4×C127—81no—
60C2×C4×C127—81no—
61C2×C4×C127—81no—
62C2×C4×C127—81no—
63C2×C4×C127—81no—
64C2×C4×C127—81no—
65C2×C4×C127#9911yescharacteristic
66C2×C4×C127#10411yescharacteristic
67C8×C127—41no—
68C8×C127—41no—
69C8×C127—82no—
70C22×C127—21no—
71C22×C127—21no—
72C22×C127—42no—
73C22×C127—41no—
74C22×C127—41no—
75C22×C127—41no—
76C22×C127—81no—
77C22×C127#32711yescharacteristic
78C22×C127#35911yescharacteristic
79C22×C127#36111yescharacteristic
80C4×C127—21no—
81C4×C127—41no—
82C4×C127—161no—
83C4×C127—161no—
84C4×C127#35211yescharacteristic
85C4×C127#35411yescharacteristic
86#7087C12711yesmaximal, characteristic, direct product factor, Sylow
87C2×C127—21no—
88C2×C127—21no—
89C2×C127—81no—
90C2×C127#134211yescharacteristic
91C2×C127#134411yescharacteristic
92C2×C127#134911yescharacteristic
93#2075C2×C12711yescharacteristic
94#1314C2×C12711yescharacteristic
95#1293C2×C12711yescharacteristic
96C127#708711yescharacteristic, direct product factor, Sylow
97C2×#107C4×C12711yescharacteristic
98#407—21no—
99C2×C22⋊C8C22×C12711yescharacteristic
100#380—21no—
101C22⋊C16—21no—
102#340—21no—
103#340C4×C12711yescharacteristic
104C23×C4D4×C12711yescharacteristic
105C2×M16—41no—
106C22×C8C2×C4×C12711yescharacteristic
107C22×C8D4×C12711yescharacteristic
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C22⋊C4—41no—
111C2×C16—41no—
112#107—41no—
113C22⋊C8—22no—
114C22⋊C8—41no—
115C22⋊C8—41no—
116#95—41no—
117C24SD16×C12711yescharacteristic
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—41no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—41no—
124C22×C4C22⋊C4×C12711yescharacteristic
125C22×C4D8×C12711yescharacteristic
126M16—81no—
127M16—81no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—41no—
131C2×C8—41no—
132C2×C8—42no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—41no—
137C22⋊C4—82no—
138C16—81no—
139C23—21no—
140C23—21no—
141C23—21no—
142C23—41no—
143C23—41no—
144C23#102×C12711yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4#99×C12711yescharacteristic
159C2×C4#104×C12711yescharacteristic
160C8—41no—
161C8—41no—
162C8—82no—
163C22—21no—
164C22—21no—
165C22—42no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22#327×C12711yescharacteristic
171C22#359×C12711yescharacteristic
172C22#361×C12711yescharacteristic
173C4—21no—
174C4—41no—
175C4—161no—
176C4—161no—
177C4#352×C12711yescharacteristic
178C4#354×C12711yescharacteristic
179C2—21no—
180C2—21no—
181C2—81no—
182C2C127×#134211yescharacteristic
183C2C127×#134411yescharacteristic
184C2C127×#134911yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC22×C8C2×C4×C127
Frattini, cosocleC2×C22⋊C8C22×C127
prime radicalC24×C127SD16
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C22⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
86. #7087C127direct (N × H)
96. C127#7087direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#20752
C127×#13142
C127×#12932
#7087127