Finite Group Databasebeta

← C127×#7235 #44570908

Subgroups — C127×#7235 #44570908

Order 32512.

286 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2112C211yesmaximal, characteristic
2C127×#1810C211yesmaximal, characteristic
3C127×#1808C211yesmaximal, characteristic
4C23×C8×C127C2211yescharacteristic
5C2×M32×C127C412yescomplemented
6C2×#108×C127—21no—
7C2×#107×C127—21no—
8#407×C127—21no—
9#380×C127—21no—
10C22⋊C16×C127—21no—
11C22⋊C16×C127—21no—
12#341×C127C412yescomplemented
13#340×C127C412yes—
14C23×C4×C127D411yescharacteristic
15C2×M16×C127—22no—
16C22×C8×C127—42no—
17C22×C8×C127C2×C411yescharacteristic
18C22×C8×C127C2×C411yescharacteristic
19C22×C8×C127C2×C411yescharacteristic
20C22×C8×C127D411yescharacteristic
21C22×C8×C127D411yescharacteristic
22C22×C8×C127Q811yescharacteristic
23C2×C4⋊C4×C127—22no—
24C2×C22⋊C4×C127—41no—
25M32×C127—42no—
26C2×C16×C127—22no—
27#108×C127—42no—
28#107×C127—42no—
29C22⋊C8×C127—41no—
30C22⋊C8×C127—41no—
31#95×C127—41no—
32C24×C127SD1611yescharacteristic
33C22×C4×C127—41no—
34C22×C4×C127—41no—
35C22×C4×C127—42no—
36C22×C4×C127C22⋊C411yescharacteristic
37C22×C4×C127C22⋊C411yescharacteristic
38C22×C4×C127C4⋊C411yescharacteristic
39C22×C4×C127D811yescharacteristic
40C22×C4×C127SD1611yescharacteristic
41C22×C4×C127Q1611yescharacteristic
42M16×C127—42no—
43M16×C127—42no—
44C2×C8×C127—22no—
45C2×C8×C127—22no—
46C2×C8×C127—22no—
47C2×C8×C127—41no—
48C2×C8×C127—41no—
49C2×C8×C127—41no—
50C2×C8×C127—42no—
51C2×C8×C127C4211yescharacteristic
52C2×C8×C127C22⋊C411yescharacteristic
53C2×C8×C127C4⋊C411yescharacteristic
54C2×C8×C127C4⋊C411yescharacteristic
55C4⋊C4×C127—42no—
56C4⋊C4×C127—42no—
57C22⋊C4×C127—82no—
58C16×C127—42no—
59C23×C127—21no—
60C23×C127—21no—
61C23×C127—41no—
62C23×C127—41no—
63C23×C127#10211yescharacteristic
64C23×C127#10311yescharacteristic
65C23×C127#10611yescharacteristic
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—82no—
76C2×C4×C127—82no—
77C2×C4×C127—82no—
78C2×C4×C127#9511yescharacteristic
79C2×C4×C127#10211yescharacteristic
80C2×C4×C127#10311yescharacteristic
81C2×C4×C127#10711yescharacteristic
82C8×C127—21no—
83C8×C127—21no—
84C8×C127—21no—
85C8×C127—82no—
86C8×C127#9912yes—
87C22×C127—21no—
88C22×C127—21no—
89C22×C127—21no—
90C22×C127—21no—
91C22×C127—21no—
92C22×C127—21no—
93C22×C127—21no—
94C22×C127—21no—
95C22×C127—42no—
96C22×C127—42no—
97C22×C127#34011yescharacteristic
98C22×C127#36111yescharacteristic
99C22×C127#36211yescharacteristic
100C4×C127—21no—
101C4×C127—21no—
102C4×C127—21no—
103C4×C127—162no—
104C4×C127H(3,ℤ/4)11yescharacteristic
105C4×C127#34211yescharacteristic
106#7235C12711yesmaximal, characteristic, direct product factor, Sylow
107C2×C127—21no—
108C2×C127—21no—
109C2×C127—41no—
110C2×C127—41no—
111C2×C127#128911yescharacteristic
112C2×C127#138711yescharacteristic
113C2×C127#138911yescharacteristic
114#2112C2×C12711yescharacteristic
115#1810C2×C12711yescharacteristic
116#1808C2×C12711yescharacteristic
117C127#723511yescharacteristic, direct product factor, Sylow
118C23×C8C22×C12711yescharacteristic
119C2×M32C4×C12712yescomplemented
120C2×#108—21no—
121C2×#107—21no—
122#407—21no—
123#380—21no—
124C22⋊C16—21no—
125C22⋊C16—21no—
126#341C4×C12712yescomplemented
127#340C4×C12712yes—
128C23×C4D4×C12711yescharacteristic
129C2×M16—22no—
130C22×C8—42no—
131C22×C8C2×C4×C12711yescharacteristic
132C22×C8C2×C4×C12711yescharacteristic
133C22×C8C2×C4×C12711yescharacteristic
134C22×C8D4×C12711yescharacteristic
135C22×C8D4×C12711yescharacteristic
136C22×C8Q8×C12711yescharacteristic
137C2×C4⋊C4—22no—
138C2×C22⋊C4—41no—
139M32—42no—
140C2×C16—22no—
141#108—42no—
142#107—42no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145#95—41no—
146C24SD16×C12711yescharacteristic
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—42no—
150C22×C4C22⋊C4×C12711yescharacteristic
151C22×C4C22⋊C4×C12711yescharacteristic
152C22×C4C4⋊C4×C12711yescharacteristic
153C22×C4D8×C12711yescharacteristic
154C22×C4SD16×C12711yescharacteristic
155C22×C4Q16×C12711yescharacteristic
156M16—42no—
157M16—42no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—42no—
165C2×C8C42×C12711yescharacteristic
166C2×C8C22⋊C4×C12711yescharacteristic
167C2×C8C4⋊C4×C12711yescharacteristic
168C2×C8C4⋊C4×C12711yescharacteristic
169C4⋊C4—42no—
170C4⋊C4—42no—
171C22⋊C4—82no—
172C16—42no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23#102×C12711yescharacteristic
178C23#103×C12711yescharacteristic
179C23#106×C12711yescharacteristic
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—82no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4#95×C12711yescharacteristic
193C2×C4#102×C12711yescharacteristic
194C2×C4#103×C12711yescharacteristic
195C2×C4#107×C12711yescharacteristic
196C8—21no—
197C8—21no—
198C8—21no—
199C8—82no—
200C8#99×C12712yes—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—42no—
210C22—42no—
211C22#340×C12711yescharacteristic
212C22#361×C12711yescharacteristic
213C22#362×C12711yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—162no—
218C4H(3,ℤ/4)×C12711yescharacteristic
219C4#342×C12711yescharacteristic
220C2—21no—
221C2—21no—
222C2—41no—
223C2—41no—
224C2C127×#128911yescharacteristic
225C2C127×#138711yescharacteristic
226C2C127×#138911yescharacteristic
subgroupG/H
center, socleC22×C127#340
commutatorC2×C8C42×C127
Frattini, cosocleC23×C8C22×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×M32×C127C4semidirect
12. #341×C127C4semidirect
106. #7235C127direct (N × H)
117. C127#7235direct (N × H)
119. C2×M32C4×C127semidirect
126. #341C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#21122
C127×#18102
C127×#18082
#7235127