Finite Group Databasebeta

← C127×#7259 #44570932

Subgroups — C127×#7259 #44570932

Order 32512.

342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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×C22⋊C16×C127C211yesmaximal, characteristic
2C127×#1808C211yesmaximal, characteristic
3C2×#341×C127C211yesmaximal, characteristic
4C22×M16×C127—21no—
5C23×C8×C127C2211yescharacteristic
6C22×C16×C127—21no—
7C2×#107×C127C412yes—
8#380×C127—21no—
9C22⋊C16×C127—21no—
10C22⋊C16×C127C412yescomplemented
11#341×C127—21no—
12#341×C127C412yescomplemented
13#340×C127—21no—
14C23×C4×C127D411yescharacteristic
15C2×M16×C127—24no—
16C2×M16×C127—22no—
17C2×M16×C127—42no—
18C2×M16×C127—41no—
19C22×C8×C127—42no—
20C22×C8×C127—41no—
21C22×C8×C127C2×C411yescharacteristic
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127C2×C411yescharacteristic
24C22×C8×C127D411yescharacteristic
25C22×C8×C127D411yescharacteristic
26C22×C8×C127Q811yescharacteristic
27C2×C4⋊C4×C127—22no—
28C2×C22⋊C4×C127—41no—
29C2×C16×C127—22no—
30C2×C16×C127—42no—
31#107×C127—42no—
32#95×C127—41no—
33C24×C127SD1611yescharacteristic
34C22×C4×C127—22no—
35C22×C4×C127—22no—
36C22×C4×C127—42no—
37C22×C4×C127C22⋊C411yescharacteristic
38C22×C4×C127C22⋊C411yescharacteristic
39C22×C4×C127C4⋊C411yescharacteristic
40C22×C4×C127D811yescharacteristic
41C22×C4×C127SD1611yescharacteristic
42C22×C4×C127Q1611yescharacteristic
43M16×C127—24no—
44M16×C127—44no—
45M16×C127—42no—
46C2×C8×C127—22no—
47C2×C8×C127—22no—
48C2×C8×C127—41no—
49C2×C8×C127—41no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127—44no—
53C2×C8×C127—42no—
54C2×C8×C127C4211yescharacteristic
55C2×C8×C127C22⋊C411yescharacteristic
56C2×C8×C127C4⋊C411yescharacteristic
57C2×C8×C127C4⋊C411yescharacteristic
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C22⋊C4×C127—82no—
61C16×C127—42no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127—21no—
65C23×C127—21no—
66C23×C127#10211yescharacteristic
67C23×C127#10311yescharacteristic
68C23×C127#10611yescharacteristic
69C2×C4×C127—22no—
70C2×C4×C127—22no—
71C2×C4×C127—22no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—82no—
77C2×C4×C127—82no—
78C2×C4×C127—82no—
79C2×C4×C127#9511yescharacteristic
80C2×C4×C127#9912yes—
81C2×C4×C127#10211yescharacteristic
82C2×C4×C127#10311yescharacteristic
83C2×C4×C127#10412yes—
84C2×C4×C127#10711yescharacteristic
85C8×C127—21no—
86C8×C127—21no—
87C8×C127—21no—
88C8×C127—21no—
89C8×C127—44no—
90C22×C127—21no—
91C22×C127—21no—
92C22×C127—21no—
93C22×C127—21no—
94C22×C127—21no—
95C22×C127—21no—
96C22×C127—42no—
97C22×C127—42no—
98C22×C127#32712yes—
99C22×C127#34011yescharacteristic
100C22×C127#35912yes—
101C22×C127#36111yescharacteristic
102C22×C127#36211yescharacteristic
103C4×C127—21no—
104C4×C127—21no—
105C4×C127—162no—
106C4×C127#32812yes—
107C4×C127#33911yescharacteristic
108C4×C127#34211yescharacteristic
109#7259C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—41no—
111C2×C127—41no—
112C2×C127#129411yescharacteristic
113C2×C127#134912yes—
114C2×C127#135012yes—
115C2×C127#138211yescharacteristic
116C2×C127#138711yescharacteristic
117C2×C22⋊C16C2×C12711yescharacteristic
118#1808C2×C12711yescharacteristic
119C2×#341C2×C12711yescharacteristic
120C127#725911yescharacteristic, direct product factor, Sylow
121C22×M16—21no—
122C23×C8C22×C12711yescharacteristic
123C22×C16—21no—
124C2×#107C4×C12712yes—
125#380—21no—
126C22⋊C16—21no—
127C22⋊C16C4×C12712yescomplemented
128#341—21no—
129#341C4×C12712yescomplemented
130#340—21no—
131C23×C4D4×C12711yescharacteristic
132C2×M16—24no—
133C2×M16—22no—
134C2×M16—42no—
135C2×M16—41no—
136C22×C8—42no—
137C22×C8—41no—
138C22×C8C2×C4×C12711yescharacteristic
139C22×C8C2×C4×C12711yescharacteristic
140C22×C8C2×C4×C12711yescharacteristic
141C22×C8D4×C12711yescharacteristic
142C22×C8D4×C12711yescharacteristic
143C22×C8Q8×C12711yescharacteristic
144C2×C4⋊C4—22no—
145C2×C22⋊C4—41no—
146C2×C16—22no—
147C2×C16—42no—
148#107—42no—
149#95—41no—
150C24SD16×C12711yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4C22⋊C4×C12711yescharacteristic
155C22×C4C22⋊C4×C12711yescharacteristic
156C22×C4C4⋊C4×C12711yescharacteristic
157C22×C4D8×C12711yescharacteristic
158C22×C4SD16×C12711yescharacteristic
159C22×C4Q16×C12711yescharacteristic
160M16—24no—
161M16—44no—
162M16—42no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—44no—
170C2×C8—42no—
171C2×C8C42×C12711yescharacteristic
172C2×C8C22⋊C4×C12711yescharacteristic
173C2×C8C4⋊C4×C12711yescharacteristic
174C2×C8C4⋊C4×C12711yescharacteristic
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—82no—
178C16—42no—
179C23—22no—
180C23—22no—
181C23—21no—
182C23—21no—
183C23#102×C12711yescharacteristic
184C23#103×C12711yescharacteristic
185C23#106×C12711yescharacteristic
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4#95×C12711yescharacteristic
197C2×C4#99×C12712yes—
198C2×C4#102×C12711yescharacteristic
199C2×C4#103×C12711yescharacteristic
200C2×C4#104×C12712yes—
201C2×C4#107×C12711yescharacteristic
202C8—21no—
203C8—21no—
204C8—21no—
205C8—21no—
206C8—44no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—42no—
214C22—42no—
215C22#327×C12712yes—
216C22#340×C12711yescharacteristic
217C22#359×C12712yes—
218C22#361×C12711yescharacteristic
219C22#362×C12711yescharacteristic
220C4—21no—
221C4—21no—
222C4—162no—
223C4#328×C12712yes—
224C4#339×C12711yescharacteristic
225C4#342×C12711yescharacteristic
226C2—41no—
227C2—41no—
228C2C127×#129411yescharacteristic
229C2C127×#134912yes—
230C2C127×#135012yes—
231C2C127×#138211yescharacteristic
232C2C127×#138711yescharacteristic
subgroupG/H
center, socleC23×C127#102
commutatorC2×C8C42×C127
Frattini, cosocleC23×C8C22×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
10. C22⋊C16×C127C4semidirect
12. #341×C127C4semidirect
109. #7259C127direct (N × H)
120. C127#7259direct (N × H)
127. C22⋊C16C4×C127semidirect
129. #341C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C16×C1272
C127×#18082
C2×#341×C1272
#7259127