Finite Group Databasebeta

← C127×#7255 #44570928

Subgroups — C127×#7255 #44570928

Order 32512.

324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 102 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×#349×C127C211yesmaximal, characteristic
2C127×#1809C211yesmaximal, characteristic
3C2×#338×C127C211yesmaximal, characteristic
4C22×M16×C127—21no—
5C22×M16×C127C2211yescharacteristic
6C2×M32×C127—21no—
7C2×#107×C127C411yescharacteristic
8C2×#106×C127C411yescharacteristic
9#380×C127—21no—
10#349×C127—21no—
11#349×C127C412yescomplemented
12#340×C127—21no—
13#338×C127—21no—
14#338×C127C412yescomplemented
15C23×C4×C127D411yescharacteristic
16C2×M16×C127—22no—
17C2×M16×C127—22no—
18C2×M16×C127—41no—
19C2×M16×C127—41no—
20C2×M16×C127—41no—
21C2×M16×C127—41no—
22C2×M16×C127—41no—
23C2×M16×C127—41no—
24C2×M16×C127C2×C411yescharacteristic
25C2×M16×C127C2×C411yescharacteristic
26C2×M16×C127D411yescharacteristic
27C2×M16×C127Q811yescharacteristic
28C22×C8×C127—22no—
29C22×C8×C127C2×C411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C22⋊C4×C127—41no—
34M32×C127—22no—
35M32×C127—41no—
36C2×C16×C127—41no—
37#107×C127—41no—
38#106×C127—41no—
39#95×C127—41no—
40C24×C127SD1611yescharacteristic
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127—41no—
46C22×C4×C127—41no—
47C22×C4×C127C22⋊C411yescharacteristic
48C22×C4×C127C22⋊C411yescharacteristic
49C22×C4×C127C4⋊C411yescharacteristic
50C22×C4×C127D811yescharacteristic
51C22×C4×C127SD1611yescharacteristic
52C22×C4×C127Q1611yescharacteristic
53M16×C127—41no—
54M16×C127—41no—
55M16×C127—41no—
56M16×C127—41no—
57M16×C127—42no—
58M16×C127—42no—
59M16×C127—42no—
60M16×C127—42no—
61C2×C8×C127—21no—
62C2×C8×C127—21no—
63C2×C8×C127—21no—
64C2×C8×C127—21no—
65C2×C8×C127—24no—
66C2×C8×C127—42no—
67C2×C8×C127—42no—
68C2×C8×C127C4211yescharacteristic
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C4⋊C411yescharacteristic
71C2×C8×C127C4⋊C411yescharacteristic
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C22⋊C4×C127—82no—
77C16×C127—42no—
78C23×C127—21no—
79C23×C127—21no—
80C23×C127—41no—
81C23×C127—41no—
82C23×C127#10211yescharacteristic
83C23×C127#10311yescharacteristic
84C23×C127#10611yescharacteristic
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—81no—
96C2×C4×C127—81no—
97C2×C4×C127—81no—
98C2×C4×C127—81no—
99C2×C4×C127—81no—
100C2×C4×C127—81no—
101C2×C4×C127#9511yescharacteristic
102C2×C4×C127#9911yescharacteristic
103C2×C4×C127#9911yescharacteristic
104C2×C4×C127#10211yescharacteristic
105C2×C4×C127#10311yescharacteristic
106C2×C4×C127#10411yescharacteristic
107C2×C4×C127#10411yescharacteristic
108C2×C4×C127#10711yescharacteristic
109C8×C127—21no—
110C8×C127—21no—
111C8×C127—21no—
112C8×C127—21no—
113C8×C127—44no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—21no—
118C22×C127—41no—
119C22×C127—41no—
120C22×C127—41no—
121C22×C127—41no—
122C22×C127—81no—
123C22×C127#32711yescharacteristic
124C22×C127#32711yescharacteristic
125C22×C127#34011yescharacteristic
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—161no—
129C4×C127—161no—
130C4×C127#32811yescharacteristic
131C4×C127#32811yescharacteristic
132C4×C127#33911yescharacteristic
133C4×C127#34211yescharacteristic
134#7255C12711yesmaximal, characteristic, direct product factor, Sylow
135C2×C127—21no—
136C2×C127—21no—
137C2×C127—41no—
138C2×C127—41no—
139C2×C127#129411yescharacteristic
140C2×C127#134111yescharacteristic
141C2×C127#134211yescharacteristic
142C2×#349C2×C12711yescharacteristic
143#1809C2×C12711yescharacteristic
144C2×#338C2×C12711yescharacteristic
145C127#725511yescharacteristic, direct product factor, Sylow
146C22×M16—21no—
147C22×M16C22×C12711yescharacteristic
148C2×M32—21no—
149C2×#107C4×C12711yescharacteristic
150C2×#106C4×C12711yescharacteristic
151#380—21no—
152#349—21no—
153#349C4×C12712yescomplemented
154#340—21no—
155#338—21no—
156#338C4×C12712yescomplemented
157C23×C4D4×C12711yescharacteristic
158C2×M16—22no—
159C2×M16—22no—
160C2×M16—41no—
161C2×M16—41no—
162C2×M16—41no—
163C2×M16—41no—
164C2×M16—41no—
165C2×M16—41no—
166C2×M16C2×C4×C12711yescharacteristic
167C2×M16C2×C4×C12711yescharacteristic
168C2×M16D4×C12711yescharacteristic
169C2×M16Q8×C12711yescharacteristic
170C22×C8—22no—
171C22×C8C2×C4×C12711yescharacteristic
172C22×C8D4×C12711yescharacteristic
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C22⋊C4—41no—
176M32—22no—
177M32—41no—
178C2×C16—41no—
179#107—41no—
180#106—41no—
181#95—41no—
182C24SD16×C12711yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4C22⋊C4×C12711yescharacteristic
190C22×C4C22⋊C4×C12711yescharacteristic
191C22×C4C4⋊C4×C12711yescharacteristic
192C22×C4D8×C12711yescharacteristic
193C22×C4SD16×C12711yescharacteristic
194C22×C4Q16×C12711yescharacteristic
195M16—41no—
196M16—41no—
197M16—41no—
198M16—41no—
199M16—42no—
200M16—42no—
201M16—42no—
202M16—42no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—21no—
207C2×C8—24no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8C42×C12711yescharacteristic
211C2×C8C22⋊C4×C12711yescharacteristic
212C2×C8C4⋊C4×C12711yescharacteristic
213C2×C8C4⋊C4×C12711yescharacteristic
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C22⋊C4—82no—
219C16—42no—
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23#102×C12711yescharacteristic
225C23#103×C12711yescharacteristic
226C23#106×C12711yescharacteristic
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4#95×C12711yescharacteristic
244C2×C4#99×C12711yescharacteristic
245C2×C4#99×C12711yescharacteristic
246C2×C4#102×C12711yescharacteristic
247C2×C4#103×C12711yescharacteristic
248C2×C4#104×C12711yescharacteristic
249C2×C4#104×C12711yescharacteristic
250C2×C4#107×C12711yescharacteristic
251C8—21no—
252C8—21no—
253C8—21no—
254C8—21no—
255C8—44no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22#327×C12711yescharacteristic
266C22#327×C12711yescharacteristic
267C22#340×C12711yescharacteristic
268C4—21no—
269C4—21no—
270C4—161no—
271C4—161no—
272C4#328×C12711yescharacteristic
273C4#328×C12711yescharacteristic
274C4#339×C12711yescharacteristic
275C4#342×C12711yescharacteristic
276C2—21no—
277C2—21no—
278C2—41no—
279C2—41no—
280C2C127×#129411yescharacteristic
281C2C127×#134111yescharacteristic
282C2C127×#134211yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC2×C8C42×C127
Frattini, cosocleC22×M16C22×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
11. #349×C127C4semidirect
14. #338×C127C4semidirect
134. #7255C127direct (N × H)
145. C127#7255direct (N × H)
153. #349C4×C127semidirect
156. #338C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#349×C1272
C127×#18092
C2×#338×C1272
#7255127