Finite Group Databasebeta

← C127×#7257 #44570930

Subgroups — C127×#7257 #44570930

Order 32512.

302 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1811C211yesmaximal, characteristic
3C2×#338×C127C211yesmaximal, characteristic
4C22×M16×C127—21no—
5C22×M16×C127C2211yescharacteristic
6C2×M32×C127—21no—
7C2×#108×C127C411yescharacteristic
8C2×#108×C127C411yescharacteristic
9#407×C127—21no—
10#349×C127—21no—
11#349×C127C412yes—
12#341×C127—21no—
13#338×C127—21no—
14#338×C127C412yes—
15C23×C4×C127D411yescharacteristic
16C2×M16×C127—22no—
17C2×M16×C127—22no—
18C2×M16×C127—21no—
19C2×M16×C127—21no—
20C2×M16×C127—41no—
21C2×M16×C127—41no—
22C2×M16×C127—41no—
23C2×M16×C127—41no—
24C2×M16×C127—41no—
25C2×M16×C127—41no—
26C2×M16×C127C2×C411yescharacteristic
27C2×M16×C127C2×C411yescharacteristic
28C2×M16×C127D411yescharacteristic
29C2×M16×C127Q811yescharacteristic
30C22×C8×C127—22no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127D411yescharacteristic
33M32×C127—22no—
34M32×C127—41no—
35C2×C16×C127—41no—
36#108×C127—41no—
37#108×C127—41no—
38C22⋊C8×C127—41no—
39C22⋊C8×C127—41no—
40C24×C127Q1611yescharacteristic
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127C22⋊C411yescharacteristic
46C22×C4×C127C22⋊C411yescharacteristic
47C22×C4×C127C4⋊C411yescharacteristic
48C22×C4×C127D811yescharacteristic
49C22×C4×C127SD1611yescharacteristic
50C22×C4×C127SD1611yescharacteristic
51M16×C127—41no—
52M16×C127—41no—
53M16×C127—41no—
54M16×C127—41no—
55M16×C127—42no—
56M16×C127—42no—
57M16×C127—42no—
58M16×C127—42no—
59M16×C127—41no—
60M16×C127—41no—
61M16×C127—41no—
62M16×C127—41no—
63C2×C8×C127—21no—
64C2×C8×C127—21no—
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—24no—
68C2×C8×C127—42no—
69C2×C8×C127—42no—
70C2×C8×C127—41no—
71C2×C8×C127—41no—
72C2×C8×C127C4211yescharacteristic
73C2×C8×C127C22⋊C411yescharacteristic
74C2×C8×C127C4⋊C411yescharacteristic
75C2×C8×C127C4⋊C411yescharacteristic
76C16×C127—42no—
77C23×C127—21no—
78C23×C127—21no—
79C23×C127—81no—
80C23×C127#10311yescharacteristic
81C23×C127#10311yescharacteristic
82C23×C127#10711yescharacteristic
83C2×C4×C127—21no—
84C2×C4×C127—21no—
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#9511yescharacteristic
94C2×C4×C127#9911yescharacteristic
95C2×C4×C127#9911yescharacteristic
96C2×C4×C127#10211yescharacteristic
97C2×C4×C127#10211yescharacteristic
98C2×C4×C127#10411yescharacteristic
99C2×C4×C127#10411yescharacteristic
100C2×C4×C127#10611yescharacteristic
101C8×C127—21no—
102C8×C127—21no—
103C8×C127—21no—
104C8×C127—21no—
105C8×C127—44no—
106C8×C127—81no—
107C8×C127—81no—
108C22×C127—21no—
109C22×C127—21no—
110C22×C127—41no—
111C22×C127—41no—
112C22×C127—41no—
113C22×C127—42no—
114C22×C127—81no—
115C22×C127#32811yescharacteristic
116C22×C127#32811yescharacteristic
117C22×C127#34011yescharacteristic
118C4×C127—21no—
119C4×C127—21no—
120C4×C127#32711yescharacteristic
121C4×C127#32711yescharacteristic
122C4×C127#33911yescharacteristic
123C4×C127#34211yescharacteristic
124#7257C12711yesmaximal, characteristic, direct product factor, Sylow
125C2×C127—21no—
126C2×C127—21no—
127C2×C127—21no—
128C2×C127—41no—
129C2×C127—41no—
130C2×C127#129411yescharacteristic
131C2×#349C2×C12711yescharacteristic
132#1811C2×C12711yescharacteristic
133C2×#338C2×C12711yescharacteristic
134C127#725711yescharacteristic, direct product factor, Sylow
135C22×M16—21no—
136C22×M16C22×C12711yescharacteristic
137C2×M32—21no—
138C2×#108C4×C12711yescharacteristic
139C2×#108C4×C12711yescharacteristic
140#407—21no—
141#349—21no—
142#349C4×C12712yes—
143#341—21no—
144#338—21no—
145#338C4×C12712yes—
146C23×C4D4×C12711yescharacteristic
147C2×M16—22no—
148C2×M16—22no—
149C2×M16—21no—
150C2×M16—21no—
151C2×M16—41no—
152C2×M16—41no—
153C2×M16—41no—
154C2×M16—41no—
155C2×M16—41no—
156C2×M16—41no—
157C2×M16C2×C4×C12711yescharacteristic
158C2×M16C2×C4×C12711yescharacteristic
159C2×M16D4×C12711yescharacteristic
160C2×M16Q8×C12711yescharacteristic
161C22×C8—22no—
162C22×C8C2×C4×C12711yescharacteristic
163C22×C8D4×C12711yescharacteristic
164M32—22no—
165M32—41no—
166C2×C16—41no—
167#108—41no—
168#108—41no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C24Q16×C12711yescharacteristic
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4C22⋊C4×C12711yescharacteristic
177C22×C4C22⋊C4×C12711yescharacteristic
178C22×C4C4⋊C4×C12711yescharacteristic
179C22×C4D8×C12711yescharacteristic
180C22×C4SD16×C12711yescharacteristic
181C22×C4SD16×C12711yescharacteristic
182M16—41no—
183M16—41no—
184M16—41no—
185M16—41no—
186M16—42no—
187M16—42no—
188M16—42no—
189M16—42no—
190M16—41no—
191M16—41no—
192M16—41no—
193M16—41no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—24no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8C42×C12711yescharacteristic
204C2×C8C22⋊C4×C12711yescharacteristic
205C2×C8C4⋊C4×C12711yescharacteristic
206C2×C8C4⋊C4×C12711yescharacteristic
207C16—42no—
208C23—21no—
209C23—21no—
210C23—81no—
211C23#103×C12711yescharacteristic
212C23#103×C12711yescharacteristic
213C23#107×C12711yescharacteristic
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4#95×C12711yescharacteristic
225C2×C4#99×C12711yescharacteristic
226C2×C4#99×C12711yescharacteristic
227C2×C4#102×C12711yescharacteristic
228C2×C4#102×C12711yescharacteristic
229C2×C4#104×C12711yescharacteristic
230C2×C4#104×C12711yescharacteristic
231C2×C4#106×C12711yescharacteristic
232C8—21no—
233C8—21no—
234C8—21no—
235C8—21no—
236C8—44no—
237C8—81no—
238C8—81no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—81no—
246C22#328×C12711yescharacteristic
247C22#328×C12711yescharacteristic
248C22#340×C12711yescharacteristic
249C4—21no—
250C4—21no—
251C4#327×C12711yescharacteristic
252C4#327×C12711yescharacteristic
253C4#339×C12711yescharacteristic
254C4#342×C12711yescharacteristic
255C2—21no—
256C2—21no—
257C2—21no—
258C2—41no—
259C2—41no—
260C2C127×#129411yescharacteristic
subgroupG/H
centerC4×C127#327
commutatorC2×C8C42×C127
Frattini, cosocleC22×M16C22×C127
socleC2×C127#1294
prime radicalC24×C127Q16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
124. #7257C127direct (N × H)
134. C127#7257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#349×C1272
C127×#18112
C2×#338×C1272
#7257127