Finite Group Databasebeta

← C127×#11483 #44575156

Subgroups — C127×#11483 #44575156

Order 32512.

382 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2929C211yesmaximal, characteristic
2C127×#2115C212yesmaximal, complemented
3C127×#1328C212yesmaximal, complemented
4C127×#1320C212yesmaximal, complemented
5C2×#131×C127C2211yescharacteristic
6C23×C8×C127C411yescharacteristic
7#525×C127C411yescharacteristic
8C2×M32×C127—22no—
9#435×C127—22no—
10C8×D4×C127—22no—
11#424×C127C2211yescharacteristic
12#408×C127C411yescharacteristic
13#407×C127C2211yescharacteristic
14#405×C127C411yescharacteristic
15#349×C127—22no—
16#349×C127C2214yes—
17C2×#41×C127C2×C411yescharacteristic
18C23×C4×C127C2×C411yescharacteristic
19#131×C127—41no—
20#131×C127—41no—
21C2×M16×C127C2×C411yescharacteristic
22C2×M16×C127D412yes—
23C2×M16×C127C2311yescharacteristic
24C22×C8×C127—21no—
25C22×C8×C127—21no—
26C22×C8×C127—41no—
27C22×C8×C127—41no—
28C22×C8×C127C2×C411yescharacteristic
29C22×C8×C127C2×C411yescharacteristic
30C22×C8×C127D412yes—
31#123×C127C812yes—
32C22⋊Q8×C127—21no—
33#121×C127—21no—
34#120×C127C812yes—
35C4×D4×C127—22no—
36#117×C127C2×C411yescharacteristic
37M32×C127—24no—
38M32×C127—42no—
39C2×C16×C127—42no—
40C4⋊C8×C127—22no—
41C22⋊C8×C127—22no—
42C22⋊C8×C127—22no—
43#97×C127—21no—
44C4×C8×C127—21no—
45C24×C127C2×C811yescharacteristic
46#41×C127—41no—
47#41×C127—41no—
48C2×Q8×C127M1611yescharacteristic
49C2×D4×C127—22no—
50C2×D4×C127C2×C812yes—
51C2×D4×C127M1611yescharacteristic
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—41no—
55C22×C4×C127—41no—
56C22×C4×C127C22⋊C412yes—
57C22×C4×C127C2×C811yescharacteristic
58C22×C4×C127C22×C411yescharacteristic
59M16×C127—42no—
60M16×C127—41no—
61M16×C127—41no—
62C2×C8×C127—22no—
63C2×C8×C127—21no—
64C2×C8×C127—22no—
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—21no—
68C2×C8×C127—42no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127—41no—
72C2×C8×C127C22⋊C411yescharacteristic
73C2×C8×C127C22⋊C411yescharacteristic
74C2×C8×C127C2×D412yes—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—21no—
77C22⋊C4×C127—22no—
78C22⋊C4×C127—22no—
79C22⋊C4×C127C2×C812yes—
80C42×C127—21no—
81C16×C127—44no—
82C23×C127—21no—
83C23×C127—41no—
84C23×C127—42no—
85C23×C127C22⋊C812yes—
86C23×C127C22×C811yescharacteristic
87Q8×C127—41no—
88D4×C127—42no—
89D4×C127—41no—
90D4×C127—44no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—21no—
94C2×C4×C127—22no—
95C2×C4×C127—22no—
96C2×C4×C127—21no—
97C2×C4×C127—42no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127C22⋊C812yes—
102C2×C4×C127C2×C22⋊C411yescharacteristic
103C2×C4×C127C2×M1611yescharacteristic
104C8×C127—22no—
105C8×C127—21no—
106C8×C127—41no—
107C8×C127—41no—
108C8×C127#9911yescharacteristic
109C8×C127#9911yescharacteristic
110C22×C127—22no—
111C22×C127—21no—
112C22×C127—22no—
113C22×C127—42no—
114C22×C127—41no—
115C22×C127—41no—
116C22×C127—42no—
117C22×C127—42no—
118C22×C127—41no—
119C22×C127C2×C22⋊C811yescharacteristic
120C4×C127—21no—
121C4×C127—22no—
122C4×C127—42no—
123C4×C127—41no—
124C4×C127C2×#9911yescharacteristic
125C4×C127#41311yescharacteristic
126#11483C12711yesmaximal, characteristic, direct product factor, Sylow
127C2×C127—21no—
128C2×C127—42no—
129C2×C127—42no—
130C2×C127—41no—
131C2×C127#145911yescharacteristic
132#2929C2×C12711yescharacteristic
133#2115C2×C12712yescomplemented
134#1328C2×C12712yescomplemented
135#1320C2×C12712yescomplemented
136C127#1148311yescharacteristic, direct product factor, Sylow
137C2×#131C22×C12711yescharacteristic
138C23×C8C4×C12711yescharacteristic
139#525C4×C12711yescharacteristic
140C2×M32—22no—
141#435—22no—
142C8×D4—22no—
143#424C22×C12711yescharacteristic
144#408C4×C12711yescharacteristic
145#407C22×C12711yescharacteristic
146#405C4×C12711yescharacteristic
147#349—22no—
148#349C22×C12714yes—
149C2×#41C2×C4×C12711yescharacteristic
150C23×C4C2×C4×C12711yescharacteristic
151#131—41no—
152#131—41no—
153C2×M16C2×C4×C12711yescharacteristic
154C2×M16D4×C12712yes—
155C2×M16C23×C12711yescharacteristic
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—41no—
159C22×C8—41no—
160C22×C8C2×C4×C12711yescharacteristic
161C22×C8C2×C4×C12711yescharacteristic
162C22×C8D4×C12712yes—
163#123C8×C12712yes—
164C22⋊Q8—21no—
165#121—21no—
166#120C8×C12712yes—
167C4×D4—22no—
168#117C2×C4×C12711yescharacteristic
169M32—24no—
170M32—42no—
171C2×C16—42no—
172C4⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#97—21no—
176C4×C8—21no—
177C24C2×C8×C12711yescharacteristic
178#41—41no—
179#41—41no—
180C2×Q8M16×C12711yescharacteristic
181C2×D4—22no—
182C2×D4C2×C8×C12712yes—
183C2×D4M16×C12711yescharacteristic
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4C22⋊C4×C12712yes—
189C22×C4C2×C8×C12711yescharacteristic
190C22×C4C22×C4×C12711yescharacteristic
191M16—42no—
192M16—41no—
193M16—41no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—42no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8C22⋊C4×C12711yescharacteristic
205C2×C8C22⋊C4×C12711yescharacteristic
206C2×C8C2×D4×C12712yes—
207C4⋊C4—22no—
208C4⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—22no—
211C22⋊C4C2×C8×C12712yes—
212C42—21no—
213C16—44no—
214C23—21no—
215C23—41no—
216C23—42no—
217C23C22⋊C8×C12712yes—
218C23C22×C8×C12711yescharacteristic
219Q8—41no—
220D4—42no—
221D4—41no—
222D4—44no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4C22⋊C8×C12712yes—
234C2×C4C2×C22⋊C4×C12711yescharacteristic
235C2×C4C2×M16×C12711yescharacteristic
236C8—22no—
237C8—21no—
238C8—41no—
239C8—41no—
240C8#99×C12711yescharacteristic
241C8#99×C12711yescharacteristic
242C22—22no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—42no—
249C22—42no—
250C22—41no—
251C22C2×C22⋊C8×C12711yescharacteristic
252C4—21no—
253C4—22no—
254C4—42no—
255C4—41no—
256C4C2×#99×C12711yescharacteristic
257C4#413×C12711yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—42no—
262C2C127×#145911yescharacteristic
subgroupG/H
centerC8×C127#99
commutatorC23C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127#1459
prime radical#525×C127C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C8×C127 ◁ C2×C8×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2115C2semidirect
3. C127×#1328C2semidirect
4. C127×#1320C2semidirect
126. #11483C127direct (N × H)
133. #2115C2×C127semidirect
134. #1328C2×C127semidirect
135. #1320C2×C127semidirect
136. C127#11483direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29292
C127×#21152
C127×#13282
C127×#13202
#11483127