Finite Group Databasebeta

← C127×#11519 #44575192

Subgroups — C127×#11519 #44575192

Order 32512.

542 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2315C211yesmaximal, characteristic
2C127×#1462C212yesmaximal
3C127×#1326C214yesmaximal, complemented
4C22×C22⋊C4×C127C411yescharacteristic
5C22×C22⋊C4×C127C411yescharacteristic
6C22×C22⋊C4×C127C2211yescharacteristic
7#407×C127—22no—
8#385×C127—22no—
9#385×C127C412yes—
10#385×C127C2212yes—
11#380×C127—22no—
12#323×C127—22no—
13#323×C127C2214yes—
14C25×C127C2×C411yescharacteristic
15C23×C4×C127—21no—
16C23×C4×C127C2×C412yes—
17C23×C4×C127D412yes—
18C2×M16×C127—42no—
19C2×C4⋊C4×C127—22no—
20C2×C4⋊C4×C127—22no—
21C2×C22⋊C4×C127—21no—
22C2×C22⋊C4×C127—24no—
23C2×C22⋊C4×C127—21no—
24C2×C22⋊C4×C127—21no—
25C2×C22⋊C4×C127—41no—
26C2×C22⋊C4×C127—41no—
27C2×C22⋊C4×C127—41no—
28C2×C22⋊C4×C127—41no—
29C2×C22⋊C4×C127C2×C412yes—
30C2×C22⋊C4×C127C2×C411yescharacteristic
31C2×C22⋊C4×C127D412yes—
32C2×C22⋊C4×C127C2311yescharacteristic
33C22⋊C8×C127—24no—
34C22⋊C8×C127—42no—
35#95×C127—22no—
36#95×C127—22no—
37C24×C127—21no—
38C24×C127—21no—
39C24×C127—22no—
40C24×C127—22no—
41C24×C127—82no—
42C24×C127C22⋊C411yescharacteristic
43C24×C127C22⋊C411yescharacteristic
44C24×C127C22×C411yescharacteristic
45C22×C4×C127—22no—
46C22×C4×C127—22no—
47C22×C4×C127—24no—
48C22×C4×C127—22no—
49C22×C4×C127—22no—
50C22×C4×C127—42no—
51C22×C4×C127—82no—
52C22×C4×C127—82no—
53C22×C4×C127—82no—
54C22×C4×C127C22⋊C412yes—
55C22×C4×C127C2×D412yes—
56M16×C127—84no—
57C2×C8×C127—44no—
58C4⋊C4×C127—82no—
59C4⋊C4×C127—82no—
60C22⋊C4×C127—24no—
61C22⋊C4×C127—22no—
62C22⋊C4×C127—41no—
63C22⋊C4×C127—42no—
64C22⋊C4×C127—41no—
65C22⋊C4×C127—42no—
66C22⋊C4×C127—41no—
67C22⋊C4×C127—41no—
68C22⋊C4×C127M1614yescomplemented
69C23×C127—24no—
70C23×C127—24no—
71C23×C127—21no—
72C23×C127—21no—
73C23×C127—21no—
74C23×C127—21no—
75C23×C127—21no—
76C23×C127—21no—
77C23×C127—42no—
78C23×C127—42no—
79C23×C127—42no—
80C23×C127—82no—
81C23×C127—82no—
82C23×C127—84no—
83C23×C127—84no—
84C23×C127#9911yescharacteristic
85C23×C127#9911yescharacteristic
86C23×C127#10112yes—
87C23×C127C2×C22⋊C411yescharacteristic
88C23×C127C2×M1612yes—
89C2×C4×C127—24no—
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—42no—
93C2×C4×C127—42no—
94C2×C4×C127—44no—
95C2×C4×C127—42no—
96C2×C4×C127—42no—
97C2×C4×C127—42no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127—82no—
101C2×C4×C127—84no—
102C2×C4×C127—84no—
103C8×C127—84no—
104C22×C127—22no—
105C22×C127—22no—
106C22×C127—22no—
107C22×C127—21no—
108C22×C127—21no—
109C22×C127—22no—
110C22×C127—22no—
111C22×C127—42no—
112C22×C127—42no—
113C22×C127—42no—
114C22×C127—42no—
115C22×C127—42no—
116C22×C127—42no—
117C22×C127—42no—
118C22×C127—42no—
119C22×C127—84no—
120C22×C127—84no—
121C22×C127#40711yescharacteristic
122C22×C127C2×#9911yescharacteristic
123C22×C127C2×#10111yescharacteristic
124C4×C127—44no—
125C4×C127—42no—
126C4×C127—42no—
127C4×C127—82no—
128#11519C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—21no—
130C2×C127—21no—
131C2×C127—41no—
132C2×C127—41no—
133C2×C127—42no—
134C2×C127—42no—
135C2×C127#146311yescharacteristic
136C2×C127#212112yes—
137#2315C2×C12711yescharacteristic
138#1462C2×C12712yes—
139#1326C2×C12714yescomplemented
140C127#1151911yescharacteristic, direct product factor, Sylow
141C22×C22⋊C4C4×C12711yescharacteristic
142C22×C22⋊C4C4×C12711yescharacteristic
143C22×C22⋊C4C22×C12711yescharacteristic
144#407—22no—
145#385—22no—
146#385C4×C12712yes—
147#385C22×C12712yes—
148#380—22no—
149#323—22no—
150#323C22×C12714yes—
151C25C2×C4×C12711yescharacteristic
152C23×C4—21no—
153C23×C4C2×C4×C12712yes—
154C23×C4D4×C12712yes—
155C2×M16—42no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4C2×C4×C12712yes—
167C2×C22⋊C4C2×C4×C12711yescharacteristic
168C2×C22⋊C4D4×C12712yes—
169C2×C22⋊C4C23×C12711yescharacteristic
170C22⋊C8—24no—
171C22⋊C8—42no—
172#95—22no—
173#95—22no—
174C24—21no—
175C24—21no—
176C24—22no—
177C24—22no—
178C24—82no—
179C24C22⋊C4×C12711yescharacteristic
180C24C22⋊C4×C12711yescharacteristic
181C24C22×C4×C12711yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—82no—
189C22×C4—82no—
190C22×C4—82no—
191C22×C4C22⋊C4×C12712yes—
192C22×C4C2×D4×C12712yes—
193M16—84no—
194C2×C8—44no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C22⋊C4—24no—
198C22⋊C4—22no—
199C22⋊C4—41no—
200C22⋊C4—42no—
201C22⋊C4—41no—
202C22⋊C4—42no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4M16×C12714yescomplemented
206C23—24no—
207C23—24no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—42no—
215C23—42no—
216C23—42no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23#99×C12711yescharacteristic
222C23#99×C12711yescharacteristic
223C23#101×C12712yes—
224C23C2×C22⋊C4×C12711yescharacteristic
225C23C2×M16×C12712yes—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—84no—
239C2×C4—84no—
240C8—84no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—22no—
247C22—22no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—84no—
257C22—84no—
258C22#407×C12711yescharacteristic
259C22C2×#99×C12711yescharacteristic
260C22C2×#101×C12711yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—41no—
268C2—41no—
269C2—42no—
270C2—42no—
271C2C127×#146311yescharacteristic
272C2C127×#212112yes—
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC25×C127C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1326C2semidirect
68. C22⋊C4×C127M16semidirect
128. #11519C127direct (N × H)
139. #1326C2×C127semidirect
140. C127#11519direct (N × H)
205. C22⋊C4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23152
C127×#14622
C127×#13262
#11519127