Finite Group Databasebeta

← C127×#9456 #44573129

Subgroups — C127×#9456 #44573129

Order 32512.

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

normal subgroups only

This group has 432 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×#2983C211yesmaximal, characteristic
2C127×#2568C211yesmaximal, characteristic
3C127×#1556C212yesmaximal
4C127×#1467C211yesmaximal, characteristic
5C127×#1285C212yesmaximal
6C2×C4⋊Q8×C127C2211yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#446×C127—24no—
9#432×C127—21no—
10#432×C127C2212yes—
11#432×C127C2212yes—
12#431×C127—21no—
13#400×C127—21no—
14#400×C127—21no—
15#391×C127—21no—
16#391×C127—21no—
17#391×C127C412yes—
18#382×C127C412yes—
19C4×C4⋊C4×C127C2211yescharacteristic
20#332×C127—24no—
21#324×C127—21no—
22#324×C127—21no—
23C22×Q8×C127—21no—
24C22×Q8×C127C2×C411yescharacteristic
25C4⋊Q8×C127—22no—
26C4⋊Q8×C127—22no—
27C4×Q8×C127—22no—
28C4×Q8×C127—22no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127C2×C412yes—
32C2×C4⋊C4×C127C2×C411yescharacteristic
33C2×C4⋊C4×C127D411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C42×C127C2×C412yes—
36C2×C42×C127D411yescharacteristic
37C2×C42×C127D411yescharacteristic
38C2×C42×C127C2311yescharacteristic
39C4⋊C8×C127—22no—
40C4⋊C8×C127—22no—
41C4⋊C8×C127—22no—
42C4⋊C8×C127D414yes—
43C22⋊C8×C127—22no—
44C22⋊C8×C127—22no—
45#97×C127—22no—
46#97×C127—22no—
47#97×C127—22no—
48C4×C8×C127—22no—
49#95×C127—22no—
50#95×C127—22no—
51#95×C127—22no—
52#95×C127—22no—
53#95×C127—21no—
54C2×Q8×C127—22no—
55C2×Q8×C127—22no—
56C2×Q8×C127—41no—
57C2×Q8×C127—44no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127C22⋊C411yescharacteristic
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127C22⋊C411yescharacteristic
65C22×C4×C127C22⋊C411yescharacteristic
66C22×C4×C127C22×C411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69C2×C8×C127—24no—
70C2×C8×C127—42no—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—22no—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—24no—
75C4⋊C4×C127—42no—
76C4⋊C4×C127—42no—
77C42×C127—21no—
78C42×C127—21no—
79C42×C127—21no—
80C42×C127—21no—
81C42×C127—42no—
82C42×C127C2×D412yes—
83C42×C127#4112yes—
84C23×C127C2×C22⋊C411yescharacteristic
85Q8×C127—44no—
86Q8×C127—82no—
87Q8×C127—82no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—42no—
102C2×C4×C127—42no—
103C2×C4×C127—44no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127#10112yes—
107C2×C4×C127C4×D412yes—
108C2×C4×C127#12011yescharacteristic
109C2×C4×C127#12112yes—
110C2×C4×C127#12311yescharacteristic
111C8×C127—44no—
112C8×C127—82no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127#38611yescharacteristic
116C22×C127C2×#10111yescharacteristic
117C22×C127#41311yescharacteristic
118C4×C127—21no—
119C4×C127—22no—
120C4×C127—22no—
121C4×C127—22no—
122C4×C127—41no—
123C4×C127—41no—
124C4×C127—41no—
125C4×C127—82no—
126C4×C127—82no—
127C4×C127#45412yes—
128#9456C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—21no—
130C2×C127—21no—
131C2×C127#188811yescharacteristic
132C2×C127#190111yescharacteristic
133C2×C127#190911yescharacteristic
134#2983C2×C12711yescharacteristic
135#2568C2×C12711yescharacteristic
136#1556C2×C12712yes—
137#1467C2×C12711yescharacteristic
138#1285C2×C12712yes—
139C127#945611yescharacteristic, direct product factor, Sylow
140C2×C4⋊Q8C22×C12711yescharacteristic
141C2×C4×Q8C22×C12711yescharacteristic
142#446—24no—
143#432—21no—
144#432C22×C12712yes—
145#432C22×C12712yes—
146#431—21no—
147#400—21no—
148#400—21no—
149#391—21no—
150#391—21no—
151#391C4×C12712yes—
152#382C4×C12712yes—
153C4×C4⋊C4C22×C12711yescharacteristic
154#332—24no—
155#324—21no—
156#324—21no—
157C22×Q8—21no—
158C22×Q8C2×C4×C12711yescharacteristic
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×C4×C12712yes—
166C2×C4⋊C4C2×C4×C12711yescharacteristic
167C2×C4⋊C4D4×C12711yescharacteristic
168C2×C4⋊C4D4×C12711yescharacteristic
169C2×C42C2×C4×C12712yes—
170C2×C42D4×C12711yescharacteristic
171C2×C42D4×C12711yescharacteristic
172C2×C42C23×C12711yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C12714yes—
177C22⋊C8—22no—
178C22⋊C8—22no—
179#97—22no—
180#97—22no—
181#97—22no—
182C4×C8—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—21no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—44no—
192C2×Q8—41no—
193C2×Q8—41no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4C22⋊C4×C12711yescharacteristic
197C22×C4C22⋊C4×C12711yescharacteristic
198C22×C4C22⋊C4×C12711yescharacteristic
199C22×C4C22⋊C4×C12711yescharacteristic
200C22×C4C22×C4×C12711yescharacteristic
201C22×C4C2×D4×C12711yescharacteristic
202C22×C4C2×D4×C12711yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—24no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—42no—
216C42C2×D4×C12712yes—
217C42#41×C12712yes—
218C23C2×C22⋊C4×C12711yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—82no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4#101×C12712yes—
241C2×C4C4×D4×C12712yes—
242C2×C4#120×C12711yescharacteristic
243C2×C4#121×C12712yes—
244C2×C4#123×C12711yescharacteristic
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22#386×C12711yescharacteristic
250C22C2×#101×C12711yescharacteristic
251C22#413×C12711yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4#454×C12712yes—
262C2—21no—
263C2—21no—
264C2C127×#188811yescharacteristic
265C2C127×#190111yescharacteristic
266C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
128. #9456C127direct (N × H)
139. C127#9456direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29832
C127×#25682
C127×#15562
C127×#14672
C127×#12852
#9456127