Finite Group Databasebeta

← C127×#14712 #44578385

Subgroups — C127×#14712 #44578385

Order 32512.

1854 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C216yesmaximal
2C2×#384×C127C211yesmaximal, characteristic
3C2×#384×C127C211yesmaximal, characteristic
4C2×C43×C127C211yesmaximal, characteristic
5C127×C4⋊#95C216yesmaximal
6C22×C4⋊C4×C127C2216yes—
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2216yes—
9C22×C42×C127C2213yes—
10C22×C42×C127C2213yes—
11C22×C42×C127C2211yescharacteristic
12#389×C127—224no—
13#384×C127—24no—
14#384×C127C418yescomplemented
15C2×#95×C127C22112yes—
16C43×C127—24no—
17C23×C4×C127C2314yes—
18C23×C4×C127C2314yes—
19C23×C4×C127C2311yescharacteristic
20C23×C4×C127C2313yes—
21C23×C4×C127C2313yes—
22C2×C4⋊C4×C127—212no—
23C2×C4⋊C4×C127—212no—
24C2×C4⋊C4×C127—212no—
25C2×C4⋊C4×C127—212no—
26C2×C4⋊C4×C127—224no—
27C2×C4⋊C4×C127—212no—
28C2×C4⋊C4×C127C2×C4124yes—
29C2×C42×C127—26no—
30C2×C42×C127—26no—
31C2×C42×C127—26no—
32C2×C42×C127—26no—
33C2×C42×C127C2×C414yes—
34C2×C42×C127D4112yes—
35C2×C42×C127D414yes—
36C2×C42×C127Q8112yes—
37C2×C42×C127Q814yes—
38#95×C127—224no—
39C24×C127C2411yescharacteristic
40C22×C4×C127—21no—
41C22×C4×C127—23no—
42C22×C4×C127—23no—
43C22×C4×C127—23no—
44C22×C4×C127—26no—
45C22×C4×C127—212no—
46C22×C4×C127—212no—
47C22×C4×C127—212no—
48C22×C4×C127—24no—
49C22×C4×C127—212no—
50C22×C4×C127C22×C418yes—
51C22×C4×C127C22×C416yes—
52C22×C4×C127C2×D416yes—
53C22×C4×C127C2×D416yes—
54C22×C4×C127C2×D416yes—
55C22×C4×C127C2×D416yes—
56C22×C4×C127C2×Q8112yes—
57C22×C4×C127C2×Q816yes—
58C22×C4×C127C2×Q816yes—
59C22×C4×C127#4116yes—
60C22×C4×C127#4116yes—
61C4⋊C4×C127—248no—
62C4⋊C4×C127—424no—
63C4⋊C4×C127—416no—
64C42×C127—224no—
65C42×C127—224no—
66C42×C127C4⋊C4116yescomplemented
67C23×C127C23×C411yescharacteristic
68C23×C127C22×D411yescharacteristic
69C23×C127C22×D413yes—
70C23×C127C22×Q811yescharacteristic
71C23×C127C22×Q813yes—
72C23×C127C2×#4113yes—
73C23×C127C2×#4113yes—
74C2×C4×C127—26no—
75C2×C4×C127—26no—
76C2×C4×C127—212no—
77C2×C4×C127—26no—
78C2×C4×C127—26no—
79C2×C4×C127—212no—
80C2×C4×C127—224no—
81C2×C4×C127—44no—
82C2×C4×C127—412no—
83C2×C4×C127—412no—
84C2×C4×C127—44no—
85C2×C4×C127—412no—
86C2×C4×C127C2×C4⋊C4112yes—
87C2×C4×C127C4×D4112yes—
88C2×C4×C127C4×Q8112yes—
89C2×C4×C127#121112yes—
90C2×C4×C127C22⋊Q8112yes—
91C2×C4×C127#125112yes—
92C2×C4×C127#12714yes—
93C2×C4×C127C4⋊Q8112yes—
94C2×C4×C127C4⋊Q8112yes—
95C22×C127C22×C4⋊C411yescharacteristic
96C22×C127C2×C4×D413yes—
97C22×C127C2×C4×Q813yes—
98C22×C127C2×#12113yes—
99C22×C127C2×C22⋊Q813yes—
100C22×C127C2×#12513yes—
101C22×C127C2×#12711yescharacteristic
102C22×C127C2×C4⋊Q813yes—
103C22×C127C2×C4⋊Q813yes—
104C22×C127#53213yes—
105C22×C127#53213yes—
106C22×C127#53316yes—
107C4×C127—24no—
108C4×C127—212no—
109C4×C127—48no—
110C4×C127—84no—
111C4×C127#389124yescomplemented
112#14712C12711yesmaximal, characteristic, direct product factor, Sylow
113C2×C127C2×#38913yes—
114C2×C127C4×#12711yescharacteristic
115C2×C127C4×C4⋊Q813yes—
116C2×C127#285611yescharacteristic
117C2×C127#285713yes—
118C2×C127#285913yes—
119C2×C127#286811yescharacteristic
120C2×#389C2×C12716yes—
121C2×#384C2×C12711yescharacteristic
122C2×#384C2×C12711yescharacteristic
123C2×C43C2×C12711yescharacteristic
124C4⋊#95C2×C12716yes—
125C127#1471211yescharacteristic, direct product factor, Sylow
126C22×C4⋊C4C22×C12716yes—
127C22×C4⋊C4C22×C12714yes—
128C22×C4⋊C4C22×C12716yes—
129C22×C42C22×C12713yes—
130C22×C42C22×C12713yes—
131C22×C42C22×C12711yescharacteristic
132#389—224no—
133#384—24no—
134#384C4×C12718yescomplemented
135C2×#95C22×C127112yes—
136C43—24no—
137C23×C4C23×C12714yes—
138C23×C4C23×C12714yes—
139C23×C4C23×C12711yescharacteristic
140C23×C4C23×C12713yes—
141C23×C4C23×C12713yes—
142C2×C4⋊C4—212no—
143C2×C4⋊C4—212no—
144C2×C4⋊C4—212no—
145C2×C4⋊C4—212no—
146C2×C4⋊C4—224no—
147C2×C4⋊C4—212no—
148C2×C4⋊C4C2×C4×C127124yes—
149C2×C42—26no—
150C2×C42—26no—
151C2×C42—26no—
152C2×C42—26no—
153C2×C42C2×C4×C12714yes—
154C2×C42D4×C127112yes—
155C2×C42D4×C12714yes—
156C2×C42Q8×C127112yes—
157C2×C42Q8×C12714yes—
158#95—224no—
159C24C24×C12711yescharacteristic
160C22×C4—21no—
161C22×C4—23no—
162C22×C4—23no—
163C22×C4—23no—
164C22×C4—26no—
165C22×C4—212no—
166C22×C4—212no—
167C22×C4—212no—
168C22×C4—24no—
169C22×C4—212no—
170C22×C4C22×C4×C12718yes—
171C22×C4C22×C4×C12716yes—
172C22×C4C2×D4×C12716yes—
173C22×C4C2×D4×C12716yes—
174C22×C4C2×D4×C12716yes—
175C22×C4C2×D4×C12716yes—
176C22×C4C2×Q8×C127112yes—
177C22×C4C2×Q8×C12716yes—
178C22×C4C2×Q8×C12716yes—
179C22×C4#41×C12716yes—
180C22×C4#41×C12716yes—
181C4⋊C4—248no—
182C4⋊C4—424no—
183C4⋊C4—416no—
184C42—224no—
185C42—224no—
186C42C4⋊C4×C127116yescomplemented
187C23C23×C4×C12711yescharacteristic
188C23C22×D4×C12711yescharacteristic
189C23C22×D4×C12713yes—
190C23C22×Q8×C12711yescharacteristic
191C23C22×Q8×C12713yes—
192C23C2×#41×C12713yes—
193C23C2×#41×C12713yes—
194C2×C4—26no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—26no—
198C2×C4—26no—
199C2×C4—212no—
200C2×C4—224no—
201C2×C4—44no—
202C2×C4—412no—
203C2×C4—412no—
204C2×C4—44no—
205C2×C4—412no—
206C2×C4C2×C4⋊C4×C127112yes—
207C2×C4C4×D4×C127112yes—
208C2×C4C4×Q8×C127112yes—
209C2×C4#121×C127112yes—
210C2×C4C22⋊Q8×C127112yes—
211C2×C4#125×C127112yes—
212C2×C4#127×C12714yes—
213C2×C4C4⋊Q8×C127112yes—
214C2×C4C4⋊Q8×C127112yes—
215C22C22×C4⋊C4×C12711yescharacteristic
216C22C2×C4×D4×C12713yes—
217C22C2×C4×Q8×C12713yes—
218C22C2×#121×C12713yes—
219C22C2×C22⋊Q8×C12713yes—
220C22C2×#125×C12713yes—
221C22C2×#127×C12711yescharacteristic
222C22C2×C4⋊Q8×C12713yes—
223C22C2×C4⋊Q8×C12713yes—
224C22#532×C12713yes—
225C22#532×C12713yes—
226C22#533×C12716yes—
227C4—24no—
228C4—212no—
229C4—48no—
230C4—84no—
231C4#389×C127124yescomplemented
232C2C2×#389×C12713yes—
233C2C4×#127×C12711yescharacteristic
234C2C4×C4⋊Q8×C12713yes—
235C2C127×#285611yescharacteristic
236C2C127×#285713yes—
237C2C127×#285913yes—
238C2C127×#286811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
14. #384×C127C4semidirect
66. C42×C127C4⋊C4semidirect
111. C4×C127#389semidirect
112. #14712C127direct (N × H)
125. C127#14712direct (N × H)
134. #384C4×C127semidirect
186. C42C4⋊C4×C127semidirect
231. C4#389×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#384×C1272
C2×C43×C1272
C127×C4⋊#952
#14712127