Finite Group Databasebeta

← C127×#14339 #44578012

Subgroups — C127×#14339 #44578012

Order 32512.

2142 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C127C211yesmaximal, characteristic
2C2×#381×C127C212yesmaximal
3C2×#380×C127C212yesmaximal
4C127×#1441C218yesmaximal, complemented
5C127×C22⋊#95C212yesmaximal
6C24×C4×C127C2211yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C24×C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127—28no—
10C22×C4⋊C4×C127C418yescomplemented
11C22×C4⋊C4×C127C2214yes—
12C22×C4⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2214yes—
14#381×C127—28no—
15#380×C127—28no—
16C2×#95×C127C2214yes—
17C2×#95×C127C2218yes—
18C2×#95×C127C2218yes—
19C25×C127C2311yescharacteristic
20C23×C4×C127—24no—
21C23×C4×C127—24no—
22C23×C4×C127—24no—
23C23×C4×C127—44no—
24C23×C4×C127—44no—
25C23×C4×C127C2×C414yes—
26C23×C4×C127C2×C414yes—
27C23×C4×C127C2×C414yes—
28C23×C4×C127D414yes—
29C23×C4×C127D418yes—
30C23×C4×C127Q814yes—
31C23×C4×C127C2318yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C2×C4⋊C4×C127—232no—
36C2×C4⋊C4×C127—28no—
37C2×C4⋊C4×C127—28no—
38C2×C4⋊C4×C127—28no—
39C2×C4⋊C4×C127—48no—
40C2×C4⋊C4×C127C2×C4116yes—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127—28no—
43C2×C22⋊C4×C127—28no—
44#95×C127—28no—
45#95×C127—216no—
46#95×C127—48no—
47C24×C127—24no—
48C24×C127—24no—
49C24×C127C22×C412yes—
50C24×C127C2×D414yes—
51C24×C127C2×D412yes—
52C24×C127C2×Q812yes—
53C24×C127#4114yes—
54C24×C127C2411yescharacteristic
55C22×C4×C127—28no—
56C22×C4×C127—28no—
57C22×C4×C127—216no—
58C22×C4×C127—216no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—28no—
62C22×C4×C127—28no—
63C22×C4×C127—24no—
64C22×C4×C127—28no—
65C22×C4×C127—28no—
66C22×C4×C127—28no—
67C22×C4×C127—28no—
68C22×C4×C127—216no—
69C22×C4×C127—216no—
70C22×C4×C127—48no—
71C22×C4×C127—48no—
72C22×C4×C127—416no—
73C22×C4×C127—416no—
74C22×C4×C127C22⋊C4116yes—
75C22×C4×C127C4⋊C4116yescomplemented
76C22×C4×C127C22×C414yes—
77C22×C4×C127C22×C414yes—
78C22×C4×C127C22×C414yes—
79C22×C4×C127C2×D414yes—
80C22×C4×C127C2×D414yes—
81C22×C4×C127C2×D414yes—
82C22×C4×C127C2×Q814yes—
83C4⋊C4×C127—232no—
84C4⋊C4×C127—416no—
85C22⋊C4×C127—416no—
86C23×C127—24no—
87C23×C127—24no—
88C23×C127—28no—
89C23×C127—28no—
90C23×C127—28no—
91C23×C127—216no—
92C23×C127—28no—
93C23×C127C2×C22⋊C414yes—
94C23×C127C2×C4⋊C414yes—
95C23×C127#11714yes—
96C23×C127#12118yes—
97C23×C127C22⋊Q818yes—
98C23×C127C23×C411yescharacteristic
99C23×C127C22×D412yes—
100C23×C127C22×D411yescharacteristic
101C23×C127C22×Q811yescharacteristic
102C23×C127C2×#4112yes—
103C23×C127H(5,𝔽2)14yes—
104C23×C1272−1+414yes—
105C2×C4×C127—24no—
106C2×C4×C127—24no—
107C2×C4×C127—28no—
108C2×C4×C127—28no—
109C2×C4×C127—28no—
110C2×C4×C127—28no—
111C2×C4×C127—28no—
112C2×C4×C127—232no—
113C2×C4×C127—24no—
114C2×C4×C127—28no—
115C2×C4×C127—416no—
116C2×C4×C127—416no—
117C2×C4×C127—48no—
118C2×C4×C127—48no—
119C2×C4×C127—48no—
120C2×C4×C127—48no—
121C2×C4×C127—416no—
122C2×C4×C127—416no—
123C2×C4×C127C2×C22⋊C418yes—
124C2×C4×C127C2×C4⋊C418yes—
125C22×C127—24no—
126C22×C127—24no—
127C22×C127—28no—
128C22×C127—28no—
129C22×C127—216no—
130C22×C127—216no—
131C22×C127#38018yes—
132C22×C127C22×C22⋊C411yescharacteristic
133C22×C127C22×C4⋊C411yescharacteristic
134C22×C127C2×#11711yescharacteristic
135C22×C127#51812yes—
136C22×C127#51912yes—
137C22×C127C2×#12112yes—
138C22×C127C2×C22⋊Q812yes—
139C22×C127#53414yes—
140C22×C127#53614yes—
141C22×C127#53714yes—
142C22×C127#53918yes—
143C22×C127#54414yes—
144C4×C127—28no—
145C4×C127—28no—
146C4×C127—44no—
147C4×C127—88no—
148#14339C12711yesmaximal, characteristic, direct product factor, Sylow
149C2×C127—28no—
150C2×C127C2×#38011yescharacteristic
151C2×C127#230811yescharacteristic
152C2×C127#231011yescharacteristic
153C2×C127#231312yes—
154C2×C127#231612yes—
155C2×C127#261814yes—
156C2×C127#262714yes—
157C23×C4⋊C4C2×C12711yescharacteristic
158C2×#381C2×C12712yes—
159C2×#380C2×C12712yes—
160#1441C2×C12718yescomplemented
161C22⋊#95C2×C12712yes—
162C127#1433911yescharacteristic, direct product factor, Sylow
163C24×C4C22×C12711yescharacteristic
164C24×C4C22×C12711yescharacteristic
165C24×C4C22×C12711yescharacteristic
166C22×C4⋊C4—28no—
167C22×C4⋊C4C4×C12718yescomplemented
168C22×C4⋊C4C22×C12714yes—
169C22×C4⋊C4C22×C12714yes—
170C22×C22⋊C4C22×C12714yes—
171#381—28no—
172#380—28no—
173C2×#95C22×C12714yes—
174C2×#95C22×C12718yes—
175C2×#95C22×C12718yes—
176C25C23×C12711yescharacteristic
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—24no—
180C23×C4—44no—
181C23×C4—44no—
182C23×C4C2×C4×C12714yes—
183C23×C4C2×C4×C12714yes—
184C23×C4C2×C4×C12714yes—
185C23×C4D4×C12714yes—
186C23×C4D4×C12718yes—
187C23×C4Q8×C12714yes—
188C23×C4C23×C12718yes—
189C23×C4C23×C12712yes—
190C23×C4C23×C12712yes—
191C23×C4C23×C12712yes—
192C2×C4⋊C4—232no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—28no—
196C2×C4⋊C4—48no—
197C2×C4⋊C4C2×C4×C127116yes—
198C2×C22⋊C4—28no—
199C2×C22⋊C4—28no—
200C2×C22⋊C4—28no—
201#95—28no—
202#95—216no—
203#95—48no—
204C24—24no—
205C24—24no—
206C24C22×C4×C12712yes—
207C24C2×D4×C12714yes—
208C24C2×D4×C12712yes—
209C24C2×Q8×C12712yes—
210C24#41×C12714yes—
211C24C24×C12711yescharacteristic
212C22×C4—28no—
213C22×C4—28no—
214C22×C4—216no—
215C22×C4—216no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—28no—
219C22×C4—28no—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—28no—
223C22×C4—28no—
224C22×C4—28no—
225C22×C4—216no—
226C22×C4—216no—
227C22×C4—48no—
228C22×C4—48no—
229C22×C4—416no—
230C22×C4—416no—
231C22×C4C22⋊C4×C127116yes—
232C22×C4C4⋊C4×C127116yescomplemented
233C22×C4C22×C4×C12714yes—
234C22×C4C22×C4×C12714yes—
235C22×C4C22×C4×C12714yes—
236C22×C4C2×D4×C12714yes—
237C22×C4C2×D4×C12714yes—
238C22×C4C2×D4×C12714yes—
239C22×C4C2×Q8×C12714yes—
240C4⋊C4—232no—
241C4⋊C4—416no—
242C22⋊C4—416no—
243C23—24no—
244C23—24no—
245C23—28no—
246C23—28no—
247C23—28no—
248C23—216no—
249C23—28no—
250C23C2×C22⋊C4×C12714yes—
251C23C2×C4⋊C4×C12714yes—
252C23#117×C12714yes—
253C23#121×C12718yes—
254C23C22⋊Q8×C12718yes—
255C23C23×C4×C12711yescharacteristic
256C23C22×D4×C12712yes—
257C23C22×D4×C12711yescharacteristic
258C23C22×Q8×C12711yescharacteristic
259C23C2×#41×C12712yes—
260C23H(5,𝔽2)×C12714yes—
261C232−1+4×C12714yes—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—232no—
270C2×C4—24no—
271C2×C4—28no—
272C2×C4—416no—
273C2×C4—416no—
274C2×C4—48no—
275C2×C4—48no—
276C2×C4—48no—
277C2×C4—48no—
278C2×C4—416no—
279C2×C4—416no—
280C2×C4C2×C22⋊C4×C12718yes—
281C2×C4C2×C4⋊C4×C12718yes—
282C22—28no—
283C22—28no—
284C22—216no—
285C22—216no—
286C22—24no—
287C22—24no—
288C22#380×C12718yes—
289C22C22×C22⋊C4×C12711yescharacteristic
290C22C22×C4⋊C4×C12711yescharacteristic
291C22C2×#117×C12711yescharacteristic
292C22#518×C12712yes—
293C22#519×C12712yes—
294C22C2×#121×C12712yes—
295C22C2×C22⋊Q8×C12712yes—
296C22#534×C12714yes—
297C22#536×C12714yes—
298C22#537×C12714yes—
299C22#539×C12718yes—
300C22#544×C12714yes—
301C4—28no—
302C4—28no—
303C4—44no—
304C4—88no—
305C2—28no—
306C2C2×#380×C12711yescharacteristic
307C2C127×#230811yescharacteristic
308C2C127×#231011yescharacteristic
309C2C127×#231312yes—
310C2C127×#231612yes—
311C2C127×#261814yes—
312C2C127×#262714yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1441C2semidirect
10. C22×C4⋊C4×C127C4semidirect
75. C22×C4×C127C4⋊C4semidirect
148. #14339C127direct (N × H)
160. #1441C2×C127semidirect
162. C127#14339direct (N × H)
167. C22×C4⋊C4C4×C127semidirect
232. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C1272
C2×#381×C1272
C2×#380×C1272
C127×#14412
C127×C22⋊#952
#14339127