Finite Group Databasebeta

← C2×C127×#1438 #44577508

Subgroups — C2×C127×#1438 #44577508

Order 32512.

8190 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D4×C127C211yesmaximal, characteristic
2C23×C22⋊C4×C127C214yesmaximal, complemented
3C22×#95×C127C212yesmaximal, complemented
4C127×#1438C218yesmaximal, direct product factor
5C26×C127C2212yes—
6C23×D4×C127—216no—
7C23×D4×C127—28no—
8C23×D4×C127C418yescomplemented
9C23×D4×C127C2214yes—
10C24×C4×C127C2214yes—
11C24×C4×C127C2211yescharacteristic
12C22×C22⋊C4×C127—216no—
13C22×C22⋊C4×C127—232no—
14C22×C22⋊C4×C127C22116yescomplemented
15C2×#95×C127—28no—
16C2×#95×C127C2218yescomplemented
17C25×C127—216no—
18C25×C127—28no—
19C25×C127—28no—
20C25×C127—216no—
21C25×C127C2×C418yes—
22C25×C127D4116yes—
23C25×C127C2314yes—
24C25×C127C2311yescharacteristic
25C22×D4×C127—2128no—
26C22×D4×C127—264no—
27C22×D4×C127—232no—
28C22×D4×C127—232no—
29C22×D4×C127—216no—
30C22×D4×C127C2×C4116yescomplemented
31C23×C4×C127—28no—
32C23×C4×C127—216no—
33C23×C4×C127—216no—
34C23×C4×C127—28no—
35C23×C4×C127—28no—
36C23×C4×C127C2×C414yes—
37C23×C4×C127D418yes—
38C23×C4×C127D4116yescomplemented
39C23×C4×C127C2318yes—
40C23×C4×C127C2312yes—
41C2×C22⋊C4×C127—2128no—
42C2×C22⋊C4×C127—232no—
43C2×C22⋊C4×C127—264no—
44#95×C127—216no—
45C24×C127—216no—
46C24×C127—216no—
47C24×C127—264no—
48C24×C127—232no—
49C24×C127—264no—
50C24×C127—264no—
51C24×C127—232no—
52C24×C127—216no—
53C24×C127—28no—
54C24×C127—28no—
55C24×C127—216no—
56C24×C127—416no—
57C24×C127—432no—
58C24×C127—432no—
59C24×C127—416no—
60C24×C127—416no—
61C24×C127—416no—
62C24×C127C22⋊C4132yescomplemented
63C24×C127C22×C418yes—
64C24×C127C22×C412yes—
65C24×C127C2×D4116yes—
66C24×C127C2×D418yes—
67C24×C127C2×D414yes—
68C24×C127C2×D418yes—
69C24×C127#4118yes—
70C24×C127C2411yescharacteristic
71C2×D4×C127—2128no—
72C2×D4×C127—2256no—
73C2×D4×C127—264no—
74C2×D4×C127—232no—
75C22×C4×C127—216no—
76C22×C4×C127—232no—
77C22×C4×C127—28no—
78C22×C4×C127—264no—
79C22×C4×C127—232no—
80C22×C4×C127—28no—
81C22×C4×C127—216no—
82C22×C4×C127—216no—
83C22×C4×C127—28no—
84C22×C4×C127—416no—
85C22×C4×C127—432no—
86C22×C4×C127—416no—
87C22×C4×C127C22⋊C4116yescomplemented
88C22×C4×C127C22×C414yes—
89C22×C4×C127C2×D418yes—
90C22×C4×C127C2×D4116yescomplemented
91C22⋊C4×C127—2128no—
92C23×C127—28no—
93C23×C127—28no—
94C23×C127—232no—
95C23×C127—216no—
96C23×C127—232no—
97C23×C127—232no—
98C23×C127—216no—
99C23×C127—264no—
100C23×C127—2128no—
101C23×C127—48no—
102C23×C127—416no—
103C23×C127—416no—
104C23×C127—48no—
105C23×C127—48no—
106C23×C127—48no—
107C23×C127—464no—
108C23×C127—464no—
109C23×C127—4128no—
110C23×C127—4128no—
111C23×C127C2×C22⋊C418yes—
112C23×C127C2×C22⋊C414yes—
113C23×C127C2×C22⋊C4116yescomplemented
114C23×C127C4×D4116yes—
115C23×C127#120116yes—
116C23×C127#120116yes—
117C23×C127#121132yes—
118C23×C127#121116yes—
119C23×C127#123116yes—
120C23×C127#12418yes—
121C23×C127#12718yes—
122C23×C127C23×C411yescharacteristic
123C23×C127C22×D414yes—
124C23×C127C22×D412yes—
125C23×C127C22×D414yes—
126C23×C127C2×#4114yes—
127D4×C127—2128no—
128C2×C4×C127—28no—
129C2×C4×C127—216no—
130C2×C4×C127—232no—
131C2×C4×C127—232no—
132C2×C4×C127—216no—
133C2×C4×C127—48no—
134C2×C4×C127—416no—
135C2×C4×C127—48no—
136C2×C4×C127—464no—
137C2×C4×C127C2×C22⋊C418yescomplemented
138C22×C127—216no—
139C22×C127—232no—
140C22×C127—432no—
141C22×C127—432no—
142C22×C127—4128no—
143C22×C127—416no—
144C22×C127—416no—
145C22×C127#37918yes—
146C22×C127#386132yes—
147C22×C127#390116yes—
148C22×C127#392132yes—
149C22×C127#394132yes—
150C22×C127C22×C22⋊C412yes—
151C22×C127C22×C22⋊C411yescharacteristic
152C22×C127C2×C4×D414yes—
153C22×C127C2×#12014yes—
154C22×C127C2×#12014yes—
155C22×C127C2×#12118yes—
156C22×C127C2×#12114yes—
157C22×C127C2×#12314yes—
158C22×C127C2×#12412yes—
159C22×C127C2×#12712yes—
160C4×C127—28no—
161C4×C127—416no—
162C2×#1438C12711yesmaximal, characteristic, direct product factor, Sylow
163C2×C127—416no—
164C2×C127#1438116yesdirect product factor
165C2×C127C2×#37911yescharacteristic
166C2×C127C2×#38614yes—
167C2×C127C2×#39012yes—
168C2×C127C2×#39214yes—
169C2×C127C2×#39414yes—
170C24×D4C2×C12711yescharacteristic
171C23×C22⋊C4C2×C12714yescomplemented
172C22×#95C2×C12712yescomplemented
173#1438C2×C12718yesdirect product factor
174C127C2×#143811yescharacteristic, direct product factor, Sylow
175C26C22×C12712yes—
176C23×D4—216no—
177C23×D4—28no—
178C23×D4C4×C12718yescomplemented
179C23×D4C22×C12714yes—
180C24×C4C22×C12714yes—
181C24×C4C22×C12711yescharacteristic
182C22×C22⋊C4—216no—
183C22×C22⋊C4—232no—
184C22×C22⋊C4C22×C127116yescomplemented
185C2×#95—28no—
186C2×#95C22×C12718yescomplemented
187C25—216no—
188C25—28no—
189C25—28no—
190C25—216no—
191C25C2×C4×C12718yes—
192C25D4×C127116yes—
193C25C23×C12714yes—
194C25C23×C12711yescharacteristic
195C22×D4—2128no—
196C22×D4—264no—
197C22×D4—232no—
198C22×D4—232no—
199C22×D4—216no—
200C22×D4C2×C4×C127116yescomplemented
201C23×C4—28no—
202C23×C4—216no—
203C23×C4—216no—
204C23×C4—28no—
205C23×C4—28no—
206C23×C4C2×C4×C12714yes—
207C23×C4D4×C12718yes—
208C23×C4D4×C127116yescomplemented
209C23×C4C23×C12718yes—
210C23×C4C23×C12712yes—
211C2×C22⋊C4—2128no—
212C2×C22⋊C4—232no—
213C2×C22⋊C4—264no—
214#95—216no—
215C24—216no—
216C24—216no—
217C24—264no—
218C24—232no—
219C24—264no—
220C24—264no—
221C24—232no—
222C24—216no—
223C24—28no—
224C24—28no—
225C24—216no—
226C24—416no—
227C24—432no—
228C24—432no—
229C24—416no—
230C24—416no—
231C24—416no—
232C24C22⋊C4×C127132yescomplemented
233C24C22×C4×C12718yes—
234C24C22×C4×C12712yes—
235C24C2×D4×C127116yes—
236C24C2×D4×C12718yes—
237C24C2×D4×C12714yes—
238C24C2×D4×C12718yes—
239C24#41×C12718yes—
240C24C24×C12711yescharacteristic
241C2×D4—2128no—
242C2×D4—2256no—
243C2×D4—264no—
244C2×D4—232no—
245C22×C4—216no—
246C22×C4—232no—
247C22×C4—28no—
248C22×C4—264no—
249C22×C4—232no—
250C22×C4—28no—
251C22×C4—216no—
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—416no—
255C22×C4—432no—
256C22×C4—416no—
257C22×C4C22⋊C4×C127116yescomplemented
258C22×C4C22×C4×C12714yes—
259C22×C4C2×D4×C12718yes—
260C22×C4C2×D4×C127116yescomplemented
261C22⋊C4—2128no—
262C23—28no—
263C23—28no—
264C23—232no—
265C23—216no—
266C23—232no—
267C23—232no—
268C23—216no—
269C23—264no—
270C23—2128no—
271C23—48no—
272C23—416no—
273C23—416no—
274C23—48no—
275C23—48no—
276C23—48no—
277C23—464no—
278C23—464no—
279C23—4128no—
280C23—4128no—
281C23C2×C22⋊C4×C12718yes—
282C23C2×C22⋊C4×C12714yes—
283C23C2×C22⋊C4×C127116yescomplemented
284C23C4×D4×C127116yes—
285C23#120×C127116yes—
286C23#120×C127116yes—
287C23#121×C127132yes—
288C23#121×C127116yes—
289C23#123×C127116yes—
290C23#124×C12718yes—
291C23#127×C12718yes—
292C23C23×C4×C12711yescharacteristic
293C23C22×D4×C12714yes—
294C23C22×D4×C12712yes—
295C23C22×D4×C12714yes—
296C23C2×#41×C12714yes—
297D4—2128no—
298C2×C4—28no—
299C2×C4—216no—
300C2×C4—232no—
301C2×C4—232no—
302C2×C4—216no—
303C2×C4—48no—
304C2×C4—416no—
305C2×C4—48no—
306C2×C4—464no—
307C2×C4C2×C22⋊C4×C12718yescomplemented
308C22—216no—
309C22—232no—
310C22—432no—
311C22—432no—
312C22—4128no—
313C22—416no—
314C22—416no—
315C22#379×C12718yes—
316C22#386×C127132yes—
317C22#390×C127116yes—
318C22#392×C127132yes—
319C22#394×C127132yes—
320C22C22×C22⋊C4×C12712yes—
321C22C22×C22⋊C4×C12711yescharacteristic
322C22C2×C4×D4×C12714yes—
323C22C2×#120×C12714yes—
324C22C2×#120×C12714yes—
325C22C2×#121×C12718yes—
326C22C2×#121×C12714yes—
327C22C2×#123×C12714yes—
328C22C2×#124×C12712yes—
329C22C2×#127×C12712yes—
330C4—28no—
331C4—416no—
332C2—416no—
333C2C127×#1438116yesdirect product factor
334C2C2×#379×C12711yescharacteristic
335C2C2×#386×C12714yes—
336C2C2×#390×C12712yes—
337C2C2×#392×C12714yes—
338C2C2×#394×C12714yes—
subgroupG/H
center, socleC25×C127C23
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC24×D4×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C127C2semidirect
3. C22×#95×C127C2semidirect
4. C127×#1438C2direct (N × H)
8. C23×D4×C127C4semidirect
14. C22×C22⋊C4×C127C22semidirect
16. C2×#95×C127C22semidirect
30. C22×D4×C127C2×C4semidirect
38. C23×C4×C127D4semidirect
62. C24×C127C22⋊C4semidirect
87. C22×C4×C127C22⋊C4semidirect
90. C22×C4×C127C2×D4semidirect
113. C23×C127C2×C22⋊C4semidirect
137. C2×C4×C127C2×C22⋊C4semidirect
162. C2×#1438C127direct (N × H)
164. C2×C127#1438direct (N × H)
171. C23×C22⋊C4C2×C127semidirect
172. C22×#95C2×C127semidirect
173. #1438C2×C127direct (N × H)
174. C127C2×#1438direct (N × H)
178. C23×D4C4×C127semidirect
184. C22×C22⋊C4C22×C127semidirect
186. C2×#95C22×C127semidirect
200. C22×D4C2×C4×C127semidirect
208. C23×C4D4×C127semidirect
232. C24C22⋊C4×C127semidirect
257. C22×C4C22⋊C4×C127semidirect
260. C22×C4C2×D4×C127semidirect
283. C23C2×C22⋊C4×C127semidirect
307. C2×C4C2×C22⋊C4×C127semidirect
333. C2C127×#1438direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D4×C1272
C23×C22⋊C4×C1272
C22×#95×C1272
C127×#14382
C2×#1438127