Finite Group Databasebeta

← C127×#16014 #44579687

Subgroups — C127×#16014 #44579687

Order 32512.

1762 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#386×C127C212yesmaximal
2C127×#1443C214yesmaximal, complemented
3C127×#1440C214yesmaximal, complemented
4C127×#1438C211yesmaximal, characteristic
5C127×C22⋊#95C214yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C24×C4×C127C2212yes—
8C22×C22⋊C4×C127C2212yes—
9C22×C22⋊C4×C127C2214yes—
10C22×C22⋊C4×C127C2214yes—
11#386×C127—28no—
12C2×#95×C127C2214yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2212yes—
17C2×#95×C127C2214yes—
18C25×C127C2312yes—
19C22×D4×C127—28no—
20C22×D4×C127—42no—
21C22×D4×C127D414yes—
22C23×C4×C127—24no—
23C23×C4×C127—28no—
24C23×C4×C127—42no—
25C23×C4×C127—42no—
26C23×C4×C127—44no—
27C23×C4×C127C2314yes—
28C23×C4×C127C2314yes—
29C23×C4×C127C2311yescharacteristic
30C23×C4×C127C2314yes—
31C2×C22⋊C4×C127—28no—
32C2×C22⋊C4×C127—24no—
33C2×C22⋊C4×C127—28no—
34C2×C22⋊C4×C127—28no—
35C2×C22⋊C4×C127—28no—
36C2×C22⋊C4×C127—44no—
37C2×C22⋊C4×C127—44no—
38C2×C22⋊C4×C127—44no—
39#95×C127—28no—
40#95×C127—28no—
41#95×C127—44no—
42#95×C127—44no—
43#95×C127—42no—
44#95×C127—44no—
45C24×C127—24no—
46C24×C127—24no—
47C24×C127—24no—
48C24×C127—24no—
49C24×C127—24no—
50C24×C127—22no—
51C24×C127—22no—
52C24×C127C2×D414yes—
53C24×C127#4118yes—
54C24×C127C2411yescharacteristic
55C2×D4×C127—216no—
56C2×D4×C127—44no—
57C2×D4×C127—416no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—22no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—24no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—48no—
81C22×C4×C127—416no—
82C22×C4×C127—416no—
83C22×C4×C127—48no—
84C22×C4×C127—48no—
85C22×C4×C127C2×D412yes—
86C22×C4×C127#4118yes—
87C22⋊C4×C127—416no—
88C22⋊C4×C127—416no—
89C22⋊C4×C127—48no—
90C23×C127—24no—
91C23×C127—28no—
92C23×C127—24no—
93C23×C127—28no—
94C23×C127—28no—
95C23×C127—28no—
96C23×C127—28no—
97C23×C127—28no—
98C23×C127—28no—
99C23×C127—28no—
100C23×C127—44no—
101C23×C127—44no—
102C23×C127—44no—
103C23×C127—44no—
104C23×C127—42no—
105C23×C127—42no—
106C23×C127—44no—
107C23×C127—44no—
108C23×C127—42no—
109C23×C127—42no—
110C23×C127#12318yes—
111C23×C127C22×D411yescharacteristic
112C23×C127C2×#4114yes—
113C23×C127C2×#4114yes—
114C23×C127H(5,𝔽2)12yes—
115C23×C127H(5,𝔽2)14yes—
116D4×C127—416no—
117C2×C4×C127—24no—
118C2×C4×C127—22no—
119C2×C4×C127—28no—
120C2×C4×C127—28no—
121C2×C4×C127—28no—
122C2×C4×C127—432no—
123C2×C4×C127—44no—
124C2×C4×C127—44no—
125C2×C4×C127—44no—
126C2×C4×C127—44no—
127C2×C4×C127—44no—
128C2×C4×C127—44no—
129C2×C4×C127—44no—
130C2×C4×C127—44no—
131C2×C4×C127—44no—
132C2×C4×C127—44no—
133C2×C4×C127—44no—
134C2×C4×C127—44no—
135C2×C4×C127—44no—
136C2×C4×C127—44no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—44no—
142C22×C127—216no—
143C22×C127—28no—
144C22×C127—48no—
145C22×C127—48no—
146C22×C127—44no—
147C22×C127—44no—
148C22×C127—48no—
149C22×C127—48no—
150C22×C127—48no—
151C22×C127C2×#12312yes—
152C22×C127#52914yes—
153C22×C127#53411yescharacteristic
154C22×C127#53814yes—
155C22×C127#53814yes—
156C22×C127#54614yes—
157C22×C127#55112yes—
158C22×C127#55114yes—
159C22×C127#55314yes—
160C22×C127#55314yes—
161C22×C127#56012yes—
162C4×C127—48no—
163C4×C127—42no—
164C4×C127—84no—
165C4×C127—84no—
166#16014C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—48no—
168C2×C127#244414yes—
169C2×C127#248311yescharacteristic
170C2×C127#257814yes—
171C2×C127#269712yes—
172C2×C127#277814yes—
173C2×#386C2×C12712yes—
174#1443C2×C12714yescomplemented
175#1440C2×C12714yescomplemented
176#1438C2×C12711yescharacteristic
177C22⋊#95C2×C12714yescomplemented
178C127#1601411yescharacteristic, direct product factor, Sylow
179C23×D4C22×C12711yescharacteristic
180C24×C4C22×C12712yes—
181C22×C22⋊C4C22×C12712yes—
182C22×C22⋊C4C22×C12714yes—
183C22×C22⋊C4C22×C12714yes—
184#386—28no—
185C2×#95C22×C12714yes—
186C2×#95C22×C12714yes—
187C2×#95C22×C12714yes—
188C2×#95C22×C12714yes—
189C2×#95C22×C12712yes—
190C2×#95C22×C12714yes—
191C25C23×C12712yes—
192C22×D4—28no—
193C22×D4—42no—
194C22×D4D4×C12714yes—
195C23×C4—24no—
196C23×C4—28no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—44no—
200C23×C4C23×C12714yes—
201C23×C4C23×C12714yes—
202C23×C4C23×C12711yescharacteristic
203C23×C4C23×C12714yes—
204C2×C22⋊C4—28no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—28no—
207C2×C22⋊C4—28no—
208C2×C22⋊C4—28no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—44no—
211C2×C22⋊C4—44no—
212#95—28no—
213#95—28no—
214#95—44no—
215#95—44no—
216#95—42no—
217#95—44no—
218C24—24no—
219C24—24no—
220C24—24no—
221C24—24no—
222C24—24no—
223C24—22no—
224C24—22no—
225C24C2×D4×C12714yes—
226C24#41×C12718yes—
227C24C24×C12711yescharacteristic
228C2×D4—216no—
229C2×D4—44no—
230C2×D4—416no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—48no—
254C22×C4—416no—
255C22×C4—416no—
256C22×C4—48no—
257C22×C4—48no—
258C22×C4C2×D4×C12712yes—
259C22×C4#41×C12718yes—
260C22⋊C4—416no—
261C22⋊C4—416no—
262C22⋊C4—48no—
263C23—24no—
264C23—28no—
265C23—24no—
266C23—28no—
267C23—28no—
268C23—28no—
269C23—28no—
270C23—28no—
271C23—28no—
272C23—28no—
273C23—44no—
274C23—44no—
275C23—44no—
276C23—44no—
277C23—42no—
278C23—42no—
279C23—44no—
280C23—44no—
281C23—42no—
282C23—42no—
283C23#123×C12718yes—
284C23C22×D4×C12711yescharacteristic
285C23C2×#41×C12714yes—
286C23C2×#41×C12714yes—
287C23H(5,𝔽2)×C12712yes—
288C23H(5,𝔽2)×C12714yes—
289D4—416no—
290C2×C4—24no—
291C2×C4—22no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—28no—
295C2×C4—432no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C22—216no—
316C22—28no—
317C22—48no—
318C22—48no—
319C22—44no—
320C22—44no—
321C22—48no—
322C22—48no—
323C22—48no—
324C22C2×#123×C12712yes—
325C22#529×C12714yes—
326C22#534×C12711yescharacteristic
327C22#538×C12714yes—
328C22#538×C12714yes—
329C22#546×C12714yes—
330C22#551×C12712yes—
331C22#551×C12714yes—
332C22#553×C12714yes—
333C22#553×C12714yes—
334C22#560×C12712yes—
335C4—48no—
336C4—42no—
337C4—84no—
338C4—84no—
339C2—48no—
340C2C127×#244414yes—
341C2C127×#248311yescharacteristic
342C2C127×#257814yes—
343C2C127×#269712yes—
344C2C127×#277814yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1443C2semidirect
3. C127×#1440C2semidirect
5. C127×C22⋊#95C2semidirect
166. #16014C127direct (N × H)
174. #1443C2×C127semidirect
175. #1440C2×C127semidirect
177. C22⋊#95C2×C127semidirect
178. C127#16014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#386×C1272
C127×#14432
C127×#14402
C127×#14382
C127×C22⋊#952
#16014127