Finite Group Databasebeta

← C127×#14685 #44578358

Subgroups — C127×#14685 #44578358

Order 32512.

2430 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C127C211yesmaximal, characteristic
2C2×#381×C127C212yesmaximal
3C2×#380×C127C212yesmaximal
4C127×C4⋊#95C214yesmaximal, complemented
5C127×#1434C214yesmaximal, complemented
6C127×C22⋊#95C212yesmaximal
7C24×C4×C127C2211yescharacteristic
8C24×C4×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2214yes—
11C22×C22⋊C4×C127C2214yes—
12C22×C42×C127—28no—
13C22×C42×C127C418yescomplemented
14C22×C42×C127C2212yes—
15C22×C42×C127C2212yes—
16#381×C127—28no—
17#380×C127—28no—
18C2×#95×C127C2218yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2218yes—
21C25×C127C2311yescharacteristic
22C23×C4×C127—24no—
23C23×C4×C127—24no—
24C23×C4×C127—24no—
25C23×C4×C127—28no—
26C23×C4×C127—28no—
27C23×C4×C127C2×C414yes—
28C23×C4×C127C2×C414yes—
29C23×C4×C127C2×C414yes—
30C23×C4×C127D418yes—
31C23×C4×C127D414yes—
32C23×C4×C127Q814yes—
33C23×C4×C127C2318yes—
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2311yescharacteristic
38C2×C4⋊C4×C127—28no—
39C2×C4⋊C4×C127—216no—
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127—28no—
43C2×C42×C127—232no—
44C2×C42×C127—28no—
45C2×C42×C127—28no—
46C2×C42×C127C2×C418yes—
47C2×C42×C127C2×C418yes—
48#95×C127—28no—
49#95×C127—216no—
50#95×C127—216no—
51C24×C127—24no—
52C24×C127—24no—
53C24×C127C22×C412yes—
54C24×C127C2×D414yes—
55C24×C127C2×D412yes—
56C24×C127C2×Q812yes—
57C24×C127#4114yes—
58C24×C127C2411yescharacteristic
59C22×C4×C127—232no—
60C22×C4×C127—28no—
61C22×C4×C127—28no—
62C22×C4×C127—28no—
63C22×C4×C127—216no—
64C22×C4×C127—216no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—24no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—216no—
71C22×C4×C127—216no—
72C22×C4×C127—232no—
73C22×C4×C127—28no—
74C22×C4×C127—28no—
75C22×C4×C127—216no—
76C22×C4×C127—28no—
77C22×C4×C127—216no—
78C22×C4×C127C22⋊C4116yes—
79C22×C4×C127C4⋊C4116yescomplemented
80C22×C4×C127C22×C412yes—
81C22×C4×C127C22×C414yes—
82C22×C4×C127C22×C414yes—
83C22×C4×C127C22×C412yes—
84C22×C4×C127C2×D414yes—
85C22×C4×C127C2×D414yes—
86C22×C4×C127C2×D414yes—
87C22×C4×C127C2×Q814yes—
88C22×C4×C127#4118yes—
89C22×C4×C127#4118yes—
90C4⋊C4×C127—416no—
91C22⋊C4×C127—416no—
92C42×C127—216no—
93C42×C127—216no—
94C23×C127—24no—
95C23×C127—24no—
96C23×C127—28no—
97C23×C127—28no—
98C23×C127—216no—
99C23×C127—28no—
100C23×C127—28no—
101C23×C127C2×C22⋊C414yes—
102C23×C127C2×C4⋊C414yes—
103C23×C127#11714yes—
104C23×C127#12118yes—
105C23×C127C22⋊Q818yes—
106C23×C127C23×C411yescharacteristic
107C23×C127C22×D412yes—
108C23×C127C22×D411yescharacteristic
109C23×C127C22×Q811yescharacteristic
110C23×C127C2×#4112yes—
111C23×C127C2×#4114yes—
112C23×C127C2×#4114yes—
113C2×C4×C127—232no—
114C2×C4×C127—24no—
115C2×C4×C127—24no—
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—24no—
119C2×C4×C127—28no—
120C2×C4×C127—28no—
121C2×C4×C127—28no—
122C2×C4×C127—216no—
123C2×C4×C127—232no—
124C2×C4×C127—232no—
125C2×C4×C127—48no—
126C2×C4×C127—48no—
127C2×C4×C127—48no—
128C2×C4×C127—416no—
129C2×C4×C127—416no—
130C2×C4×C127C2×C22⋊C414yes—
131C2×C4×C127C2×C22⋊C414yes—
132C2×C4×C127C2×C4⋊C418yes—
133C2×C4×C127#11718yes—
134C2×C4×C127#11718yes—
135C2×C4×C127#123116yes—
136C22×C127—216no—
137C22×C127—216no—
138C22×C127—24no—
139C22×C127—24no—
140C22×C127—28no—
141C22×C127—28no—
142C22×C127#38018yes—
143C22×C127C22×C22⋊C411yescharacteristic
144C22×C127C22×C4⋊C411yescharacteristic
145C22×C127C2×#11711yescharacteristic
146C22×C127C2×#11712yes—
147C22×C127C2×#11712yes—
148C22×C127C2×#12112yes—
149C22×C127C2×C22⋊Q812yes—
150C22×C127C2×#12314yes—
151C22×C127#52514yes—
152C22×C127#52918yes—
153C22×C127#53214yes—
154C22×C127#53314yes—
155C4×C127—28no—
156C4×C127—24no—
157C4×C127—28no—
158C4×C127—88no—
159C4×C127#38118yescomplemented
160#14685C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—28no—
162C2×C127C2×#38011yescharacteristic
163C2×C127C2×#38111yescharacteristic
164C2×C127#228011yescharacteristic
165C2×C127#228312yes—
166C2×C127#228512yes—
167C2×C127#285414yes—
168C2×C127#285514yes—
169C23×C42C2×C12711yescharacteristic
170C2×#381C2×C12712yes—
171C2×#380C2×C12712yes—
172C4⋊#95C2×C12714yescomplemented
173#1434C2×C12714yescomplemented
174C22⋊#95C2×C12712yes—
175C127#1468511yescharacteristic, direct product factor, Sylow
176C24×C4C22×C12711yescharacteristic
177C24×C4C22×C12711yescharacteristic
178C24×C4C22×C12711yescharacteristic
179C22×C4⋊C4C22×C12714yes—
180C22×C22⋊C4C22×C12714yes—
181C22×C42—28no—
182C22×C42C4×C12718yescomplemented
183C22×C42C22×C12712yes—
184C22×C42C22×C12712yes—
185#381—28no—
186#380—28no—
187C2×#95C22×C12718yes—
188C2×#95C22×C12714yes—
189C2×#95C22×C12718yes—
190C25C23×C12711yescharacteristic
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—28no—
195C23×C4—28no—
196C23×C4C2×C4×C12714yes—
197C23×C4C2×C4×C12714yes—
198C23×C4C2×C4×C12714yes—
199C23×C4D4×C12718yes—
200C23×C4D4×C12714yes—
201C23×C4Q8×C12714yes—
202C23×C4C23×C12718yes—
203C23×C4C23×C12711yescharacteristic
204C23×C4C23×C12712yes—
205C23×C4C23×C12712yes—
206C23×C4C23×C12711yescharacteristic
207C2×C4⋊C4—28no—
208C2×C4⋊C4—216no—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—28no—
211C2×C22⋊C4—28no—
212C2×C42—232no—
213C2×C42—28no—
214C2×C42—28no—
215C2×C42C2×C4×C12718yes—
216C2×C42C2×C4×C12718yes—
217#95—28no—
218#95—216no—
219#95—216no—
220C24—24no—
221C24—24no—
222C24C22×C4×C12712yes—
223C24C2×D4×C12714yes—
224C24C2×D4×C12712yes—
225C24C2×Q8×C12712yes—
226C24#41×C12714yes—
227C24C24×C12711yescharacteristic
228C22×C4—232no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—216no—
233C22×C4—216no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—216no—
240C22×C4—216no—
241C22×C4—232no—
242C22×C4—28no—
243C22×C4—28no—
244C22×C4—216no—
245C22×C4—28no—
246C22×C4—216no—
247C22×C4C22⋊C4×C127116yes—
248C22×C4C4⋊C4×C127116yescomplemented
249C22×C4C22×C4×C12712yes—
250C22×C4C22×C4×C12714yes—
251C22×C4C22×C4×C12714yes—
252C22×C4C22×C4×C12712yes—
253C22×C4C2×D4×C12714yes—
254C22×C4C2×D4×C12714yes—
255C22×C4C2×D4×C12714yes—
256C22×C4C2×Q8×C12714yes—
257C22×C4#41×C12718yes—
258C22×C4#41×C12718yes—
259C4⋊C4—416no—
260C22⋊C4—416no—
261C42—216no—
262C42—216no—
263C23—24no—
264C23—24no—
265C23—28no—
266C23—28no—
267C23—216no—
268C23—28no—
269C23—28no—
270C23C2×C22⋊C4×C12714yes—
271C23C2×C4⋊C4×C12714yes—
272C23#117×C12714yes—
273C23#121×C12718yes—
274C23C22⋊Q8×C12718yes—
275C23C23×C4×C12711yescharacteristic
276C23C22×D4×C12712yes—
277C23C22×D4×C12711yescharacteristic
278C23C22×Q8×C12711yescharacteristic
279C23C2×#41×C12712yes—
280C23C2×#41×C12714yes—
281C23C2×#41×C12714yes—
282C2×C4—232no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—216no—
292C2×C4—232no—
293C2×C4—232no—
294C2×C4—48no—
295C2×C4—48no—
296C2×C4—48no—
297C2×C4—416no—
298C2×C4—416no—
299C2×C4C2×C22⋊C4×C12714yes—
300C2×C4C2×C22⋊C4×C12714yes—
301C2×C4C2×C4⋊C4×C12718yes—
302C2×C4#117×C12718yes—
303C2×C4#117×C12718yes—
304C2×C4#123×C127116yes—
305C22—216no—
306C22—216no—
307C22—24no—
308C22—24no—
309C22—28no—
310C22—28no—
311C22#380×C12718yes—
312C22C22×C22⋊C4×C12711yescharacteristic
313C22C22×C4⋊C4×C12711yescharacteristic
314C22C2×#117×C12711yescharacteristic
315C22C2×#117×C12712yes—
316C22C2×#117×C12712yes—
317C22C2×#121×C12712yes—
318C22C2×C22⋊Q8×C12712yes—
319C22C2×#123×C12714yes—
320C22#525×C12714yes—
321C22#529×C12718yes—
322C22#532×C12714yes—
323C22#533×C12714yes—
324C4—28no—
325C4—24no—
326C4—28no—
327C4—88no—
328C4#381×C12718yescomplemented
329C2—28no—
330C2C2×#380×C12711yescharacteristic
331C2C2×#381×C12711yescharacteristic
332C2C127×#228011yescharacteristic
333C2C127×#228312yes—
334C2C127×#228512yes—
335C2C127×#285414yes—
336C2C127×#285514yes—
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×C4⋊#95C2semidirect
5. C127×#1434C2semidirect
13. C22×C42×C127C4semidirect
79. C22×C4×C127C4⋊C4semidirect
159. C4×C127#381semidirect
160. #14685C127direct (N × H)
172. C4⋊#95C2×C127semidirect
173. #1434C2×C127semidirect
175. C127#14685direct (N × H)
182. C22×C42C4×C127semidirect
248. C22×C4C4⋊C4×C127semidirect
328. C4#381×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C1272
C2×#381×C1272
C2×#380×C1272
C127×C4⋊#952
C127×#14342
C127×C22⋊#952
#14685127