Finite Group Databasebeta

← C127×#14298 #44577971

Subgroups — C127×#14298 #44577971

Order 32512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#383×C127C211yesmaximal, characteristic
2C2×#382×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
4C127×#1444C212yesmaximal
5C127×#1444C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1436C214yesmaximal
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2214yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#383×C127C418yescomplemented
17#382×C127—24no—
18C4×C4⋊C4×C127—24no—
19C2×#95×C127C2212yes—
20C2×#95×C127C2214yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2214yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C23×C4×C127C2312yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2312yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—24no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—28no—
43C2×C4⋊C4×C127—42no—
44C2×C4⋊C4×C127—42no—
45C2×C4⋊C4×C127—44no—
46C2×C4⋊C4×C127—44no—
47C2×C42×C127—24no—
48C2×C42×C127—44no—
49C2×C42×C127C2×C414yes—
50C2×C42×C127D414yes—
51C2×C42×C127Q814yes—
52#95×C127—24no—
53#95×C127—24no—
54#95×C127—24no—
55#95×C127—28no—
56#95×C127—44no—
57#95×C127—44no—
58#95×C127C2×C418yes—
59#95×C127C2×C418yes—
60#95×C127C2×C418yes—
61C24×C127C2411yescharacteristic
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
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—24no—
81C22×C4×C127—24no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—22no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127C22×C418yes—
92C22×C4×C127C22×C412yes—
93C22×C4×C127C22×C412yes—
94C22×C4×C127C22×C412yes—
95C22×C4×C127C2×D412yes—
96C22×C4×C127C2×D412yes—
97C22×C4×C127C2×D412yes—
98C22×C4×C127C2×Q812yes—
99C22×C4×C127C2×Q812yes—
100C22×C4×C127C2×Q812yes—
101C22×C4×C127#4114yes—
102C22×C4×C127#4114yes—
103C4⋊C4×C127—28no—
104C4⋊C4×C127—28no—
105C4⋊C4×C127—44no—
106C4⋊C4×C127—44no—
107C4⋊C4×C127—416no—
108C42×C127—48no—
109C42×C127C4⋊C4116yescomplemented
110C23×C127C23×C411yescharacteristic
111C23×C127C22×D411yescharacteristic
112C23×C127C22×Q811yescharacteristic
113C23×C127C2×#4112yes—
114C23×C127C2×#4112yes—
115C23×C127H(5,𝔽2)12yes—
116C23×C127H(5,𝔽2)12yes—
117C23×C1272−1+412yes—
118C23×C1272−1+412yes—
119C2×C4×C127—24no—
120C2×C4×C127—24no—
121C2×C4×C127—24no—
122C2×C4×C127—22no—
123C2×C4×C127—22no—
124C2×C4×C127—24no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—24no—
130C2×C4×C127—24no—
131C2×C4×C127—28no—
132C2×C4×C127—28no—
133C2×C4×C127—28no—
134C2×C4×C127—24no—
135C2×C4×C127—24no—
136C2×C4×C127—28no—
137C2×C4×C127—28no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—44no—
143C2×C4×C127—44no—
144C2×C4×C127—44no—
145C2×C4×C127—44no—
146C2×C4×C127—44no—
147C2×C4×C127—44no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127—48no—
157C2×C4×C127C2×C4⋊C414yes—
158C2×C4×C127C2×C4⋊C414yes—
159C2×C4×C127C2×C4⋊C414yes—
160C22×C127C22×C4⋊C411yescharacteristic
161C22×C127C4×#4112yes—
162C22×C127#52012yes—
163C22×C127#52012yes—
164C22×C127#52511yescharacteristic
165C22×C127#52511yescharacteristic
166C22×C127#53312yes—
167C22×C127#53511yescharacteristic
168C22×C127#53511yescharacteristic
169C22×C127#53611yescharacteristic
170C22×C127#53611yescharacteristic
171C22×C127#53814yes—
172C22×C127#53914yes—
173C22×C127#54114yes—
174C22×C127#54214yes—
175C22×C127#54412yes—
176C22×C127#54412yes—
177C4×C127—24no—
178C4×C127—24no—
179C4×C127—24no—
180C4×C127—48no—
181C4×C127—44no—
182C4×C127—44no—
183C4×C127—82no—
184C4×C127—82no—
185#14298C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127#229611yescharacteristic
187C2×C127#231711yescharacteristic
188C2×C127#231711yescharacteristic
189C2×C127#233414yes—
190C2×C127#263111yescharacteristic
191C2×C127#263211yescharacteristic
192C2×C127#263311yescharacteristic
193C2×C127#263411yescharacteristic
194C2×C127#266614yes—
195C2×#383C2×C12711yescharacteristic
196C2×#382C2×C12711yescharacteristic
197C2×C4×C4⋊C4C2×C12711yescharacteristic
198#1444C2×C12712yes—
199#1444C2×C12712yes—
200#1442C2×C12712yes—
201#1442C2×C12712yes—
202#1436C2×C12714yes—
203C127#1429811yescharacteristic, direct product factor, Sylow
204C22×C4⋊C4C22×C12711yescharacteristic
205C22×C4⋊C4C22×C12711yescharacteristic
206C22×C4⋊C4C22×C12714yes—
207C22×C4⋊C4C22×C12711yescharacteristic
208C22×C4⋊C4C22×C12711yescharacteristic
209C22×C42C22×C12712yes—
210C22×C42C22×C12711yescharacteristic
211#383C4×C12718yescomplemented
212#382—24no—
213C4×C4⋊C4—24no—
214C2×#95C22×C12712yes—
215C2×#95C22×C12714yes—
216C2×#95C22×C12712yes—
217C2×#95C22×C12712yes—
218C2×#95C22×C12714yes—
219C2×#95C22×C12714yes—
220C2×#95C22×C12712yes—
221C2×#95C22×C12712yes—
222C2×#95C22×C12712yes—
223C23×C4C23×C12712yes—
224C23×C4C23×C12712yes—
225C23×C4C23×C12714yes—
226C23×C4C23×C12712yes—
227C23×C4C23×C12712yes—
228C23×C4C23×C12711yescharacteristic
229C23×C4C23×C12711yescharacteristic
230C23×C4C23×C12711yescharacteristic
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—44no—
241C2×C4⋊C4—44no—
242C2×C42—24no—
243C2×C42—44no—
244C2×C42C2×C4×C12714yes—
245C2×C42D4×C12714yes—
246C2×C42Q8×C12714yes—
247#95—24no—
248#95—24no—
249#95—24no—
250#95—28no—
251#95—44no—
252#95—44no—
253#95C2×C4×C12718yes—
254#95C2×C4×C12718yes—
255#95C2×C4×C12718yes—
256C24C24×C12711yescharacteristic
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4C22×C4×C12718yes—
287C22×C4C22×C4×C12712yes—
288C22×C4C22×C4×C12712yes—
289C22×C4C22×C4×C12712yes—
290C22×C4C2×D4×C12712yes—
291C22×C4C2×D4×C12712yes—
292C22×C4C2×D4×C12712yes—
293C22×C4C2×Q8×C12712yes—
294C22×C4C2×Q8×C12712yes—
295C22×C4C2×Q8×C12712yes—
296C22×C4#41×C12714yes—
297C22×C4#41×C12714yes—
298C4⋊C4—28no—
299C4⋊C4—28no—
300C4⋊C4—44no—
301C4⋊C4—44no—
302C4⋊C4—416no—
303C42—48no—
304C42C4⋊C4×C127116yescomplemented
305C23C23×C4×C12711yescharacteristic
306C23C22×D4×C12711yescharacteristic
307C23C22×Q8×C12711yescharacteristic
308C23C2×#41×C12712yes—
309C23C2×#41×C12712yes—
310C23H(5,𝔽2)×C12712yes—
311C23H(5,𝔽2)×C12712yes—
312C232−1+4×C12712yes—
313C232−1+4×C12712yes—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—28no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—48no—
352C2×C4C2×C4⋊C4×C12714yes—
353C2×C4C2×C4⋊C4×C12714yes—
354C2×C4C2×C4⋊C4×C12714yes—
355C22C22×C4⋊C4×C12711yescharacteristic
356C22C4×#41×C12712yes—
357C22#520×C12712yes—
358C22#520×C12712yes—
359C22#525×C12711yescharacteristic
360C22#525×C12711yescharacteristic
361C22#533×C12712yes—
362C22#535×C12711yescharacteristic
363C22#535×C12711yescharacteristic
364C22#536×C12711yescharacteristic
365C22#536×C12711yescharacteristic
366C22#538×C12714yes—
367C22#539×C12714yes—
368C22#541×C12714yes—
369C22#542×C12714yes—
370C22#544×C12712yes—
371C22#544×C12712yes—
372C4—24no—
373C4—24no—
374C4—24no—
375C4—48no—
376C4—44no—
377C4—44no—
378C4—82no—
379C4—82no—
380C2C127×#229611yescharacteristic
381C2C127×#231711yescharacteristic
382C2C127×#231711yescharacteristic
383C2C127×#233414yes—
384C2C127×#263111yescharacteristic
385C2C127×#263211yescharacteristic
386C2C127×#263311yescharacteristic
387C2C127×#263411yescharacteristic
388C2C127×#266614yes—
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
16. #383×C127C4semidirect
109. C42×C127C4⋊C4semidirect
185. #14298C127direct (N × H)
203. C127#14298direct (N × H)
211. #383C4×C127semidirect
304. C42C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#383×C1272
C2×#382×C1272
C2×C4×C4⋊C4×C1272
C127×#14442
C127×#14422
C127×#14362
#14298127