Finite Group Databasebeta

← C127×#15149 #44578822

Subgroups — C127×#15149 #44578822

Order 32512.

1410 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C212yesmaximal
2C2×#389×C127C212yesmaximal
3C2×#389×C127C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
5C127×#1442C214yesmaximal
6C127×#1441C212yesmaximal
7C127×C4⋊#95C212yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2214yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C42×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18#398×C127—28no—
19#389×C127—28no—
20#389×C127—24no—
21C4×C4⋊C4×C127—24no—
22C2×#95×C127C2212yes—
23C2×#95×C127C2214yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2312yes—
33C23×C4×C127C2314yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—28no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—28no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—44no—
53C2×C4⋊C4×C127D414yes—
54C2×C4⋊C4×C127D414yes—
55C2×C4⋊C4×C127Q818yes—
56C2×C42×C127—24no—
57C2×C42×C127—24no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127D414yes—
61#95×C127—24no—
62#95×C127—28no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—28no—
66#95×C127—28no—
67#95×C127—42no—
68C24×C127C2411yescharacteristic
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—24no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—24no—
77C22×C4×C127—22no—
78C22×C4×C127—22no—
79C22×C4×C127—24no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—21no—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—24no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D414yes—
106C22×C4×C127C2×D414yes—
107C22×C4×C127C2×D412yes—
108C22×C4×C127C2×D412yes—
109C22×C4×C127C2×D412yes—
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×Q818yes—
112C22×C4×C127C2×Q814yes—
113C22×C4×C127#4114yes—
114C22×C4×C127#4112yes—
115C22×C4×C127#4112yes—
116C22×C4×C127#4114yes—
117C4⋊C4×C127—28no—
118C4⋊C4×C127—28no—
119C4⋊C4×C127—28no—
120C4⋊C4×C127—216no—
121C4⋊C4×C127—416no—
122C4⋊C4×C127—48no—
123C4⋊C4×C127—44no—
124C42×C127—28no—
125C42×C127—48no—
126C23×C127C22×D411yescharacteristic
127C23×C127C22×D411yescharacteristic
128C23×C127C22×D411yescharacteristic
129C23×C127C22×Q812yes—
130C23×C127C2×#4111yescharacteristic
131C23×C127C2×#4111yescharacteristic
132C23×C127C2×#4112yes—
133C23×C127C2×#4112yes—
134C23×C127H(5,𝔽2)11yescharacteristic
135C23×C1272−1+412yes—
136C23×C1272−1+411yescharacteristic
137C2×C4×C127—22no—
138C2×C4×C127—22no—
139C2×C4×C127—24no—
140C2×C4×C127—24no—
141C2×C4×C127—24no—
142C2×C4×C127—24no—
143C2×C4×C127—28no—
144C2×C4×C127—22no—
145C2×C4×C127—24no—
146C2×C4×C127—22no—
147C2×C4×C127—22no—
148C2×C4×C127—24no—
149C2×C4×C127—24no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—28no—
154C2×C4×C127—24no—
155C2×C4×C127—28no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—44no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—44no—
166C2×C4×C127—44no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—44no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—44no—
178C2×C4×C127—44no—
179C2×C4×C127#12114yes—
180C2×C4×C127#12114yes—
181C2×C4×C127C22⋊Q818yes—
182C2×C4×C127#12314yes—
183C2×C4×C127#12518yes—
184C2×C4×C127C4⋊Q814yes—
185C22×C127C2×#12111yescharacteristic
186C22×C127C2×#12111yescharacteristic
187C22×C127C2×C22⋊Q812yes—
188C22×C127C2×#12311yescharacteristic
189C22×C127#52511yescharacteristic
190C22×C127C2×#12512yes—
191C22×C127#52912yes—
192C22×C127C2×C4⋊Q811yescharacteristic
193C22×C127#53212yes—
194C22×C127#53611yescharacteristic
195C22×C127#53711yescharacteristic
196C22×C127#54112yes—
197C22×C127#54212yes—
198C22×C127D4211yescharacteristic
199C22×C127#54711yescharacteristic
200C22×C127#54711yescharacteristic
201C22×C127#54812yes—
202C22×C127D4×Q812yes—
203C22×C127#55212yes—
204C22×C127#55412yes—
205C22×C127#55511yescharacteristic
206C22×C127#55712yes—
207C22×C127#55712yes—
208C4×C127—24no—
209C4×C127—42no—
210C4×C127—48no—
211C4×C127—44no—
212C4×C127—44no—
213C4×C127—44no—
214C4×C127—82no—
215C4×C127#39818yescomplemented
216#15149C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127C2×#39811yescharacteristic
218C2×C127#245212yes—
219C2×C127#245312yes—
220C2×C127#250612yes—
221C2×C127#250812yes—
222C2×C127#253611yescharacteristic
223C2×C127#253711yescharacteristic
224C2×C127#254611yescharacteristic
225C2×C127#258411yescharacteristic
226C2×C127#262511yescharacteristic
227C2×C127#285411yescharacteristic
228C2×#398C2×C12712yes—
229C2×#389C2×C12711yescharacteristic
230C2×#389C2×C12712yes—
231C2×C4×C4⋊C4C2×C12711yescharacteristic
232#1442C2×C12714yes—
233#1441C2×C12712yes—
234C4⋊#95C2×C12712yes—
235C4⋊#95C2×C12711yescharacteristic
236C127#1514911yescharacteristic, direct product factor, Sylow
237C22×C4⋊C4C22×C12712yes—
238C22×C4⋊C4C22×C12711yescharacteristic
239C22×C4⋊C4C22×C12711yescharacteristic
240C22×C4⋊C4C22×C12714yes—
241C22×C4⋊C4C22×C12711yescharacteristic
242C22×C4⋊C4C22×C12711yescharacteristic
243C22×C4⋊C4C22×C12712yes—
244C22×C42C22×C12712yes—
245C22×C42C22×C12711yescharacteristic
246#398—28no—
247#389—28no—
248#389—24no—
249C4×C4⋊C4—24no—
250C2×#95C22×C12712yes—
251C2×#95C22×C12714yes—
252C2×#95C22×C12714yes—
253C2×#95C22×C12714yes—
254C2×#95C22×C12712yes—
255C2×#95C22×C12712yes—
256C2×#95C22×C12712yes—
257C23×C4C23×C12712yes—
258C23×C4C23×C12712yes—
259C23×C4C23×C12712yes—
260C23×C4C23×C12711yescharacteristic
261C23×C4C23×C12714yes—
262C23×C4C23×C12712yes—
263C23×C4C23×C12711yescharacteristic
264C23×C4C23×C12711yescharacteristic
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4D4×C12714yes—
282C2×C4⋊C4D4×C12714yes—
283C2×C4⋊C4Q8×C12718yes—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—24no—
287C2×C42—24no—
288C2×C42D4×C12714yes—
289#95—24no—
290#95—28no—
291#95—24no—
292#95—24no—
293#95—28no—
294#95—28no—
295#95—42no—
296C24C24×C12711yescharacteristic
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—24no—
332C22×C4C2×D4×C12712yes—
333C22×C4C2×D4×C12714yes—
334C22×C4C2×D4×C12714yes—
335C22×C4C2×D4×C12712yes—
336C22×C4C2×D4×C12712yes—
337C22×C4C2×D4×C12712yes—
338C22×C4C2×D4×C12712yes—
339C22×C4C2×Q8×C12718yes—
340C22×C4C2×Q8×C12714yes—
341C22×C4#41×C12714yes—
342C22×C4#41×C12712yes—
343C22×C4#41×C12712yes—
344C22×C4#41×C12714yes—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—216no—
349C4⋊C4—416no—
350C4⋊C4—48no—
351C4⋊C4—44no—
352C42—28no—
353C42—48no—
354C23C22×D4×C12711yescharacteristic
355C23C22×D4×C12711yescharacteristic
356C23C22×D4×C12711yescharacteristic
357C23C22×Q8×C12712yes—
358C23C2×#41×C12711yescharacteristic
359C23C2×#41×C12711yescharacteristic
360C23C2×#41×C12712yes—
361C23C2×#41×C12712yes—
362C23H(5,𝔽2)×C12711yescharacteristic
363C232−1+4×C12712yes—
364C232−1+4×C12711yescharacteristic
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—28no—
382C2×C4—24no—
383C2×C4—28no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4#121×C12714yes—
408C2×C4#121×C12714yes—
409C2×C4C22⋊Q8×C12718yes—
410C2×C4#123×C12714yes—
411C2×C4#125×C12718yes—
412C2×C4C4⋊Q8×C12714yes—
413C22C2×#121×C12711yescharacteristic
414C22C2×#121×C12711yescharacteristic
415C22C2×C22⋊Q8×C12712yes—
416C22C2×#123×C12711yescharacteristic
417C22#525×C12711yescharacteristic
418C22C2×#125×C12712yes—
419C22#529×C12712yes—
420C22C2×C4⋊Q8×C12711yescharacteristic
421C22#532×C12712yes—
422C22#536×C12711yescharacteristic
423C22#537×C12711yescharacteristic
424C22#541×C12712yes—
425C22#542×C12712yes—
426C22D42×C12711yescharacteristic
427C22#547×C12711yescharacteristic
428C22#547×C12711yescharacteristic
429C22#548×C12712yes—
430C22D4×Q8×C12712yes—
431C22#552×C12712yes—
432C22#554×C12712yes—
433C22#555×C12711yescharacteristic
434C22#557×C12712yes—
435C22#557×C12712yes—
436C4—24no—
437C4—42no—
438C4—48no—
439C4—44no—
440C4—44no—
441C4—44no—
442C4—82no—
443C4#398×C12718yescomplemented
444C2C2×#398×C12711yescharacteristic
445C2C127×#245212yes—
446C2C127×#245312yes—
447C2C127×#250612yes—
448C2C127×#250812yes—
449C2C127×#253611yescharacteristic
450C2C127×#253711yescharacteristic
451C2C127×#254611yescharacteristic
452C2C127×#258411yescharacteristic
453C2C127×#262511yescharacteristic
454C2C127×#285411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
215. C4×C127#398semidirect
216. #15149C127direct (N × H)
236. C127#15149direct (N × H)
443. C4#398×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#389×C1272
C2×C4×C4⋊C4×C1272
C127×#14422
C127×#14412
C127×C4⋊#952
#15149127