Finite Group Databasebeta

← C127×#14600 #44578273

Subgroups — C127×#14600 #44578273

Order 32512.

1182 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C211yesmaximal, characteristic
2C127×#1445C211yesmaximal, characteristic
3C127×#1441C212yesmaximal
4C127×#1441C212yesmaximal
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C127×#1436C211yesmaximal, characteristic
8C127×#1436C212yesmaximal
9C127×C4⋊#95C212yesmaximal
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C42×C127C2212yes—
16C22×C42×C127C2211yescharacteristic
17#398×C127C418yescomplemented
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2211yescharacteristic
23C2×#95×C127C2212yes—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C23×C4×C127C2312yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2312yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—42no—
43C2×C4⋊C4×C127—42no—
44C2×C4⋊C4×C127—41no—
45C2×C4⋊C4×C127—41no—
46C2×C4⋊C4×C127—41no—
47C2×C4⋊C4×C127—41no—
48C2×C4⋊C4×C127—42no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—42no—
52C2×C4⋊C4×C127C2×C414yes—
53C2×C4⋊C4×C127C2×C414yes—
54C2×C4⋊C4×C127C2×C418yes—
55C2×C4⋊C4×C127Q818yes—
56C2×C42×C127—24no—
57C2×C42×C127—42no—
58C2×C42×C127—42no—
59C2×C42×C127—42no—
60C2×C42×C127—41no—
61#95×C127—24no—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—41no—
66#95×C127—42no—
67#95×C127—42no—
68#95×C127—42no—
69#95×C127—42no—
70#95×C127—41no—
71#95×C127—42no—
72#95×C127—41no—
73#95×C127C2×C418yes—
74#95×C127C2×C414yes—
75C24×C127C2411yescharacteristic
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127C22×C412yes—
124C22×C4×C127C22×C414yes—
125C22×C4×C127C22×C412yes—
126C22×C4×C127C22×C412yes—
127C22×C4×C127C22×C414yes—
128C22×C4×C127C2×Q814yes—
129C22×C4×C127C2×Q814yes—
130C22×C4×C127C2×Q814yes—
131C22×C4×C127#4114yes—
132C22×C4×C127#4114yes—
133C4⋊C4×C127—48no—
134C4⋊C4×C127—44no—
135C4⋊C4×C127—44no—
136C4⋊C4×C127—48no—
137C4⋊C4×C127—48no—
138C42×C127—48no—
139C42×C127—44no—
140C23×C127C23×C411yescharacteristic
141C23×C127C22×Q812yes—
142C23×C127C2×#4112yes—
143C23×C127C2×#4112yes—
144C23×C127H(5,𝔽2)12yes—
145C23×C127H(5,𝔽2)11yescharacteristic
146C23×C127H(5,𝔽2)11yescharacteristic
147C23×C127H(5,𝔽2)12yes—
148C23×C1272−1+412yes—
149C2×C4×C127—24no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—22no—
156C2×C4×C127—24no—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—24no—
160C2×C4×C127—22no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—41no—
190C2×C4×C127—42no—
191C2×C4×C127—41no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—41no—
197C2×C4×C127—41no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127C4×Q818yes—
206C22×C127C2×C4×Q812yes—
207C22×C127C4×#4111yescharacteristic
208C22×C127#51811yescharacteristic
209C22×C127#51811yescharacteristic
210C22×C127#52012yes—
211C22×C127#53812yes—
212C22×C127#53812yes—
213C22×C127#53912yes—
214C22×C127#54012yes—
215C22×C127#54312yes—
216C22×C127#54412yes—
217C22×C127#55212yes—
218C22×C127#55312yes—
219C22×C127#55412yes—
220C22×C127#55412yes—
221C22×C127#55511yescharacteristic
222C22×C127#55712yes—
223C22×C127Q8211yescharacteristic
224C22×C127#56011yescharacteristic
225C22×C127#56212yes—
226C22×C127#56311yescharacteristic
227C4×C127—28no—
228C4×C127—42no—
229C4×C127—44no—
230C4×C127—42no—
231C4×C127—42no—
232C4×C127—44no—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—82no—
236#14600C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127#232912yes—
238C2×C127#233311yescharacteristic
239C2×C127#236911yescharacteristic
240C2×C127#237012yes—
241C2×C127#237611yescharacteristic
242C2×C127#278012yes—
243C2×C127#278112yes—
244C2×C127#279112yes—
245C2×C127#280612yes—
246C2×#398C2×C12711yescharacteristic
247#1445C2×C12711yescharacteristic
248#1441C2×C12712yes—
249#1441C2×C12712yes—
250#1436C2×C12712yes—
251#1436C2×C12711yescharacteristic
252#1436C2×C12712yes—
253#1436C2×C12712yes—
254C4⋊#95C2×C12712yes—
255C127#1460011yescharacteristic, direct product factor, Sylow
256C22×C4⋊C4C22×C12712yes—
257C22×C4⋊C4C22×C12712yes—
258C22×C4⋊C4C22×C12711yescharacteristic
259C22×C4⋊C4C22×C12711yescharacteristic
260C22×C4⋊C4C22×C12712yes—
261C22×C42C22×C12712yes—
262C22×C42C22×C12711yescharacteristic
263#398C4×C12718yescomplemented
264C2×#95C22×C12712yes—
265C2×#95C22×C12712yes—
266C2×#95C22×C12712yes—
267C2×#95C22×C12712yes—
268C2×#95C22×C12711yescharacteristic
269C2×#95C22×C12712yes—
270C2×#95C22×C12711yescharacteristic
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12712yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12711yescharacteristic
276C2×#95C22×C12712yes—
277C2×#95C22×C12711yescharacteristic
278C23×C4C23×C12712yes—
279C23×C4C23×C12711yescharacteristic
280C23×C4C23×C12712yes—
281C23×C4C23×C12711yescharacteristic
282C23×C4C23×C12711yescharacteristic
283C23×C4C23×C12712yes—
284C23×C4C23×C12712yes—
285C23×C4C23×C12712yes—
286C23×C4C23×C12712yes—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×C4×C12714yes—
299C2×C4⋊C4C2×C4×C12714yes—
300C2×C4⋊C4C2×C4×C12718yes—
301C2×C4⋊C4Q8×C12718yes—
302C2×C42—24no—
303C2×C42—42no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—41no—
307#95—24no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—41no—
312#95—42no—
313#95—42no—
314#95—42no—
315#95—42no—
316#95—41no—
317#95—42no—
318#95—41no—
319#95C2×C4×C12718yes—
320#95C2×C4×C12714yes—
321C24C24×C12711yescharacteristic
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4C22×C4×C12712yes—
370C22×C4C22×C4×C12714yes—
371C22×C4C22×C4×C12712yes—
372C22×C4C22×C4×C12712yes—
373C22×C4C22×C4×C12714yes—
374C22×C4C2×Q8×C12714yes—
375C22×C4C2×Q8×C12714yes—
376C22×C4C2×Q8×C12714yes—
377C22×C4#41×C12714yes—
378C22×C4#41×C12714yes—
379C4⋊C4—48no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C4⋊C4—48no—
383C4⋊C4—48no—
384C42—48no—
385C42—44no—
386C23C23×C4×C12711yescharacteristic
387C23C22×Q8×C12712yes—
388C23C2×#41×C12712yes—
389C23C2×#41×C12712yes—
390C23H(5,𝔽2)×C12712yes—
391C23H(5,𝔽2)×C12711yescharacteristic
392C23H(5,𝔽2)×C12711yescharacteristic
393C23H(5,𝔽2)×C12712yes—
394C232−1+4×C12712yes—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4C4×Q8×C12718yes—
452C22C2×C4×Q8×C12712yes—
453C22C4×#41×C12711yescharacteristic
454C22#518×C12711yescharacteristic
455C22#518×C12711yescharacteristic
456C22#520×C12712yes—
457C22#538×C12712yes—
458C22#538×C12712yes—
459C22#539×C12712yes—
460C22#540×C12712yes—
461C22#543×C12712yes—
462C22#544×C12712yes—
463C22#552×C12712yes—
464C22#553×C12712yes—
465C22#554×C12712yes—
466C22#554×C12712yes—
467C22#555×C12711yescharacteristic
468C22#557×C12712yes—
469C22Q82×C12711yescharacteristic
470C22#560×C12711yescharacteristic
471C22#562×C12712yes—
472C22#563×C12711yescharacteristic
473C4—28no—
474C4—42no—
475C4—44no—
476C4—42no—
477C4—42no—
478C4—44no—
479C4—44no—
480C4—44no—
481C4—82no—
482C2C127×#232912yes—
483C2C127×#233311yescharacteristic
484C2C127×#236911yescharacteristic
485C2C127×#237012yes—
486C2C127×#237611yescharacteristic
487C2C127×#278012yes—
488C2C127×#278112yes—
489C2C127×#279112yes—
490C2C127×#280612yes—
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
17. #398×C127C4semidirect
236. #14600C127direct (N × H)
255. C127#14600direct (N × H)
263. #398C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C127×#14452
C127×#14412
C127×#14362
C127×C4⋊#952
#14600127