Finite Group Databasebeta

← C4×#385×C127 #44577437

Subgroups — C4×#385×C127 #44577437

Order 32512.

2782 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
1C23×C42×C127C211yesmaximal, characteristic
2C2×#385×C127C212yesmaximal
3C2×C4×C4⋊C4×C127C212yesmaximal, complemented
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
6C127×#1436C214yesmaximal, complemented
7C127×C22⋊#95C212yesmaximal
8C4×#95×C127C212yesmaximal, complemented
9C24×C4×C127C2212yes—
10C24×C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C42×C127—24no—
16C22×C42×C127—28no—
17C22×C42×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2212yes—
21C22×C42×C127C2212yes—
22#385×C127C4116yesdirect product factor
23C4×C4⋊C4×C127—28no—
24C4×C22⋊C4×C127—24no—
25C4×C22⋊C4×C127C418yescomplemented
26C2×#95×C127C2214yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2214yes—
30C2×#95×C127C2212yes—
31C25×C127C2311yescharacteristic
32C23×C4×C127—24no—
33C23×C4×C127—24no—
34C23×C4×C127—28no—
35C23×C4×C127—24no—
36C23×C4×C127—28no—
37C23×C4×C127—24no—
38C23×C4×C127C2×C418yes—
39C23×C4×C127C2×C414yes—
40C23×C4×C127D414yes—
41C23×C4×C127Q814yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2314yes—
48C23×C4×C127C2311yescharacteristic
49C2×C4⋊C4×C127—28no—
50C2×C4⋊C4×C127—28no—
51C2×C4⋊C4×C127C2×C4116yescomplemented
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—24no—
55C2×C22⋊C4×C127C2×C414yes—
56C2×C22⋊C4×C127C2×C418yes—
57C2×C22⋊C4×C127C2×C414yes—
58C2×C22⋊C4×C127C2×C418yes—
59C2×C42×C127—232no—
60C2×C42×C127—24no—
61C2×C42×C127—28no—
62C2×C42×C127—24no—
63C2×C42×C127—24no—
64C2×C42×C127—24no—
65C2×C42×C127—24no—
66C2×C42×C127—22no—
67C2×C42×C127—22no—
68C2×C42×C127—24no—
69C2×C42×C127—24no—
70C2×C42×C127C2×C418yescomplemented
71C2×C42×C127D418yes—
72#95×C127—24no—
73#95×C127—28no—
74#95×C127—28no—
75#95×C127C2×C418yescomplemented
76#95×C127C2×C4116yescomplemented
77C24×C127—22no—
78C24×C127—22no—
79C24×C127—24no—
80C24×C127C22×C412yes—
81C24×C127C22×C414yes—
82C24×C127C2×D412yes—
83C24×C127C2×Q812yes—
84C24×C127#4114yes—
85C24×C127C2411yescharacteristic
86C22×C4×C127—216no—
87C22×C4×C127—232no—
88C22×C4×C127—216no—
89C22×C4×C127—216no—
90C22×C4×C127—22no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—22no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—232no—
100C22×C4×C127—216no—
101C22×C4×C127—28no—
102C22×C4×C127—216no—
103C22×C4×C127—28no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—22no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—24no—
116C22×C4×C127C4⋊C4116yescomplemented
117C22×C4×C127C22×C414yes—
118C22×C4×C127C22×C414yes—
119C22×C4×C127C22×C414yes—
120C22×C4×C127C22×C414yes—
121C22×C4×C127C22×C418yes—
122C22×C4×C127C22×C412yes—
123C22×C4×C127C22×C418yes—
124C22×C4×C127C22×C412yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D418yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D414yes—
129C22×C4×C127C2×Q812yes—
130C22×C4×C127C2×Q812yes—
131C22×C4×C127#4118yes—
132C22×C4×C127#4114yes—
133C4⋊C4×C127—232no—
134C22⋊C4×C127—28no—
135C22⋊C4×C127—216no—
136C22⋊C4×C127C42116yescomplemented
137C42×C127—216no—
138C42×C127—216no—
139C42×C127—216no—
140C42×C127—44no—
141C42×C127—44no—
142C23×C127—24no—
143C23×C127—28no—
144C23×C127—24no—
145C23×C127—28no—
146C23×C127—22no—
147C23×C127—24no—
148C23×C127—22no—
149C23×C127—24no—
150C23×C127—28no—
151C23×C127—28no—
152C23×C127—24no—
153C23×C127C2×C4214yes—
154C23×C127C2×C4⋊C414yes—
155C23×C127#11714yes—
156C23×C127C4×D418yes—
157C23×C127C4×Q818yes—
158C23×C127C23×C411yescharacteristic
159C23×C127C23×C412yes—
160C23×C127C22×D411yescharacteristic
161C23×C127C22×D412yes—
162C23×C127C22×Q811yescharacteristic
163C23×C127C2×#4112yes—
164C23×C127C2×#4112yes—
165C23×C127C2×#4114yes—
166C2×C4×C127—264no—
167C2×C4×C127—24no—
168C2×C4×C127—28no—
169C2×C4×C127—24no—
170C2×C4×C127—28no—
171C2×C4×C127—28no—
172C2×C4×C127—24no—
173C2×C4×C127—28no—
174C2×C4×C127—22no—
175C2×C4×C127—28no—
176C2×C4×C127—24no—
177C2×C4×C127—22no—
178C2×C4×C127—28no—
179C2×C4×C127—28no—
180C2×C4×C127—28no—
181C2×C4×C127—232no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—28no—
187C2×C4×C127—24no—
188C2×C4×C127—28no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127C2×C4218yescomplemented
198C2×C4×C127C2×C4⋊C414yes—
199C2×C4×C127C2×C4⋊C414yes—
200C2×C4×C127C4×D4116yes—
201C2×C4×C127C4×D418yes—
202C2×C4×C127#12014yes—
203C2×C4×C127C22⋊Q818yes—
204C2×C4×C127#12314yes—
205C22×C127—28no—
206C22×C127—24no—
207C22×C127—28no—
208C22×C127—24no—
209C22×C127—28no—
210C22×C127—28no—
211C22×C127—216no—
212C22×C127C4×C4⋊C418yescomplemented
213C22×C127C22×C4211yescharacteristic
214C22×C127C22×C4⋊C411yescharacteristic
215C22×C127C2×#11711yescharacteristic
216C22×C127C2×C4×D412yes—
217C22×C127C2×C4×D412yes—
218C22×C127C2×C4×D414yes—
219C22×C127C2×C4×Q812yes—
220C22×C127C4×#4112yes—
221C22×C127C4×#4114yes—
222C22×C127C2×#12011yescharacteristic
223C22×C127C2×C22⋊Q812yes—
224C22×C127C2×#12311yescharacteristic
225C22×C127#52514yes—
226C22×C127#52512yes—
227C22×C127#52914yes—
228C22×C127#53312yes—
229C4×C127—28no—
230C4×C127—24no—
231C4×C127—216no—
232C4×C127—44no—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127#38518yesdirect product factor
236C4×#385C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127—28no—
238C2×C127C2×C4×C4⋊C411yescharacteristic
239C2×C127C42×D412yes—
240C2×C127C2×#38511yescharacteristic
241C2×C127#229012yes—
242C2×C127#229611yescharacteristic
243C2×C127C4×#12012yes—
244C2×C127C4×#12312yes—
245C2×C127C4×C22⋊Q814yes—
246C23×C42C2×C12711yescharacteristic
247C2×#385C2×C12712yes—
248C2×C4×C4⋊C4C2×C12712yescomplemented
249C2×C4×C22⋊C4C2×C12711yescharacteristic
250C2×C4×C22⋊C4C2×C12711yescharacteristic
251#1436C2×C12714yescomplemented
252C22⋊#95C2×C12712yes—
253C4×#95C2×C12712yescomplemented
254C127C4×#38511yescharacteristic, direct product factor, Sylow
255C24×C4C22×C12712yes—
256C24×C4C22×C12711yescharacteristic
257C22×C4⋊C4C22×C12714yes—
258C22×C22⋊C4C22×C12711yescharacteristic
259C22×C22⋊C4C22×C12712yes—
260C22×C22⋊C4C22×C12711yescharacteristic
261C22×C42—24no—
262C22×C42—28no—
263C22×C42C22×C12712yes—
264C22×C42C22×C12711yescharacteristic
265C22×C42C22×C12711yescharacteristic
266C22×C42C22×C12712yes—
267C22×C42C22×C12712yes—
268#385C4×C127116yesdirect product factor
269C4×C4⋊C4—28no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4C4×C12718yescomplemented
272C2×#95C22×C12714yes—
273C2×#95C22×C12714yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12714yes—
276C2×#95C22×C12712yes—
277C25C23×C12711yescharacteristic
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—28no—
281C23×C4—24no—
282C23×C4—28no—
283C23×C4—24no—
284C23×C4C2×C4×C12718yes—
285C23×C4C2×C4×C12714yes—
286C23×C4D4×C12714yes—
287C23×C4Q8×C12714yes—
288C23×C4C23×C12712yes—
289C23×C4C23×C12712yes—
290C23×C4C23×C12712yes—
291C23×C4C23×C12712yes—
292C23×C4C23×C12711yescharacteristic
293C23×C4C23×C12714yes—
294C23×C4C23×C12711yescharacteristic
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4C2×C4×C127116yescomplemented
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4C2×C4×C12714yes—
302C2×C22⋊C4C2×C4×C12718yes—
303C2×C22⋊C4C2×C4×C12714yes—
304C2×C22⋊C4C2×C4×C12718yes—
305C2×C42—232no—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—28no—
309C2×C42—24no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42C2×C4×C12718yescomplemented
317C2×C42D4×C12718yes—
318#95—24no—
319#95—28no—
320#95—28no—
321#95C2×C4×C12718yescomplemented
322#95C2×C4×C127116yescomplemented
323C24—22no—
324C24—22no—
325C24—24no—
326C24C22×C4×C12712yes—
327C24C22×C4×C12714yes—
328C24C2×D4×C12712yes—
329C24C2×Q8×C12712yes—
330C24#41×C12714yes—
331C24C24×C12711yescharacteristic
332C22×C4—216no—
333C22×C4—232no—
334C22×C4—216no—
335C22×C4—216no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—232no—
346C22×C4—216no—
347C22×C4—28no—
348C22×C4—216no—
349C22×C4—28no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4C4⋊C4×C127116yescomplemented
363C22×C4C22×C4×C12714yes—
364C22×C4C22×C4×C12714yes—
365C22×C4C22×C4×C12714yes—
366C22×C4C22×C4×C12714yes—
367C22×C4C22×C4×C12718yes—
368C22×C4C22×C4×C12712yes—
369C22×C4C22×C4×C12718yes—
370C22×C4C22×C4×C12712yes—
371C22×C4C2×D4×C12712yes—
372C22×C4C2×D4×C12718yes—
373C22×C4C2×D4×C12712yes—
374C22×C4C2×D4×C12714yes—
375C22×C4C2×Q8×C12712yes—
376C22×C4C2×Q8×C12712yes—
377C22×C4#41×C12718yes—
378C22×C4#41×C12714yes—
379C4⋊C4—232no—
380C22⋊C4—28no—
381C22⋊C4—216no—
382C22⋊C4C42×C127116yescomplemented
383C42—216no—
384C42—216no—
385C42—216no—
386C42—44no—
387C42—44no—
388C23—24no—
389C23—28no—
390C23—24no—
391C23—28no—
392C23—22no—
393C23—24no—
394C23—22no—
395C23—24no—
396C23—28no—
397C23—28no—
398C23—24no—
399C23C2×C42×C12714yes—
400C23C2×C4⋊C4×C12714yes—
401C23#117×C12714yes—
402C23C4×D4×C12718yes—
403C23C4×Q8×C12718yes—
404C23C23×C4×C12711yescharacteristic
405C23C23×C4×C12712yes—
406C23C22×D4×C12711yescharacteristic
407C23C22×D4×C12712yes—
408C23C22×Q8×C12711yescharacteristic
409C23C2×#41×C12712yes—
410C23C2×#41×C12712yes—
411C23C2×#41×C12714yes—
412C2×C4—264no—
413C2×C4—24no—
414C2×C4—28no—
415C2×C4—24no—
416C2×C4—28no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—28no—
420C2×C4—22no—
421C2×C4—28no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—28no—
425C2×C4—28no—
426C2×C4—28no—
427C2×C4—232no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—28no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4C2×C42×C12718yescomplemented
444C2×C4C2×C4⋊C4×C12714yes—
445C2×C4C2×C4⋊C4×C12714yes—
446C2×C4C4×D4×C127116yes—
447C2×C4C4×D4×C12718yes—
448C2×C4#120×C12714yes—
449C2×C4C22⋊Q8×C12718yes—
450C2×C4#123×C12714yes—
451C22—28no—
452C22—24no—
453C22—28no—
454C22—24no—
455C22—28no—
456C22—28no—
457C22—216no—
458C22C4×C4⋊C4×C12718yescomplemented
459C22C22×C42×C12711yescharacteristic
460C22C22×C4⋊C4×C12711yescharacteristic
461C22C2×#117×C12711yescharacteristic
462C22C2×C4×D4×C12712yes—
463C22C2×C4×D4×C12712yes—
464C22C2×C4×D4×C12714yes—
465C22C2×C4×Q8×C12712yes—
466C22C4×#41×C12712yes—
467C22C4×#41×C12714yes—
468C22C2×#120×C12711yescharacteristic
469C22C2×C22⋊Q8×C12712yes—
470C22C2×#123×C12711yescharacteristic
471C22#525×C12714yes—
472C22#525×C12712yes—
473C22#529×C12714yes—
474C22#533×C12712yes—
475C4—28no—
476C4—24no—
477C4—216no—
478C4—44no—
479C4—44no—
480C4—44no—
481C4#385×C12718yesdirect product factor
482C2—28no—
483C2C2×C4×C4⋊C4×C12711yescharacteristic
484C2C42×D4×C12712yes—
485C2C2×#385×C12711yescharacteristic
486C2C127×#229012yes—
487C2C127×#229611yescharacteristic
488C2C4×#120×C12712yes—
489C2C4×#123×C12712yes—
490C2C4×C22⋊Q8×C12714yes—
subgroupG/H
centerC23×C4×C127C23
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
socleC24×C127C24
prime radicalC25×C127C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊C4×C127C2semidirect
6. C127×#1436C2semidirect
8. C4×#95×C127C2semidirect
22. #385×C127C4direct (N × H)
25. C4×C22⋊C4×C127C4semidirect
51. C2×C4⋊C4×C127C2×C4semidirect
70. C2×C42×C127C2×C4semidirect
75. #95×C127C2×C4semidirect
76. #95×C127C2×C4semidirect
116. C22×C4×C127C4⋊C4semidirect
136. C22⋊C4×C127C42semidirect
197. C2×C4×C127C2×C42semidirect
212. C22×C127C4×C4⋊C4semidirect
235. C4×C127#385direct (N × H)
236. C4×#385C127direct (N × H)
248. C2×C4×C4⋊C4C2×C127semidirect
251. #1436C2×C127semidirect
253. C4×#95C2×C127semidirect
254. C127C4×#385direct (N × H)
268. #385C4×C127direct (N × H)
271. C4×C22⋊C4C4×C127semidirect
297. C2×C4⋊C4C2×C4×C127semidirect
316. C2×C42C2×C4×C127semidirect
321. #95C2×C4×C127semidirect
322. #95C2×C4×C127semidirect
362. C22×C4C4⋊C4×C127semidirect
382. C22⋊C4C42×C127semidirect
443. C2×C4C2×C42×C127semidirect
458. C22C4×C4⋊C4×C127semidirect
481. C4#385×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C42×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14362
C127×C22⋊#952
C4×#95×C1272
C4×#385127