Finite Group Databasebeta

← C4×#462×C127 #44585173

Subgroups — C4×#462×C127 #44585173

Order 32512.

984 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C127C211yesmaximal, characteristic
2C2×C4×Q16×C127C212yesmaximal
3C4×C4⋊Q8×C127C211yesmaximal, characteristic
4C42×Q8×C127C211yesmaximal, characteristic
5C127×#1981C211yesmaximal, characteristic
6C127×#1947C211yesmaximal, characteristic
7C127×#1928C212yesmaximal
8C127×#1878C212yesmaximal
9C127×#1803C211yesmaximal, characteristic
10C4×C4⋊C8×C127C211yesmaximal, characteristic
11C4×#103×C127C212yesmaximal
12C22×Q16×C127C2212yes—
13C2×C4⋊Q8×C127C2211yescharacteristic
14C2×C4×Q8×C127C2211yescharacteristic
15C2×C4×Q8×C127C2212yes—
16C2×C4×Q8×C127C2211yescharacteristic
17C2×C4×Q8×C127C2211yescharacteristic
18#462×C127C418yesdirect product factor
19C4×Q16×C127—28no—
20C2×#107×C127C2212yes—
21C2×C4⋊C8×C127C2211yescharacteristic
22C2×C4⋊C8×C127C2211yescharacteristic
23C2×#103×C127C2212yes—
24C2×#103×C127C2212yes—
25C2×#103×C127C2212yes—
26C2×#103×C127C2212yes—
27C2×C4×C8×C127C2212yes—
28#391×C127C2212yes—
29#389×C127—21no—
30#389×C127—21no—
31#384×C127C2211yescharacteristic
32C4×C4⋊C4×C127—21no—
33C4×C4⋊C4×C127—21no—
34C4×C4⋊C4×C127—21no—
35C4×C4⋊C4×C127—21no—
36C4×C4⋊C4×C127—21no—
37C4×C4⋊C4×C127C2211yescharacteristic
38C4×C4⋊C4×C127C2211yescharacteristic
39C4×C4⋊C4×C127C2211yescharacteristic
40C43×C127—21no—
41C43×C127C2211yescharacteristic
42#340×C127C2212yes—
43#340×C127C2212yes—
44#336×C127C2212yes—
45C22×Q8×C127C2312yes—
46C22×Q8×C127C2311yescharacteristic
47C2×Q16×C127—24no—
48C2×Q16×C127—24no—
49C2×Q16×C127C2×C418yes—
50C22×C8×C127C2312yes—
51C22×C8×C127C2312yes—
52C4⋊Q8×C127—22no—
53C4⋊Q8×C127C2×C414yes—
54C4×Q8×C127—22no—
55C4×Q8×C127—22no—
56C4×Q8×C127—22no—
57C4×Q8×C127—22no—
58C4×Q8×C127—24no—
59C4×Q8×C127—24no—
60C4×Q8×C127C2×C414yes—
61C4×Q8×C127D414yes—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127C2312yes—
71C2×C4⋊C4×C127C2311yescharacteristic
72C2×C4⋊C4×C127C2311yescharacteristic
73C2×C4⋊C4×C127C2311yescharacteristic
74C2×C42×C127—21no—
75C2×C42×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—21no—
78C2×C42×C127—21no—
79C2×C42×C127—22no—
80C2×C42×C127—21no—
81C2×C42×C127D411yescharacteristic
82C2×C42×C127D411yescharacteristic
83C2×C42×C127D411yescharacteristic
84C2×C42×C127D411yescharacteristic
85C2×C42×C127C2311yescharacteristic
86C2×C42×C127C2311yescharacteristic
87C2×C42×C127C2311yescharacteristic
88#107×C127—24no—
89C4⋊C8×C127—22no—
90C4⋊C8×C127C2×C414yes—
91#103×C127—24no—
92#103×C127—24no—
93#103×C127—24no—
94#103×C127C2×C418yes—
95C4×C8×C127—24no—
96#95×C127—21no—
97#95×C127—21no—
98#95×C127—21no—
99#95×C127—22no—
100#95×C127—22no—
101C2×Q8×C127—21no—
102C2×Q8×C127—21no—
103C2×Q8×C127—21no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—22no—
108C2×Q8×C127—22no—
109C2×Q8×C127C22×C414yes—
110C2×Q8×C127C22×C412yes—
111C2×Q8×C127C2×D412yes—
112C2×Q8×C127#4112yes—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127C2×D411yescharacteristic
122C22×C4×C127C2×D411yescharacteristic
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2411yescharacteristic
126Q16×C127—216no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127C22×C414yes—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—24no—
135C4⋊C4×C127—24no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—24no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—42no—
144C4⋊C4×C127—44no—
145C4⋊C4×C127—42no—
146C4⋊C4×C127C22×C412yes—
147C4⋊C4×C127C2×D412yes—
148C4⋊C4×C127#4112yes—
149C42×C127—24no—
150C42×C127—24no—
151C42×C127—24no—
152C42×C127—22no—
153C42×C127—22no—
154C42×C127—21no—
155C42×C127—21no—
156C42×C127—41no—
157C42×C127—42no—
158C42×C127—44no—
159C42×C127—42no—
160C42×C127—42no—
161C42×C127Q1614yescomplemented
162C42×C127C22×C412yes—
163C42×C127C2×D412yes—
164C42×C127#4112yes—
165C42×C127#4112yes—
166C23×C127C22×D411yescharacteristic
167Q8×C127—22no—
168Q8×C127—22no—
169Q8×C127—22no—
170Q8×C127—24no—
171Q8×C127—24no—
172Q8×C127—42no—
173Q8×C127—42no—
174Q8×C127C4×D414yes—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—21no—
178C2×C4×C127—22no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
183C2×C4×C127—21no—
184C2×C4×C127—22no—
185C2×C4×C127—24no—
186C2×C4×C127—22no—
187C2×C4×C127—21no—
188C2×C4×C127—22no—
189C2×C4×C127—21no—
190C2×C4×C127—21no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—41no—
194C2×C4×C127—41no—
195C2×C4×C127—41no—
196C2×C4×C127—41no—
197C2×C4×C127—41no—
198C2×C4×C127—41no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127C4×D412yes—
203C2×C4×C127C4×D412yes—
204C2×C4×C127#12112yes—
205C2×C4×C127#12112yes—
206C2×C4×C127C2×Q1612yes—
207C2×C4×C127C2×Q1612yes—
208C2×C4×C127C2×Q1612yes—
209C2×C4×C127#13512yes—
210C2×C4×C127#13712yes—
211C2×C4×C127C23×C411yescharacteristic
212C2×C4×C127C22×D411yescharacteristic
213C2×C4×C127C2×#4111yescharacteristic
214C2×C4×C127C2×#4111yescharacteristic
215C2×C4×C127C2×#4111yescharacteristic
216C2×C4×C127C2×#4111yescharacteristic
217C8×C127—24no—
218C8×C127—42no—
219C22×C127C2×C4×D411yescharacteristic
220C22×C127C2×#12111yescharacteristic
221C22×C127#52511yescharacteristic
222C22×C127C22×Q1611yescharacteristic
223C22×C127C2×#13511yescharacteristic
224C22×C127C2×#13711yescharacteristic
225C22×C127#57511yescharacteristic
226C4×C127—22no—
227C4×C127—22no—
228C4×C127—22no—
229C4×C127—24no—
230C4×C127—41no—
231C4×C127—42no—
232C4×C127—42no—
233C4×C127—42no—
234C4×C127—44no—
235C4×C127—82no—
236C4×C127C4×Q1614yescomplemented
237C4×C127#46214yesdirect product factor
238C4×C127C2×C4×D411yescharacteristic
239C4×C127C4×#4111yescharacteristic
240C4×C127#52911yescharacteristic
241C4×C127#53211yescharacteristic
242C4×#462C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127C4×#12111yescharacteristic
244C2×C127C2×C4×Q1611yescharacteristic
245C2×C127C4×#13711yescharacteristic
246C2×C127C2×#46211yescharacteristic
247C2×C127#303511yescharacteristic
248C2×C127#310411yescharacteristic
249C2×C127#310711yescharacteristic
250C2×#462C2×C12711yescharacteristic
251C2×C4×Q16C2×C12712yes—
252C4×C4⋊Q8C2×C12711yescharacteristic
253C42×Q8C2×C12711yescharacteristic
254#1981C2×C12711yescharacteristic
255#1947C2×C12711yescharacteristic
256#1928C2×C12712yes—
257#1878C2×C12712yes—
258#1803C2×C12711yescharacteristic
259C4×C4⋊C8C2×C12711yescharacteristic
260C4×#103C2×C12712yes—
261C127C4×#46211yescharacteristic, direct product factor, Sylow
262C22×Q16C22×C12712yes—
263C2×C4⋊Q8C22×C12711yescharacteristic
264C2×C4×Q8C22×C12712yes—
265C2×C4×Q8C22×C12711yescharacteristic
266C2×C4×Q8C22×C12711yescharacteristic
267C2×C4×Q8C22×C12711yescharacteristic
268#462C4×C12718yesdirect product factor
269C4×Q16—28no—
270C2×#107C22×C12712yes—
271C2×C4⋊C8C22×C12711yescharacteristic
272C2×C4⋊C8C22×C12711yescharacteristic
273C2×#103C22×C12712yes—
274C2×#103C22×C12712yes—
275C2×#103C22×C12712yes—
276C2×#103C22×C12712yes—
277C2×C4×C8C22×C12712yes—
278#391C22×C12712yes—
279#389—21no—
280#389—21no—
281#384C22×C12711yescharacteristic
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4C22×C12711yescharacteristic
288C4×C4⋊C4C22×C12711yescharacteristic
289C4×C4⋊C4C22×C12711yescharacteristic
290C43—21no—
291C43C22×C12711yescharacteristic
292#340C22×C12712yes—
293#340C22×C12712yes—
294#336C22×C12712yes—
295C22×Q8C23×C12712yes—
296C22×Q8C23×C12711yescharacteristic
297C2×Q16—24no—
298C2×Q16—24no—
299C2×Q16C2×C4×C12718yes—
300C22×C8C23×C12712yes—
301C22×C8C23×C12712yes—
302C4⋊Q8—22no—
303C4⋊Q8C2×C4×C12714yes—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—24no—
309C4×Q8—24no—
310C4×Q8C2×C4×C12714yes—
311C4×Q8D4×C12714yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C23×C12712yes—
321C2×C4⋊C4C23×C12711yescharacteristic
322C2×C4⋊C4C23×C12711yescharacteristic
323C2×C4⋊C4C23×C12711yescharacteristic
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—22no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42D4×C12711yescharacteristic
332C2×C42D4×C12711yescharacteristic
333C2×C42D4×C12711yescharacteristic
334C2×C42D4×C12711yescharacteristic
335C2×C42C23×C12711yescharacteristic
336C2×C42C23×C12711yescharacteristic
337C2×C42C23×C12711yescharacteristic
338#107—24no—
339C4⋊C8—22no—
340C4⋊C8C2×C4×C12714yes—
341#103—24no—
342#103—24no—
343#103—24no—
344#103C2×C4×C12718yes—
345C4×C8—24no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—22no—
350#95—22no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8C22×C4×C12714yes—
360C2×Q8C22×C4×C12712yes—
361C2×Q8C2×D4×C12712yes—
362C2×Q8#41×C12712yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4C2×D4×C12711yescharacteristic
372C22×C4C2×D4×C12711yescharacteristic
373C22×C4C2×D4×C12711yescharacteristic
374C22×C4C2×D4×C12711yescharacteristic
375C22×C4C24×C12711yescharacteristic
376Q16—216no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8C22×C4×C12714yes—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4C22×C4×C12712yes—
397C4⋊C4C2×D4×C12712yes—
398C4⋊C4#41×C12712yes—
399C42—24no—
400C42—24no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—21no—
405C42—21no—
406C42—41no—
407C42—42no—
408C42—44no—
409C42—42no—
410C42—42no—
411C42Q16×C12714yescomplemented
412C42C22×C4×C12712yes—
413C42C2×D4×C12712yes—
414C42#41×C12712yes—
415C42#41×C12712yes—
416C23C22×D4×C12711yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—22no—
420Q8—24no—
421Q8—24no—
422Q8—42no—
423Q8—42no—
424Q8C4×D4×C12714yes—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4C4×D4×C12712yes—
453C2×C4C4×D4×C12712yes—
454C2×C4#121×C12712yes—
455C2×C4#121×C12712yes—
456C2×C4C2×Q16×C12712yes—
457C2×C4C2×Q16×C12712yes—
458C2×C4C2×Q16×C12712yes—
459C2×C4#135×C12712yes—
460C2×C4#137×C12712yes—
461C2×C4C23×C4×C12711yescharacteristic
462C2×C4C22×D4×C12711yescharacteristic
463C2×C4C2×#41×C12711yescharacteristic
464C2×C4C2×#41×C12711yescharacteristic
465C2×C4C2×#41×C12711yescharacteristic
466C2×C4C2×#41×C12711yescharacteristic
467C8—24no—
468C8—42no—
469C22C2×C4×D4×C12711yescharacteristic
470C22C2×#121×C12711yescharacteristic
471C22#525×C12711yescharacteristic
472C22C22×Q16×C12711yescharacteristic
473C22C2×#135×C12711yescharacteristic
474C22C2×#137×C12711yescharacteristic
475C22#575×C12711yescharacteristic
476C4—22no—
477C4—22no—
478C4—22no—
479C4—24no—
480C4—41no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—44no—
485C4—82no—
486C4C4×Q16×C12714yescomplemented
487C4#462×C12714yesdirect product factor
488C4C2×C4×D4×C12711yescharacteristic
489C4C4×#41×C12711yescharacteristic
490C4#529×C12711yescharacteristic
491C4#532×C12711yescharacteristic
492C2C4×#121×C12711yescharacteristic
493C2C2×C4×Q16×C12711yescharacteristic
494C2C4×#137×C12711yescharacteristic
495C2C2×#462×C12711yescharacteristic
496C2C127×#303511yescharacteristic
497C2C127×#310411yescharacteristic
498C2C127×#310711yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socle, prime radicalC23×C127C22×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
18. #462×C127C4direct (N × H)
161. C42×C127Q16semidirect
236. C4×C127C4×Q16semidirect
237. C4×C127#462direct (N × H)
242. C4×#462C127direct (N × H)
261. C127C4×#462direct (N × H)
268. #462C4×C127direct (N × H)
411. C42Q16×C127semidirect
486. C4C4×Q16×C127semidirect
487. C4#462×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#462×C1272
C2×C4×Q16×C1272
C4×C4⋊Q8×C1272
C42×Q8×C1272
C127×#19812
C127×#19472
C127×#19282
C127×#18782
C127×#18032
C4×C4⋊C8×C1272
C4×#103×C1272
C4×#462127