Finite Group Databasebeta

← C127×#8424 #44572097

Subgroups — C127×#8424 #44572097

Order 32512.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3503C211yesmaximal, characteristic
2C127×#1987C211yesmaximal, characteristic, complemented
3C127×#1806C211yesmaximal, characteristic
4C127×#1550C211yesmaximal, characteristic, complemented
5C127×#1549C211yesmaximal, characteristic, complemented
6C127×#1503C211yesmaximal, characteristic, complemented
7C127×#1477C211yesmaximal, characteristic
8Q82×C127—21no—
9#557×C127C412yescomplemented
10#554×C127—21no—
11#554×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127C412yescomplemented
14#544×C127—22no—
15#544×C127—21no—
16#533×C127—21no—
17#533×C127C2211yescharacteristic
18C2×C4⋊Q8×C127—21no—
19C2×C4⋊Q8×C127C2211yescharacteristic
20#520×C127—21no—
21C4×#41×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×#104×C127—21no—
26C4×C4⋊C4×C127C2211yescharacteristic
27#340×C127—22no—
28#339×C127—21no—
29#333×C127—21no—
30#332×C127—22no—
31#332×C127—21no—
32#328×C127—22no—
33Q8⋊C8×C127—21no—
34D4⋊C8×C127—21no—
35C2×#41×C127D411yescharacteristic
36C22×Q8×C127—22no—
37C22×Q8×C127—21no—
38C2×M16×C127—21no—
39C22×C8×C127—21no—
40C4⋊Q8×C127—22no—
41C4⋊Q8×C127—22no—
42C4⋊Q8×C127—24no—
43C4⋊Q8×C127—22no—
44C4⋊Q8×C127—22no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127C2×C412yes—
48C4⋊Q8×C127D411yescharacteristic
49C4⋊Q8×C127D412yes—
50C4⋊Q8×C127D411yescharacteristic
51#125×C127—22no—
52#125×C127—24no—
53#125×C127—22no—
54#125×C127—21no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—24no—
57C22⋊Q8×C127—24no—
58C22⋊Q8×C127—21no—
59C22⋊Q8×C127—22no—
60C22⋊Q8×C127—24no—
61C22⋊Q8×C127D412yes—
62C4×Q8×C127—22no—
63C4×Q8×C127—22no—
64C4×Q8×C127—22no—
65C4×Q8×C127—21no—
66C4×Q8×C127C2×C411yescharacteristic
67C4×Q8×C127C2×C412yes—
68C4×Q8×C127D411yescharacteristic
69C4×D4×C127—24no—
70C4×D4×C127—22no—
71C4×D4×C127—21no—
72C4×D4×C127—21no—
73C4×D4×C127C2×C411yescharacteristic
74C4×D4×C127D411yescharacteristic
75#117×C127—22no—
76#117×C127—21no—
77#117×C127—21no—
78#117×C127D411yescharacteristic
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127D412yes—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92#104×C127—42no—
93C22⋊C8×C127—21no—
94C4×C8×C127—21no—
95#95×C127—21no—
96#41×C127—21no—
97#41×C127—21no—
98#41×C127SD1612yes—
99#41×C127Q1612yes—
100C2×Q8×C127—24no—
101C2×Q8×C127—22no—
102C2×Q8×C127—21no—
103C2×Q8×C127—22no—
104C2×Q8×C127—82no—
105C2×Q8×C127—84no—
106C2×Q8×C127C22⋊C411yescharacteristic
107C2×Q8×C127C22⋊C412yes—
108C2×D4×C127—21no—
109C2×D4×C127C22⋊C411yescharacteristic
110C22×C4×C127—21no—
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—41no—
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119M16×C127—41no—
120M16×C127—41no—
121C2×C8×C127—42no—
122C2×C8×C127—41no—
123C2×C8×C127—41no—
124C2×C8×C127—41no—
125C4⋊C4×C127—24no—
126C4⋊C4×C127—24no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—24no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—41no—
141C4⋊C4×C127C22⋊C414yes—
142C4⋊C4×C127C22⋊C411yescharacteristic
143C4⋊C4×C127C22⋊C411yescharacteristic
144C4⋊C4×C127C22⋊C412yes—
145C22⋊C4×C127—24no—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—21no—
148C22⋊C4×C127—21no—
149C22⋊C4×C127—21no—
150C42×C127—24no—
151C42×C127—21no—
152C42×C127—22no—
153C42×C127—21no—
154C42×C127—21no—
155C42×C127—41no—
156C42×C127—41no—
157C42×C127C22×C411yescharacteristic
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C42×C127C2×D411yescharacteristic
161C23×C127—21no—
162C23×C127#12011yescharacteristic
163Q8×C127—21no—
164Q8×C127—42no—
165Q8×C127—44no—
166Q8×C127—41no—
167Q8×C127—41no—
168Q8×C127—82no—
169Q8×C127—84no—
170Q8×C127#10312yes—
171D4×C127—22no—
172D4×C127—22no—
173D4×C127—21no—
174D4×C127#10312yes—
175C2×C4×C127—21no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—22no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
183C2×C4×C127—22no—
184C2×C4×C127—24no—
185C2×C4×C127—41no—
186C2×C4×C127—42no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—42no—
190C2×C4×C127—82no—
191C2×C4×C127—84no—
192C2×C4×C127—81no—
193C2×C4×C127—81no—
194C2×C4×C127C2×C22⋊C411yescharacteristic
195C2×C4×C127C2×C22⋊C411yescharacteristic
196C2×C4×C127C2×C22⋊C411yescharacteristic
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127C2×SD1611yescharacteristic
201C2×C4×C127C2×Q1611yescharacteristic
202C2×C4×C127#13711yescharacteristic
203C2×C4×C127#13711yescharacteristic
204C8×C127—81no—
205C8×C127—81no—
206C8×C127—81no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—22no—
210C22×C127—41no—
211C22×C127—41no—
212C22×C127#37911yescharacteristic
213C22×C127#44811yescharacteristic
214C22×C127#45111yescharacteristic
215C4×C127—21no—
216C4×C127—21no—
217C4×C127—21no—
218C4×C127—22no—
219C4×C127—41no—
220C4×C127—42no—
221C4×C127—41no—
222C4×C127—44no—
223C4×C127—42no—
224C4×C127—82no—
225C4×C127C2×#10311yescharacteristic
226C4×C127#41911yescharacteristic
227C4×C127#44811yescharacteristic
228C4×C127#45111yescharacteristic
229C4×C127#45411yescharacteristic
230C4×C127#45611yescharacteristic
231#8424C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—21no—
233C2×C127—21no—
234C2×C127—42no—
235C2×C127#178711yescharacteristic
236C2×C127#179311yescharacteristic
237C2×C127#179511yescharacteristic
238#3503C2×C12711yescharacteristic
239#1987C2×C12711yescharacteristic, complemented
240#1806C2×C12711yescharacteristic
241#1550C2×C12711yescharacteristic, complemented
242#1549C2×C12711yescharacteristic, complemented
243#1503C2×C12711yescharacteristic, complemented
244#1477C2×C12711yescharacteristic
245C127#842411yescharacteristic, direct product factor, Sylow
246Q82—21no—
247#557C4×C12712yescomplemented
248#554—21no—
249#554—22no—
250D4×Q8—22no—
251D4×Q8C4×C12712yescomplemented
252#544—22no—
253#544—21no—
254#533—21no—
255#533C22×C12711yescharacteristic
256C2×C4⋊Q8—21no—
257C2×C4⋊Q8C22×C12711yescharacteristic
258#520—21no—
259C4×#41C22×C12711yescharacteristic
260#431C22×C12711yescharacteristic
261#423C22×C12711yescharacteristic
262C2×C4⋊C8C22×C12711yescharacteristic
263C2×#104—21no—
264C4×C4⋊C4C22×C12711yescharacteristic
265#340—22no—
266#339—21no—
267#333—21no—
268#332—22no—
269#332—21no—
270#328—22no—
271Q8⋊C8—21no—
272D4⋊C8—21no—
273C2×#41D4×C12711yescharacteristic
274C22×Q8—22no—
275C22×Q8—21no—
276C2×M16—21no—
277C22×C8—21no—
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C4⋊Q8—24no—
281C4⋊Q8—22no—
282C4⋊Q8—22no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8C2×C4×C12712yes—
286C4⋊Q8D4×C12711yescharacteristic
287C4⋊Q8D4×C12712yes—
288C4⋊Q8D4×C12711yescharacteristic
289#125—22no—
290#125—24no—
291#125—22no—
292#125—21no—
293C22⋊Q8—22no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296C22⋊Q8—21no—
297C22⋊Q8—22no—
298C22⋊Q8—24no—
299C22⋊Q8D4×C12712yes—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—21no—
304C4×Q8C2×C4×C12711yescharacteristic
305C4×Q8C2×C4×C12712yes—
306C4×Q8D4×C12711yescharacteristic
307C4×D4—24no—
308C4×D4—22no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4C2×C4×C12711yescharacteristic
312C4×D4D4×C12711yescharacteristic
313#117—22no—
314#117—21no—
315#117—21no—
316#117D4×C12711yescharacteristic
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4D4×C12712yes—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42C23×C12711yescharacteristic
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330#104—42no—
331C22⋊C8—21no—
332C4×C8—21no—
333#95—21no—
334#41—21no—
335#41—21no—
336#41SD16×C12712yes—
337#41Q16×C12712yes—
338C2×Q8—24no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—82no—
343C2×Q8—84no—
344C2×Q8C22⋊C4×C12711yescharacteristic
345C2×Q8C22⋊C4×C12712yes—
346C2×D4—21no—
347C2×D4C22⋊C4×C12711yescharacteristic
348C22×C4—21no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4C2×D4×C12711yescharacteristic
355C22×C4C2×D4×C12711yescharacteristic
356C22×C4C2×D4×C12711yescharacteristic
357M16—41no—
358M16—41no—
359C2×C8—42no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—41no—
379C4⋊C4C22⋊C4×C12714yes—
380C4⋊C4C22⋊C4×C12711yescharacteristic
381C4⋊C4C22⋊C4×C12711yescharacteristic
382C4⋊C4C22⋊C4×C12712yes—
383C22⋊C4—24no—
384C22⋊C4—22no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C42—24no—
389C42—21no—
390C42—22no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42—41no—
395C42C22×C4×C12711yescharacteristic
396C42C2×D4×C12711yescharacteristic
397C42C2×D4×C12711yescharacteristic
398C42C2×D4×C12711yescharacteristic
399C23—21no—
400C23#120×C12711yescharacteristic
401Q8—21no—
402Q8—42no—
403Q8—44no—
404Q8—41no—
405Q8—41no—
406Q8—82no—
407Q8—84no—
408Q8#103×C12712yes—
409D4—22no—
410D4—22no—
411D4—21no—
412D4#103×C12712yes—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—84no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4C2×C22⋊C4×C12711yescharacteristic
433C2×C4C2×C22⋊C4×C12711yescharacteristic
434C2×C4C2×C22⋊C4×C12711yescharacteristic
435C2×C4#120×C12711yescharacteristic
436C2×C4#120×C12711yescharacteristic
437C2×C4#120×C12711yescharacteristic
438C2×C4C2×SD16×C12711yescharacteristic
439C2×C4C2×Q16×C12711yescharacteristic
440C2×C4#137×C12711yescharacteristic
441C2×C4#137×C12711yescharacteristic
442C8—81no—
443C8—81no—
444C8—81no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22#379×C12711yescharacteristic
451C22#448×C12711yescharacteristic
452C22#451×C12711yescharacteristic
453C4—22no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—41no—
458C4—42no—
459C4—41no—
460C4—44no—
461C4—42no—
462C4—82no—
463C4C2×#103×C12711yescharacteristic
464C4#419×C12711yescharacteristic
465C4#448×C12711yescharacteristic
466C4#451×C12711yescharacteristic
467C4#454×C12711yescharacteristic
468C4#456×C12711yescharacteristic
469C2—21no—
470C2—21no—
471C2—42no—
472C2C127×#178711yescharacteristic
473C2C127×#179311yescharacteristic
474C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1987C2semidirect
4. C127×#1550C2semidirect
5. C127×#1549C2semidirect
6. C127×#1503C2semidirect
9. #557×C127C4semidirect
13. D4×Q8×C127C4semidirect
231. #8424C127direct (N × H)
239. #1987C2×C127semidirect
241. #1550C2×C127semidirect
242. #1549C2×C127semidirect
243. #1503C2×C127semidirect
245. C127#8424direct (N × H)
247. #557C4×C127semidirect
251. D4×Q8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35032
C127×#19872
C127×#18062
C127×#15502
C127×#15492
C127×#15032
C127×#14772
#8424127