Finite Group Databasebeta

← C127×#8409 #44572082

Subgroups — C127×#8409 #44572082

Order 32512.

972 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3449C211yesmaximal, characteristic
2C127×#1798C211yesmaximal, characteristic, complemented
3C127×#1540C212yesmaximal, complemented
4C127×#1480C212yesmaximal, complemented
5C127×#1458C211yesmaximal, characteristic, complemented
6C22×#41×C127—21no—
7#537×C127—21no—
8#537×C127C412yes—
9#536×C127—22no—
10#535×C127—22no—
11#534×C127—21no—
12#534×C127C412yes—
13#532×C127—21no—
14#532×C127C2212yes—
15#525×C127—24no—
16C2×#117×C127C2211yescharacteristic
17#431×C127C2212yescomplemented
18C2×C4⋊C8×C127C2211yescharacteristic, complemented
19C2×C4⋊C8×C127C2211yescharacteristic, complemented
20C2×C22⋊C8×C127—21no—
21#336×C127—21no—
22#332×C127—22no—
23#331×C127—22no—
24D4⋊C8×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—22no—
31C2×#41×C127—42no—
32C2×#41×C127—42no—
33C2×#41×C127—42no—
34C2×#41×C127—42no—
35C22×Q8×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C23×C4×C127—22no—
39C23×C4×C127D411yescharacteristic
40C22×C8×C127—21no—
41C22×C8×C127—21no—
42C4⋊Q8×C127—21no—
43C4⋊Q8×C127D412yes—
44#127×C127—21no—
45#127×C127D412yes—
46#124×C127—22no—
47#124×C127—22no—
48#123×C127—24no—
49#123×C127—24no—
50C22⋊Q8×C127—24no—
51C22⋊Q8×C127—24no—
52#121×C127—24no—
53#121×C127—24no—
54#121×C127—22no—
55#121×C127—22no—
56#121×C127—22no—
57#121×C127C2×C414yes—
58#120×C127—24no—
59#120×C127—24no—
60C4×D4×C127—22no—
61C4×D4×C127—22no—
62C4×D4×C127—22no—
63C4×D4×C127D414yes—
64#117×C127—22no—
65#117×C127—22no—
66C2×C4⋊C4×C127C2×C411yescharacteristic
67C2×C4⋊C4×C127D411yescharacteristic
68C2×C22⋊C4×C127C2×C411yescharacteristic
69C2×C22⋊C4×C127D411yescharacteristic
70C2×C42×C127D411yescharacteristic
71C2×C42×C127C2311yescharacteristic
72C4⋊C8×C127—22no—
73C4⋊C8×C127—22no—
74C4⋊C8×C127—22no—
75C22⋊C8×C127—22no—
76C22⋊C8×C127—42no—
77C4×C8×C127—22no—
78C24×C127—22no—
79C24×C127C22⋊C411yescharacteristic
80#41×C127—44no—
81#41×C127—44no—
82#41×C127—44no—
83#41×C127—44no—
84#41×C127—44no—
85#41×C127—44no—
86#41×C127—42no—
87#41×C127—42no—
88#41×C127—42no—
89#41×C127—42no—
90C2×Q8×C127—22no—
91C2×Q8×C127—22no—
92C2×Q8×C127—42no—
93C2×Q8×C127—42no—
94C2×D4×C127—24no—
95C2×D4×C127—22no—
96C2×D4×C127—24no—
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—42no—
102C2×D4×C127—42no—
103C2×D4×C127—44no—
104C2×D4×C127—44no—
105C2×D4×C127C22⋊C414yes—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—24no—
111C22×C4×C127—22no—
112C22×C4×C127—24no—
113C22×C4×C127—44no—
114C22×C4×C127—44no—
115C22×C4×C127C22⋊C411yescharacteristic
116C22×C4×C127C22⋊C411yescharacteristic
117C22×C4×C127C22⋊C411yescharacteristic
118C22×C4×C127D812yes—
119C22×C4×C127SD1612yes—
120C22×C4×C127C22×C411yescharacteristic
121C22×C4×C127C2×D411yescharacteristic
122C22×C4×C127C2×D411yescharacteristic
123C2×C8×C127—42no—
124C2×C8×C127—41no—
125C2×C8×C127—41no—
126C2×C8×C127—41no—
127C2×C8×C127—41no—
128C2×C8×C127—41no—
129C2×C8×C127—41no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127C22⋊C414yes—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—24no—
138C22⋊C4×C127—22no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—24no—
142C42×C127—21no—
143C42×C127—21no—
144C42×C127C2×D412yes—
145C42×C127C2×D412yes—
146C23×C127—21no—
147C23×C127—21no—
148C23×C127—24no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—44no—
152C23×C127—82no—
153C23×C127—82no—
154C23×C127#10212yes—
155C23×C127C2×C22⋊C411yescharacteristic
156Q8×C127—44no—
157Q8×C127—42no—
158Q8×C127—42no—
159D4×C127—44no—
160D4×C127—44no—
161D4×C127—48no—
162D4×C127—44no—
163D4×C127—44no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—82no—
167D4×C127—82no—
168D4×C127—82no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—21no—
176C2×C4×C127—21no—
177C2×C4×C127—24no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—48no—
181C2×C4×C127—44no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127#10212yes—
187C2×C4×C127C2×C22⋊C412yes—
188C2×C4×C127#12012yes—
189C2×C4×C127#12011yescharacteristic
190C2×C4×C127#12011yescharacteristic
191C2×C4×C127C2×D811yescharacteristic
192C2×C4×C127C2×SD1611yescharacteristic
193C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
195C8×C127—82no—
196C8×C127—81no—
197C8×C127—81no—
198C22×C127—21no—
199C22×C127—21no—
200C22×C127—22no—
201C22×C127—42no—
202C22×C127—41no—
203C22×C127—41no—
204C22×C127—44no—
205C22×C127—44no—
206C22×C127—44no—
207C22×C127—81no—
208C22×C127—88no—
209C22×C127#37911yescharacteristic
210C22×C127C2×#10211yescharacteristic
211C22×C127#41811yescharacteristic
212C4×C127—22no—
213C4×C127—22no—
214C4×C127—22no—
215C4×C127—41no—
216C4×C127—44no—
217C4×C127—41no—
218C4×C127#44711yescharacteristic
219C4×C127#44711yescharacteristic
220C4×C127#45011yescharacteristic
221C4×C127#45011yescharacteristic
222#8409C12711yesmaximal, characteristic, direct product factor, Sylow
223C2×C127—21no—
224C2×C127—21no—
225C2×C127—42no—
226C2×C127—84no—
227C2×C127#178611yescharacteristic
228C2×C127#179111yescharacteristic
229C2×C127#179411yescharacteristic
230#3449C2×C12711yescharacteristic
231#1798C2×C12711yescharacteristic, complemented
232#1540C2×C12712yescomplemented
233#1480C2×C12712yescomplemented
234#1458C2×C12711yescharacteristic, complemented
235C127#840911yescharacteristic, direct product factor, Sylow
236C22×#41—21no—
237#537—21no—
238#537C4×C12712yes—
239#536—22no—
240#535—22no—
241#534—21no—
242#534C4×C12712yes—
243#532—21no—
244#532C22×C12712yes—
245#525—24no—
246C2×#117C22×C12711yescharacteristic
247#431C22×C12712yescomplemented
248C2×C4⋊C8C22×C12711yescharacteristic, complemented
249C2×C4⋊C8C22×C12711yescharacteristic, complemented
250C2×C22⋊C8—21no—
251#336—21no—
252#332—22no—
253#331—22no—
254D4⋊C8—24no—
255#324—21no—
256#323—21no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—42no—
262C2×#41—42no—
263C2×#41—42no—
264C2×#41—42no—
265C22×Q8—21no—
266C22×D4—21no—
267C22×D4—22no—
268C23×C4—22no—
269C23×C4D4×C12711yescharacteristic
270C22×C8—21no—
271C22×C8—21no—
272C4⋊Q8—21no—
273C4⋊Q8D4×C12712yes—
274#127—21no—
275#127D4×C12712yes—
276#124—22no—
277#124—22no—
278#123—24no—
279#123—24no—
280C22⋊Q8—24no—
281C22⋊Q8—24no—
282#121—24no—
283#121—24no—
284#121—22no—
285#121—22no—
286#121—22no—
287#121C2×C4×C12714yes—
288#120—24no—
289#120—24no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4D4×C12714yes—
294#117—22no—
295#117—22no—
296C2×C4⋊C4C2×C4×C12711yescharacteristic
297C2×C4⋊C4D4×C12711yescharacteristic
298C2×C22⋊C4C2×C4×C12711yescharacteristic
299C2×C22⋊C4D4×C12711yescharacteristic
300C2×C42D4×C12711yescharacteristic
301C2×C42C23×C12711yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C22⋊C8—22no—
306C22⋊C8—42no—
307C4×C8—22no—
308C24—22no—
309C24C22⋊C4×C12711yescharacteristic
310#41—44no—
311#41—44no—
312#41—44no—
313#41—44no—
314#41—44no—
315#41—44no—
316#41—42no—
317#41—42no—
318#41—42no—
319#41—42no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×D4—24no—
325C2×D4—22no—
326C2×D4—24no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4C22⋊C4×C12714yes—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4C22⋊C4×C12711yescharacteristic
346C22×C4C22⋊C4×C12711yescharacteristic
347C22×C4C22⋊C4×C12711yescharacteristic
348C22×C4D8×C12712yes—
349C22×C4SD16×C12712yes—
350C22×C4C22×C4×C12711yescharacteristic
351C22×C4C2×D4×C12711yescharacteristic
352C22×C4C2×D4×C12711yescharacteristic
353C2×C8—42no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4C22⋊C4×C12714yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—22no—
371C22⋊C4—24no—
372C42—21no—
373C42—21no—
374C42C2×D4×C12712yes—
375C42C2×D4×C12712yes—
376C23—21no—
377C23—21no—
378C23—24no—
379C23—41no—
380C23—41no—
381C23—44no—
382C23—82no—
383C23—82no—
384C23#102×C12712yes—
385C23C2×C22⋊C4×C12711yescharacteristic
386Q8—44no—
387Q8—42no—
388Q8—42no—
389D4—44no—
390D4—44no—
391D4—48no—
392D4—44no—
393D4—44no—
394D4—42no—
395D4—42no—
396D4—82no—
397D4—82no—
398D4—82no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—48no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4#102×C12712yes—
417C2×C4C2×C22⋊C4×C12712yes—
418C2×C4#120×C12712yes—
419C2×C4#120×C12711yescharacteristic
420C2×C4#120×C12711yescharacteristic
421C2×C4C2×D8×C12711yescharacteristic
422C2×C4C2×SD16×C12711yescharacteristic
423C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
424C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
425C8—82no—
426C8—81no—
427C8—81no—
428C22—21no—
429C22—21no—
430C22—22no—
431C22—42no—
432C22—41no—
433C22—41no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—81no—
438C22—88no—
439C22#379×C12711yescharacteristic
440C22C2×#102×C12711yescharacteristic
441C22#418×C12711yescharacteristic
442C4—22no—
443C4—22no—
444C4—22no—
445C4—44no—
446C4—41no—
447C4—41no—
448C4#447×C12711yescharacteristic
449C4#447×C12711yescharacteristic
450C4#450×C12711yescharacteristic
451C4#450×C12711yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—84no—
456C2C127×#178611yescharacteristic
457C2C127×#179111yescharacteristic
458C2C127×#179411yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#379
prime radicalC127×#3449C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1798C2semidirect
3. C127×#1540C2semidirect
4. C127×#1480C2semidirect
5. C127×#1458C2semidirect
17. #431×C127C22semidirect
18. C2×C4⋊C8×C127C22semidirect
19. C2×C4⋊C8×C127C22semidirect
222. #8409C127direct (N × H)
231. #1798C2×C127semidirect
232. #1540C2×C127semidirect
233. #1480C2×C127semidirect
234. #1458C2×C127semidirect
235. C127#8409direct (N × H)
247. #431C22×C127semidirect
248. C2×C4⋊C8C22×C127semidirect
249. C2×C4⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34492
C127×#17982
C127×#15402
C127×#14802
C127×#14582
#8409127