Finite Group Databasebeta

← C127×#8475 #44572148

Subgroups — C127×#8475 #44572148

Order 32512.

932 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3500C211yesmaximal, characteristic
2C127×#1543C211yesmaximal, characteristic, complemented
3C127×#1536C211yesmaximal, characteristic, complemented
4C127×#1488C212yesmaximal, complemented
5C127×#1469C212yesmaximal, complemented
6C2×2−1+4×C127C411yescharacteristic
7C2×H(5,𝔽2)×C127C411yescharacteristic
8#548×C127—22no—
9#546×C127—22no—
10#546×C127—24no—
11#536×C127—21no—
12#536×C127C411yescharacteristic
13#535×C127—21no—
14#535×C127C411yescharacteristic
15#532×C127—21no—
16#532×C127C2211yescharacteristic
17C2×#124×C127—21no—
18C2×#124×C127C2211yescharacteristic
19C4×#41×C127C2211yescharacteristic
20#432×C127C2212yescomplemented
21#431×C127C2212yescomplemented
22#333×C127—21no—
23#331×C127—21no—
24#329×C127—21no—
25#329×C127—21no—
26Q8⋊C8×C127—22no—
27D4⋊C8×C127—22no—
28#323×C127—24no—
292−1+4×C127—42no—
302−1+4×C127—42no—
31H(5,𝔽2)×C127—42no—
32H(5,𝔽2)×C127—42no—
33C2×#41×C127—21no—
34C2×#41×C127—21no—
35C2×#41×C127—21no—
36C2×#41×C127—21no—
37C2×#41×C127—22no—
38C2×#41×C127C2×C411yescharacteristic
39C2×#41×C127C2×C411yescharacteristic
40C2×#41×C127C2×C411yescharacteristic
41C22×Q8×C127—21no—
42C22×Q8×C127—21no—
43C22×Q8×C127C2×C411yescharacteristic
44C22×D4×C127—22no—
45C22×D4×C127—21no—
46C22×D4×C127—21no—
47C22×D4×C127C2×C411yescharacteristic
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127D411yescharacteristic
50#127×C127—21no—
51#127×C127D411yescharacteristic
52#124×C127—24no—
53#124×C127—21no—
54#124×C127—21no—
55#124×C127—21no—
56#124×C127—21no—
57#124×C127—22no—
58#124×C127D411yescharacteristic
59#124×C127D411yescharacteristic
60#123×C127—24no—
61#123×C127—22no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127—22no—
64#121×C127—24no—
65#121×C127—24no—
66#121×C127—22no—
67#121×C127—22no—
68#120×C127—24no—
69#120×C127—22no—
70C4×Q8×C127D412yes—
71C4×D4×C127—24no—
72C4×D4×C127—22no—
73C4×D4×C127—22no—
74C4×D4×C127D412yes—
75#117×C127—21no—
76#117×C127C2×C411yescharacteristic
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127D414yes—
79C2×C42×C127—21no—
80C2×C42×C127C2311yescharacteristic
81C4⋊C8×C127—22no—
82C4⋊C8×C127—22no—
83C22⋊C8×C127—22no—
84C22⋊C8×C127—22no—
85#97×C127—22no—
86C4×C8×C127—22no—
87C24×C127—22no—
88C24×C127C22⋊C412yes—
89#41×C127—22no—
90#41×C127—22no—
91#41×C127—44no—
92#41×C127—44no—
93#41×C127—41no—
94#41×C127—41no—
95#41×C127—41no—
96#41×C127—41no—
97#41×C127—48no—
98#41×C127—42no—
99#41×C127—42no—
100#41×C127—42no—
101#41×C127—42no—
102C2×Q8×C127—22no—
103C2×Q8×C127—21no—
104C2×Q8×C127—21no—
105C2×Q8×C127—41no—
106C2×Q8×C127—41no—
107C2×Q8×C127—44no—
108C2×Q8×C127—42no—
109C2×Q8×C127—42no—
110C2×Q8×C127C22⋊C411yescharacteristic
111C2×Q8×C127C22⋊C411yescharacteristic
112C2×Q8×C127C22⋊C411yescharacteristic
113C2×D4×C127—21no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—22no—
117C2×D4×C127—21no—
118C2×D4×C127—21no—
119C2×D4×C127—24no—
120C2×D4×C127—21no—
121C2×D4×C127—21no—
122C2×D4×C127—22no—
123C2×D4×C127—44no—
124C2×D4×C127—41no—
125C2×D4×C127—41no—
126C2×D4×C127—48no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127C22⋊C411yescharacteristic
130C2×D4×C127C22⋊C411yescharacteristic
131C2×D4×C127C22⋊C411yescharacteristic
132C22×C4×C127—21no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—22no—
139C22×C4×C127C22⋊C412yes—
140C22×C4×C127C22×C411yescharacteristic
141C22×C4×C127C2×D412yes—
142C2×C8×C127—42no—
143C2×C8×C127—42no—
144C4⋊C4×C127—24no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127C22⋊C412yes—
148C22⋊C4×C127—24no—
149C22⋊C4×C127—24no—
150C22⋊C4×C127—21no—
151C22⋊C4×C127—22no—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—24no—
154C22⋊C4×C127—22no—
155C22⋊C4×C127—22no—
156C42×C127—21no—
157C42×C127—22no—
158C42×C127C2×D412yes—
159C42×C127C2×D411yescharacteristic
160C42×C127C2×D411yescharacteristic
161C23×C127—21no—
162C23×C127—22no—
163C23×C127—21no—
164C23×C127—21no—
165C23×C127—44no—
166C23×C127—42no—
167C23×C127—44no—
168C23×C127—84no—
169C23×C127C2×C22⋊C411yescharacteristic
170Q8×C127—21no—
171Q8×C127—41no—
172Q8×C127—41no—
173Q8×C127—42no—
174Q8×C127—44no—
175Q8×C127—41no—
176Q8×C127—41no—
177Q8×C127#10012yes—
178D4×C127—24no—
179D4×C127—21no—
180D4×C127—41no—
181D4×C127—41no—
182D4×C127—42no—
183D4×C127—44no—
184D4×C127—42no—
185D4×C127—44no—
186D4×C127—42no—
187D4×C127—44no—
188D4×C127—41no—
189D4×C127—41no—
190D4×C127—82no—
191D4×C127—84no—
192D4×C127#10012yes—
193C2×C4×C127—24no—
194C2×C4×C127—21no—
195C2×C4×C127—21no—
196C2×C4×C127—21no—
197C2×C4×C127—22no—
198C2×C4×C127—21no—
199C2×C4×C127—22no—
200C2×C4×C127—21no—
201C2×C4×C127—42no—
202C2×C4×C127—44no—
203C2×C4×C127—44no—
204C2×C4×C127—44no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—42no—
210C2×C4×C127—82no—
211C2×C4×C127C2×C22⋊C411yescharacteristic
212C2×C4×C127C2×C22⋊C411yescharacteristic
213C2×C4×C127#12012yes—
214C2×C4×C127#12012yes—
215C8×C127—82no—
216C8×C127—82no—
217C22×C127—22no—
218C22×C127—21no—
219C22×C127—22no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—44no—
223C22×C127—42no—
224C22×C127—41no—
225C22×C127—42no—
226C22×C127—41no—
227C22×C127—162no—
228C22×C127—164no—
229C22×C127#37911yescharacteristic
230C4×C127—22no—
231C4×C127—22no—
232C4×C127—21no—
233C4×C127—22no—
234C4×C127—42no—
235C4×C127—41no—
236C4×C127—41no—
237C4×C127—42no—
238C4×C127C2×#10011yescharacteristic
239C4×C127C2×#10011yescharacteristic
240#8475C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—41no—
242C2×C127—42no—
243C2×C127—81no—
244C2×C127—82no—
245C2×C127—81no—
246C2×C127#178311yescharacteristic
247C2×C127#179412yes—
248#3500C2×C12711yescharacteristic
249#1543C2×C12711yescharacteristic, complemented
250#1536C2×C12711yescharacteristic, complemented
251#1488C2×C12712yescomplemented
252#1469C2×C12712yescomplemented
253C127#847511yescharacteristic, direct product factor, Sylow
254C2×2−1+4C4×C12711yescharacteristic
255C2×H(5,𝔽2)C4×C12711yescharacteristic
256#548—22no—
257#546—22no—
258#546—24no—
259#536—21no—
260#536C4×C12711yescharacteristic
261#535—21no—
262#535C4×C12711yescharacteristic
263#532—21no—
264#532C22×C12711yescharacteristic
265C2×#124—21no—
266C2×#124C22×C12711yescharacteristic
267C4×#41C22×C12711yescharacteristic
268#432C22×C12712yescomplemented
269#431C22×C12712yescomplemented
270#333—21no—
271#331—21no—
272#329—21no—
273#329—21no—
274Q8⋊C8—22no—
275D4⋊C8—22no—
276#323—24no—
2772−1+4—42no—
2782−1+4—42no—
279H(5,𝔽2)—42no—
280H(5,𝔽2)—42no—
281C2×#41—21no—
282C2×#41—21no—
283C2×#41—21no—
284C2×#41—21no—
285C2×#41—22no—
286C2×#41C2×C4×C12711yescharacteristic
287C2×#41C2×C4×C12711yescharacteristic
288C2×#41C2×C4×C12711yescharacteristic
289C22×Q8—21no—
290C22×Q8—21no—
291C22×Q8C2×C4×C12711yescharacteristic
292C22×D4—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4C2×C4×C12711yescharacteristic
296C4⋊Q8—21no—
297C4⋊Q8D4×C12711yescharacteristic
298#127—21no—
299#127D4×C12711yescharacteristic
300#124—24no—
301#124—21no—
302#124—21no—
303#124—21no—
304#124—21no—
305#124—22no—
306#124D4×C12711yescharacteristic
307#124D4×C12711yescharacteristic
308#123—24no—
309#123—22no—
310C22⋊Q8—24no—
311C22⋊Q8—22no—
312#121—24no—
313#121—24no—
314#121—22no—
315#121—22no—
316#120—24no—
317#120—22no—
318C4×Q8D4×C12712yes—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4D4×C12712yes—
323#117—21no—
324#117C2×C4×C12711yescharacteristic
325C2×C22⋊C4—24no—
326C2×C22⋊C4D4×C12714yes—
327C2×C42—21no—
328C2×C42C23×C12711yescharacteristic
329C4⋊C8—22no—
330C4⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8—22no—
333#97—22no—
334C4×C8—22no—
335C24—22no—
336C24C22⋊C4×C12712yes—
337#41—22no—
338#41—22no—
339#41—44no—
340#41—44no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—48no—
346#41—42no—
347#41—42no—
348#41—42no—
349#41—42no—
350C2×Q8—22no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—44no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8C22⋊C4×C12711yescharacteristic
359C2×Q8C22⋊C4×C12711yescharacteristic
360C2×Q8C22⋊C4×C12711yescharacteristic
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—24no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—44no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—48no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4C22⋊C4×C12711yescharacteristic
378C2×D4C22⋊C4×C12711yescharacteristic
379C2×D4C22⋊C4×C12711yescharacteristic
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4C22⋊C4×C12712yes—
388C22×C4C22×C4×C12711yescharacteristic
389C22×C4C2×D4×C12712yes—
390C2×C8—42no—
391C2×C8—42no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4C22⋊C4×C12712yes—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—21no—
399C22⋊C4—22no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C42—21no—
405C42—22no—
406C42C2×D4×C12712yes—
407C42C2×D4×C12711yescharacteristic
408C42C2×D4×C12711yescharacteristic
409C23—21no—
410C23—22no—
411C23—21no—
412C23—21no—
413C23—44no—
414C23—42no—
415C23—44no—
416C23—84no—
417C23C2×C22⋊C4×C12711yescharacteristic
418Q8—21no—
419Q8—41no—
420Q8—41no—
421Q8—42no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8#100×C12712yes—
426D4—24no—
427D4—21no—
428D4—41no—
429D4—41no—
430D4—42no—
431D4—44no—
432D4—42no—
433D4—44no—
434D4—42no—
435D4—44no—
436D4—41no—
437D4—41no—
438D4—82no—
439D4—84no—
440D4#100×C12712yes—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4C2×C22⋊C4×C12711yescharacteristic
460C2×C4C2×C22⋊C4×C12711yescharacteristic
461C2×C4#120×C12712yes—
462C2×C4#120×C12712yes—
463C8—82no—
464C8—82no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—41no—
470C22—42no—
471C22—41no—
472C22—42no—
473C22—44no—
474C22—42no—
475C22—162no—
476C22—164no—
477C22#379×C12711yescharacteristic
478C4—21no—
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—42no—
485C4—42no—
486C4C2×#100×C12711yescharacteristic
487C4C2×#100×C12711yescharacteristic
488C2—41no—
489C2—42no—
490C2—81no—
491C2—82no—
492C2—81no—
493C2C127×#178311yescharacteristic
494C2C127×#179412yes—
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3500C2
LCSG ▷ C22×C4 ▷ 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×#1543C2semidirect
3. C127×#1536C2semidirect
4. C127×#1488C2semidirect
5. C127×#1469C2semidirect
20. #432×C127C22semidirect
21. #431×C127C22semidirect
240. #8475C127direct (N × H)
249. #1543C2×C127semidirect
250. #1536C2×C127semidirect
251. #1488C2×C127semidirect
252. #1469C2×C127semidirect
253. C127#8475direct (N × H)
268. #432C22×C127semidirect
269. #431C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35002
C127×#15432
C127×#15362
C127×#14882
C127×#14692
#8475127