Finite Group Databasebeta

← C127×#8358 #44572031

Subgroups — C127×#8358 #44572031

Order 32512.

794 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×#3506C211yesmaximal, characteristic
2C127×#1954C211yesmaximal, characteristic, complemented
3C127×#1800C211yesmaximal, characteristic, complemented
4C127×#1550C211yesmaximal, characteristic, complemented
5C127×#1547C211yesmaximal, characteristic, complemented
6C127×#1493C211yesmaximal, characteristic, complemented
7C127×#1492C211yesmaximal, characteristic, complemented
8#559×C127—22no—
9#556×C127—21no—
10#555×C127—21no—
11#553×C127—22no—
12#550×C127—21no—
13#547×C127—21no—
14#538×C127C414yes—
15#535×C127—21no—
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#525×C127—22no—
19#520×C127—21no—
20C2×C4×D4×C127C2211yescharacteristic
21#423×C127C2211yescharacteristic
22#423×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#100×C127—21no—
25C2×C22⋊C8×C127—22no—
26C2×C4×C8×C127C2211yescharacteristic
27#343×C127—21no—
28#333×C127—21no—
29#332×C127—21no—
30#332×C127—21no—
31#331×C127—21no—
32Q8⋊C8×C127—22no—
33D4⋊C8×C127—22no—
34C2×#41×C127—22no—
35C2×#41×C127—21no—
36C22×D4×C127D411yescharacteristic
37C23×C4×C127D412yes—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C22×C8×C127—21no—
41C22×C8×C127—21no—
42C4⋊Q8×C127D411yescharacteristic
43C4⋊Q8×C127D411yescharacteristic
44C4⋊Q8×C127D411yescharacteristic
45#127×C127—22no—
46#127×C127D411yescharacteristic
47#126×C127—24no—
48#125×C127—21no—
49#124×C127—22no—
50#124×C127—24no—
51#124×C127—21no—
52#123×C127—24no—
53#123×C127—24no—
54C22⋊Q8×C127—22no—
55C22⋊Q8×C127—21no—
56C22⋊Q8×C127C2×C412yes—
57#121×C127—22no—
58#121×C127—22no—
59#121×C127—22no—
60#121×C127—24no—
61#121×C127—21no—
62#121×C127C2×C412yes—
63#120×C127—24no—
64C4×Q8×C127—22no—
65C4×Q8×C127—21no—
66C4×Q8×C127D412yes—
67C4×D4×C127—22no—
68C4×D4×C127—24no—
69C4×D4×C127—24no—
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127—21no—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127D412yes—
76#117×C127—22no—
77#117×C127—22no—
78#117×C127—21no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127D411yescharacteristic
81C2×C22⋊C4×C127C2×C412yes—
82C2×C42×C127C2311yescharacteristic
83C4⋊C8×C127—21no—
84C4⋊C8×C127—21no—
85C4⋊C8×C127—21no—
86C4⋊C8×C127—21no—
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89#100×C127—42no—
90C22⋊C8×C127—44no—
91C4×C8×C127—21no—
92C4×C8×C127—21no—
93C24×C127C22⋊C412yes—
94#41×C127—41no—
95#41×C127—41no—
96#41×C127—41no—
97#41×C127—41no—
98#41×C127—82no—
99#41×C127—82no—
100C2×Q8×C127—21no—
101C2×Q8×C127—21no—
102C2×Q8×C127C22⋊C412yes—
103C2×D4×C127—22no—
104C2×D4×C127—24no—
105C2×D4×C127—24no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—21no—
112C2×D4×C127—21no—
113C2×D4×C127—21no—
114C2×D4×C127C22⋊C412yes—
115C22×C4×C127—24no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—42no—
120C22×C4×C127—42no—
121C22×C4×C127C22⋊C412yes—
122C22×C4×C127C22×C411yescharacteristic
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125M16×C127—41no—
126M16×C127—41no—
127M16×C127—41no—
128M16×C127—41no—
129C2×C8×C127—22no—
130C2×C8×C127—41no—
131C2×C8×C127—41no—
132C2×C8×C127—42no—
133C2×C8×C127—41no—
134C2×C8×C127—41no—
135C2×C8×C127—41no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127C22⋊C412yes—
146C4⋊C4×C127C22⋊C412yes—
147C22⋊C4×C127—24no—
148C22⋊C4×C127—24no—
149C22⋊C4×C127—24no—
150C22⋊C4×C127—22no—
151C22⋊C4×C127—22no—
152C22⋊C4×C127—22no—
153C22⋊C4×C127—22no—
154C22⋊C4×C127—22no—
155C42×C127—24no—
156C42×C127—22no—
157C42×C127C2×D411yescharacteristic
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C42×C127C2×D411yescharacteristic
161C23×C127—22no—
162C23×C127—22no—
163C23×C127—22no—
164C23×C127—22no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127C2×C22⋊C411yescharacteristic
168Q8×C127—42no—
169Q8×C127—41no—
170Q8×C127—41no—
171Q8×C127—41no—
172Q8×C127—41no—
173D4×C127—42no—
174D4×C127—42no—
175D4×C127—42no—
176D4×C127—41no—
177D4×C127—41no—
178D4×C127—41no—
179D4×C127—41no—
180D4×C127—41no—
181D4×C127—41no—
182D4×C127—41no—
183D4×C127—41no—
184D4×C127—84no—
185D4×C127—84no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—41no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—82no—
199C2×C4×C127—84no—
200C2×C4×C127C2×C22⋊C411yescharacteristic
201C2×C4×C127C2×C22⋊C411yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127#12011yescharacteristic
205C2×C4×C127#12011yescharacteristic
206C2×C4×C127#13511yescharacteristic
207C2×C4×C127#13511yescharacteristic
208C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C127#13711yescharacteristic
210C8×C127—42no—
211C8×C127—81no—
212C8×C127—81no—
213C8×C127—81no—
214C22×C127—21no—
215C22×C127—21no—
216C22×C127—44no—
217C22×C127—42no—
218C22×C127—42no—
219C22×C127—42no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—42no—
223C22×C127—82no—
224C22×C127#37911yescharacteristic
225C22×C127#41611yescharacteristic
226C22×C127#41711yescharacteristic
227C4×C127—21no—
228C4×C127—21no—
229C4×C127—21no—
230C4×C127—42no—
231C4×C127—42no—
232C4×C127—42no—
233C4×C127—42no—
234C4×C127#44911yescharacteristic
235C4×C127#44911yescharacteristic
236C4×C127#45211yescharacteristic
237C4×C127#45211yescharacteristic
238C4×C127#45311yescharacteristic
239C4×C127#45511yescharacteristic
240#8358C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—21no—
242C2×C127—21no—
243C2×C127—82no—
244C2×C127—82no—
245C2×C127#178811yescharacteristic
246C2×C127#179111yescharacteristic
247C2×C127#179211yescharacteristic
248#3506C2×C12711yescharacteristic
249#1954C2×C12711yescharacteristic, complemented
250#1800C2×C12711yescharacteristic, complemented
251#1550C2×C12711yescharacteristic, complemented
252#1547C2×C12711yescharacteristic, complemented
253#1493C2×C12711yescharacteristic, complemented
254#1492C2×C12711yescharacteristic, complemented
255C127#835811yescharacteristic, direct product factor, Sylow
256#559—22no—
257#556—21no—
258#555—21no—
259#553—22no—
260#550—21no—
261#547—21no—
262#538C4×C12714yes—
263#535—21no—
264#533C22×C12711yescharacteristic
265#532C22×C12711yescharacteristic
266#525—22no—
267#520—21no—
268C2×C4×D4C22×C12711yescharacteristic
269#423C22×C12711yescharacteristic
270#423C22×C12711yescharacteristic
271C2×C4⋊C8C22×C12711yescharacteristic
272C2×#100—21no—
273C2×C22⋊C8—22no—
274C2×C4×C8C22×C12711yescharacteristic
275#343—21no—
276#333—21no—
277#332—21no—
278#332—21no—
279#331—21no—
280Q8⋊C8—22no—
281D4⋊C8—22no—
282C2×#41—22no—
283C2×#41—21no—
284C22×D4D4×C12711yescharacteristic
285C23×C4D4×C12712yes—
286C2×M16—21no—
287C2×M16—21no—
288C22×C8—21no—
289C22×C8—21no—
290C4⋊Q8D4×C12711yescharacteristic
291C4⋊Q8D4×C12711yescharacteristic
292C4⋊Q8D4×C12711yescharacteristic
293#127—22no—
294#127D4×C12711yescharacteristic
295#126—24no—
296#125—21no—
297#124—22no—
298#124—24no—
299#124—21no—
300#123—24no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—21no—
304C22⋊Q8C2×C4×C12712yes—
305#121—22no—
306#121—22no—
307#121—22no—
308#121—24no—
309#121—21no—
310#121C2×C4×C12712yes—
311#120—24no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8D4×C12712yes—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4D4×C12712yes—
324#117—22no—
325#117—22no—
326#117—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4D4×C12711yescharacteristic
329C2×C22⋊C4C2×C4×C12712yes—
330C2×C42C23×C12711yescharacteristic
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337#100—42no—
338C22⋊C8—44no—
339C4×C8—21no—
340C4×C8—21no—
341C24C22⋊C4×C12712yes—
342#41—41no—
343#41—41no—
344#41—41no—
345#41—41no—
346#41—82no—
347#41—82no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8C22⋊C4×C12712yes—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C22⋊C4×C12712yes—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C22⋊C4×C12712yes—
370C22×C4C22×C4×C12711yescharacteristic
371C22×C4C2×D4×C12711yescharacteristic
372C22×C4C2×D4×C12711yescharacteristic
373M16—41no—
374M16—41no—
375M16—41no—
376M16—41no—
377C2×C8—22no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—42no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—41no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4C22⋊C4×C12712yes—
394C4⋊C4C22⋊C4×C12712yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C42—24no—
404C42—22no—
405C42C2×D4×C12711yescharacteristic
406C42C2×D4×C12711yescharacteristic
407C42C2×D4×C12711yescharacteristic
408C42C2×D4×C12711yescharacteristic
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23C2×C22⋊C4×C12711yescharacteristic
416Q8—42no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—41no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—84no—
433D4—84no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—84no—
448C2×C4C2×C22⋊C4×C12711yescharacteristic
449C2×C4C2×C22⋊C4×C12711yescharacteristic
450C2×C4#120×C12711yescharacteristic
451C2×C4#120×C12711yescharacteristic
452C2×C4#120×C12711yescharacteristic
453C2×C4#120×C12711yescharacteristic
454C2×C4#135×C12711yescharacteristic
455C2×C4#135×C12711yescharacteristic
456C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
457C2×C4#137×C12711yescharacteristic
458C8—42no—
459C8—81no—
460C8—81no—
461C8—81no—
462C22—21no—
463C22—21no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—82no—
472C22#379×C12711yescharacteristic
473C22#416×C12711yescharacteristic
474C22#417×C12711yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4#449×C12711yescharacteristic
483C4#449×C12711yescharacteristic
484C4#452×C12711yescharacteristic
485C4#452×C12711yescharacteristic
486C4#453×C12711yescharacteristic
487C4#455×C12711yescharacteristic
488C2—21no—
489C2—21no—
490C2—82no—
491C2—82no—
492C2C127×#178811yescharacteristic
493C2C127×#179111yescharacteristic
494C2C127×#179211yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3506C2
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×#1954C2semidirect
3. C127×#1800C2semidirect
4. C127×#1550C2semidirect
5. C127×#1547C2semidirect
6. C127×#1493C2semidirect
7. C127×#1492C2semidirect
240. #8358C127direct (N × H)
249. #1954C2×C127semidirect
250. #1800C2×C127semidirect
251. #1550C2×C127semidirect
252. #1547C2×C127semidirect
253. #1493C2×C127semidirect
254. #1492C2×C127semidirect
255. C127#8358direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35062
C127×#19542
C127×#18002
C127×#15502
C127×#15472
C127×#14932
C127×#14922
#8358127