Finite Group Databasebeta

← C127×#8573 #44572246

Subgroups — C127×#8573 #44572246

Order 32512.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C127C211yesmaximal, characteristic
2C127×#1797C211yesmaximal, characteristic, complemented
3C2×#327×C127C212yesmaximal
4C127×#1434C211yesmaximal, characteristic, complemented
5C127×#1294C212yesmaximal, complemented
6C2×#121×C127C2211yescharacteristic
7C2×C4×D4×C127—21no—
8C2×C4×D4×C127C411yescharacteristic, complemented
9C22×C42×C127C2211yescharacteristic
10C2×C4⋊C8×C127—21no—
11C2×C22⋊C8×C127C2212yes—
12#390×C127C411yescharacteristic, complemented
13#389×C127C411yescharacteristic, complemented
14#388×C127—21no—
15#386×C127—21no—
16#380×C127C2211yescharacteristic
17C4×C4⋊C4×C127C411yescharacteristic, complemented
18C4×C22⋊C4×C127—21no—
19C2×#95×C127—21no—
20C2×#95×C127—21no—
21C2×#95×C127C2212yes—
22#336×C127—21no—
23#327×C127—24no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C23×C4×C127—22no—
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C23×C4×C127C2311yescharacteristic
31C22×C8×C127—22no—
32#121×C127—21no—
33#121×C127—21no—
34#121×C127D412yes—
35#121×C127Q812yes—
36C4×D4×C127—42no—
37C4×D4×C127—44no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C42×C127—21no—
48C2×C42×C127—42no—
49C2×C42×C127C2×C411yescharacteristic
50C2×C42×C127C2×C411yescharacteristic
51C2×C42×C127D411yescharacteristic
52C2×C42×C127D411yescharacteristic
53C4⋊C8×C127—42no—
54C22⋊C8×C127—22no—
55C22⋊C8×C127—22no—
56#95×C127—24no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—22no—
61#95×C127—22no—
62#95×C127—42no—
63C24×C127—21no—
64C24×C127C2×D411yescharacteristic
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127—21no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127C4⋊C412yes—
73C22×C4×C127—21no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—24no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—42no—
86C22×C4×C127—42no—
87C22×C4×C127—42no—
88C22×C4×C127—42no—
89C22×C4×C127—42no—
90C22×C4×C127—42no—
91C22×C4×C127—42no—
92C22×C4×C127—42no—
93C22×C4×C127—42no—
94C22×C4×C127C22⋊C411yescharacteristic
95C22×C4×C127C22⋊C411yescharacteristic
96C22×C4×C127C22⋊C411yescharacteristic
97C22×C4×C127C22⋊C411yescharacteristic
98C22×C4×C127C22×C411yescharacteristic
99C22×C4×C127C2×D411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127C2×Q811yescharacteristic
102C22×C4×C127#4111yescharacteristic
103C22×C4×C127#4111yescharacteristic
104C2×C8×C127—42no—
105C2×C8×C127—42no—
106C2×C8×C127—42no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—42no—
111C4⋊C4×C127C4⋊C412yes—
112C22⋊C4×C127—22no—
113C22⋊C4×C127—22no—
114C22⋊C4×C127—42no—
115C22⋊C4×C127—42no—
116C22⋊C4×C127—42no—
117C22⋊C4×C127—42no—
118C42×C127—22no—
119C42×C127—22no—
120C42×C127—41no—
121C42×C127—41no—
122C42×C127—42no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—22no—
128C23×C127—41no—
129C23×C127—41no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127C2×C22⋊C411yescharacteristic
135C23×C127#12111yescharacteristic
136C23×C127C22⋊Q811yescharacteristic
137C23×C127#13512yes—
138C23×C127AGL(1,ℤ/8)12yes—
139D4×C127—42no—
140D4×C127—42no—
141D4×C127—44no—
142D4×C127—44no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—22no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—84no—
176C2×C4×C127—82no—
177C2×C4×C127—82no—
178C2×C4×C127—82no—
179C2×C4×C127—82no—
180C2×C4×C127#9912yes—
181C2×C4×C127#10412yes—
182C2×C4×C127C2×C4⋊C411yescharacteristic
183C2×C4×C127#11711yescharacteristic
184C2×C4×C127#12111yescharacteristic
185C2×C4×C127C22⋊Q811yescharacteristic
186C8×C127—82no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—22no—
192C22×C127—22no—
193C22×C127—22no—
194C22×C127—22no—
195C22×C127—42no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127—81no—
202C22×C127#38011yescharacteristic
203C22×C127C2×#9911yescharacteristic
204C22×C127#41011yescharacteristic
205C22×C127#41611yescharacteristic
206C22×C127#41811yescharacteristic
207C22×C127C2×#10411yescharacteristic
208C22×C127#42111yescharacteristic
209C22×C127#46312yes—
210C22×C127#47812yes—
211C4×C127—21no—
212C4×C127—21no—
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—22no—
216C4×C127—22no—
217C4×C127—42no—
218C4×C127—41no—
219C4×C127—41no—
220C4×C127—84no—
221C4×C127—81no—
222C4×C127—81no—
223#8573C12711yesmaximal, characteristic, direct product factor, Sylow
224C2×C127—22no—
225C2×C127—22no—
226C2×C127—82no—
227C2×C127#150011yescharacteristic
228C2×C127#150711yescharacteristic
229C2×C127#151411yescharacteristic
230C2×C127#151611yescharacteristic
231C2×C127#179911yescharacteristic
232C2×C127#180411yescharacteristic
233C2×C127#180611yescharacteristic
234C4×#121C2×C12711yescharacteristic
235#1797C2×C12711yescharacteristic, complemented
236C2×#327C2×C12712yes—
237#1434C2×C12711yescharacteristic, complemented
238#1294C2×C12712yescomplemented
239C127#857311yescharacteristic, direct product factor, Sylow
240C2×#121C22×C12711yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C4×C12711yescharacteristic, complemented
243C22×C42C22×C12711yescharacteristic
244C2×C4⋊C8—21no—
245C2×C22⋊C8C22×C12712yes—
246#390C4×C12711yescharacteristic, complemented
247#389C4×C12711yescharacteristic, complemented
248#388—21no—
249#386—21no—
250#380C22×C12711yescharacteristic
251C4×C4⋊C4C4×C12711yescharacteristic, complemented
252C4×C22⋊C4—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95C22×C12712yes—
256#336—21no—
257#327—24no—
258C22×D4—21no—
259C22×D4C2×C4×C12711yescharacteristic
260C23×C4—22no—
261C23×C4—21no—
262C23×C4D4×C12711yescharacteristic
263C23×C4D4×C12711yescharacteristic
264C23×C4C23×C12711yescharacteristic
265C22×C8—22no—
266#121—21no—
267#121—21no—
268#121D4×C12712yes—
269#121Q8×C12712yes—
270C4×D4—42no—
271C4×D4—44no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C2×C4×C12711yescharacteristic
274C2×C4⋊C4C2×C4×C12711yescharacteristic
275C2×C4⋊C4C2×C4×C12711yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282C2×C42—42no—
283C2×C42C2×C4×C12711yescharacteristic
284C2×C42C2×C4×C12711yescharacteristic
285C2×C42D4×C12711yescharacteristic
286C2×C42D4×C12711yescharacteristic
287C4⋊C8—42no—
288C22⋊C8—22no—
289C22⋊C8—22no—
290#95—24no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—22no—
295#95—22no—
296#95—42no—
297C24—21no—
298C24C2×D4×C12711yescharacteristic
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4C4⋊C4×C12712yes—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C22⋊C4×C12711yescharacteristic
329C22×C4C22⋊C4×C12711yescharacteristic
330C22×C4C22⋊C4×C12711yescharacteristic
331C22×C4C22⋊C4×C12711yescharacteristic
332C22×C4C22×C4×C12711yescharacteristic
333C22×C4C2×D4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4C2×Q8×C12711yescharacteristic
336C22×C4#41×C12711yescharacteristic
337C22×C4#41×C12711yescharacteristic
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—42no—
345C4⋊C4C4⋊C4×C12712yes—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C42—22no—
353C42—22no—
354C42—41no—
355C42—41no—
356C42—42no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23C2×C22⋊C4×C12711yescharacteristic
369C23#121×C12711yescharacteristic
370C23C22⋊Q8×C12711yescharacteristic
371C23#135×C12712yes—
372C23AGL(1,ℤ/8)×C12712yes—
373D4—42no—
374D4—42no—
375D4—44no—
376D4—44no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—84no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4#99×C12712yes—
415C2×C4#104×C12712yes—
416C2×C4C2×C4⋊C4×C12711yescharacteristic
417C2×C4#117×C12711yescharacteristic
418C2×C4#121×C12711yescharacteristic
419C2×C4C22⋊Q8×C12711yescharacteristic
420C8—82no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—21no—
428C22—21no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22#380×C12711yescharacteristic
437C22C2×#99×C12711yescharacteristic
438C22#410×C12711yescharacteristic
439C22#416×C12711yescharacteristic
440C22#418×C12711yescharacteristic
441C22C2×#104×C12711yescharacteristic
442C22#421×C12711yescharacteristic
443C22#463×C12712yes—
444C22#478×C12712yes—
445C4—22no—
446C4—22no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—42no—
452C4—41no—
453C4—41no—
454C4—84no—
455C4—81no—
456C4—81no—
457C2—22no—
458C2—22no—
459C2—82no—
460C2C127×#150011yescharacteristic
461C2C127×#150711yescharacteristic
462C2C127×#151411yescharacteristic
463C2C127×#151611yescharacteristic
464C2C127×#179911yescharacteristic
465C2C127×#180411yescharacteristic
466C2C127×#180611yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#121×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1797C2semidirect
4. C127×#1434C2semidirect
5. C127×#1294C2semidirect
8. C2×C4×D4×C127C4semidirect
12. #390×C127C4semidirect
13. #389×C127C4semidirect
17. C4×C4⋊C4×C127C4semidirect
223. #8573C127direct (N × H)
235. #1797C2×C127semidirect
237. #1434C2×C127semidirect
238. #1294C2×C127semidirect
239. C127#8573direct (N × H)
242. C2×C4×D4C4×C127semidirect
246. #390C4×C127semidirect
247. #389C4×C127semidirect
251. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1272
C127×#17972
C2×#327×C1272
C127×#14342
C127×#12942
#8573127