Finite Group Databasebeta

← C127×#10572 #44574245

Subgroups — C127×#10572 #44574245

Order 32512.

560 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2646C211yesmaximal, characteristic
2C127×#1853C211yesmaximal, characteristic
3C127×#1852C211yesmaximal, characteristic
4C127×#1444C211yesmaximal, characteristic
5C127×#1294C211yesmaximal, characteristic
6C127×#1294C211yesmaximal, characteristic
7C127×#1280C211yesmaximal, characteristic
8C22×C4⋊C4×C127—21no—
9C22×C4⋊C4×C127C2211yescharacteristic
10C2×#107×C127—21no—
11C2×#106×C127—21no—
12C2×C22⋊C8×C127C2211yescharacteristic
13C2×C22⋊C8×C127C2211yescharacteristic
14#400×C127—21no—
15#400×C127—21no—
16#398×C127—21no—
17#398×C127—21no—
18#385×C127—21no—
19#385×C127—21no—
20#380×C127C2211yescharacteristic
21#380×C127C2211yescharacteristic
22C2×#95×C127—21no—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25#340×C127—21no—
26#340×C127—21no—
27C23×C4×C127—21no—
28C23×C4×C127—21no—
29C23×C4×C127D411yescharacteristic
30C23×C4×C127D411yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C22×C8×C127—21no—
33C22×C8×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—42no—
41C2×C4⋊C4×C127—42no—
42C2×C4⋊C4×C127—42no—
43C2×C4⋊C4×C127—42no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C4⋊C4×C127D411yescharacteristic
46C2×C4⋊C4×C127D411yescharacteristic
47C2×C4⋊C4×C127D411yescharacteristic
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50#107×C127—42no—
51#106×C127—42no—
52C22⋊C8×C127—21no—
53C22⋊C8×C127—21no—
54C22⋊C8×C127Q812yes—
55C22⋊C8×C127Q812yes—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127—21no—
63#95×C127—21no—
64#95×C127—21no—
65#95×C127—42no—
66#95×C127Q812yes—
67C24×C127C2×D411yescharacteristic
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127—41no—
89C22×C4×C127—41no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127—41no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127—41no—
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×D411yescharacteristic
100C22×C4×C127C2×Q811yescharacteristic
101C22×C4×C127C2×Q811yescharacteristic
102C22×C4×C127C2×Q811yescharacteristic
103C22×C4×C127#4111yescharacteristic
104C2×C8×C127—22no—
105C2×C8×C127—22no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C4⋊C4×C127—22no—
111C4⋊C4×C127—22no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—48no—
119C4⋊C4×C127—81no—
120C4⋊C4×C127—81no—
121C4⋊C4×C127—81no—
122C4⋊C4×C127—81no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C23×C127—21no—
128C23×C127—21no—
129C23×C127—21no—
130C23×C127—21no—
131C23×C127#12011yescharacteristic
132C23×C127C22⋊Q811yescharacteristic
133C23×C127C4⋊Q811yescharacteristic
134C23×C127#13511yescharacteristic
135C23×C127#13511yescharacteristic
136C23×C127AGL(1,ℤ/8)11yescharacteristic
137C23×C127#13711yescharacteristic
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—24no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—42no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—81no—
177C2×C4×C127—81no—
178C2×C4×C127—81no—
179C2×C4×C127—81no—
180C2×C4×C127—81no—
181C2×C4×C127—81no—
182C2×C4×C127C22⋊Q811yescharacteristic
183C2×C4×C127C22⋊Q811yescharacteristic
184C2×C4×C127C4⋊Q811yescharacteristic
185C2×C4×C127C4⋊Q811yescharacteristic
186C8×C127—42no—
187C8×C127—42no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—21no—
199C22×C127—21no—
200C22×C127#39511yescharacteristic
201C22×C127#44911yescharacteristic
202C22×C127#45211yescharacteristic
203C22×C127#45311yescharacteristic
204C22×C127#45611yescharacteristic
205C22×C127B(4,𝔽2)11yescharacteristic
206C22×C127#45811yescharacteristic
207C22×C127#47811yescharacteristic
208C22×C127#47911yescharacteristic
209C22×C127#49911yescharacteristic
210C22×C127#50111yescharacteristic
211C4×C127—21no—
212C4×C127—21no—
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—44no—
216C4×C127—81no—
217C4×C127—81no—
218C4×C127—82no—
219C4×C127—81no—
220C4×C127—81no—
221C4×C127—81no—
222C4×C127—81no—
223#10572C12711yesmaximal, characteristic, direct product factor, Sylow
224C2×C127—21no—
225C2×C127—21no—
226C2×C127—21no—
227C2×C127—21no—
228C2×C127#160011yescharacteristic
229C2×C127#160311yescharacteristic
230C2×C127#160911yescharacteristic
231C2×C127#161811yescharacteristic
232C2×C127#205911yescharacteristic
233C2×C127#206011yescharacteristic
234C2×C127#206211yescharacteristic
235#2646C2×C12711yescharacteristic
236#1853C2×C12711yescharacteristic
237#1852C2×C12711yescharacteristic
238#1444C2×C12711yescharacteristic
239#1294C2×C12711yescharacteristic
240#1294C2×C12711yescharacteristic
241#1280C2×C12711yescharacteristic
242C127#1057211yescharacteristic, direct product factor, Sylow
243C22×C4⋊C4—21no—
244C22×C4⋊C4C22×C12711yescharacteristic
245C2×#107—21no—
246C2×#106—21no—
247C2×C22⋊C8C22×C12711yescharacteristic
248C2×C22⋊C8C22×C12711yescharacteristic
249#400—21no—
250#400—21no—
251#398—21no—
252#398—21no—
253#385—21no—
254#385—21no—
255#380C22×C12711yescharacteristic
256#380C22×C12711yescharacteristic
257C2×#95—21no—
258C2×#95C22×C12711yescharacteristic
259C2×#95C22×C12711yescharacteristic
260#340—21no—
261#340—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4D4×C12711yescharacteristic
265C23×C4D4×C12711yescharacteristic
266C23×C4C23×C12711yescharacteristic
267C22×C8—21no—
268C22×C8—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4D4×C12711yescharacteristic
280C2×C4⋊C4D4×C12711yescharacteristic
281C2×C4⋊C4D4×C12711yescharacteristic
282C2×C4⋊C4D4×C12711yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285#107—42no—
286#106—42no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8Q8×C12712yes—
290C22⋊C8Q8×C12712yes—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—42no—
301#95Q8×C12712yes—
302C24C2×D4×C12711yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C2×D4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4C2×Q8×C12711yescharacteristic
336C22×C4C2×Q8×C12711yescharacteristic
337C22×C4C2×Q8×C12711yescharacteristic
338C22×C4#41×C12711yescharacteristic
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—48no—
354C4⋊C4—81no—
355C4⋊C4—81no—
356C4⋊C4—81no—
357C4⋊C4—81no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23#120×C12711yescharacteristic
367C23C22⋊Q8×C12711yescharacteristic
368C23C4⋊Q8×C12711yescharacteristic
369C23#135×C12711yescharacteristic
370C23#135×C12711yescharacteristic
371C23AGL(1,ℤ/8)×C12711yescharacteristic
372C23#137×C12711yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4C22⋊Q8×C12711yescharacteristic
418C2×C4C22⋊Q8×C12711yescharacteristic
419C2×C4C4⋊Q8×C12711yescharacteristic
420C2×C4C4⋊Q8×C12711yescharacteristic
421C8—42no—
422C8—42no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22#395×C12711yescharacteristic
436C22#449×C12711yescharacteristic
437C22#452×C12711yescharacteristic
438C22#453×C12711yescharacteristic
439C22#456×C12711yescharacteristic
440C22B(4,𝔽2)×C12711yescharacteristic
441C22#458×C12711yescharacteristic
442C22#478×C12711yescharacteristic
443C22#479×C12711yescharacteristic
444C22#499×C12711yescharacteristic
445C22#501×C12711yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—44no—
451C4—81no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2C127×#160011yescharacteristic
463C2C127×#160311yescharacteristic
464C2C127×#160911yescharacteristic
465C2C127×#161811yescharacteristic
466C2C127×#205911yescharacteristic
467C2C127×#206011yescharacteristic
468C2C127×#206211yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
223. #10572C127direct (N × H)
242. C127#10572direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26462
C127×#18532
C127×#18522
C127×#14442
C127×#12942
C127×#12802
#10572127