Finite Group Databasebeta

← C127×#10571 #44574244

Subgroups — C127×#10571 #44574244

Order 32512.

516 conjugacy classes of subgroups.

The subgroup lattice has 464 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×#1442C211yesmaximal, characteristic
5C127×#1294C211yesmaximal, characteristic
6C127×#1294C211yesmaximal, characteristic
7C127×#1280C211yesmaximal, characteristic
8C22×C4⋊C4×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×#106×C127—21no—
11C2×C22⋊C8×C127C2211yescharacteristic
12C2×C22⋊C8×C127C2211yescharacteristic
13#400×C127—21no—
14#400×C127—21no—
15#398×C127—21no—
16#398×C127—21no—
17#385×C127—21no—
18#385×C127—21no—
19#380×C127C2211yescharacteristic
20#380×C127C2211yescharacteristic
21C2×#95×C127—21no—
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×C127D411yescharacteristic
42C2×C4⋊C4×C127D411yescharacteristic
43C2×C4⋊C4×C127D411yescharacteristic
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47#107×C127—42no—
48#106×C127—42no—
49C22⋊C8×C127—21no—
50C22⋊C8×C127—21no—
51C22⋊C8×C127Q812yes—
52C22⋊C8×C127Q812yes—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
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—42no—
63#95×C127—42no—
64#95×C127Q812yes—
65C24×C127C2×D411yescharacteristic
66C22×C4×C127—22no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—22no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
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×C127C2×D411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127C2×Q811yescharacteristic
99C22×C4×C127C2×Q811yescharacteristic
100C22×C4×C127C2×Q811yescharacteristic
101C22×C4×C127#4111yescharacteristic
102C2×C8×C127—22no—
103C2×C8×C127—22no—
104C2×C8×C127—41no—
105C2×C8×C127—41no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C4⋊C4×C127—22no—
109C4⋊C4×C127—22no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—81no—
117C4⋊C4×C127—81no—
118C4⋊C4×C127—81no—
119C4⋊C4×C127—81no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—21no—
128C23×C127#12011yescharacteristic
129C23×C127C22⋊Q811yescharacteristic
130C23×C127C4⋊Q811yescharacteristic
131C23×C127#13511yescharacteristic
132C23×C127#13511yescharacteristic
133C23×C127AGL(1,ℤ/8)11yescharacteristic
134C23×C127#13711yescharacteristic
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—42no—
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—42no—
169C2×C4×C127—81no—
170C2×C4×C127—81no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127—81no—
174C2×C4×C127—81no—
175C2×C4×C127—81no—
176C2×C4×C127—81no—
177C2×C4×C127—81no—
178C2×C4×C127—81no—
179C2×C4×C127C22⋊Q811yescharacteristic
180C2×C4×C127C22⋊Q811yescharacteristic
181C2×C4×C127C4⋊Q811yescharacteristic
182C2×C4×C127C4⋊Q811yescharacteristic
183C8×C127—42no—
184C8×C127—42no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
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#39511yescharacteristic
198C22×C127#44911yescharacteristic
199C22×C127#45211yescharacteristic
200C22×C127#45411yescharacteristic
201C22×C127#45511yescharacteristic
202C22×C127B(4,𝔽2)11yescharacteristic
203C22×C127#45811yescharacteristic
204C22×C127#47811yescharacteristic
205C22×C127#47911yescharacteristic
206C22×C127#49911yescharacteristic
207C22×C127#50111yescharacteristic
208C4×C127—21no—
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—21no—
212C4×C127—82no—
213C4×C127—81no—
214C4×C127—82no—
215C4×C127—81no—
216C4×C127—81no—
217C4×C127—81no—
218C4×C127—81no—
219C4×C127—81no—
220#10571C12711yesmaximal, characteristic, direct product factor, Sylow
221C2×C127—21no—
222C2×C127—21no—
223C2×C127—21no—
224C2×C127—21no—
225C2×C127#159711yescharacteristic
226C2×C127#160611yescharacteristic
227C2×C127#161211yescharacteristic
228C2×C127#161511yescharacteristic
229C2×C127#205911yescharacteristic
230C2×C127#206111yescharacteristic
231C2×C127#206211yescharacteristic
232#2646C2×C12711yescharacteristic
233#1853C2×C12711yescharacteristic
234#1852C2×C12711yescharacteristic
235#1442C2×C12711yescharacteristic
236#1294C2×C12711yescharacteristic
237#1294C2×C12711yescharacteristic
238#1280C2×C12711yescharacteristic
239C127#1057111yescharacteristic, direct product factor, Sylow
240C22×C4⋊C4C22×C12711yescharacteristic
241C2×#107—21no—
242C2×#106—21no—
243C2×C22⋊C8C22×C12711yescharacteristic
244C2×C22⋊C8C22×C12711yescharacteristic
245#400—21no—
246#400—21no—
247#398—21no—
248#398—21no—
249#385—21no—
250#385—21no—
251#380C22×C12711yescharacteristic
252#380C22×C12711yescharacteristic
253C2×#95—21no—
254C2×#95—21no—
255C2×#95C22×C12711yescharacteristic
256C2×#95C22×C12711yescharacteristic
257#340—21no—
258#340—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4D4×C12711yescharacteristic
262C23×C4D4×C12711yescharacteristic
263C23×C4C23×C12711yescharacteristic
264C22×C8—21no—
265C22×C8—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4D4×C12711yescharacteristic
274C2×C4⋊C4D4×C12711yescharacteristic
275C2×C4⋊C4D4×C12711yescharacteristic
276C2×C4⋊C4D4×C12711yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279#107—42no—
280#106—42no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8Q8×C12712yes—
284C22⋊C8Q8×C12712yes—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—42no—
295#95—42no—
296#95Q8×C12712yes—
297C24C2×D4×C12711yescharacteristic
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
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×C4C2×D4×C12711yescharacteristic
329C22×C4C2×D4×C12711yescharacteristic
330C22×C4C2×Q8×C12711yescharacteristic
331C22×C4C2×Q8×C12711yescharacteristic
332C22×C4C2×Q8×C12711yescharacteristic
333C22×C4#41×C12711yescharacteristic
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—81no—
349C4⋊C4—81no—
350C4⋊C4—81no—
351C4⋊C4—81no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23#120×C12711yescharacteristic
361C23C22⋊Q8×C12711yescharacteristic
362C23C4⋊Q8×C12711yescharacteristic
363C23#135×C12711yescharacteristic
364C23#135×C12711yescharacteristic
365C23AGL(1,ℤ/8)×C12711yescharacteristic
366C23#137×C12711yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4C22⋊Q8×C12711yescharacteristic
412C2×C4C22⋊Q8×C12711yescharacteristic
413C2×C4C4⋊Q8×C12711yescharacteristic
414C2×C4C4⋊Q8×C12711yescharacteristic
415C8—42no—
416C8—42no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22#395×C12711yescharacteristic
430C22#449×C12711yescharacteristic
431C22#452×C12711yescharacteristic
432C22#454×C12711yescharacteristic
433C22#455×C12711yescharacteristic
434C22B(4,𝔽2)×C12711yescharacteristic
435C22#458×C12711yescharacteristic
436C22#478×C12711yescharacteristic
437C22#479×C12711yescharacteristic
438C22#499×C12711yescharacteristic
439C22#501×C12711yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—82no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2C127×#159711yescharacteristic
457C2C127×#160611yescharacteristic
458C2C127×#161211yescharacteristic
459C2C127×#161511yescharacteristic
460C2C127×#205911yescharacteristic
461C2C127×#206111yescharacteristic
462C2C127×#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
220. #10571C127direct (N × H)
239. C127#10571direct (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×#14422
C127×#12942
C127×#12802
#10571127