Finite Group Databasebeta

← C127×#10918 #44574591

Subgroups — C127×#10918 #44574591

Order 32512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C127C211yesmaximal, characteristic
2C127×#2273C211yesmaximal, characteristic
3C2×#342×C127C211yesmaximal, characteristic
4C2×#342×C127C212yesmaximal
5C127×C22⋊#95C212yesmaximal
6C24×C4×C127C2211yescharacteristic
7C22×C4⋊C4×C127—21no—
8C22×C22⋊C4×C127C2212yes—
9C22×C22⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2212yes—
11C22×C22⋊C4×C127C2211yescharacteristic
12#385×C127—22no—
13#385×C127C414yescomplemented
14C4×C22⋊C4×C127—21no—
15C4×C22⋊C4×C127—21no—
16C4×C22⋊C4×C127—24no—
17C2×#95×C127—21no—
18C2×#95×C127—24no—
19#342×C127—22no—
20#342×C127C418yescomplemented
21C25×C127C2311yescharacteristic
22C23×C4×C127—21no—
23C23×C4×C127—21no—
24C23×C4×C127—22no—
25C23×C4×C127—22no—
26C23×C4×C127—21no—
27C23×C4×C127—22no—
28C23×C4×C127—44no—
29C23×C4×C127C2×C412yes—
30C23×C4×C127D411yescharacteristic
31C23×C4×C127D411yescharacteristic
32C23×C4×C127D414yes—
33C2×C4⋊C4×C127—24no—
34C2×C4⋊C4×C127—44no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127—22no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127C2×C414yes—
49C2×C22⋊C4×C127C2×C412yes—
50C2×C22⋊C4×C127C2×C414yes—
51C2×C22⋊C4×C127C2×C414yes—
52C2×C22⋊C4×C127C2×C412yes—
53C2×C22⋊C4×C127D412yes—
54C2×C22⋊C4×C127Q814yes—
55C2×C42×C127—22no—
56C2×C42×C127—22no—
57#95×C127—22no—
58#95×C127—22no—
59#95×C127—24no—
60#95×C127—48no—
61C24×C127—42no—
62C24×C127—42no—
63C24×C127C22×C411yescharacteristic
64C24×C127C22×C412yes—
65C24×C127C2×D411yescharacteristic
66C24×C127C2×D412yes—
67C24×C127C2×D411yescharacteristic
68C24×C127C2×Q812yes—
69C24×C127#4112yes—
70C24×C127#4112yes—
71C24×C127#4112yes—
72C22×C4×C127—28no—
73C22×C4×C127—24no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—24no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—24no—
85C22×C4×C127—44no—
86C22×C4×C127—44no—
87C22×C4×C127—48no—
88C22×C4×C127—42no—
89C22×C4×C127—42no—
90C22×C4×C127—42no—
91C22×C4×C127—44no—
92C22×C4×C127—41no—
93C22×C4×C127—42no—
94C22×C4×C127—41no—
95C22×C4×C127—44no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127—44no—
99C22×C4×C127—44no—
100C22×C4×C127—44no—
101C22×C4×C127—42no—
102C22×C4×C127—42no—
103C22×C4×C127C22⋊C412yes—
104C22×C4×C127C22⋊C412yes—
105C22×C4×C127C4⋊C418yescomplemented
106C4⋊C4×C127—48no—
107C22⋊C4×C127—22no—
108C22⋊C4×C127—24no—
109C22⋊C4×C127—24no—
110C22⋊C4×C127—24no—
111C22⋊C4×C127—24no—
112C22⋊C4×C127—24no—
113C22⋊C4×C127—24no—
114C22⋊C4×C127—24no—
115C22⋊C4×C127—24no—
116C22⋊C4×C127—24no—
117C22⋊C4×C127—42no—
118C22⋊C4×C127—42no—
119C22⋊C4×C127C4214yescomplemented
120C42×C127—82no—
121C42×C127—82no—
122C23×C127—24no—
123C23×C127—22no—
124C23×C127—24no—
125C23×C127—22no—
126C23×C127—41no—
127C23×C127—41no—
128C23×C127—42no—
129C23×C127—44no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—44no—
133C23×C127—44no—
134C23×C127—44no—
135C23×C127—42no—
136C23×C127C2×C4211yescharacteristic
137C23×C127C2×C22⋊C411yescharacteristic
138C23×C127C2×C4⋊C412yes—
139C23×C127#11711yescharacteristic
140C23×C127#11712yes—
141C23×C127C4×D412yes—
142C23×C127C4×D412yes—
143C23×C127C4×D412yes—
144C23×C127C4×D412yes—
145C23×C127C4×Q812yes—
146C23×C127C4×Q812yes—
147C23×C127#12011yescharacteristic
148C23×C127#12112yes—
149C23×C127C22⋊Q812yes—
150C23×C127C22⋊Q812yes—
151C23×C127#12312yes—
152C23×C127#12311yescharacteristic
153C23×C127#12411yescharacteristic
154C23×C127#12512yes—
155C23×C127#12612yes—
156C23×C127C4⋊Q811yescharacteristic
157C2×C4×C127—24no—
158C2×C4×C127—28no—
159C2×C4×C127—24no—
160C2×C4×C127—28no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—42no—
164C2×C4×C127—48no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—44no—
168C2×C4×C127—48no—
169C2×C4×C127—44no—
170C2×C4×C127—42no—
171C2×C4×C127—44no—
172C2×C4×C127—42no—
173C2×C4×C127—44no—
174C2×C4×C127—44no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—48no—
179C2×C4×C127—48no—
180C2×C4×C127—44no—
181C2×C4×C127—84no—
182C2×C4×C127—81no—
183C2×C4×C127—81no—
184C2×C4×C127—84no—
185C2×C4×C127—82no—
186C2×C4×C127—82no—
187C22×C127—24no—
188C22×C127—24no—
189C22×C127—24no—
190C22×C127—24no—
191C22×C127—24no—
192C22×C127—24no—
193C22×C127—21no—
194C22×C127—22no—
195C22×C127—22no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—22no—
199C22×C127—21no—
200C22×C127—22no—
201C22×C127—41no—
202C22×C127—41no—
203C22×C127—42no—
204C22×C127—42no—
205C22×C127—42no—
206C22×C127—42no—
207C22×C127—41no—
208C22×C127—42no—
209C22×C127—42no—
210C22×C127—41no—
211C22×C127C4×C22⋊C411yescharacteristic
212C22×C127C4×C4⋊C412yes—
213C22×C127#38512yes—
214C22×C127#38611yescharacteristic
215C22×C127#38712yes—
216C22×C127#38712yes—
217C22×C127#38812yes—
218C22×C127#38912yes—
219C22×C127#39111yescharacteristic
220C22×C127B(4,𝔽2)12yes—
221C22×C127#45812yes—
222C4×C127—44no—
223C4×C127—48no—
224C4×C127—44no—
225C4×C127—42no—
226C4×C127—42no—
227C4×C127—84no—
228#10918C12711yesmaximal, characteristic, direct product factor, Sylow
229C2×C127—21no—
230C2×C127—22no—
231C2×C127—22no—
232C2×C127—22no—
233C2×C127—22no—
234C2×C127—22no—
235C2×C127—21no—
236C2×C127#143611yescharacteristic
237C2×C127#186714yes—
238C2×C127#188911yescharacteristic
239C2×C127#189011yescharacteristic
240C2×#385C2×C12711yescharacteristic
241#2273C2×C12711yescharacteristic
242C2×#342C2×C12711yescharacteristic
243C2×#342C2×C12712yes—
244C22⋊#95C2×C12712yes—
245C127#1091811yescharacteristic, direct product factor, Sylow
246C24×C4C22×C12711yescharacteristic
247C22×C4⋊C4—21no—
248C22×C22⋊C4C22×C12712yes—
249C22×C22⋊C4C22×C12711yescharacteristic
250C22×C22⋊C4C22×C12712yes—
251C22×C22⋊C4C22×C12711yescharacteristic
252#385—22no—
253#385C4×C12714yescomplemented
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—24no—
257C2×#95—21no—
258C2×#95—24no—
259#342—22no—
260#342C4×C12718yescomplemented
261C25C23×C12711yescharacteristic
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—21no—
267C23×C4—22no—
268C23×C4—44no—
269C23×C4C2×C4×C12712yes—
270C23×C4D4×C12711yescharacteristic
271C23×C4D4×C12711yescharacteristic
272C23×C4D4×C12714yes—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—44no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4C2×C4×C12714yes—
289C2×C22⋊C4C2×C4×C12712yes—
290C2×C22⋊C4C2×C4×C12714yes—
291C2×C22⋊C4C2×C4×C12714yes—
292C2×C22⋊C4C2×C4×C12712yes—
293C2×C22⋊C4D4×C12712yes—
294C2×C22⋊C4Q8×C12714yes—
295C2×C42—22no—
296C2×C42—22no—
297#95—22no—
298#95—22no—
299#95—24no—
300#95—48no—
301C24—42no—
302C24—42no—
303C24C22×C4×C12711yescharacteristic
304C24C22×C4×C12712yes—
305C24C2×D4×C12711yescharacteristic
306C24C2×D4×C12712yes—
307C24C2×D4×C12711yescharacteristic
308C24C2×Q8×C12712yes—
309C24#41×C12712yes—
310C24#41×C12712yes—
311C24#41×C12712yes—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—24no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—24no—
325C22×C4—44no—
326C22×C4—44no—
327C22×C4—48no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—41no—
333C22×C4—42no—
334C22×C4—41no—
335C22×C4—44no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4C22⋊C4×C12712yes—
344C22×C4C22⋊C4×C12712yes—
345C22×C4C4⋊C4×C12718yescomplemented
346C4⋊C4—48no—
347C22⋊C4—22no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4C42×C12714yescomplemented
360C42—82no—
361C42—82no—
362C23—24no—
363C23—22no—
364C23—24no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—44no—
370C23—41no—
371C23—41no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—42no—
376C23C2×C42×C12711yescharacteristic
377C23C2×C22⋊C4×C12711yescharacteristic
378C23C2×C4⋊C4×C12712yes—
379C23#117×C12711yescharacteristic
380C23#117×C12712yes—
381C23C4×D4×C12712yes—
382C23C4×D4×C12712yes—
383C23C4×D4×C12712yes—
384C23C4×D4×C12712yes—
385C23C4×Q8×C12712yes—
386C23C4×Q8×C12712yes—
387C23#120×C12711yescharacteristic
388C23#121×C12712yes—
389C23C22⋊Q8×C12712yes—
390C23C22⋊Q8×C12712yes—
391C23#123×C12712yes—
392C23#123×C12711yescharacteristic
393C23#124×C12711yescharacteristic
394C23#125×C12712yes—
395C23#126×C12712yes—
396C23C4⋊Q8×C12711yescharacteristic
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—24no—
400C2×C4—28no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—48no—
407C2×C4—44no—
408C2×C4—48no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—48no—
419C2×C4—48no—
420C2×C4—44no—
421C2×C4—84no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—84no—
425C2×C4—82no—
426C2×C4—82no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—24no—
431C22—24no—
432C22—24no—
433C22—21no—
434C22—22no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—22no—
441C22—41no—
442C22—41no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—41no—
448C22—42no—
449C22—42no—
450C22—41no—
451C22C4×C22⋊C4×C12711yescharacteristic
452C22C4×C4⋊C4×C12712yes—
453C22#385×C12712yes—
454C22#386×C12711yescharacteristic
455C22#387×C12712yes—
456C22#387×C12712yes—
457C22#388×C12712yes—
458C22#389×C12712yes—
459C22#391×C12711yescharacteristic
460C22B(4,𝔽2)×C12712yes—
461C22#458×C12712yes—
462C4—44no—
463C4—48no—
464C4—44no—
465C4—42no—
466C4—42no—
467C4—84no—
468C2—21no—
469C2—22no—
470C2—22no—
471C2—22no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2C127×#143611yescharacteristic
476C2C127×#186714yes—
477C2C127×#188911yescharacteristic
478C2C127×#189011yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC23C2×C42×C127
Frattini, cosocleC25C23×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
13. #385×C127C4semidirect
20. #342×C127C4semidirect
105. C22×C4×C127C4⋊C4semidirect
119. C22⋊C4×C127C42semidirect
228. #10918C127direct (N × H)
245. C127#10918direct (N × H)
253. #385C4×C127semidirect
260. #342C4×C127semidirect
345. C22×C4C4⋊C4×C127semidirect
359. C22⋊C4C42×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C127×#22732
C2×#342×C1272
C127×C22⋊#952
#10918127