Finite Group Databasebeta

← C127×#11344 #44575017

Subgroups — C127×#11344 #44575017

Order 32512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2315C211yesmaximal, characteristic
2C2×#385×C127C212yesmaximal
3C2×#342×C127C212yesmaximal
4C2×#342×C127C211yesmaximal, characteristic
5C127×C22⋊#95C211yesmaximal, characteristic
6C24×C4×C127C2211yescharacteristic
7C22×C4⋊C4×C127—22no—
8C22×C22⋊C4×C127C2212yes—
9C22×C22⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2211yescharacteristic
11C22×C22⋊C4×C127C2212yes—
12#385×C127—22no—
13#385×C127—22no—
14#385×C127—24no—
15#385×C127—24no—
16#380×C127—22no—
17C2×#95×C127—22no—
18C2×#95×C127—22no—
19#342×C127—24no—
20#342×C127C414yescomplemented
21C25×C127C2311yescharacteristic
22C23×C4×C127—22no—
23C23×C4×C127—22no—
24C23×C4×C127—21no—
25C23×C4×C127—21no—
26C23×C4×C127—22no—
27C23×C4×C127—21no—
28C23×C4×C127—44no—
29C23×C4×C127D412yes—
30C23×C4×C127D412yes—
31C23×C4×C127D412yes—
32C23×C4×C127D412yes—
33C2×C4⋊C4×C127—28no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—48no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—22no—
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×C127—22no—
49C2×C22⋊C4×C127—22no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127C2×C412yes—
52C2×C22⋊C4×C127C2×C414yes—
53C2×C22⋊C4×C127D414yes—
54C2×C22⋊C4×C127Q812yes—
55C2×C22⋊C4×C127Q812yes—
56C2×C22⋊C4×C127Q814yes—
57#95×C127—28no—
58#95×C127—24no—
59#95×C127—44no—
60C24×C127—42no—
61C24×C127—42no—
62C24×C127C22×C411yescharacteristic
63C24×C127C2×D411yescharacteristic
64C24×C127C2×D412yes—
65C24×C127C2×D412yes—
66C24×C127C2×D411yescharacteristic
67C24×C127C2×Q811yescharacteristic
68C24×C127C2×Q812yes—
69C24×C127C2×Q811yescharacteristic
70C24×C127#4112yes—
71C24×C127#4111yescharacteristic
72C24×C127#4111yescharacteristic
73C22×C4×C127—24no—
74C22×C4×C127—28no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—24no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—44no—
90C22×C4×C127—48no—
91C22×C4×C127—44no—
92C22×C4×C127—44no—
93C22×C4×C127—44no—
94C22×C4×C127—44no—
95C22×C4×C127—42no—
96C22×C4×C127—41no—
97C22×C4×C127—42no—
98C22×C4×C127—41no—
99C22×C4×C127—42no—
100C22×C4×C127—44no—
101C22×C4×C127—42no—
102C22×C4×C127—44no—
103C22×C4×C127—42no—
104C22×C4×C127—42no—
105C22×C4×C127—41no—
106C22×C4×C127—41no—
107C22×C4×C127C4⋊C414yescomplemented
108C4⋊C4×C127—416no—
109C4⋊C4×C127—82no—
110C4⋊C4×C127—82no—
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×C127—42no—
120C22⋊C4×C127—42no—
121C22⋊C4×C127—42no—
122C22⋊C4×C127C4⋊C418yescomplemented
123C23×C127—22no—
124C23×C127—24no—
125C23×C127—22no—
126C23×C127—24no—
127C23×C127—41no—
128C23×C127—42no—
129C23×C127—41no—
130C23×C127—42no—
131C23×C127—41no—
132C23×C127—42no—
133C23×C127—44no—
134C23×C127—42no—
135C23×C127—42no—
136C23×C127—42no—
137C23×C127—44no—
138C23×C127—41no—
139C23×C127C2×C4⋊C411yescharacteristic
140C23×C127C2×C4⋊C412yes—
141C23×C127C4×D412yes—
142C23×C127C4×D411yescharacteristic
143C23×C127C4×Q811yescharacteristic
144C23×C127#12012yes—
145C23×C127#12011yescharacteristic
146C23×C127#12111yescharacteristic
147C23×C127#12112yes—
148C23×C127C22⋊Q812yes—
149C23×C127C22⋊Q812yes—
150C23×C127C22⋊Q811yescharacteristic
151C23×C127C22⋊Q812yes—
152C23×C127C22⋊Q812yes—
153C23×C127#12311yescharacteristic
154C23×C127#12312yes—
155C23×C127#12511yescharacteristic
156C23×C127#12512yes—
157C23×C127#12711yescharacteristic
158C23×C127C4⋊Q811yescharacteristic
159C23×C127C4⋊Q812yes—
160C23×C127C4⋊Q812yes—
161C23×C127C4⋊Q811yescharacteristic
162C2×C4×C127—28no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—28no—
166C2×C4×C127—44no—
167C2×C4×C127—48no—
168C2×C4×C127—48no—
169C2×C4×C127—44no—
170C2×C4×C127—44no—
171C2×C4×C127—42no—
172C2×C4×C127—48no—
173C2×C4×C127—44no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—44no—
177C2×C4×C127—42no—
178C2×C4×C127—44no—
179C2×C4×C127—44no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—44no—
186C2×C4×C127—44no—
187C2×C4×C127—82no—
188C2×C4×C127—82no—
189C2×C4×C127—81no—
190C2×C4×C127—81no—
191C2×C4×C127—82no—
192C2×C4×C127—82no—
193C22×C127—24no—
194C22×C127—22no—
195C22×C127—22no—
196C22×C127—24no—
197C22×C127—22no—
198C22×C127—24no—
199C22×C127—22no—
200C22×C127—24no—
201C22×C127—22no—
202C22×C127—21no—
203C22×C127—22no—
204C22×C127—21no—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—42no—
210C22×C127—41no—
211C22×C127—41no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—41no—
216C22×C127—42no—
217C22×C127—42no—
218C22×C127—41no—
219C22×C127#38411yescharacteristic
220C22×C127#38512yes—
221C22×C127#38511yescharacteristic
222C22×C127#38911yescharacteristic
223C22×C127#38912yes—
224C22×C127#39211yescharacteristic
225C22×C127#39512yes—
226C22×C127#39511yescharacteristic
227C22×C127#39811yescharacteristic
228C22×C127#39812yes—
229C22×C127#39911yescharacteristic
230C22×C127B(4,𝔽2)12yes—
231C22×C127#45812yes—
232C4×C127—48no—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—82no—
236C4×C127—82no—
237C4×C127—82no—
238#11344C12711yesmaximal, characteristic, direct product factor, Sylow
239C2×C127—22no—
240C2×C127—21no—
241C2×C127—21no—
242C2×C127—21no—
243C2×C127—22no—
244C2×C127—22no—
245C2×C127—22no—
246C2×C127—21no—
247C2×C127#144411yescharacteristic
248C2×C127#186712yes—
249C2×C127#202111yescharacteristic
250C2×C127#202211yescharacteristic
251C2×C127#206212yes—
252#2315C2×C12711yescharacteristic
253C2×#385C2×C12712yes—
254C2×#342C2×C12712yes—
255C2×#342C2×C12711yescharacteristic
256C22⋊#95C2×C12711yescharacteristic
257C127#1134411yescharacteristic, direct product factor, Sylow
258C24×C4C22×C12711yescharacteristic
259C22×C4⋊C4—22no—
260C22×C22⋊C4C22×C12712yes—
261C22×C22⋊C4C22×C12711yescharacteristic
262C22×C22⋊C4C22×C12711yescharacteristic
263C22×C22⋊C4C22×C12712yes—
264#385—22no—
265#385—22no—
266#385—24no—
267#385—24no—
268#380—22no—
269C2×#95—22no—
270C2×#95—22no—
271#342—24no—
272#342C4×C12714yescomplemented
273C25C23×C12711yescharacteristic
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—44no—
281C23×C4D4×C12712yes—
282C23×C4D4×C12712yes—
283C23×C4D4×C12712yes—
284C23×C4D4×C12712yes—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—48no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4C2×C4×C12712yes—
304C2×C22⋊C4C2×C4×C12714yes—
305C2×C22⋊C4D4×C12714yes—
306C2×C22⋊C4Q8×C12712yes—
307C2×C22⋊C4Q8×C12712yes—
308C2×C22⋊C4Q8×C12714yes—
309#95—28no—
310#95—24no—
311#95—44no—
312C24—42no—
313C24—42no—
314C24C22×C4×C12711yescharacteristic
315C24C2×D4×C12711yescharacteristic
316C24C2×D4×C12712yes—
317C24C2×D4×C12712yes—
318C24C2×D4×C12711yescharacteristic
319C24C2×Q8×C12711yescharacteristic
320C24C2×Q8×C12712yes—
321C24C2×Q8×C12711yescharacteristic
322C24#41×C12712yes—
323C24#41×C12711yescharacteristic
324C24#41×C12711yescharacteristic
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—44no—
342C22×C4—48no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—44no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C4⋊C4×C12714yescomplemented
360C4⋊C4—416no—
361C4⋊C4—82no—
362C4⋊C4—82no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4C4⋊C4×C12718yescomplemented
375C23—22no—
376C23—24no—
377C23—22no—
378C23—24no—
379C23—41no—
380C23—42no—
381C23—41no—
382C23—42no—
383C23—41no—
384C23—42no—
385C23—44no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—41no—
391C23C2×C4⋊C4×C12711yescharacteristic
392C23C2×C4⋊C4×C12712yes—
393C23C4×D4×C12712yes—
394C23C4×D4×C12711yescharacteristic
395C23C4×Q8×C12711yescharacteristic
396C23#120×C12712yes—
397C23#120×C12711yescharacteristic
398C23#121×C12711yescharacteristic
399C23#121×C12712yes—
400C23C22⋊Q8×C12712yes—
401C23C22⋊Q8×C12712yes—
402C23C22⋊Q8×C12711yescharacteristic
403C23C22⋊Q8×C12712yes—
404C23C22⋊Q8×C12712yes—
405C23#123×C12711yescharacteristic
406C23#123×C12712yes—
407C23#125×C12711yescharacteristic
408C23#125×C12712yes—
409C23#127×C12711yescharacteristic
410C23C4⋊Q8×C12711yescharacteristic
411C23C4⋊Q8×C12712yes—
412C23C4⋊Q8×C12712yes—
413C23C4⋊Q8×C12711yescharacteristic
414C2×C4—28no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—28no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—48no—
422C2×C4—44no—
423C2×C4—48no—
424C2×C4—48no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—82no—
445C22—24no—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—22no—
450C22—24no—
451C22—22no—
452C22—24no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—41no—
463C22—41no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—41no—
468C22—42no—
469C22—42no—
470C22—41no—
471C22#384×C12711yescharacteristic
472C22#385×C12712yes—
473C22#385×C12711yescharacteristic
474C22#389×C12711yescharacteristic
475C22#389×C12712yes—
476C22#392×C12711yescharacteristic
477C22#395×C12712yes—
478C22#395×C12711yescharacteristic
479C22#398×C12711yescharacteristic
480C22#398×C12712yes—
481C22#399×C12711yescharacteristic
482C22B(4,𝔽2)×C12712yes—
483C22#458×C12712yes—
484C4—48no—
485C4—44no—
486C4—44no—
487C4—82no—
488C4—82no—
489C4—82no—
490C2—22no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—22no—
496C2—22no—
497C2—21no—
498C2C127×#144411yescharacteristic
499C2C127×#186712yes—
500C2C127×#202111yescharacteristic
501C2C127×#202211yescharacteristic
502C2C127×#206212yes—
subgroupG/H
center, socleC23×C127#120
commutatorC24C22×C4×C127
Frattini, cosocleC25C23×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
20. #342×C127C4semidirect
107. C22×C4×C127C4⋊C4semidirect
122. C22⋊C4×C127C4⋊C4semidirect
238. #11344C127direct (N × H)
257. C127#11344direct (N × H)
272. #342C4×C127semidirect
359. C22×C4C4⋊C4×C127semidirect
374. C22⋊C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23152
C2×#385×C1272
C2×#342×C1272
C127×C22⋊#952
#11344127