Finite Group Databasebeta

← C127×#21035 #44584708

Subgroups — C127×#21035 #44584708

Order 32512.

898 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C127C211yesmaximal, characteristic
2C127×#2317C211yesmaximal, characteristic
3C127×#2274C211yesmaximal, characteristic
4C127×#1921C212yesmaximal, complemented
5C127×#1920C212yesmaximal, complemented
6C127×#1919C212yesmaximal, complemented
7C127×#1918C212yesmaximal, complemented
8C127×#1736C211yesmaximal, characteristic
9C127×#1735C211yesmaximal, characteristic
10C2×#340×C127C211yesmaximal, characteristic
11C127×#1729C211yesmaximal, characteristic
12C22×M16×C127C2211yescharacteristic
13C23×C8×C127C2211yescharacteristic
14C2×#117×C127C2211yescharacteristic
15C2×#117×C127C2211yescharacteristic
16C2×#117×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19#428×C127C418yescomplemented
20C2×#107×C127C2212yes—
21C2×#106×C127C2212yes—
22#389×C127C2212yes—
23#389×C127C2212yes—
24#385×C127—22no—
25#384×C127—21no—
26#382×C127—21no—
27C4×C4⋊C4×C127—21no—
28C4×C4⋊C4×C127—21no—
29C4×C4⋊C4×C127C2212yes—
30C4×C4⋊C4×C127C2212yes—
31C4×C22⋊C4×C127—22no—
32#340×C127C2211yescharacteristic
33#340×C127C2212yes—
34#340×C127C2212yes—
35#340×C127C2211yescharacteristic
36#340×C127C2212yes—
37#340×C127C2211yescharacteristic
38#340×C127C2212yes—
39#340×C127C2211yescharacteristic
40#336×C127C2212yes—
41#336×C127C2212yes—
42C23×C4×C127—21no—
43C23×C4×C127—21no—
44C23×C4×C127C2311yescharacteristic
45C2×M16×C127—22no—
46C2×M16×C127—22no—
47C2×M16×C127C2×C414yes—
48C22×C8×C127—22no—
49C22×C8×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127C2311yescharacteristic
52C22×C8×C127C2311yescharacteristic
53C22×C8×C127C2312yes—
54#117×C127—22no—
55#117×C127—22no—
56#117×C127—22no—
57#117×C127—22no—
58#117×C127C2×C414yes—
59#117×C127Q814yes—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127C2×C414yes—
68C2×C4⋊C4×C127D411yescharacteristic
69C2×C4⋊C4×C127D411yescharacteristic
70C2×C4⋊C4×C127C2312yes—
71C2×C4⋊C4×C127C2312yes—
72C2×C4⋊C4×C127C2311yescharacteristic
73C2×C4⋊C4×C127C2311yescharacteristic
74C2×C4⋊C4×C127C2311yescharacteristic
75C2×C4⋊C4×C127C2311yescharacteristic
76C2×C22⋊C4×C127—21no—
77C2×C22⋊C4×C127—21no—
78C2×C22⋊C4×C127D412yes—
79C2×C42×C127—21no—
80C2×C42×C127—21no—
81C2×C42×C127—22no—
82C2×C42×C127—22no—
83C2×C42×C127C2312yes—
84#107×C127C2×C418yescomplemented
85#106×C127C2×C418yescomplemented
86#95×C127—22no—
87#95×C127—22no—
88#95×C127—22no—
89#95×C127—22no—
90C24×C127C2×D411yescharacteristic
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—24no—
97C22×C4×C127—22no—
98C22×C4×C127—42no—
99C22×C4×C127—81no—
100C22×C4×C127—81no—
101C22×C4×C127—81no—
102C22×C4×C127—81no—
103C22×C4×C127C22×C412yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×Q812yes—
108C22×C4×C127#4112yes—
109C22×C4×C127#4112yes—
110C22×C4×C127#4112yes—
111C22×C4×C127#4112yes—
112C22×C4×C127C2411yescharacteristic
113M16×C127—28no—
114C2×C8×C127—22no—
115C2×C8×C127—22no—
116C2×C8×C127—21no—
117C2×C8×C127—21no—
118C2×C8×C127—21no—
119C2×C8×C127—21no—
120C2×C8×C127—21no—
121C2×C8×C127—21no—
122C2×C8×C127—44no—
123C2×C8×C127C22×C414yes—
124C4⋊C4×C127—24no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—42no—
135C4⋊C4×C127—82no—
136C4⋊C4×C127—82no—
137C4⋊C4×C127C22×C412yes—
138C4⋊C4×C127C22×C414yes—
139C4⋊C4×C127C22×C412yes—
140C4⋊C4×C127C2×Q812yes—
141C4⋊C4×C127C2×Q812yes—
142C22⋊C4×C127—24no—
143C22⋊C4×C127—24no—
144C22⋊C4×C127—24no—
145C42×C127—24no—
146C42×C127—24no—
147C42×C127—22no—
148C42×C127—22no—
149C42×C127—82no—
150C42×C127—82no—
151C23×C127—21no—
152C23×C127—21no—
153C23×C127—21no—
154C23×C127—21no—
155C23×C127C4×D412yes—
156C23×C127C22⋊Q812yes—
157C23×C127#12312yes—
158C23×C127C22×D411yescharacteristic
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—41no—
171C2×C4×C127—42no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—42no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—84no—
184C2×C4×C127—84no—
185C2×C4×C127#11714yes—
186C2×C4×C127C4×D412yes—
187C2×C4×C127C4×Q814yes—
188C2×C4×C127C22⋊Q812yes—
189C2×C4×C127#12312yes—
190C2×C4×C127#12514yes—
191C2×C4×C127#12614yes—
192C2×C4×C127C23×C411yescharacteristic
193C2×C4×C127C22×Q811yescharacteristic
194C2×C4×C127C2×#4111yescharacteristic
195C2×C4×C127C2×#4111yescharacteristic
196C2×C4×C127C2×#4111yescharacteristic
197C2×C4×C127C2×#4111yescharacteristic
198C8×C127—24no—
199C8×C127—41no—
200C8×C127—41no—
201C22×C127—22no—
202C22×C127—22no—
203C22×C127—22no—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127#38714yes—
208C22×C127C2×C4×D411yescharacteristic
209C22×C127C2×C22⋊Q811yescharacteristic
210C22×C127C2×#12311yescharacteristic
211C22×C127#57611yescharacteristic
212C22×C127#57711yescharacteristic
213C22×C127#57711yescharacteristic
214C22×C127#57811yescharacteristic
215C4×C127—42no—
216C4×C127—42no—
217C4×C127—42no—
218C4×C127—42no—
219C4×C127—42no—
220C4×C127—44no—
221C4×C127—42no—
222C4×C127—82no—
223C4×C127#38714yes—
224C4×C127C2×#11711yescharacteristic
225C4×C127C2×C4×Q811yescharacteristic
226C4×C127C2×#12511yescharacteristic
227C4×C127C2×#12611yescharacteristic
228#21035C12711yesmaximal, characteristic, direct product factor, Sylow
229C2×C127—24no—
230C2×C127C2×#38711yescharacteristic
231C2×C127#294611yescharacteristic
232C2×C127#294711yescharacteristic
233C2×C127#308311yescharacteristic
234C2×C127#308411yescharacteristic
235C2×C127#309611yescharacteristic
236C2×C127#309711yescharacteristic
237C2×#428C2×C12711yescharacteristic
238#2317C2×C12711yescharacteristic
239#2274C2×C12711yescharacteristic
240#1921C2×C12712yescomplemented
241#1920C2×C12712yescomplemented
242#1919C2×C12712yescomplemented
243#1918C2×C12712yescomplemented
244#1736C2×C12711yescharacteristic
245#1735C2×C12711yescharacteristic
246C2×#340C2×C12711yescharacteristic
247#1729C2×C12711yescharacteristic
248C127#2103511yescharacteristic, direct product factor, Sylow
249C22×M16C22×C12711yescharacteristic
250C23×C8C22×C12711yescharacteristic
251C2×#117C22×C12711yescharacteristic
252C2×#117C22×C12711yescharacteristic
253C2×#117C22×C12711yescharacteristic
254C22×C4⋊C4C22×C12711yescharacteristic
255C22×C4⋊C4C22×C12711yescharacteristic
256#428C4×C12718yescomplemented
257C2×#107C22×C12712yes—
258C2×#106C22×C12712yes—
259#389C22×C12712yes—
260#389C22×C12712yes—
261#385—22no—
262#384—21no—
263#382—21no—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4C22×C12712yes—
267C4×C4⋊C4C22×C12712yes—
268C4×C22⋊C4—22no—
269#340C22×C12711yescharacteristic
270#340C22×C12712yes—
271#340C22×C12712yes—
272#340C22×C12711yescharacteristic
273#340C22×C12712yes—
274#340C22×C12711yescharacteristic
275#340C22×C12712yes—
276#340C22×C12711yescharacteristic
277#336C22×C12712yes—
278#336C22×C12712yes—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4C23×C12711yescharacteristic
282C2×M16—22no—
283C2×M16—22no—
284C2×M16C2×C4×C12714yes—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8C23×C12711yescharacteristic
289C22×C8C23×C12711yescharacteristic
290C22×C8C23×C12712yes—
291#117—22no—
292#117—22no—
293#117—22no—
294#117—22no—
295#117C2×C4×C12714yes—
296#117Q8×C12714yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4C2×C4×C12714yes—
305C2×C4⋊C4D4×C12711yescharacteristic
306C2×C4⋊C4D4×C12711yescharacteristic
307C2×C4⋊C4C23×C12712yes—
308C2×C4⋊C4C23×C12712yes—
309C2×C4⋊C4C23×C12711yescharacteristic
310C2×C4⋊C4C23×C12711yescharacteristic
311C2×C4⋊C4C23×C12711yescharacteristic
312C2×C4⋊C4C23×C12711yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4D4×C12712yes—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42C23×C12712yes—
321#107C2×C4×C12718yescomplemented
322#106C2×C4×C12718yescomplemented
323#95—22no—
324#95—22no—
325#95—22no—
326#95—22no—
327C24C2×D4×C12711yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—42no—
336C22×C4—81no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4C22×C4×C12712yes—
341C22×C4C2×D4×C12712yes—
342C22×C4C2×D4×C12712yes—
343C22×C4C2×D4×C12711yescharacteristic
344C22×C4C2×Q8×C12712yes—
345C22×C4#41×C12712yes—
346C22×C4#41×C12712yes—
347C22×C4#41×C12712yes—
348C22×C4#41×C12712yes—
349C22×C4C24×C12711yescharacteristic
350M16—28no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—44no—
360C2×C8C22×C4×C12714yes—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—42no—
372C4⋊C4—82no—
373C4⋊C4—82no—
374C4⋊C4C22×C4×C12712yes—
375C4⋊C4C22×C4×C12714yes—
376C4⋊C4C22×C4×C12712yes—
377C4⋊C4C2×Q8×C12712yes—
378C4⋊C4C2×Q8×C12712yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C42—24no—
383C42—24no—
384C42—22no—
385C42—22no—
386C42—82no—
387C42—82no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23C4×D4×C12712yes—
393C23C22⋊Q8×C12712yes—
394C23#123×C12712yes—
395C23C22×D4×C12711yescharacteristic
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—84no—
421C2×C4—84no—
422C2×C4#117×C12714yes—
423C2×C4C4×D4×C12712yes—
424C2×C4C4×Q8×C12714yes—
425C2×C4C22⋊Q8×C12712yes—
426C2×C4#123×C12712yes—
427C2×C4#125×C12714yes—
428C2×C4#126×C12714yes—
429C2×C4C23×C4×C12711yescharacteristic
430C2×C4C22×Q8×C12711yescharacteristic
431C2×C4C2×#41×C12711yescharacteristic
432C2×C4C2×#41×C12711yescharacteristic
433C2×C4C2×#41×C12711yescharacteristic
434C2×C4C2×#41×C12711yescharacteristic
435C8—24no—
436C8—41no—
437C8—41no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22#387×C12714yes—
445C22C2×C4×D4×C12711yescharacteristic
446C22C2×C22⋊Q8×C12711yescharacteristic
447C22C2×#123×C12711yescharacteristic
448C22#576×C12711yescharacteristic
449C22#577×C12711yescharacteristic
450C22#577×C12711yescharacteristic
451C22#578×C12711yescharacteristic
452C4—42no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—44no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4#387×C12714yes—
461C4C2×#117×C12711yescharacteristic
462C4C2×C4×Q8×C12711yescharacteristic
463C4C2×#125×C12711yescharacteristic
464C4C2×#126×C12711yescharacteristic
465C2—24no—
466C2C2×#387×C12711yescharacteristic
467C2C127×#294611yescharacteristic
468C2C127×#294711yescharacteristic
469C2C127×#308311yescharacteristic
470C2C127×#308411yescharacteristic
471C2C127×#309611yescharacteristic
472C2C127×#309711yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1921C2semidirect
5. C127×#1920C2semidirect
6. C127×#1919C2semidirect
7. C127×#1918C2semidirect
19. #428×C127C4semidirect
84. #107×C127C2×C4semidirect
85. #106×C127C2×C4semidirect
228. #21035C127direct (N × H)
240. #1921C2×C127semidirect
241. #1920C2×C127semidirect
242. #1919C2×C127semidirect
243. #1918C2×C127semidirect
248. C127#21035direct (N × H)
256. #428C4×C127semidirect
321. #107C2×C4×C127semidirect
322. #106C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1272
C127×#23172
C127×#22742
C127×#19212
C127×#19202
C127×#19192
C127×#19182
C127×#17362
C127×#17352
C2×#340×C1272
C127×#17292
#21035127