Finite Group Databasebeta

← C127×#21078 #44584751

Subgroups — C127×#21078 #44584751

Order 32512.

1118 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2911C211yesmaximal, characteristic, complemented
2C2×#418×C127C211yesmaximal, characteristic
3C2×#418×C127C211yesmaximal, characteristic
4C22×#100×C127C211yesmaximal, characteristic
5C127×#2873C211yesmaximal, characteristic, complemented
6C127×#1931C218yesmaximal, complemented
7C127×#1742C211yesmaximal, characteristic, complemented
8C127×#1738C211yesmaximal, characteristic, complemented
9C23×D4×C127C2211yescharacteristic
10C22×M16×C127C2211yescharacteristic
11C22×M16×C127C2211yescharacteristic
12C22×M16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C2×#117×C127C2211yescharacteristic
15C2×#117×C127C2211yescharacteristic
16#428×C127—22no—
17#428×C127C2214yescomplemented
18#427×C127—22no—
19#418×C127—22no—
20#418×C127—22no—
21#418×C127—22no—
22#418×C127C2214yes—
23C2×#102×C127—22no—
24C2×#102×C127C2214yes—
25C2×#100×C127C418yescomplemented
26C2×#100×C127C2214yes—
27#405×C127—22no—
28#405×C127C2214yescomplemented
29C4×M16×C127—22no—
30#343×C127C2214yescomplemented
31#341×C127C2214yescomplemented
32C25×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—21no—
35C22×D4×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—21no—
40C22×D4×C127—22no—
41C22×D4×C127C2×C414yes—
42C22×D4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C2×M16×C127—21no—
45C2×M16×C127—21no—
46C2×M16×C127—22no—
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C2×M16×C127—21no—
51C2×M16×C127—22no—
52C2×M16×C127—22no—
53C2×M16×C127C2×C414yes—
54C2×M16×C127C2×C414yes—
55C2×M16×C127D412yes—
56C2×M16×C127D412yes—
57C2×M16×C127C2312yes—
58C2×M16×C127C2312yes—
59C2×M16×C127C2312yes—
60C22×C8×C127—21no—
61C22×C8×C127—21no—
62C22×C8×C127—21no—
63C22×C8×C127C2312yes—
64#117×C127—21no—
65#117×C127—21no—
66#117×C127—21no—
67#117×C127—21no—
68#117×C127—21no—
69#117×C127—21no—
70#117×C127D412yes—
71#117×C127C2312yes—
72C2×C4⋊C4×C127D412yes—
73C2×C4⋊C4×C127C2312yes—
74C2×C22⋊C4×C127—21no—
75C2×C22⋊C4×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—21no—
78#107×C127—24no—
79#106×C127—24no—
80#102×C127—28no—
81#102×C127—28no—
82#100×C127C2×C4116yescomplemented
83#97×C127—24no—
84C4×C8×C127—24no—
85C24×C127—24no—
86C24×C127—22no—
87C24×C127—41no—
88C24×C127—41no—
89C24×C127—42no—
90C24×C127—84no—
91C24×C127#4111yescharacteristic
92C2×D4×C127—24no—
93C2×D4×C127—24no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—22no—
102C2×D4×C127—41no—
103C2×D4×C127—41no—
104C2×D4×C127—42no—
105C2×D4×C127—42no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127—42no—
109C2×D4×C127C22×C414yes—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127C22×C412yes—
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127#4111yescharacteristic
118C22×C4×C127#4112yes—
119C22×C4×C127#4112yes—
120C22×C4×C127#4112yes—
121C22×C4×C127C2411yescharacteristic
122M16×C127—24no—
123M16×C127—24no—
124M16×C127—24no—
125M16×C127—24no—
126M16×C127—22no—
127M16×C127—22no—
128M16×C127—22no—
129M16×C127—22no—
130M16×C127—42no—
131M16×C127C22×C414yes—
132M16×C127C22×C414yes—
133C2×C8×C127—24no—
134C2×C8×C127—24no—
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—42no—
141C2×C8×C127C2×D414yes—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127C2×D414yes—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—41no—
149C22⋊C4×C127—41no—
150C42×C127—22no—
151C42×C127—22no—
152C42×C127—41no—
153C42×C127—41no—
154C23×C127—24no—
155C23×C127—42no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127—44no—
159C23×C127—44no—
160C23×C127—84no—
161C23×C127—84no—
162C23×C127—84no—
163C23×C127—88no—
164C23×C127—88no—
165C23×C127#11712yes—
166C23×C127#12111yescharacteristic
167C23×C127#12111yescharacteristic
168C23×C127#12612yes—
169C23×C127C2×#4111yescharacteristic
170D4×C127—24no—
171D4×C127—24no—
172D4×C127—42no—
173D4×C127—42no—
174D4×C127—44no—
175D4×C127—44no—
176C2×C4×C127—24no—
177C2×C4×C127—42no—
178C2×C4×C127—82no—
179C2×C4×C127—82no—
180C2×C4×C127#11712yes—
181C2×C4×C127C4×D412yes—
182C2×C4×C127C4×D412yes—
183C2×C4×C127C4×D412yes—
184C2×C4×C127C4×D412yes—
185C2×C4×C127#12111yescharacteristic
186C2×C4×C127#12111yescharacteristic
187C2×C4×C127#12312yes—
188C2×C4×C127#12312yes—
189C2×C4×C127#12412yes—
190C2×C4×C127#12412yes—
191C2×C4×C127#12612yes—
192C2×C4×C127C23×C411yescharacteristic
193C2×C4×C127C22×D411yescharacteristic
194C2×C4×C127C22×D411yescharacteristic
195C2×C4×C127C2×#4111yescharacteristic
196C2×C4×C127C2×#4111yescharacteristic
197C2×C4×C127C2×#4111yescharacteristic
198C8×C127—24no—
199C8×C127—24no—
200C8×C127—24no—
201C8×C127—42no—
202C22×C127—22no—
203C22×C127—22no—
204C22×C127—22no—
205C22×C127—42no—
206C22×C127—42no—
207C22×C127—44no—
208C22×C127—84no—
209C22×C127—88no—
210C22×C127—84no—
211C22×C127—88no—
212C22×C127—84no—
213C22×C127#38812yes—
214C22×C127#38812yes—
215C22×C127C2×#11711yescharacteristic
216C22×C127C2×#12111yescharacteristic
217C22×C127C2×#12611yescharacteristic
218C4×C127—44no—
219C4×C127—82no—
220C4×C127#38812yes—
221C4×C127#38812yes—
222C4×C127C2×C4×D411yescharacteristic
223C4×C127C2×C4×D411yescharacteristic
224C4×C127C2×#12311yescharacteristic
225C4×C127C2×#12411yescharacteristic
226#21078C12711yesmaximal, characteristic, direct product factor, Sylow
227C2×C127—21no—
228C2×C127—21no—
229C2×C127—22no—
230C2×C127—22no—
231C2×C127—84no—
232C2×C127C2×#38811yescharacteristic
233C2×C127#306812yes—
234#2911C2×C12711yescharacteristic, complemented
235C2×#418C2×C12711yescharacteristic
236C2×#418C2×C12711yescharacteristic
237C22×#100C2×C12711yescharacteristic
238#2873C2×C12711yescharacteristic, complemented
239#1931C2×C12718yescomplemented
240#1742C2×C12711yescharacteristic, complemented
241#1738C2×C12711yescharacteristic, complemented
242C127#2107811yescharacteristic, direct product factor, Sylow
243C23×D4C22×C12711yescharacteristic
244C22×M16C22×C12711yescharacteristic
245C22×M16C22×C12711yescharacteristic
246C22×M16C22×C12711yescharacteristic
247C22×M16C22×C12711yescharacteristic
248C2×#117C22×C12711yescharacteristic
249C2×#117C22×C12711yescharacteristic
250#428—22no—
251#428C22×C12714yescomplemented
252#427—22no—
253#418—22no—
254#418—22no—
255#418—22no—
256#418C22×C12714yes—
257C2×#102—22no—
258C2×#102C22×C12714yes—
259C2×#100C4×C12718yescomplemented
260C2×#100C22×C12714yes—
261#405—22no—
262#405C22×C12714yescomplemented
263C4×M16—22no—
264#343C22×C12714yescomplemented
265#341C22×C12714yescomplemented
266C25—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4C2×C4×C12714yes—
276C22×D4C23×C12712yes—
277C23×C4C23×C12711yescharacteristic
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16—22no—
283C2×M16—22no—
284C2×M16—21no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16C2×C4×C12714yes—
288C2×M16C2×C4×C12714yes—
289C2×M16D4×C12712yes—
290C2×M16D4×C12712yes—
291C2×M16C23×C12712yes—
292C2×M16C23×C12712yes—
293C2×M16C23×C12712yes—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8C23×C12712yes—
298#117—21no—
299#117—21no—
300#117—21no—
301#117—21no—
302#117—21no—
303#117—21no—
304#117D4×C12712yes—
305#117C23×C12712yes—
306C2×C4⋊C4D4×C12712yes—
307C2×C4⋊C4C23×C12712yes—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C42—21no—
311C2×C42—21no—
312#107—24no—
313#106—24no—
314#102—28no—
315#102—28no—
316#100C2×C4×C127116yescomplemented
317#97—24no—
318C4×C8—24no—
319C24—24no—
320C24—22no—
321C24—41no—
322C24—41no—
323C24—42no—
324C24—84no—
325C24#41×C12711yescharacteristic
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4C22×C4×C12714yes—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4C22×C4×C12712yes—
347C22×C4C2×D4×C12711yescharacteristic
348C22×C4C2×D4×C12711yescharacteristic
349C22×C4C2×D4×C12711yescharacteristic
350C22×C4C2×D4×C12711yescharacteristic
351C22×C4#41×C12711yescharacteristic
352C22×C4#41×C12712yes—
353C22×C4#41×C12712yes—
354C22×C4#41×C12712yes—
355C22×C4C24×C12711yescharacteristic
356M16—24no—
357M16—24no—
358M16—24no—
359M16—24no—
360M16—22no—
361M16—22no—
362M16—22no—
363M16—22no—
364M16—42no—
365M16C22×C4×C12714yes—
366M16C22×C4×C12714yes—
367C2×C8—24no—
368C2×C8—24no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8C2×D4×C12714yes—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4C2×D4×C12714yes—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C42—22no—
385C42—22no—
386C42—41no—
387C42—41no—
388C23—24no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—44no—
393C23—44no—
394C23—84no—
395C23—84no—
396C23—84no—
397C23—88no—
398C23—88no—
399C23#117×C12712yes—
400C23#121×C12711yescharacteristic
401C23#121×C12711yescharacteristic
402C23#126×C12712yes—
403C23C2×#41×C12711yescharacteristic
404D4—24no—
405D4—24no—
406D4—42no—
407D4—42no—
408D4—44no—
409D4—44no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4#117×C12712yes—
415C2×C4C4×D4×C12712yes—
416C2×C4C4×D4×C12712yes—
417C2×C4C4×D4×C12712yes—
418C2×C4C4×D4×C12712yes—
419C2×C4#121×C12711yescharacteristic
420C2×C4#121×C12711yescharacteristic
421C2×C4#123×C12712yes—
422C2×C4#123×C12712yes—
423C2×C4#124×C12712yes—
424C2×C4#124×C12712yes—
425C2×C4#126×C12712yes—
426C2×C4C23×C4×C12711yescharacteristic
427C2×C4C22×D4×C12711yescharacteristic
428C2×C4C22×D4×C12711yescharacteristic
429C2×C4C2×#41×C12711yescharacteristic
430C2×C4C2×#41×C12711yescharacteristic
431C2×C4C2×#41×C12711yescharacteristic
432C8—24no—
433C8—24no—
434C8—24no—
435C8—42no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—44no—
442C22—84no—
443C22—84no—
444C22—88no—
445C22—88no—
446C22—84no—
447C22#388×C12712yes—
448C22#388×C12712yes—
449C22C2×#117×C12711yescharacteristic
450C22C2×#121×C12711yescharacteristic
451C22C2×#126×C12711yescharacteristic
452C4—44no—
453C4—82no—
454C4#388×C12712yes—
455C4#388×C12712yes—
456C4C2×C4×D4×C12711yescharacteristic
457C4C2×C4×D4×C12711yescharacteristic
458C4C2×#123×C12711yescharacteristic
459C4C2×#124×C12711yescharacteristic
460C2—21no—
461C2—21no—
462C2—22no—
463C2—22no—
464C2—84no—
465C2C2×#388×C12711yescharacteristic
466C2C127×#306812yes—
subgroupG/H
center, socleC22×C127C2×#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2911C2semidirect
5. C127×#2873C2semidirect
6. C127×#1931C2semidirect
7. C127×#1742C2semidirect
8. C127×#1738C2semidirect
17. #428×C127C22semidirect
25. C2×#100×C127C4semidirect
28. #405×C127C22semidirect
30. #343×C127C22semidirect
31. #341×C127C22semidirect
82. #100×C127C2×C4semidirect
226. #21078C127direct (N × H)
234. #2911C2×C127semidirect
238. #2873C2×C127semidirect
239. #1931C2×C127semidirect
240. #1742C2×C127semidirect
241. #1738C2×C127semidirect
242. C127#21078direct (N × H)
251. #428C22×C127semidirect
259. C2×#100C4×C127semidirect
262. #405C22×C127semidirect
264. #343C22×C127semidirect
265. #341C22×C127semidirect
316. #100C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29112
C2×#418×C1272
C22×#100×C1272
C127×#28732
C127×#19312
C127×#17422
C127×#17382
#21078127