Finite Group Databasebeta

← C127×#18535 #44582208

Subgroups — C127×#18535 #44582208

Order 32512.

908 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic, complemented
2C127×#3141C211yesmaximal, characteristic
3C127×#3112C211yesmaximal, characteristic
4C127×#3112C211yesmaximal, characteristic
5C127×#1636C214yesmaximal, complemented
6C127×#1626C214yesmaximal, complemented
7C127×#1556C211yesmaximal, characteristic, complemented
8C127×#1491C211yesmaximal, characteristic, complemented
9C127×#1491C211yesmaximal, characteristic, complemented
10#557×C127—22no—
11#557×C127—22no—
12#557×C127—22no—
13#557×C127C2214yes—
14#532×C127C2211yescharacteristic
15C2×C4⋊Q8×C127—21no—
16C2×C4⋊Q8×C127C2211yescharacteristic
17C2×#125×C127—22no—
18C2×#125×C127—21no—
19C2×C4×Q8×C127—21no—
20C2×C4×Q8×C127—21no—
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×Q8×C127C2211yescharacteristic
23#489×C127—22no—
24#487×C127C2212yes—
25#486×C127C2212yes—
26#480×C127—21no—
27#480×C127—21no—
28#477×C127C2212yes—
29#477×C127C2212yes—
30#460×C127C2212yes—
31#460×C127C2212yes—
32#448×C127—21no—
33#448×C127—21no—
34#440×C127—22no—
35#440×C127—22no—
36#432×C127C2211yescharacteristic
37#432×C127C2211yescharacteristic
38#417×C127—22no—
39C4×M16×C127C2211yescharacteristic
40#332×C127C2214yes—
41Q8⋊C8×C127C2214yes—
42Q8⋊C8×C127C2214yes—
43C2×#41×C127—21no—
44C22×Q8×C127—21no—
45C22×Q8×C127D411yescharacteristic
46C22×Q8×C127D411yescharacteristic
47C2×SD16×C127—22no—
48C2×SD16×C127—22no—
49C2×M16×C127—21no—
50C4⋊Q8×C127—24no—
51C4⋊Q8×C127—24no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127D412yes—
55C4⋊Q8×C127C2311yescharacteristic
56C4⋊Q8×C127C2312yes—
57#127×C127C2311yescharacteristic
58#125×C127—28no—
59#125×C127—24no—
60#125×C127—28no—
61#125×C127—24no—
62#124×C127—21no—
63#121×C127—21no—
64#121×C127—21no—
65C4×Q8×C127—24no—
66C4×Q8×C127—24no—
67C4×Q8×C127—24no—
68C4×Q8×C127—24no—
69C4×Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×Q8×C127—21no—
72C4×Q8×C127—21no—
73C4×Q8×C127D412yes—
74C4×Q8×C127D412yes—
75C4×Q8×C127C2312yes—
76C4×Q8×C127C2312yes—
77C4×D4×C127—21no—
78C4×D4×C127—21no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127D411yescharacteristic
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C4⋊C4×C127D412yes—
88C2×C42×C127—22no—
89C2×C42×C127—21no—
90C2×C42×C127—21no—
91C2×C42×C127C2311yescharacteristic
92#107×C127—22no—
93#107×C127—22no—
94C4⋊C8×C127C2312yes—
95C4⋊C8×C127C2312yes—
96#103×C127—22no—
97#103×C127—22no—
98#103×C127—24no—
99#102×C127—24no—
100#102×C127—22no—
101#102×C127—22no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106#97×C127—21no—
107C4×C8×C127C2312yes—
108#41×C127—44no—
109C2×Q8×C127—24no—
110C2×Q8×C127—21no—
111C2×Q8×C127—21no—
112C2×Q8×C127—22no—
113C2×Q8×C127—22no—
114C2×Q8×C127—21no—
115C2×Q8×C127—42no—
116C2×Q8×C127—44no—
117C2×Q8×C127C2×D412yes—
118C2×Q8×C127C2×D412yes—
119C2×D4×C127—21no—
120C2×D4×C127—21no—
121C2×D4×C127—21no—
122C2×D4×C127—41no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127—41no—
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132SD16×C127—44no—
133SD16×C127—44no—
134M16×C127—42no—
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C4⋊C4×C127—28no—
139C4⋊C4×C127—28no—
140C4⋊C4×C127—28no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127C2×D414yes—
153C4⋊C4×C127C2×D412yes—
154C4⋊C4×C127C2×D412yes—
155C22⋊C4×C127—41no—
156C22⋊C4×C127—41no—
157C42×C127—28no—
158C42×C127—22no—
159C42×C127—22no—
160C42×C127—22no—
161C42×C127—22no—
162C42×C127C2×D411yescharacteristic
163C42×C127C2×D411yescharacteristic
164C42×C127C2×D411yescharacteristic
165C42×C127C2411yescharacteristic
166C23×C127—41no—
167C23×C127#12011yescharacteristic
168Q8×C127—24no—
169Q8×C127—22no—
170Q8×C127—22no—
171Q8×C127—22no—
172Q8×C127—42no—
173Q8×C127—44no—
174Q8×C127—42no—
175Q8×C127—44no—
176Q8×C127#13714yes—
177D4×C127—42no—
178D4×C127—42no—
179D4×C127—42no—
180D4×C127—82no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—24no—
190C2×C4×C127—42no—
191C2×C4×C127—44no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—41no—
195C2×C4×C127—82no—
196C2×C4×C127#12011yescharacteristic
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127C22×D411yescharacteristic
200C2×C4×C127C22×D411yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C8×C127—42no—
203C8×C127—42no—
204C8×C127—42no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—81no—
208C22×C127—81no—
209C22×C127—81no—
210C22×C127#45412yes—
211C22×C127C2×#12011yescharacteristic
212C4×C127—24no—
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—21no—
216C4×C127—21no—
217C4×C127—42no—
218C4×C127—44no—
219C4×C127—42no—
220C4×C127—42no—
221C4×C127—81no—
222C4×C127C2×#13712yes—
223C4×C127#57512yes—
224#18535C12711yesmaximal, characteristic, direct product factor, Sylow
225C2×C127—22no—
226C2×C127—161no—
227C2×C127#300411yescharacteristic
228C2×C127#300511yescharacteristic
229C2×C127C2×#45411yescharacteristic
230C2×#557C2×C12711yescharacteristic, complemented
231#3141C2×C12711yescharacteristic
232#3112C2×C12711yescharacteristic
233#3112C2×C12711yescharacteristic
234#1636C2×C12714yescomplemented
235#1626C2×C12714yescomplemented
236#1556C2×C12711yescharacteristic, complemented
237#1491C2×C12711yescharacteristic, complemented
238#1491C2×C12711yescharacteristic, complemented
239C127#1853511yescharacteristic, direct product factor, Sylow
240#557—22no—
241#557—22no—
242#557—22no—
243#557C22×C12714yes—
244#532C22×C12711yescharacteristic
245C2×C4⋊Q8—21no—
246C2×C4⋊Q8C22×C12711yescharacteristic
247C2×#125—22no—
248C2×#125—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C22×C12711yescharacteristic
252C2×C4×Q8C22×C12711yescharacteristic
253#489—22no—
254#487C22×C12712yes—
255#486C22×C12712yes—
256#480—21no—
257#480—21no—
258#477C22×C12712yes—
259#477C22×C12712yes—
260#460C22×C12712yes—
261#460C22×C12712yes—
262#448—21no—
263#448—21no—
264#440—22no—
265#440—22no—
266#432C22×C12711yescharacteristic
267#432C22×C12711yescharacteristic
268#417—22no—
269C4×M16C22×C12711yescharacteristic
270#332C22×C12714yes—
271Q8⋊C8C22×C12714yes—
272Q8⋊C8C22×C12714yes—
273C2×#41—21no—
274C22×Q8—21no—
275C22×Q8D4×C12711yescharacteristic
276C22×Q8D4×C12711yescharacteristic
277C2×SD16—22no—
278C2×SD16—22no—
279C2×M16—21no—
280C4⋊Q8—24no—
281C4⋊Q8—24no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8D4×C12712yes—
285C4⋊Q8C23×C12711yescharacteristic
286C4⋊Q8C23×C12712yes—
287#127C23×C12711yescharacteristic
288#125—28no—
289#125—24no—
290#125—28no—
291#125—24no—
292#124—21no—
293#121—21no—
294#121—21no—
295C4×Q8—24no—
296C4×Q8—24no—
297C4×Q8—24no—
298C4×Q8—24no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8D4×C12712yes—
304C4×Q8D4×C12712yes—
305C4×Q8C23×C12712yes—
306C4×Q8C23×C12712yes—
307C4×D4—21no—
308C4×D4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C12711yescharacteristic
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C4⋊C4D4×C12712yes—
318C2×C42—22no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42C23×C12711yescharacteristic
322#107—22no—
323#107—22no—
324C4⋊C8C23×C12712yes—
325C4⋊C8C23×C12712yes—
326#103—22no—
327#103—22no—
328#103—24no—
329#102—24no—
330#102—22no—
331#102—22no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334#97—21no—
335#97—21no—
336#97—21no—
337C4×C8C23×C12712yes—
338#41—44no—
339C2×Q8—24no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8C2×D4×C12712yes—
348C2×Q8C2×D4×C12712yes—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—41no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—41no—
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361C22×C4C2×D4×C12711yescharacteristic
362SD16—44no—
363SD16—44no—
364M16—42no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—28no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4C2×D4×C12714yes—
383C4⋊C4C2×D4×C12712yes—
384C4⋊C4C2×D4×C12712yes—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C42—28no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42—22no—
392C42C2×D4×C12711yescharacteristic
393C42C2×D4×C12711yescharacteristic
394C42C2×D4×C12711yescharacteristic
395C42C24×C12711yescharacteristic
396C23—41no—
397C23#120×C12711yescharacteristic
398Q8—24no—
399Q8—22no—
400Q8—22no—
401Q8—22no—
402Q8—42no—
403Q8—44no—
404Q8—42no—
405Q8—44no—
406Q8#137×C12714yes—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—82no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—82no—
426C2×C4#120×C12711yescharacteristic
427C2×C4#120×C12711yescharacteristic
428C2×C4#120×C12711yescharacteristic
429C2×C4C22×D4×C12711yescharacteristic
430C2×C4C22×D4×C12711yescharacteristic
431C2×C4C22×D4×C12711yescharacteristic
432C8—42no—
433C8—42no—
434C8—42no—
435C22—21no—
436C22—21no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22#454×C12712yes—
441C22C2×#120×C12711yescharacteristic
442C4—24no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—44no—
449C4—42no—
450C4—42no—
451C4—81no—
452C4C2×#137×C12712yes—
453C4#575×C12712yes—
454C2—22no—
455C2—161no—
456C2C127×#300411yescharacteristic
457C2C127×#300511yescharacteristic
458C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#557×C127C2semidirect
5. C127×#1636C2semidirect
6. C127×#1626C2semidirect
7. C127×#1556C2semidirect
8. C127×#1491C2semidirect
9. C127×#1491C2semidirect
224. #18535C127direct (N × H)
230. C2×#557C2×C127semidirect
234. #1636C2×C127semidirect
235. #1626C2×C127semidirect
236. #1556C2×C127semidirect
237. #1491C2×C127semidirect
238. #1491C2×C127semidirect
239. C127#18535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#557×C1272
C127×#31412
C127×#31122
C127×#16362
C127×#16262
C127×#15562
C127×#14912
#18535127