Finite Group Databasebeta

← C127×#19424 #44583097

Subgroups — C127×#19424 #44583097

Order 32512.

638 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3210C211yesmaximal, characteristic, complemented
2C127×#3110C211yesmaximal, characteristic, complemented
3C127×#3100C211yesmaximal, characteristic
4C127×#2975C211yesmaximal, characteristic, complemented
5C127×#1701C212yesmaximal, complemented
6C127×#1699C212yesmaximal, complemented
7C127×#1689C212yesmaximal, complemented
8C127×#1685C212yesmaximal, complemented
9C127×#1572C211yesmaximal, characteristic, complemented
10C127×#1553C211yesmaximal, characteristic, complemented
11C127×#1544C211yesmaximal, characteristic, complemented
12#533×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4×D4×C127C2211yescharacteristic
15#494×C127C2211yescharacteristic, complemented
16#492×C127C2211yescharacteristic, complemented
17#487×C127C2211yescharacteristic, complemented
18#486×C127C2211yescharacteristic, complemented
19#484×C127—21no—
20#480×C127—21no—
21#474×C127C2212yes—
22#474×C127C2212yes—
23#464×C127—22no—
24#461×C127C2212yes—
25#459×C127C2212yes—
26#452×C127—22no—
27#450×C127—21no—
28#447×C127—21no—
29#440×C127—22no—
30C4×D8×C127—22no—
31#436×C127—22no—
32#436×C127C2212yes—
33#436×C127C2212yes—
34#432×C127C2211yescharacteristic
35#431×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#407×C127—22no—
39#335×C127C2212yescomplemented
40#334×C127C2212yescomplemented
41#332×C127C2212yescomplemented
42#332×C127C2212yescomplemented
43#332×C127C2212yescomplemented
44#331×C127C2212yescomplemented
45C2×#41×C127—21no—
46C22×D4×C127D411yescharacteristic
47C23×C4×C127—21no—
48C2×Q16×C127—22no—
49C2×SD16×C127—22no—
50C2×SD16×C127—22no—
51C2×D8×C127—22no—
52C2×M16×C127—22no—
53C2×M16×C127—22no—
54C4⋊Q8×C127C2311yescharacteristic
55C4⋊Q8×C127C2311yescharacteristic
56C4⋊Q8×C127C2311yescharacteristic
57#127×C127C2311yescharacteristic
58#125×C127—21no—
59#124×C127—21no—
60C22⋊Q8×C127—21no—
61C22⋊Q8×C127—21no—
62#121×C127—21no—
63#121×C127—21no—
64C4×Q8×C127—21no—
65C4×Q8×C127—21no—
66C4×D4×C127—21no—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127—21no—
70C4×D4×C127D412yes—
71C4×D4×C127C2312yes—
72#117×C127—21no—
73C2×C4⋊C4×C127D411yescharacteristic
74C2×C22⋊C4×C127—21no—
75C2×C42×C127C2311yescharacteristic
76#107×C127—22no—
77#107×C127—22no—
78C4⋊C8×C127D412yes—
79C4⋊C8×C127C2312yes—
80C4⋊C8×C127C2312yes—
81C4⋊C8×C127C2312yes—
82#103×C127—22no—
83#103×C127—22no—
84#102×C127—22no—
85#102×C127—22no—
86#102×C127—22no—
87#102×C127—22no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—21no—
90C22⋊C8×C127—21no—
91C22⋊C8×C127—22no—
92C22⋊C8×C127—22no—
93C22⋊C8×C127D412yes—
94#97×C127—21no—
95C4×C8×C127—21no—
96C4×C8×C127—21no—
97C4×C8×C127C2311yescharacteristic
98C4×C8×C127C2311yescharacteristic
99C24×C127—21no—
100#41×C127—82no—
101C2×Q8×C127—21no—
102C2×Q8×C127—21no—
103C2×Q8×C127—21no—
104C2×D4×C127—21no—
105C2×D4×C127—21no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—42no—
109C2×D4×C127—41no—
110C2×D4×C127C2×D412yes—
111C22×C4×C127—21no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—41no—
115C22×C4×C127—82no—
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127#4111yescharacteristic
119Q16×C127—82no—
120SD16×C127—44no—
121SD16×C127—82no—
122D8×C127—44no—
123M16×C127—82no—
124M16×C127—82no—
125C2×C8×C127—22no—
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127C2×D412yes—
129C2×C8×C127C2×D412yes—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—21no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—41no—
138C4⋊C4×C127—41no—
139C4⋊C4×C127C2×D412yes—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—41no—
143C22⋊C4×C127—41no—
144C22⋊C4×C127—41no—
145C42×C127—41no—
146C42×C127C2×D411yescharacteristic
147C42×C127C2×D411yescharacteristic
148C42×C127#4111yescharacteristic
149C42×C127C2411yescharacteristic
150C23×C127—22no—
151C23×C127—42no—
152C23×C127—41no—
153C23×C127—81no—
154C23×C127—81no—
155C23×C127#12111yescharacteristic
156Q8×C127—42no—
157Q8×C127—42no—
158Q8×C127—42no—
159D4×C127—22no—
160D4×C127—22no—
161D4×C127—42no—
162D4×C127—42no—
163D4×C127—42no—
164D4×C127—81no—
165D4×C127—82no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—41no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—82no—
176C2×C4×C127—82no—
177C2×C4×C127—81no—
178C2×C4×C127#12111yescharacteristic
179C2×C4×C127#12111yescharacteristic
180C2×C4×C127#12111yescharacteristic
181C2×C4×C127C22×D411yescharacteristic
182C2×C4×C127C22×D411yescharacteristic
183C2×C4×C127C2×#4111yescharacteristic
184C8×C127—22no—
185C8×C127—22no—
186C8×C127—42no—
187C8×C127—42no—
188C8×C127—42no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—42no—
193C22×C127—42no—
194C22×C127—42no—
195C22×C127—84no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127C2×#12111yescharacteristic
200C4×C127—21no—
201C4×C127—21no—
202C4×C127—21no—
203C4×C127—21no—
204C4×C127—42no—
205C4×C127—81no—
206C4×C127—81no—
207C4×C127—81no—
208C4×C127#57512yes—
209C4×C127#57612yes—
210#19424C12711yesmaximal, characteristic, direct product factor, Sylow
211C2×C127—41no—
212C2×C127—82no—
213C2×C127—161no—
214C2×C127#304111yescharacteristic
215C2×C127#305411yescharacteristic
216C2×C127#306911yescharacteristic
217#3210C2×C12711yescharacteristic, complemented
218#3110C2×C12711yescharacteristic, complemented
219#3100C2×C12711yescharacteristic
220#2975C2×C12711yescharacteristic, complemented
221#1701C2×C12712yescomplemented
222#1699C2×C12712yescomplemented
223#1689C2×C12712yescomplemented
224#1685C2×C12712yescomplemented
225#1572C2×C12711yescharacteristic, complemented
226#1553C2×C12711yescharacteristic, complemented
227#1544C2×C12711yescharacteristic, complemented
228C127#1942411yescharacteristic, direct product factor, Sylow
229#533C22×C12711yescharacteristic
230#532C22×C12711yescharacteristic
231C2×C4×D4C22×C12711yescharacteristic
232#494C22×C12711yescharacteristic, complemented
233#492C22×C12711yescharacteristic, complemented
234#487C22×C12711yescharacteristic, complemented
235#486C22×C12711yescharacteristic, complemented
236#484—21no—
237#480—21no—
238#474C22×C12712yes—
239#474C22×C12712yes—
240#464—22no—
241#461C22×C12712yes—
242#459C22×C12712yes—
243#452—22no—
244#450—21no—
245#447—21no—
246#440—22no—
247C4×D8—22no—
248#436—22no—
249#436C22×C12712yes—
250#436C22×C12712yes—
251#432C22×C12711yescharacteristic
252#431C22×C12711yescharacteristic
253#431C22×C12711yescharacteristic
254#431C22×C12711yescharacteristic
255#407—22no—
256#335C22×C12712yescomplemented
257#334C22×C12712yescomplemented
258#332C22×C12712yescomplemented
259#332C22×C12712yescomplemented
260#332C22×C12712yescomplemented
261#331C22×C12712yescomplemented
262C2×#41—21no—
263C22×D4D4×C12711yescharacteristic
264C23×C4—21no—
265C2×Q16—22no—
266C2×SD16—22no—
267C2×SD16—22no—
268C2×D8—22no—
269C2×M16—22no—
270C2×M16—22no—
271C4⋊Q8C23×C12711yescharacteristic
272C4⋊Q8C23×C12711yescharacteristic
273C4⋊Q8C23×C12711yescharacteristic
274#127C23×C12711yescharacteristic
275#125—21no—
276#124—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279#121—21no—
280#121—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4D4×C12712yes—
288C4×D4C23×C12712yes—
289#117—21no—
290C2×C4⋊C4D4×C12711yescharacteristic
291C2×C22⋊C4—21no—
292C2×C42C23×C12711yescharacteristic
293#107—22no—
294#107—22no—
295C4⋊C8D4×C12712yes—
296C4⋊C8C23×C12712yes—
297C4⋊C8C23×C12712yes—
298C4⋊C8C23×C12712yes—
299#103—22no—
300#103—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304#102—22no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—22no—
309C22⋊C8—22no—
310C22⋊C8D4×C12712yes—
311#97—21no—
312C4×C8—21no—
313C4×C8—21no—
314C4×C8C23×C12711yescharacteristic
315C4×C8C23×C12711yescharacteristic
316C24—21no—
317#41—82no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—42no—
326C2×D4—41no—
327C2×D4C2×D4×C12712yes—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—41no—
332C22×C4—82no—
333C22×C4C2×D4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4#41×C12711yescharacteristic
336Q16—82no—
337SD16—44no—
338SD16—82no—
339D8—44no—
340M16—82no—
341M16—82no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8C2×D4×C12712yes—
346C2×C8C2×D4×C12712yes—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4C2×D4×C12712yes—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C42—41no—
363C42C2×D4×C12711yescharacteristic
364C42C2×D4×C12711yescharacteristic
365C42#41×C12711yescharacteristic
366C42C24×C12711yescharacteristic
367C23—22no—
368C23—42no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23#121×C12711yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—42no—
376D4—22no—
377D4—22no—
378D4—42no—
379D4—42no—
380D4—42no—
381D4—81no—
382D4—82no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4#121×C12711yescharacteristic
396C2×C4#121×C12711yescharacteristic
397C2×C4#121×C12711yescharacteristic
398C2×C4C22×D4×C12711yescharacteristic
399C2×C4C22×D4×C12711yescharacteristic
400C2×C4C2×#41×C12711yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—42no—
405C8—42no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C2×#121×C12711yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4#575×C12712yes—
426C4#576×C12712yes—
427C2—41no—
428C2—82no—
429C2—161no—
430C2C127×#304111yescharacteristic
431C2C127×#305411yescharacteristic
432C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3100C2
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. C127×#3210C2semidirect
2. C127×#3110C2semidirect
4. C127×#2975C2semidirect
5. C127×#1701C2semidirect
6. C127×#1699C2semidirect
7. C127×#1689C2semidirect
8. C127×#1685C2semidirect
9. C127×#1572C2semidirect
10. C127×#1553C2semidirect
11. C127×#1544C2semidirect
15. #494×C127C22semidirect
16. #492×C127C22semidirect
17. #487×C127C22semidirect
18. #486×C127C22semidirect
39. #335×C127C22semidirect
40. #334×C127C22semidirect
41. #332×C127C22semidirect
42. #332×C127C22semidirect
43. #332×C127C22semidirect
44. #331×C127C22semidirect
210. #19424C127direct (N × H)
217. #3210C2×C127semidirect
218. #3110C2×C127semidirect
220. #2975C2×C127semidirect
221. #1701C2×C127semidirect
222. #1699C2×C127semidirect
223. #1689C2×C127semidirect
224. #1685C2×C127semidirect
225. #1572C2×C127semidirect
226. #1553C2×C127semidirect
227. #1544C2×C127semidirect
228. C127#19424direct (N × H)
232. #494C22×C127semidirect
233. #492C22×C127semidirect
234. #487C22×C127semidirect
235. #486C22×C127semidirect
256. #335C22×C127semidirect
257. #334C22×C127semidirect
258. #332C22×C127semidirect
259. #332C22×C127semidirect
260. #332C22×C127semidirect
261. #331C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32102
C127×#31102
C127×#31002
C127×#29752
C127×#17012
C127×#16992
C127×#16892
C127×#16852
C127×#15722
C127×#15532
C127×#15442
#19424127