Finite Group Databasebeta

← C127×#19217 #44582890

Subgroups — C127×#19217 #44582890

Order 32512.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3249C211yesmaximal, characteristic, complemented
2C127×#3246C211yesmaximal, characteristic
3C127×#3131C211yesmaximal, characteristic
4C127×#2960C211yesmaximal, characteristic, complemented
5C127×#1700C212yesmaximal, complemented
6C127×#1698C212yesmaximal, complemented
7C127×#1684C212yesmaximal, complemented
8C127×#1682C212yesmaximal, complemented
9C2×#335×C127C211yesmaximal, characteristic, complemented
10C127×#1550C211yesmaximal, characteristic, complemented
11C127×#1547C211yesmaximal, characteristic
12#533×C127C2211yescharacteristic
13#533×C127C2211yescharacteristic
14#532×C127C2211yescharacteristic
15#488×C127—21no—
16#488×C127—21no—
17#487×C127C2211yescharacteristic
18#487×C127C2211yescharacteristic
19#486×C127C2211yescharacteristic
20#486×C127C2211yescharacteristic
21#477×C127—21no—
22#477×C127C2212yes—
23#476×C127—21no—
24#475×C127C2212yes—
25#467×C127—22no—
26#465×C127—22no—
27#462×C127—21no—
28#462×C127C2212yes—
29#461×C127—21no—
30#460×C127C2212yes—
31#446×C127—21no—
32#446×C127C2212yes—
33C8×Q8×C127—21no—
34C8×Q8×C127C2212yes—
35#424×C127—21no—
36#423×C127C2211yescharacteristic
37C2×C4⋊C8×C127C2211yescharacteristic
38C2×C4⋊C8×C127C2211yescharacteristic
39#416×C127—21no—
40#416×C127—21no—
41#405×C127—21no—
42C2×C4×C8×C127C2211yescharacteristic
43#335×C127C2212yes—
44#335×C127C2212yes—
45#333×C127C2212yes—
46#332×C127C2212yes—
47#332×C127C2212yes—
48#331×C127C2212yes—
49C2×#41×C127—21no—
50C2×Q16×C127—22no—
51C2×SD16×C127—22no—
52C2×M16×C127—21no—
53C22×C8×C127—21no—
54C22×C8×C127—21no—
55C22×C8×C127D411yescharacteristic
56C22×C8×C127D411yescharacteristic
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127D411yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60C4⋊Q8×C127C2311yescharacteristic
61C4⋊Q8×C127C2311yescharacteristic
62#127×C127C2311yescharacteristic
63#125×C127—21no—
64#125×C127—21no—
65#124×C127—21no—
66C22⋊Q8×C127—21no—
67C22⋊Q8×C127—21no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127D412yes—
70#121×C127—21no—
71#121×C127—21no—
72C4×Q8×C127—21no—
73C4×Q8×C127—21no—
74C4×Q8×C127—21no—
75C4×Q8×C127C2312yes—
76C4×D4×C127—21no—
77C4×D4×C127—21no—
78#117×C127—21no—
79#117×C127—21no—
80C2×C42×C127C2311yescharacteristic
81#107×C127—22no—
82#106×C127—22no—
83C4⋊C8×C127—22no—
84C4⋊C8×C127—22no—
85C4⋊C8×C127—21no—
86C4⋊C8×C127—21no—
87C4⋊C8×C127—21no—
88C4⋊C8×C127C2312yes—
89C4⋊C8×C127C2312yes—
90C4⋊C8×C127C2312yes—
91#103×C127—22no—
92#103×C127—22no—
93#103×C127—21no—
94#103×C127—21no—
95#103×C127—21no—
96#103×C127—21no—
97#103×C127—22no—
98#102×C127—21no—
99#102×C127—21no—
100#102×C127—21no—
101#102×C127—21no—
102#102×C127—22no—
103#97×C127—22no—
104C4×C8×C127—22no—
105C4×C8×C127D411yescharacteristic
106C4×C8×C127D411yescharacteristic
107C4×C8×C127C2311yescharacteristic
108C4×C8×C127C2311yescharacteristic
109#41×C127—42no—
110#41×C127—42no—
111C2×Q8×C127—21no—
112C2×Q8×C127—21no—
113C2×Q8×C127—21no—
114C2×Q8×C127—21no—
115C2×Q8×C127C2×D412yes—
116C2×D4×C127—21no—
117C2×D4×C127—21no—
118C2×D4×C127—21no—
119C2×D4×C127—41no—
120C22×C4×C127—41no—
121C22×C4×C127C2×D411yescharacteristic
122C22×C4×C127C2×D411yescharacteristic
123C22×C4×C127#4111yescharacteristic
124Q16×C127—82no—
125SD16×C127—82no—
126M16×C127—42no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—81no—
133C2×C8×C127—81no—
134C2×C8×C127C2×D411yescharacteristic
135C2×C8×C127C2×D411yescharacteristic
136C2×C8×C127C2×D411yescharacteristic
137C2×C8×C127C2×D411yescharacteristic
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—41no—
150C4⋊C4×C127—41no—
151C4⋊C4×C127C2×D412yes—
152C22⋊C4×C127—22no—
153C22⋊C4×C127—41no—
154C22⋊C4×C127—41no—
155C22⋊C4×C127—41no—
156C42×C127—22no—
157C42×C127—41no—
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C42×C127#4111yescharacteristic
161C42×C127C2411yescharacteristic
162C23×C127—41no—
163C23×C127#12111yescharacteristic
164Q8×C127—22no—
165Q8×C127—22no—
166Q8×C127—42no—
167Q8×C127—41no—
168Q8×C127—41no—
169Q8×C127—41no—
170Q8×C127—41no—
171Q8×C127—81no—
172D4×C127—41no—
173D4×C127—41no—
174D4×C127—41no—
175D4×C127—41no—
176D4×C127—81no—
177D4×C127—82no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—82no—
187C2×C4×C127#12111yescharacteristic
188C2×C4×C127#12111yescharacteristic
189C2×C4×C127#12111yescharacteristic
190C2×C4×C127#13512yes—
191C2×C4×C127#13712yes—
192C2×C4×C127C22×D411yescharacteristic
193C2×C4×C127C22×D411yescharacteristic
194C2×C4×C127C2×#4111yescharacteristic
195C8×C127—21no—
196C8×C127—21no—
197C8×C127—21no—
198C8×C127—21no—
199C8×C127—42no—
200C8×C127—42no—
201C8×C127—42no—
202C22×C127—21no—
203C22×C127—21no—
204C22×C127—81no—
205C22×C127—81no—
206C22×C127—81no—
207C22×C127#46412yes—
208C22×C127C2×#12111yescharacteristic
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—21no—
212C4×C127—42no—
213C4×C127—42no—
214C4×C127—81no—
215C4×C127—81no—
216C4×C127—81no—
217C4×C127#46412yes—
218C4×C127C2×#13511yescharacteristic
219C4×C127C2×#13711yescharacteristic
220C4×C127#57611yescharacteristic
221C4×C127#57811yescharacteristic
222#19217C12711yesmaximal, characteristic, direct product factor, Sylow
223C2×C127—22no—
224C2×C127—161no—
225C2×C127C2×#46411yescharacteristic
226C2×C127#306111yescharacteristic
227C2×C127#306711yescharacteristic
228#3249C2×C12711yescharacteristic, complemented
229#3246C2×C12711yescharacteristic
230#3131C2×C12711yescharacteristic
231#2960C2×C12711yescharacteristic, complemented
232#1700C2×C12712yescomplemented
233#1698C2×C12712yescomplemented
234#1684C2×C12712yescomplemented
235#1682C2×C12712yescomplemented
236C2×#335C2×C12711yescharacteristic, complemented
237#1550C2×C12711yescharacteristic, complemented
238#1547C2×C12711yescharacteristic
239C127#1921711yescharacteristic, direct product factor, Sylow
240#533C22×C12711yescharacteristic
241#533C22×C12711yescharacteristic
242#532C22×C12711yescharacteristic
243#488—21no—
244#488—21no—
245#487C22×C12711yescharacteristic
246#487C22×C12711yescharacteristic
247#486C22×C12711yescharacteristic
248#486C22×C12711yescharacteristic
249#477—21no—
250#477C22×C12712yes—
251#476—21no—
252#475C22×C12712yes—
253#467—22no—
254#465—22no—
255#462—21no—
256#462C22×C12712yes—
257#461—21no—
258#460C22×C12712yes—
259#446—21no—
260#446C22×C12712yes—
261C8×Q8—21no—
262C8×Q8C22×C12712yes—
263#424—21no—
264#423C22×C12711yescharacteristic
265C2×C4⋊C8C22×C12711yescharacteristic
266C2×C4⋊C8C22×C12711yescharacteristic
267#416—21no—
268#416—21no—
269#405—21no—
270C2×C4×C8C22×C12711yescharacteristic
271#335C22×C12712yes—
272#335C22×C12712yes—
273#333C22×C12712yes—
274#332C22×C12712yes—
275#332C22×C12712yes—
276#331C22×C12712yes—
277C2×#41—21no—
278C2×Q16—22no—
279C2×SD16—22no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8D4×C12711yescharacteristic
284C22×C8D4×C12711yescharacteristic
285C4⋊Q8D4×C12711yescharacteristic
286C4⋊Q8D4×C12711yescharacteristic
287C4⋊Q8C23×C12711yescharacteristic
288C4⋊Q8C23×C12711yescharacteristic
289C4⋊Q8C23×C12711yescharacteristic
290#127C23×C12711yescharacteristic
291#125—21no—
292#125—21no—
293#124—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8D4×C12712yes—
298#121—21no—
299#121—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8C23×C12712yes—
304C4×D4—21no—
305C4×D4—21no—
306#117—21no—
307#117—21no—
308C2×C42C23×C12711yescharacteristic
309#107—22no—
310#106—22no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8C23×C12712yes—
317C4⋊C8C23×C12712yes—
318C4⋊C8C23×C12712yes—
319#103—22no—
320#103—22no—
321#103—21no—
322#103—21no—
323#103—21no—
324#103—21no—
325#103—22no—
326#102—21no—
327#102—21no—
328#102—21no—
329#102—21no—
330#102—22no—
331#97—22no—
332C4×C8—22no—
333C4×C8D4×C12711yescharacteristic
334C4×C8D4×C12711yescharacteristic
335C4×C8C23×C12711yescharacteristic
336C4×C8C23×C12711yescharacteristic
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C12712yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C12711yescharacteristic
350C22×C4C2×D4×C12711yescharacteristic
351C22×C4#41×C12711yescharacteristic
352Q16—82no—
353SD16—82no—
354M16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—81no—
361C2×C8—81no—
362C2×C8C2×D4×C12711yescharacteristic
363C2×C8C2×D4×C12711yescharacteristic
364C2×C8C2×D4×C12711yescharacteristic
365C2×C8C2×D4×C12711yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C12712yes—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C42—22no—
385C42—41no—
386C42C2×D4×C12711yescharacteristic
387C42C2×D4×C12711yescharacteristic
388C42#41×C12711yescharacteristic
389C42C24×C12711yescharacteristic
390C23—41no—
391C23#121×C12711yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—81no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4#121×C12711yescharacteristic
416C2×C4#121×C12711yescharacteristic
417C2×C4#121×C12711yescharacteristic
418C2×C4#135×C12712yes—
419C2×C4#137×C12712yes—
420C2×C4C22×D4×C12711yescharacteristic
421C2×C4C22×D4×C12711yescharacteristic
422C2×C4C2×#41×C12711yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—42no—
429C8—42no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22#464×C12712yes—
436C22C2×#121×C12711yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4#464×C12712yes—
446C4C2×#135×C12711yescharacteristic
447C4C2×#137×C12711yescharacteristic
448C4#576×C12711yescharacteristic
449C4#578×C12711yescharacteristic
450C2—22no—
451C2—161no—
452C2C2×#464×C12711yescharacteristic
453C2C127×#306111yescharacteristic
454C2C127×#306711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
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. C127×#3249C2semidirect
4. C127×#2960C2semidirect
5. C127×#1700C2semidirect
6. C127×#1698C2semidirect
7. C127×#1684C2semidirect
8. C127×#1682C2semidirect
9. C2×#335×C127C2semidirect
10. C127×#1550C2semidirect
222. #19217C127direct (N × H)
228. #3249C2×C127semidirect
231. #2960C2×C127semidirect
232. #1700C2×C127semidirect
233. #1698C2×C127semidirect
234. #1684C2×C127semidirect
235. #1682C2×C127semidirect
236. C2×#335C2×C127semidirect
237. #1550C2×C127semidirect
239. C127#19217direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32492
C127×#32462
C127×#31312
C127×#29602
C127×#17002
C127×#16982
C127×#16842
C127×#16822
C2×#335×C1272
C127×#15502
C127×#15472
#19217127