Finite Group Databasebeta

← C127×#19288 #44582961

Subgroups — C127×#19288 #44582961

Order 32512.

608 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3167C211yesmaximal, characteristic
2C127×#3113C211yesmaximal, characteristic, complemented
3C127×#3112C211yesmaximal, characteristic
4C2×#446×C127C211yesmaximal, characteristic, complemented
5C127×#1704C212yesmaximal, complemented
6C127×#1702C212yesmaximal, complemented
7C127×#1692C212yesmaximal, complemented
8C127×#1686C212yesmaximal, complemented
9C127×#1568C211yesmaximal, characteristic, complemented
10C127×#1552C211yesmaximal, characteristic, complemented
11C127×#1551C211yesmaximal, characteristic
12#533×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4×Q8×C127C2211yescharacteristic
15#498×C127C2211yescharacteristic
16#492×C127C2211yescharacteristic
17#487×C127C2211yescharacteristic
18#486×C127C2211yescharacteristic
19#483×C127—21no—
20#480×C127—21no—
21#477×C127C2212yes—
22#475×C127C2212yes—
23#465×C127—21no—
24#465×C127—21no—
25#462×C127C2212yes—
26#460×C127C2212yes—
27#451×C127—21no—
28#448×C127—21no—
29#446×C127—21no—
30#446×C127—21no—
31#446×C127C2212yes—
32#446×C127C2212yes—
33#441×C127—22no—
34#440×C127—22no—
35C4×SD16×C127—21no—
36C4×SD16×C127—21no—
37#432×C127C2211yescharacteristic
38#432×C127C2211yescharacteristic
39C2×C4⋊C8×C127—21no—
40C2×C4⋊C8×C127C2211yescharacteristic
41C2×#97×C127—21no—
42C2×C4×C8×C127C2211yescharacteristic
43#335×C127C2212yes—
44#334×C127C2212yes—
45#333×C127C2212yes—
46#332×C127C2212yes—
47#332×C127C2212yes—
48#331×C127C2212yes—
49C2×#41×C127—21no—
50C22×Q8×C127D411yescharacteristic
51C2×Q16×C127—22no—
52C2×SD16×C127—22no—
53C2×SD16×C127—21no—
54C2×SD16×C127—21no—
55C22×C8×C127—21no—
56C22×C8×C127D411yescharacteristic
57C22×C8×C127D411yescharacteristic
58C4⋊Q8×C127C2311yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60C4⋊Q8×C127C2311yescharacteristic
61#127×C127C2311yescharacteristic
62#125×C127—21no—
63#124×C127—21no—
64C22⋊Q8×C127—21no—
65C22⋊Q8×C127—21no—
66#121×C127—21no—
67#121×C127—21no—
68C4×Q8×C127—21no—
69C4×Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×Q8×C127—21no—
72C4×Q8×C127D412yes—
73C4×Q8×C127C2312yes—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76#117×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127D411yescharacteristic
79C2×C42×C127—21no—
80C2×C42×C127C2311yescharacteristic
81#107×C127—22no—
82#106×C127—21no—
83#106×C127—21no—
84#106×C127—22no—
85C4⋊C8×C127—22no—
86C4⋊C8×C127—22no—
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—22no—
96#102×C127—21no—
97#102×C127—21no—
98#102×C127—22no—
99C22⋊C8×C127—21no—
100C22⋊C8×C127—21no—
101#97×C127—22no—
102#97×C127—22no—
103#97×C127—21no—
104#97×C127—21no—
105C4×C8×C127D411yescharacteristic
106C4×C8×C127D411yescharacteristic
107C4×C8×C127C2311yescharacteristic
108C4×C8×C127C2311yescharacteristic
109#41×C127—82no—
110C2×Q8×C127—21no—
111C2×Q8×C127—21no—
112C2×Q8×C127—21no—
113C2×Q8×C127—21no—
114C2×Q8×C127—42no—
115C2×Q8×C127C2×D412yes—
116C2×D4×C127—21no—
117C2×D4×C127—21no—
118C2×D4×C127—21no—
119C2×D4×C127—41no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—41no—
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127#4111yescharacteristic
126Q16×C127—44no—
127SD16×C127—42no—
128SD16×C127—44no—
129SD16×C127—42no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127—22no—
134C2×C8×C127—41no—
135C2×C8×C127—42no—
136C2×C8×C127C2×D411yescharacteristic
137C2×C8×C127C2×D411yescharacteristic
138C2×C8×C127C2×D411yescharacteristic
139C2×C8×C127C2×D411yescharacteristic
140C4⋊C4×C127—22no—
141C4⋊C4×C127—21no—
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—41no—
153C22⋊C4×C127—41no—
154C22⋊C4×C127—41no—
155C42×C127—22no—
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—42no—
170Q8×C127—81no—
171D4×C127—41no—
172D4×C127—41no—
173D4×C127—42no—
174D4×C127—81no—
175D4×C127—82no—
176C2×C4×C127—22no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—82no—
188C2×C4×C127#12111yescharacteristic
189C2×C4×C127#12111yescharacteristic
190C2×C4×C127#12111yescharacteristic
191C2×C4×C127C22×D411yescharacteristic
192C2×C4×C127C22×D411yescharacteristic
193C2×C4×C127C2×#4111yescharacteristic
194C8×C127—21no—
195C8×C127—21no—
196C8×C127—21no—
197C8×C127—42no—
198C8×C127—42no—
199C8×C127—42no—
200C8×C127#13712yes—
201C22×C127—21no—
202C22×C127—21no—
203C22×C127—81no—
204C22×C127—81no—
205C22×C127—81no—
206C22×C127#47112yes—
207C22×C127C2×#12111yescharacteristic
208C4×C127—21no—
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×C127C2×#13711yescharacteristic
218C4×C127#57511yescharacteristic
219C4×C127#57512yes—
220#19288C12711yesmaximal, characteristic, direct product factor, Sylow
221C2×C127—22no—
222C2×C127—161no—
223C2×C127#303711yescharacteristic
224C2×C127#305411yescharacteristic
225C2×C127C2×#47111yescharacteristic
226#3167C2×C12711yescharacteristic
227#3113C2×C12711yescharacteristic, complemented
228#3112C2×C12711yescharacteristic
229C2×#446C2×C12711yescharacteristic, complemented
230#1704C2×C12712yescomplemented
231#1702C2×C12712yescomplemented
232#1692C2×C12712yescomplemented
233#1686C2×C12712yescomplemented
234#1568C2×C12711yescharacteristic, complemented
235#1552C2×C12711yescharacteristic, complemented
236#1551C2×C12711yescharacteristic
237C127#1928811yescharacteristic, direct product factor, Sylow
238#533C22×C12711yescharacteristic
239#532C22×C12711yescharacteristic
240C2×C4×Q8C22×C12711yescharacteristic
241#498C22×C12711yescharacteristic
242#492C22×C12711yescharacteristic
243#487C22×C12711yescharacteristic
244#486C22×C12711yescharacteristic
245#483—21no—
246#480—21no—
247#477C22×C12712yes—
248#475C22×C12712yes—
249#465—21no—
250#465—21no—
251#462C22×C12712yes—
252#460C22×C12712yes—
253#451—21no—
254#448—21no—
255#446—21no—
256#446—21no—
257#446C22×C12712yes—
258#446C22×C12712yes—
259#441—22no—
260#440—22no—
261C4×SD16—21no—
262C4×SD16—21no—
263#432C22×C12711yescharacteristic
264#432C22×C12711yescharacteristic
265C2×C4⋊C8—21no—
266C2×C4⋊C8C22×C12711yescharacteristic
267C2×#97—21no—
268C2×C4×C8C22×C12711yescharacteristic
269#335C22×C12712yes—
270#334C22×C12712yes—
271#333C22×C12712yes—
272#332C22×C12712yes—
273#332C22×C12712yes—
274#331C22×C12712yes—
275C2×#41—21no—
276C22×Q8D4×C12711yescharacteristic
277C2×Q16—22no—
278C2×SD16—22no—
279C2×SD16—21no—
280C2×SD16—21no—
281C22×C8—21no—
282C22×C8D4×C12711yescharacteristic
283C22×C8D4×C12711yescharacteristic
284C4⋊Q8C23×C12711yescharacteristic
285C4⋊Q8C23×C12711yescharacteristic
286C4⋊Q8C23×C12711yescharacteristic
287#127C23×C12711yescharacteristic
288#125—21no—
289#124—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8D4×C12712yes—
299C4×Q8C23×C12712yes—
300C4×D4—21no—
301C4×D4—21no—
302#117—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C12711yescharacteristic
305C2×C42—21no—
306C2×C42C23×C12711yescharacteristic
307#107—22no—
308#106—21no—
309#106—21no—
310#106—22no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313C4⋊C8—21no—
314C4⋊C8C23×C12712yes—
315C4⋊C8C23×C12712yes—
316C4⋊C8C23×C12712yes—
317#103—22no—
318#103—22no—
319#103—21no—
320#103—21no—
321#103—22no—
322#102—21no—
323#102—21no—
324#102—22no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327#97—22no—
328#97—22no—
329#97—21no—
330#97—21no—
331C4×C8D4×C12711yescharacteristic
332C4×C8D4×C12711yescharacteristic
333C4×C8C23×C12711yescharacteristic
334C4×C8C23×C12711yescharacteristic
335#41—82no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C12712yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C12711yescharacteristic
350C22×C4C2×D4×C12711yescharacteristic
351C22×C4#41×C12711yescharacteristic
352Q16—44no—
353SD16—42no—
354SD16—44no—
355SD16—42no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8C2×D4×C12711yescharacteristic
363C2×C8C2×D4×C12711yescharacteristic
364C2×C8C2×D4×C12711yescharacteristic
365C2×C8C2×D4×C12711yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C12712yes—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C42—22no—
382C42—22no—
383C42—41no—
384C42C2×D4×C12711yescharacteristic
385C42C2×D4×C12711yescharacteristic
386C42#41×C12711yescharacteristic
387C42C24×C12711yescharacteristic
388C23—41no—
389C23#121×C12711yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—42no—
396Q8—81no—
397D4—41no—
398D4—41no—
399D4—42no—
400D4—81no—
401D4—82no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4#121×C12711yescharacteristic
415C2×C4#121×C12711yescharacteristic
416C2×C4#121×C12711yescharacteristic
417C2×C4C22×D4×C12711yescharacteristic
418C2×C4C22×D4×C12711yescharacteristic
419C2×C4C2×#41×C12711yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8—42no—
424C8—42no—
425C8—42no—
426C8#137×C12712yes—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22#471×C12712yes—
433C22C2×#121×C12711yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4C2×#137×C12711yescharacteristic
444C4#575×C12711yescharacteristic
445C4#575×C12712yes—
446C2—22no—
447C2—161no—
448C2C127×#303711yescharacteristic
449C2C127×#305411yescharacteristic
450C2C2×#471×C12711yescharacteristic
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
2. C127×#3113C2semidirect
4. C2×#446×C127C2semidirect
5. C127×#1704C2semidirect
6. C127×#1702C2semidirect
7. C127×#1692C2semidirect
8. C127×#1686C2semidirect
9. C127×#1568C2semidirect
10. C127×#1552C2semidirect
220. #19288C127direct (N × H)
227. #3113C2×C127semidirect
229. C2×#446C2×C127semidirect
230. #1704C2×C127semidirect
231. #1702C2×C127semidirect
232. #1692C2×C127semidirect
233. #1686C2×C127semidirect
234. #1568C2×C127semidirect
235. #1552C2×C127semidirect
237. C127#19288direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31672
C127×#31132
C127×#31122
C2×#446×C1272
C127×#17042
C127×#17022
C127×#16922
C127×#16862
C127×#15682
C127×#15522
C127×#15512
#19288127