Finite Group Databasebeta

← C127×#19422 #44583095

Subgroups — C127×#19422 #44583095

Order 32512.

768 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3205C211yesmaximal, characteristic, complemented
2C127×#3036C211yesmaximal, characteristic, complemented
3C2×#459×C127C211yesmaximal, characteristic, complemented
4C127×#2975C211yesmaximal, characteristic, complemented
5C127×#1701C214yesmaximal, complemented
6C127×#1687C214yesmaximal, complemented
7C127×#1570C211yesmaximal, characteristic, complemented
8C127×#1545C211yesmaximal, characteristic, complemented
9C127×#1540C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C127—21no—
11C22×D8×C127—21no—
12#532×C127C2211yescharacteristic
13C2×#127×C127C2211yescharacteristic
14C2×C4×D4×C127C2211yescharacteristic
15#493×C127C2212yescomplemented
16#486×C127C2212yescomplemented
17#463×C127—22no—
18#461×C127C2212yescomplemented
19#459×C127—22no—
20#459×C127—22no—
21#459×C127C2214yes—
22#459×C127C2212yescomplemented
23#447×C127—22no—
24#436×C127—22no—
25#436×C127C2214yescomplemented
26#431×C127C2211yescharacteristic
27#431×C127C2211yescharacteristic
28#423×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30#417×C127—21no—
31C2×#102×C127—21no—
32#407×C127—22no—
33#334×C127C2214yescomplemented
34#332×C127C2212yescomplemented
35#331×C127C2214yescomplemented
36#331×C127C2212yescomplemented
37C2×#41×C127—21no—
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127—21no—
41C22×D4×C127D411yescharacteristic
42C23×C4×C127—21no—
43AGL(1,ℤ/8)×C127—44no—
44C2×SD16×C127—22no—
45C2×D8×C127—24no—
46C2×D8×C127—22no—
47C2×D8×C127—24no—
48C2×D8×C127—44no—
49C2×M16×C127—21no—
50C2×M16×C127—24no—
51C22×C8×C127—21no—
52C4⋊Q8×C127C2311yescharacteristic
53#127×C127—21no—
54#127×C127—21no—
55#127×C127—21no—
56#127×C127C2312yes—
57#127×C127C2311yescharacteristic
58#124×C127—21no—
59#121×C127—21no—
60#121×C127—21no—
61C4×D4×C127—21no—
62C4×D4×C127—21no—
63C4×D4×C127—21no—
64C4×D4×C127—21no—
65C4×D4×C127D412yes—
66C4×D4×C127C2312yes—
67C2×C4⋊C4×C127D411yescharacteristic
68C2×C22⋊C4×C127—21no—
69C2×C42×C127C2311yescharacteristic
70C4⋊C8×C127—21no—
71C4⋊C8×C127—21no—
72C4⋊C8×C127D412yes—
73C4⋊C8×C127C2312yes—
74C4⋊C8×C127C2312yes—
75C4⋊C8×C127C2312yes—
76#103×C127—22no—
77#102×C127—24no—
78#102×C127—24no—
79#102×C127—22no—
80C22⋊C8×C127—21no—
81C22⋊C8×C127—24no—
82C22⋊C8×C127D412yes—
83C4×C8×C127—21no—
84C4×C8×C127C2312yes—
85C24×C127—21no—
86C24×C127—41no—
87#41×C127—42no—
88#41×C127—42no—
89C2×Q8×C127—21no—
90C2×D4×C127—21no—
91C2×D4×C127—22no—
92C2×D4×C127—22no—
93C2×D4×C127—21no—
94C2×D4×C127—22no—
95C2×D4×C127—22no—
96C2×D4×C127—21no—
97C2×D4×C127—21no—
98C2×D4×C127—22no—
99C2×D4×C127—41no—
100C2×D4×C127—41no—
101C2×D4×C127—41no—
102C2×D4×C127—41no—
103C2×D4×C127—42no—
104C2×D4×C127—42no—
105C2×D4×C127—82no—
106C2×D4×C127—82no—
107C2×D4×C127C2×D412yes—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—41no—
112C22×C4×C127—82no—
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127#4111yescharacteristic
116SD16×C127—44no—
117D8×C127—48no—
118D8×C127—44no—
119D8×C127—84no—
120M16×C127—42no—
121M16×C127—84no—
122C2×C8×C127—22no—
123C2×C8×C127—22no—
124C2×C8×C127—22no—
125C2×C8×C127—42no—
126C2×C8×C127C2×D414yes—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127C2×D412yes—
131C22⋊C4×C127—22no—
132C22⋊C4×C127—22no—
133C22⋊C4×C127—41no—
134C22⋊C4×C127—41no—
135C42×C127C2×D411yescharacteristic
136C42×C127C2×D411yescharacteristic
137C42×C127#4111yescharacteristic
138C42×C127C2411yescharacteristic
139C23×C127—22no—
140C23×C127—42no—
141C23×C127—41no—
142C23×C127—42no—
143C23×C127—81no—
144C23×C127—81no—
145C23×C127—82no—
146C23×C127—82no—
147C23×C127—82no—
148C23×C127#12111yescharacteristic
149Q8×C127—41no—
150Q8×C127—41no—
151D4×C127—22no—
152D4×C127—22no—
153D4×C127—42no—
154D4×C127—41no—
155D4×C127—42no—
156D4×C127—41no—
157D4×C127—42no—
158D4×C127—44no—
159D4×C127—42no—
160D4×C127—81no—
161D4×C127—82no—
162D4×C127—82no—
163D4×C127—82no—
164D4×C127—82no—
165D4×C127—82no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—41no—
169C2×C4×C127—44no—
170C2×C4×C127—41no—
171C2×C4×C127—82no—
172C2×C4×C127—81no—
173C2×C4×C127—82no—
174C2×C4×C127#12111yescharacteristic
175C2×C4×C127#12111yescharacteristic
176C2×C4×C127#12111yescharacteristic
177C2×C4×C127AGL(1,ℤ/8)12yes—
178C2×C4×C127AGL(1,ℤ/8)12yes—
179C2×C4×C127C22×D411yescharacteristic
180C2×C4×C127C22×D411yescharacteristic
181C2×C4×C127C2×#4111yescharacteristic
182C8×C127—24no—
183C8×C127—42no—
184C8×C127—42no—
185C8×C127—42no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—42no—
189C22×C127—42no—
190C22×C127—42no—
191C22×C127—84no—
192C22×C127—82no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—82no—
196C22×C127—82no—
197C22×C127—81no—
198C22×C127—164no—
199C22×C127#46912yes—
200C22×C127C2×#12111yescharacteristic
201C4×C127—21no—
202C4×C127—21no—
203C4×C127—21no—
204C4×C127—42no—
205C4×C127—81no—
206C4×C127#46912yes—
207C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
208C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
209C4×C127#57612yes—
210#19422C12711yesmaximal, characteristic, direct product factor, Sylow
211C2×C127—22no—
212C2×C127—82no—
213C2×C127—161no—
214C2×C127—162no—
215C2×C127#304111yescharacteristic
216C2×C127C2×#46911yescharacteristic
217C2×C127#306811yescharacteristic
218#3205C2×C12711yescharacteristic, complemented
219#3036C2×C12711yescharacteristic, complemented
220C2×#459C2×C12711yescharacteristic, complemented
221#2975C2×C12711yescharacteristic, complemented
222#1701C2×C12714yescomplemented
223#1687C2×C12714yescomplemented
224#1570C2×C12711yescharacteristic, complemented
225#1545C2×C12711yescharacteristic, complemented
226#1540C2×C12711yescharacteristic, complemented
227C127#1942211yescharacteristic, direct product factor, Sylow
228C2×AGL(1,ℤ/8)—21no—
229C22×D8—21no—
230#532C22×C12711yescharacteristic
231C2×#127C22×C12711yescharacteristic
232C2×C4×D4C22×C12711yescharacteristic
233#493C22×C12712yescomplemented
234#486C22×C12712yescomplemented
235#463—22no—
236#461C22×C12712yescomplemented
237#459—22no—
238#459—22no—
239#459C22×C12714yes—
240#459C22×C12712yescomplemented
241#447—22no—
242#436—22no—
243#436C22×C12714yescomplemented
244#431C22×C12711yescharacteristic
245#431C22×C12711yescharacteristic
246#423C22×C12711yescharacteristic
247C2×C4⋊C8C22×C12711yescharacteristic
248#417—21no—
249C2×#102—21no—
250#407—22no—
251#334C22×C12714yescomplemented
252#332C22×C12712yescomplemented
253#331C22×C12712yescomplemented
254#331C22×C12714yescomplemented
255C2×#41—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4D4×C12711yescharacteristic
260C23×C4—21no—
261AGL(1,ℤ/8)—44no—
262C2×SD16—22no—
263C2×D8—24no—
264C2×D8—22no—
265C2×D8—24no—
266C2×D8—44no—
267C2×M16—21no—
268C2×M16—24no—
269C22×C8—21no—
270C4⋊Q8C23×C12711yescharacteristic
271#127—21no—
272#127—21no—
273#127—21no—
274#127C23×C12712yes—
275#127C23×C12711yescharacteristic
276#124—21no—
277#121—21no—
278#121—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4D4×C12712yes—
284C4×D4C23×C12712yes—
285C2×C4⋊C4D4×C12711yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C23×C12711yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C12712yes—
291C4⋊C8C23×C12712yes—
292C4⋊C8C23×C12712yes—
293C4⋊C8C23×C12712yes—
294#103—22no—
295#102—24no—
296#102—24no—
297#102—22no—
298C22⋊C8—21no—
299C22⋊C8—24no—
300C22⋊C8D4×C12712yes—
301C4×C8—21no—
302C4×C8C23×C12712yes—
303C24—21no—
304C24—41no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4—42no—
323C2×D4—82no—
324C2×D4—82no—
325C2×D4C2×D4×C12712yes—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—82no—
331C22×C4C2×D4×C12711yescharacteristic
332C22×C4C2×D4×C12711yescharacteristic
333C22×C4#41×C12711yescharacteristic
334SD16—44no—
335D8—48no—
336D8—44no—
337D8—84no—
338M16—42no—
339M16—84no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—42no—
344C2×C8C2×D4×C12714yes—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4C2×D4×C12712yes—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42C2×D4×C12711yescharacteristic
354C42C2×D4×C12711yescharacteristic
355C42#41×C12711yescharacteristic
356C42C24×C12711yescharacteristic
357C23—22no—
358C23—42no—
359C23—41no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23—82no—
364C23—82no—
365C23—82no—
366C23#121×C12711yescharacteristic
367Q8—41no—
368Q8—41no—
369D4—22no—
370D4—22no—
371D4—42no—
372D4—41no—
373D4—42no—
374D4—41no—
375D4—42no—
376D4—44no—
377D4—42no—
378D4—82no—
379D4—81no—
380D4—82no—
381D4—82no—
382D4—82no—
383D4—82no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—82no—
392C2×C4#121×C12711yescharacteristic
393C2×C4#121×C12711yescharacteristic
394C2×C4#121×C12711yescharacteristic
395C2×C4AGL(1,ℤ/8)×C12712yes—
396C2×C4AGL(1,ℤ/8)×C12712yes—
397C2×C4C22×D4×C12711yescharacteristic
398C2×C4C22×D4×C12711yescharacteristic
399C2×C4C2×#41×C12711yescharacteristic
400C8—24no—
401C8—42no—
402C8—42no—
403C8—42no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—84no—
410C22—82no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—82no—
415C22—81no—
416C22—164no—
417C22#469×C12712yes—
418C22C2×#121×C12711yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4#469×C12712yes—
425C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
426C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
427C4#576×C12712yes—
428C2—22no—
429C2—82no—
430C2—162no—
431C2—161no—
432C2C127×#304111yescharacteristic
433C2C2×#469×C12711yescharacteristic
434C2C127×#306811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
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×#3205C2semidirect
2. C127×#3036C2semidirect
3. C2×#459×C127C2semidirect
4. C127×#2975C2semidirect
5. C127×#1701C2semidirect
6. C127×#1687C2semidirect
7. C127×#1570C2semidirect
8. C127×#1545C2semidirect
9. C127×#1540C2semidirect
15. #493×C127C22semidirect
16. #486×C127C22semidirect
18. #461×C127C22semidirect
22. #459×C127C22semidirect
25. #436×C127C22semidirect
33. #334×C127C22semidirect
34. #332×C127C22semidirect
35. #331×C127C22semidirect
36. #331×C127C22semidirect
210. #19422C127direct (N × H)
218. #3205C2×C127semidirect
219. #3036C2×C127semidirect
220. C2×#459C2×C127semidirect
221. #2975C2×C127semidirect
222. #1701C2×C127semidirect
223. #1687C2×C127semidirect
224. #1570C2×C127semidirect
225. #1545C2×C127semidirect
226. #1540C2×C127semidirect
227. C127#19422direct (N × H)
233. #493C22×C127semidirect
234. #486C22×C127semidirect
236. #461C22×C127semidirect
240. #459C22×C127semidirect
243. #436C22×C127semidirect
251. #334C22×C127semidirect
252. #332C22×C127semidirect
253. #331C22×C127semidirect
254. #331C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32052
C127×#30362
C2×#459×C1272
C127×#29752
C127×#17012
C127×#16872
C127×#15702
C127×#15452
C127×#15402
#19422127