Finite Group Databasebeta

← C127×#19420 #44583093

Subgroups — C127×#19420 #44583093

Order 32512.

714 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3208C211yesmaximal, characteristic, complemented
2C127×#3077C211yesmaximal, characteristic, complemented
3C2×#459×C127C211yesmaximal, characteristic
4C127×#2975C211yesmaximal, characteristic, complemented
5C127×#1697C214yesmaximal, complemented
6C127×#1685C214yesmaximal, complemented
7C127×#1571C211yesmaximal, characteristic, complemented
8C127×#1545C211yesmaximal, characteristic, complemented
9C127×#1542C211yesmaximal, characteristic, complemented
10C22×D8×C127—21no—
11#533×C127C2211yescharacteristic
12C2×#127×C127C2211yescharacteristic
13C2×C4×D4×C127C2211yescharacteristic
14#492×C127C2212yescomplemented
15#486×C127C2212yescomplemented
16#478×C127—22no—
17#476×C127C2212yescomplemented
18#474×C127C2212yescomplemented
19#460×C127—22no—
20#459×C127—22no—
21#459×C127C2214yes—
22#450×C127—22no—
23#436×C127—22no—
24#436×C127C2214yescomplemented
25#431×C127C2211yescharacteristic
26#431×C127C2211yescharacteristic
27#428×C127—21no—
28#423×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30#418×C127—21no—
31C2×#102×C127—21no—
32#407×C127—22no—
33#335×C127C2214yescomplemented
34#333×C127C2212yescomplemented
35#332×C127C2212yescomplemented
36#331×C127C2214yescomplemented
37C22×D4×C127—21no—
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127D411yescharacteristic
41C23×C4×C127—21no—
42C2×SD16×C127—24no—
43C2×D8×C127—24no—
44C2×D8×C127—44no—
45C2×M16×C127—21no—
46C2×M16×C127—24no—
47C22×C8×C127—21no—
48C4⋊Q8×C127C2311yescharacteristic
49C4⋊Q8×C127C2311yescharacteristic
50#127×C127—21no—
51#127×C127—21no—
52#127×C127—21no—
53#127×C127C2312yes—
54#125×C127—21no—
55C22⋊Q8×C127—21no—
56C22⋊Q8×C127—21no—
57C4×Q8×C127—21no—
58C4×Q8×C127—21no—
59C4×D4×C127—21no—
60C4×D4×C127—21no—
61C4×D4×C127D412yes—
62C4×D4×C127C2312yes—
63#117×C127—21no—
64C2×C4⋊C4×C127D411yescharacteristic
65C2×C22⋊C4×C127—21no—
66C2×C42×C127C2311yescharacteristic
67#107×C127—22no—
68#106×C127—22no—
69C4⋊C8×C127—21no—
70C4⋊C8×C127—21no—
71C4⋊C8×C127D412yes—
72C4⋊C8×C127C2312yes—
73C4⋊C8×C127C2312yes—
74C4⋊C8×C127C2312yes—
75#102×C127—22no—
76#102×C127—22no—
77#102×C127—24no—
78#102×C127—24no—
79C22⋊C8×C127—21no—
80C22⋊C8×C127—24no—
81C22⋊C8×C127D412yes—
82C4×C8×C127—21no—
83C4×C8×C127C2312yes—
84C24×C127—21no—
85C24×C127—41no—
86C2×Q8×C127—21no—
87C2×Q8×C127—21no—
88C2×D4×C127—21no—
89C2×D4×C127—22no—
90C2×D4×C127—22no—
91C2×D4×C127—22no—
92C2×D4×C127—22no—
93C2×D4×C127—22no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—42no—
98C2×D4×C127—42no—
99C2×D4×C127—82no—
100C2×D4×C127—82no—
101C2×D4×C127C2×D412yes—
102C22×C4×C127—21no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—82no—
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127#4111yescharacteristic
109SD16×C127—84no—
110D8×C127—48no—
111M16×C127—42no—
112M16×C127—84no—
113C2×C8×C127—22no—
114C2×C8×C127—22no—
115C2×C8×C127—22no—
116C2×C8×C127—42no—
117C2×C8×C127C2×D414yes—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—41no—
124C4⋊C4×C127—41no—
125C4⋊C4×C127C2×D412yes—
126C22⋊C4×C127—22no—
127C22⋊C4×C127—22no—
128C22⋊C4×C127—41no—
129C42×C127—41no—
130C42×C127C2×D411yescharacteristic
131C42×C127C2×D411yescharacteristic
132C42×C127#4111yescharacteristic
133C42×C127C2411yescharacteristic
134C23×C127—22no—
135C23×C127—42no—
136C23×C127—42no—
137C23×C127—81no—
138C23×C127—81no—
139C23×C127—82no—
140C23×C127—82no—
141C23×C127—82no—
142C23×C127#12111yescharacteristic
143Q8×C127—42no—
144Q8×C127—81no—
145D4×C127—22no—
146D4×C127—22no—
147D4×C127—42no—
148D4×C127—42no—
149D4×C127—44no—
150D4×C127—42no—
151D4×C127—82no—
152D4×C127—82no—
153D4×C127—82no—
154D4×C127—82no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—41no—
158C2×C4×C127—44no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—82no—
162C2×C4×C127—81no—
163C2×C4×C127#12111yescharacteristic
164C2×C4×C127#12111yescharacteristic
165C2×C4×C127#12111yescharacteristic
166C2×C4×C127AGL(1,ℤ/8)12yes—
167C2×C4×C127#13712yes—
168C2×C4×C127C22×D411yescharacteristic
169C2×C4×C127C22×D411yescharacteristic
170C2×C4×C127C2×#4111yescharacteristic
171C8×C127—24no—
172C8×C127—42no—
173C8×C127—42no—
174C8×C127—42no—
175C22×C127—21no—
176C22×C127—21no—
177C22×C127—42no—
178C22×C127—42no—
179C22×C127—42no—
180C22×C127—84no—
181C22×C127—82no—
182C22×C127—82no—
183C22×C127—82no—
184C22×C127—164no—
185C22×C127#46812yes—
186C22×C127C2×#12111yescharacteristic
187C4×C127—21no—
188C4×C127—21no—
189C4×C127—21no—
190C4×C127—42no—
191C4×C127—81no—
192C4×C127—81no—
193C4×C127#46812yes—
194C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
195C4×C127C2×#13711yescharacteristic
196C4×C127#57612yes—
197#19420C12711yesmaximal, characteristic, direct product factor, Sylow
198C2×C127—22no—
199C2×C127—82no—
200C2×C127—162no—
201C2×C127#304111yescharacteristic
202C2×C127C2×#46811yescharacteristic
203C2×C127#306811yescharacteristic
204#3208C2×C12711yescharacteristic, complemented
205#3077C2×C12711yescharacteristic, complemented
206C2×#459C2×C12711yescharacteristic
207#2975C2×C12711yescharacteristic, complemented
208#1697C2×C12714yescomplemented
209#1685C2×C12714yescomplemented
210#1571C2×C12711yescharacteristic, complemented
211#1545C2×C12711yescharacteristic, complemented
212#1542C2×C12711yescharacteristic, complemented
213C127#1942011yescharacteristic, direct product factor, Sylow
214C22×D8—21no—
215#533C22×C12711yescharacteristic
216C2×#127C22×C12711yescharacteristic
217C2×C4×D4C22×C12711yescharacteristic
218#492C22×C12712yescomplemented
219#486C22×C12712yescomplemented
220#478—22no—
221#476C22×C12712yescomplemented
222#474C22×C12712yescomplemented
223#460—22no—
224#459—22no—
225#459C22×C12714yes—
226#450—22no—
227#436—22no—
228#436C22×C12714yescomplemented
229#431C22×C12711yescharacteristic
230#431C22×C12711yescharacteristic
231#428—21no—
232#423C22×C12711yescharacteristic
233C2×C4⋊C8C22×C12711yescharacteristic
234#418—21no—
235C2×#102—21no—
236#407—22no—
237#335C22×C12714yescomplemented
238#333C22×C12712yescomplemented
239#332C22×C12712yescomplemented
240#331C22×C12714yescomplemented
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4D4×C12711yescharacteristic
245C23×C4—21no—
246C2×SD16—24no—
247C2×D8—24no—
248C2×D8—44no—
249C2×M16—21no—
250C2×M16—24no—
251C22×C8—21no—
252C4⋊Q8C23×C12711yescharacteristic
253C4⋊Q8C23×C12711yescharacteristic
254#127—21no—
255#127—21no—
256#127—21no—
257#127C23×C12712yes—
258#125—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4D4×C12712yes—
266C4×D4C23×C12712yes—
267#117—21no—
268C2×C4⋊C4D4×C12711yescharacteristic
269C2×C22⋊C4—21no—
270C2×C42C23×C12711yescharacteristic
271#107—22no—
272#106—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C12712yes—
276C4⋊C8C23×C12712yes—
277C4⋊C8C23×C12712yes—
278C4⋊C8C23×C12712yes—
279#102—22no—
280#102—22no—
281#102—24no—
282#102—24no—
283C22⋊C8—21no—
284C22⋊C8—24no—
285C22⋊C8D4×C12712yes—
286C4×C8—21no—
287C4×C8C23×C12712yes—
288C24—21no—
289C24—41no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4—82no—
305C2×D4C2×D4×C12712yes—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—82no—
310C22×C4C2×D4×C12711yescharacteristic
311C22×C4C2×D4×C12711yescharacteristic
312C22×C4#41×C12711yescharacteristic
313SD16—84no—
314D8—48no—
315M16—42no—
316M16—84no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8C2×D4×C12714yes—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4C2×D4×C12712yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C42—41no—
334C42C2×D4×C12711yescharacteristic
335C42C2×D4×C12711yescharacteristic
336C42#41×C12711yescharacteristic
337C42C24×C12711yescharacteristic
338C23—22no—
339C23—42no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23#121×C12711yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—22no—
350D4—22no—
351D4—42no—
352D4—42no—
353D4—44no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—82no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4#121×C12711yescharacteristic
368C2×C4#121×C12711yescharacteristic
369C2×C4#121×C12711yescharacteristic
370C2×C4AGL(1,ℤ/8)×C12712yes—
371C2×C4#137×C12712yes—
372C2×C4C22×D4×C12711yescharacteristic
373C2×C4C22×D4×C12711yescharacteristic
374C2×C4C2×#41×C12711yescharacteristic
375C8—24no—
376C8—42no—
377C8—42no—
378C8—42no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—84no—
385C22—82no—
386C22—82no—
387C22—82no—
388C22—164no—
389C22#468×C12712yes—
390C22C2×#121×C12711yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4#468×C12712yes—
398C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
399C4C2×#137×C12711yescharacteristic
400C4#576×C12712yes—
401C2—22no—
402C2—82no—
403C2—162no—
404C2C127×#304111yescharacteristic
405C2C2×#468×C12711yescharacteristic
406C2C127×#306811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#459×C127C2
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×#3208C2semidirect
2. C127×#3077C2semidirect
4. C127×#2975C2semidirect
5. C127×#1697C2semidirect
6. C127×#1685C2semidirect
7. C127×#1571C2semidirect
8. C127×#1545C2semidirect
9. C127×#1542C2semidirect
14. #492×C127C22semidirect
15. #486×C127C22semidirect
17. #476×C127C22semidirect
18. #474×C127C22semidirect
24. #436×C127C22semidirect
33. #335×C127C22semidirect
34. #333×C127C22semidirect
35. #332×C127C22semidirect
36. #331×C127C22semidirect
197. #19420C127direct (N × H)
204. #3208C2×C127semidirect
205. #3077C2×C127semidirect
207. #2975C2×C127semidirect
208. #1697C2×C127semidirect
209. #1685C2×C127semidirect
210. #1571C2×C127semidirect
211. #1545C2×C127semidirect
212. #1542C2×C127semidirect
213. C127#19420direct (N × H)
218. #492C22×C127semidirect
219. #486C22×C127semidirect
221. #476C22×C127semidirect
222. #474C22×C127semidirect
228. #436C22×C127semidirect
237. #335C22×C127semidirect
238. #333C22×C127semidirect
239. #332C22×C127semidirect
240. #331C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32082
C127×#30772
C2×#459×C1272
C127×#29752
C127×#16972
C127×#16852
C127×#15712
C127×#15452
C127×#15422
#19420127