Finite Group Databasebeta

← C127×#19214 #44582887

Subgroups — C127×#19214 #44582887

Order 32512.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3209C211yesmaximal, characteristic, complemented
2C127×#3208C211yesmaximal, characteristic
3C2×#486×C127C211yesmaximal, characteristic
4C127×#2960C211yesmaximal, characteristic, complemented
5C127×#1702C214yesmaximal, complemented
6C127×#1682C214yesmaximal, complemented
7C127×#1564C211yesmaximal, characteristic, complemented
8C127×#1549C211yesmaximal, characteristic, complemented
9C127×#1545C211yesmaximal, characteristic
10#533×C127C2211yescharacteristic
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×#127×C127C2211yescharacteristic
13#494×C127—21no—
14#492×C127—21no—
15#487×C127—21no—
16#486×C127—21no—
17#486×C127—21no—
18#486×C127—21no—
19#486×C127C2212yes—
20#486×C127C2212yes—
21#462×C127C2214yescomplemented
22#460×C127C2214yes—
23#451×C127—22no—
24#450×C127—22no—
25#446×C127—21no—
26#446×C127C2212yescomplemented
27C8×Q8×C127—21no—
28C8×Q8×C127C2212yescomplemented
29#431×C127C2211yescharacteristic
30#431×C127C2211yescharacteristic
31#424×C127—21no—
32#423×C127C2211yescharacteristic
33C2×#102×C127—21no—
34C2×#102×C127—21no—
35#405×C127—21no—
36C2×C4×C8×C127C2211yescharacteristic
37#335×C127C2212yescomplemented
38#334×C127C2212yescomplemented
39#332×C127C2214yescomplemented
40#331×C127C2214yes—
41C22×Q8×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127—21no—
45C2×Q16×C127—24no—
46C2×SD16×C127—24no—
47C2×M16×C127—21no—
48C22×C8×C127D411yescharacteristic
49C22×C8×C127D411yescharacteristic
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127D411yescharacteristic
54C4⋊Q8×C127D411yescharacteristic
55C4⋊Q8×C127C2312yes—
56#127×C127—21no—
57#127×C127—21no—
58#127×C127—21no—
59#127×C127C2312yes—
60#125×C127—21no—
61C22⋊Q8×C127—21no—
62C22⋊Q8×C127D412yes—
63C4×Q8×C127—21no—
64C4×Q8×C127C2312yes—
65#117×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—21no—
68C2×C42×C127C2311yescharacteristic
69C4⋊C8×C127—22no—
70C4⋊C8×C127—22no—
71C4⋊C8×C127—21no—
72C4⋊C8×C127C2312yes—
73C4⋊C8×C127C2312yes—
74C4⋊C8×C127C2312yes—
75#103×C127—24no—
76#102×C127—22no—
77#102×C127—22no—
78#102×C127—22no—
79#102×C127—22no—
80#102×C127—24no—
81C22⋊C8×C127—21no—
82C22⋊C8×C127—21no—
83#97×C127—22no—
84C4×C8×C127—22no—
85C4×C8×C127—21no—
86C4×C8×C127—21no—
87C4×C8×C127D411yescharacteristic
88C4×C8×C127D411yescharacteristic
89C4×C8×C127C2311yescharacteristic
90C4×C8×C127C2311yescharacteristic
91C24×C127—41no—
92C2×Q8×C127—21no—
93C2×Q8×C127—22no—
94C2×Q8×C127—41no—
95C2×Q8×C127—82no—
96C2×Q8×C127C2×D412yes—
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
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—
107C22×C4×C127—41no—
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127#4111yescharacteristic
111Q16×C127—84no—
112SD16×C127—84no—
113M16×C127—42no—
114C2×C8×C127—22no—
115C2×C8×C127—22no—
116C2×C8×C127—22no—
117C2×C8×C127—22no—
118C2×C8×C127—22no—
119C2×C8×C127C2×D411yescharacteristic
120C2×C8×C127C2×D411yescharacteristic
121C2×C8×C127C2×D411yescharacteristic
122C2×C8×C127C2×D411yescharacteristic
123C4⋊C4×C127—21no—
124C4⋊C4×C127—21no—
125C4⋊C4×C127—21no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—41no—
131C4⋊C4×C127—41no—
132C4⋊C4×C127C2×D412yes—
133C22⋊C4×C127—22no—
134C42×C127—22no—
135C42×C127C2×D411yescharacteristic
136C42×C127C2×D411yescharacteristic
137C42×C127#4111yescharacteristic
138C42×C127C2411yescharacteristic
139C23×C127—42no—
140C23×C127—82no—
141C23×C127—82no—
142C23×C127—82no—
143C23×C127#12111yescharacteristic
144Q8×C127—24no—
145Q8×C127—42no—
146Q8×C127—44no—
147Q8×C127—82no—
148D4×C127—42no—
149D4×C127—42no—
150D4×C127—44no—
151D4×C127—82no—
152D4×C127—82no—
153D4×C127—82no—
154D4×C127—82no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—42no—
160C2×C4×C127—82no—
161C2×C4×C127#12111yescharacteristic
162C2×C4×C127#12111yescharacteristic
163C2×C4×C127#12111yescharacteristic
164C2×C4×C127#13512yes—
165C2×C4×C127#13712yes—
166C2×C4×C127C22×D411yescharacteristic
167C2×C4×C127C22×D411yescharacteristic
168C2×C4×C127C2×#4111yescharacteristic
169C8×C127—21no—
170C8×C127—21no—
171C8×C127—21no—
172C8×C127—21no—
173C8×C127—42no—
174C8×C127—42no—
175C8×C127—42no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—82no—
179C22×C127—82no—
180C22×C127—82no—
181C22×C127—164no—
182C22×C127#46412yes—
183C22×C127C2×#12111yescharacteristic
184C4×C127—21no—
185C4×C127—21no—
186C4×C127—42no—
187C4×C127—42no—
188C4×C127—82no—
189C4×C127#46412yes—
190C4×C127#47112yes—
191C4×C127C2×#13511yescharacteristic
192C4×C127C2×#13711yescharacteristic
193C4×C127#57612yes—
194#19214C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—22no—
196C2×C127—162no—
197C2×C127C2×#46411yescharacteristic
198C2×C127#305811yescharacteristic
199C2×C127C2×#47111yescharacteristic
200#3209C2×C12711yescharacteristic, complemented
201#3208C2×C12711yescharacteristic
202C2×#486C2×C12711yescharacteristic
203#2960C2×C12711yescharacteristic, complemented
204#1702C2×C12714yescomplemented
205#1682C2×C12714yescomplemented
206#1564C2×C12711yescharacteristic, complemented
207#1549C2×C12711yescharacteristic, complemented
208#1545C2×C12711yescharacteristic
209C127#1921411yescharacteristic, direct product factor, Sylow
210#533C22×C12711yescharacteristic
211C2×C4⋊Q8C22×C12711yescharacteristic
212C2×#127C22×C12711yescharacteristic
213#494—21no—
214#492—21no—
215#487—21no—
216#486—21no—
217#486—21no—
218#486—21no—
219#486C22×C12712yes—
220#486C22×C12712yes—
221#462C22×C12714yescomplemented
222#460C22×C12714yes—
223#451—22no—
224#450—22no—
225#446—21no—
226#446C22×C12712yescomplemented
227C8×Q8—21no—
228C8×Q8C22×C12712yescomplemented
229#431C22×C12711yescharacteristic
230#431C22×C12711yescharacteristic
231#424—21no—
232#423C22×C12711yescharacteristic
233C2×#102—21no—
234C2×#102—21no—
235#405—21no—
236C2×C4×C8C22×C12711yescharacteristic
237#335C22×C12712yescomplemented
238#334C22×C12712yescomplemented
239#332C22×C12714yescomplemented
240#331C22×C12714yes—
241C22×Q8—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C2×Q16—24no—
246C2×SD16—24no—
247C2×M16—21no—
248C22×C8D4×C12711yescharacteristic
249C22×C8D4×C12711yescharacteristic
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8D4×C12711yescharacteristic
254C4⋊Q8D4×C12711yescharacteristic
255C4⋊Q8C23×C12712yes—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C23×C12712yes—
260#125—21no—
261C22⋊Q8—21no—
262C22⋊Q8D4×C12712yes—
263C4×Q8—21no—
264C4×Q8C23×C12712yes—
265#117—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C42C23×C12711yescharacteristic
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—21no—
272C4⋊C8C23×C12712yes—
273C4⋊C8C23×C12712yes—
274C4⋊C8C23×C12712yes—
275#103—24no—
276#102—22no—
277#102—22no—
278#102—22no—
279#102—22no—
280#102—24no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283#97—22no—
284C4×C8—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D4×C12711yescharacteristic
288C4×C8D4×C12711yescharacteristic
289C4×C8C23×C12711yescharacteristic
290C4×C8C23×C12711yescharacteristic
291C24—41no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—82no—
296C2×Q8C2×D4×C12712yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—82no—
306C2×D4—82no—
307C22×C4—41no—
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4#41×C12711yescharacteristic
311Q16—84no—
312SD16—84no—
313M16—42no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8C2×D4×C12711yescharacteristic
320C2×C8C2×D4×C12711yescharacteristic
321C2×C8C2×D4×C12711yescharacteristic
322C2×C8C2×D4×C12711yescharacteristic
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C2×D4×C12712yes—
333C22⋊C4—22no—
334C42—22no—
335C42C2×D4×C12711yescharacteristic
336C42C2×D4×C12711yescharacteristic
337C42#41×C12711yescharacteristic
338C42C24×C12711yescharacteristic
339C23—42no—
340C23—82no—
341C23—82no—
342C23—82no—
343C23#121×C12711yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347Q8—82no—
348D4—42no—
349D4—42no—
350D4—44no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—82no—
361C2×C4#121×C12711yescharacteristic
362C2×C4#121×C12711yescharacteristic
363C2×C4#121×C12711yescharacteristic
364C2×C4#135×C12712yes—
365C2×C4#137×C12712yes—
366C2×C4C22×D4×C12711yescharacteristic
367C2×C4C22×D4×C12711yescharacteristic
368C2×C4C2×#41×C12711yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—42no—
375C8—42no—
376C22—21no—
377C22—21no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—164no—
382C22#464×C12712yes—
383C22C2×#121×C12711yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4#464×C12712yes—
390C4#471×C12712yes—
391C4C2×#135×C12711yescharacteristic
392C4C2×#137×C12711yescharacteristic
393C4#576×C12712yes—
394C2—22no—
395C2—162no—
396C2C2×#464×C12711yescharacteristic
397C2C127×#305811yescharacteristic
398C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#127×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×#3209C2semidirect
4. C127×#2960C2semidirect
5. C127×#1702C2semidirect
6. C127×#1682C2semidirect
7. C127×#1564C2semidirect
8. C127×#1549C2semidirect
21. #462×C127C22semidirect
26. #446×C127C22semidirect
28. C8×Q8×C127C22semidirect
37. #335×C127C22semidirect
38. #334×C127C22semidirect
39. #332×C127C22semidirect
194. #19214C127direct (N × H)
200. #3209C2×C127semidirect
203. #2960C2×C127semidirect
204. #1702C2×C127semidirect
205. #1682C2×C127semidirect
206. #1564C2×C127semidirect
207. #1549C2×C127semidirect
209. C127#19214direct (N × H)
221. #462C22×C127semidirect
226. #446C22×C127semidirect
228. C8×Q8C22×C127semidirect
237. #335C22×C127semidirect
238. #334C22×C127semidirect
239. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32092
C127×#32082
C2×#486×C1272
C127×#29602
C127×#17022
C127×#16822
C127×#15642
C127×#15492
C127×#15452
#19214127