Finite Group Databasebeta

← C127×#14881 #44578554

Subgroups — C127×#14881 #44578554

Order 32512.

1742 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C127C211yesmaximal, characteristic
2C2×#395×C127C212yesmaximal
3C2×#391×C127C211yesmaximal, characteristic
4C127×#1446C212yesmaximal
5C127×#1444C212yesmaximal
6C127×#1441C212yesmaximal
7C127×#1436C214yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C23×Q8×C127C2211yescharacteristic
11C2×C4×Q8×C127—28no—
12C2×C4×Q8×C127—24no—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2214yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#395×C127—28no—
20#391×C127—24no—
21C2×#95×C127C2212yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2212yes—
29C22×Q8×C127—24no—
30C22×Q8×C127—22no—
31C22×Q8×C127—22no—
32C22×Q8×C127—24no—
33C22×Q8×C127—24no—
34C22×Q8×C127—22no—
35C22×Q8×C127—24no—
36C22×Q8×C127—42no—
37C22×Q8×C127Q814yescomplemented
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2314yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C4×Q8×C127—232no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—28no—
53C2×C4⋊C4×C127—28no—
54C2×C4⋊C4×C127—44no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127D418yes—
57C2×C42×C127—24no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127—24no—
61C2×C42×C127D414yes—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—28no—
66#95×C127—24no—
67#95×C127—28no—
68#95×C127—44no—
69#95×C127Q818yescomplemented
70C24×C127C2411yescharacteristic
71C2×Q8×C127—28no—
72C2×Q8×C127—28no—
73C2×Q8×C127—216no—
74C2×Q8×C127—28no—
75C2×Q8×C127—28no—
76C2×Q8×C127—216no—
77C2×Q8×C127—416no—
78C2×Q8×C127—44no—
79C2×Q8×C127—44no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127—22no—
92C22×C4×C127—24no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—24no—
103C22×C4×C127—24no—
104C22×C4×C127—22no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127C2×D414yes—
109C22×C4×C127C2×D414yes—
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×D414yes—
112C22×C4×C127C2×D412yes—
113C22×C4×C127C2×D412yes—
114C22×C4×C127C2×Q818yes—
115C22×C4×C127C2×Q814yes—
116C22×C4×C127C2×Q812yes—
117C22×C4×C127C2×Q814yes—
118C22×C4×C127#4114yes—
119C22×C4×C127#4114yes—
120C22×C4×C127#4112yes—
121C4⋊C4×C127—28no—
122C4⋊C4×C127—216no—
123C4⋊C4×C127—416no—
124C4⋊C4×C127—44no—
125C42×C127—216no—
126C42×C127—28no—
127C23×C127C22×D411yescharacteristic
128C23×C127C22×D412yes—
129C23×C127C22×Q811yescharacteristic
130C23×C127C22×Q812yes—
131C23×C127C2×#4112yes—
132C23×C127C2×#4111yescharacteristic
133C23×C127C2×#4112yes—
134C23×C127H(5,𝔽2)12yes—
135C23×C1272−1+412yes—
136Q8×C127—232no—
137Q8×C127—416no—
138C2×C4×C127—22no—
139C2×C4×C127—24no—
140C2×C4×C127—22no—
141C2×C4×C127—24no—
142C2×C4×C127—24no—
143C2×C4×C127—24no—
144C2×C4×C127—22no—
145C2×C4×C127—24no—
146C2×C4×C127—22no—
147C2×C4×C127—24no—
148C2×C4×C127—24no—
149C2×C4×C127—24no—
150C2×C4×C127—22no—
151C2×C4×C127—22no—
152C2×C4×C127—28no—
153C2×C4×C127—28no—
154C2×C4×C127—24no—
155C2×C4×C127—24no—
156C2×C4×C127—28no—
157C2×C4×C127—28no—
158C2×C4×C127—28no—
159C2×C4×C127—28no—
160C2×C4×C127—28no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—44no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—44no—
170C2×C4×C127—44no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—48no—
175C2×C4×C127#12014yes—
176C2×C4×C127C22⋊Q814yes—
177C2×C4×C127C22⋊Q818yes—
178C2×C4×C127C4⋊Q814yes—
179C22×C127C2×#12011yescharacteristic
180C22×C127C2×C22⋊Q811yescharacteristic
181C22×C127C2×C22⋊Q812yes—
182C22×C127#52511yescharacteristic
183C22×C127#52511yescharacteristic
184C22×C127#52512yes—
185C22×C127C2×C4⋊Q811yescharacteristic
186C22×C127#53314yes—
187C22×C127#53511yescharacteristic
188C22×C127#53611yescharacteristic
189C22×C127#54214yes—
190C22×C127#54614yes—
191C22×C127D4×Q814yes—
192C22×C127#55412yes—
193C22×C127#55612yes—
194C22×C127#55712yes—
195C22×C127Q8212yes—
196C4×C127—28no—
197C4×C127—24no—
198C4×C127—24no—
199C4×C127—24no—
200C4×C127—44no—
201C4×C127—44no—
202C4×C127—48no—
203C4×C127—82no—
204#14881C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127#239911yescharacteristic
206C2×C127#240411yescharacteristic
207C2×C127#243411yescharacteristic
208C2×C127#245114yes—
209C2×C127#246514yes—
210C2×C127#256711yescharacteristic
211C2×C127#258111yescharacteristic
212C2×C127#263211yescharacteristic
213C2×C127#284811yescharacteristic
214C22×C4×Q8C2×C12711yescharacteristic
215C2×#395C2×C12712yes—
216C2×#391C2×C12711yescharacteristic
217#1446C2×C12712yes—
218#1444C2×C12712yes—
219#1441C2×C12712yes—
220#1436C2×C12714yes—
221#1434C2×C12711yescharacteristic
222C127#1488111yescharacteristic, direct product factor, Sylow
223C23×Q8C22×C12711yescharacteristic
224C23×Q8C22×C12711yescharacteristic
225C2×C4×Q8—28no—
226C2×C4×Q8—24no—
227C22×C4⋊C4C22×C12711yescharacteristic
228C22×C4⋊C4C22×C12714yes—
229C22×C4⋊C4C22×C12712yes—
230C22×C4⋊C4C22×C12711yescharacteristic
231C22×C42C22×C12712yes—
232C22×C42C22×C12711yescharacteristic
233#395—28no—
234#391—24no—
235C2×#95C22×C12712yes—
236C2×#95C22×C12714yes—
237C2×#95C22×C12712yes—
238C2×#95C22×C12712yes—
239C2×#95C22×C12714yes—
240C2×#95C22×C12712yes—
241C2×#95C22×C12714yes—
242C2×#95C22×C12712yes—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—24no—
247C22×Q8—24no—
248C22×Q8—22no—
249C22×Q8—24no—
250C22×Q8—42no—
251C22×Q8Q8×C12714yescomplemented
252C23×C4C23×C12712yes—
253C23×C4C23×C12712yes—
254C23×C4C23×C12714yes—
255C23×C4C23×C12712yes—
256C23×C4C23×C12711yescharacteristic
257C23×C4C23×C12711yescharacteristic
258C23×C4C23×C12712yes—
259C23×C4C23×C12711yescharacteristic
260C4×Q8—232no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4D4×C12718yes—
271C2×C42—24no—
272C2×C42—24no—
273C2×C42—24no—
274C2×C42—24no—
275C2×C42D4×C12714yes—
276#95—24no—
277#95—24no—
278#95—24no—
279#95—28no—
280#95—24no—
281#95—28no—
282#95—44no—
283#95Q8×C12718yescomplemented
284C24C24×C12711yescharacteristic
285C2×Q8—28no—
286C2×Q8—28no—
287C2×Q8—216no—
288C2×Q8—28no—
289C2×Q8—28no—
290C2×Q8—216no—
291C2×Q8—416no—
292C2×Q8—44no—
293C2×Q8—44no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4C2×D4×C12714yes—
323C22×C4C2×D4×C12714yes—
324C22×C4C2×D4×C12712yes—
325C22×C4C2×D4×C12714yes—
326C22×C4C2×D4×C12712yes—
327C22×C4C2×D4×C12712yes—
328C22×C4C2×Q8×C12718yes—
329C22×C4C2×Q8×C12714yes—
330C22×C4C2×Q8×C12712yes—
331C22×C4C2×Q8×C12714yes—
332C22×C4#41×C12714yes—
333C22×C4#41×C12714yes—
334C22×C4#41×C12712yes—
335C4⋊C4—28no—
336C4⋊C4—216no—
337C4⋊C4—416no—
338C4⋊C4—44no—
339C42—216no—
340C42—28no—
341C23C22×D4×C12711yescharacteristic
342C23C22×D4×C12712yes—
343C23C22×Q8×C12711yescharacteristic
344C23C22×Q8×C12712yes—
345C23C2×#41×C12712yes—
346C23C2×#41×C12711yescharacteristic
347C23C2×#41×C12712yes—
348C23H(5,𝔽2)×C12712yes—
349C232−1+4×C12712yes—
350Q8—232no—
351Q8—416no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—28no—
367C2×C4—28no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—28no—
371C2×C4—28no—
372C2×C4—28no—
373C2×C4—28no—
374C2×C4—28no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—48no—
389C2×C4#120×C12714yes—
390C2×C4C22⋊Q8×C12714yes—
391C2×C4C22⋊Q8×C12718yes—
392C2×C4C4⋊Q8×C12714yes—
393C22C2×#120×C12711yescharacteristic
394C22C2×C22⋊Q8×C12711yescharacteristic
395C22C2×C22⋊Q8×C12712yes—
396C22#525×C12711yescharacteristic
397C22#525×C12711yescharacteristic
398C22#525×C12712yes—
399C22C2×C4⋊Q8×C12711yescharacteristic
400C22#533×C12714yes—
401C22#535×C12711yescharacteristic
402C22#536×C12711yescharacteristic
403C22#542×C12714yes—
404C22#546×C12714yes—
405C22D4×Q8×C12714yes—
406C22#554×C12712yes—
407C22#556×C12712yes—
408C22#557×C12712yes—
409C22Q82×C12712yes—
410C4—28no—
411C4—24no—
412C4—24no—
413C4—24no—
414C4—44no—
415C4—44no—
416C4—48no—
417C4—82no—
418C2C127×#239911yescharacteristic
419C2C127×#240411yescharacteristic
420C2C127×#243411yescharacteristic
421C2C127×#245114yes—
422C2C127×#246514yes—
423C2C127×#256711yescharacteristic
424C2C127×#258111yescharacteristic
425C2C127×#263211yescharacteristic
426C2C127×#284811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
37. C22×Q8×C127Q8semidirect
69. #95×C127Q8semidirect
204. #14881C127direct (N × H)
222. C127#14881direct (N × H)
251. C22×Q8Q8×C127semidirect
283. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#395×C1272
C2×#391×C1272
C127×#14462
C127×#14442
C127×#14412
C127×#14362
C127×#14342
#14881127