Finite Group Databasebeta

← C127×#14258 #44577931

Subgroups — C127×#14258 #44577931

Order 32512.

2142 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C22×#117×C127C211yesmaximal, characteristic
3C2×#391×C127C212yesmaximal, complemented
4C2×#380×C127C211yesmaximal, characteristic
5C127×#1441C214yesmaximal, complemented
6C127×#1440C214yesmaximal
7C127×C4⋊#95C212yesmaximal, complemented
8C23×Q8×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C2×C22⋊Q8×C127—24no—
11C2×C22⋊Q8×C127—24no—
12C2×C22⋊Q8×C127C418yescomplemented
13C2×#117×C127—24no—
14C2×#117×C127—28no—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C42×C127C2212yes—
23#391×C127—28no—
24#380×C127—24no—
25C2×#95×C127C2218yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2218yes—
28C25×C127C2311yescharacteristic
29C22×Q8×C127—22no—
30C22×Q8×C127—22no—
31C22×Q8×C127—24no—
32C22×Q8×C127—24no—
33C22×Q8×C127C2×C414yes—
34C23×C4×C127—24no—
35C23×C4×C127—24no—
36C23×C4×C127C2×C414yes—
37C23×C4×C127D414yes—
38C23×C4×C127D414yes—
39C23×C4×C127C2314yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2314yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C22⋊Q8×C127—232no—
46#117×C127—232no—
47C2×C4⋊C4×C127—28no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127C2×C414yes—
57C2×C4⋊C4×C127C2×C418yes—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—28no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—44no—
64C2×C22⋊C4×C127C2×C418yes—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127D418yes—
68#95×C127—24no—
69#95×C127—216no—
70#95×C127—48no—
71C24×C127—22no—
72C24×C127—22no—
73C24×C127—22no—
74C24×C127—24no—
75C24×C127—22no—
76C24×C127C22×C412yes—
77C24×C127C2×D412yes—
78C24×C127C2×D412yes—
79C24×C127C2411yescharacteristic
80C2×Q8×C127—28no—
81C2×Q8×C127—216no—
82C2×Q8×C127—44no—
83C2×Q8×C127—48no—
84C2×Q8×C127—44no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—216no—
88C22×C4×C127—28no—
89C22×C4×C127—216no—
90C22×C4×C127—28no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—24no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127—28no—
109C22×C4×C127—28no—
110C22×C4×C127C22⋊C4116yes—
111C22×C4×C127C22×C414yes—
112C22×C4×C127C22×C414yes—
113C22×C4×C127C22×C412yes—
114C22×C4×C127C22×C412yes—
115C22×C4×C127C2×D418yes—
116C22×C4×C127C2×D412yes—
117C22×C4×C127C2×D412yes—
118C22×C4×C127C2×D412yes—
119C22×C4×C127C2×D412yes—
120C22×C4×C127C2×D414yes—
121C22×C4×C127#4114yes—
122C4⋊C4×C127—216no—
123C4⋊C4×C127—28no—
124C4⋊C4×C127—216no—
125C4⋊C4×C127—48no—
126C22⋊C4×C127—216no—
127C22⋊C4×C127—216no—
128C22⋊C4×C127—48no—
129C42×C127—216no—
130C23×C127—24no—
131C23×C127—24no—
132C23×C127—24no—
133C23×C127—22no—
134C23×C127—24no—
135C23×C127—22no—
136C23×C127—22no—
137C23×C127—24no—
138C23×C127—24no—
139C23×C127—22no—
140C23×C127—24no—
141C23×C127—44no—
142C23×C127—44no—
143C23×C127—44no—
144C23×C127—44no—
145C23×C127C2×C22⋊C414yes—
146C23×C127C23×C411yescharacteristic
147C23×C127C22×D411yescharacteristic
148C23×C127C22×D411yescharacteristic
149C23×C127C22×D412yes—
150C23×C127C2×#4112yes—
151C23×C127H(5,𝔽2)12yes—
152C23×C1272−1+414yes—
153C23×C1272−1+412yes—
154Q8×C127—416no—
155C2×C4×C127—24no—
156C2×C4×C127—22no—
157C2×C4×C127—24no—
158C2×C4×C127—22no—
159C2×C4×C127—232no—
160C2×C4×C127—24no—
161C2×C4×C127—24no—
162C2×C4×C127—28no—
163C2×C4×C127—28no—
164C2×C4×C127—28no—
165C2×C4×C127—28no—
166C2×C4×C127—28no—
167C2×C4×C127—42no—
168C2×C4×C127—44no—
169C2×C4×C127—42no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
172C2×C4×C127—44no—
173C2×C4×C127—44no—
174C2×C4×C127—44no—
175C2×C4×C127—44no—
176C2×C4×C127—44no—
177C2×C4×C127—44no—
178C2×C4×C127—44no—
179C2×C4×C127—44no—
180C2×C4×C127—48no—
181C2×C4×C127—48no—
182C2×C4×C127C2×C22⋊C414yes—
183C2×C4×C127C2×C22⋊C414yes—
184C2×C4×C127C4×D418yes—
185C2×C4×C127#12014yes—
186C2×C4×C127#12118yes—
187C2×C4×C127#12314yes—
188C22×C127—24no—
189C22×C127—24no—
190C22×C127—24no—
191C22×C127—48no—
192C22×C127—44no—
193C22×C127—44no—
194C22×C127—44no—
195C22×C127—44no—
196C22×C127C22×C22⋊C411yescharacteristic
197C22×C127C2×C4×D412yes—
198C22×C127#51912yes—
199C22×C127#52012yes—
200C22×C127C2×#12011yescharacteristic
201C22×C127C2×#12112yes—
202C22×C127C2×#12311yescharacteristic
203C22×C127#53511yescharacteristic
204C22×C127#53612yes—
205C22×C127#53612yes—
206C22×C127#53611yescharacteristic
207C22×C127#53614yes—
208C22×C127#53712yes—
209C22×C127#53714yes—
210C22×C127#54114yes—
211C22×C127#54214yes—
212C4×C127—24no—
213C4×C127—44no—
214C4×C127—48no—
215C4×C127—44no—
216C4×C127—84no—
217C4×C127#38618yes—
218#14258C12711yesmaximal, characteristic, direct product factor, Sylow
219C2×C127—44no—
220C2×C127C2×#38611yescharacteristic
221C2×C127#231011yescharacteristic
222C2×C127#231111yescharacteristic
223C2×C127#232314yes—
224C2×C127#261612yes—
225C2×C127#262012yes—
226C2×C127#262112yes—
227C2×C127#262512yes—
228C22×C22⋊Q8C2×C12711yescharacteristic
229C22×#117C2×C12711yescharacteristic
230C2×#391C2×C12712yescomplemented
231C2×#380C2×C12711yescharacteristic
232#1441C2×C12714yescomplemented
233#1440C2×C12714yes—
234C4⋊#95C2×C12712yescomplemented
235C127#1425811yescharacteristic, direct product factor, Sylow
236C23×Q8C22×C12711yescharacteristic
237C24×C4C22×C12711yescharacteristic
238C2×C22⋊Q8—24no—
239C2×C22⋊Q8—24no—
240C2×C22⋊Q8C4×C12718yescomplemented
241C2×#117—24no—
242C2×#117—28no—
243C22×C4⋊C4C22×C12712yes—
244C22×C4⋊C4C22×C12712yes—
245C22×C4⋊C4C22×C12711yescharacteristic
246C22×C4⋊C4C22×C12712yes—
247C22×C22⋊C4C22×C12712yes—
248C22×C22⋊C4C22×C12712yes—
249C22×C22⋊C4C22×C12712yes—
250C22×C42C22×C12712yes—
251#391—28no—
252#380—24no—
253C2×#95C22×C12718yes—
254C2×#95C22×C12712yes—
255C2×#95C22×C12718yes—
256C25C23×C12711yescharacteristic
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—24no—
260C22×Q8—24no—
261C22×Q8C2×C4×C12714yes—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4C2×C4×C12714yes—
265C23×C4D4×C12714yes—
266C23×C4D4×C12714yes—
267C23×C4C23×C12714yes—
268C23×C4C23×C12712yes—
269C23×C4C23×C12712yes—
270C23×C4C23×C12714yes—
271C23×C4C23×C12711yescharacteristic
272C23×C4C23×C12711yescharacteristic
273C22⋊Q8—232no—
274#117—232no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4C2×C4×C12714yes—
285C2×C4⋊C4C2×C4×C12718yes—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4C2×C4×C12718yes—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42D4×C12718yes—
296#95—24no—
297#95—216no—
298#95—48no—
299C24—22no—
300C24—22no—
301C24—22no—
302C24—24no—
303C24—22no—
304C24C22×C4×C12712yes—
305C24C2×D4×C12712yes—
306C24C2×D4×C12712yes—
307C24C24×C12711yescharacteristic
308C2×Q8—28no—
309C2×Q8—216no—
310C2×Q8—44no—
311C2×Q8—48no—
312C2×Q8—44no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—216no—
316C22×C4—28no—
317C22×C4—216no—
318C22×C4—28no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—28no—
337C22×C4—28no—
338C22×C4C22⋊C4×C127116yes—
339C22×C4C22×C4×C12714yes—
340C22×C4C22×C4×C12714yes—
341C22×C4C22×C4×C12712yes—
342C22×C4C22×C4×C12712yes—
343C22×C4C2×D4×C12718yes—
344C22×C4C2×D4×C12712yes—
345C22×C4C2×D4×C12712yes—
346C22×C4C2×D4×C12712yes—
347C22×C4C2×D4×C12712yes—
348C22×C4C2×D4×C12714yes—
349C22×C4#41×C12714yes—
350C4⋊C4—216no—
351C4⋊C4—28no—
352C4⋊C4—216no—
353C4⋊C4—48no—
354C22⋊C4—216no—
355C22⋊C4—216no—
356C22⋊C4—48no—
357C42—216no—
358C23—24no—
359C23—24no—
360C23—24no—
361C23—22no—
362C23—24no—
363C23—22no—
364C23—22no—
365C23—24no—
366C23—24no—
367C23—22no—
368C23—24no—
369C23—44no—
370C23—44no—
371C23—44no—
372C23—44no—
373C23C2×C22⋊C4×C12714yes—
374C23C23×C4×C12711yescharacteristic
375C23C22×D4×C12711yescharacteristic
376C23C22×D4×C12711yescharacteristic
377C23C22×D4×C12712yes—
378C23C2×#41×C12712yes—
379C23H(5,𝔽2)×C12712yes—
380C232−1+4×C12714yes—
381C232−1+4×C12712yes—
382Q8—416no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—232no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—28no—
392C2×C4—28no—
393C2×C4—28no—
394C2×C4—28no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—48no—
409C2×C4—48no—
410C2×C4C2×C22⋊C4×C12714yes—
411C2×C4C2×C22⋊C4×C12714yes—
412C2×C4C4×D4×C12718yes—
413C2×C4#120×C12714yes—
414C2×C4#121×C12718yes—
415C2×C4#123×C12714yes—
416C22—24no—
417C22—24no—
418C22—24no—
419C22—48no—
420C22—44no—
421C22—44no—
422C22—44no—
423C22—44no—
424C22C22×C22⋊C4×C12711yescharacteristic
425C22C2×C4×D4×C12712yes—
426C22#519×C12712yes—
427C22#520×C12712yes—
428C22C2×#120×C12711yescharacteristic
429C22C2×#121×C12712yes—
430C22C2×#123×C12711yescharacteristic
431C22#535×C12711yescharacteristic
432C22#536×C12714yes—
433C22#536×C12712yes—
434C22#536×C12712yes—
435C22#536×C12711yescharacteristic
436C22#537×C12714yes—
437C22#537×C12712yes—
438C22#541×C12714yes—
439C22#542×C12714yes—
440C4—24no—
441C4—48no—
442C4—44no—
443C4—44no—
444C4—84no—
445C4#386×C12718yes—
446C2—44no—
447C2C2×#386×C12711yescharacteristic
448C2C127×#231011yescharacteristic
449C2C127×#231111yescharacteristic
450C2C127×#232314yes—
451C2C127×#261612yes—
452C2C127×#262012yes—
453C2C127×#262112yes—
454C2C127×#262512yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#391×C127C2semidirect
5. C127×#1441C2semidirect
7. C127×C4⋊#95C2semidirect
12. C2×C22⋊Q8×C127C4semidirect
218. #14258C127direct (N × H)
230. C2×#391C2×C127semidirect
232. #1441C2×C127semidirect
234. C4⋊#95C2×C127semidirect
235. C127#14258direct (N × H)
240. C2×C22⋊Q8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C22×#117×C1272
C2×#391×C1272
C2×#380×C1272
C127×#14412
C127×#14402
C127×C4⋊#952
#14258127