Finite Group Databasebeta

← C127×#9468 #44573141

Subgroups — C127×#9468 #44573141

Order 32512.

934 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2972C211yesmaximal, characteristic, complemented
2C127×#2408C211yesmaximal, characteristic
3C127×#1799C211yesmaximal, characteristic, complemented
4C127×#1786C212yesmaximal, complemented
5C127×#1289C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C2×#121×C127—21no—
8C2×#120×C127—21no—
9C2×C4×D4×C127C2211yescharacteristic
10C8×D4×C127—24no—
11#431×C127—21no—
12C2×#102×C127—24no—
13C2×#99×C127—21no—
14C2×C22⋊C8×C127—21no—
15C2×C22⋊C8×C127C2212yes—
16#394×C127C412yescomplemented
17#392×C127C412yescomplemented
18#390×C127—21no—
19#380×C127C2212yes—
20#380×C127C2211yescharacteristic
21#379×C127—21no—
22#342×C127—21no—
23C25×C127—21no—
24C22×D4×C127—22no—
25C22×D4×C127—22no—
26C22×D4×C127—21no—
27C22×D4×C127—22no—
28C22×D4×C127—44no—
29C22×D4×C127C2×C412yes—
30C22×D4×C127D411yescharacteristic
31C23×C4×C127D411yescharacteristic
32C23×C4×C127C2311yescharacteristic
33C22×C8×C127—22no—
34C22×C8×C127D414yescomplemented
35#121×C127—44no—
36#120×C127—42no—
37#120×C127—42no—
38C4×D4×C127—22no—
39C4×D4×C127—22no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127—22no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127C2×C411yescharacteristic
49C2×C22⋊C4×C127D411yescharacteristic
50C2×C42×C127D411yescharacteristic
51C4⋊C8×C127—22no—
52#102×C127—48no—
53#99×C127—42no—
54C22⋊C8×C127—22no—
55C22⋊C8×C127—22no—
56C22⋊C8×C127—22no—
57C4×C8×C127—22no—
58#95×C127—22no—
59#95×C127C2×C412yes—
60C24×C127—22no—
61C24×C127—44no—
62C24×C127—42no—
63C24×C127—41no—
64C24×C127—41no—
65C24×C127—42no—
66C24×C127—82no—
67C24×C127C22⋊C411yescharacteristic
68C24×C127C2×D411yescharacteristic
69C2×D4×C127—22no—
70C2×D4×C127—22no—
71C2×D4×C127—28no—
72C2×D4×C127—24no—
73C2×D4×C127—24no—
74C2×D4×C127—44no—
75C2×D4×C127—42no—
76C2×D4×C127—44no—
77C2×D4×C127—48no—
78C2×D4×C127—44no—
79C2×D4×C127—44no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C2×D4×C127—82no—
83C2×D4×C127D812yes—
84C2×D4×C127SD1612yes—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—22no—
88C22×C4×C127—42no—
89C22×C4×C127—42no—
90C22×C4×C127—42no—
91C22×C4×C127C22⋊C411yescharacteristic
92C22×C4×C127C22⋊C411yescharacteristic
93C22×C4×C127C22⋊C411yescharacteristic
94C22×C4×C127C22×C411yescharacteristic
95C22×C4×C127C2×D412yes—
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127#4112yes—
98C2×C8×C127—24no—
99C2×C8×C127—44no—
100C2×C8×C127—82no—
101C4⋊C4×C127—22no—
102C4⋊C4×C127—42no—
103C4⋊C4×C127—44no—
104C22⋊C4×C127—22no—
105C22⋊C4×C127—22no—
106C22⋊C4×C127—44no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—44no—
110C22⋊C4×C127—42no—
111C22⋊C4×C127—42no—
112C22⋊C4×C127—82no—
113C42×C127—21no—
114C42×C127—21no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—24no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—42no—
123C23×C127—48no—
124C23×C127—42no—
125C23×C127—42no—
126C23×C127—42no—
127C23×C127—42no—
128C23×C127—42no—
129C23×C127—84no—
130C23×C127—84no—
131C23×C127—84no—
132C23×C127—88no—
133C23×C127—82no—
134C23×C127—82no—
135C23×C127#10212yescomplemented
136C23×C127C2×C22⋊C411yescharacteristic
137C23×C127#12112yes—
138C23×C127C2×D811yescharacteristic
139C23×C127C2×SD1611yescharacteristic
140C23×C127#13512yes—
141D4×C127—24no—
142D4×C127—24no—
143D4×C127—28no—
144D4×C127—44no—
145D4×C127—44no—
146D4×C127—44no—
147D4×C127—88no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—24no—
151C2×C4×C127—22no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—41no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—81no—
163C2×C4×C127—82no—
164C2×C4×C127—82no—
165C2×C4×C127—82no—
166C2×C4×C127#10212yescomplemented
167C2×C4×C127C4×D412yes—
168C2×C4×C127#12011yescharacteristic
169C2×C4×C127#12311yescharacteristic
170C8×C127—44no—
171C22×C127—21no—
172C22×C127—22no—
173C22×C127—21no—
174C22×C127—22no—
175C22×C127—22no—
176C22×C127—41no—
177C22×C127—41no—
178C22×C127—42no—
179C22×C127—42no—
180C22×C127—44no—
181C22×C127—44no—
182C22×C127—41no—
183C22×C127—41no—
184C22×C127—44no—
185C22×C127—81no—
186C22×C127—82no—
187C22×C127—82no—
188C22×C127—88no—
189C22×C127—88no—
190C22×C127—82no—
191C22×C127—82no—
192C22×C127#38611yescharacteristic
193C22×C127C2×#10211yescharacteristic
194C22×C127#41611yescharacteristic
195C22×C127#46512yes—
196C22×C127#46612yes—
197C4×C127—21no—
198C4×C127—22no—
199C4×C127—22no—
200C4×C127—41no—
201C4×C127—41no—
202C4×C127—82no—
203C4×C127—162no—
204C4×C127B(4,𝔽2)12yes—
205#9468C12711yesmaximal, characteristic, direct product factor, Sylow
206C2×C127—21no—
207C2×C127—22no—
208C2×C127—21no—
209C2×C127—22no—
210C2×C127—42no—
211C2×C127—84no—
212C2×C127#188911yescharacteristic
213C2×C127#189311yescharacteristic
214C2×C127#191011yescharacteristic
215#2972C2×C12711yescharacteristic, complemented
216#2408C2×C12711yescharacteristic
217#1799C2×C12711yescharacteristic, complemented
218#1786C2×C12712yescomplemented
219#1289C2×C12712yescomplemented
220C127#946811yescharacteristic, direct product factor, Sylow
221C23×D4C22×C12711yescharacteristic
222C2×#121—21no—
223C2×#120—21no—
224C2×C4×D4C22×C12711yescharacteristic
225C8×D4—24no—
226#431—21no—
227C2×#102—24no—
228C2×#99—21no—
229C2×C22⋊C8—21no—
230C2×C22⋊C8C22×C12712yes—
231#394C4×C12712yescomplemented
232#392C4×C12712yescomplemented
233#390—21no—
234#380C22×C12712yes—
235#380C22×C12711yescharacteristic
236#379—21no—
237#342—21no—
238C25—21no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—44no—
244C22×D4C2×C4×C12712yes—
245C22×D4D4×C12711yescharacteristic
246C23×C4D4×C12711yescharacteristic
247C23×C4C23×C12711yescharacteristic
248C22×C8—22no—
249C22×C8D4×C12714yescomplemented
250#121—44no—
251#120—42no—
252#120—42no—
253C4×D4—22no—
254C4×D4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4C2×C4×C12711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4C2×C4×C12711yescharacteristic
264C2×C22⋊C4D4×C12711yescharacteristic
265C2×C42D4×C12711yescharacteristic
266C4⋊C8—22no—
267#102—48no—
268#99—42no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271C22⋊C8—22no—
272C4×C8—22no—
273#95—22no—
274#95C2×C4×C12712yes—
275C24—22no—
276C24—44no—
277C24—42no—
278C24—41no—
279C24—41no—
280C24—42no—
281C24—82no—
282C24C22⋊C4×C12711yescharacteristic
283C24C2×D4×C12711yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—28no—
287C2×D4—24no—
288C2×D4—24no—
289C2×D4—44no—
290C2×D4—42no—
291C2×D4—44no—
292C2×D4—48no—
293C2×D4—44no—
294C2×D4—44no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—82no—
298C2×D4D8×C12712yes—
299C2×D4SD16×C12712yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4C22⋊C4×C12711yescharacteristic
307C22×C4C22⋊C4×C12711yescharacteristic
308C22×C4C22⋊C4×C12711yescharacteristic
309C22×C4C22×C4×C12711yescharacteristic
310C22×C4C2×D4×C12712yes—
311C22×C4C2×D4×C12711yescharacteristic
312C22×C4#41×C12712yes—
313C2×C8—24no—
314C2×C8—44no—
315C2×C8—82no—
316C4⋊C4—22no—
317C4⋊C4—42no—
318C4⋊C4—44no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—44no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—44no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—82no—
328C42—21no—
329C42—21no—
330C23—21no—
331C23—21no—
332C23—24no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—42no—
338C23—48no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—84no—
345C23—84no—
346C23—84no—
347C23—88no—
348C23—82no—
349C23—82no—
350C23#102×C12712yescomplemented
351C23C2×C22⋊C4×C12711yescharacteristic
352C23#121×C12712yes—
353C23C2×D8×C12711yescharacteristic
354C23C2×SD16×C12711yescharacteristic
355C23#135×C12712yes—
356D4—24no—
357D4—24no—
358D4—28no—
359D4—44no—
360D4—44no—
361D4—44no—
362D4—88no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4#102×C12712yescomplemented
382C2×C4C4×D4×C12712yes—
383C2×C4#120×C12711yescharacteristic
384C2×C4#123×C12711yescharacteristic
385C8—44no—
386C22—21no—
387C22—22no—
388C22—21no—
389C22—22no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—42no—
394C22—42no—
395C22—44no—
396C22—44no—
397C22—41no—
398C22—41no—
399C22—44no—
400C22—81no—
401C22—82no—
402C22—82no—
403C22—88no—
404C22—88no—
405C22—82no—
406C22—82no—
407C22#386×C12711yescharacteristic
408C22C2×#102×C12711yescharacteristic
409C22#416×C12711yescharacteristic
410C22#465×C12712yes—
411C22#466×C12712yes—
412C4—21no—
413C4—22no—
414C4—22no—
415C4—41no—
416C4—41no—
417C4—82no—
418C4—162no—
419C4B(4,𝔽2)×C12712yes—
420C2—21no—
421C2—22no—
422C2—21no—
423C2—22no—
424C2—42no—
425C2—84no—
426C2C127×#188911yescharacteristic
427C2C127×#189311yescharacteristic
428C2C127×#191011yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#2408C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2972C2semidirect
3. C127×#1799C2semidirect
4. C127×#1786C2semidirect
5. C127×#1289C2semidirect
16. #394×C127C4semidirect
17. #392×C127C4semidirect
34. C22×C8×C127D4semidirect
135. C23×C127#102semidirect
166. C2×C4×C127#102semidirect
205. #9468C127direct (N × H)
215. #2972C2×C127semidirect
217. #1799C2×C127semidirect
218. #1786C2×C127semidirect
219. #1289C2×C127semidirect
220. C127#9468direct (N × H)
231. #394C4×C127semidirect
232. #392C4×C127semidirect
249. C22×C8D4×C127semidirect
350. C23#102×C127semidirect
381. C2×C4#102×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29722
C127×#24082
C127×#17992
C127×#17862
C127×#12892
#9468127