Finite Group Databasebeta

← C127×#9463 #44573136

Subgroups — C127×#9463 #44573136

Order 32512.

1034 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2433C211yesmaximal, characteristic
2C127×#2308C211yesmaximal, characteristic, complemented
3C127×#1783C211yesmaximal, characteristic, complemented
4C127×#1510C212yesmaximal, complemented
5C127×#1284C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C2×#127×C127C412yescomplemented
8C2×#121×C127C2211yescharacteristic
9C2×#120×C127—21no—
10C2×#120×C127—21no—
11C22×C22⋊C4×C127—21no—
12C2×#100×C127—22no—
13#407×C127C2212yes—
14#392×C127—22no—
15#390×C127C412yescomplemented
16#386×C127—24no—
17#381×C127C2212yes—
18#379×C127—21no—
19C4×C22⋊C4×C127C2211yescharacteristic
20#327×C127—24no—
21C25×C127D411yescharacteristic
22C25×C127D411yescharacteristic
23C22×D4×C127—21no—
24C22×D4×C127—22no—
25C22×D4×C127—22no—
26C22×D4×C127—22no—
27C22×D4×C127—22no—
28C22×D4×C127—44no—
29C22×D4×C127C2×C412yes—
30C22×D4×C127C2×C411yescharacteristic, complemented
31C22×D4×C127D412yes—
32C23×C4×C127—22no—
33C23×C4×C127C2311yescharacteristic
34C2×M16×C127—22no—
35#127×C127—44no—
36#121×C127—22no—
37#121×C127—22no—
38#120×C127—44no—
39#120×C127—44no—
40C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—44no—
50C2×C42×C127C2×C412yescomplemented
51#100×C127—44no—
52C22⋊C8×C127—22no—
53C22⋊C8×C127—22no—
54#95×C127—21no—
55#95×C127—22no—
56#95×C127D414yescomplemented
57C24×C127—21no—
58C24×C127—24no—
59C24×C127—21no—
60C24×C127—21no—
61C24×C127—21no—
62C24×C127—21no—
63C24×C127—42no—
64C24×C127—42no—
65C24×C127—42no—
66C24×C127—81no—
67C24×C127—81no—
68C24×C127C22⋊C412yes—
69C24×C127C22⋊C412yes—
70C24×C127C2×D411yescharacteristic
71C2×D4×C127—24no—
72C2×D4×C127—24no—
73C2×D4×C127—24no—
74C2×D4×C127—22no—
75C2×D4×C127—24no—
76C2×D4×C127—42no—
77C2×D4×C127—42no—
78C2×D4×C127—42no—
79C2×D4×C127—44no—
80C2×D4×C127—44no—
81C2×D4×C127—44no—
82C2×D4×C127—44no—
83C2×D4×C127—48no—
84C2×D4×C127—42no—
85C2×D4×C127—42no—
86C2×D4×C127—44no—
87C2×D4×C127—44no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—82no—
91C2×D4×C127—82no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—24no—
95C22×C4×C127—42no—
96C22×C4×C127—44no—
97C22×C4×C127—82no—
98C22×C4×C127—82no—
99C22×C4×C127C22×C411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127C2×D412yes—
102C22×C4×C127#4112yes—
103M16×C127—44no—
104C2×C8×C127—42no—
105C4⋊C4×C127—22no—
106C22⋊C4×C127—24no—
107C22⋊C4×C127—44no—
108C22⋊C4×C127—44no—
109C22⋊C4×C127—44no—
110C22⋊C4×C127—44no—
111C22⋊C4×C127—42no—
112C22⋊C4×C127—82no—
113C22⋊C4×C127—82no—
114C42×C127—42no—
115C23×C127—22no—
116C23×C127—22no—
117C23×C127—24no—
118C23×C127—22no—
119C23×C127—22no—
120C23×C127—22no—
121C23×C127—22no—
122C23×C127—22no—
123C23×C127—22no—
124C23×C127—22no—
125C23×C127—41no—
126C23×C127—42no—
127C23×C127—42no—
128C23×C127—42no—
129C23×C127—42no—
130C23×C127—42no—
131C23×C127—42no—
132C23×C127—42no—
133C23×C127—42no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—42no—
138C23×C127—42no—
139C23×C127—41no—
140C23×C127—42no—
141C23×C127—81no—
142C23×C127—81no—
143C23×C127—81no—
144C23×C127—81no—
145C23×C127—88no—
146C23×C127—88no—
147C23×C127#9914yes—
148C23×C127C2×C22⋊C411yescharacteristic
149C23×C127#12011yescharacteristic
150C23×C127#12311yescharacteristic
151D4×C127—48no—
152D4×C127—48no—
153D4×C127—82no—
154D4×C127—88no—
155D4×C127—88no—
156D4×C127—82no—
157D4×C127—82no—
158C2×C4×C127—22no—
159C2×C4×C127—22no—
160C2×C4×C127—24no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—44no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—44no—
169C2×C4×C127—41no—
170C2×C4×C127—44no—
171C2×C4×C127—88no—
172C2×C4×C127C4×D412yes—
173C2×C4×C127#12112yes—
174C8×C127—82no—
175C22×C127—21no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—24no—
182C22×C127—21no—
183C22×C127—44no—
184C22×C127—44no—
185C22×C127—44no—
186C22×C127—44no—
187C22×C127—44no—
188C22×C127—42no—
189C22×C127—42no—
190C22×C127—42no—
191C22×C127—42no—
192C22×C127—42no—
193C22×C127—82no—
194C22×C127—82no—
195C22×C127—84no—
196C22×C127—82no—
197C22×C127—82no—
198C22×C127—84no—
199C22×C127—84no—
200C22×C127—81no—
201C22×C127—81no—
202C22×C127—81no—
203C22×C127#38611yescharacteristic
204C22×C127C2×#9912yes—
205C22×C127#45312yes—
206C4×C127—22no—
207C4×C127—22no—
208C4×C127—44no—
209C4×C127—84no—
210C4×C127—81no—
211#9463C12711yesmaximal, characteristic, direct product factor, Sylow
212C2×C127—22no—
213C2×C127—22no—
214C2×C127—41no—
215C2×C127—44no—
216C2×C127—82no—
217C2×C127—161no—
218C2×C127#188711yescharacteristic
219C2×C127#189811yescharacteristic
220C2×C127#191111yescharacteristic
221#2433C2×C12711yescharacteristic
222#2308C2×C12711yescharacteristic, complemented
223#1783C2×C12711yescharacteristic, complemented
224#1510C2×C12712yescomplemented
225#1284C2×C12712yescomplemented
226C127#946311yescharacteristic, direct product factor, Sylow
227C23×D4C22×C12711yescharacteristic
228C2×#127C4×C12712yescomplemented
229C2×#121C22×C12711yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C22×C22⋊C4—21no—
233C2×#100—22no—
234#407C22×C12712yes—
235#392—22no—
236#390C4×C12712yescomplemented
237#386—24no—
238#381C22×C12712yes—
239#379—21no—
240C4×C22⋊C4C22×C12711yescharacteristic
241#327—24no—
242C25D4×C12711yescharacteristic
243C25D4×C12711yescharacteristic
244C22×D4—21no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—44no—
250C22×D4C2×C4×C12712yes—
251C22×D4C2×C4×C12711yescharacteristic, complemented
252C22×D4D4×C12712yes—
253C23×C4—22no—
254C23×C4C23×C12711yescharacteristic
255C2×M16—22no—
256#127—44no—
257#121—22no—
258#121—22no—
259#120—44no—
260#120—44no—
261C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—44no—
271C2×C42C2×C4×C12712yescomplemented
272#100—44no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275#95—21no—
276#95—22no—
277#95D4×C12714yescomplemented
278C24—21no—
279C24—24no—
280C24—21no—
281C24—21no—
282C24—21no—
283C24—21no—
284C24—42no—
285C24—42no—
286C24—42no—
287C24—81no—
288C24—81no—
289C24C22⋊C4×C12712yes—
290C24C22⋊C4×C12712yes—
291C24C2×D4×C12711yescharacteristic
292C2×D4—24no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—48no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—44no—
308C2×D4—44no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—82no—
312C2×D4—82no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—24no—
316C22×C4—42no—
317C22×C4—44no—
318C22×C4—82no—
319C22×C4—82no—
320C22×C4C22×C4×C12711yescharacteristic
321C22×C4C2×D4×C12711yescharacteristic
322C22×C4C2×D4×C12712yes—
323C22×C4#41×C12712yes—
324M16—44no—
325C2×C8—42no—
326C4⋊C4—22no—
327C22⋊C4—24no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C22⋊C4—44no—
332C22⋊C4—42no—
333C22⋊C4—82no—
334C22⋊C4—82no—
335C42—42no—
336C23—22no—
337C23—22no—
338C23—24no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—88no—
367C23—88no—
368C23#99×C12714yes—
369C23C2×C22⋊C4×C12711yescharacteristic
370C23#120×C12711yescharacteristic
371C23#123×C12711yescharacteristic
372D4—48no—
373D4—48no—
374D4—82no—
375D4—88no—
376D4—88no—
377D4—82no—
378D4—82no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—88no—
393C2×C4C4×D4×C12712yes—
394C2×C4#121×C12712yes—
395C8—82no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—24no—
403C22—21no—
404C22—44no—
405C22—44no—
406C22—44no—
407C22—44no—
408C22—44no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—82no—
415C22—82no—
416C22—84no—
417C22—82no—
418C22—82no—
419C22—84no—
420C22—84no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22#386×C12711yescharacteristic
425C22C2×#99×C12712yes—
426C22#453×C12712yes—
427C4—22no—
428C4—22no—
429C4—44no—
430C4—84no—
431C4—81no—
432C2—22no—
433C2—22no—
434C2—41no—
435C2—44no—
436C2—82no—
437C2—161no—
438C2C127×#188711yescharacteristic
439C2C127×#189811yescharacteristic
440C2C127×#191111yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#2433C2
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
2. C127×#2308C2semidirect
3. C127×#1783C2semidirect
4. C127×#1510C2semidirect
5. C127×#1284C2semidirect
7. C2×#127×C127C4semidirect
15. #390×C127C4semidirect
30. C22×D4×C127C2×C4semidirect
40. C2×C4⋊C4×C127C2×C4semidirect
50. C2×C42×C127C2×C4semidirect
56. #95×C127D4semidirect
211. #9463C127direct (N × H)
222. #2308C2×C127semidirect
223. #1783C2×C127semidirect
224. #1510C2×C127semidirect
225. #1284C2×C127semidirect
226. C127#9463direct (N × H)
228. C2×#127C4×C127semidirect
236. #390C4×C127semidirect
251. C22×D4C2×C4×C127semidirect
261. C2×C4⋊C4C2×C4×C127semidirect
271. C2×C42C2×C4×C127semidirect
277. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24332
C127×#23082
C127×#17832
C127×#15102
C127×#12842
#9463127