Finite Group Databasebeta

← C127×#11525 #44575198

Subgroups — C127×#11525 #44575198

Order 32512.

738 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C4×#120×C127C211yesmaximal, characteristic
2C127×#1466C211yesmaximal, characteristic, complemented
3C127×#1465C211yesmaximal, characteristic, complemented
4C127×#1326C212yesmaximal, complemented
5C127×#1316C212yesmaximal, complemented
6C24×C4×C127C411yescharacteristic
7C2×#120×C127C411yescharacteristic
8C2×C4×D4×C127—21no—
9C2×C4×D4×C127C2211yescharacteristic
10#432×C127—21no—
11#407×C127—21no—
12#386×C127—21no—
13#386×C127C411yescharacteristic
14#385×C127—21no—
15#385×C127C2211yescharacteristic
16#379×C127C2211yescharacteristic
17C4×C22⋊C4×C127—21no—
18C4×C22⋊C4×C127C411yescharacteristic
19#324×C127—21no—
20#323×C127—21no—
21#323×C127C2212yes—
22#323×C127C2212yes—
23C25×C127C2×C411yescharacteristic
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C23×C4×C127—21no—
27C23×C4×C127—21no—
28C23×C4×C127—44no—
29C23×C4×C127—41no—
30C23×C4×C127—41no—
31C23×C4×C127C2×C411yescharacteristic
32C23×C4×C127C2×C411yescharacteristic
33C23×C4×C127D411yescharacteristic
34C2×M16×C127—41no—
35#120×C127—22no—
36#120×C127—22no—
37C4×D4×C127—41no—
38C4×D4×C127—41no—
39C4×D4×C127—44no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127C2×C411yescharacteristic
47C2×C22⋊C4×C127C2×C411yescharacteristic
48C2×C22⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127C2311yescharacteristic
50C2×C42×C127—21no—
51C2×C42×C127D411yescharacteristic
52C4⋊C8×C127—41no—
53C22⋊C8×C127—22no—
54C22⋊C8×C127—22no—
55C22⋊C8×C127—41no—
56#97×C127—41no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60C24×C127—21no—
61C24×C127—21no—
62C24×C127—42no—
63C24×C127—41no—
64C24×C127—42no—
65C24×C127—41no—
66C24×C127C22⋊C411yescharacteristic
67C24×C127M1612yescomplemented
68C24×C127C22×C411yescharacteristic
69C2×D4×C127—24no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C22×C4×C127—24no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—42no—
85C22×C4×C127—42no—
86C22×C4×C127—42no—
87C22×C4×C127—42no—
88C22×C4×C127—42no—
89C22×C4×C127—42no—
90C22×C4×C127—42no—
91C22×C4×C127—44no—
92C22×C4×C127—44no—
93C22×C4×C127—44no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127—44no—
98C22×C4×C127C22⋊C411yescharacteristic
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C411yescharacteristic
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127C2×D411yescharacteristic
103M16×C127—82no—
104C2×C8×C127—42no—
105C2×C8×C127—42no—
106C4⋊C4×C127—41no—
107C4⋊C4×C127—42no—
108C22⋊C4×C127—24no—
109C22⋊C4×C127—21no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—42no—
113C22⋊C4×C127—42no—
114C22⋊C4×C127—42no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127M1612yescomplemented
117C42×C127—21no—
118C42×C127—21no—
119C42×C127—42no—
120C23×C127—22no—
121C23×C127—22no—
122C23×C127—22no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—21no—
128C23×C127—41no—
129C23×C127—44no—
130C23×C127—42no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127—44no—
135C23×C127—42no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127—42no—
141C23×C127—48no—
142C23×C127—42no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127C2×C22⋊C411yescharacteristic
146C23×C127C2×M1611yescharacteristic
147C23×C127C2×M1611yescharacteristic
148D4×C127—48no—
149D4×C127—42no—
150D4×C127—42no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—21no—
154C2×C4×C127—22no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—21no—
159C2×C4×C127—21no—
160C2×C4×C127—44no—
161C2×C4×C127—42no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—48no—
166C2×C4×C127—42no—
167C2×C4×C127—41no—
168C2×C4×C127—42no—
169C2×C4×C127—44no—
170C2×C4×C127—42no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—42no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—81no—
179C2×C4×C127#9911yescharacteristic
180C2×C4×C127#9911yescharacteristic
181C8×C127—82no—
182C8×C127—82no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—24no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—41no—
189C22×C127—41no—
190C22×C127—42no—
191C22×C127—42no—
192C22×C127—42no—
193C22×C127—42no—
194C22×C127—42no—
195C22×C127—44no—
196C22×C127—44no—
197C22×C127—44no—
198C22×C127—44no—
199C22×C127—42no—
200C22×C127—41no—
201C22×C127—42no—
202C22×C127—41no—
203C22×C127—42no—
204C22×C127—41no—
205C22×C127—41no—
206C22×C127—41no—
207C22×C127—81no—
208C22×C127#40711yescharacteristic
209C22×C127C2×#9911yescharacteristic
210C22×C127#41311yescharacteristic
211C4×C127—21no—
212C4×C127—42no—
213C4×C127—41no—
214C4×C127—42no—
215C4×C127—41no—
216C4×C127—41no—
217C4×C127—41no—
218C4×C127—81no—
219C4×C127AΣL(1,𝔽16)12yes—
220#11525C12711yesmaximal, characteristic, direct product factor, Sylow
221C2×C127—21no—
222C2×C127—21no—
223C2×C127—44no—
224C2×C127—41no—
225C2×C127—41no—
226C2×C127—81no—
227C2×C127#146511yescharacteristic
228C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
229C2×C127#212011yescharacteristic
230C4×#120C2×C12711yescharacteristic
231#1466C2×C12711yescharacteristic, complemented
232#1465C2×C12711yescharacteristic, complemented
233#1326C2×C12712yescomplemented
234#1316C2×C12712yescomplemented
235C127#1152511yescharacteristic, direct product factor, Sylow
236C24×C4C4×C12711yescharacteristic
237C2×#120C4×C12711yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4C22×C12711yescharacteristic
240#432—21no—
241#407—21no—
242#386—21no—
243#386C4×C12711yescharacteristic
244#385—21no—
245#385C22×C12711yescharacteristic
246#379C22×C12711yescharacteristic
247C4×C22⋊C4—21no—
248C4×C22⋊C4C4×C12711yescharacteristic
249#324—21no—
250#323—21no—
251#323C22×C12712yes—
252#323C22×C12712yes—
253C25C2×C4×C12711yescharacteristic
254C22×D4—21no—
255C22×D4C2×C4×C12711yescharacteristic
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—44no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4C2×C4×C12711yescharacteristic
262C23×C4C2×C4×C12711yescharacteristic
263C23×C4D4×C12711yescharacteristic
264C2×M16—41no—
265#120—22no—
266#120—22no—
267C4×D4—41no—
268C4×D4—41no—
269C4×D4—44no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C12711yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4C2×C4×C12711yescharacteristic
277C2×C22⋊C4C2×C4×C12711yescharacteristic
278C2×C22⋊C4D4×C12711yescharacteristic
279C2×C22⋊C4C23×C12711yescharacteristic
280C2×C42—21no—
281C2×C42D4×C12711yescharacteristic
282C4⋊C8—41no—
283C22⋊C8—22no—
284C22⋊C8—22no—
285C22⋊C8—41no—
286#97—41no—
287#95—21no—
288#95—21no—
289#95—21no—
290C24—21no—
291C24—21no—
292C24—42no—
293C24—41no—
294C24—42no—
295C24—41no—
296C24C22⋊C4×C12711yescharacteristic
297C24M16×C12712yescomplemented
298C24C22×C4×C12711yescharacteristic
299C2×D4—24no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C22×C4—24no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—44no—
322C22×C4—44no—
323C22×C4—44no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—44no—
328C22×C4C22⋊C4×C12711yescharacteristic
329C22×C4C22⋊C4×C12711yescharacteristic
330C22×C4C22⋊C4×C12711yescharacteristic
331C22×C4C2×D4×C12711yescharacteristic
332C22×C4C2×D4×C12711yescharacteristic
333M16—82no—
334C2×C8—42no—
335C2×C8—42no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C22⋊C4—24no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—41no—
346C22⋊C4M16×C12712yescomplemented
347C42—21no—
348C42—21no—
349C42—42no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—44no—
360C23—42no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—44no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—48no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23C2×C22⋊C4×C12711yescharacteristic
376C23C2×M16×C12711yescharacteristic
377C23C2×M16×C12711yescharacteristic
378D4—48no—
379D4—42no—
380D4—42no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—48no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4#99×C12711yescharacteristic
410C2×C4#99×C12711yescharacteristic
411C8—82no—
412C8—82no—
413C22—21no—
414C22—21no—
415C22—24no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—42no—
430C22—41no—
431C22—42no—
432C22—41no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—81no—
438C22#407×C12711yescharacteristic
439C22C2×#99×C12711yescharacteristic
440C22#413×C12711yescharacteristic
441C4—21no—
442C4—42no—
443C4—41no—
444C4—42no—
445C4—41no—
446C4—41no—
447C4—41no—
448C4—81no—
449C4AΣL(1,𝔽16)×C12712yes—
450C2—21no—
451C2—21no—
452C2—44no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2C127×#146511yescharacteristic
457C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
458C2C127×#212011yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC2×#120×C127C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1466C2semidirect
3. C127×#1465C2semidirect
4. C127×#1326C2semidirect
5. C127×#1316C2semidirect
67. C24×C127M16semidirect
116. C22⋊C4×C127M16semidirect
220. #11525C127direct (N × H)
231. #1466C2×C127semidirect
232. #1465C2×C127semidirect
233. #1326C2×C127semidirect
234. #1316C2×C127semidirect
235. C127#11525direct (N × H)
297. C24M16×C127semidirect
346. C22⋊C4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C4×#120×C1272
C127×#14662
C127×#14652
C127×#13262
C127×#13162
#11525127