Finite Group Databasebeta

← C127×#9504 #44573177

Subgroups — C127×#9504 #44573177

Order 32512.

878 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2975C211yesmaximal, characteristic, complemented
2C127×#2408C211yesmaximal, characteristic
3C127×#1783C212yesmaximal, complemented
4C127×#1465C211yesmaximal, characteristic, complemented
5C127×#1305C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C2×#121×C127—21no—
8C2×#120×C127C412yes—
9C2×C4×D4×C127C2211yescharacteristic
10#436×C127—24no—
11#431×C127—21no—
12C2×#100×C127—24no—
13#407×C127—21no—
14#407×C127C2212yes—
15#407×C127C2212yes—
16#394×C127—21no—
17#392×C127—21no—
18#390×C127—21no—
19#380×C127C2211yescharacteristic
20#379×C127C412yes—
21#324×C127—21no—
22#323×C127—21no—
23C25×C127C2×C412yes—
24C22×D4×C127—22no—
25C22×D4×C127—21no—
26C22×D4×C127—22no—
27C22×D4×C127—21no—
28C22×D4×C127—22no—
29C22×D4×C127—44no—
30C22×D4×C127C2×C411yescharacteristic
31C23×C4×C127D411yescharacteristic
32C23×C4×C127C2311yescharacteristic
33C2×M16×C127—22no—
34C2×M16×C127—22no—
35C2×M16×C127D414yescomplemented
36#121×C127—44no—
37#120×C127—44no—
38C4×D4×C127—22no—
39C4×D4×C127—22no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127C2×C411yescharacteristic
46C2×C22⋊C4×C127C2×C412yes—
47C2×C22⋊C4×C127D411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C4⋊C8×C127—22no—
50#100×C127—48no—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53C22⋊C8×C127—22no—
54C22⋊C8×C127—22no—
55C22⋊C8×C127—22no—
56C4×C8×C127—22no—
57#95×C127—21no—
58C24×C127—22no—
59C24×C127—24no—
60C24×C127—44no—
61C24×C127—42no—
62C24×C127—42no—
63C24×C127—82no—
64C24×C127C22⋊C411yescharacteristic
65C24×C127C22×C411yescharacteristic
66C2×D4×C127—28no—
67C2×D4×C127—24no—
68C2×D4×C127—22no—
69C2×D4×C127—22no—
70C2×D4×C127—41no—
71C2×D4×C127—42no—
72C2×D4×C127—44no—
73C2×D4×C127—44no—
74C2×D4×C127—48no—
75C2×D4×C127—44no—
76C2×D4×C127—44no—
77C2×D4×C127—41no—
78C2×D4×C127—42no—
79C2×D4×C127—41no—
80C2×D4×C127—82no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—22no—
84C22×C4×C127—42no—
85C22×C4×C127—42no—
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22⋊C411yescharacteristic
88C22×C4×C127C22⋊C411yescharacteristic
89C22×C4×C127C2×D412yes—
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127#4112yes—
93M16×C127—44no—
94M16×C127—44no—
95M16×C127—82no—
96C2×C8×C127—24no—
97C2×C8×C127—42no—
98C4⋊C4×C127—22no—
99C4⋊C4×C127—42no—
100C22⋊C4×C127—22no—
101C22⋊C4×C127—22no—
102C22⋊C4×C127—44no—
103C22⋊C4×C127—44no—
104C22⋊C4×C127—42no—
105C22⋊C4×C127—82no—
106C42×C127—21no—
107C42×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—24no—
111C23×C127—28no—
112C23×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—42no—
120C23×C127—42no—
121C23×C127—44no—
122C23×C127—42no—
123C23×C127—42no—
124C23×C127—42no—
125C23×C127—42no—
126C23×C127—84no—
127C23×C127—84no—
128C23×C127—88no—
129C23×C127—88no—
130C23×C127C2×C22⋊C411yescharacteristic
131C23×C127C4×D412yes—
132D4×C127—44no—
133D4×C127—48no—
134D4×C127—44no—
135D4×C127—44no—
136D4×C127—88no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—22no—
140C2×C4×C127—24no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—41no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—81no—
152C2×C4×C127#10012yescomplemented
153C2×C4×C127#12011yescharacteristic
154C2×C4×C127#12112yes—
155C2×C4×C127#12311yescharacteristic
156C8×C127—44no—
157C8×C127—82no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—22no—
161C22×C127—22no—
162C22×C127—22no—
163C22×C127—42no—
164C22×C127—42no—
165C22×C127—42no—
166C22×C127—44no—
167C22×C127—44no—
168C22×C127—41no—
169C22×C127—44no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—81no—
173C22×C127—82no—
174C22×C127—82no—
175C22×C127—88no—
176C22×C127—88no—
177C22×C127—82no—
178C22×C127—82no—
179C22×C127#38611yescharacteristic
180C22×C127C2×#10011yescharacteristic
181C22×C127#41311yescharacteristic
182C4×C127—22no—
183C4×C127—21no—
184C4×C127—22no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—82no—
188C4×C127B(4,𝔽2)12yes—
189#9504C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—21no—
191C2×C127—21no—
192C2×C127—42no—
193C2×C127—81no—
194C2×C127—84no—
195C2×C127#188911yescharacteristic
196C2×C127#190011yescharacteristic
197C2×C127#191411yescharacteristic
198#2975C2×C12711yescharacteristic, complemented
199#2408C2×C12711yescharacteristic
200#1783C2×C12712yescomplemented
201#1465C2×C12711yescharacteristic, complemented
202#1305C2×C12712yescomplemented
203C127#950411yescharacteristic, direct product factor, Sylow
204C23×D4C22×C12711yescharacteristic
205C2×#121—21no—
206C2×#120C4×C12712yes—
207C2×C4×D4C22×C12711yescharacteristic
208#436—24no—
209#431—21no—
210C2×#100—24no—
211#407—21no—
212#407C22×C12712yes—
213#407C22×C12712yes—
214#394—21no—
215#392—21no—
216#390—21no—
217#380C22×C12711yescharacteristic
218#379C4×C12712yes—
219#324—21no—
220#323—21no—
221C25C2×C4×C12712yes—
222C22×D4—22no—
223C22×D4—21no—
224C22×D4—22no—
225C22×D4—21no—
226C22×D4—22no—
227C22×D4—44no—
228C22×D4C2×C4×C12711yescharacteristic
229C23×C4D4×C12711yescharacteristic
230C23×C4C23×C12711yescharacteristic
231C2×M16—22no—
232C2×M16—22no—
233C2×M16D4×C12714yescomplemented
234#121—44no—
235#120—44no—
236C4×D4—22no—
237C4×D4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C12711yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4C2×C4×C12711yescharacteristic
244C2×C22⋊C4C2×C4×C12712yes—
245C2×C22⋊C4D4×C12711yescharacteristic
246C2×C42D4×C12711yescharacteristic
247C4⋊C8—22no—
248#100—48no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254C4×C8—22no—
255#95—21no—
256C24—22no—
257C24—24no—
258C24—44no—
259C24—42no—
260C24—42no—
261C24—82no—
262C24C22⋊C4×C12711yescharacteristic
263C24C22×C4×C12711yescharacteristic
264C2×D4—28no—
265C2×D4—24no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—48no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—42no—
277C2×D4—41no—
278C2×D4—82no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4C22⋊C4×C12711yescharacteristic
285C22×C4C22⋊C4×C12711yescharacteristic
286C22×C4C22⋊C4×C12711yescharacteristic
287C22×C4C2×D4×C12712yes—
288C22×C4C2×D4×C12711yescharacteristic
289C22×C4C2×D4×C12711yescharacteristic
290C22×C4#41×C12712yes—
291M16—44no—
292M16—44no—
293M16—82no—
294C2×C8—24no—
295C2×C8—42no—
296C4⋊C4—22no—
297C4⋊C4—42no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—44no—
301C22⋊C4—44no—
302C22⋊C4—42no—
303C22⋊C4—82no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—24no—
309C23—28no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—44no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—84no—
325C23—84no—
326C23—88no—
327C23—88no—
328C23C2×C22⋊C4×C12711yescharacteristic
329C23C4×D4×C12712yes—
330D4—44no—
331D4—48no—
332D4—44no—
333D4—44no—
334D4—88no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4#100×C12712yescomplemented
351C2×C4#120×C12711yescharacteristic
352C2×C4#121×C12712yes—
353C2×C4#123×C12711yescharacteristic
354C8—44no—
355C8—82no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—44no—
365C22—44no—
366C22—41no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—82no—
372C22—82no—
373C22—88no—
374C22—88no—
375C22—82no—
376C22—82no—
377C22#386×C12711yescharacteristic
378C22C2×#100×C12711yescharacteristic
379C22#413×C12711yescharacteristic
380C4—22no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4B(4,𝔽2)×C12712yes—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—81no—
391C2—84no—
392C2C127×#188911yescharacteristic
393C2C127×#190011yescharacteristic
394C2C127×#191411yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#2408C2
LCSG ▷ C24 ▷ 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×#2975C2semidirect
3. C127×#1783C2semidirect
4. C127×#1465C2semidirect
5. C127×#1305C2semidirect
35. C2×M16×C127D4semidirect
152. C2×C4×C127#100semidirect
189. #9504C127direct (N × H)
198. #2975C2×C127semidirect
200. #1783C2×C127semidirect
201. #1465C2×C127semidirect
202. #1305C2×C127semidirect
203. C127#9504direct (N × H)
233. C2×M16D4×C127semidirect
350. C2×C4#100×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29752
C127×#24082
C127×#17832
C127×#14652
C127×#13052
#9504127