Finite Group Databasebeta

← C127×#11783 #44575456

Subgroups — C127×#11783 #44575456

Order 32512.

514 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2543C211yesmaximal, characteristic
2C4×#100×C127C211yesmaximal, characteristic, complemented
3C127×#1465C211yesmaximal, characteristic, complemented
4C127×#1346C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C2×#121×C127—21no—
7C2×#121×C127C411yescharacteristic
8C2×C4×D4×C127C2211yescharacteristic
9C2×#100×C127—21no—
10#407×C127—21no—
11C4×M16×C127—21no—
12#398×C127C2211yescharacteristic
13#397×C127C411yescharacteristic
14#394×C127C2211yescharacteristic
15#392×C127C411yescharacteristic
16#388×C127—21no—
17#386×C127—21no—
18#386×C127—21no—
19C2×#95×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C22×D4×C127D411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C2×M16×C127—22no—
31C2×M16×C127—41no—
32#121×C127—44no—
33#121×C127—41no—
34#121×C127—41no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2311yescharacteristic
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127C2×C411yescharacteristic
46C2×C22⋊C4×C127D411yescharacteristic
47C2×C42×C127D411yescharacteristic
48#100×C127—24no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—41no—
51#97×C127—41no—
52C4×C8×C127—41no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127C2×C411yescharacteristic
57#95×C127C2×C411yescharacteristic
58C24×C127—21no—
59C24×C127C22⋊C411yescharacteristic
60C24×C127C22⋊C411yescharacteristic
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—42no—
68C2×D4×C127—42no—
69C2×D4×C127—42no—
70C2×D4×C127—81no—
71C2×D4×C127—81no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—42no—
80C22×C4×C127—42no—
81C22×C4×C127—81no—
82C22×C4×C127—81no—
83C22×C4×C127—81no—
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127C22×C411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88C22×C4×C127C2×D411yescharacteristic
89M16×C127—24no—
90M16×C127—42no—
91M16×C127—82no—
92C2×C8×C127—42no—
93C2×C8×C127—42no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—42no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—81no—
105C42×C127—21no—
106C42×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127#10412yes—
124C23×C127C2×C22⋊C411yescharacteristic
125D4×C127—44no—
126D4×C127—84no—
127D4×C127—82no—
128D4×C127—84no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—22no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—41no—
136C2×C4×C127—42no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—81no—
149C2×C4×C127—81no—
150C2×C4×C127—81no—
151C2×C4×C127—84no—
152C2×C4×C127#9911yescharacteristic
153C2×C4×C127#9911yescharacteristic
154C2×C4×C127AGL(1,ℤ/8)12yes—
155C8×C127—44no—
156C8×C127—82no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—22no—
160C22×C127—42no—
161C22×C127—42no—
162C22×C127—42no—
163C22×C127—41no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127C2×#9911yescharacteristic
177C22×C127#41811yescharacteristic
178C22×C127C2×#10411yescharacteristic
179C4×C127—21no—
180C4×C127—21no—
181C4×C127—22no—
182C4×C127—42no—
183C4×C127—41no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—81no—
187C4×C127—81no—
188#11783C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127—21no—
190C2×C127—21no—
191C2×C127—42no—
192C2×C127—81no—
193C2×C127—161no—
194C2×C127#150711yescharacteristic
195C2×C127#212111yescharacteristic
196C2×C127#213211yescharacteristic
197#2543C2×C12711yescharacteristic
198C4×#100C2×C12711yescharacteristic, complemented
199#1465C2×C12711yescharacteristic, complemented
200#1346C2×C12712yescomplemented
201#1345C2×C12712yescomplemented
202C127#1178311yescharacteristic, direct product factor, Sylow
203C2×#121—21no—
204C2×#121C4×C12711yescharacteristic
205C2×C4×D4C22×C12711yescharacteristic
206C2×#100—21no—
207#407—21no—
208C4×M16—21no—
209#398C22×C12711yescharacteristic
210#397C4×C12711yescharacteristic
211#394C22×C12711yescharacteristic
212#392C4×C12711yescharacteristic
213#388—21no—
214#386—21no—
215#386—21no—
216C2×#95C4×C12711yescharacteristic
217#343C22×C12712yes—
218#324C22×C12712yes—
219#323—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C2×C4×C12711yescharacteristic
223C22×D4D4×C12711yescharacteristic
224C23×C4—21no—
225C23×C4C2×C4×C12711yescharacteristic
226C23×C4D4×C12711yescharacteristic
227C2×M16—22no—
228C2×M16—41no—
229#121—44no—
230#121—41no—
231#121—41no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×C4×C12711yescharacteristic
236C2×C4⋊C4C23×C12711yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4C2×C4×C12711yescharacteristic
243C2×C22⋊C4D4×C12711yescharacteristic
244C2×C42D4×C12711yescharacteristic
245#100—24no—
246C22⋊C8—22no—
247C22⋊C8—41no—
248#97—41no—
249C4×C8—41no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95C2×C4×C12711yescharacteristic
254#95C2×C4×C12711yescharacteristic
255C24—21no—
256C24C22⋊C4×C12711yescharacteristic
257C24C22⋊C4×C12711yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—81no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4C22⋊C4×C12711yescharacteristic
282C22×C4C22⋊C4×C12711yescharacteristic
283C22×C4C22×C4×C12711yescharacteristic
284C22×C4C2×D4×C12711yescharacteristic
285C22×C4C2×D4×C12711yescharacteristic
286M16—24no—
287M16—42no—
288M16—82no—
289C2×C8—42no—
290C2×C8—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—81no—
302C42—21no—
303C42—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23#104×C12712yes—
321C23C2×C22⋊C4×C12711yescharacteristic
322D4—44no—
323D4—84no—
324D4—82no—
325D4—84no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—84no—
349C2×C4#99×C12711yescharacteristic
350C2×C4#99×C12711yescharacteristic
351C2×C4AGL(1,ℤ/8)×C12712yes—
352C8—44no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22C2×#99×C12711yescharacteristic
374C22#418×C12711yescharacteristic
375C22C2×#104×C12711yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C2—21no—
386C2—21no—
387C2—42no—
388C2—81no—
389C2—161no—
390C2C127×#150711yescharacteristic
391C2C127×#212111yescharacteristic
392C2C127×#213211yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ 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. C4×#100×C127C2semidirect
3. C127×#1465C2semidirect
4. C127×#1346C2semidirect
5. C127×#1345C2semidirect
188. #11783C127direct (N × H)
198. C4×#100C2×C127semidirect
199. #1465C2×C127semidirect
200. #1346C2×C127semidirect
201. #1345C2×C127semidirect
202. C127#11783direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25432
C4×#100×C1272
C127×#14652
C127×#13462
C127×#13452
#11783127