Finite Group Databasebeta

← C127×#11766 #44575439

Subgroups — C127×#11766 #44575439

Order 32512.

488 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2591C211yesmaximal, characteristic
2C2×#343×C127C211yesmaximal, characteristic, complemented
3C127×#1463C211yesmaximal, characteristic, complemented
4C127×#1353C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×#121×C127C411yescharacteristic
8C22×C4⋊C4×C127C2211yescharacteristic
9#407×C127—21no—
10#400×C127C411yescharacteristic
11#400×C127C2211yescharacteristic
12#394×C127C411yescharacteristic
13#394×C127C2211yescharacteristic
14#388×C127—21no—
15#388×C127—21no—
16#386×C127—21no—
17#386×C127—21no—
18C4×C22⋊C4×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×D4×C127—21no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C2×M16×C127—24no—
29C2×M16×C127—22no—
30C2×M16×C127—41no—
31C2×M16×C127—42no—
32C2×M16×C127—41no—
33C22×C8×C127—41no—
34#121×C127—41no—
35#121×C127—41no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127C2311yescharacteristic
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—21no—
48C2×C22⋊C4×C127—21no—
49C2×C42×C127—21no—
50C22⋊C8×C127—22no—
51C22⋊C8×C127—41no—
52#95×C127—21no—
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
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—81no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
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—81no—
79C22×C4×C127—81no—
80C22×C4×C127C22⋊C411yescharacteristic
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127C22×C411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86M16×C127—24no—
87M16×C127—44no—
88M16×C127—42no—
89M16×C127—82no—
90C2×C8×C127—44no—
91C2×C8×C127—42no—
92C2×C8×C127—42no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C22⋊C4×C127—42no—
99C22⋊C4×C127—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—81no—
104C22⋊C4×C127—81no—
105C42×C127—81no—
106C23×C127—22no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127#9911yescharacteristic
118C23×C127#9911yescharacteristic
119C23×C127C2×C22⋊C411yescharacteristic
120D4×C127—82no—
121D4×C127—82no—
122D4×C127—82no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—42no—
136C2×C4×C127—41no—
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—41no—
149C2×C4×C127—81no—
150C2×C4×C127—81no—
151C2×C4×C127—81no—
152C2×C4×C127#10412yes—
153C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C127#13711yescharacteristic
155C8×C127—44no—
156C8×C127—82no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—21no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—42no—
165C22×C127—42no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127#35512yes—
174C22×C127C2×#9911yescharacteristic
175C22×C127#41711yescharacteristic
176C22×C127C2×#10411yescharacteristic
177C4×C127—21no—
178C4×C127—22no—
179C4×C127—21no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—41no—
183C4×C127—41no—
184C4×C127—81no—
185C4×C127—81no—
186C4×C127—81no—
187#11766C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—21no—
189C2×C127—21no—
190C2×C127—22no—
191C2×C127—41no—
192C2×C127—161no—
193C2×C127#150411yescharacteristic
194C2×C127#212111yescharacteristic
195C2×C127C2×#35511yescharacteristic
196#2591C2×C12711yescharacteristic
197C2×#343C2×C12711yescharacteristic, complemented
198#1463C2×C12711yescharacteristic, complemented
199#1353C2×C12712yescomplemented
200#1345C2×C12712yescomplemented
201C127#1176611yescharacteristic, direct product factor, Sylow
202C22×M16—21no—
203C2×#121C4×C12711yescharacteristic
204C22×C4⋊C4C22×C12711yescharacteristic
205#407—21no—
206#400C4×C12711yescharacteristic
207#400C22×C12711yescharacteristic
208#394C4×C12711yescharacteristic
209#394C22×C12711yescharacteristic
210#388—21no—
211#388—21no—
212#386—21no—
213#386—21no—
214C4×C22⋊C4C4×C12711yescharacteristic
215#343—21no—
216#343C22×C12712yes—
217#324—21no—
218#324C22×C12712yes—
219C22×D4—21no—
220C22×D4C2×C4×C12711yescharacteristic
221C23×C4C2×C4×C12711yescharacteristic
222C23×C4D4×C12711yescharacteristic
223C23×C4D4×C12711yescharacteristic
224C2×M16—24no—
225C2×M16—22no—
226C2×M16—41no—
227C2×M16—42no—
228C2×M16—41no—
229C22×C8—41no—
230#121—41no—
231#121—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4C2×C4×C12711yescharacteristic
235C2×C4⋊C4C2×C4×C12711yescharacteristic
236C2×C4⋊C4D4×C12711yescharacteristic
237C2×C4⋊C4D4×C12711yescharacteristic
238C2×C4⋊C4C23×C12711yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—21no—
246C22⋊C8—22no—
247C22⋊C8—41no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×C4×C12711yescharacteristic
253#95C2×C4×C12711yescharacteristic
254C24—21no—
255C24C22⋊C4×C12711yescharacteristic
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—81no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4C22⋊C4×C12711yescharacteristic
277C22×C4C22⋊C4×C12711yescharacteristic
278C22×C4C22⋊C4×C12711yescharacteristic
279C22×C4C22×C4×C12711yescharacteristic
280C22×C4C2×D4×C12711yescharacteristic
281C22×C4C2×D4×C12711yescharacteristic
282M16—24no—
283M16—44no—
284M16—42no—
285M16—82no—
286C2×C8—44no—
287C2×C8—42no—
288C2×C8—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C42—81no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#99×C12711yescharacteristic
314C23#99×C12711yescharacteristic
315C23C2×C22⋊C4×C12711yescharacteristic
316D4—82no—
317D4—82no—
318D4—82no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
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#104×C12712yes—
349C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
350C2×C4#137×C12711yescharacteristic
351C8—44no—
352C8—82no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#355×C12712yes—
370C22C2×#99×C12711yescharacteristic
371C22#417×C12711yescharacteristic
372C22C2×#104×C12711yescharacteristic
373C4—21no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—161no—
388C2C127×#150411yescharacteristic
389C2C127×#212111yescharacteristic
390C2C2×#355×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC2×#121×C127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#343×C127C2semidirect
3. C127×#1463C2semidirect
4. C127×#1353C2semidirect
5. C127×#1345C2semidirect
187. #11766C127direct (N × H)
197. C2×#343C2×C127semidirect
198. #1463C2×C127semidirect
199. #1353C2×C127semidirect
200. #1345C2×C127semidirect
201. C127#11766direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25912
C2×#343×C1272
C127×#14632
C127×#13532
C127×#13452
#11766127