Finite Group Databasebeta

← C127×#11764 #44575437

Subgroups — C127×#11764 #44575437

Order 32512.

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

normal subgroups only

This group has 446 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×#2484C211yesmaximal, characteristic
2C2×#343×C127C211yesmaximal, characteristic
3C127×#1463C211yesmaximal, characteristic
4C127×#1353C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×#117×C127C411yescharacteristic
8C22×C4⋊C4×C127C2211yescharacteristic
9#407×C127—21no—
10#400×C127C411yescharacteristic
11#400×C127C2211yescharacteristic
12#398×C127C411yescharacteristic
13#398×C127C2211yescharacteristic
14#387×C127—21no—
15#387×C127—21no—
16#385×C127—21no—
17#381×C127—21no—
18#381×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C23×C4×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C2×M16×C127—24no—
27C2×M16×C127—22no—
28C2×M16×C127—41no—
29C2×M16×C127—42no—
30C2×M16×C127—41no—
31C22×C8×C127—41no—
32#117×C127—41no—
33#117×C127—41no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127D411yescharacteristic
43C2×C4⋊C4×C127C2311yescharacteristic
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C42×C127—21no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—41no—
49#95×C127—21no—
50#95×C127—21no—
51#95×C127—21no—
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×C127C22⋊C411yescharacteristic
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—22no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—42no—
73C22×C4×C127—42no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22×C411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80M16×C127—24no—
81M16×C127—44no—
82M16×C127—42no—
83M16×C127—82no—
84C2×C8×C127—44no—
85C2×C8×C127—42no—
86C2×C8×C127—42no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C42×C127—42no—
100C23×C127—22no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—41no—
104C23×C127#9911yescharacteristic
105C23×C127#9911yescharacteristic
106C23×C127C2×C22⋊C411yescharacteristic
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—42no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—81no—
138C2×C4×C127#10412yes—
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C127#13711yescharacteristic
141C8×C127—44no—
142C8×C127—82no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—42no—
151C22×C127—42no—
152C22×C127#35212yes—
153C22×C127C2×#9911yescharacteristic
154C22×C127#41711yescharacteristic
155C22×C127C2×#10411yescharacteristic
156C4×C127—21no—
157C4×C127—22no—
158C4×C127—21no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—81no—
164C4×C127—81no—
165C4×C127—81no—
166C4×C127—81no—
167#11764C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—21no—
169C2×C127—21no—
170C2×C127—22no—
171C2×C127—41no—
172C2×C127#150411yescharacteristic
173C2×C127C2×#35211yescharacteristic
174C2×C127#213311yescharacteristic
175#2484C2×C12711yescharacteristic
176C2×#343C2×C12711yescharacteristic
177#1463C2×C12711yescharacteristic
178#1353C2×C12712yescomplemented
179#1346C2×C12712yescomplemented
180C127#1176411yescharacteristic, direct product factor, Sylow
181C22×M16—21no—
182C2×#117C4×C12711yescharacteristic
183C22×C4⋊C4C22×C12711yescharacteristic
184#407—21no—
185#400C4×C12711yescharacteristic
186#400C22×C12711yescharacteristic
187#398C4×C12711yescharacteristic
188#398C22×C12711yescharacteristic
189#387—21no—
190#387—21no—
191#385—21no—
192#381—21no—
193#381C4×C12711yescharacteristic
194#343—21no—
195#343C22×C12712yes—
196#324—21no—
197#324C22×C12712yes—
198C23×C4C2×C4×C12711yescharacteristic
199C23×C4D4×C12711yescharacteristic
200C23×C4D4×C12711yescharacteristic
201C2×M16—24no—
202C2×M16—22no—
203C2×M16—41no—
204C2×M16—42no—
205C2×M16—41no—
206C22×C8—41no—
207#117—41no—
208#117—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4C2×C4×C12711yescharacteristic
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C4⋊C4C2×C4×C12711yescharacteristic
216C2×C4⋊C4D4×C12711yescharacteristic
217C2×C4⋊C4D4×C12711yescharacteristic
218C2×C4⋊C4C23×C12711yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C42—21no—
222C22⋊C8—22no—
223C22⋊C8—41no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C2×C4×C12711yescharacteristic
232#95C2×C4×C12711yescharacteristic
233C24C22⋊C4×C12711yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4C22⋊C4×C12711yescharacteristic
250C22×C4C22⋊C4×C12711yescharacteristic
251C22×C4C22⋊C4×C12711yescharacteristic
252C22×C4C22×C4×C12711yescharacteristic
253C22×C4C2×D4×C12711yescharacteristic
254C22×C4C2×D4×C12711yescharacteristic
255M16—24no—
256M16—44no—
257M16—42no—
258M16—82no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—42no—
275C23—22no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23#99×C12711yescharacteristic
280C23#99×C12711yescharacteristic
281C23C2×C22⋊C4×C12711yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4#104×C12712yes—
314C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
315C2×C4#137×C12711yescharacteristic
316C8—44no—
317C8—82no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#352×C12712yes—
328C22C2×#99×C12711yescharacteristic
329C22#417×C12711yescharacteristic
330C22C2×#104×C12711yescharacteristic
331C4—21no—
332C4—22no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—81no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2C127×#150411yescharacteristic
347C2C2×#352×C12711yescharacteristic
348C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
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
4. C127×#1353C2semidirect
5. C127×#1346C2semidirect
167. #11764C127direct (N × H)
178. #1353C2×C127semidirect
179. #1346C2×C127semidirect
180. C127#11764direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#24842
C2×#343×C1272
C127×#14632
C127×#13532
C127×#13462
#11764127