Finite Group Databasebeta

← C127×#9476 #44573149

Subgroups — C127×#9476 #44573149

Order 32512.

818 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2406C211yesmaximal, characteristic
2C127×#2274C211yesmaximal, characteristic, complemented
3C127×#1789C212yesmaximal
4C127×#1463C211yesmaximal, characteristic, complemented
5C127×#1284C212yesmaximal, complemented
6C22×#41×C127C2211yescharacteristic
7C2×#123×C127—21no—
8C2×#117×C127—21no—
9C22×C4⋊C4×C127C2211yescharacteristic
10C2×#104×C127—24no—
11#407×C127C2212yes—
12#395×C127C412yescomplemented
13#394×C127C412yescomplemented
14#386×C127—21no—
15#385×C127—22no—
16#381×C127C2211yescharacteristic
17C4×C4⋊C4×C127—24no—
18C4×C22⋊C4×C127—21no—
19C4×C22⋊C4×C127C2212yes—
20#324×C127—22no—
21C2×#41×C127—22no—
22C2×#41×C127—22no—
23C2×#41×C127—44no—
24C22×Q8×C127C2×C411yescharacteristic
25C22×D4×C127—21no—
26C22×D4×C127C2×C411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C23×C4×C127C2311yescharacteristic
31C2×M16×C127—22no—
32#123×C127—44no—
33#117×C127—28no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127C2×C412yes—
39C2×C4⋊C4×C127D412yes—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C42×C127—22no—
45C2×C42×C127—22no—
46C2×C42×C127D414yes—
47#104×C127—48no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50#95×C127—22no—
51#95×C127—22no—
52#95×C127—22no—
53#95×C127—21no—
54#95×C127C2×C412yes—
55C24×C127—21no—
56C24×C127C2×D411yescharacteristic
57#41×C127—28no—
58#41×C127—44no—
59#41×C127—44no—
60#41×C127—44no—
61C2×Q8×C127—22no—
62C2×Q8×C127—42no—
63C2×D4×C127—24no—
64C2×D4×C127—22no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—24no—
72C22×C4×C127—21no—
73C22×C4×C127—24no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—22no—
77C22×C4×C127—42no—
78C22×C4×C127—42no—
79C22×C4×C127—42no—
80C22×C4×C127—42no—
81C22×C4×C127—42no—
82C22×C4×C127C22⋊C412yes—
83C22×C4×C127C22⋊C412yes—
84C22×C4×C127C22×C411yescharacteristic
85C22×C4×C127C2×D412yes—
86C22×C4×C127C2×D411yescharacteristic
87C22×C4×C127#4112yes—
88M16×C127—44no—
89C2×C8×C127—42no—
90C4⋊C4×C127—28no—
91C4⋊C4×C127—24no—
92C4⋊C4×C127—24no—
93C4⋊C4×C127—44no—
94C22⋊C4×C127—28no—
95C22⋊C4×C127—44no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—44no—
98C42×C127—28no—
99C42×C127—44no—
100C42×C127—82no—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127—22no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—42no—
107C23×C127—41no—
108C23×C127—42no—
109C23×C127C2×C22⋊C411yescharacteristic
110C23×C127#12011yescharacteristic
111C23×C127#12311yescharacteristic
112Q8×C127—24no—
113Q8×C127—42no—
114D4×C127—24no—
115D4×C127—42no—
116D4×C127—44no—
117D4×C127—44no—
118C2×C4×C127—22no—
119C2×C4×C127—22no—
120C2×C4×C127—24no—
121C2×C4×C127—22no—
122C2×C4×C127—22no—
123C2×C4×C127—24no—
124C2×C4×C127—28no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—42no—
130C2×C4×C127—48no—
131C2×C4×C127—44no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—44no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—81no—
141C2×C4×C127#10414yescomplemented
142C2×C4×C127C4×D412yes—
143C2×C4×C127#12112yes—
144C8×C127—82no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—44no—
153C22×C127—44no—
154C22×C127—42no—
155C22×C127—82no—
156C22×C127—81no—
157C22×C127—81no—
158C22×C127#38611yescharacteristic
159C22×C127C2×#10412yes—
160C22×C127B(4,𝔽2)12yes—
161C4×C127—22no—
162C4×C127—22no—
163C4×C127—24no—
164C4×C127—48no—
165C4×C127—42no—
166C4×C127—42no—
167C4×C127—82no—
168#9476C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—22no—
170C2×C127—22no—
171C2×C127—41no—
172C2×C127—82no—
173C2×C127#188911yescharacteristic
174C2×C127#189611yescharacteristic
175C2×C127#191211yescharacteristic
176#2406C2×C12711yescharacteristic
177#2274C2×C12711yescharacteristic, complemented
178#1789C2×C12712yes—
179#1463C2×C12711yescharacteristic, complemented
180#1284C2×C12712yescomplemented
181C127#947611yescharacteristic, direct product factor, Sylow
182C22×#41C22×C12711yescharacteristic
183C2×#123—21no—
184C2×#117—21no—
185C22×C4⋊C4C22×C12711yescharacteristic
186C2×#104—24no—
187#407C22×C12712yes—
188#395C4×C12712yescomplemented
189#394C4×C12712yescomplemented
190#386—21no—
191#385—22no—
192#381C22×C12711yescharacteristic
193C4×C4⋊C4—24no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4C22×C12712yes—
196#324—22no—
197C2×#41—22no—
198C2×#41—22no—
199C2×#41—44no—
200C22×Q8C2×C4×C12711yescharacteristic
201C22×D4—21no—
202C22×D4C2×C4×C12711yescharacteristic
203C23×C4—21no—
204C23×C4D4×C12711yescharacteristic
205C23×C4D4×C12711yescharacteristic
206C23×C4C23×C12711yescharacteristic
207C2×M16—22no—
208#123—44no—
209#117—28no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×C4×C12712yes—
215C2×C4⋊C4D4×C12712yes—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42D4×C12714yes—
223#104—48no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—21no—
230#95C2×C4×C12712yes—
231C24—21no—
232C24C2×D4×C12711yescharacteristic
233#41—28no—
234#41—44no—
235#41—44no—
236#41—44no—
237C2×Q8—22no—
238C2×Q8—42no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—21no—
249C22×C4—24no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C22⋊C4×C12712yes—
259C22×C4C22⋊C4×C12712yes—
260C22×C4C22×C4×C12711yescharacteristic
261C22×C4C2×D4×C12712yes—
262C22×C4C2×D4×C12711yescharacteristic
263C22×C4#41×C12712yes—
264M16—44no—
265C2×C8—42no—
266C4⋊C4—28no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—44no—
270C22⋊C4—28no—
271C22⋊C4—44no—
272C22⋊C4—42no—
273C22⋊C4—44no—
274C42—28no—
275C42—44no—
276C42—82no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—41no—
281C23—41no—
282C23—42no—
283C23—41no—
284C23—42no—
285C23C2×C22⋊C4×C12711yescharacteristic
286C23#120×C12711yescharacteristic
287C23#123×C12711yescharacteristic
288Q8—24no—
289Q8—42no—
290D4—24no—
291D4—42no—
292D4—44no—
293D4—44no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—28no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—48no—
307C2×C4—41no—
308C2×C4—44no—
309C2×C4—41no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4#104×C12714yescomplemented
318C2×C4C4×D4×C12712yes—
319C2×C4#121×C12712yes—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—44no—
329C22—44no—
330C22—42no—
331C22—82no—
332C22—81no—
333C22—81no—
334C22#386×C12711yescharacteristic
335C22C2×#104×C12712yes—
336C22B(4,𝔽2)×C12712yes—
337C4—22no—
338C4—22no—
339C4—24no—
340C4—48no—
341C4—42no—
342C4—42no—
343C4—82no—
344C2—22no—
345C2—22no—
346C2—41no—
347C2—82no—
348C2C127×#188911yescharacteristic
349C2C127×#189611yescharacteristic
350C2C127×#191211yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×#41×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2274C2semidirect
4. C127×#1463C2semidirect
5. C127×#1284C2semidirect
12. #395×C127C4semidirect
13. #394×C127C4semidirect
141. C2×C4×C127#104semidirect
168. #9476C127direct (N × H)
177. #2274C2×C127semidirect
179. #1463C2×C127semidirect
180. #1284C2×C127semidirect
181. C127#9476direct (N × H)
188. #395C4×C127semidirect
189. #394C4×C127semidirect
317. C2×C4#104×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24062
C127×#22742
C127×#17892
C127×#14632
C127×#12842
#9476127