Finite Group Databasebeta

← C127×#9510 #44573183

Subgroups — C127×#9510 #44573183

Order 32512.

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

normal subgroups only

This group has 522 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
2C127×#2487C211yesmaximal, characteristic
3C127×#1821C212yesmaximal, complemented
4C127×#1465C211yesmaximal, characteristic
5C127×#1305C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8#436×C127—24no—
9#431×C127—21no—
10#407×C127—21no—
11#407×C127C2212yes—
12#407×C127C2212yes—
13#400×C127—21no—
14#399×C127—21no—
15#389×C127—21no—
16#386×C127C412yes—
17#385×C127C412yes—
18#380×C127—21no—
19#380×C127C2211yescharacteristic
20#343×C127—24no—
21#324×C127—21no—
22#323×C127—21no—
23C22×D4×C127C2×C411yescharacteristic
24C23×C4×C127C2×C412yes—
25C23×C4×C127D411yescharacteristic
26C23×C4×C127C2311yescharacteristic
27C2×M16×C127—22no—
28C2×M16×C127—22no—
29C2×M16×C127D414yes—
30C4×D4×C127—22no—
31C4×D4×C127—22no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127C2×C412yes—
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C4⋊C8×C127—22no—
45C22⋊C8×C127—22no—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50C4×C8×C127—22no—
51#95×C127—22no—
52#95×C127—22no—
53#95×C127—21no—
54C24×C127C22⋊C411yescharacteristic
55C24×C127C22×C411yescharacteristic
56C2×D4×C127—22no—
57C2×D4×C127—22no—
58C2×D4×C127—41no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—22no—
62C22×C4×C127—22no—
63C22×C4×C127—24no—
64C22×C4×C127—42no—
65C22×C4×C127—42no—
66C22×C4×C127—82no—
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C2×D412yes—
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73C22×C4×C127#4112yes—
74M16×C127—44no—
75M16×C127—44no—
76M16×C127—82no—
77C2×C8×C127—24no—
78C2×C8×C127—42no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—82no—
85C22⋊C4×C127—22no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—82no—
89C42×C127—21no—
90C42×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—41no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127C2×C22⋊C411yescharacteristic
101C23×C127C4×D412yes—
102D4×C127—44no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—22no—
106C2×C4×C127—24no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—41no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—81no—
121C2×C4×C127—84no—
122C2×C4×C127#10112yes—
123C2×C4×C127#12011yescharacteristic
124C2×C4×C127#12112yes—
125C2×C4×C127#12311yescharacteristic
126C8×C127—44no—
127C8×C127—82no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127—22no—
131C22×C127—22no—
132C22×C127—22no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127—41no—
137C22×C127—41no—
138C22×C127—41no—
139C22×C127—81no—
140C22×C127#38611yescharacteristic
141C22×C127C2×#10111yescharacteristic
142C22×C127#41311yescharacteristic
143C4×C127—22no—
144C4×C127—21no—
145C4×C127—22no—
146C4×C127—41no—
147C4×C127—41no—
148C4×C127—82no—
149C4×C127—82no—
150C4×C127#45812yes—
151#9510C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—21no—
153C2×C127—21no—
154C2×C127—42no—
155C2×C127—81no—
156C2×C127#189011yescharacteristic
157C2×C127#190111yescharacteristic
158C2×C127#191411yescharacteristic
159#2975C2×C12711yescharacteristic
160#2487C2×C12711yescharacteristic
161#1821C2×C12712yescomplemented
162#1465C2×C12711yescharacteristic
163#1305C2×C12712yescomplemented
164C127#951011yescharacteristic, direct product factor, Sylow
165C2×C4×D4C22×C12711yescharacteristic
166C22×C4⋊C4C22×C12711yescharacteristic
167#436—24no—
168#431—21no—
169#407—21no—
170#407C22×C12712yes—
171#407C22×C12712yes—
172#400—21no—
173#399—21no—
174#389—21no—
175#386C4×C12712yes—
176#385C4×C12712yes—
177#380—21no—
178#380C22×C12711yescharacteristic
179#343—24no—
180#324—21no—
181#323—21no—
182C22×D4C2×C4×C12711yescharacteristic
183C23×C4C2×C4×C12712yes—
184C23×C4D4×C12711yescharacteristic
185C23×C4C23×C12711yescharacteristic
186C2×M16—22no—
187C2×M16—22no—
188C2×M16D4×C12714yes—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4D4×C12711yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4C2×C4×C12711yescharacteristic
200C2×C22⋊C4C2×C4×C12712yes—
201C2×C22⋊C4D4×C12711yescharacteristic
202C2×C42D4×C12711yescharacteristic
203C4⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C4×C8—22no—
210#95—22no—
211#95—22no—
212#95—21no—
213C24C22⋊C4×C12711yescharacteristic
214C24C22×C4×C12711yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—82no—
226C22×C4C22⋊C4×C12711yescharacteristic
227C22×C4C22⋊C4×C12711yescharacteristic
228C22×C4C22⋊C4×C12711yescharacteristic
229C22×C4C2×D4×C12712yes—
230C22×C4C2×D4×C12711yescharacteristic
231C22×C4C2×D4×C12711yescharacteristic
232C22×C4#41×C12712yes—
233M16—44no—
234M16—44no—
235M16—82no—
236C2×C8—24no—
237C2×C8—42no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—82no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—42no—
247C22⋊C4—82no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23C2×C22⋊C4×C12711yescharacteristic
260C23C4×D4×C12712yes—
261D4—44no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—81no—
280C2×C4—84no—
281C2×C4#101×C12712yes—
282C2×C4#120×C12711yescharacteristic
283C2×C4#121×C12712yes—
284C2×C4#123×C12711yescharacteristic
285C8—44no—
286C8—82no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22#386×C12711yescharacteristic
300C22C2×#101×C12711yescharacteristic
301C22#413×C12711yescharacteristic
302C4—22no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—82no—
308C4—82no—
309C4#458×C12712yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2C127×#189011yescharacteristic
315C2C127×#190111yescharacteristic
316C2C127×#191411yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×D4×C127C2×C4
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
3. C127×#1821C2semidirect
5. C127×#1305C2semidirect
151. #9510C127direct (N × H)
161. #1821C2×C127semidirect
163. #1305C2×C127semidirect
164. C127#9510direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29752
C127×#24872
C127×#18212
C127×#14652
C127×#13052
#9510127