Finite Group Databasebeta

← C127×#9451 #44573124

Subgroups — C127×#9451 #44573124

Order 32512.

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

normal subgroups only

This group has 518 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×#2973C211yesmaximal, characteristic
2C127×#2547C211yesmaximal, characteristic
3C127×#1558C212yesmaximal, complemented
4C127×#1466C211yesmaximal, characteristic
5C127×#1285C212yesmaximal, complemented
6C2×C4⋊Q8×C127C2211yescharacteristic
7C2×#124×C127C412yes—
8C2×C4×D4×C127C2211yescharacteristic
9#435×C127—24no—
10#432×C127C2212yes—
11#432×C127C2212yes—
12#407×C127—21no—
13C2×C22⋊C8×C127—21no—
14#397×C127—21no—
15#397×C127—21no—
16#391×C127C412yes—
17#380×C127—21no—
18#380×C127—21no—
19C4×C4⋊C4×C127C2211yescharacteristic
20#333×C127—24no—
21#323×C127—21no—
22#323×C127—21no—
23C22×Q8×C127C2×C412yes—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C22×C8×C127—22no—
29C4⋊Q8×C127—22no—
30C4⋊Q8×C127—22no—
31#124×C127—44no—
32C4×D4×C127—22no—
33C4×D4×C127—22no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127D411yescharacteristic
41C2×C22⋊C4×C127D411yescharacteristic
42C2×C42×C127C2×C412yes—
43C2×C42×C127C2311yescharacteristic
44C4⋊C8×C127—22no—
45C4⋊C8×C127D414yes—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50#97×C127—22no—
51#97×C127—22no—
52#95×C127—22no—
53#95×C127—22no—
54#95×C127—21no—
55C24×C127C22⋊C411yescharacteristic
56C24×C127C22⋊C411yescharacteristic
57C2×Q8×C127—24no—
58C2×Q8×C127—42no—
59C2×Q8×C127—42no—
60C2×D4×C127—22no—
61C2×D4×C127—22no—
62C2×D4×C127—41no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76M16×C127—82no—
77C2×C8×C127—24no—
78C2×C8×C127—42no—
79C2×C8×C127—82no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—42no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—22no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—44no—
88C22⋊C4×C127—44no—
89C42×C127—42no—
90C42×C127C2×D412yes—
91C42×C127#4112yes—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127#10012yes—
102C23×C127C2×C22⋊C411yescharacteristic
103Q8×C127—84no—
104D4×C127—44no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—41no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—81no—
122C2×C4×C127—81no—
123C2×C4×C127C4×D412yes—
124C2×C4×C127#12011yescharacteristic
125C2×C4×C127#12112yes—
126C2×C4×C127#12311yescharacteristic
127C8×C127—44no—
128C8×C127—82no—
129C22×C127—21no—
130C22×C127—21no—
131C22×C127—22no—
132C22×C127—42no—
133C22×C127—42no—
134C22×C127—41no—
135C22×C127—41no—
136C22×C127—41no—
137C22×C127—41no—
138C22×C127—41no—
139C22×C127—81no—
140C22×C127—81no—
141C22×C127#38611yescharacteristic
142C22×C127C2×#10011yescharacteristic
143C22×C127#41311yescharacteristic
144C4×C127—21no—
145C4×C127—22no—
146C4×C127—22no—
147C4×C127—41no—
148C4×C127—41no—
149C4×C127—82no—
150C4×C127—82no—
151C4×C127#45512yes—
152#9451C12711yesmaximal, characteristic, direct product factor, Sylow
153C2×C127—21no—
154C2×C127—21no—
155C2×C127—42no—
156C2×C127—81no—
157C2×C127#188511yescharacteristic
158C2×C127#190011yescharacteristic
159C2×C127#190911yescharacteristic
160#2973C2×C12711yescharacteristic
161#2547C2×C12711yescharacteristic
162#1558C2×C12712yescomplemented
163#1466C2×C12711yescharacteristic
164#1285C2×C12712yescomplemented
165C127#945111yescharacteristic, direct product factor, Sylow
166C2×C4⋊Q8C22×C12711yescharacteristic
167C2×#124C4×C12712yes—
168C2×C4×D4C22×C12711yescharacteristic
169#435—24no—
170#432C22×C12712yes—
171#432C22×C12712yes—
172#407—21no—
173C2×C22⋊C8—21no—
174#397—21no—
175#397—21no—
176#391C4×C12712yes—
177#380—21no—
178#380—21no—
179C4×C4⋊C4C22×C12711yescharacteristic
180#333—24no—
181#323—21no—
182#323—21no—
183C22×Q8C2×C4×C12712yes—
184C22×D4C2×C4×C12711yescharacteristic
185C23×C4D4×C12711yescharacteristic
186C23×C4D4×C12711yescharacteristic
187C2×M16—22no—
188C22×C8—22no—
189C4⋊Q8—22no—
190C4⋊Q8—22no—
191#124—44no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C12711yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4D4×C12711yescharacteristic
201C2×C22⋊C4D4×C12711yescharacteristic
202C2×C42C2×C4×C12712yes—
203C2×C42C23×C12711yescharacteristic
204C4⋊C8—22no—
205C4⋊C8D4×C12714yes—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#97—22no—
211#97—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215C24C22⋊C4×C12711yescharacteristic
216C24C22⋊C4×C12711yescharacteristic
217C2×Q8—24no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C12711yescharacteristic
232C22×C4C22⋊C4×C12711yescharacteristic
233C22×C4C22×C4×C12711yescharacteristic
234C22×C4C2×D4×C12711yescharacteristic
235C22×C4C2×D4×C12711yescharacteristic
236M16—82no—
237C2×C8—24no—
238C2×C8—42no—
239C2×C8—82no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—44no—
248C22⋊C4—44no—
249C42—42no—
250C42C2×D4×C12712yes—
251C42#41×C12712yes—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#100×C12712yes—
262C23C2×C22⋊C4×C12711yescharacteristic
263Q8—84no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4C4×D4×C12712yes—
284C2×C4#120×C12711yescharacteristic
285C2×C4#121×C12712yes—
286C2×C4#123×C12711yescharacteristic
287C8—44no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22#386×C12711yescharacteristic
302C22C2×#100×C12711yescharacteristic
303C22#413×C12711yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4#455×C12712yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2C127×#188511yescharacteristic
317C2C127×#190011yescharacteristic
318C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1558C2semidirect
5. C127×#1285C2semidirect
152. #9451C127direct (N × H)
162. #1558C2×C127semidirect
164. #1285C2×C127semidirect
165. C127#9451direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29732
C127×#25472
C127×#15582
C127×#14662
C127×#12852
#9451127