Finite Group Databasebeta

← C127×#9458 #44573131

Subgroups — C127×#9458 #44573131

Order 32512.

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

normal subgroups only

This group has 536 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×#2983C211yesmaximal, characteristic, complemented
2C127×#2548C211yesmaximal, characteristic
3C127×#1555C212yesmaximal
4C127×#1467C211yesmaximal, characteristic, complemented
5C127×#1285C212yesmaximal, complemented
6C2×#127×C127C2211yescharacteristic
7C2×#124×C127C412yes—
8C2×C4×Q8×C127C2211yescharacteristic
9#446×C127—24no—
10#432×C127—21no—
11#432×C127C2212yes—
12#432×C127C2212yes—
13#431×C127—21no—
14#394×C127—21no—
15#394×C127—21no—
16#390×C127—21no—
17#390×C127—21no—
18#390×C127C412yes—
19C4×C4⋊C4×C127C2211yescharacteristic
20#331×C127—24no—
21#324×C127—21no—
22#324×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C22×D4×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127C2×C412yes—
27#127×C127—22no—
28#127×C127—22no—
29#124×C127—44no—
30C4×Q8×C127—22no—
31C4×Q8×C127—22no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127D411yescharacteristic
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127—22no—
40C2×C42×C127C2×C412yes—
41C2×C42×C127D411yescharacteristic
42C2×C42×C127D411yescharacteristic
43C2×C42×C127C2311yescharacteristic
44C4⋊C8×C127—22no—
45C4⋊C8×C127—22no—
46C4⋊C8×C127—22no—
47C4⋊C8×C127D414yes—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50#97×C127—22no—
51#97×C127—22no—
52#97×C127—22no—
53C4×C8×C127—22no—
54#95×C127—21no—
55C24×C127—22no—
56C2×Q8×C127—22no—
57C2×Q8×C127—22no—
58C2×Q8×C127—41no—
59C2×D4×C127—24no—
60C2×D4×C127—42no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—42no—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C2×D4×C127—41no—
67C2×D4×C127—82no—
68C22×C4×C127—22no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C2×C8×C127—24no—
77C2×C8×C127—42no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—42no—
82C22⋊C4×C127—44no—
83C22⋊C4×C127—44no—
84C22⋊C4×C127—82no—
85C22⋊C4×C127—82no—
86C42×C127—21no—
87C42×C127—21no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—42no—
91C42×C127C2×D412yes—
92C42×C127#4112yes—
93C23×C127—42no—
94C23×C127—42no—
95C23×C127—42no—
96C23×C127—42no—
97C23×C127—42no—
98C23×C127—42no—
99C23×C127—42no—
100C23×C127C2×C22⋊C411yescharacteristic
101Q8×C127—44no—
102D4×C127—84no—
103D4×C127—82no—
104D4×C127—84no—
105D4×C127—82no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
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—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127#10012yes—
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—82no—
132C22×C127—82no—
133C22×C127—82no—
134C22×C127—82no—
135C22×C127—82no—
136C22×C127—82no—
137C22×C127—82no—
138C22×C127#38611yescharacteristic
139C22×C127C2×#10011yescharacteristic
140C22×C127#41311yescharacteristic
141C4×C127—21no—
142C4×C127—22no—
143C4×C127—22no—
144C4×C127—22no—
145C4×C127—41no—
146C4×C127—41no—
147C4×C127—41no—
148C4×C127—82no—
149C4×C127#45412yes—
150#9458C12711yesmaximal, characteristic, direct product factor, Sylow
151C2×C127—21no—
152C2×C127—21no—
153C2×C127—162no—
154C2×C127#188811yescharacteristic
155C2×C127#190011yescharacteristic
156C2×C127#191011yescharacteristic
157#2983C2×C12711yescharacteristic, complemented
158#2548C2×C12711yescharacteristic
159#1555C2×C12712yes—
160#1467C2×C12711yescharacteristic, complemented
161#1285C2×C12712yescomplemented
162C127#945811yescharacteristic, direct product factor, Sylow
163C2×#127C22×C12711yescharacteristic
164C2×#124C4×C12712yes—
165C2×C4×Q8C22×C12711yescharacteristic
166#446—24no—
167#432—21no—
168#432C22×C12712yes—
169#432C22×C12712yes—
170#431—21no—
171#394—21no—
172#394—21no—
173#390—21no—
174#390—21no—
175#390C4×C12712yes—
176C4×C4⋊C4C22×C12711yescharacteristic
177#331—24no—
178#324—21no—
179#324—21no—
180C22×Q8C2×C4×C12711yescharacteristic
181C22×D4—21no—
182C22×D4—21no—
183C22×D4C2×C4×C12712yes—
184#127—22no—
185#127—22no—
186#124—44no—
187C4×Q8—22no—
188C4×Q8—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C12711yescharacteristic
191C2×C4⋊C4D4×C12711yescharacteristic
192C2×C4⋊C4D4×C12711yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C42C2×C4×C12712yes—
198C2×C42D4×C12711yescharacteristic
199C2×C42D4×C12711yescharacteristic
200C2×C42C23×C12711yescharacteristic
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8D4×C12714yes—
205C22⋊C8—22no—
206C22⋊C8—22no—
207#97—22no—
208#97—22no—
209#97—22no—
210C4×C8—22no—
211#95—21no—
212C24—22no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—41no—
216C2×D4—24no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—41no—
224C2×D4—82no—
225C22×C4—22no—
226C22×C4C22⋊C4×C12711yescharacteristic
227C22×C4C22⋊C4×C12711yescharacteristic
228C22×C4C22⋊C4×C12711yescharacteristic
229C22×C4C22⋊C4×C12711yescharacteristic
230C22×C4C22×C4×C12711yescharacteristic
231C22×C4C2×D4×C12711yescharacteristic
232C22×C4C2×D4×C12711yescharacteristic
233C2×C8—24no—
234C2×C8—42no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—42no—
248C42C2×D4×C12712yes—
249C42#41×C12712yes—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23C2×C22⋊C4×C12711yescharacteristic
258Q8—44no—
259D4—84no—
260D4—82no—
261D4—84no—
262D4—82no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4#100×C12712yes—
280C2×C4C4×D4×C12712yes—
281C2×C4#120×C12711yescharacteristic
282C2×C4#121×C12712yes—
283C2×C4#123×C12711yescharacteristic
284C8—44no—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22#386×C12711yescharacteristic
296C22C2×#100×C12711yescharacteristic
297C22#413×C12711yescharacteristic
298C4—21no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—82no—
306C4#454×C12712yes—
307C2—21no—
308C2—21no—
309C2—162no—
310C2C127×#188811yescharacteristic
311C2C127×#190011yescharacteristic
312C2C127×#191011yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
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
1. C127×#2983C2semidirect
4. C127×#1467C2semidirect
5. C127×#1285C2semidirect
150. #9458C127direct (N × H)
157. #2983C2×C127semidirect
160. #1467C2×C127semidirect
161. #1285C2×C127semidirect
162. C127#9458direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29832
C127×#25482
C127×#15552
C127×#14672
C127×#12852
#9458127