Finite Group Databasebeta

← C127×#8936 #44572609

Subgroups — C127×#8936 #44572609

Order 32512.

356 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2986C211yesmaximal, characteristic
2C127×#1994C211yesmaximal, characteristic
3C127×#1574C211yesmaximal, characteristic
4C127×#1574C211yesmaximal, characteristic
5C127×#1544C211yesmaximal, characteristic
6C127×#1276C211yesmaximal, characteristic
7C127×#1276C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9#446×C127—21no—
10#446×C127—21no—
11C8×Q8×C127—21no—
12C8×Q8×C127—21no—
13#433×C127—22no—
14#431×C127C2211yescharacteristic
15#431×C127C2211yescharacteristic
16#431×C127C2211yescharacteristic
17#431×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19C43×C127C2211yescharacteristic
20#339×C127—22no—
21#335×C127—21no—
22#335×C127—21no—
23#334×C127—21no—
24#334×C127—21no—
25#332×C127C411yescharacteristic, complemented
26#332×C127C411yescharacteristic, complemented
27#332×C127C411yescharacteristic, complemented
28#332×C127C411yescharacteristic, complemented
29C2×M16×C127—21no—
30C4⋊Q8×C127C2×C411yescharacteristic
31C4⋊Q8×C127C2×C411yescharacteristic
32#125×C127Q812yes—
33C22⋊Q8×C127—21no—
34C22⋊Q8×C127—21no—
35C4×Q8×C127—21no—
36C4×Q8×C127—21no—
37#117×C127D412yes—
38C2×C42×C127—21no—
39C2×C42×C127—21no—
40C2×C42×C127—21no—
41C2×C42×C127C2311yescharacteristic
42C4⋊C8×C127—22no—
43C4⋊C8×C127—22no—
44C4⋊C8×C127—21no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127C2×C411yescharacteristic
47C4⋊C8×C127C2×C411yescharacteristic
48C4⋊C8×C127C2×C411yescharacteristic
49C4⋊C8×C127C2×C411yescharacteristic
50C4⋊C8×C127D411yescharacteristic
51C4⋊C8×C127D411yescharacteristic
52C4⋊C8×C127D411yescharacteristic
53C4⋊C8×C127D411yescharacteristic
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56C22⋊C8×C127—21no—
57C22⋊C8×C127—21no—
58#97×C127—22no—
59C4×C8×C127—22no—
60C4×C8×C127—21no—
61C4×C8×C127—21no—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C22×C4×C127—41no—
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127#4111yescharacteristic
69C22×C4×C127#4111yescharacteristic
70M16×C127—42no—
71C2×C8×C127—21no—
72C2×C8×C127—21no—
73C2×C8×C127—21no—
74C2×C8×C127—21no—
75C2×C8×C127—21no—
76C2×C8×C127—21no—
77C2×C8×C127—21no—
78C2×C8×C127—21no—
79C2×C8×C127—41no—
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127C4⋊C412yes—
85C4⋊C4×C127C4⋊C412yes—
86C22⋊C4×C127—22no—
87C42×C127—22no—
88C42×C127—22no—
89C42×C127—22no—
90C42×C127—22no—
91C42×C127—41no—
92C42×C127—41no—
93C42×C127—41no—
94C42×C127C22×C411yescharacteristic
95C42×C127C2×D411yescharacteristic
96C42×C127C2×D411yescharacteristic
97C42×C127C2×Q811yescharacteristic
98C23×C127#12311yescharacteristic
99Q8×C127—41no—
100Q8×C127—41no—
101Q8×C127—41no—
102Q8×C127—41no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127C2×C4⋊C411yescharacteristic
115C2×C4×C127C4×D411yescharacteristic
116C2×C4×C127C4×D411yescharacteristic
117C2×C4×C127#12011yescharacteristic
118C2×C4×C127C22⋊Q811yescharacteristic
119C2×C4×C127C22⋊Q811yescharacteristic
120C8×C127—41no—
121C8×C127—41no—
122C8×C127—41no—
123C8×C127—41no—
124C8×C127—41no—
125C8×C127—41no—
126C8×C127—41no—
127C8×C127—41no—
128C8×C127—81no—
129C22×C127—21no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127#38511yescharacteristic
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—44no—
137C4×C127—42no—
138C4×C127—42no—
139C4×C127#44311yescharacteristic
140C4×C127#44311yescharacteristic
141C4×C127#44411yescharacteristic
142C4×C127#44411yescharacteristic
143C4×C127#45411yescharacteristic
144C4×C127#45611yescharacteristic
145#8936C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—41no—
147C2×C127#185711yescharacteristic
148C2×C127#186611yescharacteristic
149C2×C127#186611yescharacteristic
150#2986C2×C12711yescharacteristic
151#1994C2×C12711yescharacteristic
152#1574C2×C12711yescharacteristic
153#1574C2×C12711yescharacteristic
154#1544C2×C12711yescharacteristic
155#1276C2×C12711yescharacteristic
156#1276C2×C12711yescharacteristic
157C127#893611yescharacteristic, direct product factor, Sylow
158#533C22×C12711yescharacteristic
159#446—21no—
160#446—21no—
161C8×Q8—21no—
162C8×Q8—21no—
163#433—22no—
164#431C22×C12711yescharacteristic
165#431C22×C12711yescharacteristic
166#431C22×C12711yescharacteristic
167#431C22×C12711yescharacteristic
168#423C22×C12711yescharacteristic
169C43C22×C12711yescharacteristic
170#339—22no—
171#335—21no—
172#335—21no—
173#334—21no—
174#334—21no—
175#332C4×C12711yescharacteristic, complemented
176#332C4×C12711yescharacteristic, complemented
177#332C4×C12711yescharacteristic, complemented
178#332C4×C12711yescharacteristic, complemented
179C2×M16—21no—
180C4⋊Q8C2×C4×C12711yescharacteristic
181C4⋊Q8C2×C4×C12711yescharacteristic
182#125Q8×C12712yes—
183C22⋊Q8—21no—
184C22⋊Q8—21no—
185C4×Q8—21no—
186C4×Q8—21no—
187#117D4×C12712yes—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42C23×C12711yescharacteristic
192C4⋊C8—22no—
193C4⋊C8—22no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8C2×C4×C12711yescharacteristic
197C4⋊C8C2×C4×C12711yescharacteristic
198C4⋊C8C2×C4×C12711yescharacteristic
199C4⋊C8C2×C4×C12711yescharacteristic
200C4⋊C8D4×C12711yescharacteristic
201C4⋊C8D4×C12711yescharacteristic
202C4⋊C8D4×C12711yescharacteristic
203C4⋊C8D4×C12711yescharacteristic
204C22⋊C8—21no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208#97—22no—
209C4×C8—22no—
210C4×C8—21no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—21no—
214C2×Q8—21no—
215C2×Q8—21no—
216C22×C4—41no—
217C22×C4C2×D4×C12711yescharacteristic
218C22×C4#41×C12711yescharacteristic
219C22×C4#41×C12711yescharacteristic
220M16—42no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—41no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4C4⋊C4×C12712yes—
235C4⋊C4C4⋊C4×C12712yes—
236C22⋊C4—22no—
237C42—22no—
238C42—22no—
239C42—22no—
240C42—22no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42C22×C4×C12711yescharacteristic
245C42C2×D4×C12711yescharacteristic
246C42C2×D4×C12711yescharacteristic
247C42C2×Q8×C12711yescharacteristic
248C23#123×C12711yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—41no—
252Q8—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4C2×C4⋊C4×C12711yescharacteristic
265C2×C4C4×D4×C12711yescharacteristic
266C2×C4C4×D4×C12711yescharacteristic
267C2×C4#120×C12711yescharacteristic
268C2×C4C22⋊Q8×C12711yescharacteristic
269C2×C4C22⋊Q8×C12711yescharacteristic
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—41no—
275C8—41no—
276C8—41no—
277C8—41no—
278C8—81no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#385×C12711yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—44no—
287C4—42no—
288C4—42no—
289C4#443×C12711yescharacteristic
290C4#443×C12711yescharacteristic
291C4#444×C12711yescharacteristic
292C4#444×C12711yescharacteristic
293C4#454×C12711yescharacteristic
294C4#456×C12711yescharacteristic
295C2—41no—
296C2C127×#185711yescharacteristic
297C2C127×#186611yescharacteristic
298C2C127×#186611yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#385
prime radicalC23×C127#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
25. #332×C127C4semidirect
26. #332×C127C4semidirect
27. #332×C127C4semidirect
28. #332×C127C4semidirect
145. #8936C127direct (N × H)
157. C127#8936direct (N × H)
175. #332C4×C127semidirect
176. #332C4×C127semidirect
177. #332C4×C127semidirect
178. #332C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29862
C127×#19942
C127×#15742
C127×#15442
C127×#12762
#8936127