Finite Group Databasebeta

← C127×#9589 #44573262

Subgroups — C127×#9589 #44573262

Order 32512.

326 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1986C211yesmaximal, characteristic
2C127×#1950C211yesmaximal, characteristic
3C127×#1542C211yesmaximal, characteristic
4C127×#1493C211yesmaximal, characteristic
5C8×M16×C127C211yesmaximal, characteristic
6C127×#1303C211yesmaximal, characteristic
7C127×#1279C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10C2×#108×C127—21no—
11#423×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C4×M16×C127C2211yescharacteristic
14C2×C4×C8×C127C2211yescharacteristic
15C4×C4⋊C4×C127C2211yescharacteristic
16#341×C127—21no—
17#339×C127—21no—
18#339×C127—21no—
19#333×C127C411yescharacteristic, complemented
20#333×C127C411yescharacteristic, complemented
21#332×C127C411yescharacteristic, complemented
22#332×C127C411yescharacteristic, complemented
23Q8⋊C8×C127—21no—
24Q8⋊C8×C127—21no—
25#322×C127—21no—
26C82×C127—21no—
27C2×M16×C127—21no—
28C2×M16×C127D411yescharacteristic
29C2×M16×C127D411yescharacteristic
30C22×C8×C127—21no—
31C22×C8×C127—21no—
32C4⋊Q8×C127C2×C411yescharacteristic
33C4⋊Q8×C127C2×C411yescharacteristic
34#125×C127—21no—
35C22⋊Q8×C127—21no—
36C22⋊Q8×C127—21no—
37C4×Q8×C127—21no—
38C4×Q8×C127—21no—
39#117×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C42×C127—21no—
42C2×C42×C127C2311yescharacteristic
43#108×C127—42no—
44C4⋊C8×C127—21no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127C2×C411yescharacteristic
48C4⋊C8×C127C2×C411yescharacteristic
49C4⋊C8×C127C2×C411yescharacteristic
50C4⋊C8×C127C2×C411yescharacteristic
51C22⋊C8×C127—21no—
52#97×C127—21no—
53C4×C8×C127—21no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127D411yescharacteristic
57C4×C8×C127D411yescharacteristic
58#95×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—21no—
61C22×C4×C127—41no—
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127#4111yescharacteristic
64C22×C4×C127#4111yescharacteristic
65M16×C127—21no—
66M16×C127—21no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127SD1612yes—
70M16×C127Q1612yes—
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—42no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C2×C8×C127—41no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—21no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C42×C127—41no—
93C42×C127—41no—
94C42×C127—41no—
95C42×C127C22×C411yescharacteristic
96C42×C127C2×D411yescharacteristic
97C42×C127#4111yescharacteristic
98C42×C127#4111yescharacteristic
99C23×C127#12411yescharacteristic
100Q8×C127—41no—
101Q8×C127—41no—
102Q8×C127—81no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—41no—
106C2×C4×C127—42no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—81no—
110C2×C4×C127—81no—
111C2×C4×C127#11711yescharacteristic
112C2×C4×C127C4×D411yescharacteristic
113C2×C4×C127C4×D411yescharacteristic
114C2×C4×C127#12111yescharacteristic
115C2×C4×C127#12311yescharacteristic
116C2×C4×C127#12611yescharacteristic
117C2×C4×C127C2×SD1611yescharacteristic
118C2×C4×C127C2×Q1611yescharacteristic
119C2×C4×C127#13511yescharacteristic
120C2×C4×C127#13511yescharacteristic
121C8×C127—22no—
122C8×C127—22no—
123C8×C127—22no—
124C8×C127—41no—
125C8×C127—41no—
126C8×C127—41no—
127C8×C127—41no—
128C8×C127—41no—
129C8×C127—81no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127#38811yescharacteristic
133C22×C127#48711yescharacteristic
134C22×C127#48811yescharacteristic
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—82no—
139C4×C127—81no—
140C4×C127—81no—
141C4×C127C4×SD1611yescharacteristic
142C4×C127C4×Q1611yescharacteristic
143C4×C127#44311yescharacteristic
144C4×C127#44411yescharacteristic
145C4×C127#46511yescharacteristic
146C4×C127#46711yescharacteristic
147#9589C12711yesmaximal, characteristic, direct product factor, Sylow
148C2×C127—21no—
149C2×C127—21no—
150C2×C127#192911yescharacteristic
151C2×C127#193211yescharacteristic
152C2×C127#193311yescharacteristic
153#1986C2×C12711yescharacteristic
154#1950C2×C12711yescharacteristic
155#1542C2×C12711yescharacteristic
156#1493C2×C12711yescharacteristic
157C8×M16C2×C12711yescharacteristic
158#1303C2×C12711yescharacteristic
159#1279C2×C12711yescharacteristic
160C127#958911yescharacteristic, direct product factor, Sylow
161#533C22×C12711yescharacteristic
162#431C22×C12711yescharacteristic
163C2×#108—21no—
164#423C22×C12711yescharacteristic
165C2×C4⋊C8C22×C12711yescharacteristic
166C4×M16C22×C12711yescharacteristic
167C2×C4×C8C22×C12711yescharacteristic
168C4×C4⋊C4C22×C12711yescharacteristic
169#341—21no—
170#339—21no—
171#339—21no—
172#333C4×C12711yescharacteristic, complemented
173#333C4×C12711yescharacteristic, complemented
174#332C4×C12711yescharacteristic, complemented
175#332C4×C12711yescharacteristic, complemented
176Q8⋊C8—21no—
177Q8⋊C8—21no—
178#322—21no—
179C82—21no—
180C2×M16—21no—
181C2×M16D4×C12711yescharacteristic
182C2×M16D4×C12711yescharacteristic
183C22×C8—21no—
184C22×C8—21no—
185C4⋊Q8C2×C4×C12711yescharacteristic
186C4⋊Q8C2×C4×C12711yescharacteristic
187#125—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192#117—21no—
193C2×C4⋊C4—21no—
194C2×C42—21no—
195C2×C42C23×C12711yescharacteristic
196#108—42no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8C2×C4×C12711yescharacteristic
201C4⋊C8C2×C4×C12711yescharacteristic
202C4⋊C8C2×C4×C12711yescharacteristic
203C4⋊C8C2×C4×C12711yescharacteristic
204C22⋊C8—21no—
205#97—21no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8D4×C12711yescharacteristic
210C4×C8D4×C12711yescharacteristic
211#95—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C22×C4—41no—
215C22×C4C2×D4×C12711yescharacteristic
216C22×C4#41×C12711yescharacteristic
217C22×C4#41×C12711yescharacteristic
218M16—21no—
219M16—21no—
220M16—41no—
221M16—41no—
222M16SD16×C12712yes—
223M16Q16×C12712yes—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—42no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C4⋊C4—22no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C22⋊C4—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42C22×C4×C12711yescharacteristic
249C42C2×D4×C12711yescharacteristic
250C42#41×C12711yescharacteristic
251C42#41×C12711yescharacteristic
252C23#124×C12711yescharacteristic
253Q8—41no—
254Q8—41no—
255Q8—81no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4#117×C12711yescharacteristic
265C2×C4C4×D4×C12711yescharacteristic
266C2×C4C4×D4×C12711yescharacteristic
267C2×C4#121×C12711yescharacteristic
268C2×C4#123×C12711yescharacteristic
269C2×C4#126×C12711yescharacteristic
270C2×C4C2×SD16×C12711yescharacteristic
271C2×C4C2×Q16×C12711yescharacteristic
272C2×C4#135×C12711yescharacteristic
273C2×C4#135×C12711yescharacteristic
274C8—22no—
275C8—22no—
276C8—22no—
277C8—41no—
278C8—41no—
279C8—41no—
280C8—41no—
281C8—41no—
282C8—81no—
283C22—21no—
284C22—21no—
285C22#388×C12711yescharacteristic
286C22#487×C12711yescharacteristic
287C22#488×C12711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—82no—
292C4—81no—
293C4—81no—
294C4C4×SD16×C12711yescharacteristic
295C4C4×Q16×C12711yescharacteristic
296C4#443×C12711yescharacteristic
297C4#444×C12711yescharacteristic
298C4#465×C12711yescharacteristic
299C4#467×C12711yescharacteristic
300C2—21no—
301C2—21no—
302C2C127×#192911yescharacteristic
303C2C127×#193211yescharacteristic
304C2C127×#193311yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#388
prime radicalC23×C127#124
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
19. #333×C127C4semidirect
20. #333×C127C4semidirect
21. #332×C127C4semidirect
22. #332×C127C4semidirect
147. #9589C127direct (N × H)
160. C127#9589direct (N × H)
172. #333C4×C127semidirect
173. #333C4×C127semidirect
174. #332C4×C127semidirect
175. #332C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19862
C127×#19502
C127×#15422
C127×#14932
C8×M16×C1272
C127×#13032
C127×#12792
#9589127