Finite Group Databasebeta

← C127×#11674 #44575347

Subgroups — C127×#11674 #44575347

Order 32512.

330 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C4×M32×C127C211yesmaximal, characteristic, complemented
3C127×#1567C211yesmaximal, characteristic, complemented
4C127×#1332C212yesmaximal, complemented
5C127×#1331C212yesmaximal, complemented
6#529×C127—21no—
7C2×M32×C127—21no—
8#499×C127C411yescharacteristic
9#495×C127C411yescharacteristic
10#488×C127—21no—
11#467×C127C411yescharacteristic
12#466×C127C411yescharacteristic
13#465×C127—21no—
14C4×Q16×C127C2211yescharacteristic
15C4×SD16×C127—21no—
16C4×D8×C127C2211yescharacteristic
17#423×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19#346×C127—21no—
20C4×C16×C127C2212yes—
21#335×C127—21no—
22#335×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C2×M16×C127—41no—
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127D411yescharacteristic
29#126×C127—41no—
30#125×C127—21no—
31#124×C127—21no—
32#123×C127—41no—
33C22⋊Q8×C127—21no—
34#121×C127—21no—
35C4×Q8×C127—21no—
36C4×D4×C127—21no—
37C4×D4×C127—41no—
38#117×C127—41no—
39C2×C42×C127D411yescharacteristic
40M32×C127—24no—
41C2×C16×C127—22no—
42#107×C127C2×C411yescharacteristic
43#107×C127C2×C411yescharacteristic
44#106×C127—21no—
45C4⋊C8×C127—22no—
46C4⋊C8×C127—41no—
47#103×C127—21no—
48#103×C127—21no—
49#102×C127—21no—
50#102×C127—21no—
51C4×C8×C127C2×C411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C4×C8×C127C2311yescharacteristic
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127D811yescharacteristic
61C22×C4×C127SD1611yescharacteristic
62Q16×C127—22no—
63SD16×C127—42no—
64D8×C127—22no—
65M16×C127—82no—
66C2×C8×C127—22no—
67C2×C8×C127—22no—
68C2×C8×C127—42no—
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22⋊C411yescharacteristic
71C2×C8×C127C22×C411yescharacteristic
72C2×C8×C127C2×D411yescharacteristic
73C4⋊C4×C127—21no—
74C4⋊C4×C127—21no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C42×C127—41no—
85C42×C127C22⋊C411yescharacteristic
86C42×C127D811yescharacteristic
87C42×C127SD1611yescharacteristic
88C42×C127C2×D411yescharacteristic
89C16×C127—24no—
90C23×C127—41no—
91C23×C127#10211yescharacteristic
92Q8×C127—41no—
93Q8×C127—41no—
94D4×C127—41no—
95D4×C127—41no—
96D4×C127—82no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—41no—
105C2×C4×C127—81no—
106C2×C4×C127—81no—
107C2×C4×C127#10211yescharacteristic
108C2×C4×C127#10211yescharacteristic
109C2×C4×C127#10211yescharacteristic
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127C2×D811yescharacteristic
112C2×C4×C127C2×SD1611yescharacteristic
113C8×C127—21no—
114C8×C127—21no—
115C8×C127—82no—
116C8×C127#10412yes—
117C8×C127#13112yes—
118C22×C127—21no—
119C22×C127—21no—
120C22×C127—21no—
121C22×C127—81no—
122C22×C127—81no—
123C22×C127—81no—
124C22×C127C2×#10211yescharacteristic
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—21no—
129C4×C127—81no—
130C4×C127—81no—
131C4×C127—81no—
132C4×C127#40811yescharacteristic
133C4×C127C2×#10411yescharacteristic
134C4×C127#50911yescharacteristic
135C4×C127#51011yescharacteristic
136#11674C12711yesmaximal, characteristic, direct product factor, Sylow
137C2×C127—41no—
138C2×C127—161no—
139C2×C127#149211yescharacteristic
140C2×C127#213911yescharacteristic
141C2×C127#214311yescharacteristic
142#3168C2×C12711yescharacteristic
143C4×M32C2×C12711yescharacteristic, complemented
144#1567C2×C12711yescharacteristic, complemented
145#1332C2×C12712yescomplemented
146#1331C2×C12712yescomplemented
147C127#1167411yescharacteristic, direct product factor, Sylow
148#529—21no—
149C2×M32—21no—
150#499C4×C12711yescharacteristic
151#495C4×C12711yescharacteristic
152#488—21no—
153#467C4×C12711yescharacteristic
154#466C4×C12711yescharacteristic
155#465—21no—
156C4×Q16C22×C12711yescharacteristic
157C4×SD16—21no—
158C4×D8C22×C12711yescharacteristic
159#423—21no—
160C2×C4×C8C22×C12711yescharacteristic
161#346—21no—
162C4×C16C22×C12712yes—
163#335—21no—
164#335C22×C12712yes—
165C2×Q16C2×C4×C12711yescharacteristic
166C2×SD16—21no—
167C2×D8C2×C4×C12711yescharacteristic
168C2×M16—41no—
169C22×C8C2×C4×C12711yescharacteristic
170C22×C8D4×C12711yescharacteristic
171#126—41no—
172#125—21no—
173#124—21no—
174#123—41no—
175C22⋊Q8—21no—
176#121—21no—
177C4×Q8—21no—
178C4×D4—21no—
179C4×D4—41no—
180#117—41no—
181C2×C42D4×C12711yescharacteristic
182M32—24no—
183C2×C16—22no—
184#107C2×C4×C12711yescharacteristic
185#107C2×C4×C12711yescharacteristic
186#106—21no—
187C4⋊C8—22no—
188C4⋊C8—41no—
189#103—21no—
190#103—21no—
191#102—21no—
192#102—21no—
193C4×C8C2×C4×C12711yescharacteristic
194C4×C8D4×C12711yescharacteristic
195C4×C8D4×C12711yescharacteristic
196C4×C8C23×C12711yescharacteristic
197C2×Q8—21no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—41no—
201C22×C4C22⋊C4×C12711yescharacteristic
202C22×C4D8×C12711yescharacteristic
203C22×C4SD16×C12711yescharacteristic
204Q16—22no—
205SD16—42no—
206D8—22no—
207M16—82no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—42no—
211C2×C8C22⋊C4×C12711yescharacteristic
212C2×C8C22⋊C4×C12711yescharacteristic
213C2×C8C22×C4×C12711yescharacteristic
214C2×C8C2×D4×C12711yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C42—41no—
227C42C22⋊C4×C12711yescharacteristic
228C42D8×C12711yescharacteristic
229C42SD16×C12711yescharacteristic
230C42C2×D4×C12711yescharacteristic
231C16—24no—
232C23—41no—
233C23#102×C12711yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—82no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4#102×C12711yescharacteristic
250C2×C4#102×C12711yescharacteristic
251C2×C4#102×C12711yescharacteristic
252C2×C4C2×C22⋊C4×C12711yescharacteristic
253C2×C4C2×D8×C12711yescharacteristic
254C2×C4C2×SD16×C12711yescharacteristic
255C8—21no—
256C8—21no—
257C8—82no—
258C8#104×C12712yes—
259C8#131×C12712yes—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—81no—
264C22—81no—
265C22—81no—
266C22C2×#102×C12711yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4#408×C12711yescharacteristic
275C4C2×#104×C12711yescharacteristic
276C4#509×C12711yescharacteristic
277C4#510×C12711yescharacteristic
278C2—41no—
279C2—161no—
280C2C127×#149211yescharacteristic
281C2C127×#213911yescharacteristic
282C2C127×#214311yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socleC22×C127C2×#102
prime radical#466×C127C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×M32×C127C2semidirect
3. C127×#1567C2semidirect
4. C127×#1332C2semidirect
5. C127×#1331C2semidirect
136. #11674C127direct (N × H)
143. C4×M32C2×C127semidirect
144. #1567C2×C127semidirect
145. #1332C2×C127semidirect
146. #1331C2×C127semidirect
147. C127#11674direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31682
C4×M32×C1272
C127×#15672
C127×#13322
C127×#13312
#11674127