Finite Group Databasebeta

← C127×#11665 #44575338

Subgroups — C127×#11665 #44575338

Order 32512.

360 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#135×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1568C211yesmaximal, characteristic, complemented
4C127×#1334C212yesmaximal, complemented
5C127×#1333C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic
7C4×#41×C127—21no—
8C4×Q16×C127C411yescharacteristic
9C4×Q16×C127C2211yescharacteristic
10C4×SD16×C127—21no—
11C4×SD16×C127—21no—
12C4×D8×C127C411yescharacteristic
13C4×D8×C127C2211yescharacteristic
14#432×C127—21no—
15#427×C127C411yescharacteristic
16#416×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4⋊C16×C127—21no—
19C22⋊C16×C127—21no—
20#346×C127C2212yes—
21#335×C127—21no—
22#334×C127C2212yes—
23C2×#41×C127—21no—
24#135×C127—22no—
25#135×C127—22no—
26C2×Q16×C127C2×C411yescharacteristic
27C2×SD16×C127—21no—
28C2×D8×C127C2×C411yescharacteristic
29C22×C8×C127C2×C411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C4×Q8×C127—21no—
32C4×Q8×C127—21no—
33C4×D4×C127—21no—
34C4×D4×C127—21no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37#117×C127—21no—
38#117×C127—41no—
39C2×C42×C127—41no—
40C2×C42×C127D411yescharacteristic
41C2×C16×C127—22no—
42#107×C127C2×C411yescharacteristic
43#107×C127C2×C411yescharacteristic
44#106×C127—21no—
45C4⋊C8×C127—22no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#102×C127—21no—
50C22⋊C8×C127—41no—
51#97×C127—41no—
52C4×C8×C127C2×C411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C4×C8×C127D411yescharacteristic
55C4×C8×C127C2311yescharacteristic
56#41×C127—24no—
57#41×C127—42no—
58C2×Q8×C127—21no—
59C2×D4×C127—21no—
60C2×D4×C127—41no—
61C22×C4×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127C22⋊C411yescharacteristic
65C22×C4×C127D811yescharacteristic
66C22×C4×C127SD1611yescharacteristic
67Q16×C127—21no—
68Q16×C127M1612yes—
69SD16×C127—24no—
70D8×C127—21no—
71D8×C127M1612yes—
72C2×C8×C127—21no—
73C2×C8×C127—21no—
74C2×C8×C127—41no—
75C2×C8×C127—42no—
76C2×C8×C127C22⋊C411yescharacteristic
77C2×C8×C127C22⋊C411yescharacteristic
78C2×C8×C127C22×C411yescharacteristic
79C2×C8×C127C2×D411yescharacteristic
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C42×C127—41no—
88C42×C127—41no—
89C42×C127—41no—
90C42×C127C22⋊C411yescharacteristic
91C42×C127D811yescharacteristic
92C42×C127SD1611yescharacteristic
93C42×C127C2×D411yescharacteristic
94C16×C127—42no—
95C23×C127—41no—
96C23×C127#10211yescharacteristic
97Q8×C127—22no—
98Q8×C127—41no—
99D4×C127—22no—
100D4×C127—44no—
101D4×C127—41no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—44no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—82no—
111C2×C4×C127—82no—
112C2×C4×C127#10211yescharacteristic
113C2×C4×C127#10211yescharacteristic
114C2×C4×C127#10211yescharacteristic
115C2×C4×C127C2×C22⋊C411yescharacteristic
116C2×C4×C127C2×D811yescharacteristic
117C2×C4×C127C2×SD1611yescharacteristic
118C8×C127—21no—
119C8×C127—21no—
120C8×C127—21no—
121C8×C127—82no—
122C8×C127C2×M1611yescharacteristic
123C8×C127C2×M1611yescharacteristic
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—42no—
128C22×C127—81no—
129C22×C127—81no—
130C22×C127C2×#10211yescharacteristic
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—42no—
137C4×C127—81no—
138C4×C127—81no—
139C4×C127#40711yescharacteristic
140C4×C127#42111yescharacteristic
141#11665C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—41no—
143C2×C127—82no—
144C2×C127#148611yescharacteristic
145C2×C127#214511yescharacteristic
146C2×C127#214811yescharacteristic
147C4×#135C2×C12711yescharacteristic
148#2163C2×C12711yescharacteristic, complemented
149#1568C2×C12711yescharacteristic, complemented
150#1334C2×C12712yescomplemented
151#1333C2×C12712yescomplemented
152C127#1166511yescharacteristic, direct product factor, Sylow
153C2×#135C4×C12711yescharacteristic
154C4×#41—21no—
155C4×Q16C4×C12711yescharacteristic
156C4×Q16C22×C12711yescharacteristic
157C4×SD16—21no—
158C4×SD16—21no—
159C4×D8C4×C12711yescharacteristic
160C4×D8C22×C12711yescharacteristic
161#432—21no—
162#427C4×C12711yescharacteristic
163#416—21no—
164C2×C4×C8C22×C12711yescharacteristic
165C4⋊C16—21no—
166C22⋊C16—21no—
167#346C22×C12712yes—
168#335—21no—
169#334C22×C12712yes—
170C2×#41—21no—
171#135—22no—
172#135—22no—
173C2×Q16C2×C4×C12711yescharacteristic
174C2×SD16—21no—
175C2×D8C2×C4×C12711yescharacteristic
176C22×C8C2×C4×C12711yescharacteristic
177C22×C8D4×C12711yescharacteristic
178C4×Q8—21no—
179C4×Q8—21no—
180C4×D4—21no—
181C4×D4—21no—
182C4×D4—41no—
183C4×D4—41no—
184#117—21no—
185#117—41no—
186C2×C42—41no—
187C2×C42D4×C12711yescharacteristic
188C2×C16—22no—
189#107C2×C4×C12711yescharacteristic
190#107C2×C4×C12711yescharacteristic
191#106—21no—
192C4⋊C8—22no—
193#103—21no—
194#103—21no—
195#102—21no—
196#102—21no—
197C22⋊C8—41no—
198#97—41no—
199C4×C8C2×C4×C12711yescharacteristic
200C4×C8D4×C12711yescharacteristic
201C4×C8D4×C12711yescharacteristic
202C4×C8C23×C12711yescharacteristic
203#41—24no—
204#41—42no—
205C2×Q8—21no—
206C2×D4—21no—
207C2×D4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4C22⋊C4×C12711yescharacteristic
212C22×C4D8×C12711yescharacteristic
213C22×C4SD16×C12711yescharacteristic
214Q16—21no—
215Q16M16×C12712yes—
216SD16—24no—
217D8—21no—
218D8M16×C12712yes—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8C22⋊C4×C12711yescharacteristic
224C2×C8C22⋊C4×C12711yescharacteristic
225C2×C8C22×C4×C12711yescharacteristic
226C2×C8C2×D4×C12711yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42C22⋊C4×C12711yescharacteristic
238C42D8×C12711yescharacteristic
239C42SD16×C12711yescharacteristic
240C42C2×D4×C12711yescharacteristic
241C16—42no—
242C23—41no—
243C23#102×C12711yescharacteristic
244Q8—22no—
245Q8—41no—
246D4—22no—
247D4—44no—
248D4—41no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4#102×C12711yescharacteristic
260C2×C4#102×C12711yescharacteristic
261C2×C4#102×C12711yescharacteristic
262C2×C4C2×C22⋊C4×C12711yescharacteristic
263C2×C4C2×D8×C12711yescharacteristic
264C2×C4C2×SD16×C12711yescharacteristic
265C8—21no—
266C8—21no—
267C8—21no—
268C8—82no—
269C8C2×M16×C12711yescharacteristic
270C8C2×M16×C12711yescharacteristic
271C22—21no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—81no—
276C22—81no—
277C22C2×#102×C12711yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—42no—
284C4—81no—
285C4—81no—
286C4#407×C12711yescharacteristic
287C4#421×C12711yescharacteristic
288C2—41no—
289C2—82no—
290C2C127×#148611yescharacteristic
291C2C127×#214511yescharacteristic
292C2C127×#214811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC2×#135×C127C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C127×#1568C2semidirect
4. C127×#1334C2semidirect
5. C127×#1333C2semidirect
141. #11665C127direct (N × H)
148. #2163C2×C127semidirect
149. #1568C2×C127semidirect
150. #1334C2×C127semidirect
151. #1333C2×C127semidirect
152. C127#11665direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#135×C1272
C127×#21632
C127×#15682
C127×#13342
C127×#13332
#11665127