Finite Group Databasebeta

← C127×#11666 #44575339

Subgroups — C127×#11666 #44575339

Order 32512.

368 conjugacy classes of subgroups.

The subgroup lattice has 296 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×#1566C211yesmaximal, 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#427×C127C411yescharacteristic
15#423×C127—21no—
16#416×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4⋊C16×C127—21no—
19C22⋊C16×C127—21no—
20#346×C127C2212yes—
21#334×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
29C2×M16×C127—41no—
30C22×C8×C127C2×C411yescharacteristic
31C22×C8×C127D411yescharacteristic
32C4×Q8×C127—21no—
33C4×Q8×C127—21no—
34C4×D4×C127—21no—
35C4×D4×C127—21no—
36C4×D4×C127—41no—
37C4×D4×C127—41no—
38#117×C127—21no—
39#117×C127—41no—
40C2×C42×C127—41no—
41C2×C42×C127D411yescharacteristic
42C2×C16×C127—22no—
43#107×C127C2×C411yescharacteristic
44#107×C127C2×C411yescharacteristic
45#106×C127—21no—
46C4⋊C8×C127—22no—
47C4⋊C8×C127—41no—
48#103×C127—21no—
49#103×C127—21no—
50#102×C127—21no—
51#102×C127—21no—
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×C127M1612yescomplemented
69SD16×C127—24no—
70D8×C127—21no—
71D8×C127M1612yescomplemented
72M16×C127—82no—
73C2×C8×C127—21no—
74C2×C8×C127—21no—
75C2×C8×C127—41no—
76C2×C8×C127—42no—
77C2×C8×C127C22⋊C411yescharacteristic
78C2×C8×C127C22⋊C411yescharacteristic
79C2×C8×C127C22×C411yescharacteristic
80C2×C8×C127C2×D411yescharacteristic
81C4⋊C4×C127—21no—
82C4⋊C4×C127—21no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—41no—
88C42×C127—41no—
89C42×C127—41no—
90C42×C127—41no—
91C42×C127C22⋊C411yescharacteristic
92C42×C127D811yescharacteristic
93C42×C127SD1611yescharacteristic
94C42×C127C2×D411yescharacteristic
95C16×C127—42no—
96C23×C127—41no—
97C23×C127#10211yescharacteristic
98Q8×C127—22no—
99Q8×C127—41no—
100D4×C127—22no—
101D4×C127—44no—
102D4×C127—41no—
103C2×C4×C127—22no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—41no—
107C2×C4×C127—44no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—82no—
112C2×C4×C127—82no—
113C2×C4×C127#10211yescharacteristic
114C2×C4×C127#10211yescharacteristic
115C2×C4×C127#10211yescharacteristic
116C2×C4×C127C2×C22⋊C411yescharacteristic
117C2×C4×C127C2×D811yescharacteristic
118C2×C4×C127C2×SD1611yescharacteristic
119C8×C127—21no—
120C8×C127—21no—
121C8×C127—21no—
122C8×C127—82no—
123C8×C127C2×M1611yescharacteristic
124C8×C127C2×M1611yescharacteristic
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—42no—
129C22×C127—81no—
130C22×C127—81no—
131C22×C127C2×#10211yescharacteristic
132C4×C127—21no—
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—42no—
137C4×C127—81no—
138C4×C127—81no—
139C4×C127#36012yes—
140C4×C127#40711yescharacteristic
141C4×C127#42111yescharacteristic
142#11666C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—41no—
144C2×C127—82no—
145C2×C127#148611yescharacteristic
146C2×C127C2×#36011yescharacteristic
147C2×C127#214811yescharacteristic
148C4×#135C2×C12711yescharacteristic
149#2163C2×C12711yescharacteristic, complemented
150#1566C2×C12711yescharacteristic, complemented
151#1334C2×C12712yescomplemented
152#1333C2×C12712yescomplemented
153C127#1166611yescharacteristic, direct product factor, Sylow
154C2×#135C4×C12711yescharacteristic
155C4×#41—21no—
156C4×Q16C4×C12711yescharacteristic
157C4×Q16C22×C12711yescharacteristic
158C4×SD16—21no—
159C4×SD16—21no—
160C4×D8C4×C12711yescharacteristic
161C4×D8C22×C12711yescharacteristic
162#427C4×C12711yescharacteristic
163#423—21no—
164#416—21no—
165C2×C4×C8C22×C12711yescharacteristic
166C4⋊C16—21no—
167C22⋊C16—21no—
168#346C22×C12712yes—
169#334—21no—
170#334C22×C12712yes—
171C2×#41—21no—
172#135—22no—
173#135—22no—
174C2×Q16C2×C4×C12711yescharacteristic
175C2×SD16—21no—
176C2×D8C2×C4×C12711yescharacteristic
177C2×M16—41no—
178C22×C8C2×C4×C12711yescharacteristic
179C22×C8D4×C12711yescharacteristic
180C4×Q8—21no—
181C4×Q8—21no—
182C4×D4—21no—
183C4×D4—21no—
184C4×D4—41no—
185C4×D4—41no—
186#117—21no—
187#117—41no—
188C2×C42—41no—
189C2×C42D4×C12711yescharacteristic
190C2×C16—22no—
191#107C2×C4×C12711yescharacteristic
192#107C2×C4×C12711yescharacteristic
193#106—21no—
194C4⋊C8—22no—
195C4⋊C8—41no—
196#103—21no—
197#103—21no—
198#102—21no—
199#102—21no—
200C4×C8C2×C4×C12711yescharacteristic
201C4×C8D4×C12711yescharacteristic
202C4×C8D4×C12711yescharacteristic
203C4×C8C23×C12711yescharacteristic
204#41—24no—
205#41—42no—
206C2×Q8—21no—
207C2×D4—21no—
208C2×D4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C22⋊C4×C12711yescharacteristic
213C22×C4D8×C12711yescharacteristic
214C22×C4SD16×C12711yescharacteristic
215Q16—21no—
216Q16M16×C12712yescomplemented
217SD16—24no—
218D8—21no—
219D8M16×C12712yescomplemented
220M16—82no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—42no—
225C2×C8C22⋊C4×C12711yescharacteristic
226C2×C8C22⋊C4×C12711yescharacteristic
227C2×C8C22×C4×C12711yescharacteristic
228C2×C8C2×D4×C12711yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42C22⋊C4×C12711yescharacteristic
240C42D8×C12711yescharacteristic
241C42SD16×C12711yescharacteristic
242C42C2×D4×C12711yescharacteristic
243C16—42no—
244C23—41no—
245C23#102×C12711yescharacteristic
246Q8—22no—
247Q8—41no—
248D4—22no—
249D4—44no—
250D4—41no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—44no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4#102×C12711yescharacteristic
262C2×C4#102×C12711yescharacteristic
263C2×C4#102×C12711yescharacteristic
264C2×C4C2×C22⋊C4×C12711yescharacteristic
265C2×C4C2×D8×C12711yescharacteristic
266C2×C4C2×SD16×C12711yescharacteristic
267C8—21no—
268C8—21no—
269C8—21no—
270C8—82no—
271C8C2×M16×C12711yescharacteristic
272C8C2×M16×C12711yescharacteristic
273C22—21no—
274C22—21no—
275C22—21no—
276C22—42no—
277C22—81no—
278C22—81no—
279C22C2×#102×C12711yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—42no—
285C4—81no—
286C4—81no—
287C4#360×C12712yes—
288C4#407×C12711yescharacteristic
289C4#421×C12711yescharacteristic
290C2—41no—
291C2—82no—
292C2C127×#148611yescharacteristic
293C2C2×#360×C12711yescharacteristic
294C2C127×#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×#1566C2semidirect
4. C127×#1334C2semidirect
5. C127×#1333C2semidirect
68. Q16×C127M16semidirect
71. D8×C127M16semidirect
142. #11666C127direct (N × H)
149. #2163C2×C127semidirect
150. #1566C2×C127semidirect
151. #1334C2×C127semidirect
152. #1333C2×C127semidirect
153. C127#11666direct (N × H)
216. Q16M16×C127semidirect
219. D8M16×C127semidirect

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×#15662
C127×#13342
C127×#13332
#11666127