Finite Group Databasebeta

← C127×#11959 #44575632

Subgroups — C127×#11959 #44575632

Order 32512.

410 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#495×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1566C211yesmaximal, characteristic, complemented
4C127×#1360C214yesmaximal, complemented
5C22×Q16×C127C411yescharacteristic
6C22×SD16×C127—21no—
7C22×D8×C127C411yescharacteristic
8C2×#124×C127—21no—
9#495×C127—21no—
10#495×C127—21no—
11#495×C127C412yes—
12#495×C127C2212yes—
13#423×C127—21no—
14C2×C4×C8×C127C2211yescharacteristic
15C4⋊C16×C127C2212yescomplemented
16C22⋊C16×C127—21no—
17#346×C127—21no—
18#334×C127—21no—
19#334×C127C2212yescomplemented
20C22×Q8×C127—21no—
21C22×D4×C127—21no—
22C2×Q16×C127—21no—
23C2×Q16×C127—42no—
24C2×Q16×C127C2×C412yes—
25C2×SD16×C127—22no—
26C2×SD16×C127—22no—
27C2×SD16×C127—44no—
28C2×D8×C127—21no—
29C2×D8×C127—42no—
30C2×D8×C127C2×C412yes—
31C2×M16×C127—41no—
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34#124×C127—22no—
35#124×C127—22no—
36#124×C127—41no—
37#124×C127—41no—
38C2×C22⋊C4×C127—41no—
39C2×C22⋊C4×C127—41no—
40C2×C42×C127D411yescharacteristic
41C2×C16×C127—22no—
42C4⋊C8×C127—22no—
43C4⋊C8×C127—41no—
44C4×C8×C127C2×C411yescharacteristic
45C4×C8×C127D411yescharacteristic
46C4×C8×C127D411yescharacteristic
47C4×C8×C127C2311yescharacteristic
48C24×C127—41no—
49C2×Q8×C127—22no—
50C2×Q8×C127—42no—
51C2×Q8×C127—42no—
52C2×Q8×C127—41no—
53C2×D4×C127—22no—
54C2×D4×C127—42no—
55C2×D4×C127—42no—
56C2×D4×C127—41no—
57C22×C4×C127—41no—
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127D811yescharacteristic
60C22×C4×C127SD1611yescharacteristic
61Q16×C127—42no—
62Q16×C127—42no—
63SD16×C127—44no—
64SD16×C127—44no—
65D8×C127—42no—
66D8×C127—42no—
67M16×C127—82no—
68C2×C8×C127—22no—
69C2×C8×C127—22no—
70C2×C8×C127—42no—
71C2×C8×C127C22⋊C411yescharacteristic
72C2×C8×C127C22⋊C411yescharacteristic
73C2×C8×C127C22×C411yescharacteristic
74C2×C8×C127C2×D411yescharacteristic
75C22⋊C4×C127—42no—
76C22⋊C4×C127—42no—
77C22⋊C4×C127—42no—
78C22⋊C4×C127—42no—
79C42×C127C22⋊C411yescharacteristic
80C42×C127D811yescharacteristic
81C42×C127SD1611yescharacteristic
82C42×C127C2×D411yescharacteristic
83C16×C127—42no—
84C23×C127—42no—
85C23×C127—82no—
86C23×C127—82no—
87C23×C127—82no—
88C23×C127#10211yescharacteristic
89Q8×C127—42no—
90Q8×C127—42no—
91Q8×C127—82no—
92D4×C127—42no—
93D4×C127—42no—
94D4×C127—82no—
95C2×C4×C127—22no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—41no—
99C2×C4×C127—42no—
100C2×C4×C127—82no—
101C2×C4×C127#10211yescharacteristic
102C2×C4×C127#10211yescharacteristic
103C2×C4×C127#10211yescharacteristic
104C2×C4×C127C2×C22⋊C411yescharacteristic
105C2×C4×C127C2×D811yescharacteristic
106C2×C4×C127C2×SD1611yescharacteristic
107C8×C127—21no—
108C8×C127—21no—
109C8×C127—82no—
110C8×C127#10012yes—
111C8×C127AGL(1,ℤ/8)12yes—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—82no—
115C22×C127—82no—
116C22×C127—82no—
117C22×C127—164no—
118C22×C127#36012yes—
119C22×C127C2×#10211yescharacteristic
120C4×C127—21no—
121C4×C127—21no—
122C4×C127—21no—
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—82no—
126C4×C127C2×#10011yescharacteristic
127C4×C127#41811yescharacteristic
128#11959C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—22no—
130C2×C127—162no—
131C2×C127#154511yescharacteristic
132C2×C127#214311yescharacteristic
133C2×C127C2×#36011yescharacteristic
134C2×#495C2×C12711yescharacteristic
135#2163C2×C12711yescharacteristic, complemented
136#1566C2×C12711yescharacteristic, complemented
137#1360C2×C12714yescomplemented
138C127#1195911yescharacteristic, direct product factor, Sylow
139C22×Q16C4×C12711yescharacteristic
140C22×SD16—21no—
141C22×D8C4×C12711yescharacteristic
142C2×#124—21no—
143#495—21no—
144#495—21no—
145#495C4×C12712yes—
146#495C22×C12712yes—
147#423—21no—
148C2×C4×C8C22×C12711yescharacteristic
149C4⋊C16C22×C12712yescomplemented
150C22⋊C16—21no—
151#346—21no—
152#334—21no—
153#334C22×C12712yescomplemented
154C22×Q8—21no—
155C22×D4—21no—
156C2×Q16—21no—
157C2×Q16—42no—
158C2×Q16C2×C4×C12712yes—
159C2×SD16—22no—
160C2×SD16—22no—
161C2×SD16—44no—
162C2×D8—21no—
163C2×D8—42no—
164C2×D8C2×C4×C12712yes—
165C2×M16—41no—
166C22×C8C2×C4×C12711yescharacteristic
167C22×C8D4×C12711yescharacteristic
168#124—22no—
169#124—22no—
170#124—41no—
171#124—41no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—41no—
174C2×C42D4×C12711yescharacteristic
175C2×C16—22no—
176C4⋊C8—22no—
177C4⋊C8—41no—
178C4×C8C2×C4×C12711yescharacteristic
179C4×C8D4×C12711yescharacteristic
180C4×C8D4×C12711yescharacteristic
181C4×C8C23×C12711yescharacteristic
182C24—41no—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—41no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—41no—
191C22×C4—41no—
192C22×C4C22⋊C4×C12711yescharacteristic
193C22×C4D8×C12711yescharacteristic
194C22×C4SD16×C12711yescharacteristic
195Q16—42no—
196Q16—42no—
197SD16—44no—
198SD16—44no—
199D8—42no—
200D8—42no—
201M16—82no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—42no—
205C2×C8C22⋊C4×C12711yescharacteristic
206C2×C8C22⋊C4×C12711yescharacteristic
207C2×C8C22×C4×C12711yescharacteristic
208C2×C8C2×D4×C12711yescharacteristic
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C42C22⋊C4×C12711yescharacteristic
214C42D8×C12711yescharacteristic
215C42SD16×C12711yescharacteristic
216C42C2×D4×C12711yescharacteristic
217C16—42no—
218C23—42no—
219C23—82no—
220C23—82no—
221C23—82no—
222C23#102×C12711yescharacteristic
223Q8—42no—
224Q8—42no—
225Q8—82no—
226D4—42no—
227D4—42no—
228D4—82no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4#102×C12711yescharacteristic
236C2×C4#102×C12711yescharacteristic
237C2×C4#102×C12711yescharacteristic
238C2×C4C2×C22⋊C4×C12711yescharacteristic
239C2×C4C2×D8×C12711yescharacteristic
240C2×C4C2×SD16×C12711yescharacteristic
241C8—21no—
242C8—21no—
243C8—82no—
244C8#100×C12712yes—
245C8AGL(1,ℤ/8)×C12712yes—
246C22—21no—
247C22—21no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—164no—
252C22#360×C12712yes—
253C22C2×#102×C12711yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—21no—
259C4—82no—
260C4C2×#100×C12711yescharacteristic
261C4#418×C12711yescharacteristic
262C2—22no—
263C2—162no—
264C2C127×#154511yescharacteristic
265C2C127×#214311yescharacteristic
266C2C2×#360×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC22×D8×C127C4
LCSG ▷ C2×C8 ▷ C2×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×#1360C2semidirect
15. C4⋊C16×C127C22semidirect
19. #334×C127C22semidirect
128. #11959C127direct (N × H)
135. #2163C2×C127semidirect
136. #1566C2×C127semidirect
137. #1360C2×C127semidirect
138. C127#11959direct (N × H)
149. C4⋊C16C22×C127semidirect
153. #334C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#495×C1272
C127×#21632
C127×#15662
C127×#13602
#11959127