Finite Group Databasebeta

← C127×#11964 #44575637

Subgroups — C127×#11964 #44575637

Order 32512.

486 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 126 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×#493×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#1568C211yesmaximal, characteristic, complemented
4C127×#1361C214yesmaximal, complemented
5C22×D8×C127—21no—
6C22×D8×C127C412yes—
7C2×#127×C127—21no—
8#493×C127—21no—
9#493×C127—21no—
10#493×C127C412yes—
11#493×C127C2212yes—
12#432×C127—21no—
13C2×C4×C8×C127C2211yescharacteristic
14C4⋊C16×C127C2212yescomplemented
15C22⋊C16×C127—21no—
16#346×C127—21no—
17#335×C127C2212yescomplemented
18#334×C127—21no—
19C22×D4×C127—22no—
20C22×D4×C127—41no—
21C22×D4×C127—41no—
22C2×D8×C127—22no—
23C2×D8×C127—22no—
24C2×D8×C127—22no—
25C2×D8×C127—44no—
26C2×D8×C127—44no—
27C2×D8×C127C2×C414yes—
28C22×C8×C127C2×C411yescharacteristic
29C22×C8×C127D411yescharacteristic
30#127×C127—22no—
31#127×C127—22no—
32#127×C127—41no—
33#127×C127—41no—
34C2×C42×C127D411yescharacteristic
35C2×C16×C127—22no—
36C4⋊C8×C127—22no—
37C22⋊C8×C127—41no—
38#97×C127—41no—
39C4×C8×C127C2×C411yescharacteristic
40C4×C8×C127D411yescharacteristic
41C4×C8×C127D411yescharacteristic
42C4×C8×C127C2311yescharacteristic
43C24×C127—42no—
44C2×D4×C127—24no—
45C2×D4×C127—44no—
46C2×D4×C127—44no—
47C2×D4×C127—42no—
48C2×D4×C127—42no—
49C2×D4×C127—42no—
50C2×D4×C127—42no—
51C2×D4×C127—42no—
52C2×D4×C127—84no—
53C2×D4×C127—84no—
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127D811yescharacteristic
56C22×C4×C127SD1611yescharacteristic
57D8×C127—44no—
58D8×C127—44no—
59D8×C127—44no—
60D8×C127—44no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—42no—
64C2×C8×C127C22⋊C411yescharacteristic
65C2×C8×C127C22⋊C411yescharacteristic
66C2×C8×C127C22×C411yescharacteristic
67C2×C8×C127C2×D411yescharacteristic
68C42×C127C22⋊C411yescharacteristic
69C42×C127D811yescharacteristic
70C42×C127SD1611yescharacteristic
71C42×C127C2×D411yescharacteristic
72C16×C127—42no—
73C23×C127—44no—
74C23×C127—84no—
75C23×C127—84no—
76C23×C127—84no—
77C23×C127#10211yescharacteristic
78D4×C127—44no—
79D4×C127—44no—
80D4×C127—84no—
81D4×C127—84no—
82D4×C127—84no—
83D4×C127—84no—
84D4×C127—84no—
85C2×C4×C127—22no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—22no—
89C2×C4×C127#10211yescharacteristic
90C2×C4×C127#10211yescharacteristic
91C2×C4×C127#10211yescharacteristic
92C2×C4×C127C2×C22⋊C411yescharacteristic
93C2×C4×C127C2×D811yescharacteristic
94C2×C4×C127C2×SD1611yescharacteristic
95C8×C127—21no—
96C8×C127—21no—
97C8×C127—82no—
98C8×C127#10012yes—
99C8×C127AGL(1,ℤ/8)12yes—
100C22×C127—21no—
101C22×C127—21no—
102C22×C127—84no—
103C22×C127—84no—
104C22×C127—84no—
105C22×C127—168no—
106C22×C127#36112yes—
107C22×C127C2×#10211yescharacteristic
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—21no—
111C4×C127—21no—
112C4×C127C2×#10011yescharacteristic
113C4×C127#41811yescharacteristic
114C4×C127#50912yes—
115#11964C12711yesmaximal, characteristic, direct product factor, Sylow
116C2×C127—22no—
117C2×C127—164no—
118C2×C127#154511yescharacteristic
119C2×C127#214011yescharacteristic
120C2×C127C2×#36111yescharacteristic
121C2×#493C2×C12711yescharacteristic
122#2163C2×C12711yescharacteristic, complemented
123#1568C2×C12711yescharacteristic, complemented
124#1361C2×C12714yescomplemented
125C127#1196411yescharacteristic, direct product factor, Sylow
126C22×D8—21no—
127C22×D8C4×C12712yes—
128C2×#127—21no—
129#493—21no—
130#493—21no—
131#493C4×C12712yes—
132#493C22×C12712yes—
133#432—21no—
134C2×C4×C8C22×C12711yescharacteristic
135C4⋊C16C22×C12712yescomplemented
136C22⋊C16—21no—
137#346—21no—
138#335C22×C12712yescomplemented
139#334—21no—
140C22×D4—22no—
141C22×D4—41no—
142C22×D4—41no—
143C2×D8—22no—
144C2×D8—22no—
145C2×D8—22no—
146C2×D8—44no—
147C2×D8—44no—
148C2×D8C2×C4×C12714yes—
149C22×C8C2×C4×C12711yescharacteristic
150C22×C8D4×C12711yescharacteristic
151#127—22no—
152#127—22no—
153#127—41no—
154#127—41no—
155C2×C42D4×C12711yescharacteristic
156C2×C16—22no—
157C4⋊C8—22no—
158C22⋊C8—41no—
159#97—41no—
160C4×C8C2×C4×C12711yescharacteristic
161C4×C8D4×C12711yescharacteristic
162C4×C8D4×C12711yescharacteristic
163C4×C8C23×C12711yescharacteristic
164C24—42no—
165C2×D4—24no—
166C2×D4—44no—
167C2×D4—44no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—42no—
172C2×D4—42no—
173C2×D4—84no—
174C2×D4—84no—
175C22×C4C22⋊C4×C12711yescharacteristic
176C22×C4D8×C12711yescharacteristic
177C22×C4SD16×C12711yescharacteristic
178D8—44no—
179D8—44no—
180D8—44no—
181D8—44no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—42no—
185C2×C8C22⋊C4×C12711yescharacteristic
186C2×C8C22⋊C4×C12711yescharacteristic
187C2×C8C22×C4×C12711yescharacteristic
188C2×C8C2×D4×C12711yescharacteristic
189C42C22⋊C4×C12711yescharacteristic
190C42D8×C12711yescharacteristic
191C42SD16×C12711yescharacteristic
192C42C2×D4×C12711yescharacteristic
193C16—42no—
194C23—44no—
195C23—84no—
196C23—84no—
197C23—84no—
198C23#102×C12711yescharacteristic
199D4—44no—
200D4—44no—
201D4—84no—
202D4—84no—
203D4—84no—
204D4—84no—
205D4—84no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4#102×C12711yescharacteristic
211C2×C4#102×C12711yescharacteristic
212C2×C4#102×C12711yescharacteristic
213C2×C4C2×C22⋊C4×C12711yescharacteristic
214C2×C4C2×D8×C12711yescharacteristic
215C2×C4C2×SD16×C12711yescharacteristic
216C8—21no—
217C8—21no—
218C8—82no—
219C8#100×C12712yes—
220C8AGL(1,ℤ/8)×C12712yes—
221C22—21no—
222C22—21no—
223C22—84no—
224C22—84no—
225C22—84no—
226C22—168no—
227C22#361×C12712yes—
228C22C2×#102×C12711yescharacteristic
229C4—21no—
230C4—21no—
231C4—21no—
232C4—21no—
233C4C2×#100×C12711yescharacteristic
234C4#418×C12711yescharacteristic
235C4#509×C12712yes—
236C2—22no—
237C2—164no—
238C2C127×#154511yescharacteristic
239C2C127×#214011yescharacteristic
240C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC2×#493×C127C2
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×#1568C2semidirect
4. C127×#1361C2semidirect
14. C4⋊C16×C127C22semidirect
17. #335×C127C22semidirect
115. #11964C127direct (N × H)
122. #2163C2×C127semidirect
123. #1568C2×C127semidirect
124. #1361C2×C127semidirect
125. C127#11964direct (N × H)
135. C4⋊C16C22×C127semidirect
138. #335C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#493×C1272
C127×#21632
C127×#15682
C127×#13612
#11964127