Finite Group Databasebeta

← C127×#8835 #44572508

Subgroups — C127×#8835 #44572508

Order 32512.

482 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2972C211yesmaximal, characteristic
2C127×#1954C211yesmaximal, characteristic
3C4×#100×C127C211yesmaximal, characteristic
4C127×#1565C212yesmaximal, complemented
5C127×#1278C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C8×D4×C127—22no—
8C8×D4×C127—22no—
9#431×C127C2212yes—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×#100×C127C411yescharacteristic
12C2×#100×C127C411yescharacteristic
13C2×C22⋊C8×C127—22no—
14C2×C22⋊C8×C127—22no—
15C4×M16×C127C2212yes—
16C2×C4×C8×C127C2211yescharacteristic
17#343×C127C412yes—
18#335×C127—22no—
19#334×C127—22no—
20C22×D4×C127C2×C411yescharacteristic
21C23×C4×C127D412yes—
22C2×M16×C127C2×C412yes—
23C2×M16×C127C2×C412yes—
24C22×C8×C127—21no—
25C22×C8×C127—22no—
26C22×C8×C127—22no—
27C22×C8×C127—21no—
28C4×D4×C127—22no—
29C4×D4×C127—22no—
30C2×C4⋊C4×C127C2×C411yescharacteristic
31C2×C22⋊C4×C127Q812yes—
32C2×C42×C127C2311yescharacteristic
33C4⋊C8×C127—22no—
34C4⋊C8×C127D412yes—
35C4⋊C8×C127D412yes—
36#100×C127—22no—
37#100×C127C814yescomplemented
38C22⋊C8×C127—24no—
39C22⋊C8×C127—22no—
40C22⋊C8×C127—44no—
41#97×C127—22no—
42C4×C8×C127—22no—
43C4×C8×C127—22no—
44C4×C8×C127—22no—
45C24×C127C4⋊C412yes—
46C2×D4×C127—22no—
47C2×D4×C127—22no—
48C2×D4×C127C2×C812yes—
49C2×D4×C127M1612yes—
50C22×C4×C127—22no—
51C22×C4×C127—22no—
52C22×C4×C127—42no—
53C22×C4×C127—42no—
54C22×C4×C127C4⋊C412yes—
55C22×C4×C127C22×C411yescharacteristic
56C22×C4×C127C2×D411yescharacteristic
57C22×C4×C127C2×Q811yescharacteristic
58M16×C127—22no—
59M16×C127—22no—
60M16×C127—22no—
61M16×C127C2×C814yescomplemented
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—22no—
66C2×C8×C127—22no—
67C2×C8×C127—41no—
68C2×C8×C127—41no—
69C2×C8×C127—42no—
70C2×C8×C127—41no—
71C2×C8×C127—82no—
72C2×C8×C127—82no—
73C4⋊C4×C127—22no—
74C22⋊C4×C127—24no—
75C42×C127C2×D412yes—
76C42×C127#4112yes—
77C23×C127—22no—
78C23×C127—22no—
79C23×C127—42no—
80C23×C127—42no—
81C23×C127C4⋊C814yes—
82C23×C127C2×C4⋊C411yescharacteristic
83D4×C127—24no—
84D4×C127—24no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—22no—
88C2×C4×C127—41no—
89C2×C4×C127—42no—
90C2×C4×C127—42no—
91C2×C4×C127—42no—
92C2×C4×C127—82no—
93C2×C4×C127C4×D412yes—
94C2×C4×C127#12011yescharacteristic
95C2×C4×C127C22⋊Q812yes—
96C2×C4×C127#12311yescharacteristic
97C2×C4×C127C22×C811yescharacteristic
98C2×C4×C127C2×M1611yescharacteristic
99C2×C4×C127#13112yes—
100C8×C127—24no—
101C8×C127—42no—
102C8×C127—42no—
103C8×C127—42no—
104C8×C127—42no—
105C8×C127—81no—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127—24no—
109C22×C127—44no—
110C22×C127—42no—
111C22×C127—42no—
112C22×C127—82no—
113C22×C127#38511yescharacteristic
114C22×C127C2×C4⋊C811yescharacteristic
115C22×C127#42411yescharacteristic
116C4×C127—21no—
117C4×C127—22no—
118C4×C127—42no—
119C4×C127C8×D412yes—
120C4×C127#43512yes—
121C4×C127#45311yescharacteristic
122C4×C127#45511yescharacteristic
123#8835C12711yesmaximal, characteristic, direct product factor, Sylow
124C2×C127—21no—
125C2×C127—21no—
126C2×C127—44no—
127C2×C127#185011yescharacteristic
128C2×C127#185611yescharacteristic
129C2×C127#185811yescharacteristic
130#2972C2×C12711yescharacteristic
131#1954C2×C12711yescharacteristic
132C4×#100C2×C12711yescharacteristic
133#1565C2×C12712yescomplemented
134#1278C2×C12712yescomplemented
135C127#883511yescharacteristic, direct product factor, Sylow
136C2×C4×D4C22×C12711yescharacteristic
137C8×D4—22no—
138C8×D4—22no—
139#431C22×C12712yes—
140C2×C4⋊C8C22×C12711yescharacteristic
141C2×#100C4×C12711yescharacteristic
142C2×#100C4×C12711yescharacteristic
143C2×C22⋊C8—22no—
144C2×C22⋊C8—22no—
145C4×M16C22×C12712yes—
146C2×C4×C8C22×C12711yescharacteristic
147#343C4×C12712yes—
148#335—22no—
149#334—22no—
150C22×D4C2×C4×C12711yescharacteristic
151C23×C4D4×C12712yes—
152C2×M16C2×C4×C12712yes—
153C2×M16C2×C4×C12712yes—
154C22×C8—21no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—21no—
158C4×D4—22no—
159C4×D4—22no—
160C2×C4⋊C4C2×C4×C12711yescharacteristic
161C2×C22⋊C4Q8×C12712yes—
162C2×C42C23×C12711yescharacteristic
163C4⋊C8—22no—
164C4⋊C8D4×C12712yes—
165C4⋊C8D4×C12712yes—
166#100—22no—
167#100C8×C12714yescomplemented
168C22⋊C8—24no—
169C22⋊C8—22no—
170C22⋊C8—44no—
171#97—22no—
172C4×C8—22no—
173C4×C8—22no—
174C4×C8—22no—
175C24C4⋊C4×C12712yes—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4C2×C8×C12712yes—
179C2×D4M16×C12712yes—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4C4⋊C4×C12712yes—
185C22×C4C22×C4×C12711yescharacteristic
186C22×C4C2×D4×C12711yescharacteristic
187C22×C4C2×Q8×C12711yescharacteristic
188M16—22no—
189M16—22no—
190M16—22no—
191M16C2×C8×C12714yescomplemented
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—82no—
202C2×C8—82no—
203C4⋊C4—22no—
204C22⋊C4—24no—
205C42C2×D4×C12712yes—
206C42#41×C12712yes—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C4⋊C8×C12714yes—
212C23C2×C4⋊C4×C12711yescharacteristic
213D4—24no—
214D4—24no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4C4×D4×C12712yes—
224C2×C4#120×C12711yescharacteristic
225C2×C4C22⋊Q8×C12712yes—
226C2×C4#123×C12711yescharacteristic
227C2×C4C22×C8×C12711yescharacteristic
228C2×C4C2×M16×C12711yescharacteristic
229C2×C4#131×C12712yes—
230C8—24no—
231C8—42no—
232C8—42no—
233C8—42no—
234C8—42no—
235C8—81no—
236C22—21no—
237C22—21no—
238C22—24no—
239C22—44no—
240C22—42no—
241C22—42no—
242C22—82no—
243C22#385×C12711yescharacteristic
244C22C2×C4⋊C8×C12711yescharacteristic
245C22#424×C12711yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4C8×D4×C12712yes—
250C4#435×C12712yes—
251C4#453×C12711yescharacteristic
252C4#455×C12711yescharacteristic
253C2—21no—
254C2—21no—
255C2—44no—
256C2C127×#185011yescharacteristic
257C2C127×#185611yescharacteristic
258C2C127×#185811yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#385
prime radicalC22×D4×C127C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1565C2semidirect
5. C127×#1278C2semidirect
37. #100×C127C8semidirect
61. M16×C127C2×C8semidirect
123. #8835C127direct (N × H)
133. #1565C2×C127semidirect
134. #1278C2×C127semidirect
135. C127#8835direct (N × H)
167. #100C8×C127semidirect
191. M16C2×C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29722
C127×#19542
C4×#100×C1272
C127×#15652
C127×#12782
#8835127