Finite Group Databasebeta

← C127×#13155 #44576828

Subgroups — C127×#13155 #44576828

Order 32512.

350 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#361×C127C211yesmaximal, characteristic
2C127×#2140C211yesmaximal, characteristic
3C2×#347×C127C211yesmaximal, characteristic, complemented
4C127×#1972C211yesmaximal, characteristic
5C127×#1946C211yesmaximal, characteristic, complemented
6C127×#1386C211yesmaximal, characteristic, complemented
7C127×#1383C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#427×C127C2211yescharacteristic
13C2×#106×C127C2211yescharacteristic
14#424×C127—21no—
15C2×#102×C127—21no—
16C2×#97×C127C2211yescharacteristic
17#390×C127—21no—
18#361×C127—22no—
19#357×C127C414yescomplemented
20#347×C127—22no—
21#339×C127—21no—
22C22×D4×C127—21no—
23C2×D8×C127—21no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127C2×C412yes—
29C2×M16×C127—21no—
30C22×C8×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#117×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C22⋊C4×C127—42no—
35C2×C42×C127D411yescharacteristic
36M32×C127—21no—
37M32×C127—21no—
38M32×C127—21no—
39M32×C127D412yes—
40C2×C16×C127—21no—
41C2×C16×C127C2×C412yes—
42#108×C127—21no—
43#108×C127—21no—
44#107×C127C2×C412yes—
45#106×C127—21no—
46#106×C127—21no—
47#106×C127—21no—
48C4⋊C8×C127—42no—
49#102×C127—42no—
50#97×C127—21no—
51#97×C127—21no—
52C24×C127—41no—
53C2×D4×C127—22no—
54C2×D4×C127—41no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C2×D4×C127—41no—
59C22×C4×C127—21no—
60C22×C4×C127—41no—
61C22×C4×C127C2×D411yescharacteristic
62D8×C127—22no—
63D8×C127—22no—
64D8×C127—41no—
65D8×C127—41no—
66M16×C127—41no—
67M16×C127—41no—
68C2×C8×C127—21no—
69C2×C8×C127—21no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127C22×C411yescharacteristic
73C2×C8×C127C2×D411yescharacteristic
74C2×C8×C127#4111yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C4⋊C4×C127—22no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—84no—
83C42×C127—21no—
84C42×C127—21no—
85C42×C127—41no—
86C16×C127—22no—
87C16×C127—22no—
88C23×C127—42no—
89C23×C127—82no—
90C23×C127—82no—
91C23×C127—81no—
92C23×C127—81no—
93C23×C127AGL(1,ℤ/8)11yescharacteristic
94D4×C127—42no—
95D4×C127—42no—
96D4×C127—81no—
97D4×C127—81no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127—41no—
101C2×C4×C127—82no—
102C2×C4×C127—81no—
103C2×C4×C127C4×D411yescharacteristic
104C2×C4×C127#12111yescharacteristic
105C2×C4×C127#12411yescharacteristic
106C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C127#13711yescharacteristic
109C8×C127—41no—
110C8×C127—81no—
111C8×C127#11711yescharacteristic
112C8×C127C4×D411yescharacteristic
113C8×C127#12311yescharacteristic
114C8×C127#12611yescharacteristic
115C22×C127—22no—
116C22×C127—84no—
117C22×C127—82no—
118C22×C127—162no—
119C22×C127—161no—
120C22×C127—161no—
121C22×C127#44211yescharacteristic
122C22×C127#46811yescharacteristic
123C22×C127#49011yescharacteristic
124C4×C127—81no—
125C4×C127—82no—
126C4×C127—161no—
127C4×C127#38811yescharacteristic
128C4×C127#44011yescharacteristic
129C4×C127#46911yescharacteristic
130C4×C127#48911yescharacteristic
131#13155C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—21no—
133C2×C127—21no—
134C2×C127—162no—
135C2×C127#193611yescharacteristic
136C2×C127AGL(1,ℤ/16)12yes—
137C2×#361C2×C12711yescharacteristic
138#2140C2×C12711yescharacteristic
139C2×#347C2×C12711yescharacteristic, complemented
140#1972C2×C12711yescharacteristic
141#1946C2×C12711yescharacteristic, complemented
142#1386C2×C12711yescharacteristic, complemented
143#1383C2×C12711yescharacteristic, complemented
144C127#1315511yescharacteristic, direct product factor, Sylow
145C22×D8C22×C12711yescharacteristic
146C2×M32C22×C12711yescharacteristic
147C2×M32C22×C12711yescharacteristic
148C2×#108C22×C12711yescharacteristic
149#427C22×C12711yescharacteristic
150C2×#106C22×C12711yescharacteristic
151#424—21no—
152C2×#102—21no—
153C2×#97C22×C12711yescharacteristic
154#390—21no—
155#361—22no—
156#357C4×C12714yescomplemented
157#347—22no—
158#339—21no—
159C22×D4—21no—
160C2×D8—21no—
161C2×D8—21no—
162C2×D8—21no—
163C2×D8—21no—
164C2×D8—21no—
165C2×D8C2×C4×C12712yes—
166C2×M16—21no—
167C22×C8D4×C12711yescharacteristic
168C22×C8C23×C12711yescharacteristic
169#117—21no—
170C2×C4⋊C4—21no—
171C2×C22⋊C4—42no—
172C2×C42D4×C12711yescharacteristic
173M32—21no—
174M32—21no—
175M32—21no—
176M32D4×C12712yes—
177C2×C16—21no—
178C2×C16C2×C4×C12712yes—
179#108—21no—
180#108—21no—
181#107C2×C4×C12712yes—
182#106—21no—
183#106—21no—
184#106—21no—
185C4⋊C8—42no—
186#102—42no—
187#97—21no—
188#97—21no—
189C24—41no—
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4C2×D4×C12711yescharacteristic
199D8—22no—
200D8—22no—
201D8—41no—
202D8—41no—
203M16—41no—
204M16—41no—
205C2×C8—21no—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8C22×C4×C12711yescharacteristic
210C2×C8C2×D4×C12711yescharacteristic
211C2×C8#41×C12711yescharacteristic
212C2×C8#41×C12711yescharacteristic
213C2×C8#41×C12711yescharacteristic
214C2×C8#41×C12711yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—84no—
220C42—21no—
221C42—21no—
222C42—41no—
223C16—22no—
224C16—22no—
225C23—42no—
226C23—82no—
227C23—82no—
228C23—81no—
229C23—81no—
230C23AGL(1,ℤ/8)×C12711yescharacteristic
231D4—42no—
232D4—42no—
233D4—81no—
234D4—81no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4C4×D4×C12711yescharacteristic
241C2×C4#121×C12711yescharacteristic
242C2×C4#124×C12711yescharacteristic
243C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
244C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
245C2×C4#137×C12711yescharacteristic
246C8—41no—
247C8—81no—
248C8#117×C12711yescharacteristic
249C8C4×D4×C12711yescharacteristic
250C8#123×C12711yescharacteristic
251C8#126×C12711yescharacteristic
252C22—22no—
253C22—84no—
254C22—82no—
255C22—162no—
256C22—161no—
257C22—161no—
258C22#442×C12711yescharacteristic
259C22#468×C12711yescharacteristic
260C22#490×C12711yescharacteristic
261C4—81no—
262C4—82no—
263C4—161no—
264C4#388×C12711yescharacteristic
265C4#440×C12711yescharacteristic
266C4#469×C12711yescharacteristic
267C4#489×C12711yescharacteristic
268C2—21no—
269C2—21no—
270C2—162no—
271C2C127×#193611yescharacteristic
272C2C127×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C127#442
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#347×C127C2semidirect
5. C127×#1946C2semidirect
6. C127×#1386C2semidirect
7. C127×#1383C2semidirect
19. #357×C127C4semidirect
131. #13155C127direct (N × H)
139. C2×#347C2×C127semidirect
141. #1946C2×C127semidirect
142. #1386C2×C127semidirect
143. #1383C2×C127semidirect
144. C127#13155direct (N × H)
156. #357C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#361×C1272
C127×#21402
C2×#347×C1272
C127×#19722
C127×#19462
C127×#13862
C127×#13832
#13155127