Finite Group Databasebeta

← C127×#13501 #44577174

Subgroups — C127×#13501 #44577174

Order 32512.

302 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#365×C127C211yesmaximal, characteristic, complemented
2C2×#349×C127C211yesmaximal, characteristic
3C127×#1811C211yesmaximal, characteristic
4C127×#1809C211yesmaximal, characteristic
5C127×#1387C211yesmaximal, characteristic, complemented
6C127×#1387C211yesmaximal, characteristic, complemented
7C127×#1383C211yesmaximal, characteristic, complemented
8C22×M16×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13C2×#107×C127C2211yescharacteristic
14C2×#106×C127C2211yescharacteristic
15#407×C127—21no—
16#380×C127—21no—
17#365×C127—22no—
18#349×C127—22no—
19#341×C127—21no—
20#340×C127—21no—
21C23×C4×C127D411yescharacteristic
22C2×M16×C127—21no—
23C2×M16×C127—21no—
24C2×M16×C127—21no—
25C2×M16×C127—21no—
26C2×M16×C127—21no—
27C2×M16×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C22×C8×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C22⋊C4×C127—41no—
35M32×C127—21no—
36M32×C127—21no—
37M32×C127—21no—
38M32×C127D412yes—
39C2×C16×C127—21no—
40C2×C16×C127—21no—
41#108×C127—21no—
42#108×C127—21no—
43#108×C127—21no—
44#108×C127—21no—
45#107×C127—21no—
46#107×C127—21no—
47#106×C127—21no—
48#106×C127—21no—
49C22⋊C8×C127—42no—
50#95×C127—41no—
51C24×C127SD1611yescharacteristic
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—21no—
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127—21no—
58C22×C4×C127—41no—
59C22×C4×C127—41no—
60C22×C4×C127SD1611yescharacteristic
61C22×C4×C127C2×D411yescharacteristic
62M16×C127—41no—
63M16×C127—41no—
64M16×C127—41no—
65M16×C127—41no—
66M16×C127—41no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127—41no—
70C2×C8×C127—21no—
71C2×C8×C127—21no—
72C2×C8×C127—21no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127C2×D411yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C2×C8×C127#4111yescharacteristic
79C2×C8×C127#4111yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—82no—
86C16×C127—22no—
87C16×C127—41no—
88C23×C127—21no—
89C23×C127—21no—
90C23×C127—21no—
91C23×C127—41no—
92C23×C127—41no—
93C23×C127C2×SD1611yescharacteristic
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—41no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—81no—
102C2×C4×C127—81no—
103C2×C4×C127—81no—
104C2×C4×C127—81no—
105C2×C4×C127—81no—
106C2×C4×C127—81no—
107C2×C4×C127#12111yescharacteristic
108C2×C4×C127#12311yescharacteristic
109C2×C4×C127#12311yescharacteristic
110C2×C4×C127#13511yescharacteristic
111C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C127#13711yescharacteristic
113C8×C127—41no—
114C8×C127—81no—
115C8×C127—81no—
116C8×C127#12311yescharacteristic
117C8×C127#12411yescharacteristic
118C8×C127#12611yescharacteristic
119C8×C127#12611yescharacteristic
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—42no—
123C22×C127—41no—
124C22×C127—41no—
125C22×C127—41no—
126C22×C127—81no—
127C22×C127#46511yescharacteristic
128C22×C127#48111yescharacteristic
129C22×C127#48311yescharacteristic
130C4×C127—41no—
131C4×C127—161no—
132C4×C127—161no—
133C4×C127#39711yescharacteristic
134C4×C127#46811yescharacteristic
135C4×C127#48211yescharacteristic
136C4×C127#48511yescharacteristic
137#13501C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—21no—
139C2×C127—21no—
140C2×C127—81no—
141C2×C127#207711yescharacteristic
142C2×C127#223811yescharacteristic
143C2×C127#223911yescharacteristic
144C2×#365C2×C12711yescharacteristic, complemented
145C2×#349C2×C12711yescharacteristic
146#1811C2×C12711yescharacteristic
147#1809C2×C12711yescharacteristic
148#1387C2×C12711yescharacteristic, complemented
149#1387C2×C12711yescharacteristic, complemented
150#1383C2×C12711yescharacteristic, complemented
151C127#1350111yescharacteristic, direct product factor, Sylow
152C22×M16C22×C12711yescharacteristic
153C2×M32C22×C12711yescharacteristic
154C2×M32C22×C12711yescharacteristic
155C2×#108C22×C12711yescharacteristic
156C2×#108C22×C12711yescharacteristic
157C2×#107C22×C12711yescharacteristic
158C2×#106C22×C12711yescharacteristic
159#407—21no—
160#380—21no—
161#365—22no—
162#349—22no—
163#341—21no—
164#340—21no—
165C23×C4D4×C12711yescharacteristic
166C2×M16—21no—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—21no—
170C2×M16—21no—
171C2×M16—21no—
172C2×M16—21no—
173C2×M16—21no—
174C22×C8D4×C12711yescharacteristic
175C22×C8C23×C12711yescharacteristic
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C22⋊C4—41no—
179M32—21no—
180M32—21no—
181M32—21no—
182M32D4×C12712yes—
183C2×C16—21no—
184C2×C16—21no—
185#108—21no—
186#108—21no—
187#108—21no—
188#108—21no—
189#107—21no—
190#107—21no—
191#106—21no—
192#106—21no—
193C22⋊C8—42no—
194#95—41no—
195C24SD16×C12711yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4SD16×C12711yescharacteristic
205C22×C4C2×D4×C12711yescharacteristic
206M16—41no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211M16—41no—
212M16—41no—
213M16—41no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8C2×D4×C12711yescharacteristic
220C2×C8#41×C12711yescharacteristic
221C2×C8#41×C12711yescharacteristic
222C2×C8#41×C12711yescharacteristic
223C2×C8#41×C12711yescharacteristic
224C2×C8#41×C12711yescharacteristic
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C22⋊C4—82no—
230C16—22no—
231C16—41no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—41no—
236C23—41no—
237C23C2×SD16×C12711yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4#121×C12711yescharacteristic
252C2×C4#123×C12711yescharacteristic
253C2×C4#123×C12711yescharacteristic
254C2×C4#135×C12711yescharacteristic
255C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
256C2×C4#137×C12711yescharacteristic
257C8—41no—
258C8—81no—
259C8—81no—
260C8#123×C12711yescharacteristic
261C8#124×C12711yescharacteristic
262C8#126×C12711yescharacteristic
263C8#126×C12711yescharacteristic
264C22—21no—
265C22—21no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—81no—
271C22#465×C12711yescharacteristic
272C22#481×C12711yescharacteristic
273C22#483×C12711yescharacteristic
274C4—41no—
275C4—161no—
276C4—161no—
277C4#397×C12711yescharacteristic
278C4#468×C12711yescharacteristic
279C4#482×C12711yescharacteristic
280C4#485×C12711yescharacteristic
281C2—21no—
282C2—21no—
283C2—81no—
284C2C127×#207711yescharacteristic
285C2C127×#223811yescharacteristic
286C2C127×#223911yescharacteristic
subgroupG/H
center, socleC22×C127#481
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#365×C127C2semidirect
5. C127×#1387C2semidirect
6. C127×#1387C2semidirect
7. C127×#1383C2semidirect
137. #13501C127direct (N × H)
144. C2×#365C2×C127semidirect
148. #1387C2×C127semidirect
149. #1387C2×C127semidirect
150. #1383C2×C127semidirect
151. C127#13501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#365×C1272
C2×#349×C1272
C127×#18112
C127×#18092
C127×#13872
C127×#13832
#13501127