Finite Group Databasebeta

← C2×C127×#1350 #44575381

Subgroups — C2×C127×#1350 #44575381

Order 32512.

446 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C127C211yesmaximal, characteristic
2C2×C22⋊C16×C127C211yesmaximal, characteristic
3C2×#341×C127C211yesmaximal, characteristic
4C127×#1350C214yesmaximal, direct product factor
5C22×Q16×C127C411yescharacteristic
6C22×M16×C127—21no—
7C23×C8×C127C2211yescharacteristic
8C2×C22⋊Q8×C127—21no—
9C22×C16×C127—21no—
10#467×C127—21no—
11#467×C127—21no—
12#467×C127C412yes—
13#467×C127C2212yes—
14C2×#107×C127C411yescharacteristic
15C2×#103×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127C2212yes—
18#341×C127—21no—
19#341×C127C2212yes—
20C22×Q8×C127—21no—
21C23×C4×C127D411yescharacteristic
22C2×Q16×C127—21no—
23C2×Q16×C127—42no—
24C2×Q16×C127C2×C412yes—
25C2×M16×C127—24no—
26C2×M16×C127—22no—
27C2×M16×C127—42no—
28C2×M16×C127—41no—
29C22×C8×C127—42no—
30C22×C8×C127—41no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127C2311yescharacteristic
37C22⋊Q8×C127—22no—
38C22⋊Q8×C127—22no—
39C22⋊Q8×C127—41no—
40C22⋊Q8×C127—41no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—41no—
43C2×C22⋊C4×C127—41no—
44C2×C16×C127—22no—
45C2×C16×C127—42no—
46#107×C127—21no—
47#107×C127C2×C412yes—
48#103×C127—22no—
49#103×C127—22no—
50C24×C127SD1611yescharacteristic
51C2×Q8×C127—22no—
52C2×Q8×C127—41no—
53C2×Q8×C127—42no—
54C2×Q8×C127—42no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127C22⋊C411yescharacteristic
61C22×C4×C127D811yescharacteristic
62C22×C4×C127D811yescharacteristic
63C22×C4×C127SD1611yescharacteristic
64C22×C4×C127C2×D411yescharacteristic
65Q16×C127—42no—
66Q16×C127—42no—
67M16×C127—24no—
68M16×C127—44no—
69M16×C127—42no—
70C2×C8×C127—22no—
71C2×C8×C127—22no—
72C2×C8×C127—41no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—44no—
77C2×C8×C127—42no—
78C2×C8×C127C22⋊C411yescharacteristic
79C2×C8×C127C22⋊C411yescharacteristic
80C2×C8×C127C22×C411yescharacteristic
81C2×C8×C127C2×D411yescharacteristic
82C4⋊C4×C127—22no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—42no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C16×C127—42no—
89C23×C127—22no—
90C23×C127—22no—
91C23×C127—22no—
92C23×C127#10211yescharacteristic
93C23×C127#10211yescharacteristic
94C23×C127C2×SD1611yescharacteristic
95Q8×C127—42no—
96Q8×C127—42no—
97Q8×C127—82no—
98C2×C4×C127—22no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—42no—
106C2×C4×C127—42no—
107C2×C4×C127—82no—
108C2×C4×C127—82no—
109C2×C4×C127#9912yes—
110C2×C4×C127#10211yescharacteristic
111C2×C4×C127#10211yescharacteristic
112C2×C4×C127#10412yes—
113C2×C4×C127C2×C22⋊C411yescharacteristic
114C2×C4×C127C2×D811yescharacteristic
115C8×C127—21no—
116C8×C127—21no—
117C8×C127—21no—
118C8×C127—21no—
119C8×C127—44no—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—44no—
127C22×C127#32712yes—
128C22×C127#35912yes—
129C22×C127#36212yes—
130C22×C127C2×#10211yescharacteristic
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—82no—
134C4×C127—82no—
135C4×C127#32712yes—
136C4×C127C2×#9911yescharacteristic
137C4×C127C2×#10411yescharacteristic
138C2×#1350C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—41no—
140C2×C127—41no—
141C2×C127#135014yesdirect product factor
142C2×C127C2×#32711yescharacteristic
143C2×C127C2×#35911yescharacteristic
144C2×C127C2×#36211yescharacteristic
145C2×#467C2×C12711yescharacteristic
146C2×C22⋊C16C2×C12711yescharacteristic
147C2×#341C2×C12711yescharacteristic
148#1350C2×C12714yesdirect product factor
149C127C2×#135011yescharacteristic, direct product factor, Sylow
150C22×Q16C4×C12711yescharacteristic
151C22×M16—21no—
152C23×C8C22×C12711yescharacteristic
153C2×C22⋊Q8—21no—
154C22×C16—21no—
155#467—21no—
156#467—21no—
157#467C4×C12712yes—
158#467C22×C12712yes—
159C2×#107C4×C12711yescharacteristic
160C2×#103—21no—
161C22⋊C16—21no—
162C22⋊C16C22×C12712yes—
163#341—21no—
164#341C22×C12712yes—
165C22×Q8—21no—
166C23×C4D4×C12711yescharacteristic
167C2×Q16—21no—
168C2×Q16—42no—
169C2×Q16C2×C4×C12712yes—
170C2×M16—24no—
171C2×M16—22no—
172C2×M16—42no—
173C2×M16—41no—
174C22×C8—42no—
175C22×C8—41no—
176C22×C8C2×C4×C12711yescharacteristic
177C22×C8C2×C4×C12711yescharacteristic
178C22×C8D4×C12711yescharacteristic
179C22×C8D4×C12711yescharacteristic
180C22×C8D4×C12711yescharacteristic
181C22×C8C23×C12711yescharacteristic
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—41no—
185C22⋊Q8—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C16—22no—
190C2×C16—42no—
191#107—21no—
192#107C2×C4×C12712yes—
193#103—22no—
194#103—22no—
195C24SD16×C12711yescharacteristic
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4C22⋊C4×C12711yescharacteristic
205C22×C4C22⋊C4×C12711yescharacteristic
206C22×C4D8×C12711yescharacteristic
207C22×C4D8×C12711yescharacteristic
208C22×C4SD16×C12711yescharacteristic
209C22×C4C2×D4×C12711yescharacteristic
210Q16—42no—
211Q16—42no—
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—44no—
222C2×C8—42no—
223C2×C8C22⋊C4×C12711yescharacteristic
224C2×C8C22⋊C4×C12711yescharacteristic
225C2×C8C22×C4×C12711yescharacteristic
226C2×C8C2×D4×C12711yescharacteristic
227C4⋊C4—22no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C16—42no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23#102×C12711yescharacteristic
238C23#102×C12711yescharacteristic
239C23C2×SD16×C12711yescharacteristic
240Q8—42no—
241Q8—42no—
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4#99×C12712yes—
255C2×C4#102×C12711yescharacteristic
256C2×C4#102×C12711yescharacteristic
257C2×C4#104×C12712yes—
258C2×C4C2×C22⋊C4×C12711yescharacteristic
259C2×C4C2×D8×C12711yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—21no—
264C8—44no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22#327×C12712yes—
273C22#359×C12712yes—
274C22#362×C12712yes—
275C22C2×#102×C12711yescharacteristic
276C4—21no—
277C4—21no—
278C4—82no—
279C4—82no—
280C4#327×C12712yes—
281C4C2×#99×C12711yescharacteristic
282C4C2×#104×C12711yescharacteristic
283C2—41no—
284C2—41no—
285C2C127×#135014yesdirect product factor
286C2C2×#327×C12711yescharacteristic
287C2C2×#359×C12711yescharacteristic
288C2C2×#362×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1350C2direct (N × H)
138. C2×#1350C127direct (N × H)
141. C2×C127#1350direct (N × H)
148. #1350C2×C127direct (N × H)
149. C127C2×#1350direct (N × H)
285. C2C127×#1350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#467×C1272
C2×C22⋊C16×C1272
C2×#341×C1272
C127×#13502
C2×#1350127