Finite Group Databasebeta

← C2×C127×#1340 #44575357

Subgroups — C2×C127×#1340 #44575357

Order 32512.

444 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C127C211yesmaximal, characteristic
2C2×#349×C127C211yesmaximal, characteristic
3C2×H(3,ℤ/4)×C127C211yesmaximal, characteristic
4C127×#1340C214yesmaximal, direct product factor
5C22×Q16×C127C411yescharacteristic, complemented
6C22×M16×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×#117×C127—21no—
9C2×M32×C127—21no—
10#470×C127—21no—
11#470×C127—21no—
12#470×C127C412yescomplemented
13#470×C127C2212yes—
14C2×#106×C127C411yescharacteristic, complemented
15C2×#103×C127—21no—
16#349×C127—21no—
17#349×C127C2212yes—
18H(3,ℤ/4)×C127—21no—
19H(3,ℤ/4)×C127C2212yes—
20C22×Q8×C127—21no—
21C23×C4×C127D411yescharacteristic
22C2×Q16×C127—21no—
23C2×Q16×C127—41no—
24C2×Q16×C127—41no—
25C2×Q16×C127C2×C412yescomplemented
26C2×M16×C127—41no—
27C2×M16×C127—41no—
28C2×M16×C127C2×C411yescharacteristic
29C2×M16×C127D411yescharacteristic
30C2×M16×C127D411yescharacteristic
31C2×M16×C127C2311yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22⋊Q8×C127—22no—
35C22⋊Q8×C127—22no—
36C22⋊Q8×C127—41no—
37C22⋊Q8×C127—41no—
38#117×C127—22no—
39#117×C127—22no—
40#117×C127—41no—
41#117×C127—41no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—41no—
44C2×C4⋊C4×C127—41no—
45C2×C22⋊C4×C127—41no—
46C2×C22⋊C4×C127—41no—
47C2×C42×C127—22no—
48M32×C127—22no—
49M32×C127—41no—
50C2×C16×C127—41no—
51#106×C127—21no—
52#106×C127C2×C412yescomplemented
53#103×C127—22no—
54#103×C127—22no—
55C24×C127D811yescharacteristic
56C2×Q8×C127—22no—
57C2×Q8×C127—41no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—42no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127D811yescharacteristic
72C22×C4×C127SD1611yescharacteristic
73C22×C4×C127SD1611yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75Q16×C127—42no—
76Q16×C127—42no—
77M16×C127—41no—
78M16×C127—41no—
79M16×C127—41no—
80M16×C127—41no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—21no—
84C2×C8×C127—21no—
85C2×C8×C127C22⋊C411yescharacteristic
86C2×C8×C127C22⋊C411yescharacteristic
87C2×C8×C127C22×C411yescharacteristic
88C2×C8×C127C2×D411yescharacteristic
89C4⋊C4×C127—22no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C22⋊C4×C127—42no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—42no—
99C42×C127—24no—
100C42×C127—42no—
101C16×C127—42no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—42no—
105C23×C127#10211yescharacteristic
106C23×C127#10211yescharacteristic
107C23×C127C2×D811yescharacteristic
108Q8×C127—42no—
109Q8×C127—42no—
110Q8×C127—81no—
111Q8×C127—81no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—44no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—82no—
126C2×C4×C127—84no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127#9911yescharacteristic
130C2×C4×C127#9911yescharacteristic
131C2×C4×C127#10211yescharacteristic
132C2×C4×C127#10211yescharacteristic
133C2×C4×C127#10411yescharacteristic
134C2×C4×C127#10411yescharacteristic
135C2×C4×C127C2×C22⋊C411yescharacteristic
136C2×C4×C127C2×SD1611yescharacteristic
137C8×C127—21no—
138C8×C127—21no—
139C8×C127—21no—
140C8×C127—21no—
141C22×C127—22no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—41no—
145C22×C127—41no—
146C22×C127—42no—
147C22×C127—81no—
148C22×C127#32711yescharacteristic
149C22×C127#32711yescharacteristic
150C22×C127C2×#10211yescharacteristic
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—82no—
154C4×C127—84no—
155C4×C127—82no—
156C4×C127#32711yescharacteristic
157C4×C127#32711yescharacteristic
158C4×C127C2×#9911yescharacteristic
159C4×C127C2×#10411yescharacteristic
160C2×#1340C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—21no—
162C2×C127—21no—
163C2×C127—41no—
164C2×C127—41no—
165C2×C127#134012yesdirect product factor
166C2×C127C2×#32711yescharacteristic
167C2×#470C2×C12711yescharacteristic
168C2×#349C2×C12711yescharacteristic
169C2×H(3,ℤ/4)C2×C12711yescharacteristic
170#1340C2×C12714yesdirect product factor
171C127C2×#134011yescharacteristic, direct product factor, Sylow
172C22×Q16C4×C12711yescharacteristic, complemented
173C22×M16C22×C12711yescharacteristic
174C2×C22⋊Q8—21no—
175C2×#117—21no—
176C2×M32—21no—
177#470—21no—
178#470—21no—
179#470C4×C12712yescomplemented
180#470C22×C12712yes—
181C2×#106C4×C12711yescharacteristic, complemented
182C2×#103—21no—
183#349—21no—
184#349C22×C12712yes—
185H(3,ℤ/4)—21no—
186H(3,ℤ/4)C22×C12712yes—
187C22×Q8—21no—
188C23×C4D4×C12711yescharacteristic
189C2×Q16—21no—
190C2×Q16—41no—
191C2×Q16—41no—
192C2×Q16C2×C4×C12712yescomplemented
193C2×M16—41no—
194C2×M16—41no—
195C2×M16C2×C4×C12711yescharacteristic
196C2×M16D4×C12711yescharacteristic
197C2×M16D4×C12711yescharacteristic
198C2×M16C23×C12711yescharacteristic
199C22×C8C2×C4×C12711yescharacteristic
200C22×C8D4×C12711yescharacteristic
201C22⋊Q8—22no—
202C22⋊Q8—22no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205#117—22no—
206#117—22no—
207#117—41no—
208#117—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C22⋊C4—41no—
213C2×C22⋊C4—41no—
214C2×C42—22no—
215M32—22no—
216M32—41no—
217C2×C16—41no—
218#106—21no—
219#106C2×C4×C12712yescomplemented
220#103—22no—
221#103—22no—
222C24D8×C12711yescharacteristic
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4D8×C12711yescharacteristic
239C22×C4SD16×C12711yescharacteristic
240C22×C4SD16×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242Q16—42no—
243Q16—42no—
244M16—41no—
245M16—41no—
246M16—41no—
247M16—41no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8C22⋊C4×C12711yescharacteristic
253C2×C8C22⋊C4×C12711yescharacteristic
254C2×C8C22×C4×C12711yescharacteristic
255C2×C8C2×D4×C12711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—24no—
267C42—42no—
268C16—42no—
269C23—21no—
270C23—21no—
271C23—42no—
272C23#102×C12711yescharacteristic
273C23#102×C12711yescharacteristic
274C23C2×D8×C12711yescharacteristic
275Q8—42no—
276Q8—42no—
277Q8—81no—
278Q8—81no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—82no—
293C2×C4—84no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4#99×C12711yescharacteristic
297C2×C4#99×C12711yescharacteristic
298C2×C4#102×C12711yescharacteristic
299C2×C4#102×C12711yescharacteristic
300C2×C4#104×C12711yescharacteristic
301C2×C4#104×C12711yescharacteristic
302C2×C4C2×C22⋊C4×C12711yescharacteristic
303C2×C4C2×SD16×C12711yescharacteristic
304C8—21no—
305C8—21no—
306C8—21no—
307C8—21no—
308C22—22no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—81no—
315C22#327×C12711yescharacteristic
316C22#327×C12711yescharacteristic
317C22C2×#102×C12711yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—84no—
322C4—82no—
323C4#327×C12711yescharacteristic
324C4#327×C12711yescharacteristic
325C4C2×#99×C12711yescharacteristic
326C4C2×#104×C12711yescharacteristic
327C2—21no—
328C2—21no—
329C2—41no—
330C2—41no—
331C2C127×#134012yesdirect product factor
332C2C2×#327×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC24×C127D8
LCSG ▷ C2×C8 ▷ C2×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
4. C127×#1340C2direct (N × H)
5. C22×Q16×C127C4semidirect
12. #470×C127C4semidirect
14. C2×#106×C127C4semidirect
25. C2×Q16×C127C2×C4semidirect
52. #106×C127C2×C4semidirect
160. C2×#1340C127direct (N × H)
165. C2×C127#1340direct (N × H)
170. #1340C2×C127direct (N × H)
171. C127C2×#1340direct (N × H)
172. C22×Q16C4×C127semidirect
179. #470C4×C127semidirect
181. C2×#106C4×C127semidirect
192. C2×Q16C2×C4×C127semidirect
219. #106C2×C4×C127semidirect
331. C2C127×#1340direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#470×C1272
C2×#349×C1272
C2×H(3,ℤ/4)×C1272
C127×#13402
C2×#1340127