Finite Group Databasebeta

← C2×C127×#1394 #44576257

Subgroups — C2×C127×#1394 #44576257

Order 32512.

818 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#101×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C127×#1394C214yesmaximal, direct product factor
4C23×Q8×C127C2211yescharacteristic
5C22×M16×C127—22no—
6C22×C4⋊C4×C127C411yescharacteristic
7C22×C42×C127C411yescharacteristic
8C2×#101×C127—22no—
9C2×#101×C127—24no—
10C2×#101×C127C418yescomplemented
11C2×#101×C127C2214yes—
12#391×C127—22no—
13#391×C127C412yes—
14#391×C127C2212yes—
15C2×#95×C127—22no—
16C22×Q8×C127—42no—
17C22×Q8×C127—41no—
18C22×Q8×C127—41no—
19C22×Q8×C127C2×C414yes—
20C22×Q8×C127C2×C411yescharacteristic
21C22×Q8×C127D412yes—
22C22×Q8×C127D412yes—
23C22×Q8×C127Q812yes—
24C22×Q8×C127C2311yescharacteristic
25C23×C4×C127—21no—
26C23×C4×C127—21no—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D412yes—
29C2×M16×C127—28no—
30C2×M16×C127—24no—
31C2×M16×C127—44no—
32C2×M16×C127—42no—
33C22×C8×C127—42no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—41no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127C2×C412yes—
38C2×C42×C127—21no—
39C2×C42×C127—42no—
40C2×C42×C127C2×C412yes—
41#101×C127—28no—
42#101×C127—24no—
43#101×C127C2×C418yescomplemented
44#95×C127—24no—
45#95×C127—24no—
46C24×C127C22⋊C411yescharacteristic
47C2×Q8×C127—44no—
48C2×Q8×C127—44no—
49C2×Q8×C127—41no—
50C2×Q8×C127—41no—
51C2×Q8×C127—42no—
52C2×Q8×C127—42no—
53C2×Q8×C127—42no—
54C2×Q8×C127—42no—
55C2×Q8×C127—42no—
56C2×Q8×C127—42no—
57C2×Q8×C127—41no—
58C2×Q8×C127—41no—
59C2×Q8×C127C4212yes—
60C2×Q8×C127C22⋊C414yes—
61C2×Q8×C127C4⋊C414yes—
62C2×Q8×C127C4⋊C412yes—
63C2×Q8×C127C22×C412yes—
64C2×Q8×C127C2×D411yescharacteristic
65C2×Q8×C127C2×Q811yescharacteristic
66C22×C4×C127—22no—
67C22×C4×C127—21no—
68C22×C4×C127—24no—
69C22×C4×C127—22no—
70C22×C4×C127—21no—
71C22×C4×C127—22no—
72C22×C4×C127—24no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—42no—
76C22×C4×C127—42no—
77C22×C4×C127—44no—
78C22×C4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127C4212yes—
81C22×C4×C127C22⋊C412yes—
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127C22⋊C414yes—
84C22×C4×C127C4⋊C412yes—
85C22×C4×C127C4⋊C414yes—
86C22×C4×C127C22×C411yescharacteristic
87C22×C4×C127C2×D412yes—
88M16×C127—28no—
89M16×C127—48no—
90M16×C127—44no—
91C2×C8×C127—48no—
92C2×C8×C127—44no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C42×C127—42no—
96C42×C127—42no—
97C23×C127—22no—
98C23×C127—22no—
99C23×C127#9512yes—
100C23×C127#9911yescharacteristic
101C23×C127#9912yes—
102C23×C127#9911yescharacteristic
103C23×C127C2×C22⋊C411yescharacteristic
104Q8×C127—42no—
105Q8×C127—44no—
106Q8×C127—42no—
107Q8×C127—44no—
108Q8×C127—42no—
109Q8×C127—41no—
110Q8×C127—41no—
111C2×C4×C127—24no—
112C2×C4×C127—24no—
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—24no—
117C2×C4×C127—22no—
118C2×C4×C127—24no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—24no—
128C2×C4×C127—42no—
129C2×C4×C127—48no—
130C2×C4×C127—42no—
131C2×C4×C127—44no—
132C2×C4×C127—42no—
133C2×C4×C127—82no—
134C2×C4×C127—82no—
135C2×C4×C127#9512yes—
136C2×C4×C127#9514yes—
137C2×C4×C127C2×C4211yescharacteristic
138C2×C4×C127C2×C22⋊C412yes—
139C2×C4×C127C2×C4⋊C411yescharacteristic
140C2×C4×C127C2×C4⋊C412yes—
141C8×C127—48no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—24no—
147C22×C127—24no—
148C22×C127#34212yes—
149C22×C127#34212yes—
150C22×C127#35512yes—
151C22×C127#35612yes—
152C22×C127C2×#9511yescharacteristic
153C22×C127C2×#9911yescharacteristic
154C22×C127C2×#9911yescharacteristic
155C4×C127—22no—
156C4×C127—24no—
157C4×C127—22no—
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—22no—
161C4×C127—44no—
162C4×C127—82no—
163C2×#1394C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—22no—
166C2×C127—21no—
167C2×C127#139414yesdirect product factor
168C2×C127C2×#34211yescharacteristic
169C2×C127C2×#35511yescharacteristic
170C2×C127C2×#35611yescharacteristic
171C22×#101C2×C12712yes—
172C2×#391C2×C12711yescharacteristic
173#1394C2×C12714yesdirect product factor
174C127C2×#139411yescharacteristic, direct product factor, Sylow
175C23×Q8C22×C12711yescharacteristic
176C22×M16—22no—
177C22×C4⋊C4C4×C12711yescharacteristic
178C22×C42C4×C12711yescharacteristic
179C2×#101—22no—
180C2×#101—24no—
181C2×#101C4×C12718yescomplemented
182C2×#101C22×C12714yes—
183#391—22no—
184#391C4×C12712yes—
185#391C22×C12712yes—
186C2×#95—22no—
187C22×Q8—42no—
188C22×Q8—41no—
189C22×Q8—41no—
190C22×Q8C2×C4×C12714yes—
191C22×Q8C2×C4×C12711yescharacteristic
192C22×Q8D4×C12712yes—
193C22×Q8D4×C12712yes—
194C22×Q8Q8×C12712yes—
195C22×Q8C23×C12711yescharacteristic
196C23×C4—21no—
197C23×C4—21no—
198C23×C4C2×C4×C12711yescharacteristic
199C23×C4D4×C12712yes—
200C2×M16—28no—
201C2×M16—24no—
202C2×M16—44no—
203C2×M16—42no—
204C22×C8—42no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4C2×C4×C12712yes—
209C2×C42—21no—
210C2×C42—42no—
211C2×C42C2×C4×C12712yes—
212#101—28no—
213#101—24no—
214#101C2×C4×C12718yescomplemented
215#95—24no—
216#95—24no—
217C24C22⋊C4×C12711yescharacteristic
218C2×Q8—44no—
219C2×Q8—44no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8C42×C12712yes—
231C2×Q8C22⋊C4×C12714yes—
232C2×Q8C4⋊C4×C12714yes—
233C2×Q8C4⋊C4×C12712yes—
234C2×Q8C22×C4×C12712yes—
235C2×Q8C2×D4×C12711yescharacteristic
236C2×Q8C2×Q8×C12711yescharacteristic
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—44no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C42×C12712yes—
252C22×C4C22⋊C4×C12712yes—
253C22×C4C22⋊C4×C12711yescharacteristic
254C22×C4C22⋊C4×C12714yes—
255C22×C4C4⋊C4×C12712yes—
256C22×C4C4⋊C4×C12714yes—
257C22×C4C22×C4×C12711yescharacteristic
258C22×C4C2×D4×C12712yes—
259M16—28no—
260M16—48no—
261M16—44no—
262C2×C8—48no—
263C2×C8—44no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C42—42no—
267C42—42no—
268C23—22no—
269C23—22no—
270C23#95×C12712yes—
271C23#99×C12711yescharacteristic
272C23#99×C12712yes—
273C23#99×C12711yescharacteristic
274C23C2×C22⋊C4×C12711yescharacteristic
275Q8—42no—
276Q8—44no—
277Q8—42no—
278Q8—44no—
279Q8—42no—
280Q8—41no—
281Q8—41no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—42no—
300C2×C4—48no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4#95×C12712yes—
307C2×C4#95×C12714yes—
308C2×C4C2×C42×C12711yescharacteristic
309C2×C4C2×C22⋊C4×C12712yes—
310C2×C4C2×C4⋊C4×C12711yescharacteristic
311C2×C4C2×C4⋊C4×C12712yes—
312C8—48no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—24no—
318C22—24no—
319C22#342×C12712yes—
320C22#342×C12712yes—
321C22#355×C12712yes—
322C22#356×C12712yes—
323C22C2×#95×C12711yescharacteristic
324C22C2×#99×C12711yescharacteristic
325C22C2×#99×C12711yescharacteristic
326C4—22no—
327C4—24no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—22no—
332C4—44no—
333C4—82no—
334C2—21no—
335C2—22no—
336C2—21no—
337C2C127×#139414yesdirect product factor
338C2C2×#342×C12711yescharacteristic
339C2C2×#355×C12711yescharacteristic
340C2C2×#356×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×Q8C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C127 ◁ C23×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1394C2direct (N × H)
10. C2×#101×C127C4semidirect
43. #101×C127C2×C4semidirect
163. C2×#1394C127direct (N × H)
167. C2×C127#1394direct (N × H)
173. #1394C2×C127direct (N × H)
174. C127C2×#1394direct (N × H)
181. C2×#101C4×C127semidirect
214. #101C2×C4×C127semidirect
337. C2C127×#1394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#101×C1272
C2×#391×C1272
C127×#13942
C2×#1394127