Finite Group Databasebeta

← C4×#342×C127 #44574381

Subgroups — C4×#342×C127 #44574381

Order 32512.

1482 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊C4×C127C212yesmaximal
2C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
3C2×#342×C127C214yesmaximal
4C24×C4×C127C2211yescharacteristic
5C22×C22⋊C4×C127C2212yes—
6C22×C22⋊C4×C127C2214yes—
7C22×C42×C127—22no—
8C22×C42×C127C412yescomplemented
9C4×C22⋊C4×C127—24no—
10C4×C22⋊C4×C127—22no—
11C4×C22⋊C4×C127—22no—
12C4×C22⋊C4×C127C418yescomplemented
13C2×#95×C127—22no—
14C2×#95×C127C412yescomplemented
15#342×C127C4116yesdirect product factor
16C25×C127C2311yescharacteristic
17C23×C4×C127—24no—
18C23×C4×C127—44no—
19C23×C4×C127C2×C411yescharacteristic
20C23×C4×C127C2×C414yes—
21C23×C4×C127C2×C411yescharacteristic
22C23×C4×C127C2×C414yes—
23C23×C4×C127D412yes—
24C23×C4×C127D412yes—
25C23×C4×C127D412yes—
26C23×C4×C127Q812yes—
27C2×C22⋊C4×C127—24no—
28C2×C22⋊C4×C127—24no—
29C2×C22⋊C4×C127—28no—
30C2×C22⋊C4×C127—24no—
31C2×C22⋊C4×C127C2×C418yes—
32C2×C22⋊C4×C127C2×C4116yes—
33C2×C22⋊C4×C127C2×C418yes—
34C2×C42×C127—28no—
35C2×C42×C127—22no—
36C2×C42×C127—22no—
37C2×C42×C127—48no—
38C2×C42×C127—44no—
39#95×C127—28no—
40#95×C127—24no—
41C24×C127—42no—
42C24×C127—42no—
43C24×C127C22×C411yescharacteristic
44C24×C127C22×C412yes—
45C24×C127C22×C414yes—
46C24×C127C2×D412yes—
47C24×C127C2×D411yescharacteristic
48C24×C127C2×Q811yescharacteristic
49C24×C127#4114yes—
50C22×C4×C127—24no—
51C22×C4×C127—28no—
52C22×C4×C127—24no—
53C22×C4×C127—28no—
54C22×C4×C127—24no—
55C22×C4×C127—216no—
56C22×C4×C127—48no—
57C22×C4×C127—44no—
58C22×C4×C127—44no—
59C22×C4×C127—42no—
60C22×C4×C127—44no—
61C22×C4×C127—48no—
62C22×C4×C127—48no—
63C22×C4×C127—44no—
64C22×C4×C127—44no—
65C22×C4×C127C4212yes—
66C22×C4×C127C4212yes—
67C22×C4×C127C4218yescomplemented
68C22×C4×C127C22⋊C412yes—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C414yes—
71C22×C4×C127C22⋊C414yes—
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C4⋊C412yes—
74C22×C4×C127C4⋊C414yes—
75C22×C4×C127C4⋊C412yes—
76C22×C4×C127C4⋊C414yes—
77C22⋊C4×C127—28no—
78C22⋊C4×C127—216no—
79C22⋊C4×C127—216no—
80C22⋊C4×C127C42116yescomplemented
81C42×C127—44no—
82C42×C127—416no—
83C42×C127—44no—
84C23×C127—22no—
85C23×C127—24no—
86C23×C127—22no—
87C23×C127—24no—
88C23×C127—42no—
89C23×C127—41no—
90C23×C127—41no—
91C23×C127—42no—
92C23×C127—48no—
93C23×C127—41no—
94C23×C127—41no—
95C23×C127—48no—
96C23×C127C2×C4211yescharacteristic
97C23×C127C2×C4212yes—
98C23×C127C2×C4214yes—
99C23×C127C2×C22⋊C412yes—
100C23×C127C2×C22⋊C411yescharacteristic
101C23×C127C2×C4⋊C411yescharacteristic
102C23×C127C2×C4⋊C412yes—
103C23×C127#11712yes—
104C23×C127#11714yes—
105C23×C127C4×D418yes—
106C23×C127C4×D414yes—
107C23×C127C4×Q814yes—
108C2×C4×C127—22no—
109C2×C4×C127—24no—
110C2×C4×C127—28no—
111C2×C4×C127—24no—
112C2×C4×C127—24no—
113C2×C4×C127—28no—
114C2×C4×C127—28no—
115C2×C4×C127—216no—
116C2×C4×C127—42no—
117C2×C4×C127—44no—
118C2×C4×C127—44no—
119C2×C4×C127—42no—
120C2×C4×C127—48no—
121C2×C4×C127—48no—
122C2×C4×C127—432no—
123C2×C4×C127—48no—
124C2×C4×C127—44no—
125C2×C4×C127—44no—
126C2×C4×C127—48no—
127C2×C4×C127#9512yes—
128C2×C4×C127#9514yes—
129C2×C4×C127#9512yes—
130C2×C4×C127#9914yes—
131C22×C127—22no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—22no—
135C22×C127—22no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—22no—
139C22×C127—24no—
140C22×C127—24no—
141C22×C127—216no—
142C22×C127—44no—
143C22×C127—44no—
144C22×C127—44no—
145C22×C127—44no—
146C22×C127C4311yescharacteristic
147C22×C127C2×#9511yescharacteristic
148C22×C127#37611yescharacteristic
149C22×C127C4×C22⋊C414yes—
150C22×C127C4×C22⋊C412yes—
151C22×C127C4×C4⋊C412yes—
152C22×C127C4×C4⋊C414yes—
153C22×C127C2×#9912yes—
154C22×C127#41012yes—
155C4×C127—22no—
156C4×C127—24no—
157C4×C127—416no—
158C4×C127—48no—
159C4×C127#34214yesdirect product factor
160C4×#342C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—24no—
162C2×C127—21no—
163C2×C127—21no—
164C2×C127—22no—
165C2×C127—24no—
166C2×C127C4×#9511yescharacteristic
167C2×C127C2×#34211yescharacteristic
168C2×C127#174011yescharacteristic
169C2×C127C4×#9914yes—
170C2×C4×C22⋊C4C2×C12712yes—
171C2×C4×C22⋊C4C2×C12711yescharacteristic
172C2×#342C2×C12714yes—
173C127C4×#34211yescharacteristic, direct product factor, Sylow
174C24×C4C22×C12711yescharacteristic
175C22×C22⋊C4C22×C12712yes—
176C22×C22⋊C4C22×C12714yes—
177C22×C42—22no—
178C22×C42C4×C12712yescomplemented
179C4×C22⋊C4—24no—
180C4×C22⋊C4—22no—
181C4×C22⋊C4—22no—
182C4×C22⋊C4C4×C12718yescomplemented
183C2×#95—22no—
184C2×#95C4×C12712yescomplemented
185#342C4×C127116yesdirect product factor
186C25C23×C12711yescharacteristic
187C23×C4—24no—
188C23×C4—44no—
189C23×C4C2×C4×C12711yescharacteristic
190C23×C4C2×C4×C12714yes—
191C23×C4C2×C4×C12711yescharacteristic
192C23×C4C2×C4×C12714yes—
193C23×C4D4×C12712yes—
194C23×C4D4×C12712yes—
195C23×C4D4×C12712yes—
196C23×C4Q8×C12712yes—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—28no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4C2×C4×C12718yes—
202C2×C22⋊C4C2×C4×C127116yes—
203C2×C22⋊C4C2×C4×C12718yes—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—28no—
207C2×C42—48no—
208C2×C42—44no—
209#95—28no—
210#95—24no—
211C24—42no—
212C24—42no—
213C24C22×C4×C12711yescharacteristic
214C24C22×C4×C12712yes—
215C24C22×C4×C12714yes—
216C24C2×D4×C12712yes—
217C24C2×D4×C12711yescharacteristic
218C24C2×Q8×C12711yescharacteristic
219C24#41×C12714yes—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—24no—
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—216no—
226C22×C4—48no—
227C22×C4—44no—
228C22×C4—44no—
229C22×C4—42no—
230C22×C4—44no—
231C22×C4—48no—
232C22×C4—48no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4C42×C12712yes—
236C22×C4C42×C12712yes—
237C22×C4C42×C12718yescomplemented
238C22×C4C22⋊C4×C12712yes—
239C22×C4C22⋊C4×C12711yescharacteristic
240C22×C4C22⋊C4×C12714yes—
241C22×C4C22⋊C4×C12714yes—
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4C4⋊C4×C12712yes—
244C22×C4C4⋊C4×C12714yes—
245C22×C4C4⋊C4×C12712yes—
246C22×C4C4⋊C4×C12714yes—
247C22⋊C4—28no—
248C22⋊C4—216no—
249C22⋊C4—216no—
250C22⋊C4C42×C127116yescomplemented
251C42—44no—
252C42—416no—
253C42—44no—
254C23—22no—
255C23—24no—
256C23—22no—
257C23—24no—
258C23—42no—
259C23—41no—
260C23—41no—
261C23—42no—
262C23—48no—
263C23—41no—
264C23—41no—
265C23—48no—
266C23C2×C42×C12711yescharacteristic
267C23C2×C42×C12712yes—
268C23C2×C42×C12714yes—
269C23C2×C22⋊C4×C12712yes—
270C23C2×C22⋊C4×C12711yescharacteristic
271C23C2×C4⋊C4×C12711yescharacteristic
272C23C2×C4⋊C4×C12712yes—
273C23#117×C12712yes—
274C23#117×C12714yes—
275C23C4×D4×C12718yes—
276C23C4×D4×C12714yes—
277C23C4×Q8×C12714yes—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—28no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—28no—
284C2×C4—28no—
285C2×C4—216no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—48no—
291C2×C4—48no—
292C2×C4—432no—
293C2×C4—48no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—48no—
297C2×C4#95×C12712yes—
298C2×C4#95×C12714yes—
299C2×C4#95×C12712yes—
300C2×C4#99×C12714yes—
301C22—22no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—22no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—24no—
310C22—24no—
311C22—216no—
312C22—44no—
313C22—44no—
314C22—44no—
315C22—44no—
316C22C43×C12711yescharacteristic
317C22C2×#95×C12711yescharacteristic
318C22#376×C12711yescharacteristic
319C22C4×C22⋊C4×C12714yes—
320C22C4×C22⋊C4×C12712yes—
321C22C4×C4⋊C4×C12712yes—
322C22C4×C4⋊C4×C12714yes—
323C22C2×#99×C12712yes—
324C22#410×C12712yes—
325C4—22no—
326C4—24no—
327C4—416no—
328C4—48no—
329C4#342×C12714yesdirect product factor
330C2—24no—
331C2—21no—
332C2—21no—
333C2—22no—
334C2—24no—
335C2C4×#95×C12711yescharacteristic
336C2C2×#342×C12711yescharacteristic
337C2C127×#174011yescharacteristic
338C2C4×#99×C12714yes—
subgroupG/H
centerC22×C4×C127C22⋊C4
commutatorC22C43×C127
Frattini, cosocleC25C23×C127
socleC23×C127C2×C22⋊C4
prime radicalC25×C127C23
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C42×C127C4semidirect
12. C4×C22⋊C4×C127C4semidirect
14. C2×#95×C127C4semidirect
15. #342×C127C4direct (N × H)
67. C22×C4×C127C42semidirect
80. C22⋊C4×C127C42semidirect
159. C4×C127#342direct (N × H)
160. C4×#342C127direct (N × H)
173. C127C4×#342direct (N × H)
178. C22×C42C4×C127semidirect
182. C4×C22⋊C4C4×C127semidirect
184. C2×#95C4×C127semidirect
185. #342C4×C127direct (N × H)
237. C22×C4C42×C127semidirect
250. C22⋊C4C42×C127semidirect
329. C4#342×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C1272
C2×#342×C1272
C4×#342127