Finite Group Databasebeta

← C127×#14476 #44578149

Subgroups — C127×#14476 #44578149

Order 32512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#382×C127C211yesmaximal, characteristic
2C127×#1442C214yesmaximal
3C127×#1441C212yesmaximal
4C127×#1436C212yesmaximal
5C127×#1434C214yesmaximal
6C127×#1434C212yesmaximal
7C22×C4⋊C4×C127C2212yes—
8C22×C4⋊C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C42×C127C2212yes—
11C22×C42×C127C2211yescharacteristic
12#382×C127C418yescomplemented
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2212yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C23×C4×C127C2314yes—
23C23×C4×C127C2312yes—
24C23×C4×C127C2312yes—
25C23×C4×C127C2312yes—
26C23×C4×C127C2314yes—
27C23×C4×C127C2311yescharacteristic
28C2×C4⋊C4×C127—41no—
29C2×C4⋊C4×C127—41no—
30C2×C4⋊C4×C127—41no—
31C2×C4⋊C4×C127—41no—
32C2×C4⋊C4×C127—44no—
33C2×C4⋊C4×C127—42no—
34C2×C4⋊C4×C127C2×C414yes—
35C2×C4⋊C4×C127C2×C414yes—
36C2×C42×C127—24no—
37C2×C42×C127—28no—
38C2×C42×C127—42no—
39C2×C42×C127C2×C414yes—
40#95×C127—28no—
41#95×C127—28no—
42#95×C127—28no—
43#95×C127—42no—
44#95×C127—44no—
45#95×C127—42no—
46#95×C127—42no—
47#95×C127—42no—
48#95×C127C2×C4116yes—
49C24×C127C2411yescharacteristic
50C22×C4×C127—21no—
51C22×C4×C127—21no—
52C22×C4×C127—22no—
53C22×C4×C127—24no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—24no—
57C22×C4×C127—24no—
58C22×C4×C127—24no—
59C22×C4×C127—22no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—24no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127C22×C414yes—
79C22×C4×C127C22×C414yes—
80C22×C4×C127C22×C414yes—
81C22×C4×C127C22×C412yes—
82C22×C4×C127#4118yes—
83C22×C4×C127#4114yes—
84C4⋊C4×C127—44no—
85C4⋊C4×C127—44no—
86C4⋊C4×C127—48no—
87C42×C127—28no—
88C42×C127—48no—
89C23×C127C23×C411yescharacteristic
90C23×C127C2×#4112yes—
91C23×C127C2×#4114yes—
92C23×C127H(5,𝔽2)11yescharacteristic
93C23×C127H(5,𝔽2)11yescharacteristic
94C23×C127H(5,𝔽2)12yes—
95C23×C1272−1+412yes—
96C23×C1272−1+412yes—
97C2×C4×C127—22no—
98C2×C4×C127—22no—
99C2×C4×C127—24no—
100C2×C4×C127—24no—
101C2×C4×C127—24no—
102C2×C4×C127—24no—
103C2×C4×C127—28no—
104C2×C4×C127—24no—
105C2×C4×C127—24no—
106C2×C4×C127—24no—
107C2×C4×C127—28no—
108C2×C4×C127—28no—
109C2×C4×C127—28no—
110C2×C4×C127—28no—
111C2×C4×C127—44no—
112C2×C4×C127—44no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—44no—
116C2×C4×C127—44no—
117C2×C4×C127—44no—
118C2×C4×C127—44no—
119C2×C4×C127—42no—
120C2×C4×C127—44no—
121C2×C4×C127—44no—
122C2×C4×C127—42no—
123C2×C4×C127—44no—
124C2×C4×C127—44no—
125C2×C4×C127—44no—
126C2×C4×C127—44no—
127C2×C4×C127—44no—
128C2×C4×C127—44no—
129C2×C4×C127—44no—
130C2×C4×C127#11714yes—
131C22×C127C2×#11711yescharacteristic
132C22×C127C4×#4112yes—
133C22×C127#51811yescharacteristic
134C22×C127#51911yescharacteristic
135C22×C127#52012yes—
136C22×C127#53912yes—
137C22×C127#53912yes—
138C22×C127#53914yes—
139C22×C127#54114yes—
140C22×C127#55112yes—
141C22×C127#55214yes—
142C22×C127#55514yes—
143C22×C127#55512yes—
144C22×C127H(3,𝔽4)11yescharacteristic
145C22×C127#56212yes—
146C22×C127#56311yescharacteristic
147C4×C127—24no—
148C4×C127—44no—
149C4×C127—44no—
150C4×C127—44no—
151C4×C127—48no—
152C4×C127—84no—
153#14476C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127#231311yescharacteristic
155C2×C127#233612yes—
156C2×C127#234612yes—
157C2×C127#237211yescharacteristic
158C2×C127#237911yescharacteristic
159C2×C127#274414yes—
160C2×C127#276912yes—
161C2×C127#278512yes—
162C2×#382C2×C12711yescharacteristic
163#1442C2×C12714yes—
164#1441C2×C12712yes—
165#1436C2×C12712yes—
166#1434C2×C12712yes—
167#1434C2×C12714yes—
168C127#1447611yescharacteristic, direct product factor, Sylow
169C22×C4⋊C4C22×C12712yes—
170C22×C4⋊C4C22×C12711yescharacteristic
171C22×C4⋊C4C22×C12711yescharacteristic
172C22×C42C22×C12712yes—
173C22×C42C22×C12711yescharacteristic
174#382C4×C12718yescomplemented
175C2×#95C22×C12714yes—
176C2×#95C22×C12714yes—
177C2×#95C22×C12714yes—
178C2×#95C22×C12712yes—
179C2×#95C22×C12712yes—
180C2×#95C22×C12714yes—
181C2×#95C22×C12712yes—
182C2×#95C22×C12712yes—
183C2×#95C22×C12714yes—
184C23×C4C23×C12714yes—
185C23×C4C23×C12712yes—
186C23×C4C23×C12712yes—
187C23×C4C23×C12712yes—
188C23×C4C23×C12714yes—
189C23×C4C23×C12711yescharacteristic
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4C2×C4×C12714yes—
197C2×C4⋊C4C2×C4×C12714yes—
198C2×C42—24no—
199C2×C42—28no—
200C2×C42—42no—
201C2×C42C2×C4×C12714yes—
202#95—28no—
203#95—28no—
204#95—28no—
205#95—42no—
206#95—44no—
207#95—42no—
208#95—42no—
209#95—42no—
210#95C2×C4×C127116yes—
211C24C24×C12711yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4C22×C4×C12714yes—
241C22×C4C22×C4×C12714yes—
242C22×C4C22×C4×C12714yes—
243C22×C4C22×C4×C12712yes—
244C22×C4#41×C12718yes—
245C22×C4#41×C12714yes—
246C4⋊C4—44no—
247C4⋊C4—44no—
248C4⋊C4—48no—
249C42—28no—
250C42—48no—
251C23C23×C4×C12711yescharacteristic
252C23C2×#41×C12712yes—
253C23C2×#41×C12714yes—
254C23H(5,𝔽2)×C12711yescharacteristic
255C23H(5,𝔽2)×C12711yescharacteristic
256C23H(5,𝔽2)×C12712yes—
257C232−1+4×C12712yes—
258C232−1+4×C12712yes—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—28no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—28no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—28no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4#117×C12714yes—
293C22C2×#117×C12711yescharacteristic
294C22C4×#41×C12712yes—
295C22#518×C12711yescharacteristic
296C22#519×C12711yescharacteristic
297C22#520×C12712yes—
298C22#539×C12712yes—
299C22#539×C12712yes—
300C22#539×C12714yes—
301C22#541×C12714yes—
302C22#551×C12712yes—
303C22#552×C12714yes—
304C22#555×C12714yes—
305C22#555×C12712yes—
306C22H(3,𝔽4)×C12711yescharacteristic
307C22#562×C12712yes—
308C22#563×C12711yescharacteristic
309C4—24no—
310C4—44no—
311C4—44no—
312C4—44no—
313C4—48no—
314C4—84no—
315C2C127×#231311yescharacteristic
316C2C127×#233612yes—
317C2C127×#234612yes—
318C2C127×#237211yescharacteristic
319C2C127×#237911yescharacteristic
320C2C127×#274414yes—
321C2C127×#276912yes—
322C2C127×#278512yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
12. #382×C127C4semidirect
153. #14476C127direct (N × H)
168. C127#14476direct (N × H)
174. #382C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#382×C1272
C127×#14422
C127×#14412
C127×#14362
C127×#14342
#14476127