Finite Group Databasebeta

← C127×#15980 #44579653

Subgroups — C127×#15980 #44579653

Order 32512.

1234 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C127C214yesmaximal
2C127×#1445C211yesmaximal, characteristic
3C127×#1444C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1441C214yesmaximal
6C127×#1436C212yesmaximal
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C42×C127C2212yes—
12#387×C127—216no—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2212yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2214yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2211yescharacteristic
20C2×#95×C127C2211yescharacteristic
21C2×#95×C127C2212yes—
22C23×C4×C127C2314yes—
23C23×C4×C127C2312yes—
24C23×C4×C127C2312yes—
25C23×C4×C127C2311yescharacteristic
26C23×C4×C127C2312yes—
27C23×C4×C127C2314yes—
28C2×C4⋊C4×C127—28no—
29C2×C4⋊C4×C127—28no—
30C2×C4⋊C4×C127—28no—
31C2×C4⋊C4×C127—28no—
32C2×C4⋊C4×C127—28no—
33C2×C4⋊C4×C127—41no—
34C2×C4⋊C4×C127—41no—
35C2×C4⋊C4×C127—42no—
36C2×C4⋊C4×C127—42no—
37C2×C4⋊C4×C127Q814yes—
38C2×C42×C127—28no—
39C2×C42×C127—42no—
40#95×C127—28no—
41#95×C127—28no—
42#95×C127—28no—
43#95×C127—28no—
44#95×C127—24no—
45#95×C127—42no—
46#95×C127—41no—
47#95×C127—41no—
48#95×C127D418yes—
49C24×C127C2411yescharacteristic
50C22×C4×C127—24no—
51C22×C4×C127—24no—
52C22×C4×C127—24no—
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—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—24no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127C2×D414yes—
78C22×C4×C127C2×D418yes—
79C22×C4×C127C2×Q812yes—
80C22×C4×C127C2×Q814yes—
81C22×C4×C127#4114yes—
82C22×C4×C127#4118yes—
83C4⋊C4×C127—232no—
84C4⋊C4×C127—44no—
85C4⋊C4×C127—48no—
86C4⋊C4×C127—48no—
87C42×C127—48no—
88C23×C127C22×D412yes—
89C23×C127C22×Q811yescharacteristic
90C23×C127C2×#4112yes—
91C23×C127C2×#4114yes—
92C23×C127H(5,𝔽2)11yescharacteristic
93C23×C127H(5,𝔽2)11yescharacteristic
94C23×C1272−1+412yes—
95C23×C1272−1+412yes—
96C2×C4×C127—28no—
97C2×C4×C127—28no—
98C2×C4×C127—28no—
99C2×C4×C127—24no—
100C2×C4×C127—24no—
101C2×C4×C127—24no—
102C2×C4×C127—22no—
103C2×C4×C127—24no—
104C2×C4×C127—28no—
105C2×C4×C127—28no—
106C2×C4×C127—28no—
107C2×C4×C127—28no—
108C2×C4×C127—28no—
109C2×C4×C127—28no—
110C2×C4×C127—44no—
111C2×C4×C127—44no—
112C2×C4×C127—44no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—44no—
119C2×C4×C127—44no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—44no—
123C2×C4×C127—44no—
124C2×C4×C127—42no—
125C2×C4×C127—44no—
126C2×C4×C127—42no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C22×C127#52514yes—
130C22×C127#53312yes—
131C22×C127#53712yes—
132C22×C127#53912yes—
133C22×C127#54114yes—
134C22×C127#54311yescharacteristic
135C22×C127D4211yescharacteristic
136C22×C127#54714yes—
137C22×C127D4×Q812yes—
138C22×C127#55112yes—
139C22×C127#55214yes—
140C22×C127#55511yescharacteristic
141C22×C127#55712yes—
142C22×C127#55912yes—
143C22×C127#56311yescharacteristic
144C22×C127#56311yescharacteristic
145C4×C127—42no—
146C4×C127—48no—
147C4×C127—44no—
148C4×C127—48no—
149C4×C127—44no—
150C4×C127—44no—
151#15980C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127#245512yes—
153C2×C127#246214yes—
154C2×C127#260711yescharacteristic
155C2×C127#260912yes—
156C2×C127#268311yescharacteristic
157C2×C127#272212yes—
158C2×C127#279412yes—
159C2×C127#280911yescharacteristic
160C2×#387C2×C12714yes—
161#1445C2×C12711yescharacteristic
162#1444C2×C12712yes—
163#1442C2×C12712yes—
164#1441C2×C12714yes—
165#1436C2×C12712yes—
166C127#1598011yescharacteristic, direct product factor, Sylow
167C22×C4⋊C4C22×C12714yes—
168C22×C4⋊C4C22×C12712yes—
169C22×C4⋊C4C22×C12712yes—
170C22×C4⋊C4C22×C12711yescharacteristic
171C22×C42C22×C12712yes—
172#387—216no—
173C2×#95C22×C12714yes—
174C2×#95C22×C12714yes—
175C2×#95C22×C12712yes—
176C2×#95C22×C12714yes—
177C2×#95C22×C12714yes—
178C2×#95C22×C12712yes—
179C2×#95C22×C12711yescharacteristic
180C2×#95C22×C12711yescharacteristic
181C2×#95C22×C12712yes—
182C23×C4C23×C12714yes—
183C23×C4C23×C12712yes—
184C23×C4C23×C12711yescharacteristic
185C23×C4C23×C12712yes—
186C23×C4C23×C12712yes—
187C23×C4C23×C12714yes—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—28no—
191C2×C4⋊C4—28no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4Q8×C12714yes—
198C2×C42—28no—
199C2×C42—42no—
200#95—28no—
201#95—28no—
202#95—28no—
203#95—28no—
204#95—24no—
205#95—42no—
206#95—41no—
207#95—41no—
208#95D4×C12718yes—
209C24C24×C12711yescharacteristic
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4C2×D4×C12714yes—
238C22×C4C2×D4×C12718yes—
239C22×C4C2×Q8×C12712yes—
240C22×C4C2×Q8×C12714yes—
241C22×C4#41×C12714yes—
242C22×C4#41×C12718yes—
243C4⋊C4—232no—
244C4⋊C4—44no—
245C4⋊C4—48no—
246C4⋊C4—48no—
247C42—48no—
248C23C22×D4×C12712yes—
249C23C22×Q8×C12711yescharacteristic
250C23C2×#41×C12712yes—
251C23C2×#41×C12714yes—
252C23H(5,𝔽2)×C12711yescharacteristic
253C23H(5,𝔽2)×C12711yescharacteristic
254C232−1+4×C12712yes—
255C232−1+4×C12712yes—
256C2×C4—28no—
257C2×C4—28no—
258C2×C4—28no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C22#525×C12714yes—
290C22#533×C12712yes—
291C22#537×C12712yes—
292C22#539×C12712yes—
293C22#541×C12714yes—
294C22#543×C12711yescharacteristic
295C22D42×C12711yescharacteristic
296C22#547×C12714yes—
297C22D4×Q8×C12712yes—
298C22#551×C12712yes—
299C22#552×C12714yes—
300C22#555×C12711yescharacteristic
301C22#557×C12712yes—
302C22#559×C12712yes—
303C22#563×C12711yescharacteristic
304C22#563×C12711yescharacteristic
305C4—42no—
306C4—48no—
307C4—44no—
308C4—48no—
309C4—44no—
310C4—44no—
311C2C127×#245512yes—
312C2C127×#246214yes—
313C2C127×#260711yescharacteristic
314C2C127×#260912yes—
315C2C127×#268311yescharacteristic
316C2C127×#272212yes—
317C2C127×#279412yes—
318C2C127×#280911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
151. #15980C127direct (N × H)
166. C127#15980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#387×C1272
C127×#14452
C127×#14442
C127×#14422
C127×#14412
C127×#14362
#15980127