Finite Group Databasebeta

← C127×#14668 #44578341

Subgroups — C127×#14668 #44578341

Order 32512.

1102 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×#391×C127C211yesmaximal, characteristic
2C127×#1446C212yesmaximal
3C127×#1443C214yesmaximal
4C127×#1442C214yesmaximal
5C127×#1441C212yesmaximal
6C127×#1434C212yesmaximal
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C42×C127C2211yescharacteristic
11#391×C127C418yescomplemented
12C2×#95×C127C2214yes—
13C2×#95×C127C2212yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2212yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C22×Q8×C127—24no—
23C22×Q8×C127—42no—
24C22×Q8×C127—41no—
25C22×Q8×C127—41no—
26C22×Q8×C127C2×C414yes—
27C23×C4×C127C2314yes—
28C23×C4×C127C2314yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2312yes—
32C23×C4×C127C2311yescharacteristic
33C2×C4⋊C4×C127—41no—
34C2×C4⋊C4×C127—41no—
35C2×C4⋊C4×C127—44no—
36C2×C4⋊C4×C127—42no—
37C2×C4⋊C4×C127C2×C414yes—
38C2×C42×C127—42no—
39C2×C42×C127C2×C414yes—
40#95×C127—28no—
41#95×C127—42no—
42#95×C127—42no—
43#95×C127—44no—
44#95×C127—42no—
45#95×C127—44no—
46#95×C127—44no—
47#95×C127—42no—
48#95×C127—42no—
49#95×C127C2×C4116yes—
50C24×C127C2411yescharacteristic
51C2×Q8×C127—28no—
52C2×Q8×C127—44no—
53C2×Q8×C127—44no—
54C2×Q8×C127—48no—
55C2×Q8×C127—48no—
56C22×C4×C127—22no—
57C22×C4×C127—21no—
58C22×C4×C127—21no—
59C22×C4×C127—24no—
60C22×C4×C127—22no—
61C22×C4×C127—24no—
62C22×C4×C127—22no—
63C22×C4×C127—24no—
64C22×C4×C127—22no—
65C22×C4×C127—24no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—22no—
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×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127C22×C414yes—
86C22×C4×C127C22×C414yes—
87C22×C4×C127C22×C414yes—
88C22×C4×C127C22×C412yes—
89C22×C4×C127#4114yes—
90C4⋊C4×C127—44no—
91C4⋊C4×C127—48no—
92C42×C127—44no—
93C23×C127C23×C411yescharacteristic
94C23×C127C2×#4112yes—
95C23×C127H(5,𝔽2)11yescharacteristic
96C23×C127H(5,𝔽2)12yes—
97C23×C127H(5,𝔽2)11yescharacteristic
98C23×C127H(5,𝔽2)12yes—
99C23×C1272−1+414yes—
100C23×C1272−1+412yes—
101Q8×C127—416no—
102C2×C4×C127—22no—
103C2×C4×C127—22no—
104C2×C4×C127—24no—
105C2×C4×C127—24no—
106C2×C4×C127—24no—
107C2×C4×C127—24no—
108C2×C4×C127—24no—
109C2×C4×C127—24no—
110C2×C4×C127—24no—
111C2×C4×C127—24no—
112C2×C4×C127—24no—
113C2×C4×C127—28no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—42no—
117C2×C4×C127—44no—
118C2×C4×C127—44no—
119C2×C4×C127—44no—
120C2×C4×C127—42no—
121C2×C4×C127—44no—
122C2×C4×C127—44no—
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—44no—
131C2×C4×C127—44no—
132C2×C4×C127—44no—
133C2×C4×C127—44no—
134C2×C4×C127—44no—
135C2×C4×C127#11714yes—
136C22×C127C2×#11711yescharacteristic
137C22×C127#51811yescharacteristic
138C22×C127#51811yescharacteristic
139C22×C127#51912yes—
140C22×C127#52012yes—
141C22×C127#53812yes—
142C22×C127#53812yes—
143C22×C127#54114yes—
144C22×C127#54214yes—
145C22×C127H(3,𝔽4)11yescharacteristic
146C22×C127#56212yes—
147C22×C127#56214yes—
148C22×C127#56312yes—
149C22×C127#56314yes—
150C22×C127#56312yes—
151C22×C127#56311yescharacteristic
152C4×C127—24no—
153C4×C127—44no—
154C4×C127—44no—
155C4×C127—44no—
156C4×C127—84no—
157C4×C127—84no—
158#14668C12711yesmaximal, characteristic, direct product factor, Sylow
159C2×C127#231211yescharacteristic
160C2×C127#232012yes—
161C2×C127#237812yes—
162C2×C127#237911yescharacteristic
163C2×C127#238111yescharacteristic
164C2×C127#283114yes—
165C2×C127#283212yes—
166C2×C127#283312yes—
167C2×#391C2×C12711yescharacteristic
168#1446C2×C12712yes—
169#1443C2×C12714yes—
170#1442C2×C12714yes—
171#1441C2×C12712yes—
172#1434C2×C12712yes—
173C127#1466811yescharacteristic, direct product factor, Sylow
174C23×Q8C22×C12711yescharacteristic
175C22×C4⋊C4C22×C12712yes—
176C22×C4⋊C4C22×C12711yescharacteristic
177C22×C42C22×C12711yescharacteristic
178#391C4×C12718yescomplemented
179C2×#95C22×C12714yes—
180C2×#95C22×C12712yes—
181C2×#95C22×C12714yes—
182C2×#95C22×C12712yes—
183C2×#95C22×C12714yes—
184C2×#95C22×C12712yes—
185C2×#95C22×C12712yes—
186C2×#95C22×C12714yes—
187C2×#95C22×C12712yes—
188C2×#95C22×C12714yes—
189C22×Q8—24no—
190C22×Q8—42no—
191C22×Q8—41no—
192C22×Q8—41no—
193C22×Q8C2×C4×C12714yes—
194C23×C4C23×C12714yes—
195C23×C4C23×C12714yes—
196C23×C4C23×C12712yes—
197C23×C4C23×C12712yes—
198C23×C4C23×C12712yes—
199C23×C4C23×C12711yescharacteristic
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4C2×C4×C12714yes—
205C2×C42—42no—
206C2×C42C2×C4×C12714yes—
207#95—28no—
208#95—42no—
209#95—42no—
210#95—44no—
211#95—42no—
212#95—44no—
213#95—44no—
214#95—42no—
215#95—42no—
216#95C2×C4×C127116yes—
217C24C24×C12711yescharacteristic
218C2×Q8—28no—
219C2×Q8—44no—
220C2×Q8—44no—
221C2×Q8—48no—
222C2×Q8—48no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4C22×C4×C12714yes—
253C22×C4C22×C4×C12714yes—
254C22×C4C22×C4×C12714yes—
255C22×C4C22×C4×C12712yes—
256C22×C4#41×C12714yes—
257C4⋊C4—44no—
258C4⋊C4—48no—
259C42—44no—
260C23C23×C4×C12711yescharacteristic
261C23C2×#41×C12712yes—
262C23H(5,𝔽2)×C12711yescharacteristic
263C23H(5,𝔽2)×C12712yes—
264C23H(5,𝔽2)×C12711yescharacteristic
265C23H(5,𝔽2)×C12712yes—
266C232−1+4×C12714yes—
267C232−1+4×C12712yes—
268Q8—416no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—28no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4#117×C12714yes—
303C22C2×#117×C12711yescharacteristic
304C22#518×C12711yescharacteristic
305C22#518×C12711yescharacteristic
306C22#519×C12712yes—
307C22#520×C12712yes—
308C22#538×C12712yes—
309C22#538×C12712yes—
310C22#541×C12714yes—
311C22#542×C12714yes—
312C22H(3,𝔽4)×C12711yescharacteristic
313C22#562×C12712yes—
314C22#562×C12714yes—
315C22#563×C12712yes—
316C22#563×C12714yes—
317C22#563×C12712yes—
318C22#563×C12711yescharacteristic
319C4—24no—
320C4—44no—
321C4—44no—
322C4—44no—
323C4—84no—
324C4—84no—
325C2C127×#231211yescharacteristic
326C2C127×#232012yes—
327C2C127×#237812yes—
328C2C127×#237911yescharacteristic
329C2C127×#238111yescharacteristic
330C2C127×#283114yes—
331C2C127×#283212yes—
332C2C127×#283312yes—
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
11. #391×C127C4semidirect
158. #14668C127direct (N × H)
173. C127#14668direct (N × H)
178. #391C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C127×#14462
C127×#14432
C127×#14422
C127×#14412
C127×#14342
#14668127