Finite Group Databasebeta

← C127×#16110 #44579783

Subgroups — C127×#16110 #44579783

Order 32512.

1242 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C127×#1446C211yesmaximal, characteristic
3C127×#1445C212yesmaximal
4C127×#1444C214yesmaximal
5C127×#1442C212yesmaximal
6C127×#1434C214yesmaximal
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C42×C127C2212yes—
12#391×C127—28no—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2211yescharacteristic
20C2×#95×C127C2211yescharacteristic
21C2×#95×C127C2212yes—
22C22×Q8×C127—28no—
23C22×Q8×C127—41no—
24C22×Q8×C127—41no—
25C22×Q8×C127D414yes—
26C23×C4×C127C2314yes—
27C23×C4×C127C2311yescharacteristic
28C23×C4×C127C2314yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2312yes—
32C2×C4⋊C4×C127—24no—
33C2×C4⋊C4×C127—24no—
34C2×C4⋊C4×C127—42no—
35C2×C4⋊C4×C127—42no—
36C2×C4⋊C4×C127—42no—
37C2×C4⋊C4×C127—42no—
38C2×C4⋊C4×C127—44no—
39C2×C4⋊C4×C127—42no—
40C2×C42×C127—24no—
41C2×C42×C127—28no—
42#95×C127—28no—
43#95×C127—28no—
44#95×C127—28no—
45#95×C127—28no—
46#95×C127—42no—
47#95×C127—44no—
48#95×C127—41no—
49#95×C127—41no—
50#95×C127Q818yescomplemented
51C24×C127C2411yescharacteristic
52C2×Q8×C127—216no—
53C2×Q8×C127—44no—
54C2×Q8×C127—48no—
55C2×Q8×C127—48no—
56C22×C4×C127—24no—
57C22×C4×C127—22no—
58C22×C4×C127—22no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—22no—
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×C127C2×D412yes—
84C22×C4×C127C2×D414yes—
85C22×C4×C127C2×Q818yes—
86C22×C4×C127C2×Q814yes—
87C22×C4×C127#4114yes—
88C22×C4×C127#4118yes—
89C4⋊C4×C127—48no—
90C4⋊C4×C127—48no—
91C4⋊C4×C127—48no—
92C42×C127—48no—
93C23×C127C22×D411yescharacteristic
94C23×C127C22×Q812yes—
95C23×C127C2×#4114yes—
96C23×C127C2×#4112yes—
97C23×C127H(5,𝔽2)11yescharacteristic
98C23×C127H(5,𝔽2)11yescharacteristic
99C23×C127H(5,𝔽2)12yes—
100C23×C1272−1+412yes—
101Q8×C127—416no—
102C2×C4×C127—24no—
103C2×C4×C127—24no—
104C2×C4×C127—28no—
105C2×C4×C127—28no—
106C2×C4×C127—24no—
107C2×C4×C127—28no—
108C2×C4×C127—22no—
109C2×C4×C127—24no—
110C2×C4×C127—24no—
111C2×C4×C127—28no—
112C2×C4×C127—28no—
113C2×C4×C127—28no—
114C2×C4×C127—28no—
115C2×C4×C127—44no—
116C2×C4×C127—44no—
117C2×C4×C127—44no—
118C2×C4×C127—44no—
119C2×C4×C127—44no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—44no—
125C2×C4×C127—42no—
126C2×C4×C127—42no—
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#12318yes—
135C22×C127C2×#12312yes—
136C22×C127#53314yes—
137C22×C127#53411yescharacteristic
138C22×C127#53812yes—
139C22×C127#54214yes—
140C22×C127#54412yes—
141C22×C127D4×Q812yes—
142C22×C127#55012yes—
143C22×C127#55112yes—
144C22×C127#55112yes—
145C22×C127#55214yes—
146C22×C127#55414yes—
147C22×C127#55511yescharacteristic
148C22×C127Q8211yescharacteristic
149C22×C127H(3,𝔽4)11yescharacteristic
150C22×C127#56311yescharacteristic
151C4×C127—28no—
152C4×C127—48no—
153C4×C127—42no—
154C4×C127—44no—
155C4×C127—44no—
156C4×C127—84no—
157#16110C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127#242314yes—
159C2×C127#248311yescharacteristic
160C2×C127#258612yes—
161C2×C127#261212yes—
162C2×C127#273311yescharacteristic
163C2×C127#273411yescharacteristic
164C2×C127#276312yes—
165C2×C127#276412yes—
166C2×#391C2×C12712yes—
167#1446C2×C12711yescharacteristic
168#1445C2×C12712yes—
169#1444C2×C12714yes—
170#1442C2×C12712yes—
171#1434C2×C12714yes—
172C127#1611011yescharacteristic, direct product factor, Sylow
173C23×Q8C22×C12711yescharacteristic
174C22×C4⋊C4C22×C12712yes—
175C22×C4⋊C4C22×C12712yes—
176C22×C4⋊C4C22×C12712yes—
177C22×C42C22×C12712yes—
178#391—28no—
179C2×#95C22×C12714yes—
180C2×#95C22×C12714yes—
181C2×#95C22×C12714yes—
182C2×#95C22×C12714yes—
183C2×#95C22×C12712yes—
184C2×#95C22×C12714yes—
185C2×#95C22×C12711yescharacteristic
186C2×#95C22×C12711yescharacteristic
187C2×#95C22×C12712yes—
188C22×Q8—28no—
189C22×Q8—41no—
190C22×Q8—41no—
191C22×Q8D4×C12714yes—
192C23×C4C23×C12714yes—
193C23×C4C23×C12711yescharacteristic
194C23×C4C23×C12712yes—
195C23×C4C23×C12714yes—
196C23×C4C23×C12712yes—
197C23×C4C23×C12712yes—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4—42no—
206C2×C42—24no—
207C2×C42—28no—
208#95—28no—
209#95—28no—
210#95—28no—
211#95—28no—
212#95—42no—
213#95—44no—
214#95—41no—
215#95—41no—
216#95Q8×C12718yescomplemented
217C24C24×C12711yescharacteristic
218C2×Q8—216no—
219C2×Q8—44no—
220C2×Q8—48no—
221C2×Q8—48no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
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×C4C2×D4×C12712yes—
250C22×C4C2×D4×C12714yes—
251C22×C4C2×Q8×C12718yes—
252C22×C4C2×Q8×C12714yes—
253C22×C4#41×C12714yes—
254C22×C4#41×C12718yes—
255C4⋊C4—48no—
256C4⋊C4—48no—
257C4⋊C4—48no—
258C42—48no—
259C23C22×D4×C12711yescharacteristic
260C23C22×Q8×C12712yes—
261C23C2×#41×C12714yes—
262C23C2×#41×C12712yes—
263C23H(5,𝔽2)×C12711yescharacteristic
264C23H(5,𝔽2)×C12711yescharacteristic
265C23H(5,𝔽2)×C12712yes—
266C232−1+4×C12712yes—
267Q8—416no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—24no—
273C2×C4—28no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—28no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4#123×C12718yes—
301C22C2×#123×C12712yes—
302C22#533×C12714yes—
303C22#534×C12711yescharacteristic
304C22#538×C12712yes—
305C22#542×C12714yes—
306C22#544×C12712yes—
307C22D4×Q8×C12712yes—
308C22#550×C12712yes—
309C22#551×C12712yes—
310C22#551×C12712yes—
311C22#552×C12714yes—
312C22#554×C12714yes—
313C22#555×C12711yescharacteristic
314C22Q82×C12711yescharacteristic
315C22H(3,𝔽4)×C12711yescharacteristic
316C22#563×C12711yescharacteristic
317C4—28no—
318C4—48no—
319C4—42no—
320C4—44no—
321C4—44no—
322C4—84no—
323C2C127×#242314yes—
324C2C127×#248311yescharacteristic
325C2C127×#258612yes—
326C2C127×#261212yes—
327C2C127×#273311yescharacteristic
328C2C127×#273411yescharacteristic
329C2C127×#276312yes—
330C2C127×#276412yes—
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
50. #95×C127Q8semidirect
157. #16110C127direct (N × H)
172. C127#16110direct (N × H)
216. #95Q8×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×#14452
C127×#14442
C127×#14422
C127×#14342
#16110127