Finite Group Databasebeta

← C127×#14501 #44578174

Subgroups — C127×#14501 #44578174

Order 32512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C127×#1442C214yesmaximal
4C127×#1441C212yesmaximal
5C127×#1436C214yesmaximal
6C127×#1434C212yesmaximal
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C42×C127C2212yes—
12C22×C42×C127C2211yescharacteristic
13#391×C127—28no—
14#391×C127C418yescomplemented
15C2×#95×C127C2214yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2214yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2214yes—
23C22×Q8×C127—41no—
24C22×Q8×C127—41no—
25C22×Q8×C127—41no—
26C22×Q8×C127—41no—
27C22×Q8×C127C2×C414yes—
28C22×Q8×C127D414yes—
29C22×Q8×C127Q814yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2312yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2314yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C2×C4⋊C4×C127—24no—
37C2×C4⋊C4×C127—28no—
38C2×C4⋊C4×C127—41no—
39C2×C4⋊C4×C127—41no—
40C2×C4⋊C4×C127—42no—
41C2×C4⋊C4×C127—42no—
42C2×C4⋊C4×C127—42no—
43C2×C4⋊C4×C127C2×C414yes—
44C2×C42×C127—24no—
45C2×C42×C127—41no—
46C2×C42×C127—41no—
47C2×C42×C127—42no—
48C2×C42×C127—42no—
49C2×C42×C127C2×C414yes—
50#95×C127—28no—
51#95×C127—28no—
52#95×C127—28no—
53#95×C127—28no—
54#95×C127—42no—
55#95×C127—42no—
56#95×C127—42no—
57#95×C127C2×C4116yes—
58C24×C127C2411yescharacteristic
59C2×Q8×C127—44no—
60C2×Q8×C127—44no—
61C2×Q8×C127—44no—
62C2×Q8×C127—44no—
63C2×Q8×C127—44no—
64C2×Q8×C127—44no—
65C2×Q8×C127C4⋊C4116yescomplemented
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—22no—
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—22no—
80C22×C4×C127—22no—
81C22×C4×C127—24no—
82C22×C4×C127—22no—
83C22×C4×C127—24no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127C22×C414yes—
96C22×C4×C127C22×C414yes—
97C22×C4×C127C22×C414yes—
98C22×C4×C127C22×C412yes—
99C22×C4×C127C2×D412yes—
100C22×C4×C127C2×D414yes—
101C22×C4×C127C2×Q814yes—
102C22×C4×C127C2×Q812yes—
103C22×C4×C127#4118yes—
104C4⋊C4×C127—44no—
105C4⋊C4×C127—48no—
106C4⋊C4×C127—48no—
107C42×C127—44no—
108C42×C127—48no—
109C23×C127C23×C411yescharacteristic
110C23×C127C22×D411yescharacteristic
111C23×C127C22×Q811yescharacteristic
112C23×C127C2×#4114yes—
113C23×C127H(5,𝔽2)11yescharacteristic
114C23×C127H(5,𝔽2)11yescharacteristic
115C23×C127H(5,𝔽2)11yescharacteristic
116C23×C127H(5,𝔽2)11yescharacteristic
117C23×C1272−1+414yes—
118Q8×C127—416no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—24no—
122C2×C4×C127—24no—
123C2×C4×C127—24no—
124C2×C4×C127—24no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—22no—
128C2×C4×C127—24no—
129C2×C4×C127—22no—
130C2×C4×C127—24no—
131C2×C4×C127—24no—
132C2×C4×C127—28no—
133C2×C4×C127—24no—
134C2×C4×C127—24no—
135C2×C4×C127—24no—
136C2×C4×C127—28no—
137C2×C4×C127—28no—
138C2×C4×C127—28no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—44no—
142C2×C4×C127—44no—
143C2×C4×C127—44no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—44no—
147C2×C4×C127—44no—
148C2×C4×C127—44no—
149C2×C4×C127—44no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—44no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127C2×C4⋊C418yes—
156C2×C4×C127C2×C4⋊C414yes—
157C22×C127C22×C4⋊C411yescharacteristic
158C22×C127C4×#4112yes—
159C22×C127#51811yescharacteristic
160C22×C127#51811yescharacteristic
161C22×C127#51912yes—
162C22×C127#53411yescharacteristic
163C22×C127#53411yescharacteristic
164C22×C127#53914yes—
165C22×C127#54214yes—
166C22×C127#54311yescharacteristic
167C22×C127#54311yescharacteristic
168C22×C127#54814yes—
169C22×C127#55112yes—
170C22×C127#55512yes—
171C22×C127#55714yes—
172C22×C127#56312yes—
173C22×C127#56312yes—
174C4×C127—24no—
175C4×C127—28no—
176C4×C127—44no—
177C4×C127—44no—
178C4×C127—48no—
179C4×C127—84no—
180#14501C12711yesmaximal, characteristic, direct product factor, Sylow
181C2×C127#231511yescharacteristic
182C2×C127#233212yes—
183C2×C127#235112yes—
184C2×C127#237211yescharacteristic
185C2×C127#238111yescharacteristic
186C2×C127#272812yes—
187C2×C127#273112yes—
188C2×C127#279912yes—
189C2×C127#280912yes—
190C2×#391C2×C12712yes—
191C2×#391C2×C12711yescharacteristic
192#1442C2×C12714yes—
193#1441C2×C12712yes—
194#1436C2×C12714yes—
195#1434C2×C12712yes—
196C127#1450111yescharacteristic, direct product factor, Sylow
197C23×Q8C22×C12711yescharacteristic
198C22×C4⋊C4C22×C12712yes—
199C22×C4⋊C4C22×C12712yes—
200C22×C4⋊C4C22×C12711yescharacteristic
201C22×C42C22×C12712yes—
202C22×C42C22×C12711yescharacteristic
203#391—28no—
204#391C4×C12718yescomplemented
205C2×#95C22×C12714yes—
206C2×#95C22×C12714yes—
207C2×#95C22×C12714yes—
208C2×#95C22×C12714yes—
209C2×#95C22×C12712yes—
210C2×#95C22×C12712yes—
211C2×#95C22×C12712yes—
212C2×#95C22×C12714yes—
213C22×Q8—41no—
214C22×Q8—41no—
215C22×Q8—41no—
216C22×Q8—41no—
217C22×Q8C2×C4×C12714yes—
218C22×Q8D4×C12714yes—
219C22×Q8Q8×C12714yes—
220C23×C4C23×C12714yes—
221C23×C4C23×C12712yes—
222C23×C4C23×C12712yes—
223C23×C4C23×C12714yes—
224C23×C4C23×C12712yes—
225C23×C4C23×C12711yescharacteristic
226C2×C4⋊C4—24no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4C2×C4×C12714yes—
234C2×C42—24no—
235C2×C42—41no—
236C2×C42—41no—
237C2×C42—42no—
238C2×C42—42no—
239C2×C42C2×C4×C12714yes—
240#95—28no—
241#95—28no—
242#95—28no—
243#95—28no—
244#95—42no—
245#95—42no—
246#95—42no—
247#95C2×C4×C127116yes—
248C24C24×C12711yescharacteristic
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—44no—
254C2×Q8—44no—
255C2×Q8C4⋊C4×C127116yescomplemented
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4C22×C4×C12714yes—
286C22×C4C22×C4×C12714yes—
287C22×C4C22×C4×C12714yes—
288C22×C4C22×C4×C12712yes—
289C22×C4C2×D4×C12712yes—
290C22×C4C2×D4×C12714yes—
291C22×C4C2×Q8×C12714yes—
292C22×C4C2×Q8×C12712yes—
293C22×C4#41×C12718yes—
294C4⋊C4—44no—
295C4⋊C4—48no—
296C4⋊C4—48no—
297C42—44no—
298C42—48no—
299C23C23×C4×C12711yescharacteristic
300C23C22×D4×C12711yescharacteristic
301C23C22×Q8×C12711yescharacteristic
302C23C2×#41×C12714yes—
303C23H(5,𝔽2)×C12711yescharacteristic
304C23H(5,𝔽2)×C12711yescharacteristic
305C23H(5,𝔽2)×C12711yescharacteristic
306C23H(5,𝔽2)×C12711yescharacteristic
307C232−1+4×C12714yes—
308Q8—416no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—28no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—28no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4C2×C4⋊C4×C12718yes—
346C2×C4C2×C4⋊C4×C12714yes—
347C22C22×C4⋊C4×C12711yescharacteristic
348C22C4×#41×C12712yes—
349C22#518×C12711yescharacteristic
350C22#518×C12711yescharacteristic
351C22#519×C12712yes—
352C22#534×C12711yescharacteristic
353C22#534×C12711yescharacteristic
354C22#539×C12714yes—
355C22#542×C12714yes—
356C22#543×C12711yescharacteristic
357C22#543×C12711yescharacteristic
358C22#548×C12714yes—
359C22#551×C12712yes—
360C22#555×C12712yes—
361C22#557×C12714yes—
362C22#563×C12712yes—
363C22#563×C12712yes—
364C4—24no—
365C4—28no—
366C4—44no—
367C4—44no—
368C4—48no—
369C4—84no—
370C2C127×#231511yescharacteristic
371C2C127×#233212yes—
372C2C127×#235112yes—
373C2C127×#237211yescharacteristic
374C2C127×#238111yescharacteristic
375C2C127×#272812yes—
376C2C127×#273112yes—
377C2C127×#279912yes—
378C2C127×#280912yes—
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
14. #391×C127C4semidirect
65. C2×Q8×C127C4⋊C4semidirect
180. #14501C127direct (N × H)
196. C127#14501direct (N × H)
204. #391C4×C127semidirect
255. C2×Q8C4⋊C4×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×#14422
C127×#14412
C127×#14362
C127×#14342
#14501127