Finite Group Databasebeta

← C127×#14955 #44578628

Subgroups — C127×#14955 #44578628

Order 32512.

1846 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C127C211yesmaximal, characteristic
2C2×#385×C127C212yesmaximal
3C22×#95×C127C211yesmaximal, characteristic
4C127×#1442C214yesmaximal, complemented
5C127×#1441C214yesmaximal, complemented
6C127×C22⋊#95C212yesmaximal
7C127×C22⋊#95C211yesmaximal, characteristic
8C24×C4×C127C2212yes—
9C24×C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2214yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2212yes—
15#385×C127—24no—
16#385×C127—28no—
17C2×#95×C127—24no—
18C2×#95×C127C2214yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2214yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2214yes—
24C25×C127C2311yescharacteristic
25C23×C4×C127—24no—
26C23×C4×C127—24no—
27C23×C4×C127—28no—
28C23×C4×C127—24no—
29C23×C4×C127—24no—
30C23×C4×C127—44no—
31C23×C4×C127—44no—
32C23×C4×C127D414yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2314yes—
38C23×C4×C127C2314yes—
39C2×C4⋊C4×C127—28no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—28no—
42C2×C4⋊C4×C127—44no—
43C2×C4⋊C4×C127—44no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—24no—
46C2×C22⋊C4×C127—22no—
47C2×C22⋊C4×C127—24no—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127D414yes—
51C2×C22⋊C4×C127Q818yes—
52#95×C127—28no—
53#95×C127—28no—
54#95×C127—24no—
55#95×C127—28no—
56#95×C127—44no—
57#95×C127—44no—
58C24×C127—24no—
59C24×C127—24no—
60C24×C127C2×D412yes—
61C24×C127C2×D412yes—
62C24×C127C2×Q814yes—
63C24×C127#4112yes—
64C24×C127#4114yes—
65C24×C127C2411yescharacteristic
66C22×C4×C127—216no—
67C22×C4×C127—28no—
68C22×C4×C127—24no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
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×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—24no—
93C22×C4×C127—48no—
94C22×C4×C127—416no—
95C22×C4×C127—416no—
96C22×C4×C127—48no—
97C22×C4×C127—416no—
98C22×C4×C127—48no—
99C22×C4×C127C2×D414yes—
100C22×C4×C127C2×D414yes—
101C22×C4×C127C2×Q818yes—
102C22×C4×C127#4118yes—
103C4⋊C4×C127—416no—
104C4⋊C4×C127—48no—
105C22⋊C4×C127—28no—
106C22⋊C4×C127—216no—
107C22⋊C4×C127—44no—
108C23×C127—24no—
109C23×C127—28no—
110C23×C127—24no—
111C23×C127—28no—
112C23×C127—28no—
113C23×C127—28no—
114C23×C127—28no—
115C23×C127—28no—
116C23×C127#12114yes—
117C23×C127C22⋊Q818yes—
118C23×C127#12314yes—
119C23×C127#12518yes—
120C23×C127C4⋊Q814yes—
121C23×C127C22×D411yescharacteristic
122C23×C127C22×D411yescharacteristic
123C23×C127C22×Q812yes—
124C23×C127C2×#4111yescharacteristic
125C23×C127C2×#4112yes—
126C23×C127C2×#4114yes—
127C23×C127H(5,𝔽2)14yes—
128C2×C4×C127—24no—
129C2×C4×C127—28no—
130C2×C4×C127—24no—
131C2×C4×C127—28no—
132C2×C4×C127—24no—
133C2×C4×C127—24no—
134C2×C4×C127—28no—
135C2×C4×C127—28no—
136C2×C4×C127—28no—
137C2×C4×C127—28no—
138C2×C4×C127—28no—
139C2×C4×C127—416no—
140C2×C4×C127—432no—
141C2×C4×C127—44no—
142C2×C4×C127—42no—
143C2×C4×C127—44no—
144C2×C4×C127—42no—
145C2×C4×C127—44no—
146C2×C4×C127—44no—
147C2×C4×C127—48no—
148C2×C4×C127—44no—
149C2×C4×C127—44no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—44no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—42no—
156C2×C4×C127—44no—
157C2×C4×C127—42no—
158C2×C4×C127—44no—
159C22×C127—28no—
160C22×C127—24no—
161C22×C127—24no—
162C22×C127—216no—
163C22×C127—216no—
164C22×C127—28no—
165C22×C127#39818yes—
166C22×C127C2×#12111yescharacteristic
167C22×C127C2×C22⋊Q812yes—
168C22×C127C2×#12311yescharacteristic
169C22×C127#52512yes—
170C22×C127C2×#12512yes—
171C22×C127#52914yes—
172C22×C127C2×C4⋊Q811yescharacteristic
173C22×C127#53412yes—
174C22×C127#53814yes—
175C22×C127#54614yes—
176C22×C127#55114yes—
177C22×C127#55414yes—
178C22×C127#55414yes—
179C4×C127—44no—
180C4×C127—48no—
181C4×C127—44no—
182C4×C127—48no—
183C4×C127—81no—
184C4×C127—81no—
185#14955C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—28no—
187C2×C127C2×#39811yescharacteristic
188C2×C127#245014yes—
189C2×C127#250514yes—
190C2×C127#253412yes—
191C2×C127#258312yes—
192C2×C127#262211yescharacteristic
193C2×C127#285311yescharacteristic
194C2×#385C2×C12711yescharacteristic
195C2×#385C2×C12712yes—
196C22×#95C2×C12711yescharacteristic
197#1442C2×C12714yescomplemented
198#1441C2×C12714yescomplemented
199C22⋊#95C2×C12712yes—
200C22⋊#95C2×C12711yescharacteristic
201C127#1495511yescharacteristic, direct product factor, Sylow
202C24×C4C22×C12712yes—
203C24×C4C22×C12711yescharacteristic
204C22×C4⋊C4C22×C12714yes—
205C22×C4⋊C4C22×C12712yes—
206C22×C22⋊C4C22×C12711yescharacteristic
207C22×C22⋊C4C22×C12711yescharacteristic
208C22×C22⋊C4C22×C12712yes—
209#385—24no—
210#385—28no—
211C2×#95—24no—
212C2×#95C22×C12714yes—
213C2×#95C22×C12714yes—
214C2×#95C22×C12714yes—
215C2×#95C22×C12712yes—
216C2×#95C22×C12714yes—
217C2×#95C22×C12714yes—
218C25C23×C12711yescharacteristic
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—28no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—44no—
225C23×C4—44no—
226C23×C4D4×C12714yes—
227C23×C4C23×C12711yescharacteristic
228C23×C4C23×C12711yescharacteristic
229C23×C4C23×C12712yes—
230C23×C4C23×C12712yes—
231C23×C4C23×C12714yes—
232C23×C4C23×C12714yes—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—28no—
236C2×C4⋊C4—44no—
237C2×C4⋊C4—44no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—24no—
244C2×C22⋊C4D4×C12714yes—
245C2×C22⋊C4Q8×C12718yes—
246#95—28no—
247#95—28no—
248#95—24no—
249#95—28no—
250#95—44no—
251#95—44no—
252C24—24no—
253C24—24no—
254C24C2×D4×C12712yes—
255C24C2×D4×C12712yes—
256C24C2×Q8×C12714yes—
257C24#41×C12712yes—
258C24#41×C12714yes—
259C24C24×C12711yescharacteristic
260C22×C4—216no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—48no—
288C22×C4—416no—
289C22×C4—416no—
290C22×C4—48no—
291C22×C4—416no—
292C22×C4—48no—
293C22×C4C2×D4×C12714yes—
294C22×C4C2×D4×C12714yes—
295C22×C4C2×Q8×C12718yes—
296C22×C4#41×C12718yes—
297C4⋊C4—416no—
298C4⋊C4—48no—
299C22⋊C4—28no—
300C22⋊C4—216no—
301C22⋊C4—44no—
302C23—24no—
303C23—28no—
304C23—24no—
305C23—28no—
306C23—28no—
307C23—28no—
308C23—28no—
309C23—28no—
310C23#121×C12714yes—
311C23C22⋊Q8×C12718yes—
312C23#123×C12714yes—
313C23#125×C12718yes—
314C23C4⋊Q8×C12714yes—
315C23C22×D4×C12711yescharacteristic
316C23C22×D4×C12711yescharacteristic
317C23C22×Q8×C12712yes—
318C23C2×#41×C12711yescharacteristic
319C23C2×#41×C12712yes—
320C23C2×#41×C12714yes—
321C23H(5,𝔽2)×C12714yes—
322C2×C4—24no—
323C2×C4—28no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—28no—
333C2×C4—416no—
334C2×C4—432no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—48no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—44no—
353C22—28no—
354C22—24no—
355C22—24no—
356C22—216no—
357C22—216no—
358C22—28no—
359C22#398×C12718yes—
360C22C2×#121×C12711yescharacteristic
361C22C2×C22⋊Q8×C12712yes—
362C22C2×#123×C12711yescharacteristic
363C22#525×C12712yes—
364C22C2×#125×C12712yes—
365C22#529×C12714yes—
366C22C2×C4⋊Q8×C12711yescharacteristic
367C22#534×C12712yes—
368C22#538×C12714yes—
369C22#546×C12714yes—
370C22#551×C12714yes—
371C22#554×C12714yes—
372C22#554×C12714yes—
373C4—44no—
374C4—48no—
375C4—48no—
376C4—44no—
377C4—81no—
378C4—81no—
379C2—28no—
380C2C2×#398×C12711yescharacteristic
381C2C127×#245014yes—
382C2C127×#250514yes—
383C2C127×#253412yes—
384C2C127×#258312yes—
385C2C127×#262211yescharacteristic
386C2C127×#285311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1442C2semidirect
5. C127×#1441C2semidirect
185. #14955C127direct (N × H)
197. #1442C2×C127semidirect
198. #1441C2×C127semidirect
201. C127#14955direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C22×#95×C1272
C127×#14422
C127×#14412
C127×C22⋊#952
#14955127