Finite Group Databasebeta

← C127×#14705 #44578378

Subgroups — C127×#14705 #44578378

Order 32512.

2430 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C127C211yesmaximal, characteristic
2C2×#385×C127C212yesmaximal
3C2×#381×C127C211yesmaximal, characteristic
4C2×#381×C127C211yesmaximal, characteristic
5C127×#1436C218yesmaximal, complemented
6C127×C22⋊#95C212yesmaximal
7C24×C4×C127C2212yes—
8C24×C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127C2214yes—
10C22×C22⋊C4×C127C2211yescharacteristic
11C22×C22⋊C4×C127C2211yescharacteristic
12C22×C22⋊C4×C127C2212yes—
13C22×C42×C127—28no—
14C22×C42×C127—24no—
15C22×C42×C127C2214yes—
16#385×C127—28no—
17#381×C127—24no—
18#381×C127C418yescomplemented
19C2×#95×C127C2218yes—
20C2×#95×C127C2214yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2214yes—
23C25×C127C2311yescharacteristic
24C23×C4×C127—24no—
25C23×C4×C127—24no—
26C23×C4×C127—24no—
27C23×C4×C127—24no—
28C23×C4×C127—216no—
29C23×C4×C127C2×C414yes—
30C23×C4×C127D418yes—
31C23×C4×C127D414yes—
32C23×C4×C127Q814yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2314yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2314yes—
38C2×C4⋊C4×C127—28no—
39C2×C4⋊C4×C127—216no—
40C2×C22⋊C4×C127—24no—
41C2×C22⋊C4×C127—24no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—24no—
45C2×C22⋊C4×C127—24no—
46C2×C22⋊C4×C127C2×C418yes—
47C2×C42×C127—232no—
48C2×C42×C127—28no—
49C2×C42×C127—216no—
50#95×C127—28no—
51#95×C127—28no—
52#95×C127—216no—
53#95×C127C2×C4116yescomplemented
54C24×C127—28no—
55C24×C127C22×C412yes—
56C24×C127C2×D412yes—
57C24×C127C2×D414yes—
58C24×C127C2×Q812yes—
59C24×C127#4114yes—
60C24×C127C2411yescharacteristic
61C22×C4×C127—232no—
62C22×C4×C127—232no—
63C22×C4×C127—216no—
64C22×C4×C127—216no—
65C22×C4×C127—28no—
66C22×C4×C127—216no—
67C22×C4×C127—28no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—28no—
73C22×C4×C127—232no—
74C22×C4×C127—24no—
75C22×C4×C127—28no—
76C22×C4×C127—24no—
77C22×C4×C127—28no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—28no—
83C22×C4×C127—24no—
84C22×C4×C127—28no—
85C22×C4×C127C4⋊C4116yescomplemented
86C22×C4×C127C22×C418yes—
87C22×C4×C127C22×C414yes—
88C22×C4×C127C2×D414yes—
89C22×C4×C127C2×D418yes—
90C22×C4×C127C2×Q814yes—
91C22×C4×C127#41116yes—
92C4⋊C4×C127—416no—
93C22⋊C4×C127—216no—
94C22⋊C4×C127—44no—
95C22⋊C4×C127—44no—
96C42×C127—232no—
97C23×C127—28no—
98C23×C127—28no—
99C23×C127—28no—
100C23×C127—28no—
101C23×C127—216no—
102C23×C127—28no—
103C23×C127C2×C4⋊C414yes—
104C23×C127C4×D418yes—
105C23×C127#12014yes—
106C23×C127C22⋊Q818yes—
107C23×C127#12314yes—
108C23×C127C23×C411yescharacteristic
109C23×C127C22×D411yescharacteristic
110C23×C127C22×D412yes—
111C23×C127C22×Q811yescharacteristic
112C23×C127C2×#4112yes—
113C23×C127C2×#4118yes—
114C2×C4×C127—264no—
115C2×C4×C127—28no—
116C2×C4×C127—28no—
117C2×C4×C127—24no—
118C2×C4×C127—28no—
119C2×C4×C127—28no—
120C2×C4×C127—24no—
121C2×C4×C127—216no—
122C2×C4×C127—216no—
123C2×C4×C127—232no—
124C2×C4×C127—28no—
125C2×C4×C127—216no—
126C2×C4×C127—44no—
127C2×C4×C127—44no—
128C2×C4×C127—48no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—44no—
132C2×C4×C127—44no—
133C2×C4×C127—44no—
134C2×C4×C127—44no—
135C2×C4×C127—48no—
136C2×C4×C127C2×C4⋊C418yes—
137C2×C4×C127#123116yes—
138C22×C127—28no—
139C22×C127—28no—
140C22×C127—216no—
141C22×C127—28no—
142C22×C127—216no—
143C22×C127#38518yes—
144C22×C127C22×C4⋊C411yescharacteristic
145C22×C127C2×C4×D412yes—
146C22×C127C4×#4114yes—
147C22×C127C2×#12011yescharacteristic
148C22×C127C2×C22⋊Q812yes—
149C22×C127C2×#12314yes—
150C22×C127C2×#12311yescharacteristic
151C22×C127#52514yes—
152C22×C127#52514yes—
153C22×C127#52918yes—
154C22×C127#53314yes—
155C4×C127—216no—
156C4×C127—28no—
157C4×C127—48no—
158C4×C127—82no—
159C4×C127—82no—
160#14705C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—28no—
162C2×C127C2×#38511yescharacteristic
163C2×C127#229612yes—
164C2×C127C4×#12314yes—
165C2×C127#284912yes—
166C2×C127#285312yes—
167C2×C127#285514yes—
168C23×C42C2×C12711yescharacteristic
169C2×#385C2×C12712yes—
170C2×#381C2×C12711yescharacteristic
171C2×#381C2×C12711yescharacteristic
172#1436C2×C12718yescomplemented
173C22⋊#95C2×C12712yes—
174C127#1470511yescharacteristic, direct product factor, Sylow
175C24×C4C22×C12712yes—
176C24×C4C22×C12711yescharacteristic
177C22×C4⋊C4C22×C12714yes—
178C22×C22⋊C4C22×C12711yescharacteristic
179C22×C22⋊C4C22×C12711yescharacteristic
180C22×C22⋊C4C22×C12712yes—
181C22×C42—28no—
182C22×C42—24no—
183C22×C42C22×C12714yes—
184#385—28no—
185#381—24no—
186#381C4×C12718yescomplemented
187C2×#95C22×C12718yes—
188C2×#95C22×C12714yes—
189C2×#95C22×C12714yes—
190C2×#95C22×C12714yes—
191C25C23×C12711yescharacteristic
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—216no—
197C23×C4C2×C4×C12714yes—
198C23×C4D4×C12718yes—
199C23×C4D4×C12714yes—
200C23×C4Q8×C12714yes—
201C23×C4C23×C12712yes—
202C23×C4C23×C12712yes—
203C23×C4C23×C12714yes—
204C23×C4C23×C12712yes—
205C23×C4C23×C12714yes—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—216no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—24no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—24no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4C2×C4×C12718yes—
215C2×C42—232no—
216C2×C42—28no—
217C2×C42—216no—
218#95—28no—
219#95—28no—
220#95—216no—
221#95C2×C4×C127116yescomplemented
222C24—28no—
223C24C22×C4×C12712yes—
224C24C2×D4×C12712yes—
225C24C2×D4×C12714yes—
226C24C2×Q8×C12712yes—
227C24#41×C12714yes—
228C24C24×C12711yescharacteristic
229C22×C4—232no—
230C22×C4—232no—
231C22×C4—216no—
232C22×C4—216no—
233C22×C4—28no—
234C22×C4—216no—
235C22×C4—28no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—28no—
241C22×C4—232no—
242C22×C4—24no—
243C22×C4—28no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—28no—
253C22×C4C4⋊C4×C127116yescomplemented
254C22×C4C22×C4×C12718yes—
255C22×C4C22×C4×C12714yes—
256C22×C4C2×D4×C12714yes—
257C22×C4C2×D4×C12718yes—
258C22×C4C2×Q8×C12714yes—
259C22×C4#41×C127116yes—
260C4⋊C4—416no—
261C22⋊C4—216no—
262C22⋊C4—44no—
263C22⋊C4—44no—
264C42—232no—
265C23—28no—
266C23—28no—
267C23—28no—
268C23—28no—
269C23—216no—
270C23—28no—
271C23C2×C4⋊C4×C12714yes—
272C23C4×D4×C12718yes—
273C23#120×C12714yes—
274C23C22⋊Q8×C12718yes—
275C23#123×C12714yes—
276C23C23×C4×C12711yescharacteristic
277C23C22×D4×C12711yescharacteristic
278C23C22×D4×C12712yes—
279C23C22×Q8×C12711yescharacteristic
280C23C2×#41×C12712yes—
281C23C2×#41×C12718yes—
282C2×C4—264no—
283C2×C4—28no—
284C2×C4—28no—
285C2×C4—24no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—24no—
289C2×C4—216no—
290C2×C4—216no—
291C2×C4—232no—
292C2×C4—28no—
293C2×C4—216no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—48no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—48no—
304C2×C4C2×C4⋊C4×C12718yes—
305C2×C4#123×C127116yes—
306C22—28no—
307C22—28no—
308C22—216no—
309C22—28no—
310C22—216no—
311C22#385×C12718yes—
312C22C22×C4⋊C4×C12711yescharacteristic
313C22C2×C4×D4×C12712yes—
314C22C4×#41×C12714yes—
315C22C2×#120×C12711yescharacteristic
316C22C2×C22⋊Q8×C12712yes—
317C22C2×#123×C12714yes—
318C22C2×#123×C12711yescharacteristic
319C22#525×C12714yes—
320C22#525×C12714yes—
321C22#529×C12718yes—
322C22#533×C12714yes—
323C4—216no—
324C4—28no—
325C4—48no—
326C4—82no—
327C4—82no—
328C2—28no—
329C2C2×#385×C12711yescharacteristic
330C2C127×#229612yes—
331C2C4×#123×C12714yes—
332C2C127×#284912yes—
333C2C127×#285312yes—
334C2C127×#285514yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C127×#1436C2semidirect
18. #381×C127C4semidirect
53. #95×C127C2×C4semidirect
85. C22×C4×C127C4⋊C4semidirect
160. #14705C127direct (N × H)
172. #1436C2×C127semidirect
174. C127#14705direct (N × H)
186. #381C4×C127semidirect
221. #95C2×C4×C127semidirect
253. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C1272
C2×#385×C1272
C2×#381×C1272
C127×#14362
C127×C22⋊#952
#14705127