Finite Group Databasebeta

← C127×#14331 #44578004

Subgroups — C127×#14331 #44578004

Order 32512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C127C211yesmaximal, characteristic
2C127×#1445C213yesmaximal, complemented
3C127×#1443C211yesmaximal, characteristic, complemented
4C127×#1440C213yesmaximal
5C127×#1437C213yesmaximal
6C127×#1436C213yesmaximal, complemented
7C4×#95×C127C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C127C2213yes—
9C22×C22⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2213yes—
11C22×C22⋊C4×C127C2213yes—
12C22×C42×C127C2213yes—
13#396×C127C418yescomplemented
14C2×#95×C127C2213yes—
15C2×#95×C127C2213yes—
16C2×#95×C127C2213yes—
17C2×#95×C127C2213yes—
18C2×#95×C127C2213yes—
19C2×#95×C127C2213yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2211yescharacteristic
22C25×C127C2311yescharacteristic
23C23×C4×C127C2313yes—
24C23×C4×C127C2311yescharacteristic
25C23×C4×C127C2313yes—
26C23×C4×C127C2313yes—
27C23×C4×C127C2313yes—
28C23×C4×C127C2311yescharacteristic
29C2×C4⋊C4×C127—43no—
30C2×C4⋊C4×C127—43no—
31C2×C4⋊C4×C127C2×C4112yes—
32C2×C22⋊C4×C127—26no—
33C2×C22⋊C4×C127—26no—
34C2×C22⋊C4×C127—43no—
35C2×C22⋊C4×C127—43no—
36C2×C22⋊C4×C127—43no—
37C2×C22⋊C4×C127—43no—
38C2×C22⋊C4×C127C2×C4112yes—
39C2×C42×C127—26no—
40C2×C42×C127—43no—
41C2×C42×C127—43no—
42#95×C127—26no—
43#95×C127—26no—
44#95×C127—26no—
45#95×C127—43no—
46#95×C127—43no—
47#95×C127—43no—
48#95×C127—43no—
49#95×C127C2×C414yes—
50C24×C127—23no—
51C24×C127—23no—
52C24×C127—23no—
53C24×C127—23no—
54C24×C127—21no—
55C24×C127—21no—
56C24×C127C22×C412yes—
57C24×C127C2411yescharacteristic
58C22×C4×C127—23no—
59C22×C4×C127—21no—
60C22×C4×C127—23no—
61C22×C4×C127—23no—
62C22×C4×C127—23no—
63C22×C4×C127—23no—
64C22×C4×C127—23no—
65C22×C4×C127—23no—
66C22×C4×C127—23no—
67C22×C4×C127—23no—
68C22×C4×C127—23no—
69C22×C4×C127—23no—
70C22×C4×C127—23no—
71C22×C4×C127—23no—
72C22×C4×C127—23no—
73C22×C4×C127—23no—
74C22×C4×C127—23no—
75C22×C4×C127—23no—
76C22×C4×C127—23no—
77C22×C4×C127—23no—
78C22×C4×C127—23no—
79C22×C4×C127—23no—
80C22×C4×C127—23no—
81C22×C4×C127—23no—
82C22×C4×C127—23no—
83C22×C4×C127—23no—
84C22×C4×C127—23no—
85C22×C4×C127—23no—
86C22×C4×C127—23no—
87C22×C4×C127—21no—
88C22×C4×C127C22×C416yes—
89C22×C4×C127C22×C416yes—
90C22×C4×C127#4116yes—
91C22×C4×C127#4116yes—
92C4⋊C4×C127—412no—
93C22⋊C4×C127—412no—
94C22⋊C4×C127—412no—
95C22⋊C4×C127—44no—
96C42×C127—412no—
97C23×C127—26no—
98C23×C127—26no—
99C23×C127—22no—
100C23×C127—41no—
101C23×C127—43no—
102C23×C127—43no—
103C23×C127—43no—
104C23×C127—43no—
105C23×C127—43no—
106C23×C127—43no—
107C23×C127—43no—
108C23×C127—43no—
109C23×C127—43no—
110C23×C127C23×C411yescharacteristic
111C23×C127C2×#4113yes—
112C23×C127C2×#4113yes—
113C23×C127H(5,𝔽2)13yes—
114C23×C127H(5,𝔽2)13yes—
115C23×C1272−1+411yescharacteristic
116C23×C1272−1+411yescharacteristic
117C2×C4×C127—26no—
118C2×C4×C127—26no—
119C2×C4×C127—26no—
120C2×C4×C127—26no—
121C2×C4×C127—26no—
122C2×C4×C127—26no—
123C2×C4×C127—26no—
124C2×C4×C127—26no—
125C2×C4×C127—26no—
126C2×C4×C127—26no—
127C2×C4×C127—26no—
128C2×C4×C127—43no—
129C2×C4×C127—43no—
130C2×C4×C127—43no—
131C2×C4×C127—43no—
132C2×C4×C127—43no—
133C2×C4×C127—43no—
134C2×C4×C127—43no—
135C2×C4×C127—43no—
136C2×C4×C127—43no—
137C2×C4×C127—43no—
138C2×C4×C127—43no—
139C2×C4×C127—43no—
140C2×C4×C127—41no—
141C2×C4×C127—43no—
142C2×C4×C127—43no—
143C2×C4×C127—43no—
144C2×C4×C127—43no—
145C2×C4×C127—43no—
146C2×C4×C127—43no—
147C2×C4×C127—43no—
148C2×C4×C127—43no—
149C2×C4×C127—43no—
150C2×C4×C127#12614yes—
151C22×C127—42no—
152C22×C127—46no—
153C22×C127—46no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127—83no—
157C22×C127—83no—
158C22×C127C4×#4113yes—
159C22×C127#51813yes—
160C22×C127#51911yescharacteristic
161C22×C127C2×#12611yescharacteristic
162C22×C127#52913yes—
163C22×C127#53813yes—
164C22×C127#53813yes—
165C22×C127#53913yes—
166C22×C127#53913yes—
167C22×C127#54013yes—
168C22×C127#54013yes—
169C22×C127#54213yes—
170C22×C127#54213yes—
171C4×C127—24no—
172C4×C127—46no—
173C4×C127—46no—
174C4×C127—46no—
175C4×C127—81no—
176C4×C127—83no—
177#14331C12711yesmaximal, characteristic, direct product factor, Sylow
178C2×C127—82no—
179C2×C127C4×#12611yescharacteristic
180C2×C127#233213yes—
181C2×C127#233313yes—
182C2×C127#264311yescharacteristic
183C2×C127#264411yescharacteristic
184C2×C127#264913yes—
185C2×C127#265113yes—
186C2×#396C2×C12711yescharacteristic
187#1445C2×C12713yescomplemented
188#1443C2×C12711yescharacteristic, complemented
189#1440C2×C12713yes—
190#1437C2×C12713yes—
191#1436C2×C12713yescomplemented
192C4×#95C2×C12711yescharacteristic, complemented
193C127#1433111yescharacteristic, direct product factor, Sylow
194C22×C4⋊C4C22×C12713yes—
195C22×C22⋊C4C22×C12711yescharacteristic
196C22×C22⋊C4C22×C12713yes—
197C22×C22⋊C4C22×C12713yes—
198C22×C42C22×C12713yes—
199#396C4×C12718yescomplemented
200C2×#95C22×C12713yes—
201C2×#95C22×C12713yes—
202C2×#95C22×C12713yes—
203C2×#95C22×C12713yes—
204C2×#95C22×C12713yes—
205C2×#95C22×C12713yes—
206C2×#95C22×C12713yes—
207C2×#95C22×C12711yescharacteristic
208C25C23×C12711yescharacteristic
209C23×C4C23×C12713yes—
210C23×C4C23×C12711yescharacteristic
211C23×C4C23×C12713yes—
212C23×C4C23×C12713yes—
213C23×C4C23×C12713yes—
214C23×C4C23×C12711yescharacteristic
215C2×C4⋊C4—43no—
216C2×C4⋊C4—43no—
217C2×C4⋊C4C2×C4×C127112yes—
218C2×C22⋊C4—26no—
219C2×C22⋊C4—26no—
220C2×C22⋊C4—43no—
221C2×C22⋊C4—43no—
222C2×C22⋊C4—43no—
223C2×C22⋊C4—43no—
224C2×C22⋊C4C2×C4×C127112yes—
225C2×C42—26no—
226C2×C42—43no—
227C2×C42—43no—
228#95—26no—
229#95—26no—
230#95—26no—
231#95—43no—
232#95—43no—
233#95—43no—
234#95—43no—
235#95C2×C4×C12714yes—
236C24—23no—
237C24—23no—
238C24—23no—
239C24—23no—
240C24—21no—
241C24—21no—
242C24C22×C4×C12712yes—
243C24C24×C12711yescharacteristic
244C22×C4—23no—
245C22×C4—21no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—21no—
274C22×C4C22×C4×C12716yes—
275C22×C4C22×C4×C12716yes—
276C22×C4#41×C12716yes—
277C22×C4#41×C12716yes—
278C4⋊C4—412no—
279C22⋊C4—412no—
280C22⋊C4—412no—
281C22⋊C4—44no—
282C42—412no—
283C23—26no—
284C23—26no—
285C23—22no—
286C23—41no—
287C23—43no—
288C23—43no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23C23×C4×C12711yescharacteristic
297C23C2×#41×C12713yes—
298C23C2×#41×C12713yes—
299C23H(5,𝔽2)×C12713yes—
300C23H(5,𝔽2)×C12713yes—
301C232−1+4×C12711yescharacteristic
302C232−1+4×C12711yescharacteristic
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—43no—
315C2×C4—43no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—41no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4#126×C12714yes—
337C22—46no—
338C22—46no—
339C22—42no—
340C22—81no—
341C22—81no—
342C22—83no—
343C22—83no—
344C22C4×#41×C12713yes—
345C22#518×C12713yes—
346C22#519×C12711yescharacteristic
347C22C2×#126×C12711yescharacteristic
348C22#529×C12713yes—
349C22#538×C12713yes—
350C22#538×C12713yes—
351C22#539×C12713yes—
352C22#539×C12713yes—
353C22#540×C12713yes—
354C22#540×C12713yes—
355C22#542×C12713yes—
356C22#542×C12713yes—
357C4—24no—
358C4—46no—
359C4—46no—
360C4—46no—
361C4—81no—
362C4—83no—
363C2—82no—
364C2C4×#126×C12711yescharacteristic
365C2C127×#233213yes—
366C2C127×#233313yes—
367C2C127×#264311yescharacteristic
368C2C127×#264411yescharacteristic
369C2C127×#264913yes—
370C2C127×#265113yes—
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
2. C127×#1445C2semidirect
3. C127×#1443C2semidirect
6. C127×#1436C2semidirect
7. C4×#95×C127C2semidirect
13. #396×C127C4semidirect
177. #14331C127direct (N × H)
187. #1445C2×C127semidirect
188. #1443C2×C127semidirect
191. #1436C2×C127semidirect
192. C4×#95C2×C127semidirect
193. C127#14331direct (N × H)
199. #396C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1272
C127×#14452
C127×#14432
C127×#14402
C127×#14372
C127×#14362
C4×#95×C1272
#14331127