Finite Group Databasebeta

← C127×#13809 #44577482

Subgroups — C127×#13809 #44577482

Order 32512.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊C4×C127C213yesmaximal
2C2×#376×C127C211yesmaximal, characteristic, complemented
3C22×#95×C127C211yesmaximal, characteristic
4C127×#1434C213yesmaximal, complemented
5C127×#1434C213yesmaximal, complemented
6C127×C22⋊#95C213yesmaximal
7C4×#95×C127C211yesmaximal, characteristic, complemented
8C24×C4×C127C2213yes—
9C22×C22⋊C4×C127C2213yes—
10C22×C22⋊C4×C127C2211yescharacteristic
11C22×C42×C127C2213yes—
12C22×C42×C127C2213yes—
13C4×C22⋊C4×C127C4124yescomplemented
14#376×C127—24no—
15C2×#95×C127—24no—
16C2×#95×C127C2213yes—
17C2×#95×C127C2213yes—
18C2×#95×C127C2213yes—
19C2×#95×C127C2216yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2213yes—
22C2×#95×C127C2211yescharacteristic
23C25×C127C2311yescharacteristic
24C23×C4×C127—212no—
25C23×C4×C127—26no—
26C23×C4×C127—26no—
27C23×C4×C127—46no—
28C23×C4×C127C2×C4112yes—
29C23×C4×C127C2313yes—
30C23×C4×C127C2313yes—
31C23×C4×C127C2313yes—
32C23×C4×C127C2311yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2313yes—
35C2×C22⋊C4×C127—26no—
36C2×C22⋊C4×C127—26no—
37C2×C22⋊C4×C127C2×C4112yes—
38C2×C22⋊C4×C127C2×C4112yes—
39C2×C42×C127—26no—
40C2×C42×C127—26no—
41C2×C42×C127—46no—
42C2×C42×C127C2×C4112yescomplemented
43C2×C42×C127C2×C4112yescomplemented
44#95×C127—26no—
45#95×C127—26no—
46#95×C127—26no—
47#95×C127—46no—
48#95×C127C2×C4112yescomplemented
49#95×C127C2×C4112yescomplemented
50#95×C127D414yes—
51C24×C127—21no—
52C24×C127—23no—
53C24×C127—23no—
54C24×C127—21no—
55C24×C127C22×C416yes—
56C24×C127#4112yes—
57C24×C127#4116yes—
58C24×C127C2411yescharacteristic
59C22×C4×C127—21no—
60C22×C4×C127—23no—
61C22×C4×C127—26no—
62C22×C4×C127—23no—
63C22×C4×C127—26no—
64C22×C4×C127—21no—
65C22×C4×C127—224no—
66C22×C4×C127—23no—
67C22×C4×C127—23no—
68C22×C4×C127—26no—
69C22×C4×C127—23no—
70C22×C4×C127—23no—
71C22×C4×C127—23no—
72C22×C4×C127—23no—
73C22×C4×C127—23no—
74C22×C4×C127—26no—
75C22×C4×C127—23no—
76C22×C4×C127—23no—
77C22×C4×C127—26no—
78C22×C4×C127—26no—
79C22×C4×C127—23no—
80C22×C4×C127—224no—
81C22×C4×C127—412no—
82C22×C4×C127—424no—
83C22×C4×C127—424no—
84C22×C4×C127C22×C416yes—
85C22×C4×C127C22×C416yes—
86C22×C4×C127C22×C416yes—
87C22×C4×C127C22×C416yes—
88C22×C4×C127C22×C416yes—
89C22×C4×C127C22×C416yes—
90C22×C4×C127C2×D416yes—
91C22×C4×C127#4116yes—
92C22⋊C4×C127—224no—
93C22⋊C4×C127C42116yes—
94C42×C127—224no—
95C42×C127—412no—
96C23×C127—26no—
97C23×C127—26no—
98C23×C127—26no—
99C23×C127—26no—
100C23×C127—26no—
101C23×C127—22no—
102C23×C127—212no—
103C23×C127—26no—
104C23×C127—26no—
105C23×C127C2×C4214yes—
106C23×C127#117112yes—
107C23×C127#117112yes—
108C23×C127C23×C413yes—
109C23×C127C22×D411yescharacteristic
110C23×C127C2×#4113yes—
111C23×C127C2×#4111yescharacteristic
112C23×C127C2×#4113yes—
113C23×C127H(5,𝔽2)13yes—
114C23×C1272−1+411yescharacteristic
115C2×C4×C127—26no—
116C2×C4×C127—26no—
117C2×C4×C127—26no—
118C2×C4×C127—26no—
119C2×C4×C127—26no—
120C2×C4×C127—26no—
121C2×C4×C127—212no—
122C2×C4×C127—212no—
123C2×C4×C127—26no—
124C2×C4×C127—26no—
125C2×C4×C127—26no—
126C2×C4×C127—26no—
127C2×C4×C127—26no—
128C2×C4×C127—26no—
129C2×C4×C127—26no—
130C2×C4×C127—26no—
131C2×C4×C127—26no—
132C2×C4×C127—448no—
133C2×C4×C127—43no—
134C2×C4×C127—46no—
135C2×C4×C127—43no—
136C2×C4×C127—46no—
137C2×C4×C127—46no—
138C2×C4×C127—43no—
139C2×C4×C127—43no—
140C2×C4×C127—46no—
141C2×C4×C127C2×C4214yes—
142C2×C4×C127C2×C4214yes—
143C2×C4×C127C4×D4112yes—
144C22×C127—212no—
145C22×C127—212no—
146C22×C127—212no—
147C22×C127—212no—
148C22×C127—24no—
149C22×C127—24no—
150C22×C127#37618yescomplemented
151C22×C127C22×C4211yescharacteristic
152C22×C127C2×#11713yes—
153C22×C127C2×#11713yes—
154C22×C127C2×C4×D413yes—
155C22×C127C4×#4113yes—
156C22×C127#51813yes—
157C22×C127#52013yes—
158C22×C127#54613yes—
159C22×C127#54811yescharacteristic
160C22×C127#55116yes—
161C22×C127#55213yes—
162C22×C127#55313yes—
163C4×C127—212no—
164C4×C127—24no—
165C4×C127—24no—
166C4×C127—46no—
167C4×C127—46no—
168C4×C127—46no—
169#13809C12711yesmaximal, characteristic, direct product factor, Sylow
170C2×C127—28no—
171C2×C127C2×#37611yescharacteristic
172C2×C127C42×D411yescharacteristic
173C2×C127#227511yescharacteristic
174C2×C127#234213yes—
175C2×C127#234313yes—
176C2×C127#235213yes—
177C2×C127#235313yes—
178C2×C4×C22⋊C4C2×C12713yes—
179C2×#376C2×C12711yescharacteristic, complemented
180C22×#95C2×C12711yescharacteristic
181#1434C2×C12713yescomplemented
182#1434C2×C12713yescomplemented
183C22⋊#95C2×C12713yes—
184C4×#95C2×C12711yescharacteristic, complemented
185C127#1380911yescharacteristic, direct product factor, Sylow
186C24×C4C22×C12713yes—
187C22×C22⋊C4C22×C12713yes—
188C22×C22⋊C4C22×C12711yescharacteristic
189C22×C42C22×C12713yes—
190C22×C42C22×C12713yes—
191C4×C22⋊C4C4×C127124yescomplemented
192#376—24no—
193C2×#95—24no—
194C2×#95C22×C12713yes—
195C2×#95C22×C12713yes—
196C2×#95C22×C12713yes—
197C2×#95C22×C12716yes—
198C2×#95C22×C12713yes—
199C2×#95C22×C12713yes—
200C2×#95C22×C12711yescharacteristic
201C25C23×C12711yescharacteristic
202C23×C4—212no—
203C23×C4—26no—
204C23×C4—26no—
205C23×C4—46no—
206C23×C4C2×C4×C127112yes—
207C23×C4C23×C12713yes—
208C23×C4C23×C12713yes—
209C23×C4C23×C12713yes—
210C23×C4C23×C12711yescharacteristic
211C23×C4C23×C12711yescharacteristic
212C23×C4C23×C12713yes—
213C2×C22⋊C4—26no—
214C2×C22⋊C4—26no—
215C2×C22⋊C4C2×C4×C127112yes—
216C2×C22⋊C4C2×C4×C127112yes—
217C2×C42—26no—
218C2×C42—26no—
219C2×C42—46no—
220C2×C42C2×C4×C127112yescomplemented
221C2×C42C2×C4×C127112yescomplemented
222#95—26no—
223#95—26no—
224#95—26no—
225#95—46no—
226#95C2×C4×C127112yescomplemented
227#95C2×C4×C127112yescomplemented
228#95D4×C12714yes—
229C24—21no—
230C24—23no—
231C24—23no—
232C24—21no—
233C24C22×C4×C12716yes—
234C24#41×C12712yes—
235C24#41×C12716yes—
236C24C24×C12711yescharacteristic
237C22×C4—21no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—21no—
243C22×C4—224no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—26no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—26no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—26no—
256C22×C4—26no—
257C22×C4—23no—
258C22×C4—224no—
259C22×C4—412no—
260C22×C4—424no—
261C22×C4—424no—
262C22×C4C22×C4×C12716yes—
263C22×C4C22×C4×C12716yes—
264C22×C4C22×C4×C12716yes—
265C22×C4C22×C4×C12716yes—
266C22×C4C22×C4×C12716yes—
267C22×C4C22×C4×C12716yes—
268C22×C4C2×D4×C12716yes—
269C22×C4#41×C12716yes—
270C22⋊C4—224no—
271C22⋊C4C42×C127116yes—
272C42—224no—
273C42—412no—
274C23—26no—
275C23—26no—
276C23—26no—
277C23—26no—
278C23—26no—
279C23—22no—
280C23—212no—
281C23—26no—
282C23—26no—
283C23C2×C42×C12714yes—
284C23#117×C127112yes—
285C23#117×C127112yes—
286C23C23×C4×C12713yes—
287C23C22×D4×C12711yescharacteristic
288C23C2×#41×C12713yes—
289C23C2×#41×C12711yescharacteristic
290C23C2×#41×C12713yes—
291C23H(5,𝔽2)×C12713yes—
292C232−1+4×C12711yescharacteristic
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—212no—
300C2×C4—212no—
301C2×C4—26no—
302C2×C4—26no—
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—448no—
311C2×C4—46no—
312C2×C4—43no—
313C2×C4—43no—
314C2×C4—46no—
315C2×C4—46no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—46no—
319C2×C4C2×C42×C12714yes—
320C2×C4C2×C42×C12714yes—
321C2×C4C4×D4×C127112yes—
322C22—212no—
323C22—212no—
324C22—212no—
325C22—212no—
326C22—24no—
327C22—24no—
328C22#376×C12718yescomplemented
329C22C22×C42×C12711yescharacteristic
330C22C2×#117×C12713yes—
331C22C2×#117×C12713yes—
332C22C2×C4×D4×C12713yes—
333C22C4×#41×C12713yes—
334C22#518×C12713yes—
335C22#520×C12713yes—
336C22#546×C12713yes—
337C22#548×C12711yescharacteristic
338C22#551×C12716yes—
339C22#552×C12713yes—
340C22#553×C12713yes—
341C4—212no—
342C4—24no—
343C4—24no—
344C4—46no—
345C4—46no—
346C4—46no—
347C2—28no—
348C2C2×#376×C12711yescharacteristic
349C2C42×D4×C12711yescharacteristic
350C2C127×#227511yescharacteristic
351C2C127×#234213yes—
352C2C127×#234313yes—
353C2C127×#235213yes—
354C2C127×#235313yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#376×C127C2semidirect
4. C127×#1434C2semidirect
5. C127×#1434C2semidirect
7. C4×#95×C127C2semidirect
13. C4×C22⋊C4×C127C4semidirect
42. C2×C42×C127C2×C4semidirect
43. C2×C42×C127C2×C4semidirect
48. #95×C127C2×C4semidirect
49. #95×C127C2×C4semidirect
150. C22×C127#376semidirect
169. #13809C127direct (N × H)
179. C2×#376C2×C127semidirect
181. #1434C2×C127semidirect
182. #1434C2×C127semidirect
184. C4×#95C2×C127semidirect
185. C127#13809direct (N × H)
191. C4×C22⋊C4C4×C127semidirect
220. C2×C42C2×C4×C127semidirect
221. C2×C42C2×C4×C127semidirect
226. #95C2×C4×C127semidirect
227. #95C2×C4×C127semidirect
328. C22#376×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C1272
C2×#376×C1272
C22×#95×C1272
C127×#14342
C127×C22⋊#952
C4×#95×C1272
#13809127