Finite Group Databasebeta

← C127×#2525 #30635477

Subgroups — C127×#2525 #30635477

Order 16256.

398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#400×C127C211yesmaximal, characteristic, complemented
2#398×C127C211yesmaximal, characteristic, complemented
3#397×C127C211yesmaximal, characteristic
4#396×C127C211yesmaximal, characteristic
5#389×C127C211yesmaximal, characteristic, complemented
6#388×C127C211yesmaximal, characteristic
7#388×C127C211yesmaximal, characteristic
8#388×C127C211yesmaximal, characteristic
9#388×C127C211yesmaximal, characteristic
10#388×C127C211yesmaximal, characteristic
11#387×C127C211yesmaximal, characteristic, complemented
12#387×C127C211yesmaximal, characteristic, complemented
13#383×C127C211yesmaximal, characteristic, complemented
14C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2211yescharacteristic
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24C2×C4⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2211yescharacteristic
26C2×C22⋊C4×C127C2211yescharacteristic
27C2×C22⋊C4×C127C2211yescharacteristic
28C2×C22⋊C4×C127C2211yescharacteristic
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2211yescharacteristic
31C2×C22⋊C4×C127C2211yescharacteristic
32C2×C42×C127C2211yescharacteristic
33C2×C42×C127C2211yescharacteristic
34C2×C42×C127C2211yescharacteristic
35C2×C42×C127C2211yescharacteristic
36C2×C42×C127C2211yescharacteristic
37#95×C127C2211yescharacteristic
38#95×C127C2211yescharacteristic
39#95×C127C2211yescharacteristic
40#95×C127C2211yescharacteristic
41#95×C127C2211yescharacteristic
42#95×C127C2211yescharacteristic
43#95×C127C2211yescharacteristic
44#95×C127C2211yescharacteristic
45#95×C127C2211yescharacteristic
46#95×C127C2211yescharacteristic
47#95×C127C2211yescharacteristic
48#95×C127C2211yescharacteristic
49#95×C127C2211yescharacteristic
50#95×C127C2211yescharacteristic
51C24×C127C2311yescharacteristic
52C22×C4×C127C2311yescharacteristic
53C22×C4×C127C2311yescharacteristic
54C22×C4×C127C2311yescharacteristic
55C22×C4×C127C2311yescharacteristic
56C22×C4×C127C2311yescharacteristic
57C22×C4×C127C2311yescharacteristic
58C22×C4×C127C2311yescharacteristic
59C22×C4×C127C2311yescharacteristic
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2311yescharacteristic
62C22×C4×C127C2311yescharacteristic
63C22×C4×C127C2311yescharacteristic
64C22×C4×C127C2311yescharacteristic
65C22×C4×C127C2311yescharacteristic
66C4⋊C4×C127—22no—
67C4⋊C4×C127—22no—
68C4⋊C4×C127—22no—
69C4⋊C4×C127—22no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—22no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—41no—
75C22⋊C4×C127—22no—
76C22⋊C4×C127—22no—
77C22⋊C4×C127—22no—
78C22⋊C4×C127—22no—
79C22⋊C4×C127—22no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C42×C127—22no—
83C42×C127—22no—
84C42×C127—22no—
85C42×C127—41no—
86C42×C127—41no—
87C23×C127—21no—
88C23×C127—21no—
89C23×C127—21no—
90C23×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127C2411yescharacteristic
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127#4112yes—
133C2×C4×C127#4112yes—
134C2×C4×C127#4112yes—
135C2×C4×C127#4112yes—
136C2×C4×C127#4112yes—
137C22×C127—41no—
138C22×C127—41no—
139C22×C127—41no—
140C22×C127—41no—
141C22×C127—41no—
142C22×C127—41no—
143C22×C127—41no—
144C22×C127C2×#4111yescharacteristic
145C22×C127C2×#4111yescharacteristic
146C22×C127C2×#4111yescharacteristic
147C22×C127C2×#4111yescharacteristic
148C22×C127C2×#4111yescharacteristic
149C22×C127H(5,𝔽2)11yescharacteristic
150C22×C1272−1+411yescharacteristic
151C4×C127—22no—
152C4×C127—22no—
153C4×C127—22no—
154C4×C127—22no—
155C4×C127—22no—
156C4×C127—41no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—41no—
165C2×C127—81no—
166C2×C127#52911yescharacteristic
167C2×C127#52911yescharacteristic
168C2×C127#54211yescharacteristic
169C2×C127#55211yescharacteristic
170C2×C127#55311yescharacteristic
171C2×C127#55311yescharacteristic
172C2×C127#55611yescharacteristic
173#2525C12711yesmaximal, characteristic, direct product factor, Sylow
174C127#252511yescharacteristic, direct product factor, Sylow
175#400C2×C12711yescharacteristic, complemented
176#398C2×C12711yescharacteristic, complemented
177#397C2×C12711yescharacteristic
178#396C2×C12711yescharacteristic
179#389C2×C12711yescharacteristic, complemented
180#388C2×C12711yescharacteristic
181#388C2×C12711yescharacteristic
182#388C2×C12711yescharacteristic
183#388C2×C12711yescharacteristic
184#388C2×C12711yescharacteristic
185#387C2×C12711yescharacteristic, complemented
186#387C2×C12711yescharacteristic, complemented
187#383C2×C12711yescharacteristic, complemented
188C4×C4⋊C4C2×C12711yescharacteristic, complemented
189C4×C4⋊C4C2×C12711yescharacteristic, complemented
190C2×C4⋊C4C22×C12711yescharacteristic
191C2×C4⋊C4C22×C12711yescharacteristic
192C2×C4⋊C4C22×C12711yescharacteristic
193C2×C4⋊C4C22×C12711yescharacteristic
194C2×C4⋊C4C22×C12711yescharacteristic
195C2×C4⋊C4C22×C12711yescharacteristic
196C2×C4⋊C4C22×C12711yescharacteristic
197C2×C4⋊C4C22×C12711yescharacteristic
198C2×C4⋊C4C22×C12711yescharacteristic
199C2×C22⋊C4C22×C12711yescharacteristic
200C2×C22⋊C4C22×C12711yescharacteristic
201C2×C22⋊C4C22×C12711yescharacteristic
202C2×C22⋊C4C22×C12711yescharacteristic
203C2×C22⋊C4C22×C12711yescharacteristic
204C2×C22⋊C4C22×C12711yescharacteristic
205C2×C22⋊C4C22×C12711yescharacteristic
206C2×C42C22×C12711yescharacteristic
207C2×C42C22×C12711yescharacteristic
208C2×C42C22×C12711yescharacteristic
209C2×C42C22×C12711yescharacteristic
210C2×C42C22×C12711yescharacteristic
211#95C22×C12711yescharacteristic
212#95C22×C12711yescharacteristic
213#95C22×C12711yescharacteristic
214#95C22×C12711yescharacteristic
215#95C22×C12711yescharacteristic
216#95C22×C12711yescharacteristic
217#95C22×C12711yescharacteristic
218#95C22×C12711yescharacteristic
219#95C22×C12711yescharacteristic
220#95C22×C12711yescharacteristic
221#95C22×C12711yescharacteristic
222#95C22×C12711yescharacteristic
223#95C22×C12711yescharacteristic
224#95C22×C12711yescharacteristic
225C24C23×C12711yescharacteristic
226C22×C4C23×C12711yescharacteristic
227C22×C4C23×C12711yescharacteristic
228C22×C4C23×C12711yescharacteristic
229C22×C4C23×C12711yescharacteristic
230C22×C4C23×C12711yescharacteristic
231C22×C4C23×C12711yescharacteristic
232C22×C4C23×C12711yescharacteristic
233C22×C4C23×C12711yescharacteristic
234C22×C4C23×C12711yescharacteristic
235C22×C4C23×C12711yescharacteristic
236C22×C4C23×C12711yescharacteristic
237C22×C4C23×C12711yescharacteristic
238C22×C4C23×C12711yescharacteristic
239C22×C4C23×C12711yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C24×C12711yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4#41×C12712yes—
307C2×C4#41×C12712yes—
308C2×C4#41×C12712yes—
309C2×C4#41×C12712yes—
310C2×C4#41×C12712yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#41×C12711yescharacteristic
319C22C2×#41×C12711yescharacteristic
320C22C2×#41×C12711yescharacteristic
321C22C2×#41×C12711yescharacteristic
322C22C2×#41×C12711yescharacteristic
323C22H(5,𝔽2)×C12711yescharacteristic
324C222−1+4×C12711yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C2—81no—
340C2#529×C12711yescharacteristic
341C2#529×C12711yescharacteristic
342C2#542×C12711yescharacteristic
343C2#552×C12711yescharacteristic
344C2#553×C12711yescharacteristic
345C2#553×C12711yescharacteristic
346C2#556×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #400×C127C2semidirect
2. #398×C127C2semidirect
5. #389×C127C2semidirect
11. #387×C127C2semidirect
12. #387×C127C2semidirect
13. #383×C127C2semidirect
14. C4×C4⋊C4×C127C2semidirect
15. C4×C4⋊C4×C127C2semidirect
173. #2525C127direct (N × H)
174. C127#2525direct (N × H)
175. #400C2×C127semidirect
176. #398C2×C127semidirect
179. #389C2×C127semidirect
185. #387C2×C127semidirect
186. #387C2×C127semidirect
187. #383C2×C127semidirect
188. C4×C4⋊C4C2×C127semidirect
189. C4×C4⋊C4C2×C127semidirect

Maximal subgroups

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

subgroupindex
#400×C1272
#398×C1272
#397×C1272
#396×C1272
#389×C1272
#388×C1272
#387×C1272
#383×C1272
C4×C4⋊C4×C1272
#2525127