Finite Group Databasebeta

← C127×#2522 #30635474

Subgroups — C127×#2522 #30635474

Order 16256.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#399×C127C211yesmaximal, characteristic
2#398×C127C211yesmaximal, characteristic, complemented
3#398×C127C211yesmaximal, characteristic, complemented
4#396×C127C211yesmaximal, characteristic
5#389×C127C211yesmaximal, characteristic, complemented
6#389×C127C211yesmaximal, characteristic, complemented
7#388×C127C211yesmaximal, characteristic
8#388×C127C211yesmaximal, characteristic
9#387×C127C211yesmaximal, characteristic, complemented
10#387×C127C211yesmaximal, characteristic, complemented
11#387×C127C211yesmaximal, characteristic, complemented
12#385×C127C211yesmaximal, characteristic
13#380×C127C211yesmaximal, characteristic
14C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C127C211yesmaximal, characteristic
16C23×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×C4⋊C4×C127C2211yescharacteristic
26C2×C4⋊C4×C127C2211yescharacteristic
27C2×C4⋊C4×C127C2211yescharacteristic
28C2×C4⋊C4×C127C2211yescharacteristic
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2211yescharacteristic
31C2×C22⋊C4×C127C2211yescharacteristic
32C2×C22⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127C2211yescharacteristic
34C2×C22⋊C4×C127C2211yescharacteristic
35C2×C42×C127C2211yescharacteristic
36C2×C42×C127C2211yescharacteristic
37C2×C42×C127C2211yescharacteristic
38C2×C42×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×C127—22no—
53C22×C4×C127—22no—
54C22×C4×C127—41no—
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
66C22×C4×C127C2311yescharacteristic
67C22×C4×C127C2311yescharacteristic
68C22×C4×C127C2311yescharacteristic
69C4⋊C4×C127—22no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—22no—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—22no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C22⋊C4×C127—22no—
82C22⋊C4×C127—22no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127Q814yes—
87C42×C127—22no—
88C42×C127—41no—
89C42×C127—41no—
90C42×C127—41no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127C2×Q812yes—
98C23×C127C2411yescharacteristic
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—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—44no—
136C2×C4×C127C2×Q812yes—
137C2×C4×C127C2×Q812yes—
138C2×C4×C127#4112yes—
139C2×C4×C127#4112yes—
140C2×C4×C127#4112yes—
141C2×C4×C127#4112yes—
142C22×C127—22no—
143C22×C127—22no—
144C22×C127—22no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127C22×Q811yescharacteristic
150C22×C127C2×#4111yescharacteristic
151C22×C127C2×#4111yescharacteristic
152C22×C127C2×#4111yescharacteristic
153C22×C127C2×#4111yescharacteristic
154C22×C127H(5,𝔽2)11yescharacteristic
155C22×C127H(5,𝔽2)11yescharacteristic
156C4×C127—22no—
157C4×C127—22no—
158C4×C127—22no—
159C4×C127—22no—
160C4×C127—22no—
161C4×C127—22no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—41no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127—41no—
168C4×C127—41no—
169C4×C127—41no—
170C2×C127—42no—
171C2×C127#52911yescharacteristic
172C2×C127#53311yescharacteristic
173C2×C127#54011yescharacteristic
174C2×C127#55111yescharacteristic
175C2×C127#55311yescharacteristic
176C2×C127#55411yescharacteristic
177C2×C127#55411yescharacteristic
178#2522C12711yesmaximal, characteristic, direct product factor, Sylow
179C127#252211yescharacteristic, direct product factor, Sylow
180#399C2×C12711yescharacteristic
181#398C2×C12711yescharacteristic, complemented
182#398C2×C12711yescharacteristic, complemented
183#396C2×C12711yescharacteristic
184#389C2×C12711yescharacteristic, complemented
185#389C2×C12711yescharacteristic, complemented
186#388C2×C12711yescharacteristic
187#388C2×C12711yescharacteristic
188#387C2×C12711yescharacteristic, complemented
189#387C2×C12711yescharacteristic, complemented
190#387C2×C12711yescharacteristic, complemented
191#385C2×C12711yescharacteristic
192#380C2×C12711yescharacteristic
193C4×C4⋊C4C2×C12711yescharacteristic, complemented
194C4×C22⋊C4C2×C12711yescharacteristic
195C23×C4C22×C12711yescharacteristic
196C2×C4⋊C4C22×C12711yescharacteristic
197C2×C4⋊C4C22×C12711yescharacteristic
198C2×C4⋊C4C22×C12711yescharacteristic
199C2×C4⋊C4C22×C12711yescharacteristic
200C2×C4⋊C4C22×C12711yescharacteristic
201C2×C4⋊C4C22×C12711yescharacteristic
202C2×C4⋊C4C22×C12711yescharacteristic
203C2×C4⋊C4C22×C12711yescharacteristic
204C2×C4⋊C4C22×C12711yescharacteristic
205C2×C4⋊C4C22×C12711yescharacteristic
206C2×C4⋊C4C22×C12711yescharacteristic
207C2×C4⋊C4C22×C12711yescharacteristic
208C2×C22⋊C4C22×C12711yescharacteristic
209C2×C22⋊C4C22×C12711yescharacteristic
210C2×C22⋊C4C22×C12711yescharacteristic
211C2×C22⋊C4C22×C12711yescharacteristic
212C2×C22⋊C4C22×C12711yescharacteristic
213C2×C22⋊C4C22×C12711yescharacteristic
214C2×C42C22×C12711yescharacteristic
215C2×C42C22×C12711yescharacteristic
216C2×C42C22×C12711yescharacteristic
217C2×C42C22×C12711yescharacteristic
218#95C22×C12711yescharacteristic
219#95C22×C12711yescharacteristic
220#95C22×C12711yescharacteristic
221#95C22×C12711yescharacteristic
222#95C22×C12711yescharacteristic
223#95C22×C12711yescharacteristic
224#95C22×C12711yescharacteristic
225#95C22×C12711yescharacteristic
226#95C22×C12711yescharacteristic
227#95C22×C12711yescharacteristic
228#95C22×C12711yescharacteristic
229#95C22×C12711yescharacteristic
230C24C23×C12711yescharacteristic
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4C23×C12711yescharacteristic
235C22×C4C23×C12711yescharacteristic
236C22×C4C23×C12711yescharacteristic
237C22×C4C23×C12711yescharacteristic
238C22×C4C23×C12711yescharacteristic
239C22×C4C23×C12711yescharacteristic
240C22×C4C23×C12711yescharacteristic
241C22×C4C23×C12711yescharacteristic
242C22×C4C23×C12711yescharacteristic
243C22×C4C23×C12711yescharacteristic
244C22×C4C23×C12711yescharacteristic
245C22×C4C23×C12711yescharacteristic
246C22×C4C23×C12711yescharacteristic
247C22×C4C23×C12711yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4Q8×C12714yes—
266C42—22no—
267C42—41no—
268C42—41no—
269C42—41no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×Q8×C12712yes—
277C23C24×C12711yescharacteristic
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—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—44no—
315C2×C4C2×Q8×C12712yes—
316C2×C4C2×Q8×C12712yes—
317C2×C4#41×C12712yes—
318C2×C4#41×C12712yes—
319C2×C4#41×C12712yes—
320C2×C4#41×C12712yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C22×Q8×C12711yescharacteristic
329C22C2×#41×C12711yescharacteristic
330C22C2×#41×C12711yescharacteristic
331C22C2×#41×C12711yescharacteristic
332C22C2×#41×C12711yescharacteristic
333C22H(5,𝔽2)×C12711yescharacteristic
334C22H(5,𝔽2)×C12711yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C2—42no—
350C2#529×C12711yescharacteristic
351C2#533×C12711yescharacteristic
352C2#540×C12711yescharacteristic
353C2#551×C12711yescharacteristic
354C2#553×C12711yescharacteristic
355C2#554×C12711yescharacteristic
356C2#554×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
2. #398×C127C2semidirect
3. #398×C127C2semidirect
5. #389×C127C2semidirect
6. #389×C127C2semidirect
9. #387×C127C2semidirect
10. #387×C127C2semidirect
11. #387×C127C2semidirect
14. C4×C4⋊C4×C127C2semidirect
178. #2522C127direct (N × H)
179. C127#2522direct (N × H)
181. #398C2×C127semidirect
182. #398C2×C127semidirect
184. #389C2×C127semidirect
185. #389C2×C127semidirect
188. #387C2×C127semidirect
189. #387C2×C127semidirect
190. #387C2×C127semidirect
193. C4×C4⋊C4C2×C127semidirect

Maximal subgroups

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

subgroupindex
#399×C1272
#398×C1272
#396×C1272
#389×C1272
#388×C1272
#387×C1272
#385×C1272
#380×C1272
C4×C4⋊C4×C1272
C4×C22⋊C4×C1272
#2522127