Finite Group Databasebeta

← C127×#2556 #30635508

Subgroups — C127×#2556 #30635508

Order 16256.

492 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×#125×C127C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×C127C211yesmaximal, characteristic
3#399×C127C211yesmaximal, characteristic
4#398×C127C211yesmaximal, characteristic, complemented
5#396×C127C211yesmaximal, characteristic
6#395×C127C211yesmaximal, characteristic, complemented
7#391×C127C211yesmaximal, characteristic, complemented
8#389×C127C211yesmaximal, characteristic, complemented
9#389×C127C211yesmaximal, characteristic, complemented
10#388×C127C211yesmaximal, characteristic
11#388×C127C211yesmaximal, characteristic
12#387×C127C211yesmaximal, characteristic, complemented
13#385×C127C211yesmaximal, characteristic
14C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C127C211yesmaximal, characteristic
16C22×Q8×C127C2211yescharacteristic
17C23×C4×C127C2211yescharacteristic
18#125×C127—24no—
19C22⋊Q8×C127—24no—
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×C4⋊C4×C127C2211yescharacteristic
30C2×C4⋊C4×C127C2211yescharacteristic
31C2×C4⋊C4×C127C2211yescharacteristic
32C2×C4⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127C2211yescharacteristic
34C2×C22⋊C4×C127C2211yescharacteristic
35C2×C22⋊C4×C127C2211yescharacteristic
36C2×C22⋊C4×C127C2211yescharacteristic
37C2×C22⋊C4×C127C2211yescharacteristic
38C2×C22⋊C4×C127C2211yescharacteristic
39C2×C42×C127C2211yescharacteristic
40C2×C42×C127C2211yescharacteristic
41C2×C42×C127C2211yescharacteristic
42C2×C42×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
51#95×C127C2211yescharacteristic
52#95×C127C2211yescharacteristic
53C24×C127C2311yescharacteristic
54C2×Q8×C127—22no—
55C2×Q8×C127—22no—
56C2×Q8×C127—41no—
57C22×C4×C127—22no—
58C22×C4×C127—22no—
59C22×C4×C127—41no—
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
69C22×C4×C127C2311yescharacteristic
70C22×C4×C127C2311yescharacteristic
71C22×C4×C127C2311yescharacteristic
72C22×C4×C127C2311yescharacteristic
73C22×C4×C127C2311yescharacteristic
74C4⋊C4×C127—22no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127D414yes—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127Q814yescomplemented
93C42×C127—22no—
94C42×C127—22no—
95C42×C127—41no—
96C42×C127—41no—
97C23×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127C2×Q812yes—
104C23×C127C2411yescharacteristic
105Q8×C127—44no—
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—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—44no—
141C2×C4×C127C2×D412yes—
142C2×C4×C127C2×D412yes—
143C2×C4×C127C2×D412yes—
144C2×C4×C127C2×Q812yes—
145C2×C4×C127C2×Q812yes—
146C2×C4×C127#4112yes—
147C2×C4×C127#4112yes—
148C2×C4×C127#4112yes—
149C22×C127—22no—
150C22×C127—22no—
151C22×C127—22no—
152C22×C127—41no—
153C22×C127—41no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127C22×D411yescharacteristic
157C22×C127C22×Q811yescharacteristic
158C22×C127C2×#4111yescharacteristic
159C22×C127C2×#4111yescharacteristic
160C22×C127C2×#4111yescharacteristic
161C22×C127H(5,𝔽2)11yescharacteristic
162C22×C1272−1+411yescharacteristic
163C4×C127—22no—
164C4×C127—22no—
165C4×C127—22no—
166C4×C127—22no—
167C4×C127—22no—
168C4×C127—22no—
169C4×C127—22no—
170C4×C127—22no—
171C4×C127—41no—
172C4×C127—41no—
173C4×C127—41no—
174C4×C127—41no—
175C4×C127—41no—
176C4×C127—41no—
177C2×C127—42no—
178C2×C127#53211yescharacteristic
179C2×C127#53311yescharacteristic
180C2×C127#53911yescharacteristic
181C2×C127#54611yescharacteristic
182C2×C127D4×Q811yescharacteristic
183C2×C127#55211yescharacteristic
184C2×C127#55411yescharacteristic
185#2556C12711yesmaximal, characteristic, direct product factor, Sylow
186C127#255611yescharacteristic, direct product factor, Sylow
187C2×#125C2×C12711yescharacteristic, complemented
188C2×C22⋊Q8C2×C12711yescharacteristic
189#399C2×C12711yescharacteristic
190#398C2×C12711yescharacteristic, complemented
191#396C2×C12711yescharacteristic
192#395C2×C12711yescharacteristic, complemented
193#391C2×C12711yescharacteristic, complemented
194#389C2×C12711yescharacteristic, complemented
195#389C2×C12711yescharacteristic, complemented
196#388C2×C12711yescharacteristic
197#388C2×C12711yescharacteristic
198#387C2×C12711yescharacteristic, complemented
199#385C2×C12711yescharacteristic
200C4×C4⋊C4C2×C12711yescharacteristic, complemented
201C4×C22⋊C4C2×C12711yescharacteristic
202C22×Q8C22×C12711yescharacteristic
203C23×C4C22×C12711yescharacteristic
204#125—24no—
205C22⋊Q8—24no—
206C2×C4⋊C4C22×C12711yescharacteristic
207C2×C4⋊C4C22×C12711yescharacteristic
208C2×C4⋊C4C22×C12711yescharacteristic
209C2×C4⋊C4C22×C12711yescharacteristic
210C2×C4⋊C4C22×C12711yescharacteristic
211C2×C4⋊C4C22×C12711yescharacteristic
212C2×C4⋊C4C22×C12711yescharacteristic
213C2×C4⋊C4C22×C12711yescharacteristic
214C2×C4⋊C4C22×C12711yescharacteristic
215C2×C4⋊C4C22×C12711yescharacteristic
216C2×C4⋊C4C22×C12711yescharacteristic
217C2×C4⋊C4C22×C12711yescharacteristic
218C2×C4⋊C4C22×C12711yescharacteristic
219C2×C22⋊C4C22×C12711yescharacteristic
220C2×C22⋊C4C22×C12711yescharacteristic
221C2×C22⋊C4C22×C12711yescharacteristic
222C2×C22⋊C4C22×C12711yescharacteristic
223C2×C22⋊C4C22×C12711yescharacteristic
224C2×C22⋊C4C22×C12711yescharacteristic
225C2×C42C22×C12711yescharacteristic
226C2×C42C22×C12711yescharacteristic
227C2×C42C22×C12711yescharacteristic
228C2×C42C22×C12711yescharacteristic
229#95C22×C12711yescharacteristic
230#95C22×C12711yescharacteristic
231#95C22×C12711yescharacteristic
232#95C22×C12711yescharacteristic
233#95C22×C12711yescharacteristic
234#95C22×C12711yescharacteristic
235#95C22×C12711yescharacteristic
236#95C22×C12711yescharacteristic
237#95C22×C12711yescharacteristic
238#95C22×C12711yescharacteristic
239C24C23×C12711yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—41no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4C23×C12711yescharacteristic
247C22×C4C23×C12711yescharacteristic
248C22×C4C23×C12711yescharacteristic
249C22×C4C23×C12711yescharacteristic
250C22×C4C23×C12711yescharacteristic
251C22×C4C23×C12711yescharacteristic
252C22×C4C23×C12711yescharacteristic
253C22×C4C23×C12711yescharacteristic
254C22×C4C23×C12711yescharacteristic
255C22×C4C23×C12711yescharacteristic
256C22×C4C23×C12711yescharacteristic
257C22×C4C23×C12711yescharacteristic
258C22×C4C23×C12711yescharacteristic
259C22×C4C23×C12711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4D4×C12714yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—41no—
278C22⋊C4Q8×C12714yescomplemented
279C42—22no—
280C42—22no—
281C42—41no—
282C42—41no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×Q8×C12712yes—
290C23C24×C12711yescharacteristic
291Q8—44no—
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—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—44no—
327C2×C4C2×D4×C12712yes—
328C2×C4C2×D4×C12712yes—
329C2×C4C2×D4×C12712yes—
330C2×C4C2×Q8×C12712yes—
331C2×C4C2×Q8×C12712yes—
332C2×C4#41×C12712yes—
333C2×C4#41×C12712yes—
334C2×C4#41×C12712yes—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C22×D4×C12711yescharacteristic
343C22C22×Q8×C12711yescharacteristic
344C22C2×#41×C12711yescharacteristic
345C22C2×#41×C12711yescharacteristic
346C22C2×#41×C12711yescharacteristic
347C22H(5,𝔽2)×C12711yescharacteristic
348C222−1+4×C12711yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—41no—
363C2—42no—
364C2#532×C12711yescharacteristic
365C2#533×C12711yescharacteristic
366C2#539×C12711yescharacteristic
367C2#546×C12711yescharacteristic
368C2D4×Q8×C12711yescharacteristic
369C2#552×C12711yescharacteristic
370C2#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
1. C2×#125×C127C2semidirect
4. #398×C127C2semidirect
6. #395×C127C2semidirect
7. #391×C127C2semidirect
8. #389×C127C2semidirect
9. #389×C127C2semidirect
12. #387×C127C2semidirect
14. C4×C4⋊C4×C127C2semidirect
92. C22⋊C4×C127Q8semidirect
185. #2556C127direct (N × H)
186. C127#2556direct (N × H)
187. C2×#125C2×C127semidirect
190. #398C2×C127semidirect
192. #395C2×C127semidirect
193. #391C2×C127semidirect
194. #389C2×C127semidirect
195. #389C2×C127semidirect
198. #387C2×C127semidirect
200. C4×C4⋊C4C2×C127semidirect
278. C22⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×C22⋊Q8×C1272
#399×C1272
#398×C1272
#396×C1272
#395×C1272
#391×C1272
#389×C1272
#388×C1272
#387×C1272
#385×C1272
C4×C4⋊C4×C1272
C4×C22⋊C4×C1272
#2556127