Finite Group Databasebeta

← C127×#2461 #30635413

Subgroups — C127×#2461 #30635413

Order 16256.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×C127C211yesmaximal, characteristic, complemented
2C2×#123×C127C211yesmaximal, characteristic, complemented
3C2×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
4C2×C4×D4×C127C211yesmaximal, characteristic, complemented
5#396×C127C211yesmaximal, characteristic, complemented
6#395×C127C211yesmaximal, characteristic, complemented
7#394×C127C211yesmaximal, characteristic, complemented
8#392×C127C211yesmaximal, characteristic
9#390×C127C211yesmaximal, characteristic, complemented
10#388×C127C211yesmaximal, characteristic, complemented
11#388×C127C211yesmaximal, characteristic, complemented
12#388×C127C211yesmaximal, characteristic, complemented
13#386×C127C211yesmaximal, characteristic, complemented
14#385×C127C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
16C22×Q8×C127C2211yescharacteristic
17C22×D4×C127C2211yescharacteristic
18C22×D4×C127C2211yescharacteristic
19C22×D4×C127C2211yescharacteristic
20C23×C4×C127C2211yescharacteristic
21C23×C4×C127C2211yescharacteristic
22#124×C127—24no—
23#123×C127—24no—
24C22⋊Q8×C127—24no—
25C4×D4×C127—24no—
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×C22⋊C4×C127C2211yescharacteristic
40C2×C22⋊C4×C127C2211yescharacteristic
41C2×C22⋊C4×C127C2211yescharacteristic
42C2×C22⋊C4×C127C2211yescharacteristic
43C2×C22⋊C4×C127C2211yescharacteristic
44C2×C22⋊C4×C127C2211yescharacteristic
45C2×C22⋊C4×C127C2211yescharacteristic
46C2×C42×C127C2211yescharacteristic
47C2×C42×C127C2211yescharacteristic
48C2×C42×C127C2211yescharacteristic
49#95×C127C2211yescharacteristic
50#95×C127C2211yescharacteristic
51#95×C127C2211yescharacteristic
52#95×C127C2211yescharacteristic
53#95×C127C2211yescharacteristic
54#95×C127C2211yescharacteristic
55C24×C127C2311yescharacteristic
56C24×C127C2311yescharacteristic
57C24×C127C2311yescharacteristic
58C2×Q8×C127—22no—
59C2×Q8×C127—22no—
60C2×Q8×C127—41no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—22no—
64C2×D4×C127—22no—
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127—22no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—41no—
75C22×C4×C127—41no—
76C22×C4×C127C2311yescharacteristic
77C22×C4×C127C2311yescharacteristic
78C22×C4×C127C2311yescharacteristic
79C22×C4×C127C2311yescharacteristic
80C22×C4×C127C2311yescharacteristic
81C22×C4×C127C2311yescharacteristic
82C22×C4×C127C2311yescharacteristic
83C22×C4×C127C2311yescharacteristic
84C22×C4×C127C2311yescharacteristic
85C22×C4×C127C2311yescharacteristic
86C22×C4×C127C2311yescharacteristic
87C22×C4×C127C2311yescharacteristic
88C4⋊C4×C127—22no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—22no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127D414yescomplemented
95C22⋊C4×C127—22no—
96C22⋊C4×C127—22no—
97C22⋊C4×C127—22no—
98C22⋊C4×C127—22no—
99C22⋊C4×C127—22no—
100C22⋊C4×C127—22no—
101C22⋊C4×C127—22no—
102C22⋊C4×C127—22no—
103C22⋊C4×C127—22no—
104C22⋊C4×C127—22no—
105C22⋊C4×C127—22no—
106C22⋊C4×C127—22no—
107C22⋊C4×C127D414yescomplemented
108C42×C127—22no—
109C42×C127—22no—
110C42×C127—22no—
111C23×C127—21no—
112C23×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—21no—
118C23×C127—21no—
119C23×C127—21no—
120C23×C127—21no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—21no—
128C23×C127—21no—
129C23×C127—21no—
130C23×C127C2×D412yes—
131C23×C127#4112yes—
132C23×C127C2411yescharacteristic
133Q8×C127—44no—
134D4×C127—28no—
135D4×C127—44no—
136D4×C127—44no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—21no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—21no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127C2×D412yes—
169C2×C4×C127C2×D412yes—
170C2×C4×C127C2×D412yes—
171C2×C4×C127C2×D412yes—
172C2×C4×C127C2×D412yes—
173C2×C4×C127#4112yes—
174C2×C4×C127#4112yes—
175C22×C127—22no—
176C22×C127—22no—
177C22×C127—22no—
178C22×C127—22no—
179C22×C127—22no—
180C22×C127—22no—
181C22×C127—41no—
182C22×C127—41no—
183C22×C127—41no—
184C22×C127—41no—
185C22×C127—41no—
186C22×C127—41no—
187C22×C127—41no—
188C22×C127—41no—
189C22×C127—41no—
190C22×C127—41no—
191C22×C127—41no—
192C22×C127—41no—
193C22×C127—41no—
194C22×C127—41no—
195C22×C127—41no—
196C22×C127C22×D411yescharacteristic
197C22×C127C22×D411yescharacteristic
198C22×C127C2×#4111yescharacteristic
199C22×C127C2×#4111yescharacteristic
200C22×C127C2×#4111yescharacteristic
201C22×C127H(5,𝔽2)11yescharacteristic
202C22×C1272−1+411yescharacteristic
203C4×C127—22no—
204C4×C127—22no—
205C4×C127—22no—
206C4×C127—22no—
207C4×C127—22no—
208C4×C127—22no—
209C4×C127—22no—
210C4×C127—41no—
211C4×C127—41no—
212C4×C127—41no—
213C4×C127—41no—
214C4×C127—41no—
215C2×C127—42no—
216C2×C127—42no—
217C2×C127—81no—
218C2×C127#52511yescharacteristic
219C2×C127#53211yescharacteristic
220C2×C127#54211yescharacteristic
221C2×C127D4211yescharacteristic
222C2×C127#54711yescharacteristic
223C2×C127#54811yescharacteristic
224C2×C127#55111yescharacteristic
225#2461C12711yesmaximal, characteristic, direct product factor, Sylow
226C127#246111yescharacteristic, direct product factor, Sylow
227C2×#124C2×C12711yescharacteristic, complemented
228C2×#123C2×C12711yescharacteristic, complemented
229C2×C22⋊Q8C2×C12711yescharacteristic, complemented
230C2×C4×D4C2×C12711yescharacteristic, complemented
231#396C2×C12711yescharacteristic, complemented
232#395C2×C12711yescharacteristic, complemented
233#394C2×C12711yescharacteristic, complemented
234#392C2×C12711yescharacteristic
235#390C2×C12711yescharacteristic, complemented
236#388C2×C12711yescharacteristic, complemented
237#388C2×C12711yescharacteristic, complemented
238#388C2×C12711yescharacteristic, complemented
239#386C2×C12711yescharacteristic, complemented
240#385C2×C12711yescharacteristic, complemented
241C4×C4⋊C4C2×C12711yescharacteristic, complemented
242C22×Q8C22×C12711yescharacteristic
243C22×D4C22×C12711yescharacteristic
244C22×D4C22×C12711yescharacteristic
245C22×D4C22×C12711yescharacteristic
246C23×C4C22×C12711yescharacteristic
247C23×C4C22×C12711yescharacteristic
248#124—24no—
249#123—24no—
250C22⋊Q8—24no—
251C4×D4—24no—
252C2×C4⋊C4C22×C12711yescharacteristic
253C2×C4⋊C4C22×C12711yescharacteristic
254C2×C4⋊C4C22×C12711yescharacteristic
255C2×C4⋊C4C22×C12711yescharacteristic
256C2×C4⋊C4C22×C12711yescharacteristic
257C2×C4⋊C4C22×C12711yescharacteristic
258C2×C4⋊C4C22×C12711yescharacteristic
259C2×C22⋊C4C22×C12711yescharacteristic
260C2×C22⋊C4C22×C12711yescharacteristic
261C2×C22⋊C4C22×C12711yescharacteristic
262C2×C22⋊C4C22×C12711yescharacteristic
263C2×C22⋊C4C22×C12711yescharacteristic
264C2×C22⋊C4C22×C12711yescharacteristic
265C2×C22⋊C4C22×C12711yescharacteristic
266C2×C22⋊C4C22×C12711yescharacteristic
267C2×C22⋊C4C22×C12711yescharacteristic
268C2×C22⋊C4C22×C12711yescharacteristic
269C2×C22⋊C4C22×C12711yescharacteristic
270C2×C22⋊C4C22×C12711yescharacteristic
271C2×C22⋊C4C22×C12711yescharacteristic
272C2×C42C22×C12711yescharacteristic
273C2×C42C22×C12711yescharacteristic
274C2×C42C22×C12711yescharacteristic
275#95C22×C12711yescharacteristic
276#95C22×C12711yescharacteristic
277#95C22×C12711yescharacteristic
278#95C22×C12711yescharacteristic
279#95C22×C12711yescharacteristic
280#95C22×C12711yescharacteristic
281C24C23×C12711yescharacteristic
282C24C23×C12711yescharacteristic
283C24C23×C12711yescharacteristic
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—41no—
295C2×D4—41no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C23×C12711yescharacteristic
303C22×C4C23×C12711yescharacteristic
304C22×C4C23×C12711yescharacteristic
305C22×C4C23×C12711yescharacteristic
306C22×C4C23×C12711yescharacteristic
307C22×C4C23×C12711yescharacteristic
308C22×C4C23×C12711yescharacteristic
309C22×C4C23×C12711yescharacteristic
310C22×C4C23×C12711yescharacteristic
311C22×C4C23×C12711yescharacteristic
312C22×C4C23×C12711yescharacteristic
313C22×C4C23×C12711yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4D4×C12714yescomplemented
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4D4×C12714yescomplemented
334C42—22no—
335C42—22no—
336C42—22no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23C2×D4×C12712yes—
357C23#41×C12712yes—
358C23C24×C12711yescharacteristic
359Q8—44no—
360D4—28no—
361D4—44no—
362D4—44no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4C2×D4×C12712yes—
395C2×C4C2×D4×C12712yes—
396C2×C4C2×D4×C12712yes—
397C2×C4C2×D4×C12712yes—
398C2×C4C2×D4×C12712yes—
399C2×C4#41×C12712yes—
400C2×C4#41×C12712yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22C22×D4×C12711yescharacteristic
423C22C22×D4×C12711yescharacteristic
424C22C2×#41×C12711yescharacteristic
425C22C2×#41×C12711yescharacteristic
426C22C2×#41×C12711yescharacteristic
427C22H(5,𝔽2)×C12711yescharacteristic
428C222−1+4×C12711yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C2—42no—
442C2—42no—
443C2—81no—
444C2#525×C12711yescharacteristic
445C2#532×C12711yescharacteristic
446C2#542×C12711yescharacteristic
447C2D42×C12711yescharacteristic
448C2#547×C12711yescharacteristic
449C2#548×C12711yescharacteristic
450C2#551×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radical#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#124×C127C2semidirect
2. C2×#123×C127C2semidirect
3. C2×C22⋊Q8×C127C2semidirect
4. C2×C4×D4×C127C2semidirect
5. #396×C127C2semidirect
6. #395×C127C2semidirect
7. #394×C127C2semidirect
9. #390×C127C2semidirect
10. #388×C127C2semidirect
11. #388×C127C2semidirect
12. #388×C127C2semidirect
13. #386×C127C2semidirect
14. #385×C127C2semidirect
15. C4×C4⋊C4×C127C2semidirect
94. C4⋊C4×C127D4semidirect
107. C22⋊C4×C127D4semidirect
225. #2461C127direct (N × H)
226. C127#2461direct (N × H)
227. C2×#124C2×C127semidirect
228. C2×#123C2×C127semidirect
229. C2×C22⋊Q8C2×C127semidirect
230. C2×C4×D4C2×C127semidirect
231. #396C2×C127semidirect
232. #395C2×C127semidirect
233. #394C2×C127semidirect
235. #390C2×C127semidirect
236. #388C2×C127semidirect
237. #388C2×C127semidirect
238. #388C2×C127semidirect
239. #386C2×C127semidirect
240. #385C2×C127semidirect
241. C4×C4⋊C4C2×C127semidirect
320. C4⋊C4D4×C127semidirect
333. C22⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1272
C2×#123×C1272
C2×C22⋊Q8×C1272
C2×C4×D4×C1272
#396×C1272
#395×C1272
#394×C1272
#392×C1272
#390×C1272
#388×C1272
#386×C1272
#385×C1272
C4×C4⋊C4×C1272
#2461127