Finite Group Databasebeta

← C127×#2778 #30635730

Subgroups — C127×#2778 #30635730

Order 16256.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#401×C127C211yesmaximal, characteristic, complemented
2#400×C127C211yesmaximal, characteristic, complemented
3#397×C127C211yesmaximal, characteristic, complemented
4#394×C127C211yesmaximal, characteristic, complemented
5#394×C127C211yesmaximal, characteristic, complemented
6#392×C127C211yesmaximal, characteristic
7#388×C127C211yesmaximal, characteristic, complemented
8#388×C127C211yesmaximal, characteristic, complemented
9#388×C127C211yesmaximal, characteristic, complemented
10#386×C127C211yesmaximal, characteristic, complemented
11#386×C127C211yesmaximal, characteristic, complemented
12#386×C127C211yesmaximal, characteristic, complemented
13#386×C127C211yesmaximal, characteristic, complemented
14#385×C127C211yesmaximal, characteristic, complemented
15#380×C127C211yesmaximal, characteristic, complemented
16C22×D4×C127C2211yescharacteristic
17C22×D4×C127C2211yescharacteristic
18C22×D4×C127C2211yescharacteristic
19C23×C4×C127C2211yescharacteristic
20C23×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×C22⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127C2211yescharacteristic
34C2×C22⋊C4×C127C2211yescharacteristic
35C2×C22⋊C4×C127C2211yescharacteristic
36C2×C22⋊C4×C127C2211yescharacteristic
37C2×C22⋊C4×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
52C24×C127C2311yescharacteristic
53C24×C127C2311yescharacteristic
54C2×D4×C127—22no—
55C2×D4×C127—22no—
56C2×D4×C127—22no—
57C2×D4×C127—22no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C2×D4×C127—41no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C22×C4×C127—22no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127C2311yescharacteristic
70C22×C4×C127C2311yescharacteristic
71C22×C4×C127C2311yescharacteristic
72C22×C4×C127C2311yescharacteristic
73C22×C4×C127C2311yescharacteristic
74C22×C4×C127C2311yescharacteristic
75C22×C4×C127C2311yescharacteristic
76C22×C4×C127C2311yescharacteristic
77C22×C4×C127C2311yescharacteristic
78C22×C4×C127C2311yescharacteristic
79C22×C4×C127C2311yescharacteristic
80C22×C4×C127C2311yescharacteristic
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—22no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C42×C127—41no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—21no—
118C23×C127#4112yes—
119C23×C127#4112yes—
120C23×C127C2411yescharacteristic
121D4×C127—44no—
122D4×C127—44no—
123D4×C127—44no—
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—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—44no—
160C2×C4×C127—44no—
161C2×C4×C127#4112yes—
162C22×C127—22no—
163C22×C127—22no—
164C22×C127—22no—
165C22×C127—22no—
166C22×C127—22no—
167C22×C127—22no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127—41no—
178C22×C127—41no—
179C22×C127—41no—
180C22×C127—41no—
181C22×C127—41no—
182C22×C127—41no—
183C22×C127C2×#4111yescharacteristic
184C22×C127C2×#4111yescharacteristic
185C22×C127C2×#4111yescharacteristic
186C22×C127H(5,𝔽2)11yescharacteristic
187C22×C127H(5,𝔽2)11yescharacteristic
188C22×C127H(5,𝔽2)11yescharacteristic
189C22×C127H(5,𝔽2)11yescharacteristic
190C4×C127—22no—
191C4×C127—41no—
192C4×C127—41no—
193C4×C127—41no—
194C4×C127—41no—
195C4×C127—41no—
196C4×C127—41no—
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—41no—
200C4×C127—41no—
201C4×C127—41no—
202C2×C127—42no—
203C2×C127—42no—
204C2×C127—81no—
205C2×C127#53811yescharacteristic
206C2×C127#53811yescharacteristic
207C2×C127#53811yescharacteristic
208C2×C127#55111yescharacteristic
209C2×C127#55311yescharacteristic
210C2×C127#55311yescharacteristic
211C2×C127#56011yescharacteristic
212#2778C12711yesmaximal, characteristic, direct product factor, Sylow
213C127#277811yescharacteristic, direct product factor, Sylow
214#401C2×C12711yescharacteristic, complemented
215#400C2×C12711yescharacteristic, complemented
216#397C2×C12711yescharacteristic, complemented
217#394C2×C12711yescharacteristic, complemented
218#394C2×C12711yescharacteristic, complemented
219#392C2×C12711yescharacteristic
220#388C2×C12711yescharacteristic, complemented
221#388C2×C12711yescharacteristic, complemented
222#388C2×C12711yescharacteristic, complemented
223#386C2×C12711yescharacteristic, complemented
224#386C2×C12711yescharacteristic, complemented
225#386C2×C12711yescharacteristic, complemented
226#386C2×C12711yescharacteristic, complemented
227#385C2×C12711yescharacteristic, complemented
228#380C2×C12711yescharacteristic, complemented
229C22×D4C22×C12711yescharacteristic
230C22×D4C22×C12711yescharacteristic
231C22×D4C22×C12711yescharacteristic
232C23×C4C22×C12711yescharacteristic
233C23×C4C22×C12711yescharacteristic
234C2×C4⋊C4C22×C12711yescharacteristic
235C2×C4⋊C4C22×C12711yescharacteristic
236C2×C4⋊C4C22×C12711yescharacteristic
237C2×C4⋊C4C22×C12711yescharacteristic
238C2×C22⋊C4C22×C12711yescharacteristic
239C2×C22⋊C4C22×C12711yescharacteristic
240C2×C22⋊C4C22×C12711yescharacteristic
241C2×C22⋊C4C22×C12711yescharacteristic
242C2×C22⋊C4C22×C12711yescharacteristic
243C2×C22⋊C4C22×C12711yescharacteristic
244C2×C22⋊C4C22×C12711yescharacteristic
245C2×C22⋊C4C22×C12711yescharacteristic
246C2×C22⋊C4C22×C12711yescharacteristic
247C2×C22⋊C4C22×C12711yescharacteristic
248C2×C22⋊C4C22×C12711yescharacteristic
249C2×C22⋊C4C22×C12711yescharacteristic
250C2×C22⋊C4C22×C12711yescharacteristic
251C2×C42C22×C12711yescharacteristic
252#95C22×C12711yescharacteristic
253#95C22×C12711yescharacteristic
254#95C22×C12711yescharacteristic
255#95C22×C12711yescharacteristic
256#95C22×C12711yescharacteristic
257#95C22×C12711yescharacteristic
258#95C22×C12711yescharacteristic
259#95C22×C12711yescharacteristic
260#95C22×C12711yescharacteristic
261#95C22×C12711yescharacteristic
262#95C22×C12711yescharacteristic
263#95C22×C12711yescharacteristic
264C24C23×C12711yescharacteristic
265C24C23×C12711yescharacteristic
266C24C23×C12711yescharacteristic
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C23×C12711yescharacteristic
283C22×C4C23×C12711yescharacteristic
284C22×C4C23×C12711yescharacteristic
285C22×C4C23×C12711yescharacteristic
286C22×C4C23×C12711yescharacteristic
287C22×C4C23×C12711yescharacteristic
288C22×C4C23×C12711yescharacteristic
289C22×C4C23×C12711yescharacteristic
290C22×C4C23×C12711yescharacteristic
291C22×C4C23×C12711yescharacteristic
292C22×C4C23×C12711yescharacteristic
293C22×C4C23×C12711yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—41no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23#41×C12712yes—
332C23#41×C12712yes—
333C23C24×C12711yescharacteristic
334D4—44no—
335D4—44no—
336D4—44no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
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—44no—
373C2×C4—44no—
374C2×C4#41×C12712yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22C2×#41×C12711yescharacteristic
397C22C2×#41×C12711yescharacteristic
398C22C2×#41×C12711yescharacteristic
399C22H(5,𝔽2)×C12711yescharacteristic
400C22H(5,𝔽2)×C12711yescharacteristic
401C22H(5,𝔽2)×C12711yescharacteristic
402C22H(5,𝔽2)×C12711yescharacteristic
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2#538×C12711yescharacteristic
419C2#538×C12711yescharacteristic
420C2#538×C12711yescharacteristic
421C2#551×C12711yescharacteristic
422C2#553×C12711yescharacteristic
423C2#553×C12711yescharacteristic
424C2#560×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. #401×C127C2semidirect
2. #400×C127C2semidirect
3. #397×C127C2semidirect
4. #394×C127C2semidirect
5. #394×C127C2semidirect
7. #388×C127C2semidirect
8. #388×C127C2semidirect
9. #388×C127C2semidirect
10. #386×C127C2semidirect
11. #386×C127C2semidirect
12. #386×C127C2semidirect
13. #386×C127C2semidirect
14. #385×C127C2semidirect
15. #380×C127C2semidirect
212. #2778C127direct (N × H)
213. C127#2778direct (N × H)
214. #401C2×C127semidirect
215. #400C2×C127semidirect
216. #397C2×C127semidirect
217. #394C2×C127semidirect
218. #394C2×C127semidirect
220. #388C2×C127semidirect
221. #388C2×C127semidirect
222. #388C2×C127semidirect
223. #386C2×C127semidirect
224. #386C2×C127semidirect
225. #386C2×C127semidirect
226. #386C2×C127semidirect
227. #385C2×C127semidirect
228. #380C2×C127semidirect

Maximal subgroups

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

subgroupindex
#401×C1272
#400×C1272
#397×C1272
#394×C1272
#392×C1272
#388×C1272
#386×C1272
#385×C1272
#380×C1272
#2778127