Finite Group Databasebeta

← C127×#2800 #30635752

Subgroups — C127×#2800 #30635752

Order 16256.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#397×C127C211yesmaximal, characteristic, complemented
2#397×C127C211yesmaximal, characteristic, complemented
3#396×C127C211yesmaximal, characteristic, complemented
4#396×C127C211yesmaximal, characteristic, complemented
5#394×C127C211yesmaximal, characteristic
6#394×C127C211yesmaximal, characteristic
7#390×C127C211yesmaximal, characteristic
8#389×C127C211yesmaximal, characteristic, complemented
9#389×C127C211yesmaximal, characteristic, complemented
10#388×C127C211yesmaximal, characteristic, complemented
11#388×C127C211yesmaximal, characteristic, complemented
12#388×C127C211yesmaximal, characteristic, complemented
13#388×C127C211yesmaximal, characteristic, complemented
14#387×C127C211yesmaximal, characteristic, complemented
15#387×C127C211yesmaximal, characteristic, complemented
16C22×D4×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×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
39C2×C42×C127C2211yescharacteristic
40C2×C42×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
53C2×D4×C127—22no—
54C2×D4×C127—41no—
55C2×D4×C127—41no—
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—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C22⋊C4×C127—22no—
79C22⋊C4×C127—22no—
80C22⋊C4×C127—22no—
81C22⋊C4×C127—22no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C42×C127—41no—
91C42×C127—41no—
92C42×C127—41no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—21no—
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×C127C2411yescharacteristic
108D4×C127—44no—
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—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127#4112yes—
146C2×C4×C127#4112yes—
147C2×C4×C127#4112yes—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—41no—
151C22×C127—41no—
152C22×C127—41no—
153C22×C127—41no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—41no—
157C22×C127—41no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127C2×#4111yescharacteristic
163C22×C127C2×#4111yescharacteristic
164C22×C127C2×#4111yescharacteristic
165C22×C127H(5,𝔽2)11yescharacteristic
166C22×C127H(5,𝔽2)11yescharacteristic
167C22×C127H(5,𝔽2)11yescharacteristic
168C22×C1272−1+411yescharacteristic
169C4×C127—22no—
170C4×C127—22no—
171C4×C127—22no—
172C4×C127—41no—
173C4×C127—41no—
174C4×C127—41no—
175C4×C127—41no—
176C4×C127—41no—
177C4×C127—41no—
178C4×C127—41no—
179C4×C127—41no—
180C4×C127—41no—
181C4×C127—41no—
182C2×C127—81no—
183C2×C127—81no—
184C2×C127#53811yescharacteristic
185C2×C127#54011yescharacteristic
186C2×C127#54211yescharacteristic
187C2×C127#55311yescharacteristic
188C2×C127#55311yescharacteristic
189C2×C127#55611yescharacteristic
190C2×C127#56211yescharacteristic
191#2800C12711yesmaximal, characteristic, direct product factor, Sylow
192C127#280011yescharacteristic, direct product factor, Sylow
193#397C2×C12711yescharacteristic, complemented
194#397C2×C12711yescharacteristic, complemented
195#396C2×C12711yescharacteristic, complemented
196#396C2×C12711yescharacteristic, complemented
197#394C2×C12711yescharacteristic
198#394C2×C12711yescharacteristic
199#390C2×C12711yescharacteristic
200#389C2×C12711yescharacteristic, complemented
201#389C2×C12711yescharacteristic, complemented
202#388C2×C12711yescharacteristic, complemented
203#388C2×C12711yescharacteristic, complemented
204#388C2×C12711yescharacteristic, complemented
205#388C2×C12711yescharacteristic, complemented
206#387C2×C12711yescharacteristic, complemented
207#387C2×C12711yescharacteristic, complemented
208C22×D4C22×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×C22⋊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×C22⋊C4C22×C12711yescharacteristic
226C2×C22⋊C4C22×C12711yescharacteristic
227C2×C22⋊C4C22×C12711yescharacteristic
228C2×C22⋊C4C22×C12711yescharacteristic
229C2×C22⋊C4C22×C12711yescharacteristic
230C2×C42C22×C12711yescharacteristic
231C2×C42C22×C12711yescharacteristic
232C2×C42C22×C12711yescharacteristic
233#95C22×C12711yescharacteristic
234#95C22×C12711yescharacteristic
235#95C22×C12711yescharacteristic
236#95C22×C12711yescharacteristic
237#95C22×C12711yescharacteristic
238#95C22×C12711yescharacteristic
239#95C22×C12711yescharacteristic
240#95C22×C12711yescharacteristic
241#95C22×C12711yescharacteristic
242#95C22×C12711yescharacteristic
243C24C23×C12711yescharacteristic
244C24C23×C12711yescharacteristic
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
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
260C22×C4C23×C12711yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42—41no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C24×C12711yescharacteristic
300D4—44no—
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—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4#41×C12712yes—
338C2×C4#41×C12712yes—
339C2×C4#41×C12712yes—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22C2×#41×C12711yescharacteristic
355C22C2×#41×C12711yescharacteristic
356C22C2×#41×C12711yescharacteristic
357C22H(5,𝔽2)×C12711yescharacteristic
358C22H(5,𝔽2)×C12711yescharacteristic
359C22H(5,𝔽2)×C12711yescharacteristic
360C222−1+4×C12711yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C2—81no—
375C2—81no—
376C2#538×C12711yescharacteristic
377C2#540×C12711yescharacteristic
378C2#542×C12711yescharacteristic
379C2#553×C12711yescharacteristic
380C2#553×C12711yescharacteristic
381C2#556×C12711yescharacteristic
382C2#562×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #397×C127C2semidirect
2. #397×C127C2semidirect
3. #396×C127C2semidirect
4. #396×C127C2semidirect
8. #389×C127C2semidirect
9. #389×C127C2semidirect
10. #388×C127C2semidirect
11. #388×C127C2semidirect
12. #388×C127C2semidirect
13. #388×C127C2semidirect
14. #387×C127C2semidirect
15. #387×C127C2semidirect
191. #2800C127direct (N × H)
192. C127#2800direct (N × H)
193. #397C2×C127semidirect
194. #397C2×C127semidirect
195. #396C2×C127semidirect
196. #396C2×C127semidirect
200. #389C2×C127semidirect
201. #389C2×C127semidirect
202. #388C2×C127semidirect
203. #388C2×C127semidirect
204. #388C2×C127semidirect
205. #388C2×C127semidirect
206. #387C2×C127semidirect
207. #387C2×C127semidirect

Maximal subgroups

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

subgroupindex
#397×C1272
#396×C1272
#394×C1272
#390×C1272
#389×C1272
#388×C1272
#387×C1272
#2800127