Finite Group Databasebeta

← C127×#11715 #44575388

Subgroups — C127×#11715 #44575388

Order 32512.

468 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2396C211yesmaximal, characteristic
2C127×#1740C211yesmaximal, characteristic
3C127×#1458C211yesmaximal, characteristic
4C127×#1352C212yesmaximal
5C127×#1351C212yesmaximal
6C2×C4×Q8×C127C411yescharacteristic, complemented
7C2×#117×C127—21no—
8C2×#117×C127C2211yescharacteristic
9#431×C127—21no—
10#400×C127C411yescharacteristic, complemented
11#399×C127C2211yescharacteristic
12#398×C127—21no—
13#396×C127—21no—
14#395×C127C411yescharacteristic, complemented
15#393×C127C2211yescharacteristic
16C4×C4⋊C4×C127—21no—
17C4×C4⋊C4×C127C411yescharacteristic, complemented
18C4×C22⋊C4×C127—21no—
19#342×C127—21no—
20#342×C127C2212yes—
21#324×C127—21no—
22#323×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C4×Q8×C127—41no—
26C4×Q8×C127—41no—
27#117×C127—24no—
28#117×C127—41no—
29#117×C127—41no—
30#117×C127—42no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—41no—
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C22⋊C4×C127C2311yescharacteristic
44C2×C42×C127—21no—
45C2×C42×C127—21no—
46C2×C42×C127—41no—
47C2×C42×C127C2×C411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C4⋊C8×C127—41no—
50C22⋊C8×C127—22no—
51C4×C8×C127—41no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127C2×C411yescharacteristic
57#95×C127C2×C411yescharacteristic
58C24×C127C2×D411yescharacteristic
59C2×Q8×C127—42no—
60C2×Q8×C127—41no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—42no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127SD1612yes—
74C22×C4×C127Q1612yes—
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C2×C8×C127—42no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—42no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—44no—
86C22⋊C4×C127—24no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C42×C127—21no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—44no—
97C42×C127—41no—
98C42×C127—41no—
99C42×C127—42no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127C2×C22⋊C411yescharacteristic
105C23×C127C2×SD1611yescharacteristic
106C23×C127C2×Q1611yescharacteristic
107Q8×C127—42no—
108Q8×C127—42no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—22no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—44no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—82no—
137C2×C4×C127—82no—
138C2×C4×C127#9911yescharacteristic
139C2×C4×C127#9911yescharacteristic
140C2×C4×C127#10312yes—
141C2×C4×C127#10312yes—
142C2×C4×C127#10412yes—
143C8×C127—82no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—41no—
151C22×C127—41no—
152C22×C127—81no—
153C22×C127C2×#9911yescharacteristic
154C22×C127C2×#10311yescharacteristic
155C22×C127C2×#10411yescharacteristic
156C4×C127—22no—
157C4×C127—42no—
158C4×C127—41no—
159C4×C127—42no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—81no—
164C4×C127—84no—
165C4×C127—81no—
166C4×C127#32812yes—
167C4×C127#32812yes—
168#11715C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—21no—
170C2×C127—21no—
171C2×C127—41no—
172C2×C127—41no—
173C2×C127C2×#32811yescharacteristic
174C2×C127#212011yescharacteristic
175C2×C127#212611yescharacteristic
176#2396C2×C12711yescharacteristic
177#1740C2×C12711yescharacteristic
178#1458C2×C12711yescharacteristic
179#1352C2×C12712yes—
180#1351C2×C12712yes—
181C127#1171511yescharacteristic, direct product factor, Sylow
182C2×C4×Q8C4×C12711yescharacteristic, complemented
183C2×#117—21no—
184C2×#117C22×C12711yescharacteristic
185#431—21no—
186#400C4×C12711yescharacteristic, complemented
187#399C22×C12711yescharacteristic
188#398—21no—
189#396—21no—
190#395C4×C12711yescharacteristic, complemented
191#393C22×C12711yescharacteristic
192C4×C4⋊C4—21no—
193C4×C4⋊C4C4×C12711yescharacteristic, complemented
194C4×C22⋊C4—21no—
195#342—21no—
196#342C22×C12712yes—
197#324—21no—
198#323C22×C12712yes—
199C22×Q8C2×C4×C12711yescharacteristic
200C23×C4D4×C12711yescharacteristic
201C4×Q8—41no—
202C4×Q8—41no—
203#117—24no—
204#117—41no—
205#117—41no—
206#117—42no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4C2×C4×C12711yescharacteristic
213C2×C4⋊C4C2×C4×C12711yescharacteristic
214C2×C4⋊C4D4×C12711yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4D4×C12711yescharacteristic
219C2×C22⋊C4C23×C12711yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—41no—
223C2×C42C2×C4×C12711yescharacteristic
224C2×C42D4×C12711yescharacteristic
225C4⋊C8—41no—
226C22⋊C8—22no—
227C4×C8—41no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C2×C4×C12711yescharacteristic
233#95C2×C4×C12711yescharacteristic
234C24C2×D4×C12711yescharacteristic
235C2×Q8—42no—
236C2×Q8—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22⋊C4×C12711yescharacteristic
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4SD16×C12712yes—
250C22×C4Q16×C12712yes—
251C22×C4C22×C4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C2×C8—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—44no—
262C22⋊C4—24no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—44no—
273C42—41no—
274C42—41no—
275C42—42no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊C4×C12711yescharacteristic
281C23C2×SD16×C12711yescharacteristic
282C23C2×Q16×C12711yescharacteristic
283Q8—42no—
284Q8—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—44no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4#99×C12711yescharacteristic
315C2×C4#99×C12711yescharacteristic
316C2×C4#103×C12712yes—
317C2×C4#103×C12712yes—
318C2×C4#104×C12712yes—
319C8—82no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22C2×#99×C12711yescharacteristic
330C22C2×#103×C12711yescharacteristic
331C22C2×#104×C12711yescharacteristic
332C4—22no—
333C4—42no—
334C4—42no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—84no—
341C4—81no—
342C4#328×C12712yes—
343C4#328×C12712yes—
344C2—21no—
345C2—21no—
346C2—41no—
347C2—41no—
348C2C2×#328×C12711yescharacteristic
349C2C127×#212011yescharacteristic
350C2C127×#212611yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
socleC22×C127C2×#99
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C127C4semidirect
10. #400×C127C4semidirect
14. #395×C127C4semidirect
17. C4×C4⋊C4×C127C4semidirect
168. #11715C127direct (N × H)
181. C127#11715direct (N × H)
182. C2×C4×Q8C4×C127semidirect
186. #400C4×C127semidirect
190. #395C4×C127semidirect
193. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23962
C127×#17402
C127×#14582
C127×#13522
C127×#13512
#11715127