Finite Group Databasebeta

← C127×#15480 #44579153

Subgroups — C127×#15480 #44579153

Order 32512.

2818 conjugacy classes of subgroups; only the 374 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C213yesmaximal, complemented
2C2×#379×C127C213yesmaximal
3C127×#1439C216yesmaximal, complemented
4C127×#1437C212yesmaximal, complemented
5C127×#1437C211yesmaximal, characteristic, complemented
6C26×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2213yescomplemented
8C22×C22⋊C4×C127C2213yes—
9C22×C22⋊C4×C127C2216yes—
10C22×C22⋊C4×C127C2216yes—
11C22×C22⋊C4×C127C2213yes—
12C22×C42×C127C2211yescharacteristic, complemented
13#397×C127—212no—
14#379×C127—212no—
15C2×#95×C127C2216yescomplemented
16C2×#95×C127C2213yescomplemented
17C2×#95×C127C2213yescomplemented
18C25×C127—26no—
19C25×C127—212no—
20C25×C127—43no—
21C25×C127—43no—
22C25×C127C2311yescharacteristic
23C25×C127C2312yes—
24C23×C4×C127C2316yes—
25C23×C4×C127C2313yes—
26C23×C4×C127C2313yes—
27C2×C4⋊C4×C127—26no—
28C2×C4⋊C4×C127—43no—
29C2×C4⋊C4×C127—43no—
30C2×C22⋊C4×C127—26no—
31C2×C22⋊C4×C127—212no—
32C2×C22⋊C4×C127—212no—
33C2×C22⋊C4×C127—212no—
34C2×C22⋊C4×C127—212no—
35C2×C22⋊C4×C127—212no—
36C2×C22⋊C4×C127—43no—
37C2×C22⋊C4×C127—43no—
38C2×C22⋊C4×C127—46no—
39C2×C22⋊C4×C127—46no—
40C2×C22⋊C4×C127D4112yes—
41C2×C42×C127—43no—
42#95×C127—26no—
43#95×C127—212no—
44#95×C127—43no—
45C24×C127—26no—
46C24×C127—26no—
47C24×C127—26no—
48C24×C127—23no—
49C24×C127—23no—
50C24×C127—26no—
51C24×C127—26no—
52C24×C127—224no—
53C24×C127—424no—
54C24×C127—424no—
55C24×C127—412no—
56C24×C127—412no—
57C24×C127—412no—
58C24×C127—424no—
59C24×C127—44no—
60C24×C127—44no—
61C24×C127—48no—
62C24×C127—44no—
63C24×C127C2×D416yes—
64C24×C127#41112yes—
65C24×C127C2411yescharacteristic
66C22×C4×C127—26no—
67C22×C4×C127—26no—
68C22×C4×C127—23no—
69C22×C4×C127—26no—
70C22×C4×C127—23no—
71C22×C4×C127—26no—
72C22×C4×C127—23no—
73C22×C4×C127—23no—
74C22×C4×C127—26no—
75C22×C4×C127—26no—
76C22×C4×C127—26no—
77C22×C4×C127—26no—
78C22×C4×C127—26no—
79C22×C4×C127—26no—
80C22×C4×C127—26no—
81C22×C4×C127C2×D416yes—
82C22×C4×C127C2×D416yes—
83C4⋊C4×C127—412no—
84C22⋊C4×C127—412no—
85C22⋊C4×C127—424no—
86C22⋊C4×C127—424no—
87C22⋊C4×C127—412no—
88C42×C127—44no—
89C23×C127—26no—
90C23×C127—212no—
91C23×C127—26no—
92C23×C127—212no—
93C23×C127—212no—
94C23×C127—212no—
95C23×C127—212no—
96C23×C127—212no—
97C23×C127—212no—
98C23×C127—212no—
99C23×C127—496no—
100C23×C127—448no—
101C23×C127—448no—
102C23×C127—448no—
103C23×C127—42no—
104C23×C127—42no—
105C23×C127—42no—
106C23×C127—46no—
107C23×C127—46no—
108C23×C127—46no—
109C23×C127—46no—
110C23×C127—46no—
111C23×C127—43no—
112C23×C127—43no—
113C23×C127—41no—
114C23×C127—42no—
115C23×C127—41no—
116C23×C127—42no—
117C23×C127#12618yes—
118C23×C127#12714yes—
119C23×C127C22×D413yes—
120C23×C127C2×#4116yes—
121C23×C127H(5,𝔽2)13yes—
122C23×C127H(5,𝔽2)13yes—
123C2×C4×C127—26no—
124C2×C4×C127—26no—
125C2×C4×C127—212no—
126C2×C4×C127—212no—
127C2×C4×C127—46no—
128C2×C4×C127—46no—
129C2×C4×C127—43no—
130C2×C4×C127—43no—
131C2×C4×C127—43no—
132C2×C4×C127—43no—
133C2×C4×C127—46no—
134C2×C4×C127—46no—
135C2×C4×C127—46no—
136C2×C4×C127—46no—
137C2×C4×C127—46no—
138C2×C4×C127—46no—
139C2×C4×C127—46no—
140C22×C127—224no—
141C22×C127—212no—
142C22×C127—464no—
143C22×C127—46no—
144C22×C127—412no—
145C22×C127—46no—
146C22×C127—412no—
147C22×C127—412no—
148C22×C127—412no—
149C22×C127—412no—
150C22×C127#52513yes—
151C22×C127C2×#12612yes—
152C22×C127C2×#12711yescharacteristic
153C22×C127#53413yes—
154C22×C127#53816yes—
155C22×C127#54616yes—
156C22×C127#54616yes—
157C22×C127#55113yes—
158C22×C127#55113yes—
159C22×C127#56011yescharacteristic
160C22×C127H(3,𝔽4)11yescharacteristic
161C4×C127—46no—
162C4×C127—46no—
163C4×C127—86no—
164#15480C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—48no—
166C2×C127—44no—
167C2×C127#248016yes—
168C2×C127#253913yes—
169C2×C127#268413yes—
170C2×C127#269713yes—
171C2×#397C2×C12713yescomplemented
172C2×#379C2×C12713yes—
173#1439C2×C12716yescomplemented
174#1437C2×C12712yescomplemented
175#1437C2×C12711yescharacteristic, complemented
176C127#1548011yescharacteristic, direct product factor, Sylow
177C26C22×C12711yescharacteristic
178C22×C4⋊C4C22×C12713yescomplemented
179C22×C22⋊C4C22×C12713yes—
180C22×C22⋊C4C22×C12716yes—
181C22×C22⋊C4C22×C12716yes—
182C22×C22⋊C4C22×C12713yes—
183C22×C42C22×C12711yescharacteristic, complemented
184#397—212no—
185#379—212no—
186C2×#95C22×C12716yescomplemented
187C2×#95C22×C12713yescomplemented
188C2×#95C22×C12713yescomplemented
189C25—26no—
190C25—212no—
191C25—43no—
192C25—43no—
193C25C23×C12711yescharacteristic
194C25C23×C12712yes—
195C23×C4C23×C12716yes—
196C23×C4C23×C12713yes—
197C23×C4C23×C12713yes—
198C2×C4⋊C4—26no—
199C2×C4⋊C4—43no—
200C2×C4⋊C4—43no—
201C2×C22⋊C4—26no—
202C2×C22⋊C4—212no—
203C2×C22⋊C4—212no—
204C2×C22⋊C4—212no—
205C2×C22⋊C4—212no—
206C2×C22⋊C4—212no—
207C2×C22⋊C4—43no—
208C2×C22⋊C4—43no—
209C2×C22⋊C4—46no—
210C2×C22⋊C4—46no—
211C2×C22⋊C4D4×C127112yes—
212C2×C42—43no—
213#95—26no—
214#95—212no—
215#95—43no—
216C24—26no—
217C24—26no—
218C24—26no—
219C24—23no—
220C24—23no—
221C24—26no—
222C24—26no—
223C24—224no—
224C24—424no—
225C24—424no—
226C24—412no—
227C24—412no—
228C24—412no—
229C24—424no—
230C24—44no—
231C24—44no—
232C24—48no—
233C24—44no—
234C24C2×D4×C12716yes—
235C24#41×C127112yes—
236C24C24×C12711yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—23no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—26no—
246C22×C4—26no—
247C22×C4—26no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4C2×D4×C12716yes—
253C22×C4C2×D4×C12716yes—
254C4⋊C4—412no—
255C22⋊C4—412no—
256C22⋊C4—424no—
257C22⋊C4—424no—
258C22⋊C4—412no—
259C42—44no—
260C23—26no—
261C23—212no—
262C23—26no—
263C23—212no—
264C23—212no—
265C23—212no—
266C23—212no—
267C23—212no—
268C23—212no—
269C23—212no—
270C23—496no—
271C23—448no—
272C23—448no—
273C23—448no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—46no—
278C23—46no—
279C23—46no—
280C23—46no—
281C23—46no—
282C23—43no—
283C23—43no—
284C23—41no—
285C23—42no—
286C23—41no—
287C23—42no—
288C23#126×C12718yes—
289C23#127×C12714yes—
290C23C22×D4×C12713yes—
291C23C2×#41×C12716yes—
292C23H(5,𝔽2)×C12713yes—
293C23H(5,𝔽2)×C12713yes—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—212no—
297C2×C4—212no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—43no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—46no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—46no—
308C2×C4—46no—
309C2×C4—46no—
310C2×C4—46no—
311C22—224no—
312C22—212no—
313C22—464no—
314C22—46no—
315C22—412no—
316C22—46no—
317C22—412no—
318C22—412no—
319C22—412no—
320C22—412no—
321C22#525×C12713yes—
322C22C2×#126×C12712yes—
323C22C2×#127×C12711yescharacteristic
324C22#534×C12713yes—
325C22#538×C12716yes—
326C22#546×C12716yes—
327C22#546×C12716yes—
328C22#551×C12713yes—
329C22#551×C12713yes—
330C22#560×C12711yescharacteristic
331C22H(3,𝔽4)×C12711yescharacteristic
332C4—46no—
333C4—46no—
334C4—86no—
335C2—48no—
336C2—44no—
337C2C127×#248016yes—
338C2C127×#253913yes—
339C2C127×#268413yes—
340C2C127×#269713yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C127C2semidirect
3. C127×#1439C2semidirect
4. C127×#1437C2semidirect
5. C127×#1437C2semidirect
7. C22×C4⋊C4×C127C22semidirect
12. C22×C42×C127C22semidirect
15. C2×#95×C127C22semidirect
16. C2×#95×C127C22semidirect
17. C2×#95×C127C22semidirect
164. #15480C127direct (N × H)
171. C2×#397C2×C127semidirect
173. #1439C2×C127semidirect
174. #1437C2×C127semidirect
175. #1437C2×C127semidirect
176. C127#15480direct (N × H)
178. C22×C4⋊C4C22×C127semidirect
183. C22×C42C22×C127semidirect
186. C2×#95C22×C127semidirect
187. C2×#95C22×C127semidirect
188. C2×#95C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C2×#379×C1272
C127×#14392
C127×#14372
#15480127