Finite Group Databasebeta

← C127×#13775 #44577448

Subgroups — C127×#13775 #44577448

Order 32512.

3566 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#379×C127C212yesmaximal
3C2×C4×C22⋊C4×C127C212yesmaximal, complemented
4C127×#1437C218yesmaximal, complemented
5C127×C22⋊#95C212yesmaximal, complemented
6C26×C127C2211yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C24×C4×C127C2211yescharacteristic
9C22×C22⋊C4×C127—28no—
10C22×C22⋊C4×C127C418yescomplemented
11C22×C22⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2218yes—
14C22×C42×C127C2214yescomplemented
15#379×C127C4116yescomplemented
16C4×C22⋊C4×C127—28no—
17C2×#95×C127C2214yescomplemented
18C2×#95×C127C2218yescomplemented
19C25×C127—24no—
20C25×C127—24no—
21C25×C127—44no—
22C25×C127—44no—
23C25×C127C2×C414yes—
24C25×C127C2×C418yes—
25C25×C127C2312yes—
26C25×C127C2311yescharacteristic
27C23×C4×C127—24no—
28C23×C4×C127—44no—
29C23×C4×C127—44no—
30C23×C4×C127C2×C414yes—
31C23×C4×C127C2×C414yes—
32C23×C4×C127D418yes—
33C23×C4×C127C2318yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C2×C22⋊C4×C127—28no—
37C2×C22⋊C4×C127—28no—
38C2×C22⋊C4×C127—232no—
39C2×C22⋊C4×C127—28no—
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—48no—
42C2×C22⋊C4×C127—48no—
43C2×C22⋊C4×C127C2×C4116yes—
44C2×C22⋊C4×C127C2×C4116yes—
45C2×C22⋊C4×C127C2×C4132yescomplemented
46C2×C42×C127—28no—
47C2×C42×C127—48no—
48#95×C127—28no—
49#95×C127—48no—
50C24×C127—24no—
51C24×C127—24no—
52C24×C127—28no—
53C24×C127—28no—
54C24×C127—232no—
55C24×C127—24no—
56C24×C127—24no—
57C24×C127—28no—
58C24×C127—28no—
59C24×C127—48no—
60C24×C127—48no—
61C24×C127—432no—
62C24×C127—416no—
63C24×C127—416no—
64C24×C127—432no—
65C24×C127C42116yescomplemented
66C24×C127C22×C414yes—
67C24×C127C22×C418yes—
68C24×C127C22×C412yes—
69C24×C127C22×C414yes—
70C24×C127C2×D414yes—
71C24×C127#4114yes—
72C24×C127C2411yescharacteristic
73C22×C4×C127—28no—
74C22×C4×C127—28no—
75C22×C4×C127—28no—
76C22×C4×C127—24no—
77C22×C4×C127—28no—
78C22×C4×C127—216no—
79C22×C4×C127—28no—
80C22×C4×C127—216no—
81C22×C4×C127—48no—
82C22×C4×C127—48no—
83C22×C4×C127—416no—
84C22×C4×C127—416no—
85C22×C4×C127C22⋊C4116yescomplemented
86C22×C4×C127C22×C414yes—
87C22×C4×C127C22×C4116yes—
88C22×C4×C127C22×C414yes—
89C22×C4×C127C2×D414yes—
90C22×C4×C127C2×D414yes—
91C22⋊C4×C127—232no—
92C22⋊C4×C127—232no—
93C22⋊C4×C127—432no—
94C42×C127—416no—
95C23×C127—24no—
96C23×C127—24no—
97C23×C127—216no—
98C23×C127—28no—
99C23×C127—28no—
100C23×C127—216no—
101C23×C127—24no—
102C23×C127—24no—
103C23×C127—216no—
104C23×C127—216no—
105C23×C127—28no—
106C23×C127—28no—
107C23×C127—216no—
108C23×C127—232no—
109C23×C127—432no—
110C23×C127—416no—
111C23×C127—416no—
112C23×C127—432no—
113C23×C127—4128no—
114C23×C127—48no—
115C23×C127—48no—
116C23×C127—416no—
117C23×C127C2×C4218yes—
118C23×C127C2×C4214yes—
119C23×C127C2×C22⋊C414yes—
120C23×C127#11714yes—
121C23×C127C4×D4116yes—
122C23×C127C23×C411yescharacteristic
123C23×C127C23×C412yes—
124C23×C127C22×D412yes—
125C23×C127C2×#4112yes—
126C23×C127H(5,𝔽2)14yes—
127C23×C127H(5,𝔽2)14yes—
128C2×C4×C127—28no—
129C2×C4×C127—28no—
130C2×C4×C127—28no—
131C2×C4×C127—24no—
132C2×C4×C127—216no—
133C2×C4×C127—232no—
134C2×C4×C127—28no—
135C2×C4×C127—416no—
136C2×C4×C127—416no—
137C2×C4×C127—48no—
138C2×C4×C127—48no—
139C2×C4×C127—48no—
140C2×C4×C127—416no—
141C2×C4×C127C2×C22⋊C418yes—
142C22×C127—24no—
143C22×C127—24no—
144C22×C127—28no—
145C22×C127—232no—
146C22×C127—28no—
147C22×C127—28no—
148C22×C127—216no—
149C22×C127—464no—
150C22×C127—44no—
151C22×C127—44no—
152C22×C127—48no—
153C22×C127—432no—
154C22×C127C4×C22⋊C418yes—
155C22×C127C22×C4211yescharacteristic
156C22×C127C22×C22⋊C411yescharacteristic
157C22×C127C2×#11711yescharacteristic
158C22×C127C2×C4×D414yes—
159C22×C127#51812yes—
160C22×C127#51812yes—
161C22×C127#51818yes—
162C22×C127#53414yes—
163C22×C127#53514yes—
164C22×C127#53818yes—
165C4×C127—28no—
166C4×C127—44no—
167C4×C127—416no—
168#13775C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—28no—
170C2×C127—48no—
171C2×C127C2×C4×C22⋊C411yescharacteristic
172C2×C127#227312yes—
173C2×C127#230811yescharacteristic
174C2×C127#230911yescharacteristic
175C2×C127#231212yes—
176C2×C127#232118yes—
177C23×C22⋊C4C2×C12711yescharacteristic
178C2×#379C2×C12712yes—
179C2×C4×C22⋊C4C2×C12712yescomplemented
180#1437C2×C12718yescomplemented
181C22⋊#95C2×C12712yescomplemented
182C127#1377511yescharacteristic, direct product factor, Sylow
183C26C22×C12711yescharacteristic
184C24×C4C22×C12711yescharacteristic
185C24×C4C22×C12711yescharacteristic
186C22×C22⋊C4—28no—
187C22×C22⋊C4C4×C12718yescomplemented
188C22×C22⋊C4C22×C12714yes—
189C22×C22⋊C4C22×C12714yes—
190C22×C22⋊C4C22×C12718yes—
191C22×C42C22×C12714yescomplemented
192#379C4×C127116yescomplemented
193C4×C22⋊C4—28no—
194C2×#95C22×C12714yescomplemented
195C2×#95C22×C12718yescomplemented
196C25—24no—
197C25—24no—
198C25—44no—
199C25—44no—
200C25C2×C4×C12714yes—
201C25C2×C4×C12718yes—
202C25C23×C12712yes—
203C25C23×C12711yescharacteristic
204C23×C4—24no—
205C23×C4—44no—
206C23×C4—44no—
207C23×C4C2×C4×C12714yes—
208C23×C4C2×C4×C12714yes—
209C23×C4D4×C12718yes—
210C23×C4C23×C12718yes—
211C23×C4C23×C12712yes—
212C23×C4C23×C12712yes—
213C2×C22⋊C4—28no—
214C2×C22⋊C4—28no—
215C2×C22⋊C4—232no—
216C2×C22⋊C4—28no—
217C2×C22⋊C4—28no—
218C2×C22⋊C4—48no—
219C2×C22⋊C4—48no—
220C2×C22⋊C4C2×C4×C127116yes—
221C2×C22⋊C4C2×C4×C127116yes—
222C2×C22⋊C4C2×C4×C127132yescomplemented
223C2×C42—28no—
224C2×C42—48no—
225#95—28no—
226#95—48no—
227C24—24no—
228C24—24no—
229C24—28no—
230C24—28no—
231C24—232no—
232C24—24no—
233C24—24no—
234C24—28no—
235C24—28no—
236C24—48no—
237C24—48no—
238C24—432no—
239C24—416no—
240C24—416no—
241C24—432no—
242C24C42×C127116yescomplemented
243C24C22×C4×C12714yes—
244C24C22×C4×C12718yes—
245C24C22×C4×C12712yes—
246C24C22×C4×C12714yes—
247C24C2×D4×C12714yes—
248C24#41×C12714yes—
249C24C24×C12711yescharacteristic
250C22×C4—28no—
251C22×C4—28no—
252C22×C4—28no—
253C22×C4—24no—
254C22×C4—28no—
255C22×C4—216no—
256C22×C4—28no—
257C22×C4—216no—
258C22×C4—48no—
259C22×C4—48no—
260C22×C4—416no—
261C22×C4—416no—
262C22×C4C22⋊C4×C127116yescomplemented
263C22×C4C22×C4×C12714yes—
264C22×C4C22×C4×C127116yes—
265C22×C4C22×C4×C12714yes—
266C22×C4C2×D4×C12714yes—
267C22×C4C2×D4×C12714yes—
268C22⋊C4—232no—
269C22⋊C4—232no—
270C22⋊C4—432no—
271C42—416no—
272C23—24no—
273C23—24no—
274C23—216no—
275C23—28no—
276C23—28no—
277C23—216no—
278C23—24no—
279C23—24no—
280C23—216no—
281C23—216no—
282C23—28no—
283C23—28no—
284C23—216no—
285C23—232no—
286C23—432no—
287C23—432no—
288C23—4128no—
289C23—416no—
290C23—416no—
291C23—48no—
292C23—48no—
293C23—416no—
294C23C2×C42×C12718yes—
295C23C2×C42×C12714yes—
296C23C2×C22⋊C4×C12714yes—
297C23#117×C12714yes—
298C23C4×D4×C127116yes—
299C23C23×C4×C12711yescharacteristic
300C23C23×C4×C12712yes—
301C23C22×D4×C12712yes—
302C23C2×#41×C12712yes—
303C23H(5,𝔽2)×C12714yes—
304C23H(5,𝔽2)×C12714yes—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—24no—
309C2×C4—216no—
310C2×C4—232no—
311C2×C4—28no—
312C2×C4—416no—
313C2×C4—416no—
314C2×C4—48no—
315C2×C4—48no—
316C2×C4—48no—
317C2×C4—416no—
318C2×C4C2×C22⋊C4×C12718yes—
319C22—28no—
320C22—232no—
321C22—28no—
322C22—24no—
323C22—24no—
324C22—28no—
325C22—216no—
326C22—464no—
327C22—48no—
328C22—432no—
329C22—44no—
330C22—44no—
331C22C4×C22⋊C4×C12718yes—
332C22C22×C42×C12711yescharacteristic
333C22C22×C22⋊C4×C12711yescharacteristic
334C22C2×#117×C12711yescharacteristic
335C22C2×C4×D4×C12714yes—
336C22#518×C12712yes—
337C22#518×C12712yes—
338C22#518×C12718yes—
339C22#534×C12714yes—
340C22#535×C12714yes—
341C22#538×C12718yes—
342C4—28no—
343C4—416no—
344C4—44no—
345C2—28no—
346C2—48no—
347C2C2×C4×C22⋊C4×C12711yescharacteristic
348C2C127×#227312yes—
349C2C127×#230811yescharacteristic
350C2C127×#230911yescharacteristic
351C2C127×#231212yes—
352C2C127×#232118yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C127C2semidirect
4. C127×#1437C2semidirect
5. C127×C22⋊#95C2semidirect
10. C22×C22⋊C4×C127C4semidirect
14. C22×C42×C127C22semidirect
15. #379×C127C4semidirect
17. C2×#95×C127C22semidirect
18. C2×#95×C127C22semidirect
45. C2×C22⋊C4×C127C2×C4semidirect
65. C24×C127C42semidirect
85. C22×C4×C127C22⋊C4semidirect
168. #13775C127direct (N × H)
179. C2×C4×C22⋊C4C2×C127semidirect
180. #1437C2×C127semidirect
181. C22⋊#95C2×C127semidirect
182. C127#13775direct (N × H)
187. C22×C22⋊C4C4×C127semidirect
191. C22×C42C22×C127semidirect
192. #379C4×C127semidirect
194. C2×#95C22×C127semidirect
195. C2×#95C22×C127semidirect
222. C2×C22⋊C4C2×C4×C127semidirect
242. C24C42×C127semidirect
262. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#379×C1272
C2×C4×C22⋊C4×C1272
C127×#14372
C127×C22⋊#952
#13775127