Finite Group Databasebeta

← C127×#20733 #44584406

Subgroups — C127×#20733 #44584406

Order 32512.

1758 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#431×C127C211yesmaximal, characteristic, complemented
3C127×#2283C211yesmaximal, characteristic, complemented
4C127×#1824C212yesmaximal, complemented
5C127×#1804C214yesmaximal, complemented
6C127×#1786C212yesmaximal
7C4×#102×C127C214yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C24×C4×C127—21no—
10C2×C4×D4×C127—21no—
11C2×C4×D4×C127—21no—
12C2×C4×D4×C127—24no—
13C2×C4×D4×C127C418yescomplemented
14C2×C4×D4×C127C2212yes—
15C2×C4×D4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127—21no—
18C22×C42×C127C2211yescharacteristic
19#431×C127—24no—
20C2×C4⋊C8×C127C2212yescomplemented
21C2×#102×C127C2218yes—
22C2×C22⋊C8×C127C2212yes—
23C2×C4×C8×C127C2212yescomplemented
24#383×C127—21no—
25#382×C127C2212yescomplemented
26#381×C127—21no—
27#380×C127C2212yes—
28C4×C4⋊C4×C127C2212yescomplemented
29C4×C22⋊C4×C127—21no—
30#376×C127—21no—
31#340×C127C2218yescomplemented
32C25×C127—21no—
33C22×D4×C127—28no—
34C22×D4×C127—21no—
35C22×D4×C127—22no—
36C22×D4×C127C2×C414yes—
37C22×D4×C127C2312yes—
38C23×C4×C127—21no—
39C23×C4×C127—28no—
40C23×C4×C127—22no—
41C23×C4×C127—22no—
42C23×C4×C127—48no—
43C23×C4×C127D411yescharacteristic
44C23×C4×C127D411yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C22×C8×C127C2314yes—
47C4×D4×C127—28no—
48C4×D4×C127—28no—
49C4×D4×C127—24no—
50C4×D4×C127—24no—
51C4×D4×C127C2×C418yes—
52C4×D4×C127C2×C418yes—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127C2×C414yes—
56C2×C4⋊C4×C127C2314yes—
57C2×C4⋊C4×C127C2312yes—
58C2×C22⋊C4×C127—28no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—22no—
62C2×C42×C127—22no—
63C2×C42×C127C2×C414yes—
64C2×C42×C127D411yescharacteristic
65C2×C42×C127D411yescharacteristic
66C2×C42×C127D414yes—
67C2×C42×C127C2311yescharacteristic
68C2×C42×C127C2311yescharacteristic
69C4⋊C8×C127—24no—
70#102×C127—216no—
71C22⋊C8×C127—24no—
72C4×C8×C127—24no—
73#95×C127—22no—
74#95×C127—22no—
75#95×C127—22no—
76#95×C127—22no—
77C24×C127—28no—
78C24×C127—24no—
79C24×C127—22no—
80C24×C127—44no—
81C24×C127—44no—
82C24×C127C2×D411yescharacteristic
83C2×D4×C127—28no—
84C2×D4×C127—216no—
85C2×D4×C127—216no—
86C2×D4×C127—24no—
87C2×D4×C127—22no—
88C2×D4×C127—24no—
89C2×D4×C127C22×C414yes—
90C2×D4×C127#4118yes—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—22no—
96C22×C4×C127—28no—
97C22×C4×C127—28no—
98C22×C4×C127—24no—
99C22×C4×C127—48no—
100C22×C4×C127—432no—
101C22×C4×C127—44no—
102C22×C4×C127—48no—
103C22×C4×C127C22⋊C414yes—
104C22×C4×C127C22⋊C414yes—
105C22×C4×C127C22×C412yes—
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2411yescharacteristic
113C2×C8×C127—24no—
114C2×C8×C127—28no—
115C4⋊C4×C127—24no—
116C4⋊C4×C127—22no—
117C4⋊C4×C127—28no—
118C4⋊C4×C127C22×C414yes—
119C22⋊C4×C127—28no—
120C22⋊C4×C127—28no—
121C22⋊C4×C127—44no—
122C42×C127—44no—
123C42×C127C22⋊C414yes—
124C42×C127C22⋊C414yes—
125C42×C127C22×C412yes—
126C42×C127C22×C412yes—
127C42×C127C2×D412yes—
128C42×C127C2×D412yes—
129C23×C127—22no—
130C23×C127—22no—
131C23×C127—216no—
132C23×C127—24no—
133C23×C127—28no—
134C23×C127—48no—
135C23×C127—432no—
136C23×C127—44no—
137C23×C127—44no—
138C23×C127—48no—
139C23×C127C2×C22⋊C412yes—
140C23×C127#13514yes—
141C23×C127C22×D411yescharacteristic
142D4×C127—216no—
143D4×C127—24no—
144D4×C127—28no—
145D4×C127#11718yes—
146C2×C4×C127—22no—
147C2×C4×C127—22no—
148C2×C4×C127—22no—
149C2×C4×C127—22no—
150C2×C4×C127—28no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—28no—
154C2×C4×C127—24no—
155C2×C4×C127—416no—
156C2×C4×C127—48no—
157C2×C4×C127—44no—
158C2×C4×C127—416no—
159C2×C4×C127—44no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127C2×C22⋊C412yes—
163C2×C4×C127C2×C22⋊C412yes—
164C2×C4×C127C2×C22⋊C412yes—
165C2×C4×C127C2×C22⋊C412yes—
166C2×C4×C127C2×C22⋊C412yes—
167C2×C4×C127AGL(1,ℤ/8)14yes—
168C2×C4×C127C23×C411yescharacteristic
169C2×C4×C127C22×D411yescharacteristic
170C2×C4×C127C2×#4114yes—
171C8×C127—44no—
172C22×C127—28no—
173C22×C127—22no—
174C22×C127—22no—
175C22×C127—28no—
176C22×C127—432no—
177C22×C127—416no—
178C22×C127—44no—
179C22×C127—44no—
180C22×C127#41614yes—
181C22×C127C22×C22⋊C411yescharacteristic
182C22×C127#52512yes—
183C22×C127C2×#13512yes—
184C22×C127C2×AGL(1,ℤ/8)12yes—
185C4×C127—22no—
186C4×C127—22no—
187C4×C127—22no—
188C4×C127—22no—
189C4×C127—44no—
190C4×C127—84no—
191C4×C127#41814yes—
192C4×C127C2×#11712yes—
193C4×C127#52512yes—
194#20733C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—24no—
196C2×C127—48no—
197C2×C127#228011yescharacteristic
198C2×C127C2×#41611yescharacteristic
199C2×C127C2×#41811yescharacteristic
200C2×C127#310514yes—
201C22×C4×D4C2×C12711yescharacteristic
202C2×#431C2×C12711yescharacteristic, complemented
203#2283C2×C12711yescharacteristic, complemented
204#1824C2×C12712yescomplemented
205#1804C2×C12714yescomplemented
206#1786C2×C12712yes—
207C4×#102C2×C12714yescomplemented
208C127#2073311yescharacteristic, direct product factor, Sylow
209C23×D4C22×C12711yescharacteristic
210C24×C4—21no—
211C2×C4×D4—21no—
212C2×C4×D4—21no—
213C2×C4×D4—24no—
214C2×C4×D4C4×C12718yescomplemented
215C2×C4×D4C22×C12712yes—
216C2×C4×D4C22×C12712yes—
217C22×C4⋊C4C22×C12711yescharacteristic
218C22×C22⋊C4—21no—
219C22×C42C22×C12711yescharacteristic
220#431—24no—
221C2×C4⋊C8C22×C12712yescomplemented
222C2×#102C22×C12718yes—
223C2×C22⋊C8C22×C12712yes—
224C2×C4×C8C22×C12712yescomplemented
225#383—21no—
226#382C22×C12712yescomplemented
227#381—21no—
228#380C22×C12712yes—
229C4×C4⋊C4C22×C12712yescomplemented
230C4×C22⋊C4—21no—
231#376—21no—
232#340C22×C12718yescomplemented
233C25—21no—
234C22×D4—28no—
235C22×D4—21no—
236C22×D4—22no—
237C22×D4C2×C4×C12714yes—
238C22×D4C23×C12712yes—
239C23×C4—21no—
240C23×C4—28no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—48no—
244C23×C4D4×C12711yescharacteristic
245C23×C4D4×C12711yescharacteristic
246C23×C4C23×C12711yescharacteristic
247C22×C8C23×C12714yes—
248C4×D4—28no—
249C4×D4—28no—
250C4×D4—24no—
251C4×D4—24no—
252C4×D4C2×C4×C12718yes—
253C4×D4C2×C4×C12718yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4C2×C4×C12714yes—
257C2×C4⋊C4C23×C12714yes—
258C2×C4⋊C4C23×C12712yes—
259C2×C22⋊C4—28no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42—22no—
264C2×C42C2×C4×C12714yes—
265C2×C42D4×C12711yescharacteristic
266C2×C42D4×C12711yescharacteristic
267C2×C42D4×C12714yes—
268C2×C42C23×C12711yescharacteristic
269C2×C42C23×C12711yescharacteristic
270C4⋊C8—24no—
271#102—216no—
272C22⋊C8—24no—
273C4×C8—24no—
274#95—22no—
275#95—22no—
276#95—22no—
277#95—22no—
278C24—28no—
279C24—24no—
280C24—22no—
281C24—44no—
282C24—44no—
283C24C2×D4×C12711yescharacteristic
284C2×D4—28no—
285C2×D4—216no—
286C2×D4—216no—
287C2×D4—24no—
288C2×D4—22no—
289C2×D4—24no—
290C2×D4C22×C4×C12714yes—
291C2×D4#41×C12718yes—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—28no—
298C22×C4—28no—
299C22×C4—24no—
300C22×C4—48no—
301C22×C4—432no—
302C22×C4—44no—
303C22×C4—48no—
304C22×C4C22⋊C4×C12714yes—
305C22×C4C22⋊C4×C12714yes—
306C22×C4C22×C4×C12712yes—
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4C2×D4×C12711yescharacteristic
311C22×C4C2×D4×C12712yes—
312C22×C4C2×D4×C12711yescharacteristic
313C22×C4C24×C12711yescharacteristic
314C2×C8—24no—
315C2×C8—28no—
316C4⋊C4—24no—
317C4⋊C4—22no—
318C4⋊C4—28no—
319C4⋊C4C22×C4×C12714yes—
320C22⋊C4—28no—
321C22⋊C4—28no—
322C22⋊C4—44no—
323C42—44no—
324C42C22⋊C4×C12714yes—
325C42C22⋊C4×C12714yes—
326C42C22×C4×C12712yes—
327C42C22×C4×C12712yes—
328C42C2×D4×C12712yes—
329C42C2×D4×C12712yes—
330C23—22no—
331C23—22no—
332C23—216no—
333C23—24no—
334C23—28no—
335C23—48no—
336C23—432no—
337C23—44no—
338C23—44no—
339C23—48no—
340C23C2×C22⋊C4×C12712yes—
341C23#135×C12714yes—
342C23C22×D4×C12711yescharacteristic
343D4—216no—
344D4—24no—
345D4—28no—
346D4#117×C12718yes—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—28no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—28no—
355C2×C4—24no—
356C2×C4—416no—
357C2×C4—48no—
358C2×C4—44no—
359C2×C4—416no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4C2×C22⋊C4×C12712yes—
364C2×C4C2×C22⋊C4×C12712yes—
365C2×C4C2×C22⋊C4×C12712yes—
366C2×C4C2×C22⋊C4×C12712yes—
367C2×C4C2×C22⋊C4×C12712yes—
368C2×C4AGL(1,ℤ/8)×C12714yes—
369C2×C4C23×C4×C12711yescharacteristic
370C2×C4C22×D4×C12711yescharacteristic
371C2×C4C2×#41×C12714yes—
372C8—44no—
373C22—28no—
374C22—22no—
375C22—22no—
376C22—28no—
377C22—432no—
378C22—416no—
379C22—44no—
380C22—44no—
381C22#416×C12714yes—
382C22C22×C22⋊C4×C12711yescharacteristic
383C22#525×C12712yes—
384C22C2×#135×C12712yes—
385C22C2×AGL(1,ℤ/8)×C12712yes—
386C4—22no—
387C4—22no—
388C4—22no—
389C4—22no—
390C4—44no—
391C4—84no—
392C4#418×C12714yes—
393C4C2×#117×C12712yes—
394C4#525×C12712yes—
395C2—24no—
396C2—48no—
397C2C127×#228011yescharacteristic
398C2C2×#416×C12711yescharacteristic
399C2C2×#418×C12711yescharacteristic
400C2C127×#310514yes—
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C127C2semidirect
3. C127×#2283C2semidirect
4. C127×#1824C2semidirect
5. C127×#1804C2semidirect
7. C4×#102×C127C2semidirect
13. C2×C4×D4×C127C4semidirect
20. C2×C4⋊C8×C127C22semidirect
23. C2×C4×C8×C127C22semidirect
25. #382×C127C22semidirect
28. C4×C4⋊C4×C127C22semidirect
31. #340×C127C22semidirect
194. #20733C127direct (N × H)
202. C2×#431C2×C127semidirect
203. #2283C2×C127semidirect
204. #1824C2×C127semidirect
205. #1804C2×C127semidirect
207. C4×#102C2×C127semidirect
208. C127#20733direct (N × H)
214. C2×C4×D4C4×C127semidirect
221. C2×C4⋊C8C22×C127semidirect
224. C2×C4×C8C22×C127semidirect
226. #382C22×C127semidirect
229. C4×C4⋊C4C22×C127semidirect
232. #340C22×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#431×C1272
C127×#22832
C127×#18242
C127×#18042
C127×#17862
C4×#102×C1272
#20733127