Finite Group Databasebeta

← C2×C127×#1326 #44575124

Subgroups — C2×C127×#1326 #44575124

Order 32512.

770 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
1C2×#385×C127C211yesmaximal, characteristic
2C2×#323×C127C211yesmaximal, characteristic
3C2×#323×C127C211yesmaximal, characteristic
4C127×#1326C214yesmaximal, direct product factor
5C24×C4×C127C411yescharacteristic
6C22×C4⋊C4×C127—21no—
7C22×C22⋊C4×C127C411yescharacteristic
8C22×C22⋊C4×C127C2211yescharacteristic
9C2×C22⋊C8×C127—21no—
10C2×C22⋊C8×C127—21no—
11#385×C127—21no—
12#385×C127—21no—
13#385×C127C412yes—
14#385×C127C2212yes—
15C2×#95×C127—21no—
16#323×C127—21no—
17#323×C127—21no—
18#323×C127C2212yes—
19#323×C127C2212yes—
20C25×C127C2×C411yescharacteristic
21C23×C4×C127—21no—
22C23×C4×C127—21no—
23C23×C4×C127—21no—
24C23×C4×C127—44no—
25C23×C4×C127—41no—
26C23×C4×C127—41no—
27C23×C4×C127C2×C412yes—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C22×C8×C127—41no—
31C22×C8×C127—41no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—22no—
34C2×C4⋊C4×C127—44no—
35C2×C22⋊C4×C127—21no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—41no—
38C2×C22⋊C4×C127—41no—
39C2×C22⋊C4×C127C814yescomplemented
40C2×C22⋊C4×C127C2×C412yes—
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C22⋊C4×C127C2311yescharacteristic
45C22⋊C8×C127—22no—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—41no—
48C22⋊C8×C127—41no—
49#95×C127—22no—
50#95×C127—22no—
51C24×C127—21no—
52C24×C127—21no—
53C24×C127—22no—
54C24×C127—42no—
55C24×C127—42no—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127C2×C812yes—
59C24×C127M1612yes—
60C24×C127C22×C411yescharacteristic
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—44no—
70C22×C4×C127—44no—
71C22×C4×C127—42no—
72C22×C4×C127—42no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127—48no—
76C22×C4×C127—44no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—42no—
80C22×C4×C127—44no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C2×C8×C127—42no—
88C2×C8×C127—42no—
89C2×C8×C127—82no—
90C2×C8×C127—82no—
91C4⋊C4×C127—44no—
92C4⋊C4×C127—44no—
93C22⋊C4×C127—24no—
94C22⋊C4×C127—22no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127C2×C814yescomplemented
100C23×C127—22no—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127—22no—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—44no—
114C23×C127—44no—
115C23×C127—41no—
116C23×C127—42no—
117C23×C127—48no—
118C23×C127—42no—
119C23×C127—42no—
120C23×C127—42no—
121C23×C127C22⋊C812yes—
122C23×C127C22⋊C812yes—
123C23×C127#9911yescharacteristic
124C23×C127#9911yescharacteristic
125C23×C127#10112yes—
126C23×C127C2×C22⋊C411yescharacteristic
127C23×C127C22×C811yescharacteristic
128C23×C127C2×M1611yescharacteristic
129C2×C4×C127—24no—
130C2×C4×C127—24no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—42no—
136C2×C4×C127—48no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—44no—
140C2×C4×C127—48no—
141C2×C4×C127—44no—
142C2×C4×C127—42no—
143C2×C4×C127—44no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—44no—
151C2×C4×C127—81no—
152C2×C4×C127—81no—
153C8×C127—82no—
154C8×C127—82no—
155C22×C127—24no—
156C22×C127—24no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—22no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—42no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—44no—
168C22×C127—44no—
169C22×C127—42no—
170C22×C127—42no—
171C22×C127—44no—
172C22×C127—44no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127#32412yes—
178C22×C127#32412yes—
179C22×C127AΣL(1,𝔽16)12yes—
180C22×C127#35212yes—
181C22×C127C2×C22⋊C811yescharacteristic
182C22×C127C2×#9911yescharacteristic
183C22×C127C2×#10111yescharacteristic
184C4×C127—44no—
185C4×C127—41no—
186C4×C127—44no—
187C4×C127—41no—
188C4×C127—41no—
189C4×C127—41no—
190C2×#1326C12711yesmaximal, characteristic, direct product factor, Sylow
191C2×C127—21no—
192C2×C127—22no—
193C2×C127—21no—
194C2×C127—42no—
195C2×C127—41no—
196C2×C127—41no—
197C2×C127#132614yesdirect product factor
198C2×C127C2×#32411yescharacteristic
199C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
200C2×C127C2×#35211yescharacteristic
201C2×#385C2×C12711yescharacteristic
202C2×#323C2×C12711yescharacteristic
203C2×#323C2×C12711yescharacteristic
204#1326C2×C12714yesdirect product factor
205C127C2×#132611yescharacteristic, direct product factor, Sylow
206C24×C4C4×C12711yescharacteristic
207C22×C4⋊C4—21no—
208C22×C22⋊C4C4×C12711yescharacteristic
209C22×C22⋊C4C22×C12711yescharacteristic
210C2×C22⋊C8—21no—
211C2×C22⋊C8—21no—
212#385—21no—
213#385—21no—
214#385C4×C12712yes—
215#385C22×C12712yes—
216C2×#95—21no—
217#323—21no—
218#323—21no—
219#323C22×C12712yes—
220#323C22×C12712yes—
221C25C2×C4×C12711yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—44no—
226C23×C4—41no—
227C23×C4—41no—
228C23×C4C2×C4×C12712yes—
229C23×C4D4×C12711yescharacteristic
230C23×C4D4×C12711yescharacteristic
231C22×C8—41no—
232C22×C8—41no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—44no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4C8×C12714yescomplemented
241C2×C22⋊C4C2×C4×C12712yes—
242C2×C22⋊C4C2×C4×C12711yescharacteristic
243C2×C22⋊C4D4×C12711yescharacteristic
244C2×C22⋊C4D4×C12711yescharacteristic
245C2×C22⋊C4C23×C12711yescharacteristic
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8—41no—
249C22⋊C8—41no—
250#95—22no—
251#95—22no—
252C24—21no—
253C24—21no—
254C24—22no—
255C24—42no—
256C24—42no—
257C24C22⋊C4×C12711yescharacteristic
258C24C22⋊C4×C12711yescharacteristic
259C24C2×C8×C12712yes—
260C24M16×C12712yes—
261C24C22×C4×C12711yescharacteristic
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—48no—
277C22×C4—44no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4C22⋊C4×C12711yescharacteristic
285C22×C4C22⋊C4×C12711yescharacteristic
286C22×C4C2×D4×C12711yescharacteristic
287C22×C4C2×D4×C12711yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—82no—
291C2×C8—82no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C22⋊C4—24no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4C2×C8×C12714yescomplemented
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—44no—
315C23—44no—
316C23—41no—
317C23—42no—
318C23—48no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23C22⋊C8×C12712yes—
323C23C22⋊C8×C12712yes—
324C23#99×C12711yescharacteristic
325C23#99×C12711yescharacteristic
326C23#101×C12712yes—
327C23C2×C22⋊C4×C12711yescharacteristic
328C23C22×C8×C12711yescharacteristic
329C23C2×M16×C12711yescharacteristic
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—48no—
340C2×C4—42no—
341C2×C4—48no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—44no—
352C2×C4—81no—
353C2×C4—81no—
354C8—82no—
355C8—82no—
356C22—24no—
357C22—24no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—21no—
364C22—21no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—44no—
369C22—44no—
370C22—42no—
371C22—42no—
372C22—44no—
373C22—44no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#324×C12712yes—
379C22#324×C12712yes—
380C22AΣL(1,𝔽16)×C12712yes—
381C22#352×C12712yes—
382C22C2×C22⋊C8×C12711yescharacteristic
383C22C2×#99×C12711yescharacteristic
384C22C2×#101×C12711yescharacteristic
385C4—44no—
386C4—41no—
387C4—44no—
388C4—41no—
389C4—41no—
390C4—41no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2—42no—
395C2—41no—
396C2—41no—
397C2C127×#132614yesdirect product factor
398C2C2×#324×C12711yescharacteristic
399C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
400C2C2×#352×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC23C22×C8×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC25×C127C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1326C2direct (N × H)
39. C2×C22⋊C4×C127C8semidirect
99. C22⋊C4×C127C2×C8semidirect
190. C2×#1326C127direct (N × H)
197. C2×C127#1326direct (N × H)
204. #1326C2×C127direct (N × H)
205. C127C2×#1326direct (N × H)
240. C2×C22⋊C4C8×C127semidirect
300. C22⋊C4C2×C8×C127semidirect
397. C2C127×#1326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C2×#323×C1272
C127×#13262
C2×#1326127