Finite Group Databasebeta

← C2×C127×#1352 #44575387

Subgroups — C2×C127×#1352 #44575387

Order 32512.

712 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×#399×C127C211yesmaximal, characteristic
2C2×#342×C127C211yesmaximal, characteristic
3C2×#323×C127C211yesmaximal, characteristic
4C127×#1352C214yesmaximal, direct product factor
5C22×C4⋊C4×C127—21no—
6C22×C4⋊C4×C127C411yescharacteristic, complemented
7C22×C22⋊C4×C127—21no—
8C22×C22⋊C4×C127—21no—
9C22×C22⋊C4×C127C2211yescharacteristic
10C2×C22⋊C8×C127—21no—
11#399×C127—21no—
12#399×C127—21no—
13#399×C127C412yescomplemented
14#399×C127C2212yes—
15C2×#95×C127C411yescharacteristic, complemented
16#342×C127—21no—
17#342×C127C2212yes—
18#323×C127—21no—
19#323×C127C2212yes—
20C25×C127D411yescharacteristic
21C23×C4×C127—21no—
22C23×C4×C127—21no—
23C23×C4×C127—41no—
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C22×C8×C127—41no—
27C2×C4⋊C4×C127—22no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127—44no—
31C2×C4⋊C4×C127—41no—
32C2×C4⋊C4×C127—41no—
33C2×C4⋊C4×C127C2×C412yescomplemented
34C2×C22⋊C4×C127—24no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—41no—
39C2×C22⋊C4×C127—41no—
40C2×C22⋊C4×C127—44no—
41C2×C22⋊C4×C127—41no—
42C2×C22⋊C4×C127—42no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C22⋊C4×C127D411yescharacteristic
46C2×C22⋊C4×C127C2311yescharacteristic
47C22⋊C8×C127—22no—
48C22⋊C8×C127—41no—
49#95×C127—21no—
50#95×C127C2×C412yescomplemented
51C24×C127—21no—
52C24×C127—21no—
53C24×C127—22no—
54C24×C127—42no—
55C24×C127—42no—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127SD1612yes—
59C24×C127Q1612yes—
60C24×C127C2×D411yescharacteristic
61C22×C4×C127—24no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—22no—
68C22×C4×C127—42no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127—42no—
72C22×C4×C127—44no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127—42no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—82no—
79C22×C4×C127—82no—
80C22×C4×C127C22⋊C411yescharacteristic
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22×C411yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84C2×C8×C127—42no—
85C2×C8×C127—82no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—44no—
88C4⋊C4×C127—44no—
89C4⋊C4×C127—42no—
90C22⋊C4×C127—24no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—44no—
96C22⋊C4×C127—44no—
97C22⋊C4×C127—44no—
98C22⋊C4×C127—42no—
99C23×C127—22no—
100C23×C127—22no—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—22no—
106C23×C127—22no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—44no—
113C23×C127—44no—
114C23×C127—41no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127—81no—
118C23×C127—84no—
119C23×C127—81no—
120C23×C127#9911yescharacteristic
121C23×C127#9911yescharacteristic
122C23×C127#10312yes—
123C23×C127#10312yes—
124C23×C127#10412yes—
125C23×C127C2×C22⋊C411yescharacteristic
126C23×C127C2×SD1611yescharacteristic
127C23×C127C2×Q1611yescharacteristic
128C2×C4×C127—24no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—42no—
134C2×C4×C127—48no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—44no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—42no—
147C2×C4×C127—81no—
148C2×C4×C127—82no—
149C2×C4×C127—82no—
150C2×C4×C127—88no—
151C2×C4×C127—82no—
152C2×C4×C127—82no—
153C8×C127—82no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—24no—
157C22×C127—24no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—22no—
162C22×C127—21no—
163C22×C127—42no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—44no—
169C22×C127—44no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127—82no—
175C22×C127—82no—
176C22×C127#32812yes—
177C22×C127#32812yes—
178C22×C127#35212yes—
179C22×C127#35312yes—
180C22×C127C2×#9911yescharacteristic
181C22×C127C2×#10311yescharacteristic
182C22×C127C2×#10411yescharacteristic
183C4×C127—44no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—84no—
189C4×C127—82no—
190C2×#1352C12711yesmaximal, characteristic, direct product factor, Sylow
191C2×C127—21no—
192C2×C127—21no—
193C2×C127—22no—
194C2×C127—41no—
195C2×C127—42no—
196C2×C127—41no—
197C2×C127#135214yesdirect product factor
198C2×C127C2×#32811yescharacteristic
199C2×C127C2×#35211yescharacteristic
200C2×C127C2×#35311yescharacteristic
201C2×#399C2×C12711yescharacteristic
202C2×#342C2×C12711yescharacteristic
203C2×#323C2×C12711yescharacteristic
204#1352C2×C12714yesdirect product factor
205C127C2×#135211yescharacteristic, direct product factor, Sylow
206C22×C4⋊C4—21no—
207C22×C4⋊C4C4×C12711yescharacteristic, complemented
208C22×C22⋊C4—21no—
209C22×C22⋊C4—21no—
210C22×C22⋊C4C22×C12711yescharacteristic
211C2×C22⋊C8—21no—
212#399—21no—
213#399—21no—
214#399C4×C12712yescomplemented
215#399C22×C12712yes—
216C2×#95C4×C12711yescharacteristic, complemented
217#342—21no—
218#342C22×C12712yes—
219#323—21no—
220#323C22×C12712yes—
221C25D4×C12711yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—41no—
225C23×C4C2×C4×C12711yescharacteristic
226C23×C4D4×C12711yescharacteristic
227C22×C8—41no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—44no—
234C2×C4⋊C4C2×C4×C12712yescomplemented
235C2×C22⋊C4—24no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4—42no—
244C2×C22⋊C4C2×C4×C12711yescharacteristic
245C2×C22⋊C4D4×C12711yescharacteristic
246C2×C22⋊C4D4×C12711yescharacteristic
247C2×C22⋊C4C23×C12711yescharacteristic
248C22⋊C8—22no—
249C22⋊C8—41no—
250#95—21no—
251#95C2×C4×C12712yescomplemented
252C24—21no—
253C24—21no—
254C24—22no—
255C24—42no—
256C24—42no—
257C24C22⋊C4×C12711yescharacteristic
258C24C22⋊C4×C12711yescharacteristic
259C24SD16×C12712yes—
260C24Q16×C12712yes—
261C24C2×D4×C12711yescharacteristic
262C22×C4—24no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—82no—
280C22×C4—82no—
281C22×C4C22⋊C4×C12711yescharacteristic
282C22×C4C22⋊C4×C12711yescharacteristic
283C22×C4C22×C4×C12711yescharacteristic
284C22×C4C2×D4×C12711yescharacteristic
285C2×C8—42no—
286C2×C8—82no—
287C4⋊C4—42no—
288C4⋊C4—44no—
289C4⋊C4—44no—
290C4⋊C4—42no—
291C22⋊C4—24no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—44no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—21no—
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—44no—
314C23—44no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—84no—
320C23—81no—
321C23#99×C12711yescharacteristic
322C23#99×C12711yescharacteristic
323C23#103×C12712yes—
324C23#103×C12712yes—
325C23#104×C12712yes—
326C23C2×C22⋊C4×C12711yescharacteristic
327C23C2×SD16×C12711yescharacteristic
328C23C2×Q16×C12711yescharacteristic
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—48no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—88no—
352C2×C4—82no—
353C2×C4—82no—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—24no—
358C22—24no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—21no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—44no—
370C22—44no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—82no—
376C22—82no—
377C22#328×C12712yes—
378C22#328×C12712yes—
379C22#352×C12712yes—
380C22#353×C12712yes—
381C22C2×#99×C12711yescharacteristic
382C22C2×#103×C12711yescharacteristic
383C22C2×#104×C12711yescharacteristic
384C4—44no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—84no—
390C4—82no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—42no—
396C2—41no—
397C2C127×#135214yesdirect product factor
398C2C2×#328×C12711yescharacteristic
399C2C2×#352×C12711yescharacteristic
400C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC25×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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×#1352C2direct (N × H)
6. C22×C4⋊C4×C127C4semidirect
13. #399×C127C4semidirect
15. C2×#95×C127C4semidirect
33. C2×C4⋊C4×C127C2×C4semidirect
50. #95×C127C2×C4semidirect
190. C2×#1352C127direct (N × H)
197. C2×C127#1352direct (N × H)
204. #1352C2×C127direct (N × H)
205. C127C2×#1352direct (N × H)
207. C22×C4⋊C4C4×C127semidirect
214. #399C4×C127semidirect
216. C2×#95C4×C127semidirect
234. C2×C4⋊C4C2×C4×C127semidirect
251. #95C2×C4×C127semidirect
397. C2C127×#1352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#342×C1272
C2×#323×C1272
C127×#13522
C2×#1352127