Finite Group Databasebeta

← C127×#13065 #44576738

Subgroups — C127×#13065 #44576738

Order 32512.

510 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M32×C127C211yesmaximal, characteristic, complemented
2C127×#3050C211yesmaximal, characteristic
3C2×#360×C127C212yesmaximal, complemented
4C127×#1807C211yesmaximal, characteristic, complemented
5C127×#1386C212yesmaximal, complemented
6C2×#135×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C2×M32×C127—21no—
10C2×M32×C127—24no—
11C2×M32×C127C2212yes—
12C22×C16×C127—21no—
13#467×C127C411yescharacteristic, complemented
14#467×C127C411yescharacteristic, complemented
15#466×C127C411yescharacteristic, complemented
16#466×C127C411yescharacteristic, complemented
17#465×C127—21no—
18#465×C127—21no—
19#427×C127C2211yescharacteristic
20C2×#106×C127C2212yes—
21#416×C127—21no—
22#380×C127—21no—
23#360×C127—24no—
24#340×C127—21no—
25C2×#41×C127—21no—
26C23×C4×C127D411yescharacteristic
27#135×C127—22no—
28#135×C127—22no—
29C2×Q16×C127C2×C411yescharacteristic
30C2×SD16×C127—21no—
31C2×D8×C127C2×C411yescharacteristic
32C22×C8×C127—22no—
33C22×C8×C127—22no—
34C22×C8×C127C2×C411yescharacteristic
35C22×C8×C127C2×C411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127D411yescharacteristic
38C22×C8×C127D411yescharacteristic
39C22×C8×C127C2311yescharacteristic
40#123×C127—41no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43#121×C127—21no—
44#121×C127—21no—
45#120×C127—41no—
46C4×D4×C127—41no—
47C4×D4×C127—41no—
48#117×C127—21no—
49C2×C4⋊C4×C127—22no—
50C2×C22⋊C4×C127—41no—
51M32×C127—24no—
52M32×C127—22no—
53M32×C127D414yescomplemented
54C2×C16×C127—24no—
55C2×C16×C127—22no—
56#107×C127C2×C411yescharacteristic
57#107×C127C2×C411yescharacteristic
58#106×C127—21no—
59#106×C127—22no—
60#106×C127—22no—
61#103×C127—21no—
62#103×C127—21no—
63#102×C127—21no—
64#102×C127—21no—
65#95×C127—41no—
66C24×C127D811yescharacteristic
67#41×C127—42no—
68#41×C127—42no—
69C2×Q8×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—41no—
77C22×C4×C127—42no—
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127D811yescharacteristic
81C22×C4×C127SD1611yescharacteristic
82C22×C4×C127SD1611yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84Q16×C127—22no—
85SD16×C127—41no—
86SD16×C127—41no—
87D8×C127—22no—
88C2×C8×C127—22no—
89C2×C8×C127—22no—
90C2×C8×C127—22no—
91C2×C8×C127—21no—
92C2×C8×C127—21no—
93C2×C8×C127—21no—
94C2×C8×C127—21no—
95C2×C8×C127C22⋊C411yescharacteristic
96C2×C8×C127C22⋊C411yescharacteristic
97C2×C8×C127C22×C411yescharacteristic
98C2×C8×C127C2×D412yes—
99C2×C8×C127C2×D411yescharacteristic
100C2×C8×C127#4112yes—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—41no—
105C4⋊C4×C127—42no—
106C4⋊C4×C127—42no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—82no—
113C42×C127—41no—
114C16×C127—24no—
115C23×C127—22no—
116C23×C127—22no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127#10211yescharacteristic
120C23×C127#10211yescharacteristic
121C23×C127C2×D811yescharacteristic
122Q8×C127—41no—
123Q8×C127—41no—
124D4×C127—41no—
125D4×C127—41no—
126D4×C127—82no—
127D4×C127—82no—
128D4×C127—82no—
129C2×C4×C127—22no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—82no—
140C2×C4×C127—82no—
141C2×C4×C127—82no—
142C2×C4×C127—82no—
143C2×C4×C127#10211yescharacteristic
144C2×C4×C127#10211yescharacteristic
145C2×C4×C127C2×C22⋊C411yescharacteristic
146C2×C4×C127#12112yes—
147C2×C4×C127C2×SD1611yescharacteristic
148C2×C4×C127#13512yes—
149C8×C127—21no—
150C8×C127—21no—
151C8×C127C4×D412yes—
152C8×C127#12011yescharacteristic
153C8×C127#12311yescharacteristic
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—44no—
162C22×C127—81no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127#36012yescomplemented
166C22×C127C2×#10211yescharacteristic
167C22×C127#46612yes—
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—81no—
171C4×C127—81no—
172C4×C127—81no—
173C4×C127—162no—
174C4×C127#38611yescharacteristic
175C4×C127#41611yescharacteristic
176C4×C127#46512yes—
177#13065C12711yesmaximal, characteristic, direct product factor, Sylow
178C2×C127—22no—
179C2×C127—22no—
180C2×C127—41no—
181C2×C127—161no—
182C2×C127#189311yescharacteristic
183C2×C127C2×#36011yescharacteristic
184C2×C127#214511yescharacteristic
185C22×M32C2×C12711yescharacteristic, complemented
186#3050C2×C12711yescharacteristic
187C2×#360C2×C12712yescomplemented
188#1807C2×C12711yescharacteristic, complemented
189#1386C2×C12712yescomplemented
190C127#1306511yescharacteristic, direct product factor, Sylow
191C2×#135C22×C12711yescharacteristic
192C23×C8C22×C12711yescharacteristic
193#525—21no—
194C2×M32—21no—
195C2×M32—24no—
196C2×M32C22×C12712yes—
197C22×C16—21no—
198#467C4×C12711yescharacteristic, complemented
199#467C4×C12711yescharacteristic, complemented
200#466C4×C12711yescharacteristic, complemented
201#466C4×C12711yescharacteristic, complemented
202#465—21no—
203#465—21no—
204#427C22×C12711yescharacteristic
205C2×#106C22×C12712yes—
206#416—21no—
207#380—21no—
208#360—24no—
209#340—21no—
210C2×#41—21no—
211C23×C4D4×C12711yescharacteristic
212#135—22no—
213#135—22no—
214C2×Q16C2×C4×C12711yescharacteristic
215C2×SD16—21no—
216C2×D8C2×C4×C12711yescharacteristic
217C22×C8—22no—
218C22×C8—22no—
219C22×C8C2×C4×C12711yescharacteristic
220C22×C8C2×C4×C12711yescharacteristic
221C22×C8D4×C12711yescharacteristic
222C22×C8D4×C12711yescharacteristic
223C22×C8D4×C12711yescharacteristic
224C22×C8C23×C12711yescharacteristic
225#123—41no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228#121—21no—
229#121—21no—
230#120—41no—
231C4×D4—41no—
232C4×D4—41no—
233#117—21no—
234C2×C4⋊C4—22no—
235C2×C22⋊C4—41no—
236M32—24no—
237M32—22no—
238M32D4×C12714yescomplemented
239C2×C16—24no—
240C2×C16—22no—
241#107C2×C4×C12711yescharacteristic
242#107C2×C4×C12711yescharacteristic
243#106—21no—
244#106—22no—
245#106—22no—
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250#95—41no—
251C24D8×C12711yescharacteristic
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4C22⋊C4×C12711yescharacteristic
264C22×C4C22⋊C4×C12711yescharacteristic
265C22×C4D8×C12711yescharacteristic
266C22×C4SD16×C12711yescharacteristic
267C22×C4SD16×C12711yescharacteristic
268C22×C4C2×D4×C12711yescharacteristic
269Q16—22no—
270SD16—41no—
271SD16—41no—
272D8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8C22⋊C4×C12711yescharacteristic
281C2×C8C22⋊C4×C12711yescharacteristic
282C2×C8C22×C4×C12711yescharacteristic
283C2×C8C2×D4×C12712yes—
284C2×C8C2×D4×C12711yescharacteristic
285C2×C8#41×C12712yes—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—82no—
298C42—41no—
299C16—24no—
300C23—22no—
301C23—22no—
302C23—41no—
303C23—41no—
304C23#102×C12711yescharacteristic
305C23#102×C12711yescharacteristic
306C23C2×D8×C12711yescharacteristic
307Q8—41no—
308Q8—41no—
309D4—41no—
310D4—41no—
311D4—82no—
312D4—82no—
313D4—82no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#102×C12711yescharacteristic
329C2×C4#102×C12711yescharacteristic
330C2×C4C2×C22⋊C4×C12711yescharacteristic
331C2×C4#121×C12712yes—
332C2×C4C2×SD16×C12711yescharacteristic
333C2×C4#135×C12712yes—
334C8—21no—
335C8—21no—
336C8C4×D4×C12712yes—
337C8#120×C12711yescharacteristic
338C8#123×C12711yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22#360×C12712yescomplemented
351C22C2×#102×C12711yescharacteristic
352C22#466×C12712yes—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—162no—
359C4#386×C12711yescharacteristic
360C4#416×C12711yescharacteristic
361C4#465×C12712yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2C127×#189311yescharacteristic
367C2C2×#360×C12711yescharacteristic
368C2C127×#214511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×M32×C127C2semidirect
3. C2×#360×C127C2semidirect
4. C127×#1807C2semidirect
5. C127×#1386C2semidirect
13. #467×C127C4semidirect
14. #467×C127C4semidirect
15. #466×C127C4semidirect
16. #466×C127C4semidirect
53. M32×C127D4semidirect
165. C22×C127#360semidirect
177. #13065C127direct (N × H)
185. C22×M32C2×C127semidirect
187. C2×#360C2×C127semidirect
188. #1807C2×C127semidirect
189. #1386C2×C127semidirect
190. C127#13065direct (N × H)
198. #467C4×C127semidirect
199. #467C4×C127semidirect
200. #466C4×C127semidirect
201. #466C4×C127semidirect
238. M32D4×C127semidirect
350. C22#360×C127semidirect

Maximal subgroups

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

subgroupindex
C22×M32×C1272
C127×#30502
C2×#360×C1272
C127×#18072
C127×#13862
#13065127