Finite Group Databasebeta

← C127×#11704 #44575377

Subgroups — C127×#11704 #44575377

Order 32512.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3050C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C2×#340×C127C211yesmaximal, characteristic, complemented
4C127×#1348C212yesmaximal, complemented
5C127×#1347C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic, complemented
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C22×C4⋊C4×C127—21no—
10C2×M32×C127—21no—
11#467×C127C411yescharacteristic, complemented
12#467×C127C2211yescharacteristic
13#466×C127C411yescharacteristic, complemented
14#466×C127C2211yescharacteristic
15#465×C127—21no—
16#465×C127—21no—
17#427×C127C411yescharacteristic, complemented
18#416×C127—21no—
19C22⋊C16×C127—21no—
20C22⋊C16×C127C2212yes—
21#340×C127—21no—
22#340×C127C2212yes—
23C2×#41×C127—21no—
24C23×C4×C127—41no—
25C23×C4×C127D411yescharacteristic
26#135×C127—42no—
27C2×Q16×C127C2×C411yescharacteristic, complemented
28C2×SD16×C127—21no—
29C2×D8×C127C2×C411yescharacteristic, complemented
30C22×C8×C127—42no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127C2311yescharacteristic
37#123×C127—41no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40#121×C127—21no—
41#121×C127—21no—
42#120×C127—41no—
43C4×D4×C127—41no—
44C4×D4×C127—41no—
45#117×C127—21no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—42no—
49C2×C4⋊C4×C127—41no—
50M32×C127—42no—
51C2×C16×C127—22no—
52#107×C127C2×C411yescharacteristic, complemented
53#107×C127C2×C411yescharacteristic, complemented
54#106×C127—21no—
55#103×C127—21no—
56#103×C127—21no—
57#102×C127—21no—
58#102×C127—21no—
59C24×C127D811yescharacteristic
60#41×C127—42no—
61#41×C127—42no—
62C2×Q8×C127—21no—
63C2×D4×C127—21no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—44no—
70C22×C4×C127—42no—
71C22×C4×C127—41no—
72C22×C4×C127—82no—
73C22×C4×C127—82no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127D811yescharacteristic
77C22×C4×C127SD1611yescharacteristic
78C22×C4×C127SD1611yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80Q16×C127—41no—
81SD16×C127—42no—
82D8×C127—41no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C2×C8×C127C22⋊C411yescharacteristic
90C2×C8×C127C22⋊C411yescharacteristic
91C2×C8×C127C22×C411yescharacteristic
92C2×C8×C127C2×D411yescharacteristic
93C4⋊C4×C127—24no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—44no—
97C4⋊C4×C127—42no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C42×C127—41no—
106C16×C127—42no—
107C23×C127—22no—
108C23×C127—22no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—41no—
112C23×C127#10211yescharacteristic
113C23×C127#10211yescharacteristic
114C23×C127C2×D811yescharacteristic
115Q8×C127—41no—
116Q8×C127—41no—
117D4×C127—41no—
118D4×C127—41no—
119D4×C127—82no—
120D4×C127—82no—
121D4×C127—81no—
122D4×C127—81no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—44no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—88no—
135C2×C4×C127—82no—
136C2×C4×C127—82no—
137C2×C4×C127—82no—
138C2×C4×C127#9912yes—
139C2×C4×C127#10211yescharacteristic
140C2×C4×C127#10211yescharacteristic
141C2×C4×C127#10412yes—
142C2×C4×C127C2×C22⋊C411yescharacteristic
143C2×C4×C127C2×SD1611yescharacteristic
144C8×C127—21no—
145C8×C127—21no—
146C8×C127—21no—
147C8×C127—21no—
148C22×C127—24no—
149C22×C127—24no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—81no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127#32712yes—
160C22×C127#36012yes—
161C22×C127C2×#10211yescharacteristic
162C22×C127#50911yescharacteristic
163C22×C127#51011yescharacteristic
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—84no—
167C4×C127—81no—
168C4×C127—81no—
169C4×C127—81no—
170C4×C127#32712yes—
171C4×C127C2×#9911yescharacteristic
172C4×C127C2×#10411yescharacteristic
173#11704C12711yesmaximal, characteristic, direct product factor, Sylow
174C2×C127—21no—
175C2×C127—22no—
176C2×C127—22no—
177C2×C127—21no—
178C2×C127—161no—
179C2×C127C2×#32711yescharacteristic
180C2×C127#213911yescharacteristic
181C2×C127C2×#36011yescharacteristic
182#3050C2×C12711yescharacteristic
183#2112C2×C12711yescharacteristic, complemented
184C2×#340C2×C12711yescharacteristic, complemented
185#1348C2×C12712yescomplemented
186#1347C2×C12712yescomplemented
187C127#1170411yescharacteristic, direct product factor, Sylow
188C2×#135C4×C12711yescharacteristic, complemented
189C23×C8C22×C12711yescharacteristic
190#525—21no—
191C22×C4⋊C4—21no—
192C2×M32—21no—
193#467C4×C12711yescharacteristic, complemented
194#467C22×C12711yescharacteristic
195#466C4×C12711yescharacteristic, complemented
196#466C22×C12711yescharacteristic
197#465—21no—
198#465—21no—
199#427C4×C12711yescharacteristic, complemented
200#416—21no—
201C22⋊C16—21no—
202C22⋊C16C22×C12712yes—
203#340—21no—
204#340C22×C12712yes—
205C2×#41—21no—
206C23×C4—41no—
207C23×C4D4×C12711yescharacteristic
208#135—42no—
209C2×Q16C2×C4×C12711yescharacteristic, complemented
210C2×SD16—21no—
211C2×D8C2×C4×C12711yescharacteristic, complemented
212C22×C8—42no—
213C22×C8C2×C4×C12711yescharacteristic
214C22×C8C2×C4×C12711yescharacteristic
215C22×C8D4×C12711yescharacteristic
216C22×C8D4×C12711yescharacteristic
217C22×C8D4×C12711yescharacteristic
218C22×C8C23×C12711yescharacteristic
219#123—41no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222#121—21no—
223#121—21no—
224#120—41no—
225C4×D4—41no—
226C4×D4—41no—
227#117—21no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—41no—
232M32—42no—
233C2×C16—22no—
234#107C2×C4×C12711yescharacteristic, complemented
235#107C2×C4×C12711yescharacteristic, complemented
236#106—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C24D8×C12711yescharacteristic
242#41—42no—
243#41—42no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—82no—
255C22×C4—82no—
256C22×C4C22⋊C4×C12711yescharacteristic
257C22×C4C22⋊C4×C12711yescharacteristic
258C22×C4D8×C12711yescharacteristic
259C22×C4SD16×C12711yescharacteristic
260C22×C4SD16×C12711yescharacteristic
261C22×C4C2×D4×C12711yescharacteristic
262Q16—41no—
263SD16—42no—
264D8—41no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊C4×C12711yescharacteristic
272C2×C8C22⋊C4×C12711yescharacteristic
273C2×C8C22×C4×C12711yescharacteristic
274C2×C8C2×D4×C12711yescharacteristic
275C4⋊C4—24no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—44no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—41no—
288C16—42no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—41no—
294C23#102×C12711yescharacteristic
295C23#102×C12711yescharacteristic
296C23C2×D8×C12711yescharacteristic
297Q8—41no—
298Q8—41no—
299D4—41no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—82no—
304D4—82no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—88no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4#99×C12712yes—
321C2×C4#102×C12711yescharacteristic
322C2×C4#102×C12711yescharacteristic
323C2×C4#104×C12712yes—
324C2×C4C2×C22⋊C4×C12711yescharacteristic
325C2×C4C2×SD16×C12711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#327×C12712yes—
342C22#360×C12712yes—
343C22C2×#102×C12711yescharacteristic
344C22#509×C12711yescharacteristic
345C22#510×C12711yescharacteristic
346C4—21no—
347C4—21no—
348C4—84no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4#327×C12712yes—
353C4C2×#99×C12711yescharacteristic
354C4C2×#104×C12711yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—161no—
360C2C2×#327×C12711yescharacteristic
361C2C127×#213911yescharacteristic
362C2C2×#360×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C2×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
2. C127×#2112C2semidirect
3. C2×#340×C127C2semidirect
4. C127×#1348C2semidirect
5. C127×#1347C2semidirect
6. C2×#135×C127C4semidirect
11. #467×C127C4semidirect
13. #466×C127C4semidirect
17. #427×C127C4semidirect
27. C2×Q16×C127C2×C4semidirect
29. C2×D8×C127C2×C4semidirect
52. #107×C127C2×C4semidirect
53. #107×C127C2×C4semidirect
173. #11704C127direct (N × H)
183. #2112C2×C127semidirect
184. C2×#340C2×C127semidirect
185. #1348C2×C127semidirect
186. #1347C2×C127semidirect
187. C127#11704direct (N × H)
188. C2×#135C4×C127semidirect
193. #467C4×C127semidirect
195. #466C4×C127semidirect
199. #427C4×C127semidirect
209. C2×Q16C2×C4×C127semidirect
211. C2×D8C2×C4×C127semidirect
234. #107C2×C4×C127semidirect
235. #107C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30502
C127×#21122
C2×#340×C1272
C127×#13482
C127×#13472
#11704127