Finite Group Databasebeta

← C127×#11885 #44575558

Subgroups — C127×#11885 #44575558

Order 32512.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3050C211yesmaximal, characteristic
2C2×C22⋊C16×C127C211yesmaximal, characteristic, complemented
3C127×#1807C211yesmaximal, characteristic, complemented
4C127×#1348C212yesmaximal, complemented
5C127×#1347C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic, complemented
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C22×C16×C127—21no—
10#467×C127C411yescharacteristic, complemented
11#467×C127C2211yescharacteristic
12#466×C127C411yescharacteristic, complemented
13#466×C127C2211yescharacteristic
14#465×C127—21no—
15#465×C127—21no—
16#427×C127C411yescharacteristic, complemented
17C2×#106×C127—21no—
18#416×C127—21no—
19#380×C127—21no—
20C22⋊C16×C127—21no—
21C22⋊C16×C127C2212yes—
22#340×C127C2212yes—
23C2×#41×C127—21no—
24C23×C4×C127D411yescharacteristic
25#135×C127—42no—
26C2×Q16×C127C2×C411yescharacteristic
27C2×SD16×C127—21no—
28C2×D8×C127C2×C411yescharacteristic
29C22×C8×C127—42no—
30C22×C8×C127C2×C411yescharacteristic
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127D411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127C2311yescharacteristic
36#123×C127—41no—
37C22⋊Q8×C127—21no—
38C22⋊Q8×C127—21no—
39#121×C127—21no—
40#121×C127—21no—
41#120×C127—41no—
42C4×D4×C127—41no—
43C4×D4×C127—41no—
44#117×C127—21no—
45C2×C4⋊C4×C127—22no—
46C2×C22⋊C4×C127—41no—
47C2×C16×C127—22no—
48C2×C16×C127—42no—
49#107×C127C2×C411yescharacteristic
50#107×C127C2×C411yescharacteristic
51#106×C127—21no—
52#106×C127—42no—
53#103×C127—21no—
54#103×C127—21no—
55#102×C127—21no—
56#102×C127—21no—
57#95×C127—41no—
58C24×C127D811yescharacteristic
59#41×C127—42no—
60#41×C127—42no—
61C2×Q8×C127—21no—
62C2×D4×C127—21no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127—42no—
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127D811yescharacteristic
73C22×C4×C127SD1611yescharacteristic
74C22×C4×C127SD1611yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76Q16×C127—41no—
77SD16×C127—42no—
78D8×C127—41no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127C22⋊C411yescharacteristic
86C2×C8×C127C22⋊C411yescharacteristic
87C2×C8×C127C22×C411yescharacteristic
88C2×C8×C127C2×D411yescharacteristic
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—82no—
101C42×C127—41no—
102C16×C127—42no—
103C23×C127—22no—
104C23×C127—22no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127#10211yescharacteristic
108C23×C127#10211yescharacteristic
109C23×C127C2×D811yescharacteristic
110Q8×C127—41no—
111Q8×C127—41no—
112D4×C127—41no—
113D4×C127—41no—
114D4×C127—82no—
115D4×C127—82no—
116D4×C127—82no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—82no—
130C2×C4×C127—82no—
131C2×C4×C127—82no—
132C2×C4×C127—82no—
133C2×C4×C127#10211yescharacteristic
134C2×C4×C127#10211yescharacteristic
135C2×C4×C127C2×C22⋊C411yescharacteristic
136C2×C4×C127C2×SD1611yescharacteristic
137C8×C127—21no—
138C8×C127—21no—
139C8×C127—21no—
140C8×C127#9912yes—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—44no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127#36012yes—
153C22×C127C2×#10211yescharacteristic
154C22×C127#50812yes—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—81no—
159C4×C127—81no—
160C4×C127—81no—
161C4×C127—162no—
162C4×C127C2×#9911yescharacteristic
163C4×C127#42111yescharacteristic
164#11885C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—22no—
166C2×C127—22no—
167C2×C127—41no—
168C2×C127—161no—
169C2×C127#151911yescharacteristic
170C2×C127#213811yescharacteristic
171C2×C127C2×#36011yescharacteristic
172#3050C2×C12711yescharacteristic
173C2×C22⋊C16C2×C12711yescharacteristic, complemented
174#1807C2×C12711yescharacteristic, complemented
175#1348C2×C12712yescomplemented
176#1347C2×C12712yescomplemented
177C127#1188511yescharacteristic, direct product factor, Sylow
178C2×#135C4×C12711yescharacteristic, complemented
179C23×C8C22×C12711yescharacteristic
180#525—21no—
181C22×C16—21no—
182#467C4×C12711yescharacteristic, complemented
183#467C22×C12711yescharacteristic
184#466C4×C12711yescharacteristic, complemented
185#466C22×C12711yescharacteristic
186#465—21no—
187#465—21no—
188#427C4×C12711yescharacteristic, complemented
189C2×#106—21no—
190#416—21no—
191#380—21no—
192C22⋊C16—21no—
193C22⋊C16C22×C12712yes—
194#340C22×C12712yes—
195C2×#41—21no—
196C23×C4D4×C12711yescharacteristic
197#135—42no—
198C2×Q16C2×C4×C12711yescharacteristic
199C2×SD16—21no—
200C2×D8C2×C4×C12711yescharacteristic
201C22×C8—42no—
202C22×C8C2×C4×C12711yescharacteristic
203C22×C8C2×C4×C12711yescharacteristic
204C22×C8D4×C12711yescharacteristic
205C22×C8D4×C12711yescharacteristic
206C22×C8D4×C12711yescharacteristic
207C22×C8C23×C12711yescharacteristic
208#123—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213#120—41no—
214C4×D4—41no—
215C4×D4—41no—
216#117—21no—
217C2×C4⋊C4—22no—
218C2×C22⋊C4—41no—
219C2×C16—22no—
220C2×C16—42no—
221#107C2×C4×C12711yescharacteristic
222#107C2×C4×C12711yescharacteristic
223#106—21no—
224#106—42no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#95—41no—
230C24D8×C12711yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4C22⋊C4×C12711yescharacteristic
244C22×C4D8×C12711yescharacteristic
245C22×C4SD16×C12711yescharacteristic
246C22×C4SD16×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊C4×C12711yescharacteristic
258C2×C8C22⋊C4×C12711yescharacteristic
259C2×C8C22×C4×C12711yescharacteristic
260C2×C8C2×D4×C12711yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—82no—
273C42—41no—
274C16—42no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#102×C12711yescharacteristic
280C23#102×C12711yescharacteristic
281C23C2×D8×C12711yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4#102×C12711yescharacteristic
306C2×C4#102×C12711yescharacteristic
307C2×C4C2×C22⋊C4×C12711yescharacteristic
308C2×C4C2×SD16×C12711yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#99×C12712yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#360×C12712yes—
325C22C2×#102×C12711yescharacteristic
326C22#508×C12712yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—162no—
334C4C2×#99×C12711yescharacteristic
335C4#421×C12711yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2C127×#151911yescharacteristic
341C2C127×#213811yescharacteristic
342C2C2×#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. C2×C22⋊C16×C127C2semidirect
3. C127×#1807C2semidirect
4. C127×#1348C2semidirect
5. C127×#1347C2semidirect
6. C2×#135×C127C4semidirect
10. #467×C127C4semidirect
12. #466×C127C4semidirect
16. #427×C127C4semidirect
164. #11885C127direct (N × H)
173. C2×C22⋊C16C2×C127semidirect
174. #1807C2×C127semidirect
175. #1348C2×C127semidirect
176. #1347C2×C127semidirect
177. C127#11885direct (N × H)
178. C2×#135C4×C127semidirect
182. #467C4×C127semidirect
184. #466C4×C127semidirect
188. #427C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30502
C2×C22⋊C16×C1272
C127×#18072
C127×#13482
C127×#13472
#11885127