Finite Group Databasebeta

← C127×#11703 #44575376

Subgroups — C127×#11703 #44575376

Order 32512.

466 conjugacy classes of subgroups.

The subgroup lattice has 348 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×#1735C211yesmaximal, characteristic, complemented
4C127×#1348C212yesmaximal, complemented
5C127×#1347C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic, complemented
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C2×#117×C127—21no—
10C22×C16×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×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—24no—
45#117×C127—21no—
46#117×C127—42no—
47C2×C4⋊C4×C127—22no—
48C2×C22⋊C4×C127—41no—
49C2×C42×C127—41no—
50C2×C16×C127—22no—
51C2×C16×C127—42no—
52#107×C127C2×C411yescharacteristic
53#107×C127C2×C411yescharacteristic
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—42no—
70C22×C4×C127—41no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127D811yescharacteristic
74C22×C4×C127SD1611yescharacteristic
75C22×C4×C127SD1611yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77Q16×C127—41no—
78SD16×C127—42no—
79D8×C127—41no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127C22⋊C411yescharacteristic
87C2×C8×C127C22⋊C411yescharacteristic
88C2×C8×C127C22×C411yescharacteristic
89C2×C8×C127C2×D411yescharacteristic
90C4⋊C4×C127—24no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C22⋊C4×C127—44no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C42×C127—44no—
103C42×C127—41no—
104C16×C127—42no—
105C23×C127—22no—
106C23×C127—22no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127#10211yescharacteristic
110C23×C127#10211yescharacteristic
111C23×C127C2×D811yescharacteristic
112Q8×C127—41no—
113Q8×C127—41no—
114D4×C127—41no—
115D4×C127—41no—
116D4×C127—82no—
117D4×C127—82no—
118D4×C127—82no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—44no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—82no—
131C2×C4×C127—82no—
132C2×C4×C127—82no—
133C2×C4×C127#9912yes—
134C2×C4×C127#10211yescharacteristic
135C2×C4×C127#10211yescharacteristic
136C2×C4×C127#10412yes—
137C2×C4×C127C2×C22⋊C411yescharacteristic
138C2×C4×C127C2×SD1611yescharacteristic
139C8×C127—21no—
140C8×C127—21no—
141C8×C127—21no—
142C8×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—44no—
151C22×C127—81no—
152C22×C127—81no—
153C22×C127—81no—
154C22×C127#32712yes—
155C22×C127C2×#10211yescharacteristic
156C22×C127#50812yes—
157C4×C127—21no—
158C4×C127—21no—
159C4×C127—84no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127—81no—
163C4×C127#32712yes—
164C4×C127C2×#9911yescharacteristic
165C4×C127C2×#10411yescharacteristic
166#11703C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—22no—
168C2×C127—22no—
169C2×C127—41no—
170C2×C127—161no—
171C2×C127C2×#32711yescharacteristic
172C2×C127#213811yescharacteristic
173C2×C127#214511yescharacteristic
174#3050C2×C12711yescharacteristic
175C2×C22⋊C16C2×C12711yescharacteristic, complemented
176#1735C2×C12711yescharacteristic, complemented
177#1348C2×C12712yescomplemented
178#1347C2×C12712yescomplemented
179C127#1170311yescharacteristic, direct product factor, Sylow
180C2×#135C4×C12711yescharacteristic, complemented
181C23×C8C22×C12711yescharacteristic
182#525—21no—
183C2×#117—21no—
184C22×C16—21no—
185#467C4×C12711yescharacteristic, complemented
186#467C22×C12711yescharacteristic
187#466C4×C12711yescharacteristic, complemented
188#466C22×C12711yescharacteristic
189#465—21no—
190#465—21no—
191#427C4×C12711yescharacteristic, complemented
192#416—21no—
193C22⋊C16—21no—
194C22⋊C16C22×C12712yes—
195#340—21no—
196#340C22×C12712yes—
197C2×#41—21no—
198C23×C4D4×C12711yescharacteristic
199#135—42no—
200C2×Q16C2×C4×C12711yescharacteristic
201C2×SD16—21no—
202C2×D8C2×C4×C12711yescharacteristic
203C22×C8—42no—
204C22×C8C2×C4×C12711yescharacteristic
205C22×C8C2×C4×C12711yescharacteristic
206C22×C8D4×C12711yescharacteristic
207C22×C8D4×C12711yescharacteristic
208C22×C8D4×C12711yescharacteristic
209C22×C8C23×C12711yescharacteristic
210#123—41no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213#121—21no—
214#121—21no—
215#120—41no—
216C4×D4—41no—
217C4×D4—41no—
218#117—24no—
219#117—21no—
220#117—42no—
221C2×C4⋊C4—22no—
222C2×C22⋊C4—41no—
223C2×C42—41no—
224C2×C16—22no—
225C2×C16—42no—
226#107C2×C4×C12711yescharacteristic
227#107C2×C4×C12711yescharacteristic
228#106—21no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233C24D8×C12711yescharacteristic
234#41—42no—
235#41—42no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4D8×C12711yescharacteristic
248C22×C4SD16×C12711yescharacteristic
249C22×C4SD16×C12711yescharacteristic
250C22×C4C2×D4×C12711yescharacteristic
251Q16—41no—
252SD16—42no—
253D8—41no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22⋊C4×C12711yescharacteristic
261C2×C8C22⋊C4×C12711yescharacteristic
262C2×C8C22×C4×C12711yescharacteristic
263C2×C8C2×D4×C12711yescharacteristic
264C4⋊C4—24no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—44no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42—44no—
277C42—41no—
278C16—42no—
279C23—22no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23#102×C12711yescharacteristic
284C23#102×C12711yescharacteristic
285C23C2×D8×C12711yescharacteristic
286Q8—41no—
287Q8—41no—
288D4—41no—
289D4—41no—
290D4—82no—
291D4—82no—
292D4—82no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—44no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4#99×C12712yes—
308C2×C4#102×C12711yescharacteristic
309C2×C4#102×C12711yescharacteristic
310C2×C4#104×C12712yes—
311C2×C4C2×C22⋊C4×C12711yescharacteristic
312C2×C4C2×SD16×C12711yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22#327×C12712yes—
329C22C2×#102×C12711yescharacteristic
330C22#508×C12712yes—
331C4—21no—
332C4—21no—
333C4—84no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4#327×C12712yes—
338C4C2×#99×C12711yescharacteristic
339C4C2×#104×C12711yescharacteristic
340C2—22no—
341C2—22no—
342C2—41no—
343C2—161no—
344C2C2×#327×C12711yescharacteristic
345C2C127×#213811yescharacteristic
346C2C127×#214511yescharacteristic
subgroupG/H
centerC2×C4×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×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×#1735C2semidirect
4. C127×#1348C2semidirect
5. C127×#1347C2semidirect
6. C2×#135×C127C4semidirect
11. #467×C127C4semidirect
13. #466×C127C4semidirect
17. #427×C127C4semidirect
166. #11703C127direct (N × H)
175. C2×C22⋊C16C2×C127semidirect
176. #1735C2×C127semidirect
177. #1348C2×C127semidirect
178. #1347C2×C127semidirect
179. C127#11703direct (N × H)
180. C2×#135C4×C127semidirect
185. #467C4×C127semidirect
187. #466C4×C127semidirect
191. #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×#17352
C127×#13482
C127×#13472
#11703127