Finite Group Databasebeta

← C127×#11685 #44575358

Subgroups — C127×#11685 #44575358

Order 32512.

448 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3054C211yesmaximal, characteristic
2C2×#349×C127C211yesmaximal, characteristic, complemented
3C2×H(3,ℤ/4)×C127C211yesmaximal, characteristic, complemented
4C127×#1340C212yesmaximal, complemented
5C127×#1339C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic, complemented
7C22×M16×C127C2211yescharacteristic
8#525×C127—21no—
9C2×#117×C127—21no—
10C2×M32×C127—21no—
11#470×C127C411yescharacteristic, complemented
12#470×C127C2211yescharacteristic
13#469×C127C411yescharacteristic, complemented
14#469×C127C2211yescharacteristic
15#468×C127—21no—
16#468×C127—21no—
17#427×C127C411yescharacteristic, complemented
18#416×C127—21no—
19#349×C127—21no—
20#349×C127C2212yes—
21H(3,ℤ/4)×C127—21no—
22H(3,ℤ/4)×C127C2212yes—
23C2×#41×C127—21no—
24C23×C4×C127D411yescharacteristic
25#135×C127—41no—
26#135×C127—41no—
27C2×Q16×C127C2×C411yescharacteristic, complemented
28C2×SD16×C127—21no—
29C2×D8×C127C2×C411yescharacteristic, complemented
30C2×M16×C127—41no—
31C2×M16×C127—41no—
32C2×M16×C127C2×C411yescharacteristic
33C2×M16×C127D411yescharacteristic
34C2×M16×C127D411yescharacteristic
35C2×M16×C127C2311yescharacteristic
36C22×C8×C127C2×C411yescharacteristic
37C22×C8×C127D411yescharacteristic
38#123×C127—41no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41#121×C127—21no—
42#121×C127—21no—
43#120×C127—41no—
44C4×D4×C127—41no—
45C4×D4×C127—41no—
46#117×C127—22no—
47#117×C127—22no—
48#117×C127—21no—
49#117×C127—41no—
50#117×C127—41no—
51C2×C4⋊C4×C127—41no—
52C2×C22⋊C4×C127—41no—
53C2×C42×C127—22no—
54M32×C127—22no—
55M32×C127—41no—
56C2×C16×C127—41no—
57#107×C127—21no—
58#106×C127C2×C411yescharacteristic, complemented
59#106×C127C2×C411yescharacteristic, complemented
60#103×C127—21no—
61#103×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64C24×C127D811yescharacteristic
65#41×C127—41no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69C2×Q8×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—42no—
79C22×C4×C127—41no—
80C22×C4×C127C22⋊C411yescharacteristic
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127D811yescharacteristic
83C22×C4×C127SD1611yescharacteristic
84C22×C4×C127SD1611yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86Q16×C127—41no—
87SD16×C127—42no—
88D8×C127—41no—
89M16×C127—41no—
90M16×C127—41no—
91M16×C127—41no—
92M16×C127—41no—
93C2×C8×C127—21no—
94C2×C8×C127—21no—
95C2×C8×C127—21no—
96C2×C8×C127—21no—
97C2×C8×C127C22⋊C411yescharacteristic
98C2×C8×C127C22⋊C411yescharacteristic
99C2×C8×C127C22×C411yescharacteristic
100C2×C8×C127C2×D411yescharacteristic
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—42no—
104C4⋊C4×C127—42no—
105C4⋊C4×C127—41no—
106C4⋊C4×C127—41no—
107C22⋊C4×C127—42no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—42no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C42×C127—24no—
115C42×C127—42no—
116C42×C127—41no—
117C16×C127—42no—
118C23×C127—21no—
119C23×C127—21no—
120C23×C127—41no—
121C23×C127—81no—
122C23×C127#10211yescharacteristic
123C23×C127#10211yescharacteristic
124C23×C127C2×D811yescharacteristic
125Q8×C127—41no—
126Q8×C127—41no—
127D4×C127—41no—
128D4×C127—41no—
129D4×C127—82no—
130D4×C127—82no—
131D4×C127—81no—
132D4×C127—81no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—44no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—84no—
148C2×C4×C127—81no—
149C2×C4×C127—81no—
150C2×C4×C127#9911yescharacteristic
151C2×C4×C127#9911yescharacteristic
152C2×C4×C127#10211yescharacteristic
153C2×C4×C127#10211yescharacteristic
154C2×C4×C127#10411yescharacteristic
155C2×C4×C127#10411yescharacteristic
156C2×C4×C127C2×C22⋊C411yescharacteristic
157C2×C4×C127C2×SD1611yescharacteristic
158C8×C127—21no—
159C8×C127—21no—
160C8×C127—21no—
161C8×C127—21no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—42no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127#32711yescharacteristic
173C22×C127#32711yescharacteristic
174C22×C127C2×#10211yescharacteristic
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—81no—
178C4×C127—81no—
179C4×C127—84no—
180C4×C127—81no—
181C4×C127#32711yescharacteristic
182C4×C127#32711yescharacteristic
183C4×C127C2×#9911yescharacteristic
184C4×C127C2×#10411yescharacteristic
185#11685C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—21no—
187C2×C127—21no—
188C2×C127—21no—
189C2×C127—41no—
190C2×C127—41no—
191C2×C127—161no—
192C2×C127C2×#32711yescharacteristic
193#3054C2×C12711yescharacteristic
194C2×#349C2×C12711yescharacteristic, complemented
195C2×H(3,ℤ/4)C2×C12711yescharacteristic, complemented
196#1340C2×C12712yescomplemented
197#1339C2×C12712yescomplemented
198C127#1168511yescharacteristic, direct product factor, Sylow
199C2×#135C4×C12711yescharacteristic, complemented
200C22×M16C22×C12711yescharacteristic
201#525—21no—
202C2×#117—21no—
203C2×M32—21no—
204#470C4×C12711yescharacteristic, complemented
205#470C22×C12711yescharacteristic
206#469C4×C12711yescharacteristic, complemented
207#469C22×C12711yescharacteristic
208#468—21no—
209#468—21no—
210#427C4×C12711yescharacteristic, complemented
211#416—21no—
212#349—21no—
213#349C22×C12712yes—
214H(3,ℤ/4)—21no—
215H(3,ℤ/4)C22×C12712yes—
216C2×#41—21no—
217C23×C4D4×C12711yescharacteristic
218#135—41no—
219#135—41no—
220C2×Q16C2×C4×C12711yescharacteristic, complemented
221C2×SD16—21no—
222C2×D8C2×C4×C12711yescharacteristic, complemented
223C2×M16—41no—
224C2×M16—41no—
225C2×M16C2×C4×C12711yescharacteristic
226C2×M16D4×C12711yescharacteristic
227C2×M16D4×C12711yescharacteristic
228C2×M16C23×C12711yescharacteristic
229C22×C8C2×C4×C12711yescharacteristic
230C22×C8D4×C12711yescharacteristic
231#123—41no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234#121—21no—
235#121—21no—
236#120—41no—
237C4×D4—41no—
238C4×D4—41no—
239#117—22no—
240#117—22no—
241#117—21no—
242#117—41no—
243#117—41no—
244C2×C4⋊C4—41no—
245C2×C22⋊C4—41no—
246C2×C42—22no—
247M32—22no—
248M32—41no—
249C2×C16—41no—
250#107—21no—
251#106C2×C4×C12711yescharacteristic, complemented
252#106C2×C4×C12711yescharacteristic, complemented
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257C24D8×C12711yescharacteristic
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4C22⋊C4×C12711yescharacteristic
274C22×C4C22⋊C4×C12711yescharacteristic
275C22×C4D8×C12711yescharacteristic
276C22×C4SD16×C12711yescharacteristic
277C22×C4SD16×C12711yescharacteristic
278C22×C4C2×D4×C12711yescharacteristic
279Q16—41no—
280SD16—42no—
281D8—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8C22⋊C4×C12711yescharacteristic
291C2×C8C22⋊C4×C12711yescharacteristic
292C2×C8C22×C4×C12711yescharacteristic
293C2×C8C2×D4×C12711yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—24no—
308C42—42no—
309C42—41no—
310C16—42no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—81no—
315C23#102×C12711yescharacteristic
316C23#102×C12711yescharacteristic
317C23C2×D8×C12711yescharacteristic
318Q8—41no—
319Q8—41no—
320D4—41no—
321D4—41no—
322D4—82no—
323D4—82no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4#99×C12711yescharacteristic
344C2×C4#99×C12711yescharacteristic
345C2×C4#102×C12711yescharacteristic
346C2×C4#102×C12711yescharacteristic
347C2×C4#104×C12711yescharacteristic
348C2×C4#104×C12711yescharacteristic
349C2×C4C2×C22⋊C4×C12711yescharacteristic
350C2×C4C2×SD16×C12711yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#327×C12711yescharacteristic
366C22#327×C12711yescharacteristic
367C22C2×#102×C12711yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—84no—
373C4—81no—
374C4#327×C12711yescharacteristic
375C4#327×C12711yescharacteristic
376C4C2×#99×C12711yescharacteristic
377C4C2×#104×C12711yescharacteristic
378C2—21no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—161no—
384C2C2×#327×C12711yescharacteristic
subgroupG/H
centerC4×C127#327
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127C2×#327
prime radicalC127×#3054C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#349×C127C2semidirect
3. C2×H(3,ℤ/4)×C127C2semidirect
4. C127×#1340C2semidirect
5. C127×#1339C2semidirect
6. C2×#135×C127C4semidirect
11. #470×C127C4semidirect
13. #469×C127C4semidirect
17. #427×C127C4semidirect
27. C2×Q16×C127C2×C4semidirect
29. C2×D8×C127C2×C4semidirect
58. #106×C127C2×C4semidirect
59. #106×C127C2×C4semidirect
185. #11685C127direct (N × H)
194. C2×#349C2×C127semidirect
195. C2×H(3,ℤ/4)C2×C127semidirect
196. #1340C2×C127semidirect
197. #1339C2×C127semidirect
198. C127#11685direct (N × H)
199. C2×#135C4×C127semidirect
204. #470C4×C127semidirect
206. #469C4×C127semidirect
210. #427C4×C127semidirect
220. C2×Q16C2×C4×C127semidirect
222. C2×D8C2×C4×C127semidirect
251. #106C2×C4×C127semidirect
252. #106C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30542
C2×#349×C1272
C2×H(3,ℤ/4)×C1272
C127×#13402
C127×#13392
#11685127