Finite Group Databasebeta

← C127×#9531 #44573204

Subgroups — C127×#9531 #44573204

Order 32512.

412 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3117C211yesmaximal, characteristic
2C127×#2967C211yesmaximal, characteristic
3C127×#1535C211yesmaximal, characteristic
4C127×#1491C211yesmaximal, characteristic, complemented
5C127×#1467C211yesmaximal, characteristic, complemented
6C127×#1308C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8#529×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#484×C127C411yescharacteristic
11#481×C127C411yescharacteristic
12#479×C127—21no—
13#464×C127—21no—
14#451×C127C411yescharacteristic
15#448×C127C411yescharacteristic
16#446×C127—21no—
17#441×C127—21no—
18#440×C127—21no—
19#436×C127—21no—
20#435×C127—21no—
21#435×C127—21no—
22#433×C127—21no—
23#432×C127C2211yescharacteristic
24#432×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic
26#432×C127C2211yescharacteristic
27#405×C127—21no—
28C4×M16×C127C2211yescharacteristic
29#330×C127—21no—
30#329×C127—21no—
31Q8⋊C8×C127—21no—
32Q8⋊C8×C127—21no—
33#324×C127—21no—
34#324×C127—21no—
35C22×Q8×C127C2×C411yescharacteristic
36C2×Q16×C127—21no—
37C2×SD16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C22×C8×C127—21no—
41#126×C127—21no—
42#125×C127D411yescharacteristic
43#124×C127D411yescharacteristic
44#123×C127—21no—
45C22⋊Q8×C127C2×C411yescharacteristic
46#121×C127C2×C411yescharacteristic
47C4×Q8×C127—21no—
48C4×Q8×C127—21no—
49C4×Q8×C127—21no—
50C4×Q8×C127—21no—
51C4×Q8×C127D411yescharacteristic
52C4×D4×C127—21no—
53C4×D4×C127D411yescharacteristic
54#117×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127C2×C411yescharacteristic
57C2×C42×C127—21no—
58C2×C42×C127C2311yescharacteristic
59#107×C127—21no—
60#106×C127—21no—
61C4⋊C8×C127—21no—
62C4⋊C8×C127—21no—
63C4⋊C8×C127—21no—
64C4⋊C8×C127—21no—
65C4⋊C8×C127—21no—
66C4⋊C8×C127—21no—
67#103×C127—21no—
68#103×C127—21no—
69#103×C127—21no—
70#102×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127—21no—
75C22⋊C8×C127C2×C411yescharacteristic
76C22⋊C8×C127C2×C411yescharacteristic
77C22⋊C8×C127D411yescharacteristic
78C22⋊C8×C127D411yescharacteristic
79#97×C127—21no—
80#97×C127—21no—
81#97×C127—21no—
82#97×C127—21no—
83#97×C127—21no—
84#97×C127—21no—
85C4×C8×C127—21no—
86C4×C8×C127D411yescharacteristic
87C4×C8×C127D411yescharacteristic
88C2×Q8×C127—21no—
89C2×Q8×C127—21no—
90C2×Q8×C127—42no—
91C2×Q8×C127C22⋊C411yescharacteristic
92C2×D4×C127—21no—
93C2×D4×C127C22⋊C411yescharacteristic
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127C22×C411yescharacteristic
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127#4111yescharacteristic
100Q16×C127—42no—
101SD16×C127—42no—
102M16×C127—42no—
103M16×C127—42no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—21no—
107C2×C8×C127—21no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—42no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C4⋊C4×C127C22⋊C411yescharacteristic
122C4⋊C4×C127C22⋊C411yescharacteristic
123C22⋊C4×C127—21no—
124C22⋊C4×C127—21no—
125C22⋊C4×C127—21no—
126C22⋊C4×C127—21no—
127C22⋊C4×C127—21no—
128C42×C127—21no—
129C42×C127—41no—
130C42×C127—41no—
131C42×C127C2×D411yescharacteristic
132C42×C127C2×D411yescharacteristic
133C42×C127C2×D411yescharacteristic
134C42×C127#4111yescharacteristic
135C23×C127—21no—
136C23×C127C4×D411yescharacteristic
137Q8×C127—22no—
138Q8×C127—22no—
139Q8×C127—41no—
140Q8×C127—41no—
141Q8×C127—41no—
142D4×C127—41no—
143D4×C127—81no—
144C2×C4×C127—22no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—81no—
157C2×C4×C127C2×C22⋊C411yescharacteristic
158C2×C4×C127C4×D411yescharacteristic
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127#12111yescharacteristic
162C2×C4×C127#12311yescharacteristic
163C8×C127—22no—
164C8×C127—41no—
165C8×C127—41no—
166C8×C127—41no—
167C8×C127—41no—
168C8×C127—41no—
169C8×C127—81no—
170C8×C127—81no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127#38611yescharacteristic
178C4×C127—21no—
179C4×C127—21no—
180C4×C127—21no—
181C4×C127—21no—
182C4×C127—21no—
183C4×C127—21no—
184C4×C127—42no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—81no—
189#9531C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—41no—
191C2×C127—81no—
192C2×C127#189111yescharacteristic
193C2×C127#190211yescharacteristic
194C2×C127#190611yescharacteristic
195#3117C2×C12711yescharacteristic
196#2967C2×C12711yescharacteristic
197#1535C2×C12711yescharacteristic
198#1491C2×C12711yescharacteristic, complemented
199#1467C2×C12711yescharacteristic, complemented
200#1308C2×C12711yescharacteristic, complemented
201#1291C2×C12711yescharacteristic, complemented
202C127#953111yescharacteristic, direct product factor, Sylow
203#529C22×C12711yescharacteristic
204C2×C4×Q8C22×C12711yescharacteristic
205#484C4×C12711yescharacteristic
206#481C4×C12711yescharacteristic
207#479—21no—
208#464—21no—
209#451C4×C12711yescharacteristic
210#448C4×C12711yescharacteristic
211#446—21no—
212#441—21no—
213#440—21no—
214#436—21no—
215#435—21no—
216#435—21no—
217#433—21no—
218#432C22×C12711yescharacteristic
219#432C22×C12711yescharacteristic
220#432C22×C12711yescharacteristic
221#432C22×C12711yescharacteristic
222#405—21no—
223C4×M16C22×C12711yescharacteristic
224#330—21no—
225#329—21no—
226Q8⋊C8—21no—
227Q8⋊C8—21no—
228#324—21no—
229#324—21no—
230C22×Q8C2×C4×C12711yescharacteristic
231C2×Q16—21no—
232C2×SD16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C22×C8—21no—
236#126—21no—
237#125D4×C12711yescharacteristic
238#124D4×C12711yescharacteristic
239#123—21no—
240C22⋊Q8C2×C4×C12711yescharacteristic
241#121C2×C4×C12711yescharacteristic
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8D4×C12711yescharacteristic
247C4×D4—21no—
248C4×D4D4×C12711yescharacteristic
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C12711yescharacteristic
252C2×C42—21no—
253C2×C42C23×C12711yescharacteristic
254#107—21no—
255#106—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262#103—21no—
263#103—21no—
264#103—21no—
265#102—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8C2×C4×C12711yescharacteristic
271C22⋊C8C2×C4×C12711yescharacteristic
272C22⋊C8D4×C12711yescharacteristic
273C22⋊C8D4×C12711yescharacteristic
274#97—21no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97—21no—
279#97—21no—
280C4×C8—21no—
281C4×C8D4×C12711yescharacteristic
282C4×C8D4×C12711yescharacteristic
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—42no—
286C2×Q8C22⋊C4×C12711yescharacteristic
287C2×D4—21no—
288C2×D4C22⋊C4×C12711yescharacteristic
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4C22×C4×C12711yescharacteristic
293C22×C4C2×D4×C12711yescharacteristic
294C22×C4#41×C12711yescharacteristic
295Q16—42no—
296SD16—42no—
297M16—42no—
298M16—42no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—42no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C22⋊C4×C12711yescharacteristic
317C4⋊C4C22⋊C4×C12711yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42—41no—
325C42—41no—
326C42C2×D4×C12711yescharacteristic
327C42C2×D4×C12711yescharacteristic
328C42C2×D4×C12711yescharacteristic
329C42#41×C12711yescharacteristic
330C23—21no—
331C23C4×D4×C12711yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—41no—
337D4—41no—
338D4—81no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4C2×C22⋊C4×C12711yescharacteristic
353C2×C4C4×D4×C12711yescharacteristic
354C2×C4#120×C12711yescharacteristic
355C2×C4#121×C12711yescharacteristic
356C2×C4#121×C12711yescharacteristic
357C2×C4#123×C12711yescharacteristic
358C8—22no—
359C8—41no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—41no—
364C8—81no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22#386×C12711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C2—41no—
385C2—81no—
386C2C127×#189111yescharacteristic
387C2C127×#190211yescharacteristic
388C2C127×#190611yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1491C2semidirect
5. C127×#1467C2semidirect
6. C127×#1308C2semidirect
7. C127×#1291C2semidirect
189. #9531C127direct (N × H)
198. #1491C2×C127semidirect
199. #1467C2×C127semidirect
200. #1308C2×C127semidirect
201. #1291C2×C127semidirect
202. C127#9531direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31172
C127×#29672
C127×#15352
C127×#14912
C127×#14672
C127×#13082
C127×#12912
#9531127