Finite Group Databasebeta

← C127×#9532 #44573205

Subgroups — C127×#9532 #44573205

Order 32512.

444 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3114C211yesmaximal, characteristic
2C127×#2967C211yesmaximal, characteristic, complemented
3C127×#1535C211yesmaximal, characteristic, complemented
4C127×#1490C211yesmaximal, characteristic, complemented
5C127×#1466C211yesmaximal, characteristic, complemented
6C127×#1308C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8#529×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#483×C127C411yescharacteristic
11#480×C127C411yescharacteristic
12#478×C127—21no—
13#463×C127—21no—
14#450×C127C411yescharacteristic
15#447×C127C411yescharacteristic
16#446×C127—21no—
17#442×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—
31D4⋊C8×C127—21no—
32D4⋊C8×C127—21no—
33#323×C127—21no—
34#323×C127—21no—
35C22×D4×C127C2×C411yescharacteristic
36C23×C4×C127—21no—
37C2×SD16×C127—21no—
38C2×D8×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C22×C8×C127—21no—
42#126×C127—21no—
43#125×C127D411yescharacteristic
44#124×C127D411yescharacteristic
45#123×C127—21no—
46C22⋊Q8×C127C2×C411yescharacteristic
47#121×C127C2×C411yescharacteristic
48C4×Q8×C127D411yescharacteristic
49C4×D4×C127—21no—
50C4×D4×C127—21no—
51C4×D4×C127—21no—
52C4×D4×C127—21no—
53C4×D4×C127—21no—
54C4×D4×C127D411yescharacteristic
55#117×C127—21no—
56C2×C4⋊C4×C127C2×C411yescharacteristic
57C2×C22⋊C4×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#102×C127—21no—
69#102×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
88C24×C127—21no—
89C2×Q8×C127C22⋊C411yescharacteristic
90C2×D4×C127—21no—
91C2×D4×C127—21no—
92C2×D4×C127—21no—
93C2×D4×C127—42no—
94C2×D4×C127C22⋊C411yescharacteristic
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—41no—
98C22×C4×C127—41no—
99C22×C4×C127—82no—
100C22×C4×C127C22×C411yescharacteristic
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127#4111yescharacteristic
103SD16×C127—42no—
104D8×C127—42no—
105M16×C127—42no—
106M16×C127—42no—
107C2×C8×C127—21no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—21no—
111C2×C8×C127—21no—
112C2×C8×C127—21no—
113C2×C8×C127—42no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127C22⋊C411yescharacteristic
123C4⋊C4×C127C22⋊C411yescharacteristic
124C22⋊C4×C127—21no—
125C22⋊C4×C127—21no—
126C22⋊C4×C127—21no—
127C22⋊C4×C127—21no—
128C22⋊C4×C127—21no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C42×C127—21no—
132C42×C127C2×D411yescharacteristic
133C42×C127C2×D411yescharacteristic
134C42×C127C2×D411yescharacteristic
135C42×C127#4111yescharacteristic
136C23×C127—22no—
137C23×C127—21no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—81no—
141C23×C127—81no—
142C23×C127C4×D411yescharacteristic
143Q8×C127—41no—
144D4×C127—22no—
145D4×C127—22no—
146D4×C127—41no—
147D4×C127—41no—
148D4×C127—41no—
149D4×C127—81no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—82no—
160C2×C4×C127—82no—
161C2×C4×C127—81no—
162C2×C4×C127C2×C22⋊C411yescharacteristic
163C2×C4×C127C4×D411yescharacteristic
164C2×C4×C127#12011yescharacteristic
165C2×C4×C127#12111yescharacteristic
166C2×C4×C127#12111yescharacteristic
167C2×C4×C127#12311yescharacteristic
168C8×C127—22no—
169C8×C127—41no—
170C8×C127—41no—
171C8×C127—41no—
172C8×C127—41no—
173C8×C127—41no—
174C8×C127—81no—
175C8×C127—81no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—21no—
179C22×C127—42no—
180C22×C127—41no—
181C22×C127—41no—
182C22×C127—41no—
183C22×C127—82no—
184C22×C127—82no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127#38611yescharacteristic
188C4×C127—21no—
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—41no—
195C4×C127—41no—
196C4×C127—41no—
197C4×C127—81no—
198#9532C12711yesmaximal, characteristic, direct product factor, Sylow
199C2×C127—41no—
200C2×C127—81no—
201C2×C127—82no—
202C2×C127#189111yescharacteristic
203C2×C127#190311yescharacteristic
204C2×C127#190611yescharacteristic
205#3114C2×C12711yescharacteristic
206#2967C2×C12711yescharacteristic, complemented
207#1535C2×C12711yescharacteristic, complemented
208#1490C2×C12711yescharacteristic, complemented
209#1466C2×C12711yescharacteristic, complemented
210#1308C2×C12711yescharacteristic, complemented
211#1291C2×C12711yescharacteristic, complemented
212C127#953211yescharacteristic, direct product factor, Sylow
213#529C22×C12711yescharacteristic
214C2×C4×D4C22×C12711yescharacteristic
215#483C4×C12711yescharacteristic
216#480C4×C12711yescharacteristic
217#478—21no—
218#463—21no—
219#450C4×C12711yescharacteristic
220#447C4×C12711yescharacteristic
221#446—21no—
222#442—21no—
223#440—21no—
224#436—21no—
225#435—21no—
226#435—21no—
227#433—21no—
228#432C22×C12711yescharacteristic
229#432C22×C12711yescharacteristic
230#432C22×C12711yescharacteristic
231#432C22×C12711yescharacteristic
232#405—21no—
233C4×M16C22×C12711yescharacteristic
234#330—21no—
235#329—21no—
236D4⋊C8—21no—
237D4⋊C8—21no—
238#323—21no—
239#323—21no—
240C22×D4C2×C4×C12711yescharacteristic
241C23×C4—21no—
242C2×SD16—21no—
243C2×D8—21no—
244C2×M16—21no—
245C2×M16—21no—
246C22×C8—21no—
247#126—21no—
248#125D4×C12711yescharacteristic
249#124D4×C12711yescharacteristic
250#123—21no—
251C22⋊Q8C2×C4×C12711yescharacteristic
252#121C2×C4×C12711yescharacteristic
253C4×Q8D4×C12711yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4D4×C12711yescharacteristic
260#117—21no—
261C2×C4⋊C4C2×C4×C12711yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C12711yescharacteristic
264#107—21no—
265#106—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272#103—21no—
273#102—21no—
274#102—21no—
275#102—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8C2×C4×C12711yescharacteristic
281C22⋊C8C2×C4×C12711yescharacteristic
282C22⋊C8D4×C12711yescharacteristic
283C22⋊C8D4×C12711yescharacteristic
284#97—21no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97—21no—
289#97—21no—
290C4×C8—21no—
291C4×C8D4×C12711yescharacteristic
292C4×C8D4×C12711yescharacteristic
293C24—21no—
294C2×Q8C22⋊C4×C12711yescharacteristic
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4C22⋊C4×C12711yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4C22×C4×C12711yescharacteristic
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4#41×C12711yescharacteristic
308SD16—42no—
309D8—42no—
310M16—42no—
311M16—42no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—41no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4C22⋊C4×C12711yescharacteristic
328C4⋊C4C22⋊C4×C12711yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—21no—
337C42C2×D4×C12711yescharacteristic
338C42C2×D4×C12711yescharacteristic
339C42C2×D4×C12711yescharacteristic
340C42#41×C12711yescharacteristic
341C23—22no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—81no—
346C23—81no—
347C23C4×D4×C12711yescharacteristic
348Q8—41no—
349D4—22no—
350D4—22no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—81no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4C2×C22⋊C4×C12711yescharacteristic
368C2×C4C4×D4×C12711yescharacteristic
369C2×C4#120×C12711yescharacteristic
370C2×C4#121×C12711yescharacteristic
371C2×C4#121×C12711yescharacteristic
372C2×C4#123×C12711yescharacteristic
373C8—22no—
374C8—41no—
375C8—41no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—81no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—82no—
389C22—82no—
390C22—81no—
391C22—81no—
392C22#386×C12711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—81no—
403C2—41no—
404C2—81no—
405C2—82no—
406C2C127×#189111yescharacteristic
407C2C127×#190311yescharacteristic
408C2C127×#190611yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#447×C127C4
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
2. C127×#2967C2semidirect
3. C127×#1535C2semidirect
4. C127×#1490C2semidirect
5. C127×#1466C2semidirect
6. C127×#1308C2semidirect
7. C127×#1291C2semidirect
198. #9532C127direct (N × H)
206. #2967C2×C127semidirect
207. #1535C2×C127semidirect
208. #1490C2×C127semidirect
209. #1466C2×C127semidirect
210. #1308C2×C127semidirect
211. #1291C2×C127semidirect
212. C127#9532direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31142
C127×#29672
C127×#15352
C127×#14902
C127×#14662
C127×#13082
C127×#12912
#9532127