Finite Group Databasebeta

← C127×#9431 #44573104

Subgroups — C127×#9431 #44573104

Order 32512.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3181C211yesmaximal, characteristic
2C127×#2968C211yesmaximal, characteristic
3C127×#1531C211yesmaximal, characteristic, complemented
4C127×#1518C211yesmaximal, characteristic, complemented
5C127×#1512C211yesmaximal, characteristic
6C127×#1302C211yesmaximal, characteristic, complemented
7C127×#1295C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9#529×C127C2211yescharacteristic
10#501×C127C411yescharacteristic, complemented
11#497×C127C411yescharacteristic, complemented
12#491×C127C411yescharacteristic, complemented
13#489×C127C411yescharacteristic, complemented
14#467×C127—21no—
15#465×C127—21no—
16#446×C127—21no—
17#441×C127—21no—
18#440×C127—21no—
19#435×C127—21no—
20#435×C127—21no—
21C8×D4×C127—21no—
22#433×C127—21no—
23#432×C127C2211yescharacteristic
24#431×C127C2211yescharacteristic
25#405×C127—21no—
26C2×#97×C127C2211yescharacteristic
27C2×#97×C127C2211yescharacteristic
28#382×C127C2211yescharacteristic
29#330×C127—21no—
30#330×C127—21no—
31#328×C127—21no—
32#328×C127—21no—
33#328×C127—21no—
34#327×C127—21no—
35C2×Q16×C127—21no—
36C2×SD16×C127—21no—
37C2×M16×C127—21no—
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—21no—
41C4⋊Q8×C127C2×C411yescharacteristic
42C4⋊Q8×C127C2×C411yescharacteristic
43#126×C127—21no—
44#125×C127—21no—
45#125×C127C2×C411yescharacteristic
46#124×C127C2×C411yescharacteristic
47#123×C127—21no—
48C22⋊Q8×C127—21no—
49C22⋊Q8×C127—21no—
50C22⋊Q8×C127D411yescharacteristic
51#121×C127D411yescharacteristic
52C4×Q8×C127—21no—
53C4×Q8×C127—21no—
54C4×Q8×C127D411yescharacteristic
55C4×D4×C127—21no—
56C4×D4×C127D411yescharacteristic
57#117×C127—21no—
58#117×C127—21no—
59C2×C4⋊C4×C127—21no—
60C2×C42×C127C2311yescharacteristic
61#107×C127—21no—
62#106×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×C127D411yescharacteristic
75C22⋊C8×C127D411yescharacteristic
76#97×C127—21no—
77#97×C127—21no—
78#97×C127—21no—
79#97×C127—21no—
80#97×C127C2×C411yescharacteristic
81#97×C127C2×C411yescharacteristic
82#97×C127D411yescharacteristic
83#97×C127D411yescharacteristic
84C4×C8×C127—21no—
85C4×C8×C127—21no—
86#95×C127—21no—
87#95×C127—21no—
88C2×Q8×C127—21no—
89C2×Q8×C127—21no—
90C2×Q8×C127C22⋊C411yescharacteristic
91C2×D4×C127—21no—
92C2×D4×C127C22⋊C411yescharacteristic
93C22×C4×C127—21no—
94C22×C4×C127—41no—
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127#4111yescharacteristic
98Q16×C127—42no—
99SD16×C127—42no—
100M16×C127—42no—
101C2×C8×C127—21no—
102C2×C8×C127—21no—
103C2×C8×C127—21no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—21no—
107C2×C8×C127—42no—
108C2×C8×C127—42no—
109C2×C8×C127—42no—
110C2×C8×C127—41no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
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×C127—81no—
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—
130C42×C127—21no—
131C42×C127—41no—
132C42×C127C22×C411yescharacteristic
133C42×C127C2×D411yescharacteristic
134C42×C127C2×D411yescharacteristic
135C42×C127#4111yescharacteristic
136C23×C127—21no—
137C23×C127#12111yescharacteristic
138Q8×C127—41no—
139Q8×C127—41no—
140Q8×C127—41no—
141Q8×C127—81no—
142D4×C127—41no—
143D4×C127—41no—
144D4×C127—41no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
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×C127—81no—
158C2×C4×C127—81no—
159C2×C4×C127C2×C22⋊C411yescharacteristic
160C2×C4×C127C4×D411yescharacteristic
161C2×C4×C127C4×D411yescharacteristic
162C2×C4×C127#12011yescharacteristic
163C2×C4×C127#12111yescharacteristic
164C2×C4×C127#12311yescharacteristic
165C8×C127—22no—
166C8×C127—22no—
167C8×C127—41no—
168C8×C127—41no—
169C8×C127—41no—
170C8×C127—41no—
171C8×C127—81no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127#38611yescharacteristic
178C22×C127#47111yescharacteristic
179C22×C127#47311yescharacteristic
180C4×C127—21no—
181C4×C127—21no—
182C4×C127—21no—
183C4×C127—21no—
184C4×C127—21no—
185C4×C127—21no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—41no—
189C4×C127—81no—
190C4×C127—81no—
191C4×C127—161no—
192#9431C12711yesmaximal, characteristic, direct product factor, Sylow
193C2×C127—21no—
194C2×C127—21no—
195C2×C127—81no—
196C2×C127#188411yescharacteristic
197C2×C127#190611yescharacteristic
198C2×C127#190811yescharacteristic
199#3181C2×C12711yescharacteristic
200#2968C2×C12711yescharacteristic
201#1531C2×C12711yescharacteristic, complemented
202#1518C2×C12711yescharacteristic, complemented
203#1512C2×C12711yescharacteristic
204#1302C2×C12711yescharacteristic, complemented
205#1295C2×C12711yescharacteristic, complemented
206C127#943111yescharacteristic, direct product factor, Sylow
207#533C22×C12711yescharacteristic
208#529C22×C12711yescharacteristic
209#501C4×C12711yescharacteristic, complemented
210#497C4×C12711yescharacteristic, complemented
211#491C4×C12711yescharacteristic, complemented
212#489C4×C12711yescharacteristic, complemented
213#467—21no—
214#465—21no—
215#446—21no—
216#441—21no—
217#440—21no—
218#435—21no—
219#435—21no—
220C8×D4—21no—
221#433—21no—
222#432C22×C12711yescharacteristic
223#431C22×C12711yescharacteristic
224#405—21no—
225C2×#97C22×C12711yescharacteristic
226C2×#97C22×C12711yescharacteristic
227#382C22×C12711yescharacteristic
228#330—21no—
229#330—21no—
230#328—21no—
231#328—21no—
232#328—21no—
233#327—21no—
234C2×Q16—21no—
235C2×SD16—21no—
236C2×M16—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8C2×C4×C12711yescharacteristic
241C4⋊Q8C2×C4×C12711yescharacteristic
242#126—21no—
243#125—21no—
244#125C2×C4×C12711yescharacteristic
245#124C2×C4×C12711yescharacteristic
246#123—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8D4×C12711yescharacteristic
250#121D4×C12711yescharacteristic
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8D4×C12711yescharacteristic
254C4×D4—21no—
255C4×D4D4×C12711yescharacteristic
256#117—21no—
257#117—21no—
258C2×C4⋊C4—21no—
259C2×C42C23×C12711yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#103—21no—
267#103—21no—
268#103—21no—
269#102—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8D4×C12711yescharacteristic
274C22⋊C8D4×C12711yescharacteristic
275#97—21no—
276#97—21no—
277#97—21no—
278#97—21no—
279#97C2×C4×C12711yescharacteristic
280#97C2×C4×C12711yescharacteristic
281#97D4×C12711yescharacteristic
282#97D4×C12711yescharacteristic
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286#95—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C12711yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C12711yescharacteristic
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C12711yescharacteristic
295C22×C4C2×D4×C12711yescharacteristic
296C22×C4#41×C12711yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4C22⋊C4×C12711yescharacteristic
322C4⋊C4C22⋊C4×C12711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—41no—
331C42C22×C4×C12711yescharacteristic
332C42C2×D4×C12711yescharacteristic
333C42C2×D4×C12711yescharacteristic
334C42#41×C12711yescharacteristic
335C23—21no—
336C23#121×C12711yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4C2×C22⋊C4×C12711yescharacteristic
359C2×C4C4×D4×C12711yescharacteristic
360C2×C4C4×D4×C12711yescharacteristic
361C2×C4#120×C12711yescharacteristic
362C2×C4#121×C12711yescharacteristic
363C2×C4#123×C12711yescharacteristic
364C8—22no—
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#386×C12711yescharacteristic
377C22#471×C12711yescharacteristic
378C22#473×C12711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2C127×#188411yescharacteristic
395C2C127×#190611yescharacteristic
396C2C127×#190811yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1531C2semidirect
4. C127×#1518C2semidirect
6. C127×#1302C2semidirect
7. C127×#1295C2semidirect
10. #501×C127C4semidirect
11. #497×C127C4semidirect
12. #491×C127C4semidirect
13. #489×C127C4semidirect
192. #9431C127direct (N × H)
201. #1531C2×C127semidirect
202. #1518C2×C127semidirect
204. #1302C2×C127semidirect
205. #1295C2×C127semidirect
206. C127#9431direct (N × H)
209. #501C4×C127semidirect
210. #497C4×C127semidirect
211. #491C4×C127semidirect
212. #489C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31812
C127×#29682
C127×#15312
C127×#15182
C127×#15122
C127×#13022
C127×#12952
#9431127