Finite Group Databasebeta

← C127×#20723 #44584396

Subgroups — C127×#20723 #44584396

Order 32512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C127C211yesmaximal, characteristic
2C127×#2283C212yesmaximal, complemented
3C127×#1820C212yesmaximal, complemented
4C127×#1799C214yesmaximal, complemented
5C127×#1782C212yesmaximal
6C4×#99×C127C214yesmaximal, complemented
7C22×#41×C127C2211yescharacteristic
8C4×#41×C127—22no—
9C4×#41×C127—22no—
10C4×#41×C127—22no—
11C4×#41×C127—22no—
12C2×C4×Q8×C127C411yescharacteristic, complemented
13C2×C4×Q8×C127C411yescharacteristic, complemented
14C2×C4×D4×C127C411yescharacteristic, complemented
15C2×C4×D4×C127C411yescharacteristic, complemented
16C2×C4×D4×C127C2212yes—
17C2×C4×D4×C127C2212yes—
18C2×#117×C127C412yescomplemented
19C2×#117×C127C2211yescharacteristic
20C22×C42×C127C412yescomplemented
21C22×C42×C127C2211yescharacteristic
22C2×#99×C127C2218yes—
23#383×C127—22no—
24#382×C127—22no—
25#381×C127C2214yes—
26#380×C127C2214yes—
27C4×C4⋊C4×C127—22no—
28C4×C22⋊C4×C127C2214yes—
29#376×C127—22no—
30#342×C127C2218yes—
31C2×#41×C127—28no—
32C2×#41×C127—22no—
33C2×#41×C127—22no—
34C22×Q8×C127C2×C411yescharacteristic
35C22×D4×C127C2×C411yescharacteristic
36C22×D4×C127C2312yes—
37C23×C4×C127C2×C412yes—
38C23×C4×C127C2×C412yes—
39C23×C4×C127C2×C412yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C4×Q8×C127—22no—
44C4×Q8×C127—22no—
45C4×Q8×C127—22no—
46C4×Q8×C127—22no—
47C4×D4×C127—24no—
48C4×D4×C127—24no—
49C4×D4×C127—24no—
50C4×D4×C127—24no—
51C4×D4×C127—22no—
52C4×D4×C127—22no—
53C4×D4×C127—22no—
54C4×D4×C127—22no—
55#117×C127—22no—
56#117×C127—22no—
57#117×C127—24no—
58#117×C127—24no—
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127C2×C412yes—
61C2×C4⋊C4×C127C2×C412yes—
62C2×C4⋊C4×C127C2×C411yescharacteristic
63C2×C4⋊C4×C127C2×C411yescharacteristic
64C2×C22⋊C4×C127C2×C412yes—
65C2×C22⋊C4×C127C2×C412yes—
66C2×C22⋊C4×C127C2318yes—
67C2×C22⋊C4×C127C2312yes—
68C2×C42×C127—22no—
69C2×C42×C127—22no—
70C2×C42×C127—22no—
71C2×C42×C127—22no—
72C2×C42×C127—24no—
73C2×C42×C127C2×C412yes—
74C2×C42×C127C2×C412yes—
75C2×C42×C127C2×C412yes—
76C2×C42×C127C2×C411yescharacteristic
77C2×C42×C127C2×C411yescharacteristic
78C2×C42×C127C2×C411yescharacteristic
79C2×C42×C127C2×C411yescharacteristic
80C2×C42×C127D412yes—
81C2×C42×C127D412yes—
82C2×C42×C127D412yes—
83C2×C42×C127D412yes—
84#99×C127—216no—
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—24no—
88#95×C127—24no—
89C24×C127C22×C412yes—
90C24×C127C2411yescharacteristic
91#41×C127—216no—
92#41×C127—216no—
93C2×Q8×C127—22no—
94C2×Q8×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—22no—
99C2×D4×C127#4118yes—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—24no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—28no—
110C22×C4×C127—42no—
111C22×C4×C127—42no—
112C22×C4×C127—44no—
113C22×C4×C127—44no—
114C22×C4×C127C22×C411yescharacteristic
115C22×C4×C127C22×C411yescharacteristic
116C22×C4×C127C22×C411yescharacteristic
117C22×C4×C127C22×C411yescharacteristic
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C412yes—
120C22×C4×C127C22×C412yes—
121C22×C4×C127C22×C411yescharacteristic
122C22×C4×C127C22×C411yescharacteristic
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D412yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D412yes—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—24no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—48no—
134C22⋊C4×C127—24no—
135C22⋊C4×C127—24no—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—216no—
138C42×C127—22no—
139C42×C127—22no—
140C42×C127—22no—
141C42×C127—22no—
142C42×C127—22no—
143C42×C127—22no—
144C42×C127—48no—
145C42×C127C22⋊C411yescharacteristic
146C42×C127C22⋊C411yescharacteristic
147C42×C127C22⋊C412yes—
148C42×C127C22⋊C412yes—
149C42×C127C22⋊C412yes—
150C42×C127C22⋊C412yes—
151C42×C127C22⋊C412yes—
152C42×C127C22⋊C411yescharacteristic
153C42×C127C22⋊C411yescharacteristic
154C42×C127C22⋊C412yes—
155C23×C127—22no—
156C23×C127—22no—
157C23×C127—41no—
158C23×C127—41no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127#11714yes—
162C23×C127C23×C411yescharacteristic
163C23×C127C22×D412yes—
164C23×C127C2×#4114yes—
165Q8×C127—28no—
166D4×C127—28no—
167D4×C127—216no—
168C2×C4×C127—28no—
169C2×C4×C127—28no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—44no—
187C2×C4×C127—44no—
188C2×C4×C127—44no—
189C2×C4×C127—44no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—48no—
193C2×C4×C127—48no—
194C2×C4×C127—48no—
195C2×C4×C127C2×C22⋊C411yescharacteristic
196C2×C4×C127C2×C22⋊C411yescharacteristic
197C2×C4×C127C2×C22⋊C411yescharacteristic
198C2×C4×C127C2×C22⋊C411yescharacteristic
199C2×C4×C127C2×C22⋊C412yes—
200C2×C4×C127C2×C22⋊C412yes—
201C2×C4×C127C2×C22⋊C412yes—
202C2×C4×C127C2×C22⋊C411yescharacteristic
203C2×C4×C127C2×C22⋊C411yescharacteristic
204C2×C4×C127#11714yes—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—24no—
210C22×C127—44no—
211C22×C127—44no—
212C22×C127—44no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127C22×C22⋊C411yescharacteristic
216C22×C127C2×#11712yes—
217C22×C127#52514yes—
218C4×C127—21no—
219C4×C127—21no—
220C4×C127—22no—
221C4×C127—22no—
222C4×C127—21no—
223C4×C127—21no—
224C4×C127—22no—
225C4×C127—24no—
226C4×C127—42no—
227C4×C127—42no—
228C4×C127—88no—
229C4×C127#41012yes—
230C4×C127#41012yes—
231#20723C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—24no—
233C2×C127—22no—
234C2×C127—44no—
235C2×C127#228011yescharacteristic
236C2×C127C2×#41011yescharacteristic
237C2×C127C2×#41011yescharacteristic
238C2×C4×#41C2×C12711yescharacteristic
239#2283C2×C12712yescomplemented
240#1820C2×C12712yescomplemented
241#1799C2×C12714yescomplemented
242#1782C2×C12712yes—
243C4×#99C2×C12714yescomplemented
244C127#2072311yescharacteristic, direct product factor, Sylow
245C22×#41C22×C12711yescharacteristic
246C4×#41—22no—
247C4×#41—22no—
248C4×#41—22no—
249C4×#41—22no—
250C2×C4×Q8C4×C12711yescharacteristic, complemented
251C2×C4×Q8C4×C12711yescharacteristic, complemented
252C2×C4×D4C4×C12711yescharacteristic, complemented
253C2×C4×D4C4×C12711yescharacteristic, complemented
254C2×C4×D4C22×C12712yes—
255C2×C4×D4C22×C12712yes—
256C2×#117C4×C12712yescomplemented
257C2×#117C22×C12711yescharacteristic
258C22×C42C4×C12712yescomplemented
259C22×C42C22×C12711yescharacteristic
260C2×#99C22×C12718yes—
261#383—22no—
262#382—22no—
263#381C22×C12714yes—
264#380C22×C12714yes—
265C4×C4⋊C4—22no—
266C4×C22⋊C4C22×C12714yes—
267#376—22no—
268#342C22×C12718yes—
269C2×#41—28no—
270C2×#41—22no—
271C2×#41—22no—
272C22×Q8C2×C4×C12711yescharacteristic
273C22×D4C2×C4×C12711yescharacteristic
274C22×D4C23×C12712yes—
275C23×C4C2×C4×C12712yes—
276C23×C4C2×C4×C12712yes—
277C23×C4C2×C4×C12712yes—
278C23×C4C23×C12711yescharacteristic
279C23×C4C23×C12711yescharacteristic
280C23×C4C23×C12711yescharacteristic
281C4×Q8—22no—
282C4×Q8—22no—
283C4×Q8—22no—
284C4×Q8—22no—
285C4×D4—24no—
286C4×D4—24no—
287C4×D4—24no—
288C4×D4—24no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—22no—
292C4×D4—22no—
293#117—22no—
294#117—22no—
295#117—24no—
296#117—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4C2×C4×C12712yes—
299C2×C4⋊C4C2×C4×C12712yes—
300C2×C4⋊C4C2×C4×C12711yescharacteristic
301C2×C4⋊C4C2×C4×C12711yescharacteristic
302C2×C22⋊C4C2×C4×C12712yes—
303C2×C22⋊C4C2×C4×C12712yes—
304C2×C22⋊C4C23×C12718yes—
305C2×C22⋊C4C23×C12712yes—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—24no—
311C2×C42C2×C4×C12712yes—
312C2×C42C2×C4×C12712yes—
313C2×C42C2×C4×C12712yes—
314C2×C42C2×C4×C12711yescharacteristic
315C2×C42C2×C4×C12711yescharacteristic
316C2×C42C2×C4×C12711yescharacteristic
317C2×C42C2×C4×C12711yescharacteristic
318C2×C42D4×C12712yes—
319C2×C42D4×C12712yes—
320C2×C42D4×C12712yes—
321C2×C42D4×C12712yes—
322#99—216no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327C24C22×C4×C12712yes—
328C24C24×C12711yescharacteristic
329#41—216no—
330#41—216no—
331C2×Q8—22no—
332C2×Q8—24no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4#41×C12718yes—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—28no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4C22×C4×C12711yescharacteristic
353C22×C4C22×C4×C12711yescharacteristic
354C22×C4C22×C4×C12711yescharacteristic
355C22×C4C22×C4×C12711yescharacteristic
356C22×C4C22×C4×C12712yes—
357C22×C4C22×C4×C12712yes—
358C22×C4C22×C4×C12712yes—
359C22×C4C22×C4×C12711yescharacteristic
360C22×C4C22×C4×C12711yescharacteristic
361C22×C4C2×D4×C12712yes—
362C22×C4C2×D4×C12712yes—
363C22×C4C2×D4×C12712yes—
364C22×C4C2×D4×C12712yes—
365C22×C4C2×D4×C12712yes—
366C22×C4C2×D4×C12712yes—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—48no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—216no—
376C42—22no—
377C42—22no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—22no—
382C42—48no—
383C42C22⋊C4×C12711yescharacteristic
384C42C22⋊C4×C12711yescharacteristic
385C42C22⋊C4×C12711yescharacteristic
386C42C22⋊C4×C12711yescharacteristic
387C42C22⋊C4×C12712yes—
388C42C22⋊C4×C12712yes—
389C42C22⋊C4×C12712yes—
390C42C22⋊C4×C12712yes—
391C42C22⋊C4×C12712yes—
392C42C22⋊C4×C12712yes—
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—42no—
398C23—42no—
399C23#117×C12714yes—
400C23C23×C4×C12711yescharacteristic
401C23C22×D4×C12712yes—
402C23C2×#41×C12714yes—
403Q8—28no—
404D4—28no—
405D4—216no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—48no—
431C2×C4—48no—
432C2×C4—48no—
433C2×C4C2×C22⋊C4×C12711yescharacteristic
434C2×C4C2×C22⋊C4×C12711yescharacteristic
435C2×C4C2×C22⋊C4×C12711yescharacteristic
436C2×C4C2×C22⋊C4×C12711yescharacteristic
437C2×C4C2×C22⋊C4×C12712yes—
438C2×C4C2×C22⋊C4×C12712yes—
439C2×C4C2×C22⋊C4×C12712yes—
440C2×C4C2×C22⋊C4×C12711yescharacteristic
441C2×C4C2×C22⋊C4×C12711yescharacteristic
442C2×C4#117×C12714yes—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—24no—
448C22—44no—
449C22—44no—
450C22—44no—
451C22—42no—
452C22—42no—
453C22C22×C22⋊C4×C12711yescharacteristic
454C22C2×#117×C12712yes—
455C22#525×C12714yes—
456C4—21no—
457C4—21no—
458C4—22no—
459C4—22no—
460C4—21no—
461C4—21no—
462C4—22no—
463C4—24no—
464C4—42no—
465C4—42no—
466C4—88no—
467C4#410×C12712yes—
468C4#410×C12712yes—
469C2—24no—
470C2—22no—
471C2—44no—
472C2C127×#228011yescharacteristic
473C2C2×#410×C12711yescharacteristic
474C2C2×#410×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC22×#41×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2283C2semidirect
3. C127×#1820C2semidirect
4. C127×#1799C2semidirect
6. C4×#99×C127C2semidirect
12. C2×C4×Q8×C127C4semidirect
13. C2×C4×Q8×C127C4semidirect
14. C2×C4×D4×C127C4semidirect
15. C2×C4×D4×C127C4semidirect
18. C2×#117×C127C4semidirect
20. C22×C42×C127C4semidirect
231. #20723C127direct (N × H)
239. #2283C2×C127semidirect
240. #1820C2×C127semidirect
241. #1799C2×C127semidirect
243. C4×#99C2×C127semidirect
244. C127#20723direct (N × H)
250. C2×C4×Q8C4×C127semidirect
251. C2×C4×Q8C4×C127semidirect
252. C2×C4×D4C4×C127semidirect
253. C2×C4×D4C4×C127semidirect
256. C2×#117C4×C127semidirect
258. C22×C42C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1272
C127×#22832
C127×#18202
C127×#17992
C127×#17822
C4×#99×C1272
#20723127