Finite Group Databasebeta

← C127×#20936 #44584609

Subgroups — C127×#20936 #44584609

Order 32512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C127C211yesmaximal, characteristic
2C2×#519×C127C211yesmaximal, characteristic, complemented
3C2×#419×C127C211yesmaximal, characteristic, complemented
4C2×#418×C127C211yesmaximal, characteristic
5C127×#2309C211yesmaximal, characteristic
6C127×#1880C218yesmaximal, complemented
7C127×#1735C211yesmaximal, characteristic, complemented
8C127×#1729C211yesmaximal, characteristic, complemented
9C23×Q8×C127C2211yescharacteristic
10C23×D4×C127C2211yescharacteristic
11C22×SD16×C127—24no—
12C22×SD16×C127—24no—
13C22×SD16×C127C418yescomplemented
14C22×SD16×C127C2214yes—
15C22×M16×C127C2211yescharacteristic
16C23×C8×C127C2211yescharacteristic
17#519×C127—24no—
18#519×C127—24no—
19C2×C4×Q8×C127—22no—
20C2×C4×Q8×C127C2214yescomplemented
21C2×#117×C127—22no—
22C2×#117×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24C2×#117×C127C2211yescharacteristic
25#419×C127—24no—
26#418×C127—24no—
27C2×#103×C127C2214yescomplemented
28C2×#102×C127C2214yes—
29#390×C127—22no—
30#390×C127C2214yes—
31#379×C127—22no—
32#340×C127C2214yescomplemented
33#336×C127C2214yescomplemented
34C25×C127—21no—
35C22×Q8×C127—21no—
36C22×Q8×C127—22no—
37C22×Q8×C127—22no—
38C22×Q8×C127—22no—
39C22×Q8×C127C2×C414yes—
40C22×Q8×C127D414yes—
41C22×Q8×C127D414yes—
42C22×Q8×C127C2312yes—
43C22×D4×C127—22no—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127—21no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127C2×C414yes—
50C22×D4×C127C2312yes—
51C23×C4×C127—21no—
52C23×C4×C127C2311yescharacteristic
53C2×SD16×C127—232no—
54C2×SD16×C127—28no—
55C2×SD16×C127—28no—
56C2×SD16×C127C2×C4116yes—
57C2×M16×C127—22no—
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C22×C8×C127—22no—
61C22×C8×C127—22no—
62C22×C8×C127C2×C414yes—
63C22×C8×C127C2312yes—
64C22×C8×C127C2312yes—
65C4×Q8×C127—216no—
66C4×Q8×C127—28no—
67C4×Q8×C127—28no—
68#117×C127—216no—
69#117×C127—22no—
70#117×C127—22no—
71#117×C127—22no—
72#117×C127—22no—
73#117×C127—22no—
74#117×C127D414yes—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127D412yes—
77C2×C4⋊C4×C127C2312yes—
78C2×C4⋊C4×C127C2312yes—
79C2×C22⋊C4×C127—21no—
80C2×C22⋊C4×C127—21no—
81C2×C22⋊C4×C127—28no—
82C2×C22⋊C4×C127D412yes—
83C2×C42×C127—24no—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2312yes—
87#103×C127—28no—
88#102×C127—28no—
89C24×C127—22no—
90C24×C127—24no—
91C24×C127—42no—
92C24×C127—42no—
93C24×C127—84no—
94C24×C127C2×D411yescharacteristic
95C2×Q8×C127—24no—
96C2×Q8×C127—28no—
97C2×Q8×C127—24no—
98C2×Q8×C127—24no—
99C2×Q8×C127—28no—
100C2×Q8×C127—28no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—22no—
104C2×Q8×C127C22⋊C4116yescomplemented
105C2×Q8×C127C22×C414yes—
106C2×Q8×C127C2×D414yes—
107C2×Q8×C127C2×D414yes—
108C2×D4×C127—28no—
109C2×D4×C127—28no—
110C2×D4×C127—24no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—42no—
117C2×D4×C127—44no—
118C2×D4×C127—42no—
119C2×D4×C127—44no—
120C2×D4×C127C22×C414yes—
121C22×C4×C127—24no—
122C22×C4×C127—24no—
123C22×C4×C127—24no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127C22×C412yes—
128C22×C4×C127C2×D414yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D412yes—
133C22×C4×C127#4112yes—
134C22×C4×C127#4112yes—
135C22×C4×C127C2411yescharacteristic
136SD16×C127—232no—
137M16×C127—44no—
138C2×C8×C127—28no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
144C2×C8×C127C22×C414yes—
145C4⋊C4×C127—216no—
146C4⋊C4×C127—24no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127C2×D414yes—
151C22⋊C4×C127—24no—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—42no—
154C22⋊C4×C127—88no—
155C42×C127—216no—
156C42×C127—24no—
157C42×C127—22no—
158C42×C127—22no—
159C42×C127—42no—
160C23×C127—24no—
161C23×C127—24no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—48no—
165C23×C127—48no—
166C23×C127—88no—
167C23×C127—88no—
168C23×C127—88no—
169C23×C127C4×D412yes—
170C23×C127#12012yes—
171C23×C127#12112yes—
172C23×C127C22×D411yescharacteristic
173Q8×C127—24no—
174Q8×C127—24no—
175Q8×C127—24no—
176Q8×C127—216no—
177Q8×C127C2×C22⋊C418yes—
178D4×C127—24no—
179D4×C127—24no—
180D4×C127—42no—
181D4×C127—42no—
182D4×C127—48no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—216no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—28no—
190C2×C4×C127—44no—
191C2×C4×C127—42no—
192C2×C4×C127—44no—
193C2×C4×C127C2×C22⋊C414yes—
194C2×C4×C127C4×D414yes—
195C2×C4×C127C4×D412yes—
196C2×C4×C127#12012yes—
197C2×C4×C127#12114yes—
198C2×C4×C127#12112yes—
199C2×C4×C127#12314yes—
200C2×C4×C127C23×C411yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C2×C4×C127C22×D411yescharacteristic
203C2×C4×C127C22×D411yescharacteristic
204C2×C4×C127C2×#4111yescharacteristic
205C2×C4×C127C2×#4111yescharacteristic
206C8×C127—24no—
207C8×C127—42no—
208C22×C127—24no—
209C22×C127—24no—
210C22×C127—24no—
211C22×C127—48no—
212C22×C127—44no—
213C22×C127—816no—
214C22×C127—84no—
215C22×C127—84no—
216C22×C127#38614yes—
217C22×C127C2×C4×D411yescharacteristic
218C22×C127C2×#12011yescharacteristic
219C22×C127C2×#12111yescharacteristic
220C22×C127#57714yes—
221C4×C127—28no—
222C4×C127—44no—
223C4×C127—44no—
224C4×C127—82no—
225C4×C127#38614yes—
226C4×C127C22×C22⋊C411yescharacteristic
227C4×C127C2×C4×D411yescharacteristic
228C4×C127C2×#12111yescharacteristic
229C4×C127C2×#12311yescharacteristic
230#20936C12711yesmaximal, characteristic, direct product factor, Sylow
231C2×C127—24no—
232C2×C127—84no—
233C2×C127C2×#38611yescharacteristic
234C2×C127#294912yes—
235C2×C127#301012yes—
236C2×C127#304312yes—
237C23×SD16C2×C12711yescharacteristic
238C2×#519C2×C12711yescharacteristic, complemented
239C2×#419C2×C12711yescharacteristic, complemented
240C2×#418C2×C12711yescharacteristic
241#2309C2×C12711yescharacteristic
242#1880C2×C12718yescomplemented
243#1735C2×C12711yescharacteristic, complemented
244#1729C2×C12711yescharacteristic, complemented
245C127#2093611yescharacteristic, direct product factor, Sylow
246C23×Q8C22×C12711yescharacteristic
247C23×D4C22×C12711yescharacteristic
248C22×SD16—24no—
249C22×SD16—24no—
250C22×SD16C4×C12718yescomplemented
251C22×SD16C22×C12714yes—
252C22×M16C22×C12711yescharacteristic
253C23×C8C22×C12711yescharacteristic
254#519—24no—
255#519—24no—
256C2×C4×Q8—22no—
257C2×C4×Q8C22×C12714yescomplemented
258C2×#117—22no—
259C2×#117C22×C12711yescharacteristic
260C2×#117C22×C12711yescharacteristic
261C2×#117C22×C12711yescharacteristic
262#419—24no—
263#418—24no—
264C2×#103C22×C12714yescomplemented
265C2×#102C22×C12714yes—
266#390—22no—
267#390C22×C12714yes—
268#379—22no—
269#340C22×C12714yescomplemented
270#336C22×C12714yescomplemented
271C25—21no—
272C22×Q8—21no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8C2×C4×C12714yes—
277C22×Q8D4×C12714yes—
278C22×Q8D4×C12714yes—
279C22×Q8C23×C12712yes—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4C2×C4×C12714yes—
287C22×D4C23×C12712yes—
288C23×C4—21no—
289C23×C4C23×C12711yescharacteristic
290C2×SD16—232no—
291C2×SD16—28no—
292C2×SD16—28no—
293C2×SD16C2×C4×C127116yes—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8C2×C4×C12714yes—
300C22×C8C23×C12712yes—
301C22×C8C23×C12712yes—
302C4×Q8—216no—
303C4×Q8—28no—
304C4×Q8—28no—
305#117—216no—
306#117—22no—
307#117—22no—
308#117—22no—
309#117—22no—
310#117—22no—
311#117D4×C12714yes—
312C2×C4⋊C4—24no—
313C2×C4⋊C4D4×C12712yes—
314C2×C4⋊C4C23×C12712yes—
315C2×C4⋊C4C23×C12712yes—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4D4×C12712yes—
320C2×C42—24no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42C23×C12712yes—
324#103—28no—
325#102—28no—
326C24—22no—
327C24—24no—
328C24—42no—
329C24—42no—
330C24—84no—
331C24C2×D4×C12711yescharacteristic
332C2×Q8—24no—
333C2×Q8—28no—
334C2×Q8—24no—
335C2×Q8—24no—
336C2×Q8—28no—
337C2×Q8—28no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8C22⋊C4×C127116yescomplemented
342C2×Q8C22×C4×C12714yes—
343C2×Q8C2×D4×C12714yes—
344C2×Q8C2×D4×C12714yes—
345C2×D4—28no—
346C2×D4—28no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—42no—
354C2×D4—44no—
355C2×D4—42no—
356C2×D4—44no—
357C2×D4C22×C4×C12714yes—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4C22×C4×C12712yes—
365C22×C4C2×D4×C12714yes—
366C22×C4C2×D4×C12712yes—
367C22×C4C2×D4×C12712yes—
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12712yes—
370C22×C4#41×C12712yes—
371C22×C4#41×C12712yes—
372C22×C4C24×C12711yescharacteristic
373SD16—232no—
374M16—44no—
375C2×C8—28no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8C22×C4×C12714yes—
382C4⋊C4—216no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4C2×D4×C12714yes—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—42no—
391C22⋊C4—88no—
392C42—216no—
393C42—24no—
394C42—22no—
395C42—22no—
396C42—42no—
397C23—24no—
398C23—24no—
399C23—42no—
400C23—42no—
401C23—48no—
402C23—48no—
403C23—88no—
404C23—88no—
405C23—88no—
406C23C4×D4×C12712yes—
407C23#120×C12712yes—
408C23#121×C12712yes—
409C23C22×D4×C12711yescharacteristic
410Q8—24no—
411Q8—24no—
412Q8—24no—
413Q8—216no—
414Q8C2×C22⋊C4×C12718yes—
415D4—24no—
416D4—24no—
417D4—42no—
418D4—42no—
419D4—48no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—216no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—28no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4C2×C22⋊C4×C12714yes—
431C2×C4C4×D4×C12714yes—
432C2×C4C4×D4×C12712yes—
433C2×C4#120×C12712yes—
434C2×C4#121×C12714yes—
435C2×C4#121×C12712yes—
436C2×C4#123×C12714yes—
437C2×C4C23×C4×C12711yescharacteristic
438C2×C4C22×D4×C12711yescharacteristic
439C2×C4C22×D4×C12711yescharacteristic
440C2×C4C22×D4×C12711yescharacteristic
441C2×C4C2×#41×C12711yescharacteristic
442C2×C4C2×#41×C12711yescharacteristic
443C8—24no—
444C8—42no—
445C22—24no—
446C22—24no—
447C22—24no—
448C22—48no—
449C22—44no—
450C22—816no—
451C22—84no—
452C22—84no—
453C22#386×C12714yes—
454C22C2×C4×D4×C12711yescharacteristic
455C22C2×#120×C12711yescharacteristic
456C22C2×#121×C12711yescharacteristic
457C22#577×C12714yes—
458C4—28no—
459C4—44no—
460C4—44no—
461C4—82no—
462C4#386×C12714yes—
463C4C22×C22⋊C4×C12711yescharacteristic
464C4C2×C4×D4×C12711yescharacteristic
465C4C2×#121×C12711yescharacteristic
466C4C2×#123×C12711yescharacteristic
467C2—24no—
468C2—84no—
469C2C2×#386×C12711yescharacteristic
470C2C127×#294912yes—
471C2C127×#301012yes—
472C2C127×#304312yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#519×C127C2semidirect
3. C2×#419×C127C2semidirect
6. C127×#1880C2semidirect
7. C127×#1735C2semidirect
8. C127×#1729C2semidirect
13. C22×SD16×C127C4semidirect
20. C2×C4×Q8×C127C22semidirect
27. C2×#103×C127C22semidirect
32. #340×C127C22semidirect
33. #336×C127C22semidirect
104. C2×Q8×C127C22⋊C4semidirect
230. #20936C127direct (N × H)
238. C2×#519C2×C127semidirect
239. C2×#419C2×C127semidirect
242. #1880C2×C127semidirect
243. #1735C2×C127semidirect
244. #1729C2×C127semidirect
245. C127#20936direct (N × H)
250. C22×SD16C4×C127semidirect
257. C2×C4×Q8C22×C127semidirect
264. C2×#103C22×C127semidirect
269. #340C22×C127semidirect
270. #336C22×C127semidirect
341. C2×Q8C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×SD16×C1272
C2×#519×C1272
C2×#419×C1272
C2×#418×C1272
C127×#23092
C127×#18802
C127×#17352
C127×#17292
#20936127