Finite Group Databasebeta

← C127×#20600 #44584273

Subgroups — C127×#20600 #44584273

Order 32512.

3966 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#41×C127C211yesmaximal, characteristic
2C2×#419×C127C212yesmaximal, complemented
3C2×#418×C127C212yesmaximal, complemented
4C2×#407×C127C211yesmaximal, characteristic, complemented
5C127×#2280C211yesmaximal, characteristic, complemented
6C127×#1788C218yesmaximal, complemented
7C22×#41×C127—28no—
8C22×#41×C127—28no—
9C22×#41×C127—24no—
10C22×#41×C127—22no—
11C22×#41×C127C418yescomplemented
12C22×#41×C127C2214yes—
13C23×Q8×C127C2211yescharacteristic
14C23×D4×C127—21no—
15C23×D4×C127C2211yescharacteristic
16C24×C4×C127—21no—
17C24×C4×C127C2211yescharacteristic
18C22×M16×C127C2212yes—
19C2×#117×C127C2212yes—
20#419×C127—28no—
21#418×C127—28no—
22C2×#103×C127C2218yescomplemented
23C2×#102×C127C2218yescomplemented
24#407×C127—24no—
25C2×C22⋊C8×C127C2214yescomplemented
26#381×C127—21no—
27#380×C127C2214yescomplemented
28#379×C127—21no—
29C4×C22⋊C4×C127—22no—
30C25×C127—21no—
31C25×C127D411yescharacteristic
32C2×#41×C127—232no—
33C2×#41×C127—264no—
34C2×#41×C127—232no—
35C2×#41×C127—216no—
36C2×#41×C127—232no—
37C2×#41×C127—216no—
38C2×#41×C127—216no—
39C2×#41×C127—28no—
40C2×#41×C127C2×C4116yes—
41C22×Q8×C127—22no—
42C22×Q8×C127—24no—
43C22×Q8×C127—21no—
44C22×Q8×C127C2×C414yes—
45C22×Q8×C127D418yes—
46C22×Q8×C127C2312yes—
47C22×D4×C127—216no—
48C22×D4×C127—28no—
49C22×D4×C127—24no—
50C22×D4×C127—21no—
51C22×D4×C127—24no—
52C22×D4×C127—22no—
53C22×D4×C127C2×C414yes—
54C22×D4×C127D418yes—
55C22×D4×C127C2312yes—
56C23×C4×C127—216no—
57C23×C4×C127—21no—
58C23×C4×C127—28no—
59C23×C4×C127—24no—
60C23×C4×C127—24no—
61C23×C4×C127—24no—
62C23×C4×C127C2×C414yes—
63C23×C4×C127D411yescharacteristic
64C23×C4×C127D412yes—
65C23×C4×C127D414yes—
66C23×C4×C127C2312yes—
67C23×C4×C127C2311yescharacteristic
68C2×M16×C127—24no—
69C2×M16×C127—24no—
70C2×M16×C127—24no—
71C22×C8×C127C2314yes—
72#117×C127—24no—
73#117×C127—24no—
74C2×C4⋊C4×C127C2314yes—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—24no—
77C2×C42×C127—22no—
78#103×C127—216no—
79#102×C127—216no—
80C22⋊C8×C127—28no—
81#95×C127—24no—
82C24×C127—24no—
83C24×C127—24no—
84C24×C127—28no—
85C24×C127—22no—
86C24×C127—44no—
87C24×C127—48no—
88C24×C127C22⋊C414yes—
89C24×C127C2×D412yes—
90C24×C127C2×D411yescharacteristic
91#41×C127—264no—
92#41×C127—2128no—
93#41×C127—232no—
94#41×C127—232no—
95C2×Q8×C127—24no—
96C2×Q8×C127—28no—
97C2×Q8×C127—28no—
98C2×Q8×C127—216no—
99C2×Q8×C127—22no—
100C2×Q8×C127—24no—
101C2×Q8×C127C22⋊C4116yescomplemented
102C2×Q8×C127C22×C414yes—
103C2×Q8×C127C2×D418yes—
104C2×D4×C127—232no—
105C2×D4×C127—264no—
106C2×D4×C127—216no—
107C2×D4×C127—28no—
108C2×D4×C127—24no—
109C2×D4×C127—216no—
110C2×D4×C127—28no—
111C2×D4×C127—24no—
112C2×D4×C127—22no—
113C2×D4×C127C22⋊C4116yescomplemented
114C2×D4×C127C22×C414yes—
115C2×D4×C127C2×D418yes—
116C22×C4×C127—232no—
117C22×C4×C127—264no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
120C22×C4×C127—28no—
121C22×C4×C127—22no—
122C22×C4×C127—216no—
123C22×C4×C127—28no—
124C22×C4×C127—28no—
125C22×C4×C127—28no—
126C22×C4×C127—216no—
127C22×C4×C127—24no—
128C22×C4×C127—24no—
129C22×C4×C127—24no—
130C22×C4×C127C22⋊C414yes—
131C22×C4×C127C22⋊C418yes—
132C22×C4×C127C22×C414yes—
133C22×C4×C127C22×C412yes—
134C22×C4×C127C2×D412yes—
135C22×C4×C127C2×D414yes—
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D414yes—
138C22×C4×C127C2×D414yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2411yescharacteristic
141M16×C127—48no—
142C2×C8×C127—24no—
143C2×C8×C127—24no—
144C2×C8×C127—24no—
145C4⋊C4×C127—24no—
146C4⋊C4×C127—24no—
147C22⋊C4×C127—48no—
148C22⋊C4×C127—44no—
149C42×C127—44no—
150C23×C127—24no—
151C23×C127—24no—
152C23×C127—24no—
153C23×C127—28no—
154C23×C127—24no—
155C23×C127—24no—
156C23×C127—28no—
157C23×C127—216no—
158C23×C127—48no—
159C23×C127—416no—
160C23×C127—416no—
161C23×C127—432no—
162C23×C127—48no—
163C23×C127C2×C22⋊C414yes—
164C23×C127C2×C22⋊C412yes—
165C23×C127#12014yes—
166C23×C127C22×D411yescharacteristic
167Q8×C127—24no—
168Q8×C127—28no—
169Q8×C127—216no—
170Q8×C127C2×C22⋊C418yes—
171D4×C127—264no—
172D4×C127—24no—
173D4×C127—28no—
174D4×C127—216no—
175D4×C127C2×C22⋊C418yes—
176C2×C4×C127—264no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—28no—
180C2×C4×C127—28no—
181C2×C4×C127—216no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—28no—
185C2×C4×C127—216no—
186C2×C4×C127—44no—
187C2×C4×C127—48no—
188C2×C4×C127C2×C22⋊C414yes—
189C2×C4×C127C2×C22⋊C414yes—
190C2×C4×C127C2×C22⋊C414yes—
191C2×C4×C127C2×C22⋊C412yes—
192C2×C4×C127#12018yes—
193C2×C4×C127#12014yes—
194C2×C4×C127C23×C411yescharacteristic
195C2×C4×C127C22×D412yes—
196C2×C4×C127C22×D412yes—
197C2×C4×C127C22×D411yescharacteristic
198C8×C127—44no—
199C22×C127—24no—
200C22×C127—28no—
201C22×C127—24no—
202C22×C127—24no—
203C22×C127—24no—
204C22×C127—28no—
205C22×C127—416no—
206C22×C127—432no—
207C22×C127—48no—
208C22×C127—48no—
209C22×C127—416no—
210C22×C127#37914yes—
211C22×C127C22×C22⋊C411yescharacteristic
212C22×C127C2×#12012yes—
213C22×C127#57514yes—
214C4×C127—24no—
215C4×C127—28no—
216C4×C127—84no—
217C4×C127#37914yes—
218C4×C127C22×C22⋊C411yescharacteristic
219C4×C127C22×C22⋊C411yescharacteristic
220C4×C127C2×#12012yes—
221#20600C12711yesmaximal, characteristic, direct product factor, Sylow
222C2×C127—24no—
223C2×C127—44no—
224C2×C127—48no—
225C2×C127C2×#37911yescharacteristic
226C2×C127#289612yes—
227C2×C127#300514yes—
228C23×#41C2×C12711yescharacteristic
229C2×#419C2×C12712yescomplemented
230C2×#418C2×C12712yescomplemented
231C2×#407C2×C12711yescharacteristic, complemented
232#2280C2×C12711yescharacteristic, complemented
233#1788C2×C12718yescomplemented
234C127#2060011yescharacteristic, direct product factor, Sylow
235C22×#41—28no—
236C22×#41—28no—
237C22×#41—24no—
238C22×#41—22no—
239C22×#41C4×C12718yescomplemented
240C22×#41C22×C12714yes—
241C23×Q8C22×C12711yescharacteristic
242C23×D4—21no—
243C23×D4C22×C12711yescharacteristic
244C24×C4—21no—
245C24×C4C22×C12711yescharacteristic
246C22×M16C22×C12712yes—
247C2×#117C22×C12712yes—
248#419—28no—
249#418—28no—
250C2×#103C22×C12718yescomplemented
251C2×#102C22×C12718yescomplemented
252#407—24no—
253C2×C22⋊C8C22×C12714yescomplemented
254#381—21no—
255#380C22×C12714yescomplemented
256#379—21no—
257C4×C22⋊C4—22no—
258C25—21no—
259C25D4×C12711yescharacteristic
260C2×#41—232no—
261C2×#41—264no—
262C2×#41—232no—
263C2×#41—216no—
264C2×#41—232no—
265C2×#41—216no—
266C2×#41—216no—
267C2×#41—28no—
268C2×#41C2×C4×C127116yes—
269C22×Q8—22no—
270C22×Q8—24no—
271C22×Q8—21no—
272C22×Q8C2×C4×C12714yes—
273C22×Q8D4×C12718yes—
274C22×Q8C23×C12712yes—
275C22×D4—216no—
276C22×D4—28no—
277C22×D4—24no—
278C22×D4—21no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4C2×C4×C12714yes—
282C22×D4D4×C12718yes—
283C22×D4C23×C12712yes—
284C23×C4—216no—
285C23×C4—21no—
286C23×C4—28no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4C2×C4×C12714yes—
291C23×C4D4×C12711yescharacteristic
292C23×C4D4×C12712yes—
293C23×C4D4×C12714yes—
294C23×C4C23×C12712yes—
295C23×C4C23×C12711yescharacteristic
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C22×C8C23×C12714yes—
300#117—24no—
301#117—24no—
302C2×C4⋊C4C23×C12714yes—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—24no—
305C2×C42—22no—
306#103—216no—
307#102—216no—
308C22⋊C8—28no—
309#95—24no—
310C24—24no—
311C24—24no—
312C24—28no—
313C24—22no—
314C24—44no—
315C24—48no—
316C24C22⋊C4×C12714yes—
317C24C2×D4×C12712yes—
318C24C2×D4×C12711yescharacteristic
319#41—264no—
320#41—2128no—
321#41—232no—
322#41—232no—
323C2×Q8—24no—
324C2×Q8—28no—
325C2×Q8—28no—
326C2×Q8—216no—
327C2×Q8—22no—
328C2×Q8—24no—
329C2×Q8C22⋊C4×C127116yescomplemented
330C2×Q8C22×C4×C12714yes—
331C2×Q8C2×D4×C12718yes—
332C2×D4—232no—
333C2×D4—264no—
334C2×D4—216no—
335C2×D4—28no—
336C2×D4—24no—
337C2×D4—216no—
338C2×D4—28no—
339C2×D4—24no—
340C2×D4—22no—
341C2×D4C22⋊C4×C127116yescomplemented
342C2×D4C22×C4×C12714yes—
343C2×D4C2×D4×C12718yes—
344C22×C4—232no—
345C22×C4—264no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—28no—
349C22×C4—22no—
350C22×C4—216no—
351C22×C4—28no—
352C22×C4—28no—
353C22×C4—28no—
354C22×C4—216no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4C22⋊C4×C12714yes—
359C22×C4C22⋊C4×C12718yes—
360C22×C4C22×C4×C12714yes—
361C22×C4C22×C4×C12712yes—
362C22×C4C2×D4×C12712yes—
363C22×C4C2×D4×C12714yes—
364C22×C4C2×D4×C12711yescharacteristic
365C22×C4C2×D4×C12714yes—
366C22×C4C2×D4×C12714yes—
367C22×C4C2×D4×C12712yes—
368C22×C4C24×C12711yescharacteristic
369M16—48no—
370C2×C8—24no—
371C2×C8—24no—
372C2×C8—24no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C22⋊C4—48no—
376C22⋊C4—44no—
377C42—44no—
378C23—24no—
379C23—24no—
380C23—24no—
381C23—28no—
382C23—24no—
383C23—24no—
384C23—28no—
385C23—216no—
386C23—48no—
387C23—416no—
388C23—416no—
389C23—432no—
390C23—48no—
391C23C2×C22⋊C4×C12714yes—
392C23C2×C22⋊C4×C12712yes—
393C23#120×C12714yes—
394C23C22×D4×C12711yescharacteristic
395Q8—24no—
396Q8—28no—
397Q8—216no—
398Q8C2×C22⋊C4×C12718yes—
399D4—264no—
400D4—24no—
401D4—28no—
402D4—216no—
403D4C2×C22⋊C4×C12718yes—
404C2×C4—264no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—28no—
408C2×C4—28no—
409C2×C4—216no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—28no—
413C2×C4—216no—
414C2×C4—44no—
415C2×C4—48no—
416C2×C4C2×C22⋊C4×C12714yes—
417C2×C4C2×C22⋊C4×C12714yes—
418C2×C4C2×C22⋊C4×C12714yes—
419C2×C4C2×C22⋊C4×C12712yes—
420C2×C4#120×C12718yes—
421C2×C4#120×C12714yes—
422C2×C4C23×C4×C12711yescharacteristic
423C2×C4C22×D4×C12712yes—
424C2×C4C22×D4×C12712yes—
425C2×C4C22×D4×C12711yescharacteristic
426C8—44no—
427C22—24no—
428C22—28no—
429C22—24no—
430C22—24no—
431C22—24no—
432C22—28no—
433C22—416no—
434C22—432no—
435C22—48no—
436C22—48no—
437C22—416no—
438C22#379×C12714yes—
439C22C22×C22⋊C4×C12711yescharacteristic
440C22C2×#120×C12712yes—
441C22#575×C12714yes—
442C4—24no—
443C4—28no—
444C4—84no—
445C4#379×C12714yes—
446C4C22×C22⋊C4×C12711yescharacteristic
447C4C22×C22⋊C4×C12711yescharacteristic
448C4C2×#120×C12712yes—
449C2—24no—
450C2—44no—
451C2—48no—
452C2C2×#379×C12711yescharacteristic
453C2C127×#289612yes—
454C2C127×#300514yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×#41×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#419×C127C2semidirect
3. C2×#418×C127C2semidirect
4. C2×#407×C127C2semidirect
5. C127×#2280C2semidirect
6. C127×#1788C2semidirect
11. C22×#41×C127C4semidirect
22. C2×#103×C127C22semidirect
23. C2×#102×C127C22semidirect
25. C2×C22⋊C8×C127C22semidirect
27. #380×C127C22semidirect
101. C2×Q8×C127C22⋊C4semidirect
113. C2×D4×C127C22⋊C4semidirect
221. #20600C127direct (N × H)
229. C2×#419C2×C127semidirect
230. C2×#418C2×C127semidirect
231. C2×#407C2×C127semidirect
232. #2280C2×C127semidirect
233. #1788C2×C127semidirect
234. C127#20600direct (N × H)
239. C22×#41C4×C127semidirect
250. C2×#103C22×C127semidirect
251. C2×#102C22×C127semidirect
253. C2×C22⋊C8C22×C127semidirect
255. #380C22×C127semidirect
329. C2×Q8C22⋊C4×C127semidirect
341. C2×D4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×#41×C1272
C2×#419×C1272
C2×#418×C1272
C2×#407×C1272
C127×#22802
C127×#17882
#20600127