Finite Group Databasebeta

← C2×C127×#1652 #44582174

Subgroups — C2×C127×#1652 #44582174

Order 32512.

978 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C127C211yesmaximal, characteristic
2C2×#498×C127C211yesmaximal, characteristic, complemented
3C2×#474×C127C211yesmaximal, characteristic
4C2×#462×C127C211yesmaximal, characteristic, complemented
5C127×#1652C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic
9C22×Q16×C127—21no—
10#556×C127—22no—
11#556×C127—22no—
12#556×C127—22no—
13#556×C127C2214yes—
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#126×C127—22no—
17C2×#124×C127—21no—
18C2×C22⋊Q8×C127—21no—
19C2×C4×Q8×C127—21no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×#117×C127—21no—
23#498×C127—22no—
24#498×C127C2214yescomplemented
25#474×C127—22no—
26#474×C127C2214yes—
27#462×C127—22no—
28#462×C127C2214yescomplemented
29C2×#107×C127—21no—
30C2×#106×C127—22no—
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×C4⋊C8×C127C2211yescharacteristic
33C2×#103×C127—21no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#332×C127C2214yescomplemented
37Q8⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yes—
39C22×Q8×C127—21no—
40C22×Q8×C127—21no—
41C22×Q8×C127D411yescharacteristic
42C22×D4×C127D411yescharacteristic
43C23×C4×C127—21no—
44C2×Q16×C127—24no—
45C2×Q16×C127—44no—
46C22×C8×C127—21no—
47C22×C8×C127—21no—
48C22×C8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127D412yes—
55C4⋊Q8×C127C2312yes—
56C4⋊Q8×C127C2312yes—
57#126×C127—28no—
58#126×C127—28no—
59#124×C127—24no—
60#124×C127—24no—
61C22⋊Q8×C127—24no—
62C22⋊Q8×C127—24no—
63C4×Q8×C127—24no—
64C4×Q8×C127—24no—
65C4×Q8×C127—21no—
66C4×Q8×C127—21no—
67C4×Q8×C127D412yes—
68C4×Q8×C127C2312yes—
69C4×D4×C127—21no—
70C4×D4×C127—21no—
71C4×D4×C127D412yes—
72C4×D4×C127C2312yes—
73#117×C127—24no—
74#117×C127—24no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127D411yescharacteristic
81C2×C4⋊C4×C127D411yescharacteristic
82C2×C4⋊C4×C127D412yes—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—21no—
86C2×C42×C127—22no—
87C2×C42×C127—21no—
88C2×C42×C127C2311yescharacteristic
89#107×C127—24no—
90#106×C127—28no—
91C4⋊C8×C127—21no—
92C4⋊C8×C127—21no—
93C4⋊C8×C127C2312yes—
94C4⋊C8×C127C2312yes—
95#103×C127—24no—
96#102×C127—24no—
97C4×C8×C127—21no—
98C4×C8×C127C2312yes—
99C24×C127—21no—
100C2×Q8×C127—21no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—41no—
107C2×Q8×C127—42no—
108C2×Q8×C127—42no—
109C2×Q8×C127—42no—
110C2×Q8×C127—42no—
111C2×Q8×C127C2×D412yes—
112C2×D4×C127—21no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127C2×D412yes—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—42no—
123C22×C4×C127—42no—
124C22×C4×C127—41no—
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D411yescharacteristic
128Q16×C127—48no—
129C2×C8×C127—24no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127—42no—
134C2×C8×C127—42no—
135C4⋊C4×C127—28no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—41no—
146C4⋊C4×C127—41no—
147C4⋊C4×C127C2×D412yes—
148C4⋊C4×C127C2×D414yes—
149C4⋊C4×C127C2×D412yes—
150C22⋊C4×C127—28no—
151C22⋊C4×C127—28no—
152C22⋊C4×C127—22no—
153C22⋊C4×C127—22no—
154C42×C127—28no—
155C42×C127—22no—
156C42×C127—22no—
157C42×C127C2×D411yescharacteristic
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C42×C127C2411yescharacteristic
161C23×C127—22no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127#12011yescharacteristic
166Q8×C127—22no—
167Q8×C127—22no—
168Q8×C127—42no—
169Q8×C127—42no—
170Q8×C127—42no—
171Q8×C127—44no—
172Q8×C127—42no—
173Q8×C127—42no—
174Q8×C127—82no—
175D4×C127—22no—
176D4×C127—22no—
177D4×C127—42no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—24no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—44no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—44no—
190C2×C4×C127—42no—
191C2×C4×C127—82no—
192C2×C4×C127#12011yescharacteristic
193C2×C4×C127#12011yescharacteristic
194C2×C4×C127#12011yescharacteristic
195C2×C4×C127#13512yes—
196C2×C4×C127#13512yes—
197C2×C4×C127AGL(1,ℤ/8)12yes—
198C2×C4×C127#13712yes—
199C2×C4×C127C22×D411yescharacteristic
200C2×C4×C127C22×D411yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C8×C127—24no—
203C8×C127—42no—
204C8×C127—42no—
205C22×C127—42no—
206C22×C127—42no—
207C22×C127—42no—
208C22×C127—84no—
209C22×C127#44912yes—
210C22×C127#45212yes—
211C22×C127#45612yes—
212C22×C127C2×#12011yescharacteristic
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—42no—
216C4×C127—42no—
217C4×C127—44no—
218C4×C127—42no—
219C4×C127—82no—
220C4×C127#44912yes—
221C4×C127#45212yes—
222C4×C127C2×#13511yescharacteristic
223C4×C127C2×#13511yescharacteristic
224C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
225C4×C127C2×#13711yescharacteristic
226C2×#1652C12711yesmaximal, characteristic, direct product factor, Sylow
227C2×C127—82no—
228C2×C127#165214yesdirect product factor
229C2×C127C2×#44911yescharacteristic
230C2×C127C2×#45211yescharacteristic
231C2×C127C2×#45611yescharacteristic
232C2×#556C2×C12711yescharacteristic
233C2×#498C2×C12711yescharacteristic, complemented
234C2×#474C2×C12711yescharacteristic
235C2×#462C2×C12711yescharacteristic, complemented
236#1652C2×C12718yesdirect product factor
237C2×#332C2×C12711yescharacteristic, complemented
238C2×Q8⋊C8C2×C12711yescharacteristic, complemented
239C2×D4⋊C8C2×C12711yescharacteristic
240C127C2×#165211yescharacteristic, direct product factor, Sylow
241C22×Q16—21no—
242#556—22no—
243#556—22no—
244#556—22no—
245#556C22×C12714yes—
246C2×C4⋊Q8C22×C12711yescharacteristic
247C2×C4⋊Q8C22×C12711yescharacteristic
248C2×#126—22no—
249C2×#124—21no—
250C2×C22⋊Q8—21no—
251C2×C4×Q8—21no—
252C2×C4×Q8C22×C12711yescharacteristic
253C2×C4×D4C22×C12711yescharacteristic
254C2×#117—21no—
255#498—22no—
256#498C22×C12714yescomplemented
257#474—22no—
258#474C22×C12714yes—
259#462—22no—
260#462C22×C12714yescomplemented
261C2×#107—21no—
262C2×#106—22no—
263C2×C4⋊C8C22×C12711yescharacteristic
264C2×C4⋊C8C22×C12711yescharacteristic
265C2×#103—21no—
266C2×#102—21no—
267C2×C4×C8C22×C12711yescharacteristic
268#332C22×C12714yescomplemented
269Q8⋊C8C22×C12714yescomplemented
270D4⋊C8C22×C12714yes—
271C22×Q8—21no—
272C22×Q8—21no—
273C22×Q8D4×C12711yescharacteristic
274C22×D4D4×C12711yescharacteristic
275C23×C4—21no—
276C2×Q16—24no—
277C2×Q16—44no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8D4×C12712yes—
287C4⋊Q8C23×C12712yes—
288C4⋊Q8C23×C12712yes—
289#126—28no—
290#126—28no—
291#124—24no—
292#124—24no—
293C22⋊Q8—24no—
294C22⋊Q8—24no—
295C4×Q8—24no—
296C4×Q8—24no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8D4×C12712yes—
300C4×Q8C23×C12712yes—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4D4×C12712yes—
304C4×D4C23×C12712yes—
305#117—24no—
306#117—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4D4×C12711yescharacteristic
313C2×C4⋊C4D4×C12711yescharacteristic
314C2×C4⋊C4D4×C12712yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C42—22no—
319C2×C42—21no—
320C2×C42C23×C12711yescharacteristic
321#107—24no—
322#106—28no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8C23×C12712yes—
326C4⋊C8C23×C12712yes—
327#103—24no—
328#102—24no—
329C4×C8—21no—
330C4×C8C23×C12712yes—
331C24—21no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—41no—
339C2×Q8—42no—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8C2×D4×C12712yes—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4C2×D4×C12712yes—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4C2×D4×C12711yescharacteristic
358C22×C4C2×D4×C12711yescharacteristic
359C22×C4C2×D4×C12711yescharacteristic
360Q16—48no—
361C2×C8—24no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—42no—
366C2×C8—42no—
367C4⋊C4—28no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C12712yes—
380C4⋊C4C2×D4×C12714yes—
381C4⋊C4C2×D4×C12712yes—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C42—28no—
387C42—22no—
388C42—22no—
389C42C2×D4×C12711yescharacteristic
390C42C2×D4×C12711yescharacteristic
391C42C2×D4×C12711yescharacteristic
392C42C24×C12711yescharacteristic
393C23—22no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23#120×C12711yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403Q8—44no—
404Q8—42no—
405Q8—42no—
406Q8—82no—
407D4—22no—
408D4—22no—
409D4—42no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4#120×C12711yescharacteristic
425C2×C4#120×C12711yescharacteristic
426C2×C4#120×C12711yescharacteristic
427C2×C4#135×C12712yes—
428C2×C4#135×C12712yes—
429C2×C4AGL(1,ℤ/8)×C12712yes—
430C2×C4#137×C12712yes—
431C2×C4C22×D4×C12711yescharacteristic
432C2×C4C22×D4×C12711yescharacteristic
433C2×C4C22×D4×C12711yescharacteristic
434C8—24no—
435C8—42no—
436C8—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—84no—
441C22#449×C12712yes—
442C22#452×C12712yes—
443C22#456×C12712yes—
444C22C2×#120×C12711yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—44no—
450C4—42no—
451C4—82no—
452C4#449×C12712yes—
453C4#452×C12712yes—
454C4C2×#135×C12711yescharacteristic
455C4C2×#135×C12711yescharacteristic
456C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
457C4C2×#137×C12711yescharacteristic
458C2—82no—
459C2C127×#165214yesdirect product factor
460C2C2×#449×C12711yescharacteristic
461C2C2×#452×C12711yescharacteristic
462C2C2×#456×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#498×C127C2semidirect
4. C2×#462×C127C2semidirect
5. C127×#1652C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
24. #498×C127C22semidirect
28. #462×C127C22semidirect
36. #332×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
226. C2×#1652C127direct (N × H)
228. C2×C127#1652direct (N × H)
233. C2×#498C2×C127semidirect
235. C2×#462C2×C127semidirect
236. #1652C2×C127direct (N × H)
237. C2×#332C2×C127semidirect
238. C2×Q8⋊C8C2×C127semidirect
240. C127C2×#1652direct (N × H)
256. #498C22×C127semidirect
260. #462C22×C127semidirect
268. #332C22×C127semidirect
269. Q8⋊C8C22×C127semidirect
459. C2C127×#1652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C1272
C2×#498×C1272
C2×#474×C1272
C2×#462×C1272
C127×#16522
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1652127