Finite Group Databasebeta

← C127×#17648 #44581321

Subgroups — C127×#17648 #44581321

Order 32512.

1036 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic
3C2×C4×M16×C127C211yesmaximal, characteristic
4C127×#1531C214yesmaximal, complemented
5C127×#1528C214yesmaximal, complemented
6C127×#1526C214yesmaximal, complemented
7C22×M16×C127—21no—
8#533×C127—21no—
9#533×C127—21no—
10#533×C127—21no—
11#533×C127—21no—
12#533×C127C412yes—
13#533×C127C412yes—
14#533×C127C2212yes—
15#533×C127C2212yes—
16C2×C4⋊Q8×C127C411yescharacteristic
17C2×C4⋊Q8×C127C411yescharacteristic
18C2×#125×C127C2212yes—
19C2×C22⋊Q8×C127—21no—
20C2×C22⋊Q8×C127—21no—
21C2×C4×Q8×C127—21no—
22C2×C4×Q8×C127—21no—
23C2×#117×C127C412yes—
24C22×C42×C127C2211yescharacteristic
25#432×C127C2212yes—
26#432×C127C2212yes—
27#431×C127—21no—
28#431×C127—21no—
29#423×C127—21no—
30#407×C127—21no—
31C4×M16×C127—21no—
32C4×M16×C127—21no—
33C4×M16×C127C2212yes—
34C4×M16×C127C2212yes—
35C4×M16×C127C2212yes—
36C2×#97×C127C2212yes—
37C2×C4×C8×C127—21no—
38#330×C127C22116yescomplemented
39C22×Q8×C127—21no—
40C22×Q8×C127—21no—
41C23×C4×C127C2×C411yescharacteristic
42C23×C4×C127D411yescharacteristic
43C23×C4×C127D411yescharacteristic
44C2×M16×C127—28no—
45C2×M16×C127—22no—
46C2×M16×C127—22no—
47C2×M16×C127—22no—
48C22×C8×C127—22no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127C2×C412yes—
54C4⋊Q8×C127C2×C412yes—
55C4⋊Q8×C127C2×C412yes—
56C4⋊Q8×C127C2×C412yes—
57#125×C127—22no—
58#125×C127—22no—
59#125×C127C2×C414yes—
60#125×C127C2314yes—
61C22⋊Q8×C127—22no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—22no—
66C22⋊Q8×C127—22no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127—22no—
69C4×Q8×C127—22no—
70C4×Q8×C127—22no—
71C4×Q8×C127—22no—
72C4×Q8×C127—22no—
73C4×Q8×C127—22no—
74C4×Q8×C127—22no—
75C4×Q8×C127—22no—
76C4×Q8×C127—22no—
77#117×C127—22no—
78#117×C127—22no—
79#117×C127C2×C414yes—
80#117×C127C2×C414yes—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127C2×C412yes—
86C2×C4⋊C4×C127C2×C412yes—
87C2×C22⋊C4×C127—22no—
88C2×C42×C127—22no—
89C2×C42×C127C2×C411yescharacteristic
90C2×C42×C127C2×C411yescharacteristic
91C2×C42×C127C2×C411yescharacteristic
92C2×C42×C127D411yescharacteristic
93C2×C42×C127D411yescharacteristic
94C2×C42×C127D411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127D411yescharacteristic
98C2×C42×C127C2311yescharacteristic
99C2×C42×C127C2311yescharacteristic
100C2×C42×C127C2311yescharacteristic
101C4⋊C8×C127—22no—
102C4⋊C8×C127—22no—
103C22⋊C8×C127—22no—
104C22⋊C8×C127—22no—
105#97×C127—22no—
106#97×C127C2314yes—
107#97×C127C2314yes—
108C4×C8×C127—22no—
109C4×C8×C127—22no—
110C4×C8×C127—22no—
111C24×C127C22⋊C411yescharacteristic
112C2×Q8×C127—22no—
113C2×Q8×C127—22no—
114C2×Q8×C127—22no—
115C2×Q8×C127—22no—
116C2×Q8×C127—44no—
117C2×Q8×C127—44no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—42no—
123C22×C4×C127C22⋊C411yescharacteristic
124C22×C4×C127C22⋊C411yescharacteristic
125C22×C4×C127C22⋊C411yescharacteristic
126C22×C4×C127C22⋊C411yescharacteristic
127C22×C4×C127C22⋊C411yescharacteristic
128C22×C4×C127C22⋊C411yescharacteristic
129C22×C4×C127C22⋊C411yescharacteristic
130C22×C4×C127C22⋊C411yescharacteristic
131C22×C4×C127C22⋊C411yescharacteristic
132C22×C4×C127C22×C411yescharacteristic
133C22×C4×C127C22×C411yescharacteristic
134C22×C4×C127C22×C411yescharacteristic
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138C22×C4×C127C2×D411yescharacteristic
139C22×C4×C127C2×D411yescharacteristic
140C22×C4×C127C2×D411yescharacteristic
141M16×C127—28no—
142M16×C127—28no—
143M16×C127—44no—
144C2×C8×C127—28no—
145C2×C8×C127—24no—
146C2×C8×C127—24no—
147C4⋊C4×C127—24no—
148C4⋊C4×C127—24no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—24no—
156C4⋊C4×C127—24no—
157C4⋊C4×C127C22×C414yes—
158C4⋊C4×C127C22×C414yes—
159C22⋊C4×C127—24no—
160C22⋊C4×C127—24no—
161C42×C127—24no—
162C42×C127—24no—
163C42×C127C22⋊C411yescharacteristic
164C42×C127C22⋊C411yescharacteristic
165C42×C127C22⋊C411yescharacteristic
166C42×C127C22⋊C411yescharacteristic
167C42×C127C22⋊C411yescharacteristic
168C42×C127C22⋊C411yescharacteristic
169C42×C127C22×C411yescharacteristic
170C42×C127C22×C411yescharacteristic
171C42×C127C22×C411yescharacteristic
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D411yescharacteristic
174C42×C127C2×D411yescharacteristic
175C42×C127C2×D411yescharacteristic
176C42×C127C2×D411yescharacteristic
177C42×C127C2×D411yescharacteristic
178C42×C127C2411yescharacteristic
179C23×C127—22no—
180C23×C127—22no—
181C23×C127—41no—
182C23×C127C2×C22⋊C411yescharacteristic
183C23×C127C2×C22⋊C411yescharacteristic
184C23×C127C2×C22⋊C411yescharacteristic
185Q8×C127—44no—
186Q8×C127—44no—
187Q8×C127—44no—
188Q8×C127—44no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—22no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—41no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—44no—
208C2×C4×C127—44no—
209C2×C4×C127#10114yes—
210C2×C4×C127#10414yes—
211C2×C4×C127C2×C22⋊C411yescharacteristic
212C2×C4×C127C2×C22⋊C411yescharacteristic
213C2×C4×C127C2×C22⋊C411yescharacteristic
214C2×C4×C127C2×C22⋊C411yescharacteristic
215C2×C4×C127C2×C22⋊C411yescharacteristic
216C2×C4×C127C2×C22⋊C411yescharacteristic
217C2×C4×C127C2×C22⋊C411yescharacteristic
218C2×C4×C127C2×C22⋊C411yescharacteristic
219C2×C4×C127C2×C22⋊C411yescharacteristic
220C2×C4×C127C23×C411yescharacteristic
221C2×C4×C127C22×D411yescharacteristic
222C2×C4×C127C22×D411yescharacteristic
223C8×C127—28no—
224C8×C127—44no—
225C22×C127—21no—
226C22×C127—21no—
227C22×C127—21no—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—21no—
232C22×C127—44no—
233C22×C127C2×#10112yes—
234C22×C127C2×#10412yes—
235C22×C127C22×C22⋊C411yescharacteristic
236C4×C127—21no—
237C4×C127—21no—
238C4×C127—21no—
239C4×C127—21no—
240C4×C127—21no—
241C4×C127—21no—
242C4×C127—21no—
243C4×C127—44no—
244C4×C127—44no—
245C4×C127C2×#10112yes—
246C4×C127C2×#10112yes—
247C4×C127C2×#10412yes—
248C4×C127C2×#10412yes—
249C4×C127#42112yes—
250#17648C12711yesmaximal, characteristic, direct product factor, Sylow
251C2×C127—22no—
252C2×C127—22no—
253C2×C127—41no—
254C2×C127C22×#10111yescharacteristic
255C2×C127C22×#10411yescharacteristic
256C2×C127C2×#42111yescharacteristic
257C2×#533C2×C12711yescharacteristic
258#2920C2×C12711yescharacteristic
259C2×C4×M16C2×C12711yescharacteristic
260#1531C2×C12714yescomplemented
261#1528C2×C12714yescomplemented
262#1526C2×C12714yescomplemented
263C127#1764811yescharacteristic, direct product factor, Sylow
264C22×M16—21no—
265#533—21no—
266#533—21no—
267#533—21no—
268#533—21no—
269#533C4×C12712yes—
270#533C4×C12712yes—
271#533C22×C12712yes—
272#533C22×C12712yes—
273C2×C4⋊Q8C4×C12711yescharacteristic
274C2×C4⋊Q8C4×C12711yescharacteristic
275C2×#125C22×C12712yes—
276C2×C22⋊Q8—21no—
277C2×C22⋊Q8—21no—
278C2×C4×Q8—21no—
279C2×C4×Q8—21no—
280C2×#117C4×C12712yes—
281C22×C42C22×C12711yescharacteristic
282#432C22×C12712yes—
283#432C22×C12712yes—
284#431—21no—
285#431—21no—
286#423—21no—
287#407—21no—
288C4×M16—21no—
289C4×M16—21no—
290C4×M16C22×C12712yes—
291C4×M16C22×C12712yes—
292C4×M16C22×C12712yes—
293C2×#97C22×C12712yes—
294C2×C4×C8—21no—
295#330C22×C127116yescomplemented
296C22×Q8—21no—
297C22×Q8—21no—
298C23×C4C2×C4×C12711yescharacteristic
299C23×C4D4×C12711yescharacteristic
300C23×C4D4×C12711yescharacteristic
301C2×M16—28no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C22×C8—22no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C2×C4×C12712yes—
311C4⋊Q8C2×C4×C12712yes—
312C4⋊Q8C2×C4×C12712yes—
313C4⋊Q8C2×C4×C12712yes—
314#125—22no—
315#125—22no—
316#125C2×C4×C12714yes—
317#125C23×C12714yes—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334#117—22no—
335#117—22no—
336#117C2×C4×C12714yes—
337#117C2×C4×C12714yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4C2×C4×C12712yes—
343C2×C4⋊C4C2×C4×C12712yes—
344C2×C22⋊C4—22no—
345C2×C42—22no—
346C2×C42C2×C4×C12711yescharacteristic
347C2×C42C2×C4×C12711yescharacteristic
348C2×C42C2×C4×C12711yescharacteristic
349C2×C42D4×C12711yescharacteristic
350C2×C42D4×C12711yescharacteristic
351C2×C42D4×C12711yescharacteristic
352C2×C42D4×C12711yescharacteristic
353C2×C42D4×C12711yescharacteristic
354C2×C42D4×C12711yescharacteristic
355C2×C42C23×C12711yescharacteristic
356C2×C42C23×C12711yescharacteristic
357C2×C42C23×C12711yescharacteristic
358C4⋊C8—22no—
359C4⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362#97—22no—
363#97C23×C12714yes—
364#97C23×C12714yes—
365C4×C8—22no—
366C4×C8—22no—
367C4×C8—22no—
368C24C22⋊C4×C12711yescharacteristic
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—44no—
374C2×Q8—44no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4C22⋊C4×C12711yescharacteristic
381C22×C4C22⋊C4×C12711yescharacteristic
382C22×C4C22⋊C4×C12711yescharacteristic
383C22×C4C22⋊C4×C12711yescharacteristic
384C22×C4C22⋊C4×C12711yescharacteristic
385C22×C4C22⋊C4×C12711yescharacteristic
386C22×C4C22⋊C4×C12711yescharacteristic
387C22×C4C22⋊C4×C12711yescharacteristic
388C22×C4C22⋊C4×C12711yescharacteristic
389C22×C4C22×C4×C12711yescharacteristic
390C22×C4C22×C4×C12711yescharacteristic
391C22×C4C22×C4×C12711yescharacteristic
392C22×C4C2×D4×C12711yescharacteristic
393C22×C4C2×D4×C12711yescharacteristic
394C22×C4C2×D4×C12711yescharacteristic
395C22×C4C2×D4×C12711yescharacteristic
396C22×C4C2×D4×C12711yescharacteristic
397C22×C4C2×D4×C12711yescharacteristic
398M16—28no—
399M16—28no—
400M16—44no—
401C2×C8—28no—
402C2×C8—24no—
403C2×C8—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4C22×C4×C12714yes—
415C4⋊C4C22×C4×C12714yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C42—24no—
419C42—24no—
420C42C22⋊C4×C12711yescharacteristic
421C42C22⋊C4×C12711yescharacteristic
422C42C22⋊C4×C12711yescharacteristic
423C42C22⋊C4×C12711yescharacteristic
424C42C22⋊C4×C12711yescharacteristic
425C42C22⋊C4×C12711yescharacteristic
426C42C22×C4×C12711yescharacteristic
427C42C22×C4×C12711yescharacteristic
428C42C22×C4×C12711yescharacteristic
429C42C2×D4×C12711yescharacteristic
430C42C2×D4×C12711yescharacteristic
431C42C2×D4×C12711yescharacteristic
432C42C2×D4×C12711yescharacteristic
433C42C2×D4×C12711yescharacteristic
434C42C2×D4×C12711yescharacteristic
435C42C24×C12711yescharacteristic
436C23—22no—
437C23—22no—
438C23—41no—
439C23C2×C22⋊C4×C12711yescharacteristic
440C23C2×C22⋊C4×C12711yescharacteristic
441C23C2×C22⋊C4×C12711yescharacteristic
442Q8—44no—
443Q8—44no—
444Q8—44no—
445Q8—44no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4#101×C12714yes—
467C2×C4#104×C12714yes—
468C2×C4C2×C22⋊C4×C12711yescharacteristic
469C2×C4C2×C22⋊C4×C12711yescharacteristic
470C2×C4C2×C22⋊C4×C12711yescharacteristic
471C2×C4C2×C22⋊C4×C12711yescharacteristic
472C2×C4C2×C22⋊C4×C12711yescharacteristic
473C2×C4C2×C22⋊C4×C12711yescharacteristic
474C2×C4C2×C22⋊C4×C12711yescharacteristic
475C2×C4C2×C22⋊C4×C12711yescharacteristic
476C2×C4C2×C22⋊C4×C12711yescharacteristic
477C2×C4C23×C4×C12711yescharacteristic
478C2×C4C22×D4×C12711yescharacteristic
479C2×C4C22×D4×C12711yescharacteristic
480C8—28no—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—44no—
490C22C2×#101×C12712yes—
491C22C2×#104×C12712yes—
492C22C22×C22⋊C4×C12711yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—44no—
501C4—44no—
502C4C2×#101×C12712yes—
503C4C2×#101×C12712yes—
504C4C2×#104×C12712yes—
505C4C2×#104×C12712yes—
506C4#421×C12712yes—
507C2—22no—
508C2—22no—
509C2—41no—
510C2C22×#101×C12711yescharacteristic
511C2C22×#104×C12711yescharacteristic
512C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC42C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC24×C127C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1531C2semidirect
5. C127×#1528C2semidirect
6. C127×#1526C2semidirect
38. #330×C127C22semidirect
250. #17648C127direct (N × H)
260. #1531C2×C127semidirect
261. #1528C2×C127semidirect
262. #1526C2×C127semidirect
263. C127#17648direct (N × H)
295. #330C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1272
C127×#29202
C2×C4×M16×C1272
C127×#15312
C127×#15282
C127×#15262
#17648127