Finite Group Databasebeta

← C2×C127×#1915 #44584689

Subgroups — C2×C127×#1915 #44584689

Order 32512.

1670 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic
2C2×#536×C127C211yesmaximal, characteristic
3C2×#413×C127C211yesmaximal, characteristic
4C22×#101×C127C212yesmaximal, complemented
5C127×#1915C218yesmaximal, direct product factor
6C2×#344×C127C212yesmaximal, complemented
7C22×#41×C127C2211yescharacteristic
8C23×Q8×C127C2211yescharacteristic
9#568×C127—22no—
10#568×C127—24no—
11#568×C127C2214yes—
12C2×#131×C127—24no—
13C22×M16×C127—22no—
14C22×M16×C127C2212yes—
15C22×M16×C127C2212yes—
16#536×C127—22no—
17#536×C127—22no—
18#536×C127C414yes—
19#536×C127C2214yes—
20C2×C4⋊Q8×C127—21no—
21C2×#124×C127—21no—
22C2×#123×C127C414yes—
23C2×C22⋊Q8×C127—22no—
24C2×#117×C127C2211yescharacteristic
25#413×C127—22no—
26#413×C127C2214yes—
27C2×#101×C127—21no—
28C2×#101×C127—24no—
29C2×#101×C127—24no—
30C2×#101×C127C2218yescomplemented
31C2×#100×C127—21no—
32#344×C127C2218yescomplemented
33C2×#41×C127—22no—
34C2×#41×C127—22no—
35C2×#41×C127—22no—
36C2×#41×C127—22no—
37C2×#41×C127C2×C412yes—
38C2×#41×C127D412yes—
39C2×#41×C127D412yes—
40C2×#41×C127C2312yes—
41C22×Q8×C127—21no—
42C22×Q8×C127—21no—
43C22×Q8×C127—21no—
44C22×Q8×C127—21no—
45C22×Q8×C127—22no—
46C22×Q8×C127—22no—
47C22×Q8×C127—22no—
48C22×Q8×C127—22no—
49C22×Q8×C127C2×C412yes—
50C22×Q8×C127D411yescharacteristic
51C22×Q8×C127C2312yes—
52C22×D4×C127C2×C412yes—
53C22×D4×C127D411yescharacteristic
54C23×C4×C127C2×C412yes—
55C23×C4×C127D412yes—
56C23×C4×C127C2311yescharacteristic
57#131×C127—216no—
58#131×C127—216no—
59C2×M16×C127—24no—
60C2×M16×C127—28no—
61C2×M16×C127—22no—
62C2×M16×C127—28no—
63C2×M16×C127—22no—
64C2×M16×C127—22no—
65C2×M16×C127—22no—
66C2×M16×C127—22no—
67C2×M16×C127—22no—
68C2×M16×C127—22no—
69C2×M16×C127—22no—
70C2×M16×C127D414yes—
71C2×M16×C127D414yes—
72C2×M16×C127C2314yes—
73C2×M16×C127C2314yes—
74C22×C8×C127—24no—
75C22×C8×C127—22no—
76C22×C8×C127—22no—
77C4⋊Q8×C127—24no—
78C4⋊Q8×C127—24no—
79#124×C127—24no—
80#124×C127—24no—
81#123×C127—28no—
82#123×C127C2×C4116yes—
83C22⋊Q8×C127—28no—
84C22⋊Q8×C127—28no—
85#117×C127—21no—
86#117×C127—21no—
87#117×C127C2×C412yes—
88#117×C127C2312yes—
89C2×C4⋊C4×C127—24no—
90C2×C4⋊C4×C127—21no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127C2×C412yes—
93C2×C42×C127—21no—
94#101×C127—24no—
95#101×C127—216no—
96#100×C127—24no—
97C24×C127C22⋊C412yes—
98C24×C127C22×C411yescharacteristic
99#41×C127—24no—
100#41×C127—24no—
101#41×C127—24no—
102#41×C127—24no—
103#41×C127—24no—
104#41×C127—24no—
105#41×C127—24no—
106#41×C127—24no—
107C2×Q8×C127—22no—
108C2×Q8×C127—22no—
109C2×Q8×C127—24no—
110C2×Q8×C127—24no—
111C2×Q8×C127—22no—
112C2×Q8×C127—22no—
113C2×Q8×C127—24no—
114C2×Q8×C127—22no—
115C2×Q8×C127—22no—
116C2×Q8×C127—24no—
117C2×Q8×C127—42no—
118C2×Q8×C127—41no—
119C2×Q8×C127—41no—
120C2×Q8×C127—42no—
121C2×Q8×C127—42no—
122C2×Q8×C127—42no—
123C2×Q8×C127—42no—
124C2×Q8×C127—41no—
125C2×Q8×C127—42no—
126C2×Q8×C127—41no—
127C2×Q8×C127C22⋊C412yes—
128C2×Q8×C127C2×D412yes—
129C2×D4×C127—24no—
130C2×D4×C127—24no—
131C2×D4×C127—22no—
132C2×D4×C127—22no—
133C2×D4×C127C22⋊C414yes—
134C2×D4×C127C22⋊C412yes—
135C2×D4×C127C22×C414yes—
136C2×D4×C127C2×D412yes—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—24no—
145C22×C4×C127—24no—
146C22×C4×C127C22⋊C412yes—
147C22×C4×C127C22⋊C414yes—
148C22×C4×C127C22×C414yes—
149C22×C4×C127C22×C411yescharacteristic
150C22×C4×C127C2×D414yes—
151C22×C4×C127C2×D411yescharacteristic
152C22×C4×C127C2×D411yescharacteristic
153C22×C4×C127C2×D411yescharacteristic
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127#4112yes—
158C22×C4×C127#4112yes—
159C22×C4×C127C2411yescharacteristic
160M16×C127—216no—
161M16×C127—24no—
162M16×C127—24no—
163M16×C127—24no—
164M16×C127—24no—
165M16×C127—24no—
166M16×C127—42no—
167M16×C127—42no—
168M16×C127C2×D418yes—
169C2×C8×C127—216no—
170C2×C8×C127—24no—
171C2×C8×C127—24no—
172C2×C8×C127—24no—
173C2×C8×C127—24no—
174C2×C8×C127—42no—
175C2×C8×C127—42no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—216no—
178C4⋊C4×C127—22no—
179C22⋊C4×C127—216no—
180C22⋊C4×C127—22no—
181C22⋊C4×C127C22×C414yes—
182C42×C127—22no—
183C42×C127—22no—
184C23×C127—22no—
185C23×C127—22no—
186C23×C127—42no—
187C23×C127—44no—
188C23×C127C2×C22⋊C411yescharacteristic
189C23×C127C2×C22⋊C414yes—
190C23×C127C2×C22⋊C411yescharacteristic
191C23×C127C4×D412yes—
192C23×C127C4×D412yes—
193C23×C127C23×C411yescharacteristic
194Q8×C127—24no—
195Q8×C127—24no—
196Q8×C127—42no—
197Q8×C127—44no—
198Q8×C127—42no—
199Q8×C127—42no—
200Q8×C127—42no—
201Q8×C127—44no—
202D4×C127—28no—
203D4×C127—28no—
204D4×C127—24no—
205D4×C127—24no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—24no—
209C2×C4×C127—24no—
210C2×C4×C127—24no—
211C2×C4×C127—24no—
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—28no—
215C2×C4×C127—44no—
216C2×C4×C127—42no—
217C2×C4×C127—44no—
218C2×C4×C127—42no—
219C2×C4×C127C2×C22⋊C414yes—
220C2×C4×C127C2×C22⋊C411yescharacteristic
221C2×C4×C127C2×C22⋊C411yescharacteristic
222C2×C4×C127C4×D412yes—
223C2×C4×C127C4×D412yes—
224C2×C4×C127#12012yes—
225C2×C4×C127#12011yescharacteristic
226C2×C4×C127#12011yescharacteristic
227C2×C4×C127#12112yes—
228C2×C4×C127#12112yes—
229C2×C4×C127#12112yes—
230C2×C4×C127#12112yes—
231C2×C4×C127#12311yescharacteristic
232C2×C4×C127#12312yes—
233C2×C4×C127#12311yescharacteristic
234C2×C4×C127C22×D412yes—
235C2×C4×C127C22×D411yescharacteristic
236C2×C4×C127C22×D411yescharacteristic
237C2×C4×C127C2×#4112yes—
238C8×C127—28no—
239C8×C127—44no—
240C22×C127—22no—
241C22×C127—24no—
242C22×C127—24no—
243C22×C127—41no—
244C22×C127—42no—
245C22×C127—41no—
246C22×C127—44no—
247C22×C127—44no—
248C22×C127—82no—
249C22×C127#38611yescharacteristic
250C22×C127#38612yes—
251C22×C127#38611yescharacteristic
252C22×C127C22×C22⋊C411yescharacteristic
253C22×C127C2×C4×D412yes—
254C4×C127—24no—
255C4×C127—44no—
256C4×C127—44no—
257C4×C127#38611yescharacteristic
258C4×C127#38611yescharacteristic
259C4×C127#38612yes—
260C4×C127C2×#12011yescharacteristic
261C4×C127C2×#12112yes—
262C4×C127C2×#12311yescharacteristic
263C2×#1915C12711yesmaximal, characteristic, direct product factor, Sylow
264C2×C127—21no—
265C2×C127—21no—
266C2×C127—22no—
267C2×C127—22no—
268C2×C127—44no—
269C2×C127#191512yesdirect product factor
270C2×C127C2×#38611yescharacteristic
271C2×#568C2×C12711yescharacteristic
272C2×#536C2×C12711yescharacteristic
273C2×#413C2×C12711yescharacteristic
274C22×#101C2×C12712yescomplemented
275#1915C2×C12718yesdirect product factor
276C2×#344C2×C12712yescomplemented
277C127C2×#191511yescharacteristic, direct product factor, Sylow
278C22×#41C22×C12711yescharacteristic
279C23×Q8C22×C12711yescharacteristic
280#568—22no—
281#568—24no—
282#568C22×C12714yes—
283C2×#131—24no—
284C22×M16—22no—
285C22×M16C22×C12712yes—
286C22×M16C22×C12712yes—
287#536—22no—
288#536—22no—
289#536C4×C12714yes—
290#536C22×C12714yes—
291C2×C4⋊Q8—21no—
292C2×#124—21no—
293C2×#123C4×C12714yes—
294C2×C22⋊Q8—22no—
295C2×#117C22×C12711yescharacteristic
296#413—22no—
297#413C22×C12714yes—
298C2×#101—21no—
299C2×#101—24no—
300C2×#101—24no—
301C2×#101C22×C12718yescomplemented
302C2×#100—21no—
303#344C22×C12718yescomplemented
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41C2×C4×C12712yes—
309C2×#41D4×C12712yes—
310C2×#41D4×C12712yes—
311C2×#41C23×C12712yes—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—21no—
315C22×Q8—21no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8C2×C4×C12712yes—
321C22×Q8D4×C12711yescharacteristic
322C22×Q8C23×C12712yes—
323C22×D4C2×C4×C12712yes—
324C22×D4D4×C12711yescharacteristic
325C23×C4C2×C4×C12712yes—
326C23×C4D4×C12712yes—
327C23×C4C23×C12711yescharacteristic
328#131—216no—
329#131—216no—
330C2×M16—24no—
331C2×M16—28no—
332C2×M16—22no—
333C2×M16—28no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16D4×C12714yes—
342C2×M16D4×C12714yes—
343C2×M16C23×C12714yes—
344C2×M16C23×C12714yes—
345C22×C8—24no—
346C22×C8—22no—
347C22×C8—22no—
348C4⋊Q8—24no—
349C4⋊Q8—24no—
350#124—24no—
351#124—24no—
352#123—28no—
353#123C2×C4×C127116yes—
354C22⋊Q8—28no—
355C22⋊Q8—28no—
356#117—21no—
357#117—21no—
358#117C2×C4×C12712yes—
359#117C23×C12712yes—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4C2×C4×C12712yes—
364C2×C42—21no—
365#101—24no—
366#101—216no—
367#100—24no—
368C24C22⋊C4×C12712yes—
369C24C22×C4×C12711yescharacteristic
370#41—24no—
371#41—24no—
372#41—24no—
373#41—24no—
374#41—24no—
375#41—24no—
376#41—24no—
377#41—24no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—24no—
388C2×Q8—41no—
389C2×Q8—42no—
390C2×Q8—41no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—42no—
398C2×Q8C22⋊C4×C12712yes—
399C2×Q8C2×D4×C12712yes—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4C22⋊C4×C12714yes—
405C2×D4C22⋊C4×C12712yes—
406C2×D4C22×C4×C12714yes—
407C2×D4C2×D4×C12712yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4C22⋊C4×C12712yes—
418C22×C4C22⋊C4×C12714yes—
419C22×C4C22×C4×C12714yes—
420C22×C4C22×C4×C12711yescharacteristic
421C22×C4C2×D4×C12714yes—
422C22×C4C2×D4×C12711yescharacteristic
423C22×C4C2×D4×C12711yescharacteristic
424C22×C4C2×D4×C12711yescharacteristic
425C22×C4C2×D4×C12711yescharacteristic
426C22×C4C2×D4×C12712yes—
427C22×C4C2×D4×C12712yes—
428C22×C4#41×C12712yes—
429C22×C4#41×C12712yes—
430C22×C4C24×C12711yescharacteristic
431M16—216no—
432M16—24no—
433M16—24no—
434M16—24no—
435M16—24no—
436M16—24no—
437M16—42no—
438M16—42no—
439M16C2×D4×C12718yes—
440C2×C8—216no—
441C2×C8—24no—
442C2×C8—24no—
443C2×C8—24no—
444C2×C8—24no—
445C2×C8—42no—
446C2×C8—42no—
447C4⋊C4—22no—
448C4⋊C4—216no—
449C4⋊C4—22no—
450C22⋊C4—216no—
451C22⋊C4—22no—
452C22⋊C4C22×C4×C12714yes—
453C42—22no—
454C42—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—44no—
459C23C2×C22⋊C4×C12711yescharacteristic
460C23C2×C22⋊C4×C12714yes—
461C23C2×C22⋊C4×C12711yescharacteristic
462C23C4×D4×C12712yes—
463C23C4×D4×C12712yes—
464C23C23×C4×C12711yescharacteristic
465Q8—24no—
466Q8—24no—
467Q8—42no—
468Q8—44no—
469Q8—42no—
470Q8—42no—
471Q8—42no—
472Q8—44no—
473D4—28no—
474D4—28no—
475D4—24no—
476D4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—42no—
490C2×C4C2×C22⋊C4×C12714yes—
491C2×C4C2×C22⋊C4×C12711yescharacteristic
492C2×C4C2×C22⋊C4×C12711yescharacteristic
493C2×C4C4×D4×C12712yes—
494C2×C4C4×D4×C12712yes—
495C2×C4#120×C12711yescharacteristic
496C2×C4#120×C12712yes—
497C2×C4#120×C12711yescharacteristic
498C2×C4#121×C12712yes—
499C2×C4#121×C12712yes—
500C2×C4#121×C12712yes—
501C2×C4#121×C12712yes—
502C2×C4#123×C12711yescharacteristic
503C2×C4#123×C12711yescharacteristic
504C2×C4#123×C12712yes—
505C2×C4C22×D4×C12712yes—
506C2×C4C22×D4×C12711yescharacteristic
507C2×C4C22×D4×C12711yescharacteristic
508C2×C4C2×#41×C12712yes—
509C8—28no—
510C8—44no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—41no—
515C22—42no—
516C22—41no—
517C22—44no—
518C22—44no—
519C22—82no—
520C22#386×C12711yescharacteristic
521C22#386×C12712yes—
522C22#386×C12711yescharacteristic
523C22C22×C22⋊C4×C12711yescharacteristic
524C22C2×C4×D4×C12712yes—
525C4—24no—
526C4—44no—
527C4—44no—
528C4#386×C12711yescharacteristic
529C4#386×C12711yescharacteristic
530C4#386×C12712yes—
531C4C2×#120×C12711yescharacteristic
532C4C2×#121×C12712yes—
533C4C2×#123×C12711yescharacteristic
534C2—21no—
535C2—21no—
536C2—22no—
537C2—22no—
538C2—44no—
539C2C127×#191512yesdirect product factor
540C2C2×#386×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×#41×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×#101×C127C2semidirect
5. C127×#1915C2direct (N × H)
6. C2×#344×C127C2semidirect
30. C2×#101×C127C22semidirect
32. #344×C127C22semidirect
263. C2×#1915C127direct (N × H)
269. C2×C127#1915direct (N × H)
274. C22×#101C2×C127semidirect
275. #1915C2×C127direct (N × H)
276. C2×#344C2×C127semidirect
277. C127C2×#1915direct (N × H)
301. C2×#101C22×C127semidirect
303. #344C22×C127semidirect
539. C2C127×#1915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C2×#536×C1272
C2×#413×C1272
C22×#101×C1272
C127×#19152
C2×#344×C1272
C2×#1915127