Finite Group Databasebeta

← C127×#13422 #44577095

Subgroups — C127×#13422 #44577095

Order 32512.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2669C211yesmaximal, characteristic
2C2×#353×C127C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C127C211yesmaximal, characteristic, complemented
4C127×#1889C211yesmaximal, characteristic, complemented
5C127×#1887C211yesmaximal, characteristic, complemented
6C127×#1867C211yesmaximal, characteristic, complemented
7C127×#1390C211yesmaximal, characteristic, complemented
8C2×#127×C127C2211yescharacteristic
9C2×#121×C127—21no—
10C2×#120×C127—21no—
11C2×#120×C127C2211yescharacteristic
12#518×C127C2211yescharacteristic
13#418×C127—21no—
14C2×#100×C127C2211yescharacteristic
15C2×#99×C127C2211yescharacteristic
16C2×#99×C127C2211yescharacteristic
17#394×C127—21no—
18#392×C127—21no—
19#392×C127—21no—
20#388×C127—21no—
21#386×C127C2211yescharacteristic
22#385×C127—21no—
23#379×C127—21no—
24#353×C127—22no—
25AΣL(1,𝔽16)×C127—22no—
26#342×C127—21no—
27#342×C127—21no—
28#339×C127—21no—
29C25×C127D411yescharacteristic
30C22×D4×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—21no—
35C22×D4×C127D411yescharacteristic
36C22×D4×C127C2311yescharacteristic
37C23×C4×C127D411yescharacteristic
38C2×M16×C127—21no—
39#127×C127—21no—
40#127×C127—21no—
41#127×C127—21no—
42#127×C127—21no—
43#121×C127—44no—
44#120×C127—21no—
45#120×C127—21no—
46#120×C127—21no—
47#120×C127—21no—
48#120×C127—44no—
49C4×D4×C127—41no—
50C4×D4×C127—41no—
51#117×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—41no—
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—21no—
60C2×C22⋊C4×C127—21no—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—41no—
65C2×C22⋊C4×C127—41no—
66C2×C22⋊C4×C127D411yescharacteristic
67C2×C22⋊C4×C127D411yescharacteristic
68C2×C42×C127D411yescharacteristic
69#102×C127—41no—
70#102×C127—41no—
71#100×C127—21no—
72#100×C127—21no—
73#99×C127—21no—
74#99×C127—21no—
75#99×C127—21no—
76#99×C127D412yescomplemented
77#95×C127—21no—
78#95×C127—21no—
79#95×C127—41no—
80C24×C127—21no—
81C24×C127—21no—
82C24×C127—21no—
83C24×C127—21no—
84C24×C127—41no—
85C24×C127—42no—
86C24×C127—41no—
87C24×C127—81no—
88C24×C127C2×D411yescharacteristic
89C24×C127C2×D411yescharacteristic
90C2×D4×C127—21no—
91C2×D4×C127—21no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—42no—
97C2×D4×C127—42no—
98C2×D4×C127—42no—
99C2×D4×C127—42no—
100C2×D4×C127—42no—
101C2×D4×C127—42no—
102C2×D4×C127—41no—
103C2×D4×C127—41no—
104C2×D4×C127—41no—
105C2×D4×C127—41no—
106C2×D4×C127—41no—
107C2×D4×C127—41no—
108C2×D4×C127—81no—
109C2×D4×C127—81no—
110C2×D4×C127—81no—
111C2×D4×C127—81no—
112C2×D4×C127—81no—
113C2×D4×C127—81no—
114C2×D4×C127C2×D411yescharacteristic
115C2×D4×C127#4111yescharacteristic
116C2×D4×C127#4111yescharacteristic
117C2×D4×C127#4111yescharacteristic
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—42no—
127C22×C4×C127—41no—
128C22×C4×C127—41no—
129C22×C4×C127—41no—
130C22×C4×C127C2×D411yescharacteristic
131M16×C127—41no—
132M16×C127—41no—
133C2×C8×C127—41no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—42no—
137C4⋊C4×C127—82no—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—22no—
140C22⋊C4×C127—21no—
141C22⋊C4×C127—21no—
142C22⋊C4×C127—42no—
143C22⋊C4×C127—42no—
144C22⋊C4×C127—42no—
145C22⋊C4×C127—41no—
146C22⋊C4×C127—41no—
147C22⋊C4×C127—41no—
148C22⋊C4×C127—41no—
149C22⋊C4×C127—41no—
150C22⋊C4×C127—41no—
151C22⋊C4×C127—41no—
152C22⋊C4×C127—41no—
153C22⋊C4×C127—41no—
154C22⋊C4×C127—81no—
155C22⋊C4×C127—82no—
156C22⋊C4×C127—82no—
157C42×C127—21no—
158C42×C127—21no—
159C42×C127—41no—
160C23×C127—21no—
161C23×C127—21no—
162C23×C127—21no—
163C23×C127—21no—
164C23×C127—22no—
165C23×C127—41no—
166C23×C127—41no—
167C23×C127—41no—
168C23×C127—41no—
169C23×C127—41no—
170C23×C127—41no—
171C23×C127—41no—
172C23×C127—42no—
173C23×C127—41no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127—41no—
177C23×C127—42no—
178C23×C127—42no—
179C23×C127—41no—
180C23×C127—41no—
181C23×C127—41no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—81no—
186C23×C127—82no—
187C23×C127—81no—
188C23×C127—82no—
189C23×C127—84no—
190C23×C127—81no—
191C23×C127#12011yescharacteristic
192C23×C127#12111yescharacteristic
193C23×C127#12111yescharacteristic
194C23×C127#12311yescharacteristic
195C23×C127#12411yescharacteristic
196D4×C127—41no—
197D4×C127—41no—
198D4×C127—41no—
199D4×C127—41no—
200D4×C127—42no—
201D4×C127—81no—
202D4×C127—82no—
203D4×C127—82no—
204D4×C127—82no—
205D4×C127—82no—
206D4×C127—84no—
207D4×C127—82no—
208D4×C127—82no—
209D4×C127—84no—
210C2×C4×C127—21no—
211C2×C4×C127—21no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—41no—
224C2×C4×C127—41no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—81no—
229C2×C4×C127—81no—
230C2×C4×C127—81no—
231C2×C4×C127—81no—
232C2×C4×C127—81no—
233C2×C4×C127—81no—
234C2×C4×C127—81no—
235C2×C4×C127—81no—
236C2×C4×C127—81no—
237C2×C4×C127—81no—
238C2×C4×C127#12111yescharacteristic
239C2×C4×C127#12311yescharacteristic
240C8×C127—81no—
241C22×C127—21no—
242C22×C127—21no—
243C22×C127—21no—
244C22×C127—21no—
245C22×C127—21no—
246C22×C127—21no—
247C22×C127—41no—
248C22×C127—41no—
249C22×C127—41no—
250C22×C127—41no—
251C22×C127—42no—
252C22×C127—42no—
253C22×C127—41no—
254C22×C127—41no—
255C22×C127—41no—
256C22×C127—41no—
257C22×C127—44no—
258C22×C127—42no—
259C22×C127—81no—
260C22×C127—81no—
261C22×C127—81no—
262C22×C127—81no—
263C22×C127—81no—
264C22×C127—81no—
265C22×C127—81no—
266C22×C127—81no—
267C22×C127—82no—
268C22×C127—82no—
269C22×C127—82no—
270C22×C127—81no—
271C22×C127—81no—
272C22×C127—81no—
273C22×C127—81no—
274C22×C127—81no—
275C22×C127#39411yescharacteristic
276C22×C127B(4,𝔽2)11yescharacteristic
277C22×C127#45811yescharacteristic
278C4×C127—21no—
279C4×C127—21no—
280C4×C127—42no—
281C4×C127—42no—
282C4×C127—81no—
283C4×C127—81no—
284C4×C127—82no—
285C4×C127—81no—
286C4×C127—81no—
287C4×C127—161no—
288#13422C12711yesmaximal, characteristic, direct product factor, Sylow
289C2×C127—21no—
290C2×C127—21no—
291C2×C127—41no—
292C2×C127—41no—
293C2×C127—41no—
294C2×C127—41no—
295C2×C127—82no—
296C2×C127—161no—
297C2×C127#204411yescharacteristic
298C2×C127#219611yescharacteristic
299C2×C127#220011yescharacteristic
300#2669C2×C12711yescharacteristic
301C2×#353C2×C12711yescharacteristic, complemented
302C2×AΣL(1,𝔽16)C2×C12711yescharacteristic, complemented
303#1889C2×C12711yescharacteristic, complemented
304#1887C2×C12711yescharacteristic, complemented
305#1867C2×C12711yescharacteristic, complemented
306#1390C2×C12711yescharacteristic, complemented
307C127#1342211yescharacteristic, direct product factor, Sylow
308C2×#127C22×C12711yescharacteristic
309C2×#121—21no—
310C2×#120—21no—
311C2×#120C22×C12711yescharacteristic
312#518C22×C12711yescharacteristic
313#418—21no—
314C2×#100C22×C12711yescharacteristic
315C2×#99C22×C12711yescharacteristic
316C2×#99C22×C12711yescharacteristic
317#394—21no—
318#392—21no—
319#392—21no—
320#388—21no—
321#386C22×C12711yescharacteristic
322#385—21no—
323#379—21no—
324#353—22no—
325AΣL(1,𝔽16)—22no—
326#342—21no—
327#342—21no—
328#339—21no—
329C25D4×C12711yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C12711yescharacteristic
336C22×D4C23×C12711yescharacteristic
337C23×C4D4×C12711yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C12711yescharacteristic
367C2×C22⋊C4D4×C12711yescharacteristic
368C2×C42D4×C12711yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C12712yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C12711yescharacteristic
389C24C2×D4×C12711yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C12711yescharacteristic
415C2×D4#41×C12711yescharacteristic
416C2×D4#41×C12711yescharacteristic
417C2×D4#41×C12711yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C12711yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C12711yescharacteristic
492C23#121×C12711yescharacteristic
493C23#121×C12711yescharacteristic
494C23#123×C12711yescharacteristic
495C23#124×C12711yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C12711yescharacteristic
539C2×C4#123×C12711yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#394×C12711yescharacteristic
576C22B(4,𝔽2)×C12711yescharacteristic
577C22#458×C12711yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2C127×#204411yescharacteristic
597C2C127×#219611yescharacteristic
598C2C127×#220011yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C127
prime radicalC127×#2669C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C127C2semidirect
3. C2×AΣL(1,𝔽16)×C127C2semidirect
4. C127×#1889C2semidirect
5. C127×#1887C2semidirect
6. C127×#1867C2semidirect
7. C127×#1390C2semidirect
76. #99×C127D4semidirect
288. #13422C127direct (N × H)
301. C2×#353C2×C127semidirect
302. C2×AΣL(1,𝔽16)C2×C127semidirect
303. #1889C2×C127semidirect
304. #1887C2×C127semidirect
305. #1867C2×C127semidirect
306. #1390C2×C127semidirect
307. C127#13422direct (N × H)
376. #99D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26692
C2×#353×C1272
C2×AΣL(1,𝔽16)×C1272
C127×#18892
C127×#18872
C127×#18672
C127×#13902
#13422127