Finite Group Databasebeta

← C127×#17680 #44581353

Subgroups — C127×#17680 #44581353

Order 32512.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3515C211yesmaximal, characteristic
2C127×#2970C211yesmaximal, characteristic, complemented
3C127×#2923C211yesmaximal, characteristic, complemented
4C127×#1537C211yesmaximal, characteristic, complemented
5C127×#1535C211yesmaximal, characteristic, complemented
6C127×#1535C211yesmaximal, characteristic, complemented
7C127×#1534C211yesmaximal, characteristic, complemented
8C127×#1532C211yesmaximal, characteristic, complemented
9C127×#1532C211yesmaximal, characteristic, complemented
10C127×#1531C211yesmaximal, characteristic, complemented
11C127×#1529C211yesmaximal, characteristic, complemented
12C127×#1528C211yesmaximal, characteristic, complemented
13C127×#1528C211yesmaximal, characteristic, complemented
14C127×#1524C211yesmaximal, characteristic, complemented
15C2×#330×C127C211yesmaximal, characteristic, complemented
16#557×C127C411yescharacteristic
17#554×C127C411yescharacteristic
18#554×C127C411yescharacteristic
19#553×C127C411yescharacteristic
20#553×C127C411yescharacteristic
21#552×C127—21no—
22#552×C127—21no—
23#552×C127—21no—
24#552×C127C411yescharacteristic
25#552×C127C411yescharacteristic
26#547×C127—21no—
27#547×C127C411yescharacteristic
28#541×C127—21no—
29#539×C127—21no—
30#539×C127—21no—
31#533×C127C2211yescharacteristic
32#529×C127C2211yescharacteristic
33#529×C127C2211yescharacteristic
34#529×C127C2211yescharacteristic
35C2×#125×C127C2211yescharacteristic
36C2×#125×C127C2211yescharacteristic
37#520×C127—21no—
38C4×#41×C127C2211yescharacteristic
39#446×C127—21no—
40#435×C127—21no—
41#435×C127—21no—
42C8×D4×C127—21no—
43#433×C127—21no—
44#433×C127—21no—
45#432×C127C2211yescharacteristic
46#432×C127C2211yescharacteristic
47#432×C127C2211yescharacteristic
48#432×C127C2211yescharacteristic
49#432×C127C2211yescharacteristic
50#432×C127C2211yescharacteristic
51#432×C127C2211yescharacteristic
52#424×C127—21no—
53#408×C127—21no—
54C4×M16×C127C2211yescharacteristic
55C4×M16×C127C2211yescharacteristic
56C2×#97×C127C2211yescharacteristic
57C2×#97×C127C2211yescharacteristic
58C2×#97×C127C2211yescharacteristic
59#330×C127C2211yescharacteristic
60#330×C127C2211yescharacteristic
61#330×C127C2211yescharacteristic
62#330×C127C2211yescharacteristic
63#330×C127C2211yescharacteristic
64#330×C127C2211yescharacteristic
65#330×C127C2211yescharacteristic
66#330×C127C2211yescharacteristic
67#330×C127C2211yescharacteristic
68#330×C127C2211yescharacteristic
69#330×C127C2211yescharacteristic
70#330×C127C2211yescharacteristic
71#329×C127C2211yescharacteristic
72#329×C127C2211yescharacteristic
73#329×C127C2211yescharacteristic
74#329×C127C2211yescharacteristic
75C2×#41×C127—21no—
76C2×#41×C127D411yescharacteristic
77C2×M16×C127—21no—
78C2×M16×C127—21no—
79C22×C8×C127—21no—
80C22×C8×C127—21no—
81C22×C8×C127—21no—
82C4⋊Q8×C127—21no—
83C4⋊Q8×C127C2×C411yescharacteristic
84C4⋊Q8×C127C2×C411yescharacteristic
85#126×C127—21no—
86#126×C127—21no—
87#126×C127—21no—
88#126×C127—21no—
89#126×C127—21no—
90#126×C127—21no—
91#126×C127—21no—
92#125×C127—21no—
93#125×C127—21no—
94#125×C127—21no—
95#125×C127—21no—
96#125×C127—21no—
97#125×C127—21no—
98#125×C127—21no—
99#125×C127—21no—
100#125×C127—21no—
101#125×C127C2×C411yescharacteristic
102#125×C127C2×C411yescharacteristic
103#125×C127C2×C411yescharacteristic
104#125×C127C2×C411yescharacteristic
105#125×C127C2311yescharacteristic
106#125×C127C2311yescharacteristic
107#125×C127C2311yescharacteristic
108#124×C127C2311yescharacteristic
109#123×C127—21no—
110#123×C127—21no—
111#123×C127—21no—
112#123×C127—21no—
113#123×C127—21no—
114#123×C127—21no—
115#123×C127—21no—
116#123×C127—21no—
117#123×C127—21no—
118C22⋊Q8×C127—21no—
119C22⋊Q8×C127—21no—
120C22⋊Q8×C127—21no—
121C22⋊Q8×C127—21no—
122C22⋊Q8×C127—21no—
123C22⋊Q8×C127—21no—
124C22⋊Q8×C127—21no—
125C22⋊Q8×C127—21no—
126C22⋊Q8×C127C2×C411yescharacteristic
127C22⋊Q8×C127C2×C411yescharacteristic
128C22⋊Q8×C127C2×C411yescharacteristic
129#121×C127—21no—
130#121×C127—21no—
131#121×C127C2×C411yescharacteristic
132#121×C127C2×C411yescharacteristic
133#121×C127C2×C411yescharacteristic
134C4×Q8×C127—21no—
135C4×Q8×C127—21no—
136C4×Q8×C127—21no—
137C4×Q8×C127C2×C411yescharacteristic
138C4×Q8×C127C2×C411yescharacteristic
139C4×Q8×C127C2×C411yescharacteristic
140C4×Q8×C127C2×C411yescharacteristic
141C4×Q8×C127D411yescharacteristic
142C4×D4×C127—21no—
143C4×D4×C127—21no—
144C4×D4×C127—21no—
145C4×D4×C127—21no—
146C4×D4×C127—21no—
147C4×D4×C127—21no—
148C4×D4×C127C2×C411yescharacteristic
149C4×D4×C127C2×C411yescharacteristic
150C4×D4×C127C2×C411yescharacteristic
151C4×D4×C127C2×C411yescharacteristic
152C4×D4×C127C2×C411yescharacteristic
153C4×D4×C127C2×C411yescharacteristic
154C4×D4×C127D411yescharacteristic
155C4×D4×C127D411yescharacteristic
156C4×D4×C127D411yescharacteristic
157#117×C127—21no—
158#117×C127—21no—
159#117×C127—21no—
160#117×C127—21no—
161#117×C127—21no—
162#117×C127C2×C411yescharacteristic
163#117×C127C2×C411yescharacteristic
164#117×C127D411yescharacteristic
165#117×C127D411yescharacteristic
166#117×C127D411yescharacteristic
167C2×C4⋊C4×C127—21no—
168C2×C4⋊C4×C127—21no—
169C2×C4⋊C4×C127—21no—
170C2×C4⋊C4×C127—21no—
171C2×C4⋊C4×C127—21no—
172C2×C4⋊C4×C127C2×C411yescharacteristic
173C2×C4⋊C4×C127C2×C411yescharacteristic
174C2×C4⋊C4×C127C2×C411yescharacteristic
175C2×C4⋊C4×C127C2×C411yescharacteristic
176C2×C42×C127C2311yescharacteristic
177C2×C42×C127C2311yescharacteristic
178C2×C42×C127C2311yescharacteristic
179C4⋊C8×C127—21no—
180C4⋊C8×C127—21no—
181C4⋊C8×C127—21no—
182C4⋊C8×C127—21no—
183C4⋊C8×C127—21no—
184C4⋊C8×C127—21no—
185C4⋊C8×C127—21no—
186C22⋊C8×C127—21no—
187C22⋊C8×C127—21no—
188C22⋊C8×C127—21no—
189C22⋊C8×C127—21no—
190C22⋊C8×C127—21no—
191C22⋊C8×C127—21no—
192C22⋊C8×C127—21no—
193#97×C127—21no—
194#97×C127—21no—
195#97×C127—21no—
196#97×C127C2311yescharacteristic
197#97×C127C2311yescharacteristic
198#97×C127C2311yescharacteristic
199#97×C127C2311yescharacteristic
200#97×C127C2311yescharacteristic
201#97×C127C2311yescharacteristic
202#97×C127C2311yescharacteristic
203#97×C127C2311yescharacteristic
204C4×C8×C127—21no—
205C4×C8×C127—21no—
206#41×C127—42no—
207#41×C127—44no—
208C2×Q8×C127—21no—
209C2×Q8×C127—21no—
210C2×Q8×C127C22⋊C411yescharacteristic
211C2×Q8×C127C22×C411yescharacteristic
212C2×D4×C127—21no—
213C2×D4×C127—21no—
214C2×D4×C127—21no—
215C2×D4×C127C22⋊C411yescharacteristic
216C2×D4×C127C22⋊C411yescharacteristic
217C2×D4×C127C22⋊C411yescharacteristic
218C2×D4×C127C22×C411yescharacteristic
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127C22×C411yescharacteristic
227C22×C4×C127C22×C411yescharacteristic
228C22×C4×C127C22×C411yescharacteristic
229C22×C4×C127C2×D411yescharacteristic
230C22×C4×C127C2×D411yescharacteristic
231C22×C4×C127C2×D411yescharacteristic
232C22×C4×C127C2×D411yescharacteristic
233C22×C4×C127C2×D411yescharacteristic
234C22×C4×C127C2×D411yescharacteristic
235M16×C127—42no—
236M16×C127—42no—
237C2×C8×C127—21no—
238C2×C8×C127—21no—
239C2×C8×C127—21no—
240C2×C8×C127—21no—
241C2×C8×C127—21no—
242C2×C8×C127—21no—
243C2×C8×C127—21no—
244C2×C8×C127—21no—
245C2×C8×C127—42no—
246C2×C8×C127—42no—
247C2×C8×C127—42no—
248C4⋊C4×C127—21no—
249C4⋊C4×C127—21no—
250C4⋊C4×C127—21no—
251C4⋊C4×C127—21no—
252C4⋊C4×C127—21no—
253C4⋊C4×C127—21no—
254C4⋊C4×C127—21no—
255C4⋊C4×C127—21no—
256C4⋊C4×C127—21no—
257C4⋊C4×C127—21no—
258C4⋊C4×C127—21no—
259C4⋊C4×C127—21no—
260C4⋊C4×C127—21no—
261C4⋊C4×C127—21no—
262C4⋊C4×C127—21no—
263C4⋊C4×C127—21no—
264C4⋊C4×C127—21no—
265C4⋊C4×C127—21no—
266C4⋊C4×C127—21no—
267C4⋊C4×C127—21no—
268C4⋊C4×C127—21no—
269C4⋊C4×C127—21no—
270C4⋊C4×C127—21no—
271C4⋊C4×C127—21no—
272C4⋊C4×C127—21no—
273C4⋊C4×C127—21no—
274C4⋊C4×C127C22⋊C411yescharacteristic
275C4⋊C4×C127C22⋊C411yescharacteristic
276C4⋊C4×C127C22⋊C411yescharacteristic
277C4⋊C4×C127C22⋊C411yescharacteristic
278C4⋊C4×C127C22⋊C411yescharacteristic
279C4⋊C4×C127C22⋊C411yescharacteristic
280C4⋊C4×C127C22×C411yescharacteristic
281C4⋊C4×C127C22×C411yescharacteristic
282C4⋊C4×C127C22×C411yescharacteristic
283C4⋊C4×C127C22×C411yescharacteristic
284C4⋊C4×C127C22×C411yescharacteristic
285C4⋊C4×C127C22×C411yescharacteristic
286C22⋊C4×C127—21no—
287C22⋊C4×C127—21no—
288C22⋊C4×C127—21no—
289C22⋊C4×C127—21no—
290C22⋊C4×C127—21no—
291C22⋊C4×C127—21no—
292C22⋊C4×C127—21no—
293C22⋊C4×C127—21no—
294C22⋊C4×C127—21no—
295C22⋊C4×C127—21no—
296C22⋊C4×C127—21no—
297C22⋊C4×C127—21no—
298C22⋊C4×C127—21no—
299C22⋊C4×C127C22⋊C411yescharacteristic
300C22⋊C4×C127C22⋊C411yescharacteristic
301C22⋊C4×C127C22⋊C411yescharacteristic
302C22⋊C4×C127C22⋊C411yescharacteristic
303C22⋊C4×C127C22⋊C411yescharacteristic
304C22⋊C4×C127C22⋊C411yescharacteristic
305C42×C127—21no—
306C42×C127—21no—
307C42×C127—21no—
308C42×C127—21no—
309C42×C127—21no—
310C42×C127C22×C411yescharacteristic
311C42×C127C22×C411yescharacteristic
312C42×C127C22×C411yescharacteristic
313C42×C127C2×D411yescharacteristic
314C42×C127C2×D411yescharacteristic
315C42×C127C2×D411yescharacteristic
316C42×C127C2×D411yescharacteristic
317C42×C127C2×D411yescharacteristic
318C42×C127C2×D411yescharacteristic
319C42×C127C2411yescharacteristic
320C23×C127—21no—
321C23×C127C2×C22⋊C411yescharacteristic
322C23×C127C2×C22⋊C411yescharacteristic
323C23×C127C2×C22⋊C411yescharacteristic
324Q8×C127—41no—
325Q8×C127—41no—
326Q8×C127—42no—
327Q8×C127—81no—
328D4×C127—22no—
329D4×C127—22no—
330D4×C127—41no—
331D4×C127—41no—
332D4×C127—42no—
333D4×C127—42no—
334D4×C127—81no—
335C2×C4×C127—22no—
336C2×C4×C127—21no—
337C2×C4×C127—21no—
338C2×C4×C127—21no—
339C2×C4×C127—21no—
340C2×C4×C127—21no—
341C2×C4×C127—21no—
342C2×C4×C127—21no—
343C2×C4×C127—41no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—41no—
347C2×C4×C127—41no—
348C2×C4×C127—41no—
349C2×C4×C127—41no—
350C2×C4×C127—41no—
351C2×C4×C127—42no—
352C2×C4×C127—42no—
353C2×C4×C127—42no—
354C2×C4×C127—81no—
355C2×C4×C127—81no—
356C2×C4×C127—81no—
357C2×C4×C127—81no—
358C2×C4×C127C2×C22⋊C411yescharacteristic
359C2×C4×C127C2×C22⋊C411yescharacteristic
360C2×C4×C127C2×C22⋊C411yescharacteristic
361C2×C4×C127C2×C22⋊C411yescharacteristic
362C2×C4×C127C2×C22⋊C411yescharacteristic
363C2×C4×C127C2×C22⋊C411yescharacteristic
364C2×C4×C127C2×C22⋊C411yescharacteristic
365C2×C4×C127C2×C22⋊C411yescharacteristic
366C2×C4×C127C2×C22⋊C411yescharacteristic
367C2×C4×C127C23×C411yescharacteristic
368C2×C4×C127C22×D411yescharacteristic
369C2×C4×C127C22×D411yescharacteristic
370C8×C127—22no—
371C8×C127—41no—
372C8×C127—41no—
373C8×C127—41no—
374C8×C127—41no—
375C8×C127—41no—
376C8×C127—41no—
377C8×C127—41no—
378C22×C127—21no—
379C22×C127—21no—
380C22×C127—21no—
381C22×C127—21no—
382C22×C127—21no—
383C22×C127—21no—
384C22×C127—21no—
385C22×C127—21no—
386C22×C127—41no—
387C22×C127—41no—
388C22×C127—41no—
389C22×C127#42112yes—
390C22×C127C22×C22⋊C411yescharacteristic
391C4×C127—21no—
392C4×C127—21no—
393C4×C127—21no—
394C4×C127—21no—
395C4×C127—21no—
396C4×C127—21no—
397C4×C127—21no—
398C4×C127—21no—
399C4×C127—21no—
400C4×C127—21no—
401C4×C127—21no—
402C4×C127—21no—
403C4×C127—41no—
404C4×C127—41no—
405C4×C127—41no—
406C4×C127—41no—
407C4×C127—41no—
408C4×C127—41no—
409C4×C127—41no—
410#17680C12711yesmaximal, characteristic, direct product factor, Sylow
411C2×C127—22no—
412C2×C127—41no—
413C2×C127—41no—
414C2×C127—81no—
415C2×C127#288911yescharacteristic
416C2×C127C2×#42111yescharacteristic
417C2×C127#290111yescharacteristic
418#3515C2×C12711yescharacteristic
419#2970C2×C12711yescharacteristic, complemented
420#2923C2×C12711yescharacteristic, complemented
421#1537C2×C12711yescharacteristic, complemented
422#1535C2×C12711yescharacteristic, complemented
423#1535C2×C12711yescharacteristic, complemented
424#1534C2×C12711yescharacteristic, complemented
425#1532C2×C12711yescharacteristic, complemented
426#1532C2×C12711yescharacteristic, complemented
427#1531C2×C12711yescharacteristic, complemented
428#1529C2×C12711yescharacteristic, complemented
429#1528C2×C12711yescharacteristic, complemented
430#1528C2×C12711yescharacteristic, complemented
431#1524C2×C12711yescharacteristic, complemented
432C2×#330C2×C12711yescharacteristic, complemented
433C127#1768011yescharacteristic, direct product factor, Sylow
434#557C4×C12711yescharacteristic
435#554C4×C12711yescharacteristic
436#554C4×C12711yescharacteristic
437#553C4×C12711yescharacteristic
438#553C4×C12711yescharacteristic
439#552—21no—
440#552—21no—
441#552—21no—
442#552C4×C12711yescharacteristic
443#552C4×C12711yescharacteristic
444#547—21no—
445#547C4×C12711yescharacteristic
446#541—21no—
447#539—21no—
448#539—21no—
449#533C22×C12711yescharacteristic
450#529C22×C12711yescharacteristic
451#529C22×C12711yescharacteristic
452#529C22×C12711yescharacteristic
453C2×#125C22×C12711yescharacteristic
454C2×#125C22×C12711yescharacteristic
455#520—21no—
456C4×#41C22×C12711yescharacteristic
457#446—21no—
458#435—21no—
459#435—21no—
460C8×D4—21no—
461#433—21no—
462#433—21no—
463#432C22×C12711yescharacteristic
464#432C22×C12711yescharacteristic
465#432C22×C12711yescharacteristic
466#432C22×C12711yescharacteristic
467#432C22×C12711yescharacteristic
468#432C22×C12711yescharacteristic
469#432C22×C12711yescharacteristic
470#424—21no—
471#408—21no—
472C4×M16C22×C12711yescharacteristic
473C4×M16C22×C12711yescharacteristic
474C2×#97C22×C12711yescharacteristic
475C2×#97C22×C12711yescharacteristic
476C2×#97C22×C12711yescharacteristic
477#330C22×C12711yescharacteristic
478#330C22×C12711yescharacteristic
479#330C22×C12711yescharacteristic
480#330C22×C12711yescharacteristic
481#330C22×C12711yescharacteristic
482#330C22×C12711yescharacteristic
483#330C22×C12711yescharacteristic
484#330C22×C12711yescharacteristic
485#330C22×C12711yescharacteristic
486#330C22×C12711yescharacteristic
487#330C22×C12711yescharacteristic
488#330C22×C12711yescharacteristic
489#329C22×C12711yescharacteristic
490#329C22×C12711yescharacteristic
491#329C22×C12711yescharacteristic
492#329C22×C12711yescharacteristic
493C2×#41—21no—
494C2×#41D4×C12711yescharacteristic
495C2×M16—21no—
496C2×M16—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—21no—
500C4⋊Q8—21no—
501C4⋊Q8C2×C4×C12711yescharacteristic
502C4⋊Q8C2×C4×C12711yescharacteristic
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#125—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125C2×C4×C12711yescharacteristic
520#125C2×C4×C12711yescharacteristic
521#125C2×C4×C12711yescharacteristic
522#125C2×C4×C12711yescharacteristic
523#125C23×C12711yescharacteristic
524#125C23×C12711yescharacteristic
525#125C23×C12711yescharacteristic
526#124C23×C12711yescharacteristic
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8C2×C4×C12711yescharacteristic
545C22⋊Q8C2×C4×C12711yescharacteristic
546C22⋊Q8C2×C4×C12711yescharacteristic
547#121—21no—
548#121—21no—
549#121C2×C4×C12711yescharacteristic
550#121C2×C4×C12711yescharacteristic
551#121C2×C4×C12711yescharacteristic
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8C2×C4×C12711yescharacteristic
556C4×Q8C2×C4×C12711yescharacteristic
557C4×Q8C2×C4×C12711yescharacteristic
558C4×Q8C2×C4×C12711yescharacteristic
559C4×Q8D4×C12711yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4C2×C4×C12711yescharacteristic
567C4×D4C2×C4×C12711yescharacteristic
568C4×D4C2×C4×C12711yescharacteristic
569C4×D4C2×C4×C12711yescharacteristic
570C4×D4C2×C4×C12711yescharacteristic
571C4×D4C2×C4×C12711yescharacteristic
572C4×D4D4×C12711yescharacteristic
573C4×D4D4×C12711yescharacteristic
574C4×D4D4×C12711yescharacteristic
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117C2×C4×C12711yescharacteristic
581#117C2×C4×C12711yescharacteristic
582#117D4×C12711yescharacteristic
583#117D4×C12711yescharacteristic
584#117D4×C12711yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4C2×C4×C12711yescharacteristic
591C2×C4⋊C4C2×C4×C12711yescharacteristic
592C2×C4⋊C4C2×C4×C12711yescharacteristic
593C2×C4⋊C4C2×C4×C12711yescharacteristic
594C2×C42C23×C12711yescharacteristic
595C2×C42C23×C12711yescharacteristic
596C2×C42C23×C12711yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8—21no—
610C22⋊C8—21no—
611#97—21no—
612#97—21no—
613#97—21no—
614#97C23×C12711yescharacteristic
615#97C23×C12711yescharacteristic
616#97C23×C12711yescharacteristic
617#97C23×C12711yescharacteristic
618#97C23×C12711yescharacteristic
619#97C23×C12711yescharacteristic
620#97C23×C12711yescharacteristic
621#97C23×C12711yescharacteristic
622C4×C8—21no—
623C4×C8—21no—
624#41—42no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C22⋊C4×C12711yescharacteristic
629C2×Q8C22×C4×C12711yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C22⋊C4×C12711yescharacteristic
634C2×D4C22⋊C4×C12711yescharacteristic
635C2×D4C22⋊C4×C12711yescharacteristic
636C2×D4C22×C4×C12711yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C22×C4×C12711yescharacteristic
645C22×C4C22×C4×C12711yescharacteristic
646C22×C4C22×C4×C12711yescharacteristic
647C22×C4C2×D4×C12711yescharacteristic
648C22×C4C2×D4×C12711yescharacteristic
649C22×C4C2×D4×C12711yescharacteristic
650C22×C4C2×D4×C12711yescharacteristic
651C22×C4C2×D4×C12711yescharacteristic
652C22×C4C2×D4×C12711yescharacteristic
653M16—42no—
654M16—42no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4C22⋊C4×C12711yescharacteristic
693C4⋊C4C22⋊C4×C12711yescharacteristic
694C4⋊C4C22⋊C4×C12711yescharacteristic
695C4⋊C4C22⋊C4×C12711yescharacteristic
696C4⋊C4C22⋊C4×C12711yescharacteristic
697C4⋊C4C22⋊C4×C12711yescharacteristic
698C4⋊C4C22×C4×C12711yescharacteristic
699C4⋊C4C22×C4×C12711yescharacteristic
700C4⋊C4C22×C4×C12711yescharacteristic
701C4⋊C4C22×C4×C12711yescharacteristic
702C4⋊C4C22×C4×C12711yescharacteristic
703C4⋊C4C22×C4×C12711yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4C22⋊C4×C12711yescharacteristic
718C22⋊C4C22⋊C4×C12711yescharacteristic
719C22⋊C4C22⋊C4×C12711yescharacteristic
720C22⋊C4C22⋊C4×C12711yescharacteristic
721C22⋊C4C22⋊C4×C12711yescharacteristic
722C22⋊C4C22⋊C4×C12711yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42C22×C4×C12711yescharacteristic
729C42C22×C4×C12711yescharacteristic
730C42C22×C4×C12711yescharacteristic
731C42C2×D4×C12711yescharacteristic
732C42C2×D4×C12711yescharacteristic
733C42C2×D4×C12711yescharacteristic
734C42C2×D4×C12711yescharacteristic
735C42C2×D4×C12711yescharacteristic
736C42C2×D4×C12711yescharacteristic
737C42C24×C12711yescharacteristic
738C23—21no—
739C23C2×C22⋊C4×C12711yescharacteristic
740C23C2×C22⋊C4×C12711yescharacteristic
741C23C2×C22⋊C4×C12711yescharacteristic
742Q8—41no—
743Q8—41no—
744Q8—42no—
745Q8—81no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—81no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4C2×C22⋊C4×C12711yescharacteristic
777C2×C4C2×C22⋊C4×C12711yescharacteristic
778C2×C4C2×C22⋊C4×C12711yescharacteristic
779C2×C4C2×C22⋊C4×C12711yescharacteristic
780C2×C4C2×C22⋊C4×C12711yescharacteristic
781C2×C4C2×C22⋊C4×C12711yescharacteristic
782C2×C4C2×C22⋊C4×C12711yescharacteristic
783C2×C4C2×C22⋊C4×C12711yescharacteristic
784C2×C4C2×C22⋊C4×C12711yescharacteristic
785C2×C4C23×C4×C12711yescharacteristic
786C2×C4C22×D4×C12711yescharacteristic
787C2×C4C22×D4×C12711yescharacteristic
788C8—22no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22#421×C12712yes—
808C22C22×C22⋊C4×C12711yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—81no—
832C2C127×#288911yescharacteristic
833C2C2×#421×C12711yescharacteristic
834C2C127×#290111yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC42C24×C127
prime radicalC127×#3515C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C4×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2970C2semidirect
3. C127×#2923C2semidirect
4. C127×#1537C2semidirect
5. C127×#1535C2semidirect
6. C127×#1535C2semidirect
7. C127×#1534C2semidirect
8. C127×#1532C2semidirect
9. C127×#1532C2semidirect
10. C127×#1531C2semidirect
11. C127×#1529C2semidirect
12. C127×#1528C2semidirect
13. C127×#1528C2semidirect
14. C127×#1524C2semidirect
15. C2×#330×C127C2semidirect
410. #17680C127direct (N × H)
419. #2970C2×C127semidirect
420. #2923C2×C127semidirect
421. #1537C2×C127semidirect
422. #1535C2×C127semidirect
423. #1535C2×C127semidirect
424. #1534C2×C127semidirect
425. #1532C2×C127semidirect
426. #1532C2×C127semidirect
427. #1531C2×C127semidirect
428. #1529C2×C127semidirect
429. #1528C2×C127semidirect
430. #1528C2×C127semidirect
431. #1524C2×C127semidirect
432. C2×#330C2×C127semidirect
433. C127#17680direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35152
C127×#29702
C127×#29232
C127×#15372
C127×#15352
C127×#15342
C127×#15322
C127×#15312
C127×#15292
C127×#15282
C127×#15242
C2×#330×C1272
#17680127