Finite Group Databasebeta

← C127×#16718 #44580391

Subgroups — C127×#16718 #44580391

Order 32512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1445C211yesmaximal, characteristic, complemented
2C127×#1445C211yesmaximal, characteristic, complemented
3C127×#1443C211yesmaximal, characteristic, complemented
4C127×#1443C211yesmaximal, characteristic, complemented
5C127×#1443C211yesmaximal, characteristic, complemented
6C127×#1443C211yesmaximal, characteristic, complemented
7C127×#1442C211yesmaximal, characteristic, complemented
8C127×#1442C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic
10C127×#1440C211yesmaximal, characteristic
11C127×#1439C211yesmaximal, characteristic
12C127×#1439C211yesmaximal, characteristic
13C127×C22⋊#95C211yesmaximal, characteristic
14C127×C22⋊#95C211yesmaximal, characteristic
15C127×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C25×C127C2311yescharacteristic
52C23×C4×C127—22no—
53C23×C4×C127—22no—
54C23×C4×C127—22no—
55C23×C4×C127—41no—
56C23×C4×C127—41no—
57C23×C4×C127—41no—
58C23×C4×C127—41no—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—41no—
76C2×C4⋊C4×C127—41no—
77C2×C4⋊C4×C127—41no—
78C2×C4⋊C4×C127—41no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—41no—
90C2×C22⋊C4×C127—41no—
91C2×C22⋊C4×C127—41no—
92C2×C22⋊C4×C127—41no—
93C2×C22⋊C4×C127—41no—
94C2×C22⋊C4×C127—41no—
95C2×C22⋊C4×C127—41no—
96C2×C22⋊C4×C127—41no—
97#95×C127—22no—
98#95×C127—22no—
99#95×C127—22no—
100#95×C127—22no—
101#95×C127—22no—
102#95×C127—22no—
103#95×C127—41no—
104#95×C127—41no—
105#95×C127—41no—
106#95×C127—41no—
107#95×C127—41no—
108#95×C127—41no—
109#95×C127—41no—
110#95×C127—41no—
111#95×C127—41no—
112#95×C127—41no—
113#95×C127—41no—
114#95×C127—41no—
115#95×C127—41no—
116#95×C127—41no—
117#95×C127—41no—
118#95×C127—41no—
119#95×C127—41no—
120#95×C127—41no—
121#95×C127—41no—
122#95×C127—41no—
123C24×C127—21no—
124C24×C127—21no—
125C24×C127—21no—
126C24×C127—21no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—21no—
133C24×C127—21no—
134C24×C127—21no—
135C24×C127#4112yes—
136C24×C127#4112yes—
137C24×C127#4112yes—
138C24×C127C2411yescharacteristic
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
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×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—44no—
234C22×C4×C127—44no—
235C22×C4×C127—44no—
236C22×C4×C127—44no—
237C22×C4×C127—44no—
238C22×C4×C127—44no—
239C22×C4×C127—44no—
240C22×C4×C127#4112yes—
241C22×C4×C127#4112yes—
242C22×C4×C127#4112yes—
243C22×C4×C127#4112yes—
244C4⋊C4×C127—44no—
245C4⋊C4×C127—44no—
246C22⋊C4×C127—44no—
247C22⋊C4×C127—44no—
248C22⋊C4×C127—44no—
249C22⋊C4×C127—44no—
250C22⋊C4×C127—44no—
251C22⋊C4×C127—44no—
252C23×C127—22no—
253C23×C127—22no—
254C23×C127—22no—
255C23×C127—22no—
256C23×C127—22no—
257C23×C127—22no—
258C23×C127—22no—
259C23×C127—22no—
260C23×C127—22no—
261C23×C127—22no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—22no—
266C23×C127—22no—
267C23×C127—22no—
268C23×C127—22no—
269C23×C127—22no—
270C23×C127—41no—
271C23×C127—41no—
272C23×C127—41no—
273C23×C127—41no—
274C23×C127—41no—
275C23×C127—41no—
276C23×C127—41no—
277C23×C127—41no—
278C23×C127—41no—
279C23×C127—41no—
280C23×C127—41no—
281C23×C127—41no—
282C23×C127—41no—
283C23×C127—41no—
284C23×C127—41no—
285C23×C127—41no—
286C23×C127#12614yes—
287C23×C127C2×#4111yescharacteristic
288C23×C127C2×#4111yescharacteristic
289C23×C127C2×#4111yescharacteristic
290C23×C127C2×#4111yescharacteristic
291C23×C127C2×#4111yescharacteristic
292C23×C127C2×#4111yescharacteristic
293C23×C127C2×#4111yescharacteristic
294C23×C127H(5,𝔽2)11yescharacteristic
295C23×C127H(5,𝔽2)11yescharacteristic
296C23×C127H(5,𝔽2)11yescharacteristic
297C23×C127H(5,𝔽2)11yescharacteristic
298C23×C127H(5,𝔽2)11yescharacteristic
299C23×C127H(5,𝔽2)11yescharacteristic
300C23×C1272−1+411yescharacteristic
301C23×C1272−1+411yescharacteristic
302C2×C4×C127—22no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—22no—
310C2×C4×C127—22no—
311C2×C4×C127—22no—
312C2×C4×C127—22no—
313C2×C4×C127—22no—
314C2×C4×C127—416no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—41no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
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—41no—
352C2×C4×C127—41no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—41no—
356C2×C4×C127—41no—
357C2×C4×C127—41no—
358C2×C4×C127—41no—
359C2×C4×C127—41no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—41no—
366C2×C4×C127—41no—
367C2×C4×C127—41no—
368C2×C4×C127—41no—
369C2×C4×C127—41no—
370C2×C4×C127—41no—
371C2×C4×C127—41no—
372C2×C4×C127—41no—
373C2×C4×C127—41no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—41no—
381C2×C4×C127—41no—
382C2×C4×C127—41no—
383C2×C4×C127—41no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—41no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C22×C127—24no—
402C22×C127—24no—
403C22×C127—24no—
404C22×C127—42no—
405C22×C127—42no—
406C22×C127—42no—
407C22×C127—42no—
408C22×C127—42no—
409C22×C127—42no—
410C22×C127—42no—
411C22×C127—42no—
412C22×C127—42no—
413C22×C127—42no—
414C22×C127—42no—
415C22×C127—42no—
416C22×C127C2×#12611yescharacteristic
417C22×C127#52911yescharacteristic
418C22×C127#52911yescharacteristic
419C22×C127#53811yescharacteristic
420C22×C127#53811yescharacteristic
421C22×C127#53811yescharacteristic
422C22×C127#53811yescharacteristic
423C22×C127#53811yescharacteristic
424C22×C127#53811yescharacteristic
425C22×C127#53811yescharacteristic
426C22×C127#53811yescharacteristic
427C22×C127#53911yescharacteristic
428C22×C127#53911yescharacteristic
429C22×C127#53911yescharacteristic
430C22×C127#53911yescharacteristic
431C22×C127#54011yescharacteristic
432C22×C127#54011yescharacteristic
433C22×C127#54211yescharacteristic
434C22×C127#54211yescharacteristic
435C22×C127#55111yescharacteristic
436C22×C127#55111yescharacteristic
437C22×C127#55111yescharacteristic
438C22×C127#55111yescharacteristic
439C22×C127#55111yescharacteristic
440C22×C127#55211yescharacteristic
441C22×C127#55211yescharacteristic
442C22×C127#55211yescharacteristic
443C22×C127#55211yescharacteristic
444C22×C127#55311yescharacteristic
445C22×C127#55311yescharacteristic
446C22×C127#55911yescharacteristic
447C22×C127#56011yescharacteristic
448C22×C127#56211yescharacteristic
449C22×C127#56211yescharacteristic
450C22×C127#56311yescharacteristic
451C4×C127—42no—
452C4×C127—42no—
453C4×C127—42no—
454C4×C127—42no—
455C4×C127—81no—
456C4×C127—81no—
457C4×C127—81no—
458C4×C127—81no—
459C4×C127—81no—
460C4×C127—81no—
461C4×C127—81no—
462C4×C127—81no—
463C4×C127—81no—
464C4×C127—81no—
465#16718C12711yesmaximal, characteristic, direct product factor, Sylow
466C2×C127—44no—
467C2×C127#249311yescharacteristic
468C2×C127#251011yescharacteristic
469C2×C127#251711yescharacteristic
470C2×C127#264311yescharacteristic
471C2×C127#264811yescharacteristic
472C2×C127#265311yescharacteristic
473C2×C127#273511yescharacteristic
474C2×C127#273811yescharacteristic
475C2×C127#274111yescharacteristic
476C2×C127#274311yescharacteristic
477C2×C127#275011yescharacteristic
478C2×C127#275111yescharacteristic
479C2×C127#277011yescharacteristic
480C2×C127#279711yescharacteristic
481C2×C127#282711yescharacteristic
482#1445C2×C12711yescharacteristic, complemented
483#1445C2×C12711yescharacteristic, complemented
484#1443C2×C12711yescharacteristic, complemented
485#1443C2×C12711yescharacteristic, complemented
486#1443C2×C12711yescharacteristic, complemented
487#1443C2×C12711yescharacteristic, complemented
488#1442C2×C12711yescharacteristic, complemented
489#1442C2×C12711yescharacteristic, complemented
490#1440C2×C12711yescharacteristic
491#1440C2×C12711yescharacteristic
492#1439C2×C12711yescharacteristic
493#1439C2×C12711yescharacteristic
494C22⋊#95C2×C12711yescharacteristic
495C22⋊#95C2×C12711yescharacteristic
496C22⋊#95C2×C12711yescharacteristic
497C127#1671811yescharacteristic, direct product factor, Sylow
498C24×C4C22×C12711yescharacteristic
499C22×C4⋊C4C22×C12711yescharacteristic
500C22×C4⋊C4C22×C12711yescharacteristic
501C22×C22⋊C4C22×C12711yescharacteristic
502C22×C22⋊C4C22×C12711yescharacteristic
503C22×C22⋊C4C22×C12711yescharacteristic
504C22×C22⋊C4C22×C12711yescharacteristic
505C22×C22⋊C4C22×C12711yescharacteristic
506C22×C22⋊C4C22×C12711yescharacteristic
507C2×#95C22×C12711yescharacteristic
508C2×#95C22×C12711yescharacteristic
509C2×#95C22×C12711yescharacteristic
510C2×#95C22×C12711yescharacteristic
511C2×#95C22×C12711yescharacteristic
512C2×#95C22×C12711yescharacteristic
513C2×#95C22×C12711yescharacteristic
514C2×#95C22×C12711yescharacteristic
515C2×#95C22×C12711yescharacteristic
516C2×#95C22×C12711yescharacteristic
517C2×#95C22×C12711yescharacteristic
518C2×#95C22×C12711yescharacteristic
519C2×#95C22×C12711yescharacteristic
520C2×#95C22×C12711yescharacteristic
521C2×#95C22×C12711yescharacteristic
522C2×#95C22×C12711yescharacteristic
523C2×#95C22×C12711yescharacteristic
524C2×#95C22×C12711yescharacteristic
525C2×#95C22×C12711yescharacteristic
526C2×#95C22×C12711yescharacteristic
527C2×#95C22×C12711yescharacteristic
528C2×#95C22×C12711yescharacteristic
529C2×#95C22×C12711yescharacteristic
530C2×#95C22×C12711yescharacteristic
531C2×#95C22×C12711yescharacteristic
532C2×#95C22×C12711yescharacteristic
533C25C23×C12711yescharacteristic
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4C23×C12711yescharacteristic
542C23×C4C23×C12711yescharacteristic
543C23×C4C23×C12711yescharacteristic
544C23×C4C23×C12711yescharacteristic
545C23×C4C23×C12711yescharacteristic
546C23×C4C23×C12711yescharacteristic
547C23×C4C23×C12711yescharacteristic
548C23×C4C23×C12711yescharacteristic
549C23×C4C23×C12711yescharacteristic
550C23×C4C23×C12711yescharacteristic
551C23×C4C23×C12711yescharacteristic
552C23×C4C23×C12711yescharacteristic
553C23×C4C23×C12711yescharacteristic
554C23×C4C23×C12711yescharacteristic
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—41no—
586#95—41no—
587#95—41no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24#41×C12712yes—
618C24#41×C12712yes—
619C24#41×C12712yes—
620C24C24×C12711yescharacteristic
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
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—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4#41×C12712yes—
723C22×C4#41×C12712yes—
724C22×C4#41×C12712yes—
725C22×C4#41×C12712yes—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23#126×C12714yes—
769C23C2×#41×C12711yescharacteristic
770C23C2×#41×C12711yescharacteristic
771C23C2×#41×C12711yescharacteristic
772C23C2×#41×C12711yescharacteristic
773C23C2×#41×C12711yescharacteristic
774C23C2×#41×C12711yescharacteristic
775C23C2×#41×C12711yescharacteristic
776C23H(5,𝔽2)×C12711yescharacteristic
777C23H(5,𝔽2)×C12711yescharacteristic
778C23H(5,𝔽2)×C12711yescharacteristic
779C23H(5,𝔽2)×C12711yescharacteristic
780C23H(5,𝔽2)×C12711yescharacteristic
781C23H(5,𝔽2)×C12711yescharacteristic
782C232−1+4×C12711yescharacteristic
783C232−1+4×C12711yescharacteristic
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—416no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22C2×#126×C12711yescharacteristic
899C22#529×C12711yescharacteristic
900C22#529×C12711yescharacteristic
901C22#538×C12711yescharacteristic
902C22#538×C12711yescharacteristic
903C22#538×C12711yescharacteristic
904C22#538×C12711yescharacteristic
905C22#538×C12711yescharacteristic
906C22#538×C12711yescharacteristic
907C22#538×C12711yescharacteristic
908C22#538×C12711yescharacteristic
909C22#539×C12711yescharacteristic
910C22#539×C12711yescharacteristic
911C22#539×C12711yescharacteristic
912C22#539×C12711yescharacteristic
913C22#540×C12711yescharacteristic
914C22#540×C12711yescharacteristic
915C22#542×C12711yescharacteristic
916C22#542×C12711yescharacteristic
917C22#551×C12711yescharacteristic
918C22#551×C12711yescharacteristic
919C22#551×C12711yescharacteristic
920C22#551×C12711yescharacteristic
921C22#551×C12711yescharacteristic
922C22#552×C12711yescharacteristic
923C22#552×C12711yescharacteristic
924C22#552×C12711yescharacteristic
925C22#552×C12711yescharacteristic
926C22#553×C12711yescharacteristic
927C22#553×C12711yescharacteristic
928C22#559×C12711yescharacteristic
929C22#560×C12711yescharacteristic
930C22#562×C12711yescharacteristic
931C22#562×C12711yescharacteristic
932C22#563×C12711yescharacteristic
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—81no—
938C4—81no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C2—44no—
948C2C127×#249311yescharacteristic
949C2C127×#251011yescharacteristic
950C2C127×#251711yescharacteristic
951C2C127×#264311yescharacteristic
952C2C127×#264811yescharacteristic
953C2C127×#265311yescharacteristic
954C2C127×#273511yescharacteristic
955C2C127×#273811yescharacteristic
956C2C127×#274111yescharacteristic
957C2C127×#274311yescharacteristic
958C2C127×#275011yescharacteristic
959C2C127×#275111yescharacteristic
960C2C127×#277011yescharacteristic
961C2C127×#279711yescharacteristic
962C2C127×#282711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#1445C2semidirect
2. C127×#1445C2semidirect
3. C127×#1443C2semidirect
4. C127×#1443C2semidirect
5. C127×#1443C2semidirect
6. C127×#1443C2semidirect
7. C127×#1442C2semidirect
8. C127×#1442C2semidirect
465. #16718C127direct (N × H)
482. #1445C2×C127semidirect
483. #1445C2×C127semidirect
484. #1443C2×C127semidirect
485. #1443C2×C127semidirect
486. #1443C2×C127semidirect
487. #1443C2×C127semidirect
488. #1442C2×C127semidirect
489. #1442C2×C127semidirect
497. C127#16718direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#14452
C127×#14432
C127×#14422
C127×#14402
C127×#14392
C127×C22⋊#952
#16718127