Finite Group Databasebeta

← C127×#15369 #44579042

Subgroups — C127×#15369 #44579042

Order 32512.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C2×#386×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C211yesmaximal, characteristic, complemented
4C2×#386×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#381×C127C211yesmaximal, characteristic, complemented
7C127×#1443C211yesmaximal, characteristic, complemented
8C127×#1443C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1438C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C24×C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35#392×C127—24no—
36#386×C127—24no—
37#386×C127—24no—
38#386×C127—24no—
39#386×C127—24no—
40#381×C127—24no—
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
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C25×C127C2311yescharacteristic
58C25×C127C2311yescharacteristic
59C25×C127C2311yescharacteristic
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—22no—
72C22×D4×C127—22no—
73C22×D4×C127—22no—
74C22×D4×C127—41no—
75C22×D4×C127—41no—
76C22×D4×C127—41no—
77C22×D4×C127—41no—
78C22×D4×C127—41no—
79C22×D4×C127—41no—
80C22×D4×C127D414yes—
81C23×C4×C127—22no—
82C23×C4×C127—22no—
83C23×C4×C127—22no—
84C23×C4×C127—22no—
85C23×C4×C127—22no—
86C23×C4×C127—22no—
87C23×C4×C127—22no—
88C23×C4×C127—22no—
89C23×C4×C127—41no—
90C23×C4×C127—41no—
91C23×C4×C127—41no—
92C23×C4×C127—41no—
93C23×C4×C127—41no—
94C23×C4×C127—41no—
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2311yescharacteristic
102C23×C4×C127C2311yescharacteristic
103C23×C4×C127C2311yescharacteristic
104C23×C4×C127C2311yescharacteristic
105C23×C4×C127C2311yescharacteristic
106C23×C4×C127C2311yescharacteristic
107C2×C4⋊C4×C127—41no—
108C2×C4⋊C4×C127—41no—
109C2×C4⋊C4×C127—41no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—22no—
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127—22no—
126C2×C22⋊C4×C127—22no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127—22no—
130C2×C22⋊C4×C127—41no—
131C2×C22⋊C4×C127—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×C127—41no—
134C2×C22⋊C4×C127—41no—
135C2×C22⋊C4×C127—41no—
136C2×C22⋊C4×C127—41no—
137C2×C22⋊C4×C127—41no—
138C2×C22⋊C4×C127—41no—
139C2×C22⋊C4×C127—41no—
140C2×C22⋊C4×C127—41no—
141C2×C22⋊C4×C127—41no—
142C2×C22⋊C4×C127—41no—
143C2×C22⋊C4×C127—41no—
144C2×C22⋊C4×C127—41no—
145C2×C22⋊C4×C127—41no—
146C2×C22⋊C4×C127—41no—
147C2×C22⋊C4×C127—41no—
148C2×C22⋊C4×C127D414yescomplemented
149#95×C127—22no—
150#95×C127—22no—
151#95×C127—22no—
152#95×C127—22no—
153#95×C127—22no—
154#95×C127—22no—
155#95×C127—22no—
156#95×C127—22no—
157#95×C127—22no—
158#95×C127—22no—
159#95×C127—22no—
160#95×C127—22no—
161#95×C127—41no—
162#95×C127—41no—
163#95×C127—41no—
164#95×C127D414yescomplemented
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127—21no—
183C24×C127—21no—
184C24×C127—21no—
185C24×C127—21no—
186C24×C127—21no—
187C24×C127—21no—
188C24×C127—21no—
189C24×C127—21no—
190C24×C127—21no—
191C24×C127—21no—
192C24×C127—21no—
193C24×C127—21no—
194C24×C127—21no—
195C24×C127—21no—
196C24×C127—21no—
197C24×C127—21no—
198C24×C127—21no—
199C24×C127—21no—
200C24×C127—21no—
201C24×C127—21no—
202C24×C127—21no—
203C24×C127C2×D412yes—
204C24×C127C2×D412yes—
205C24×C127C2×D412yes—
206C24×C127#4112yes—
207C24×C127#4112yes—
208C24×C127#4112yes—
209C24×C127#4112yes—
210C24×C127C2411yescharacteristic
211C2×D4×C127—28no—
212C2×D4×C127—28no—
213C2×D4×C127—28no—
214C2×D4×C127—28no—
215C2×D4×C127—44no—
216C2×D4×C127—44no—
217C2×D4×C127—44no—
218C2×D4×C127—44no—
219C2×D4×C127—44no—
220C2×D4×C127—44no—
221C2×D4×C127—44no—
222C2×D4×C127—44no—
223C2×D4×C127—44no—
224C2×D4×C127—44no—
225C2×D4×C127—44no—
226C2×D4×C127—44no—
227C2×D4×C127—44no—
228C2×D4×C127—44no—
229C2×D4×C127—44no—
230C2×D4×C127—44no—
231C2×D4×C127—44no—
232C22×C4×C127—28no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—21no—
269C22×C4×C127—21no—
270C22×C4×C127—21no—
271C22×C4×C127—21no—
272C22×C4×C127—21no—
273C22×C4×C127—21no—
274C22×C4×C127—21no—
275C22×C4×C127—21no—
276C22×C4×C127—21no—
277C22×C4×C127—21no—
278C22×C4×C127—21no—
279C22×C4×C127—21no—
280C22×C4×C127—21no—
281C22×C4×C127—21no—
282C22×C4×C127—21no—
283C22×C4×C127—21no—
284C22×C4×C127—21no—
285C22×C4×C127—21no—
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×C127—21no—
300C22×C4×C127—21no—
301C22×C4×C127—21no—
302C22×C4×C127—21no—
303C22×C4×C127—21no—
304C22×C4×C127—21no—
305C22×C4×C127—21no—
306C22×C4×C127—21no—
307C22×C4×C127—21no—
308C22×C4×C127—21no—
309C22×C4×C127—44no—
310C22×C4×C127—44no—
311C22×C4×C127—44no—
312C22×C4×C127—44no—
313C22×C4×C127—44no—
314C22×C4×C127—44no—
315C22×C4×C127—44no—
316C22×C4×C127—44no—
317C22×C4×C127—44no—
318C22×C4×C127—44no—
319C22×C4×C127—44no—
320C22×C4×C127—44no—
321C22×C4×C127—44no—
322C22×C4×C127C2×D412yes—
323C22×C4×C127C2×D412yes—
324C22×C4×C127C2×D412yes—
325C22×C4×C127C2×D412yes—
326C22×C4×C127C2×D412yes—
327C22×C4×C127C2×D412yes—
328C22×C4×C127#4112yes—
329C22×C4×C127#4112yes—
330C4⋊C4×C127—44no—
331C22⋊C4×C127—44no—
332C22⋊C4×C127—44no—
333C22⋊C4×C127—44no—
334C22⋊C4×C127—44no—
335C22⋊C4×C127—44no—
336C22⋊C4×C127—44no—
337C22⋊C4×C127—44no—
338C22⋊C4×C127—44no—
339C22⋊C4×C127—44no—
340C22⋊C4×C127—44no—
341C22⋊C4×C127—44no—
342C22⋊C4×C127—44no—
343C22⋊C4×C127—44no—
344C23×C127—22no—
345C23×C127—22no—
346C23×C127—22no—
347C23×C127—22no—
348C23×C127—22no—
349C23×C127—22no—
350C23×C127—22no—
351C23×C127—22no—
352C23×C127—22no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—22no—
357C23×C127—22no—
358C23×C127—22no—
359C23×C127—22no—
360C23×C127—22no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—22no—
366C23×C127—22no—
367C23×C127—22no—
368C23×C127—22no—
369C23×C127—22no—
370C23×C127—22no—
371C23×C127—22no—
372C23×C127—22no—
373C23×C127—22no—
374C23×C127—22no—
375C23×C127—22no—
376C23×C127—22no—
377C23×C127—22no—
378C23×C127—22no—
379C23×C127—22no—
380C23×C127—22no—
381C23×C127—22no—
382C23×C127—22no—
383C23×C127—22no—
384C23×C127—22no—
385C23×C127—22no—
386C23×C127—22no—
387C23×C127—41no—
388C23×C127—41no—
389C23×C127—41no—
390C23×C127—41no—
391C23×C127—41no—
392C23×C127—41no—
393C23×C127—41no—
394C23×C127—41no—
395C23×C127—41no—
396C23×C127—41no—
397C23×C127—41no—
398C23×C127—41no—
399C23×C127—41no—
400C23×C127—41no—
401C23×C127—41no—
402C23×C127—41no—
403C23×C127—41no—
404C23×C127—41no—
405C23×C127—41no—
406C23×C127—41no—
407C23×C127—41no—
408C23×C127—41no—
409C23×C127—41no—
410C23×C127—41no—
411C23×C127—41no—
412C23×C127—41no—
413C23×C127—41no—
414C23×C127—41no—
415C23×C127—41no—
416C23×C127—41no—
417C23×C127—41no—
418C23×C127—41no—
419C23×C127—41no—
420C23×C127—41no—
421C23×C127—41no—
422C23×C127—41no—
423C23×C127—41no—
424C23×C127—41no—
425C23×C127—41no—
426C23×C127—41no—
427C23×C127—41no—
428C23×C127—41no—
429C23×C127—41no—
430C23×C127—41no—
431C23×C127—41no—
432C23×C127—41no—
433C23×C127—41no—
434C23×C127—41no—
435C23×C127—41no—
436C23×C127—41no—
437C23×C127—41no—
438C23×C127—41no—
439C23×C127—41no—
440C23×C127—41no—
441C23×C127—41no—
442C23×C127—41no—
443C23×C127—41no—
444C23×C127—41no—
445C23×C127—41no—
446C23×C127—41no—
447C23×C127#12114yes—
448C23×C127#12314yes—
449C23×C127C22×D411yescharacteristic
450C23×C127C22×D411yescharacteristic
451C23×C127C22×D411yescharacteristic
452C23×C127C2×#4111yescharacteristic
453C23×C127C2×#4111yescharacteristic
454C23×C127C2×#4111yescharacteristic
455C23×C127C2×#4111yescharacteristic
456C23×C127C2×#4111yescharacteristic
457C23×C127C2×#4111yescharacteristic
458C23×C127H(5,𝔽2)11yescharacteristic
459C23×C127H(5,𝔽2)11yescharacteristic
460C23×C127H(5,𝔽2)11yescharacteristic
461C23×C127H(5,𝔽2)11yescharacteristic
462C23×C127H(5,𝔽2)11yescharacteristic
463C23×C127H(5,𝔽2)11yescharacteristic
464D4×C127—416no—
465D4×C127—416no—
466D4×C127—416no—
467C2×C4×C127—22no—
468C2×C4×C127—22no—
469C2×C4×C127—22no—
470C2×C4×C127—22no—
471C2×C4×C127—22no—
472C2×C4×C127—22no—
473C2×C4×C127—22no—
474C2×C4×C127—22no—
475C2×C4×C127—22no—
476C2×C4×C127—22no—
477C2×C4×C127—22no—
478C2×C4×C127—22no—
479C2×C4×C127—22no—
480C2×C4×C127—22no—
481C2×C4×C127—22no—
482C2×C4×C127—22no—
483C2×C4×C127—22no—
484C2×C4×C127—22no—
485C2×C4×C127—22no—
486C2×C4×C127—22no—
487C2×C4×C127—22no—
488C2×C4×C127—22no—
489C2×C4×C127—22no—
490C2×C4×C127—22no—
491C2×C4×C127—416no—
492C2×C4×C127—416no—
493C2×C4×C127—41no—
494C2×C4×C127—41no—
495C2×C4×C127—41no—
496C2×C4×C127—41no—
497C2×C4×C127—41no—
498C2×C4×C127—41no—
499C2×C4×C127—41no—
500C2×C4×C127—41no—
501C2×C4×C127—41no—
502C2×C4×C127—41no—
503C2×C4×C127—41no—
504C2×C4×C127—41no—
505C2×C4×C127—41no—
506C2×C4×C127—41no—
507C2×C4×C127—41no—
508C2×C4×C127—41no—
509C2×C4×C127—41no—
510C2×C4×C127—41no—
511C2×C4×C127—41no—
512C2×C4×C127—41no—
513C2×C4×C127—41no—
514C2×C4×C127—41no—
515C2×C4×C127—41no—
516C2×C4×C127—41no—
517C2×C4×C127—41no—
518C2×C4×C127—41no—
519C2×C4×C127—41no—
520C2×C4×C127—41no—
521C2×C4×C127—41no—
522C2×C4×C127—41no—
523C2×C4×C127—41no—
524C2×C4×C127—41no—
525C2×C4×C127—41no—
526C2×C4×C127—41no—
527C2×C4×C127—41no—
528C2×C4×C127—41no—
529C2×C4×C127—41no—
530C2×C4×C127—41no—
531C2×C4×C127—41no—
532C2×C4×C127—41no—
533C2×C4×C127—41no—
534C2×C4×C127—41no—
535C2×C4×C127—41no—
536C2×C4×C127—41no—
537C2×C4×C127—41no—
538C2×C4×C127—41no—
539C2×C4×C127—41no—
540C2×C4×C127—41no—
541C2×C4×C127—41no—
542C2×C4×C127—41no—
543C2×C4×C127—41no—
544C2×C4×C127—41no—
545C2×C4×C127—41no—
546C2×C4×C127—41no—
547C2×C4×C127—41no—
548C2×C4×C127—41no—
549C2×C4×C127—41no—
550C2×C4×C127—41no—
551C2×C4×C127—41no—
552C2×C4×C127—41no—
553C22×C127—24no—
554C22×C127—24no—
555C22×C127—24no—
556C22×C127—24no—
557C22×C127—24no—
558C22×C127—24no—
559C22×C127—42no—
560C22×C127—42no—
561C22×C127—42no—
562C22×C127—42no—
563C22×C127—42no—
564C22×C127—42no—
565C22×C127—42no—
566C22×C127—42no—
567C22×C127—42no—
568C22×C127—42no—
569C22×C127—42no—
570C22×C127—42no—
571C22×C127—42no—
572C22×C127—42no—
573C22×C127—42no—
574C22×C127—42no—
575C22×C127—42no—
576C22×C127—42no—
577C22×C127—42no—
578C22×C127—42no—
579C22×C127—42no—
580C22×C127—42no—
581C22×C127—42no—
582C22×C127—42no—
583C22×C127—42no—
584C22×C127—42no—
585C22×C127—42no—
586C22×C127—42no—
587C22×C127—42no—
588C22×C127—42no—
589C22×C127—42no—
590C22×C127—81no—
591C22×C127—81no—
592C22×C127—81no—
593C22×C127—81no—
594C22×C127—81no—
595C22×C127—81no—
596C22×C127—81no—
597C22×C127—81no—
598C22×C127C2×#12111yescharacteristic
599C22×C127C2×#12311yescharacteristic
600C22×C127#52511yescharacteristic
601C22×C127#52511yescharacteristic
602C22×C127#52511yescharacteristic
603C22×C127#52911yescharacteristic
604C22×C127#53411yescharacteristic
605C22×C127#53411yescharacteristic
606C22×C127#53511yescharacteristic
607C22×C127#53811yescharacteristic
608C22×C127#53811yescharacteristic
609C22×C127#53811yescharacteristic
610C22×C127#53811yescharacteristic
611C22×C127#54011yescharacteristic
612C22×C127#54011yescharacteristic
613C22×C127D4211yescharacteristic
614C22×C127D4211yescharacteristic
615C22×C127#54611yescharacteristic
616C22×C127#54611yescharacteristic
617C22×C127#54611yescharacteristic
618C22×C127#54611yescharacteristic
619C22×C127#54611yescharacteristic
620C22×C127#54611yescharacteristic
621C22×C127#54611yescharacteristic
622C22×C127#55011yescharacteristic
623C22×C127#55111yescharacteristic
624C22×C127#55111yescharacteristic
625C22×C127#55111yescharacteristic
626C22×C127#55111yescharacteristic
627C22×C127#55111yescharacteristic
628C22×C127#55311yescharacteristic
629C22×C127#55311yescharacteristic
630C22×C127#55311yescharacteristic
631C22×C127#56011yescharacteristic
632C22×C127#56011yescharacteristic
633C4×C127—42no—
634C4×C127—42no—
635C4×C127—42no—
636C4×C127—42no—
637C4×C127—42no—
638C4×C127—42no—
639C4×C127—42no—
640C4×C127—42no—
641C4×C127—81no—
642C4×C127—81no—
643C4×C127—81no—
644C4×C127—81no—
645#15369C12711yesmaximal, characteristic, direct product factor, Sylow
646C2×C127—44no—
647C2×C127—44no—
648C2×C127—82no—
649C2×C127#241211yescharacteristic
650C2×C127#241811yescharacteristic
651C2×C127#242411yescharacteristic
652C2×C127#244411yescharacteristic
653C2×C127#245611yescharacteristic
654C2×C127#245711yescharacteristic
655C2×C127#247111yescharacteristic
656C2×C127#253411yescharacteristic
657C2×C127#259811yescharacteristic
658C2×C127#267311yescharacteristic
659C2×C127#267811yescharacteristic
660C2×C127#268811yescharacteristic
661C2×C127#268811yescharacteristic
662C2×C127#274911yescharacteristic
663C2×C127#276011yescharacteristic
664C2×#392C2×C12711yescharacteristic
665C2×#386C2×C12711yescharacteristic, complemented
666C2×#386C2×C12711yescharacteristic, complemented
667C2×#386C2×C12711yescharacteristic, complemented
668C2×#386C2×C12711yescharacteristic, complemented
669C2×#381C2×C12711yescharacteristic, complemented
670#1443C2×C12711yescharacteristic, complemented
671#1443C2×C12711yescharacteristic, complemented
672#1440C2×C12711yescharacteristic, complemented
673#1439C2×C12711yescharacteristic, complemented
674#1439C2×C12711yescharacteristic, complemented
675#1439C2×C12711yescharacteristic, complemented
676#1438C2×C12711yescharacteristic, complemented
677#1438C2×C12711yescharacteristic, complemented
678C22⋊#95C2×C12711yescharacteristic, complemented
679C127#1536911yescharacteristic, direct product factor, Sylow
680C23×D4C22×C12711yescharacteristic
681C23×D4C22×C12711yescharacteristic
682C23×D4C22×C12711yescharacteristic
683C24×C4C22×C12711yescharacteristic
684C24×C4C22×C12711yescharacteristic
685C22×C4⋊C4C22×C12711yescharacteristic
686C22×C22⋊C4C22×C12711yescharacteristic
687C22×C22⋊C4C22×C12711yescharacteristic
688C22×C22⋊C4C22×C12711yescharacteristic
689C22×C22⋊C4C22×C12711yescharacteristic
690C22×C22⋊C4C22×C12711yescharacteristic
691C22×C22⋊C4C22×C12711yescharacteristic
692C22×C22⋊C4C22×C12711yescharacteristic
693C22×C22⋊C4C22×C12711yescharacteristic
694C22×C22⋊C4C22×C12711yescharacteristic
695C22×C22⋊C4C22×C12711yescharacteristic
696C22×C22⋊C4C22×C12711yescharacteristic
697C22×C22⋊C4C22×C12711yescharacteristic
698C22×C22⋊C4C22×C12711yescharacteristic
699#392—24no—
700#386—24no—
701#386—24no—
702#386—24no—
703#386—24no—
704#381—24no—
705C2×#95C22×C12711yescharacteristic
706C2×#95C22×C12711yescharacteristic
707C2×#95C22×C12711yescharacteristic
708C2×#95C22×C12711yescharacteristic
709C2×#95C22×C12711yescharacteristic
710C2×#95C22×C12711yescharacteristic
711C2×#95C22×C12711yescharacteristic
712C2×#95C22×C12711yescharacteristic
713C2×#95C22×C12711yescharacteristic
714C2×#95C22×C12711yescharacteristic
715C2×#95C22×C12711yescharacteristic
716C2×#95C22×C12711yescharacteristic
717C2×#95C22×C12711yescharacteristic
718C2×#95C22×C12711yescharacteristic
719C2×#95C22×C12711yescharacteristic
720C2×#95C22×C12711yescharacteristic
721C25C23×C12711yescharacteristic
722C25C23×C12711yescharacteristic
723C25C23×C12711yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4D4×C12714yes—
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—22no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4C23×C12711yescharacteristic
760C23×C4C23×C12711yescharacteristic
761C23×C4C23×C12711yescharacteristic
762C23×C4C23×C12711yescharacteristic
763C23×C4C23×C12711yescharacteristic
764C23×C4C23×C12711yescharacteristic
765C23×C4C23×C12711yescharacteristic
766C23×C4C23×C12711yescharacteristic
767C23×C4C23×C12711yescharacteristic
768C23×C4C23×C12711yescharacteristic
769C23×C4C23×C12711yescharacteristic
770C23×C4C23×C12711yescharacteristic
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4D4×C12714yescomplemented
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—22no—
821#95—22no—
822#95—22no—
823#95—22no—
824#95—22no—
825#95—41no—
826#95—41no—
827#95—41no—
828#95D4×C12714yescomplemented
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24C2×D4×C12712yes—
868C24C2×D4×C12712yes—
869C24C2×D4×C12712yes—
870C24#41×C12712yes—
871C24#41×C12712yes—
872C24#41×C12712yes—
873C24#41×C12712yes—
874C24C24×C12711yescharacteristic
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—28no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C22×C4—28no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4C2×D4×C12712yes—
987C22×C4C2×D4×C12712yes—
988C22×C4C2×D4×C12712yes—
989C22×C4C2×D4×C12712yes—
990C22×C4C2×D4×C12712yes—
991C22×C4C2×D4×C12712yes—
992C22×C4#41×C12712yes—
993C22×C4#41×C12712yes—
994C4⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23#121×C12714yes—
1112C23#123×C12714yes—
1113C23C22×D4×C12711yescharacteristic
1114C23C22×D4×C12711yescharacteristic
1115C23C22×D4×C12711yescharacteristic
1116C23C2×#41×C12711yescharacteristic
1117C23C2×#41×C12711yescharacteristic
1118C23C2×#41×C12711yescharacteristic
1119C23C2×#41×C12711yescharacteristic
1120C23C2×#41×C12711yescharacteristic
1121C23C2×#41×C12711yescharacteristic
1122C23H(5,𝔽2)×C12711yescharacteristic
1123C23H(5,𝔽2)×C12711yescharacteristic
1124C23H(5,𝔽2)×C12711yescharacteristic
1125C23H(5,𝔽2)×C12711yescharacteristic
1126C23H(5,𝔽2)×C12711yescharacteristic
1127C23H(5,𝔽2)×C12711yescharacteristic
1128D4—416no—
1129D4—416no—
1130D4—416no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22C2×#121×C12711yescharacteristic
1263C22C2×#123×C12711yescharacteristic
1264C22#525×C12711yescharacteristic
1265C22#525×C12711yescharacteristic
1266C22#525×C12711yescharacteristic
1267C22#529×C12711yescharacteristic
1268C22#534×C12711yescharacteristic
1269C22#534×C12711yescharacteristic
1270C22#535×C12711yescharacteristic
1271C22#538×C12711yescharacteristic
1272C22#538×C12711yescharacteristic
1273C22#538×C12711yescharacteristic
1274C22#538×C12711yescharacteristic
1275C22#540×C12711yescharacteristic
1276C22#540×C12711yescharacteristic
1277C22D42×C12711yescharacteristic
1278C22D42×C12711yescharacteristic
1279C22#546×C12711yescharacteristic
1280C22#546×C12711yescharacteristic
1281C22#546×C12711yescharacteristic
1282C22#546×C12711yescharacteristic
1283C22#546×C12711yescharacteristic
1284C22#546×C12711yescharacteristic
1285C22#546×C12711yescharacteristic
1286C22#550×C12711yescharacteristic
1287C22#551×C12711yescharacteristic
1288C22#551×C12711yescharacteristic
1289C22#551×C12711yescharacteristic
1290C22#551×C12711yescharacteristic
1291C22#551×C12711yescharacteristic
1292C22#553×C12711yescharacteristic
1293C22#553×C12711yescharacteristic
1294C22#553×C12711yescharacteristic
1295C22#560×C12711yescharacteristic
1296C22#560×C12711yescharacteristic
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C2—44no—
1310C2—44no—
1311C2—82no—
1312C2C127×#241211yescharacteristic
1313C2C127×#241811yescharacteristic
1314C2C127×#242411yescharacteristic
1315C2C127×#244411yescharacteristic
1316C2C127×#245611yescharacteristic
1317C2C127×#245711yescharacteristic
1318C2C127×#247111yescharacteristic
1319C2C127×#253411yescharacteristic
1320C2C127×#259811yescharacteristic
1321C2C127×#267311yescharacteristic
1322C2C127×#267811yescharacteristic
1323C2C127×#268811yescharacteristic
1324C2C127×#268811yescharacteristic
1325C2C127×#274911yescharacteristic
1326C2C127×#276011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#386×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#381×C127C2semidirect
7. C127×#1443C2semidirect
8. C127×#1443C2semidirect
9. C127×#1440C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
13. C127×#1438C2semidirect
14. C127×#1438C2semidirect
15. C127×C22⋊#95C2semidirect
148. C2×C22⋊C4×C127D4semidirect
164. #95×C127D4semidirect
645. #15369C127direct (N × H)
665. C2×#386C2×C127semidirect
666. C2×#386C2×C127semidirect
667. C2×#386C2×C127semidirect
668. C2×#386C2×C127semidirect
669. C2×#381C2×C127semidirect
670. #1443C2×C127semidirect
671. #1443C2×C127semidirect
672. #1440C2×C127semidirect
673. #1439C2×C127semidirect
674. #1439C2×C127semidirect
675. #1439C2×C127semidirect
676. #1438C2×C127semidirect
677. #1438C2×C127semidirect
678. C22⋊#95C2×C127semidirect
679. C127#15369direct (N × H)
812. C2×C22⋊C4D4×C127semidirect
828. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C2×#386×C1272
C2×#381×C1272
C127×#14432
C127×#14402
C127×#14392
C127×#14382
C127×C22⋊#952
#15369127