Finite Group Databasebeta

← C127×#15320 #44578993

Subgroups — C127×#15320 #44578993

Order 32512.

2830 conjugacy classes of subgroups.

The subgroup lattice has 1520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C211yesmaximal, characteristic, complemented
3C2×#392×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C211yesmaximal, characteristic, complemented
5C2×#392×C127C211yesmaximal, characteristic, complemented
6C2×#390×C127C211yesmaximal, characteristic, complemented
7C2×#388×C127C211yesmaximal, characteristic, complemented
8C2×#386×C127C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1440C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C23×D4×C127C2211yescharacteristic
20C23×D4×C127C2211yescharacteristic
21C23×D4×C127C2211yescharacteristic
22C24×C4×C127C2211yescharacteristic
23C2×#121×C127—24no—
24C2×#121×C127—24no—
25C2×#121×C127—24no—
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C4⋊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
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38C22×C22⋊C4×C127C2211yescharacteristic
39C22×C22⋊C4×C127C2211yescharacteristic
40C22×C22⋊C4×C127C2211yescharacteristic
41C22×C22⋊C4×C127C2211yescharacteristic
42C22×C22⋊C4×C127C2211yescharacteristic
43C22×C42×C127C2211yescharacteristic
44#394×C127—24no—
45#392×C127—24no—
46#392×C127—24no—
47#392×C127—24no—
48#390×C127—24no—
49#388×C127—24no—
50#386×C127—24no—
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C2×#95×C127C2211yescharacteristic
60C2×#95×C127C2211yescharacteristic
61C25×C127C2311yescharacteristic
62C25×C127C2311yescharacteristic
63C25×C127C2311yescharacteristic
64C25×C127C2311yescharacteristic
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—22no—
75C22×D4×C127—22no—
76C22×D4×C127—22no—
77C22×D4×C127—22no—
78C22×D4×C127—22no—
79C22×D4×C127—22no—
80C22×D4×C127—22no—
81C22×D4×C127—22no—
82C22×D4×C127—22no—
83C22×D4×C127—22no—
84C22×D4×C127—22no—
85C22×D4×C127—22no—
86C22×D4×C127—22no—
87C22×D4×C127—22no—
88C22×D4×C127—22no—
89C22×D4×C127—22no—
90C22×D4×C127—41no—
91C22×D4×C127—41no—
92C22×D4×C127—41no—
93C22×D4×C127—41no—
94C22×D4×C127—41no—
95C22×D4×C127—41no—
96C22×D4×C127—41no—
97C22×D4×C127—41no—
98C22×D4×C127—41no—
99C22×D4×C127—41no—
100C22×D4×C127—41no—
101C22×D4×C127—41no—
102C22×D4×C127—41no—
103C22×D4×C127—41no—
104C22×D4×C127—41no—
105C22×D4×C127—41no—
106C22×D4×C127D414yescomplemented
107C23×C4×C127—22no—
108C23×C4×C127—22no—
109C23×C4×C127—22no—
110C23×C4×C127—22no—
111C23×C4×C127—22no—
112C23×C4×C127—41no—
113C23×C4×C127—41no—
114C23×C4×C127C2311yescharacteristic
115C23×C4×C127C2311yescharacteristic
116C23×C4×C127C2311yescharacteristic
117C23×C4×C127C2311yescharacteristic
118C23×C4×C127C2311yescharacteristic
119C23×C4×C127C2311yescharacteristic
120C23×C4×C127C2311yescharacteristic
121C23×C4×C127C2311yescharacteristic
122C23×C4×C127C2311yescharacteristic
123C23×C4×C127C2311yescharacteristic
124C23×C4×C127C2311yescharacteristic
125#121×C127—232no—
126C2×C4⋊C4×C127—22no—
127C2×C4⋊C4×C127—22no—
128C2×C4⋊C4×C127—22no—
129C2×C4⋊C4×C127—22no—
130C2×C4⋊C4×C127—41no—
131C2×C4⋊C4×C127D414yescomplemented
132C2×C22⋊C4×C127—22no—
133C2×C22⋊C4×C127—22no—
134C2×C22⋊C4×C127—22no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—22no—
137C2×C22⋊C4×C127—22no—
138C2×C22⋊C4×C127—22no—
139C2×C22⋊C4×C127—22no—
140C2×C22⋊C4×C127—22no—
141C2×C22⋊C4×C127—22no—
142C2×C22⋊C4×C127—22no—
143C2×C22⋊C4×C127—22no—
144C2×C22⋊C4×C127—22no—
145C2×C22⋊C4×C127—22no—
146C2×C22⋊C4×C127—22no—
147C2×C22⋊C4×C127—22no—
148C2×C22⋊C4×C127—22no—
149C2×C22⋊C4×C127—22no—
150C2×C22⋊C4×C127—22no—
151C2×C22⋊C4×C127—22no—
152C2×C22⋊C4×C127—22no—
153C2×C22⋊C4×C127—22no—
154C2×C22⋊C4×C127—22no—
155C2×C22⋊C4×C127—22no—
156C2×C22⋊C4×C127—22no—
157C2×C22⋊C4×C127—22no—
158C2×C22⋊C4×C127—22no—
159C2×C22⋊C4×C127—22no—
160C2×C22⋊C4×C127—41no—
161C2×C22⋊C4×C127—41no—
162C2×C22⋊C4×C127—41no—
163C2×C22⋊C4×C127—41no—
164C2×C22⋊C4×C127—41no—
165C2×C22⋊C4×C127—41no—
166C2×C22⋊C4×C127—41no—
167C2×C22⋊C4×C127—41no—
168C2×C22⋊C4×C127—41no—
169C2×C22⋊C4×C127—41no—
170C2×C22⋊C4×C127—41no—
171C2×C22⋊C4×C127—41no—
172C2×C22⋊C4×C127—41no—
173C2×C22⋊C4×C127—41no—
174C2×C22⋊C4×C127D414yescomplemented
175C2×C22⋊C4×C127D414yescomplemented
176C2×C22⋊C4×C127D414yescomplemented
177C2×C42×C127—22no—
178C2×C42×C127—22no—
179C2×C42×C127—41no—
180#95×C127—22no—
181#95×C127—22no—
182#95×C127—22no—
183#95×C127—22no—
184#95×C127—22no—
185#95×C127—22no—
186#95×C127—22no—
187#95×C127—22no—
188#95×C127—41no—
189#95×C127—41no—
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×C127—21no—
204C24×C127—21no—
205C24×C127—21no—
206C24×C127—21no—
207C24×C127—21no—
208C24×C127—21no—
209C24×C127—21no—
210C24×C127—21no—
211C24×C127—21no—
212C24×C127—21no—
213C24×C127—21no—
214C24×C127—21no—
215C24×C127—21no—
216C24×C127—21no—
217C24×C127—21no—
218C24×C127—21no—
219C24×C127—21no—
220C24×C127—21no—
221C24×C127—21no—
222C24×C127—21no—
223C24×C127—21no—
224C24×C127—21no—
225C24×C127—21no—
226C24×C127—21no—
227C24×C127—21no—
228C24×C127—21no—
229C24×C127—21no—
230C24×C127—21no—
231C24×C127—21no—
232C24×C127—21no—
233C24×C127—21no—
234C24×C127—21no—
235C24×C127—21no—
236C24×C127—21no—
237C24×C127—21no—
238C24×C127—21no—
239C24×C127—21no—
240C24×C127—21no—
241C24×C127—21no—
242C24×C127—21no—
243C24×C127—21no—
244C24×C127C2×D412yes—
245C24×C127C2×D412yes—
246C24×C127C2×D412yes—
247C24×C127C2×D412yes—
248C24×C127C2×D412yes—
249C24×C127#4112yes—
250C24×C127C2411yescharacteristic
251C2×D4×C127—28no—
252C2×D4×C127—28no—
253C2×D4×C127—28no—
254C2×D4×C127—28no—
255C2×D4×C127—28no—
256C2×D4×C127—44no—
257C2×D4×C127—44no—
258C2×D4×C127—44no—
259C2×D4×C127—44no—
260C2×D4×C127—44no—
261C2×D4×C127—44no—
262C2×D4×C127—44no—
263C2×D4×C127—44no—
264C2×D4×C127—44no—
265C2×D4×C127—44no—
266C2×D4×C127—44no—
267C2×D4×C127—44no—
268C2×D4×C127—44no—
269C2×D4×C127—44no—
270C2×D4×C127—44no—
271C2×D4×C127—44no—
272C2×D4×C127—44no—
273C2×D4×C127—44no—
274C2×D4×C127—44no—
275C2×D4×C127—44no—
276C2×D4×C127—44no—
277C2×D4×C127—44no—
278C2×D4×C127—44no—
279C2×D4×C127—44no—
280C2×D4×C127—44no—
281C2×D4×C127—44no—
282C2×D4×C127—44no—
283C2×D4×C127—44no—
284C2×D4×C127—44no—
285C2×D4×C127—44no—
286C2×D4×C127—44no—
287C2×D4×C127—44no—
288C2×D4×C127—44no—
289C2×D4×C127—44no—
290C2×D4×C127—44no—
291C2×D4×C127—44no—
292C2×D4×C127—44no—
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—28no—
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—21no—
310C22×C4×C127—21no—
311C22×C4×C127—21no—
312C22×C4×C127—21no—
313C22×C4×C127—21no—
314C22×C4×C127—21no—
315C22×C4×C127—21no—
316C22×C4×C127—21no—
317C22×C4×C127—21no—
318C22×C4×C127—21no—
319C22×C4×C127—21no—
320C22×C4×C127—21no—
321C22×C4×C127—21no—
322C22×C4×C127—21no—
323C22×C4×C127—21no—
324C22×C4×C127—21no—
325C22×C4×C127—21no—
326C22×C4×C127—21no—
327C22×C4×C127—21no—
328C22×C4×C127—21no—
329C22×C4×C127—21no—
330C22×C4×C127—21no—
331C22×C4×C127—21no—
332C22×C4×C127—21no—
333C22×C4×C127—21no—
334C22×C4×C127—21no—
335C22×C4×C127—21no—
336C22×C4×C127—21no—
337C22×C4×C127—21no—
338C22×C4×C127—21no—
339C22×C4×C127—21no—
340C22×C4×C127—21no—
341C22×C4×C127—21no—
342C22×C4×C127—21no—
343C22×C4×C127—21no—
344C22×C4×C127—21no—
345C22×C4×C127—21no—
346C22×C4×C127—21no—
347C22×C4×C127—21no—
348C22×C4×C127—21no—
349C22×C4×C127—21no—
350C22×C4×C127—21no—
351C22×C4×C127—21no—
352C22×C4×C127—21no—
353C22×C4×C127—21no—
354C22×C4×C127—21no—
355C22×C4×C127—21no—
356C22×C4×C127—21no—
357C22×C4×C127—21no—
358C22×C4×C127—44no—
359C22×C4×C127—44no—
360C22×C4×C127—44no—
361C22×C4×C127—44no—
362C22×C4×C127—44no—
363C22×C4×C127—44no—
364C22×C4×C127C2×D412yes—
365C22×C4×C127C2×D412yes—
366C22×C4×C127C2×D412yes—
367C22×C4×C127C2×D412yes—
368C22×C4×C127C2×D412yes—
369C22×C4×C127C2×D412yes—
370C22×C4×C127C2×D412yes—
371C22×C4×C127C2×D412yes—
372C22×C4×C127C2×D412yes—
373C22×C4×C127C2×D412yes—
374C22×C4×C127#4112yes—
375C22×C4×C127#4112yes—
376C22×C4×C127#4112yes—
377C4⋊C4×C127—28no—
378C4⋊C4×C127—44no—
379C22⋊C4×C127—28no—
380C22⋊C4×C127—28no—
381C22⋊C4×C127—28no—
382C22⋊C4×C127—44no—
383C22⋊C4×C127—44no—
384C22⋊C4×C127—44no—
385C22⋊C4×C127—44no—
386C22⋊C4×C127—44no—
387C22⋊C4×C127—44no—
388C22⋊C4×C127—44no—
389C22⋊C4×C127—44no—
390C22⋊C4×C127—44no—
391C22⋊C4×C127—44no—
392C22⋊C4×C127—44no—
393C22⋊C4×C127—44no—
394C42×C127—44no—
395C23×C127—22no—
396C23×C127—22no—
397C23×C127—22no—
398C23×C127—22no—
399C23×C127—22no—
400C23×C127—22no—
401C23×C127—22no—
402C23×C127—22no—
403C23×C127—22no—
404C23×C127—22no—
405C23×C127—22no—
406C23×C127—22no—
407C23×C127—22no—
408C23×C127—22no—
409C23×C127—22no—
410C23×C127—22no—
411C23×C127—22no—
412C23×C127—22no—
413C23×C127—22no—
414C23×C127—22no—
415C23×C127—22no—
416C23×C127—22no—
417C23×C127—22no—
418C23×C127—22no—
419C23×C127—22no—
420C23×C127—22no—
421C23×C127—22no—
422C23×C127—22no—
423C23×C127—22no—
424C23×C127—22no—
425C23×C127—22no—
426C23×C127—22no—
427C23×C127—22no—
428C23×C127—22no—
429C23×C127—22no—
430C23×C127—22no—
431C23×C127—22no—
432C23×C127—22no—
433C23×C127—22no—
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—41no—
448C23×C127—41no—
449C23×C127—41no—
450C23×C127—41no—
451C23×C127—41no—
452C23×C127—41no—
453C23×C127—41no—
454C23×C127—41no—
455C23×C127—41no—
456C23×C127—41no—
457C23×C127—41no—
458C23×C127—41no—
459C23×C127—41no—
460C23×C127—41no—
461C23×C127—41no—
462C23×C127—41no—
463C23×C127—41no—
464C23×C127—41no—
465C23×C127—41no—
466C23×C127—41no—
467C23×C127—41no—
468C23×C127—41no—
469C23×C127—41no—
470C23×C127—41no—
471C23×C127—41no—
472C23×C127—41no—
473C23×C127—41no—
474C23×C127—41no—
475C23×C127—41no—
476C23×C127—41no—
477C23×C127—41no—
478C23×C127—41no—
479C23×C127—41no—
480C23×C127—41no—
481C23×C127—41no—
482C23×C127—41no—
483C23×C127—41no—
484C23×C127—41no—
485C23×C127—41no—
486C23×C127—41no—
487C23×C127—41no—
488C23×C127—41no—
489C23×C127—41no—
490C23×C127—41no—
491C23×C127—41no—
492C23×C127—41no—
493C23×C127—41no—
494C23×C127—41no—
495C23×C127—41no—
496C23×C127—41no—
497C23×C127—41no—
498C23×C127—41no—
499C23×C127—41no—
500C23×C127—41no—
501C23×C127—41no—
502C23×C127—41no—
503C23×C127—41no—
504C23×C127—41no—
505C23×C127—41no—
506C23×C127—41no—
507C23×C127—41no—
508C23×C127—41no—
509C23×C127—41no—
510C23×C127—41no—
511C23×C127—41no—
512C23×C127—41no—
513C23×C127—41no—
514C23×C127—41no—
515C23×C127—41no—
516C23×C127—41no—
517C23×C127—41no—
518C23×C127—41no—
519C23×C127—41no—
520C23×C127—41no—
521C23×C127—41no—
522C23×C127—41no—
523C23×C127—41no—
524C23×C127—41no—
525C23×C127—41no—
526C23×C127—41no—
527C23×C127—41no—
528C23×C127—41no—
529C23×C127—41no—
530C23×C127—41no—
531C23×C127—41no—
532C23×C127—41no—
533C23×C127—41no—
534C23×C127#12114yes—
535C23×C127C22×D411yescharacteristic
536C23×C127C22×D411yescharacteristic
537C23×C127C22×D411yescharacteristic
538C23×C127C22×D411yescharacteristic
539C23×C127C22×D411yescharacteristic
540C23×C127C2×#4111yescharacteristic
541C23×C127C2×#4111yescharacteristic
542C23×C127C2×#4111yescharacteristic
543C23×C127C2×#4111yescharacteristic
544C23×C127H(5,𝔽2)11yescharacteristic
545C23×C127H(5,𝔽2)11yescharacteristic
546C23×C127H(5,𝔽2)11yescharacteristic
547C23×C127H(5,𝔽2)11yescharacteristic
548C23×C127H(5,𝔽2)11yescharacteristic
549C23×C127H(5,𝔽2)11yescharacteristic
550D4×C127—416no—
551D4×C127—416no—
552D4×C127—416no—
553D4×C127—416no—
554D4×C127—416no—
555D4×C127—416no—
556C2×C4×C127—22no—
557C2×C4×C127—22no—
558C2×C4×C127—22no—
559C2×C4×C127—22no—
560C2×C4×C127—22no—
561C2×C4×C127—22no—
562C2×C4×C127—22no—
563C2×C4×C127—22no—
564C2×C4×C127—22no—
565C2×C4×C127—22no—
566C2×C4×C127—22no—
567C2×C4×C127—22no—
568C2×C4×C127—22no—
569C2×C4×C127—22no—
570C2×C4×C127—22no—
571C2×C4×C127—22no—
572C2×C4×C127—22no—
573C2×C4×C127—22no—
574C2×C4×C127—22no—
575C2×C4×C127—22no—
576C2×C4×C127—22no—
577C2×C4×C127—22no—
578C2×C4×C127—22no—
579C2×C4×C127—22no—
580C2×C4×C127—22no—
581C2×C4×C127—22no—
582C2×C4×C127—22no—
583C2×C4×C127—22no—
584C2×C4×C127—22no—
585C2×C4×C127—22no—
586C2×C4×C127—22no—
587C2×C4×C127—22no—
588C2×C4×C127—22no—
589C2×C4×C127—416no—
590C2×C4×C127—41no—
591C2×C4×C127—41no—
592C2×C4×C127—41no—
593C2×C4×C127—41no—
594C2×C4×C127—41no—
595C2×C4×C127—41no—
596C2×C4×C127—41no—
597C2×C4×C127—41no—
598C2×C4×C127—41no—
599C2×C4×C127—41no—
600C2×C4×C127—41no—
601C2×C4×C127—41no—
602C2×C4×C127—41no—
603C2×C4×C127—41no—
604C2×C4×C127—41no—
605C2×C4×C127—41no—
606C2×C4×C127—41no—
607C2×C4×C127—41no—
608C2×C4×C127—41no—
609C2×C4×C127—41no—
610C2×C4×C127—41no—
611C2×C4×C127—41no—
612C2×C4×C127—41no—
613C2×C4×C127—41no—
614C2×C4×C127—41no—
615C2×C4×C127—41no—
616C2×C4×C127—41no—
617C2×C4×C127—41no—
618C2×C4×C127—41no—
619C2×C4×C127—41no—
620C2×C4×C127—41no—
621C2×C4×C127—41no—
622C2×C4×C127—41no—
623C2×C4×C127—41no—
624C2×C4×C127—41no—
625C2×C4×C127—41no—
626C2×C4×C127—41no—
627C2×C4×C127—41no—
628C2×C4×C127—41no—
629C2×C4×C127—41no—
630C2×C4×C127—41no—
631C2×C4×C127—41no—
632C2×C4×C127#12014yes—
633C2×C4×C127#12114yes—
634C22×C127—24no—
635C22×C127—24no—
636C22×C127—24no—
637C22×C127—42no—
638C22×C127—42no—
639C22×C127—42no—
640C22×C127—42no—
641C22×C127—42no—
642C22×C127—42no—
643C22×C127—42no—
644C22×C127—42no—
645C22×C127—42no—
646C22×C127—42no—
647C22×C127—42no—
648C22×C127—42no—
649C22×C127—42no—
650C22×C127—42no—
651C22×C127—42no—
652C22×C127—42no—
653C22×C127—42no—
654C22×C127—42no—
655C22×C127—42no—
656C22×C127—42no—
657C22×C127—42no—
658C22×C127—42no—
659C22×C127—42no—
660C22×C127—42no—
661C22×C127—42no—
662C22×C127—42no—
663C22×C127—42no—
664C22×C127—42no—
665C22×C127—42no—
666C22×C127—42no—
667C22×C127—42no—
668C22×C127—42no—
669C22×C127—42no—
670C22×C127—81no—
671C22×C127—81no—
672C22×C127—81no—
673C22×C127—81no—
674C22×C127—81no—
675C22×C127—81no—
676C22×C127—81no—
677C22×C127—81no—
678C22×C127—81no—
679C22×C127—81no—
680C22×C127—81no—
681C22×C127—81no—
682C22×C127—81no—
683C22×C127—81no—
684C22×C127—81no—
685C22×C127—81no—
686C22×C127—81no—
687C22×C127—81no—
688C22×C127—81no—
689C22×C127—81no—
690C22×C127—81no—
691C22×C127—81no—
692C22×C127—81no—
693C22×C127—81no—
694C22×C127C2×#12011yescharacteristic
695C22×C127C2×#12111yescharacteristic
696C22×C127C2×#12111yescharacteristic
697C22×C127#52511yescharacteristic
698C22×C127#53211yescharacteristic
699C22×C127#53211yescharacteristic
700C22×C127#53411yescharacteristic
701C22×C127#53411yescharacteristic
702C22×C127#53511yescharacteristic
703C22×C127#53511yescharacteristic
704C22×C127#53511yescharacteristic
705C22×C127#53811yescharacteristic
706C22×C127#53811yescharacteristic
707C22×C127#54011yescharacteristic
708C22×C127#54011yescharacteristic
709C22×C127D4211yescharacteristic
710C22×C127D4211yescharacteristic
711C22×C127D4211yescharacteristic
712C22×C127D4211yescharacteristic
713C22×C127D4211yescharacteristic
714C22×C127#54611yescharacteristic
715C22×C127#54611yescharacteristic
716C22×C127#54611yescharacteristic
717C22×C127#54611yescharacteristic
718C22×C127#54611yescharacteristic
719C22×C127#54611yescharacteristic
720C22×C127#54611yescharacteristic
721C22×C127#54611yescharacteristic
722C22×C127#55011yescharacteristic
723C22×C127#55011yescharacteristic
724C22×C127#55311yescharacteristic
725C22×C127#55311yescharacteristic
726C22×C127#55511yescharacteristic
727C22×C127#56011yescharacteristic
728C22×C127#56011yescharacteristic
729C4×C127—24no—
730C4×C127—24no—
731C4×C127—42no—
732C4×C127—42no—
733C4×C127—42no—
734C4×C127—42no—
735C4×C127—42no—
736C4×C127—42no—
737C4×C127—42no—
738C4×C127—81no—
739C4×C127—81no—
740#15320C12711yesmaximal, characteristic, direct product factor, Sylow
741C2×C127—44no—
742C2×C127—82no—
743C2×C127—82no—
744C2×C127—82no—
745C2×C127#240811yescharacteristic
746C2×C127#241011yescharacteristic
747C2×C127#241411yescharacteristic
748C2×C127#242411yescharacteristic
749C2×C127#242811yescharacteristic
750C2×C127#243111yescharacteristic
751C2×C127#246411yescharacteristic
752C2×C127#254311yescharacteristic
753C2×C127#255511yescharacteristic
754C2×C127#266911yescharacteristic
755C2×C127#267311yescharacteristic
756C2×C127#267811yescharacteristic
757C2×C127#269911yescharacteristic
758C2×C127#270311yescharacteristic
759C2×C127#271411yescharacteristic
760C22×#121C2×C12711yescharacteristic, complemented
761C2×#394C2×C12711yescharacteristic, complemented
762C2×#392C2×C12711yescharacteristic, complemented
763C2×#392C2×C12711yescharacteristic, complemented
764C2×#392C2×C12711yescharacteristic, complemented
765C2×#390C2×C12711yescharacteristic, complemented
766C2×#388C2×C12711yescharacteristic, complemented
767C2×#386C2×C12711yescharacteristic, complemented
768#1441C2×C12711yescharacteristic, complemented
769#1440C2×C12711yescharacteristic, complemented
770#1438C2×C12711yescharacteristic, complemented
771#1438C2×C12711yescharacteristic, complemented
772#1438C2×C12711yescharacteristic, complemented
773#1437C2×C12711yescharacteristic, complemented
774C22⋊#95C2×C12711yescharacteristic, complemented
775C127#1532011yescharacteristic, direct product factor, Sylow
776C23×D4C22×C12711yescharacteristic
777C23×D4C22×C12711yescharacteristic
778C23×D4C22×C12711yescharacteristic
779C23×D4C22×C12711yescharacteristic
780C23×D4C22×C12711yescharacteristic
781C23×D4C22×C12711yescharacteristic
782C24×C4C22×C12711yescharacteristic
783C2×#121—24no—
784C2×#121—24no—
785C2×#121—24no—
786C22×C4⋊C4C22×C12711yescharacteristic
787C22×C4⋊C4C22×C12711yescharacteristic
788C22×C22⋊C4C22×C12711yescharacteristic
789C22×C22⋊C4C22×C12711yescharacteristic
790C22×C22⋊C4C22×C12711yescharacteristic
791C22×C22⋊C4C22×C12711yescharacteristic
792C22×C22⋊C4C22×C12711yescharacteristic
793C22×C22⋊C4C22×C12711yescharacteristic
794C22×C22⋊C4C22×C12711yescharacteristic
795C22×C22⋊C4C22×C12711yescharacteristic
796C22×C22⋊C4C22×C12711yescharacteristic
797C22×C22⋊C4C22×C12711yescharacteristic
798C22×C22⋊C4C22×C12711yescharacteristic
799C22×C22⋊C4C22×C12711yescharacteristic
800C22×C22⋊C4C22×C12711yescharacteristic
801C22×C22⋊C4C22×C12711yescharacteristic
802C22×C22⋊C4C22×C12711yescharacteristic
803C22×C42C22×C12711yescharacteristic
804#394—24no—
805#392—24no—
806#392—24no—
807#392—24no—
808#390—24no—
809#388—24no—
810#386—24no—
811C2×#95C22×C12711yescharacteristic
812C2×#95C22×C12711yescharacteristic
813C2×#95C22×C12711yescharacteristic
814C2×#95C22×C12711yescharacteristic
815C2×#95C22×C12711yescharacteristic
816C2×#95C22×C12711yescharacteristic
817C2×#95C22×C12711yescharacteristic
818C2×#95C22×C12711yescharacteristic
819C2×#95C22×C12711yescharacteristic
820C2×#95C22×C12711yescharacteristic
821C25C23×C12711yescharacteristic
822C25C23×C12711yescharacteristic
823C25C23×C12711yescharacteristic
824C25C23×C12711yescharacteristic
825C22×D4—22no—
826C22×D4—22no—
827C22×D4—22no—
828C22×D4—22no—
829C22×D4—22no—
830C22×D4—22no—
831C22×D4—22no—
832C22×D4—22no—
833C22×D4—22no—
834C22×D4—22no—
835C22×D4—22no—
836C22×D4—22no—
837C22×D4—22no—
838C22×D4—22no—
839C22×D4—22no—
840C22×D4—22no—
841C22×D4—22no—
842C22×D4—22no—
843C22×D4—22no—
844C22×D4—22no—
845C22×D4—22no—
846C22×D4—22no—
847C22×D4—22no—
848C22×D4—22no—
849C22×D4—22no—
850C22×D4—41no—
851C22×D4—41no—
852C22×D4—41no—
853C22×D4—41no—
854C22×D4—41no—
855C22×D4—41no—
856C22×D4—41no—
857C22×D4—41no—
858C22×D4—41no—
859C22×D4—41no—
860C22×D4—41no—
861C22×D4—41no—
862C22×D4—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4—41no—
866C22×D4D4×C12714yescomplemented
867C23×C4—22no—
868C23×C4—22no—
869C23×C4—22no—
870C23×C4—22no—
871C23×C4—22no—
872C23×C4—41no—
873C23×C4—41no—
874C23×C4C23×C12711yescharacteristic
875C23×C4C23×C12711yescharacteristic
876C23×C4C23×C12711yescharacteristic
877C23×C4C23×C12711yescharacteristic
878C23×C4C23×C12711yescharacteristic
879C23×C4C23×C12711yescharacteristic
880C23×C4C23×C12711yescharacteristic
881C23×C4C23×C12711yescharacteristic
882C23×C4C23×C12711yescharacteristic
883C23×C4C23×C12711yescharacteristic
884C23×C4C23×C12711yescharacteristic
885#121—232no—
886C2×C4⋊C4—22no—
887C2×C4⋊C4—22no—
888C2×C4⋊C4—22no—
889C2×C4⋊C4—22no—
890C2×C4⋊C4—41no—
891C2×C4⋊C4D4×C12714yescomplemented
892C2×C22⋊C4—22no—
893C2×C22⋊C4—22no—
894C2×C22⋊C4—22no—
895C2×C22⋊C4—22no—
896C2×C22⋊C4—22no—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—22no—
899C2×C22⋊C4—22no—
900C2×C22⋊C4—22no—
901C2×C22⋊C4—22no—
902C2×C22⋊C4—22no—
903C2×C22⋊C4—22no—
904C2×C22⋊C4—22no—
905C2×C22⋊C4—22no—
906C2×C22⋊C4—22no—
907C2×C22⋊C4—22no—
908C2×C22⋊C4—22no—
909C2×C22⋊C4—22no—
910C2×C22⋊C4—22no—
911C2×C22⋊C4—22no—
912C2×C22⋊C4—22no—
913C2×C22⋊C4—22no—
914C2×C22⋊C4—22no—
915C2×C22⋊C4—22no—
916C2×C22⋊C4—22no—
917C2×C22⋊C4—22no—
918C2×C22⋊C4—22no—
919C2×C22⋊C4—22no—
920C2×C22⋊C4—41no—
921C2×C22⋊C4—41no—
922C2×C22⋊C4—41no—
923C2×C22⋊C4—41no—
924C2×C22⋊C4—41no—
925C2×C22⋊C4—41no—
926C2×C22⋊C4—41no—
927C2×C22⋊C4—41no—
928C2×C22⋊C4—41no—
929C2×C22⋊C4—41no—
930C2×C22⋊C4—41no—
931C2×C22⋊C4—41no—
932C2×C22⋊C4—41no—
933C2×C22⋊C4—41no—
934C2×C22⋊C4D4×C12714yescomplemented
935C2×C22⋊C4D4×C12714yescomplemented
936C2×C22⋊C4D4×C12714yescomplemented
937C2×C42—22no—
938C2×C42—22no—
939C2×C42—41no—
940#95—22no—
941#95—22no—
942#95—22no—
943#95—22no—
944#95—22no—
945#95—22no—
946#95—22no—
947#95—22no—
948#95—41no—
949#95—41no—
950C24—21no—
951C24—21no—
952C24—21no—
953C24—21no—
954C24—21no—
955C24—21no—
956C24—21no—
957C24—21no—
958C24—21no—
959C24—21no—
960C24—21no—
961C24—21no—
962C24—21no—
963C24—21no—
964C24—21no—
965C24—21no—
966C24—21no—
967C24—21no—
968C24—21no—
969C24—21no—
970C24—21no—
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24—21no—
989C24—21no—
990C24—21no—
991C24—21no—
992C24—21no—
993C24—21no—
994C24—21no—
995C24—21no—
996C24—21no—
997C24—21no—
998C24—21no—
999C24—21no—
1000C24—21no—
1001C24—21no—
1002C24—21no—
1003C24—21no—
1004C24C2×D4×C12712yes—
1005C24C2×D4×C12712yes—
1006C24C2×D4×C12712yes—
1007C24C2×D4×C12712yes—
1008C24C2×D4×C12712yes—
1009C24#41×C12712yes—
1010C24C24×C12711yescharacteristic
1011C2×D4—28no—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—28no—
1015C2×D4—28no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C22×C4—21no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—21no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—28no—
1062C22×C4—21no—
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—21no—
1083C22×C4—21no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4C2×D4×C12712yes—
1125C22×C4C2×D4×C12712yes—
1126C22×C4C2×D4×C12712yes—
1127C22×C4C2×D4×C12712yes—
1128C22×C4C2×D4×C12712yes—
1129C22×C4C2×D4×C12712yes—
1130C22×C4C2×D4×C12712yes—
1131C22×C4C2×D4×C12712yes—
1132C22×C4C2×D4×C12712yes—
1133C22×C4C2×D4×C12712yes—
1134C22×C4#41×C12712yes—
1135C22×C4#41×C12712yes—
1136C22×C4#41×C12712yes—
1137C4⋊C4—28no—
1138C4⋊C4—44no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C42—44no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—41no—
1281C23—41no—
1282C23—41no—
1283C23—41no—
1284C23—41no—
1285C23—41no—
1286C23—41no—
1287C23—41no—
1288C23—41no—
1289C23—41no—
1290C23—41no—
1291C23—41no—
1292C23—41no—
1293C23—41no—
1294C23#121×C12714yes—
1295C23C22×D4×C12711yescharacteristic
1296C23C22×D4×C12711yescharacteristic
1297C23C22×D4×C12711yescharacteristic
1298C23C22×D4×C12711yescharacteristic
1299C23C22×D4×C12711yescharacteristic
1300C23C2×#41×C12711yescharacteristic
1301C23C2×#41×C12711yescharacteristic
1302C23C2×#41×C12711yescharacteristic
1303C23C2×#41×C12711yescharacteristic
1304C23H(5,𝔽2)×C12711yescharacteristic
1305C23H(5,𝔽2)×C12711yescharacteristic
1306C23H(5,𝔽2)×C12711yescharacteristic
1307C23H(5,𝔽2)×C12711yescharacteristic
1308C23H(5,𝔽2)×C12711yescharacteristic
1309C23H(5,𝔽2)×C12711yescharacteristic
1310D4—416no—
1311D4—416no—
1312D4—416no—
1313D4—416no—
1314D4—416no—
1315D4—416no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—416no—
1350C2×C4—41no—
1351C2×C4—41no—
1352C2×C4—41no—
1353C2×C4—41no—
1354C2×C4—41no—
1355C2×C4—41no—
1356C2×C4—41no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4#120×C12714yes—
1393C2×C4#121×C12714yes—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—81no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—81no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—81no—
1442C22—81no—
1443C22—81no—
1444C22—81no—
1445C22—81no—
1446C22—81no—
1447C22—81no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22C2×#120×C12711yescharacteristic
1455C22C2×#121×C12711yescharacteristic
1456C22C2×#121×C12711yescharacteristic
1457C22#525×C12711yescharacteristic
1458C22#532×C12711yescharacteristic
1459C22#532×C12711yescharacteristic
1460C22#534×C12711yescharacteristic
1461C22#534×C12711yescharacteristic
1462C22#535×C12711yescharacteristic
1463C22#535×C12711yescharacteristic
1464C22#535×C12711yescharacteristic
1465C22#538×C12711yescharacteristic
1466C22#538×C12711yescharacteristic
1467C22#540×C12711yescharacteristic
1468C22#540×C12711yescharacteristic
1469C22D42×C12711yescharacteristic
1470C22D42×C12711yescharacteristic
1471C22D42×C12711yescharacteristic
1472C22D42×C12711yescharacteristic
1473C22D42×C12711yescharacteristic
1474C22#546×C12711yescharacteristic
1475C22#546×C12711yescharacteristic
1476C22#546×C12711yescharacteristic
1477C22#546×C12711yescharacteristic
1478C22#546×C12711yescharacteristic
1479C22#546×C12711yescharacteristic
1480C22#546×C12711yescharacteristic
1481C22#546×C12711yescharacteristic
1482C22#550×C12711yescharacteristic
1483C22#550×C12711yescharacteristic
1484C22#553×C12711yescharacteristic
1485C22#553×C12711yescharacteristic
1486C22#555×C12711yescharacteristic
1487C22#560×C12711yescharacteristic
1488C22#560×C12711yescharacteristic
1489C4—24no—
1490C4—24no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—81no—
1499C4—81no—
1500C2—44no—
1501C2—82no—
1502C2—82no—
1503C2—82no—
1504C2C127×#240811yescharacteristic
1505C2C127×#241011yescharacteristic
1506C2C127×#241411yescharacteristic
1507C2C127×#242411yescharacteristic
1508C2C127×#242811yescharacteristic
1509C2C127×#243111yescharacteristic
1510C2C127×#246411yescharacteristic
1511C2C127×#254311yescharacteristic
1512C2C127×#255511yescharacteristic
1513C2C127×#266911yescharacteristic
1514C2C127×#267311yescharacteristic
1515C2C127×#267811yescharacteristic
1516C2C127×#269911yescharacteristic
1517C2C127×#270311yescharacteristic
1518C2C127×#271411yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C127C2semidirect
2. C2×#394×C127C2semidirect
3. C2×#392×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#392×C127C2semidirect
6. C2×#390×C127C2semidirect
7. C2×#388×C127C2semidirect
8. C2×#386×C127C2semidirect
9. C127×#1441C2semidirect
10. C127×#1440C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×#1437C2semidirect
15. C127×C22⋊#95C2semidirect
106. C22×D4×C127D4semidirect
131. C2×C4⋊C4×C127D4semidirect
174. C2×C22⋊C4×C127D4semidirect
175. C2×C22⋊C4×C127D4semidirect
176. C2×C22⋊C4×C127D4semidirect
740. #15320C127direct (N × H)
760. C22×#121C2×C127semidirect
761. C2×#394C2×C127semidirect
762. C2×#392C2×C127semidirect
763. C2×#392C2×C127semidirect
764. C2×#392C2×C127semidirect
765. C2×#390C2×C127semidirect
766. C2×#388C2×C127semidirect
767. C2×#386C2×C127semidirect
768. #1441C2×C127semidirect
769. #1440C2×C127semidirect
770. #1438C2×C127semidirect
771. #1438C2×C127semidirect
772. #1438C2×C127semidirect
773. #1437C2×C127semidirect
774. C22⋊#95C2×C127semidirect
775. C127#15320direct (N × H)
866. C22×D4D4×C127semidirect
891. C2×C4⋊C4D4×C127semidirect
934. C2×C22⋊C4D4×C127semidirect
935. C2×C22⋊C4D4×C127semidirect
936. C2×C22⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C2×#386×C1272
C127×#14412
C127×#14402
C127×#14382
C127×#14372
C127×C22⋊#952
#15320127