Finite Group Databasebeta

← C127×#15263 #44578936

Subgroups — C127×#15263 #44578936

Order 32512.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic, complemented
2C22×#121×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C211yesmaximal, characteristic, complemented
5C2×#392×C127C211yesmaximal, characteristic, complemented
6C2×#386×C127C211yesmaximal, characteristic, complemented
7C2×#386×C127C211yesmaximal, characteristic, complemented
8C2×#385×C127C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1438C211yesmaximal, 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
23C24×C4×C127C2211yescharacteristic
24C2×#121×C127—24no—
25C2×#121×C127—24no—
26C2×#121×C127—24no—
27C2×#121×C127—24no—
28C2×#121×C127—24no—
29C2×#121×C127—24no—
30C22×C4⋊C4×C127C2211yescharacteristic
31C22×C4⋊C4×C127C2211yescharacteristic
32C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
44C22×C22⋊C4×C127C2211yescharacteristic
45C22×C22⋊C4×C127C2211yescharacteristic
46C22×C22⋊C4×C127C2211yescharacteristic
47#394×C127—24no—
48#392×C127—24no—
49#392×C127—24no—
50#386×C127—24no—
51#386×C127—24no—
52#385×C127—24no—
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C2×#95×C127C2211yescharacteristic
60C2×#95×C127C2211yescharacteristic
61C2×#95×C127C2211yescharacteristic
62C2×#95×C127C2211yescharacteristic
63C25×C127C2311yescharacteristic
64C25×C127C2311yescharacteristic
65C25×C127C2311yescharacteristic
66C25×C127C2311yescharacteristic
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—22no—
91C22×D4×C127—22no—
92C22×D4×C127—22no—
93C22×D4×C127—22no—
94C22×D4×C127—22no—
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×C127—41no—
107C22×D4×C127D414yescomplemented
108C22×D4×C127D414yescomplemented
109C23×C4×C127—22no—
110C23×C4×C127—22no—
111C23×C4×C127—22no—
112C23×C4×C127—22no—
113C23×C4×C127—22no—
114C23×C4×C127—22no—
115C23×C4×C127—22no—
116C23×C4×C127—22no—
117C23×C4×C127—22no—
118C23×C4×C127—22no—
119C23×C4×C127—41no—
120C23×C4×C127—41no—
121C23×C4×C127—41no—
122C23×C4×C127—41no—
123C23×C4×C127C2311yescharacteristic
124C23×C4×C127C2311yescharacteristic
125C23×C4×C127C2311yescharacteristic
126C23×C4×C127C2311yescharacteristic
127C23×C4×C127C2311yescharacteristic
128C23×C4×C127C2311yescharacteristic
129C23×C4×C127C2311yescharacteristic
130C23×C4×C127C2311yescharacteristic
131C23×C4×C127C2311yescharacteristic
132C23×C4×C127C2311yescharacteristic
133C23×C4×C127C2311yescharacteristic
134#121×C127—232no—
135#121×C127—232no—
136C2×C4⋊C4×C127—22no—
137C2×C4⋊C4×C127—22no—
138C2×C4⋊C4×C127—22no—
139C2×C4⋊C4×C127—22no—
140C2×C4⋊C4×C127—22no—
141C2×C4⋊C4×C127—22no—
142C2×C4⋊C4×C127—22no—
143C2×C4⋊C4×C127—41no—
144C2×C4⋊C4×C127D414yescomplemented
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—22no—
161C2×C22⋊C4×C127—22no—
162C2×C22⋊C4×C127—22no—
163C2×C22⋊C4×C127—22no—
164C2×C22⋊C4×C127—22no—
165C2×C22⋊C4×C127—22no—
166C2×C22⋊C4×C127—22no—
167C2×C22⋊C4×C127—22no—
168C2×C22⋊C4×C127—22no—
169C2×C22⋊C4×C127—22no—
170C2×C22⋊C4×C127—22no—
171C2×C22⋊C4×C127—22no—
172C2×C22⋊C4×C127—41no—
173C2×C22⋊C4×C127—41no—
174C2×C22⋊C4×C127—41no—
175C2×C22⋊C4×C127—41no—
176C2×C22⋊C4×C127—41no—
177C2×C22⋊C4×C127—41no—
178C2×C22⋊C4×C127—41no—
179C2×C22⋊C4×C127—41no—
180C2×C22⋊C4×C127—41no—
181C2×C22⋊C4×C127—41no—
182C2×C22⋊C4×C127—41no—
183C2×C22⋊C4×C127—41no—
184C2×C22⋊C4×C127D414yescomplemented
185C2×C22⋊C4×C127D414yescomplemented
186C2×C22⋊C4×C127D414yescomplemented
187#95×C127—22no—
188#95×C127—22no—
189#95×C127—22no—
190#95×C127—22no—
191#95×C127—22no—
192#95×C127—22no—
193#95×C127—22no—
194#95×C127—22no—
195#95×C127—22no—
196#95×C127—41no—
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×C127—21no—
245C24×C127—21no—
246C24×C127—21no—
247C24×C127—21no—
248C24×C127—21no—
249C24×C127C2×D412yes—
250C24×C127C2×D412yes—
251C24×C127C2×D412yes—
252C24×C127C2×D412yes—
253C24×C127C2×D412yes—
254C24×C127C2×D412yes—
255C24×C127C2×D412yes—
256C24×C127#4112yes—
257C24×C127C2411yescharacteristic
258C2×D4×C127—28no—
259C2×D4×C127—28no—
260C2×D4×C127—28no—
261C2×D4×C127—28no—
262C2×D4×C127—28no—
263C2×D4×C127—28no—
264C2×D4×C127—28no—
265C2×D4×C127—28no—
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—
293C2×D4×C127—44no—
294C2×D4×C127—44no—
295C2×D4×C127—44no—
296C2×D4×C127—44no—
297C2×D4×C127—44no—
298C2×D4×C127—44no—
299C2×D4×C127—44no—
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—28no—
309C22×C4×C127—28no—
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—21no—
359C22×C4×C127—21no—
360C22×C4×C127—21no—
361C22×C4×C127—21no—
362C22×C4×C127—21no—
363C22×C4×C127—21no—
364C22×C4×C127—21no—
365C22×C4×C127—21no—
366C22×C4×C127—44no—
367C22×C4×C127—44no—
368C22×C4×C127—44no—
369C22×C4×C127—44no—
370C22×C4×C127—44no—
371C22×C4×C127—44no—
372C22×C4×C127—44no—
373C22×C4×C127—44no—
374C22×C4×C127—44no—
375C22×C4×C127—44no—
376C22×C4×C127—44no—
377C22×C4×C127—44no—
378C22×C4×C127C2×D412yes—
379C22×C4×C127C2×D412yes—
380C22×C4×C127C2×D412yes—
381C22×C4×C127C2×D412yes—
382C22×C4×C127C2×D412yes—
383C22×C4×C127C2×D412yes—
384C22×C4×C127C2×D412yes—
385C22×C4×C127C2×D412yes—
386C22×C4×C127C2×D412yes—
387C22×C4×C127C2×D412yes—
388C22×C4×C127C2×D412yes—
389C22×C4×C127#4112yes—
390C22×C4×C127#4112yes—
391C4⋊C4×C127—28no—
392C4⋊C4×C127—28no—
393C4⋊C4×C127—44no—
394C22⋊C4×C127—28no—
395C22⋊C4×C127—28no—
396C22⋊C4×C127—28no—
397C22⋊C4×C127—28no—
398C22⋊C4×C127—28no—
399C22⋊C4×C127—44no—
400C22⋊C4×C127—44no—
401C22⋊C4×C127—44no—
402C22⋊C4×C127—44no—
403C22⋊C4×C127—44no—
404C22⋊C4×C127—44no—
405C22⋊C4×C127—44no—
406C22⋊C4×C127—44no—
407C22⋊C4×C127—44no—
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—22no—
435C23×C127—22no—
436C23×C127—22no—
437C23×C127—22no—
438C23×C127—22no—
439C23×C127—22no—
440C23×C127—22no—
441C23×C127—22no—
442C23×C127—22no—
443C23×C127—22no—
444C23×C127—22no—
445C23×C127—22no—
446C23×C127—22no—
447C23×C127—22no—
448C23×C127—22no—
449C23×C127—22no—
450C23×C127—22no—
451C23×C127—22no—
452C23×C127—22no—
453C23×C127—22no—
454C23×C127—22no—
455C23×C127—22no—
456C23×C127—22no—
457C23×C127—22no—
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—41no—
535C23×C127—41no—
536C23×C127—41no—
537C23×C127—41no—
538C23×C127—41no—
539C23×C127—41no—
540C23×C127—41no—
541C23×C127—41no—
542C23×C127—41no—
543C23×C127—41no—
544C23×C127—41no—
545C23×C127—41no—
546C23×C127#12014yes—
547C23×C127#12114yescomplemented
548C23×C127C22×D411yescharacteristic
549C23×C127C22×D411yescharacteristic
550C23×C127C22×D411yescharacteristic
551C23×C127C22×D411yescharacteristic
552C23×C127C22×D411yescharacteristic
553C23×C127C22×D411yescharacteristic
554C23×C127C2×#4111yescharacteristic
555C23×C127C2×#4111yescharacteristic
556C23×C127C2×#4111yescharacteristic
557C23×C127H(5,𝔽2)11yescharacteristic
558C23×C127H(5,𝔽2)11yescharacteristic
559C23×C127H(5,𝔽2)11yescharacteristic
560C23×C127H(5,𝔽2)11yescharacteristic
561C23×C127H(5,𝔽2)11yescharacteristic
562C23×C1272−1+411yescharacteristic
563D4×C127—416no—
564D4×C127—416no—
565D4×C127—416no—
566D4×C127—416no—
567D4×C127—416no—
568D4×C127—416no—
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—22no—
590C2×C4×C127—22no—
591C2×C4×C127—22no—
592C2×C4×C127—22no—
593C2×C4×C127—22no—
594C2×C4×C127—22no—
595C2×C4×C127—22no—
596C2×C4×C127—22no—
597C2×C4×C127—22no—
598C2×C4×C127—22no—
599C2×C4×C127—22no—
600C2×C4×C127—22no—
601C2×C4×C127—22no—
602C2×C4×C127—416no—
603C2×C4×C127—416no—
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—41no—
633C2×C4×C127—41no—
634C2×C4×C127—41no—
635C2×C4×C127—41no—
636C2×C4×C127—41no—
637C2×C4×C127—41no—
638C2×C4×C127—41no—
639C2×C4×C127—41no—
640C2×C4×C127—41no—
641C2×C4×C127—41no—
642C2×C4×C127—41no—
643C2×C4×C127—41no—
644C2×C4×C127—41no—
645C2×C4×C127—41no—
646C2×C4×C127#12014yes—
647C2×C4×C127#12114yescomplemented
648C22×C127—24no—
649C22×C127—24no—
650C22×C127—24no—
651C22×C127—24no—
652C22×C127—24no—
653C22×C127—24no—
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—42no—
671C22×C127—42no—
672C22×C127—42no—
673C22×C127—42no—
674C22×C127—42no—
675C22×C127—42no—
676C22×C127—42no—
677C22×C127—42no—
678C22×C127—42no—
679C22×C127—42no—
680C22×C127—42no—
681C22×C127—42no—
682C22×C127—42no—
683C22×C127—42no—
684C22×C127—42no—
685C22×C127—42no—
686C22×C127—42no—
687C22×C127—42no—
688C22×C127—42no—
689C22×C127—42no—
690C22×C127—42no—
691C22×C127—42no—
692C22×C127—81no—
693C22×C127—81no—
694C22×C127—81no—
695C22×C127—81no—
696C22×C127—81no—
697C22×C127—81no—
698C22×C127—81no—
699C22×C127—81no—
700C22×C127—81no—
701C22×C127—81no—
702C22×C127—81no—
703C22×C127—81no—
704C22×C127—81no—
705C22×C127—81no—
706C22×C127—81no—
707C22×C127—81no—
708C22×C127C2×#12011yescharacteristic
709C22×C127C2×#12011yescharacteristic
710C22×C127C2×#12111yescharacteristic
711C22×C127C2×#12111yescharacteristic
712C22×C127#52511yescharacteristic
713C22×C127#53211yescharacteristic
714C22×C127#53411yescharacteristic
715C22×C127#53411yescharacteristic
716C22×C127#53511yescharacteristic
717C22×C127#53711yescharacteristic
718C22×C127#53711yescharacteristic
719C22×C127#53711yescharacteristic
720C22×C127#53811yescharacteristic
721C22×C127#54011yescharacteristic
722C22×C127#54011yescharacteristic
723C22×C127D4211yescharacteristic
724C22×C127D4211yescharacteristic
725C22×C127D4211yescharacteristic
726C22×C127D4211yescharacteristic
727C22×C127D4211yescharacteristic
728C22×C127D4211yescharacteristic
729C22×C127D4211yescharacteristic
730C22×C127#54611yescharacteristic
731C22×C127#54611yescharacteristic
732C22×C127#54611yescharacteristic
733C22×C127#54611yescharacteristic
734C22×C127#54611yescharacteristic
735C22×C127#54611yescharacteristic
736C22×C127#54711yescharacteristic
737C22×C127#54711yescharacteristic
738C22×C127#54811yescharacteristic
739C22×C127#55011yescharacteristic
740C22×C127#55311yescharacteristic
741C22×C127#56011yescharacteristic
742C22×C127#56211yescharacteristic
743C4×C127—24no—
744C4×C127—24no—
745C4×C127—42no—
746C4×C127—42no—
747C4×C127—42no—
748C4×C127—42no—
749C4×C127—42no—
750C4×C127—42no—
751C4×C127—42no—
752C4×C127—81no—
753C4×C127—81no—
754#15263C12711yesmaximal, characteristic, direct product factor, Sylow
755C2×C127—44no—
756C2×C127—44no—
757C2×C127—82no—
758C2×C127—82no—
759C2×C127#240311yescharacteristic
760C2×C127#240711yescharacteristic
761C2×C127#240811yescharacteristic
762C2×C127#241011yescharacteristic
763C2×C127#241611yescharacteristic
764C2×C127#242411yescharacteristic
765C2×C127#242811yescharacteristic
766C2×C127#243011yescharacteristic
767C2×C127#246411yescharacteristic
768C2×C127#267111yescharacteristic
769C2×C127#267111yescharacteristic
770C2×C127#267311yescharacteristic
771C2×C127#267511yescharacteristic
772C2×C127#267611yescharacteristic
773C2×C127#268811yescharacteristic
774C22×#121C2×C12711yescharacteristic, complemented
775C22×#121C2×C12711yescharacteristic, complemented
776C2×#394C2×C12711yescharacteristic, complemented
777C2×#392C2×C12711yescharacteristic, complemented
778C2×#392C2×C12711yescharacteristic, complemented
779C2×#386C2×C12711yescharacteristic, complemented
780C2×#386C2×C12711yescharacteristic, complemented
781C2×#385C2×C12711yescharacteristic, complemented
782#1441C2×C12711yescharacteristic, complemented
783#1439C2×C12711yescharacteristic, complemented
784#1439C2×C12711yescharacteristic, complemented
785#1438C2×C12711yescharacteristic, complemented
786#1438C2×C12711yescharacteristic, complemented
787#1438C2×C12711yescharacteristic, complemented
788C22⋊#95C2×C12711yescharacteristic, complemented
789C127#1526311yescharacteristic, direct product factor, Sylow
790C23×D4C22×C12711yescharacteristic
791C23×D4C22×C12711yescharacteristic
792C23×D4C22×C12711yescharacteristic
793C23×D4C22×C12711yescharacteristic
794C23×D4C22×C12711yescharacteristic
795C23×D4C22×C12711yescharacteristic
796C24×C4C22×C12711yescharacteristic
797C24×C4C22×C12711yescharacteristic
798C2×#121—24no—
799C2×#121—24no—
800C2×#121—24no—
801C2×#121—24no—
802C2×#121—24no—
803C2×#121—24no—
804C22×C4⋊C4C22×C12711yescharacteristic
805C22×C4⋊C4C22×C12711yescharacteristic
806C22×C4⋊C4C22×C12711yescharacteristic
807C22×C22⋊C4C22×C12711yescharacteristic
808C22×C22⋊C4C22×C12711yescharacteristic
809C22×C22⋊C4C22×C12711yescharacteristic
810C22×C22⋊C4C22×C12711yescharacteristic
811C22×C22⋊C4C22×C12711yescharacteristic
812C22×C22⋊C4C22×C12711yescharacteristic
813C22×C22⋊C4C22×C12711yescharacteristic
814C22×C22⋊C4C22×C12711yescharacteristic
815C22×C22⋊C4C22×C12711yescharacteristic
816C22×C22⋊C4C22×C12711yescharacteristic
817C22×C22⋊C4C22×C12711yescharacteristic
818C22×C22⋊C4C22×C12711yescharacteristic
819C22×C22⋊C4C22×C12711yescharacteristic
820C22×C22⋊C4C22×C12711yescharacteristic
821#394—24no—
822#392—24no—
823#392—24no—
824#386—24no—
825#386—24no—
826#385—24no—
827C2×#95C22×C12711yescharacteristic
828C2×#95C22×C12711yescharacteristic
829C2×#95C22×C12711yescharacteristic
830C2×#95C22×C12711yescharacteristic
831C2×#95C22×C12711yescharacteristic
832C2×#95C22×C12711yescharacteristic
833C2×#95C22×C12711yescharacteristic
834C2×#95C22×C12711yescharacteristic
835C2×#95C22×C12711yescharacteristic
836C2×#95C22×C12711yescharacteristic
837C25C23×C12711yescharacteristic
838C25C23×C12711yescharacteristic
839C25C23×C12711yescharacteristic
840C25C23×C12711yescharacteristic
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—22no—
851C22×D4—22no—
852C22×D4—22no—
853C22×D4—22no—
854C22×D4—22no—
855C22×D4—22no—
856C22×D4—22no—
857C22×D4—22no—
858C22×D4—22no—
859C22×D4—22no—
860C22×D4—22no—
861C22×D4—22no—
862C22×D4—22no—
863C22×D4—22no—
864C22×D4—22no—
865C22×D4—22no—
866C22×D4—22no—
867C22×D4—22no—
868C22×D4—22no—
869C22×D4—41no—
870C22×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4—41no—
876C22×D4—41no—
877C22×D4—41no—
878C22×D4—41no—
879C22×D4—41no—
880C22×D4—41no—
881C22×D4D4×C12714yescomplemented
882C22×D4D4×C12714yescomplemented
883C23×C4—22no—
884C23×C4—22no—
885C23×C4—22no—
886C23×C4—22no—
887C23×C4—22no—
888C23×C4—22no—
889C23×C4—22no—
890C23×C4—22no—
891C23×C4—22no—
892C23×C4—22no—
893C23×C4—41no—
894C23×C4—41no—
895C23×C4—41no—
896C23×C4—41no—
897C23×C4C23×C12711yescharacteristic
898C23×C4C23×C12711yescharacteristic
899C23×C4C23×C12711yescharacteristic
900C23×C4C23×C12711yescharacteristic
901C23×C4C23×C12711yescharacteristic
902C23×C4C23×C12711yescharacteristic
903C23×C4C23×C12711yescharacteristic
904C23×C4C23×C12711yescharacteristic
905C23×C4C23×C12711yescharacteristic
906C23×C4C23×C12711yescharacteristic
907C23×C4C23×C12711yescharacteristic
908#121—232no—
909#121—232no—
910C2×C4⋊C4—22no—
911C2×C4⋊C4—22no—
912C2×C4⋊C4—22no—
913C2×C4⋊C4—22no—
914C2×C4⋊C4—22no—
915C2×C4⋊C4—22no—
916C2×C4⋊C4—22no—
917C2×C4⋊C4—41no—
918C2×C4⋊C4D4×C12714yescomplemented
919C2×C22⋊C4—22no—
920C2×C22⋊C4—22no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—22no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—22no—
926C2×C22⋊C4—22no—
927C2×C22⋊C4—22no—
928C2×C22⋊C4—22no—
929C2×C22⋊C4—22no—
930C2×C22⋊C4—22no—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—22no—
934C2×C22⋊C4—22no—
935C2×C22⋊C4—22no—
936C2×C22⋊C4—22no—
937C2×C22⋊C4—22no—
938C2×C22⋊C4—22no—
939C2×C22⋊C4—22no—
940C2×C22⋊C4—22no—
941C2×C22⋊C4—22no—
942C2×C22⋊C4—22no—
943C2×C22⋊C4—22no—
944C2×C22⋊C4—22no—
945C2×C22⋊C4—22no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4—41no—
951C2×C22⋊C4—41no—
952C2×C22⋊C4—41no—
953C2×C22⋊C4—41no—
954C2×C22⋊C4—41no—
955C2×C22⋊C4—41no—
956C2×C22⋊C4—41no—
957C2×C22⋊C4—41no—
958C2×C22⋊C4D4×C12714yescomplemented
959C2×C22⋊C4D4×C12714yescomplemented
960C2×C22⋊C4D4×C12714yescomplemented
961#95—22no—
962#95—22no—
963#95—22no—
964#95—22no—
965#95—22no—
966#95—22no—
967#95—22no—
968#95—22no—
969#95—22no—
970#95—41no—
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—
1004C24—21no—
1005C24—21no—
1006C24—21no—
1007C24—21no—
1008C24—21no—
1009C24—21no—
1010C24—21no—
1011C24—21no—
1012C24—21no—
1013C24—21no—
1014C24—21no—
1015C24—21no—
1016C24—21no—
1017C24—21no—
1018C24—21no—
1019C24—21no—
1020C24—21no—
1021C24—21no—
1022C24—21no—
1023C24C2×D4×C12712yes—
1024C24C2×D4×C12712yes—
1025C24C2×D4×C12712yes—
1026C24C2×D4×C12712yes—
1027C24C2×D4×C12712yes—
1028C24C2×D4×C12712yes—
1029C24C2×D4×C12712yes—
1030C24#41×C12712yes—
1031C24C24×C12711yescharacteristic
1032C2×D4—28no—
1033C2×D4—28no—
1034C2×D4—28no—
1035C2×D4—28no—
1036C2×D4—28no—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—28no—
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—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
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—28no—
1083C22×C4—28no—
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—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—21no—
1126C22×C4—21no—
1127C22×C4—21no—
1128C22×C4—21no—
1129C22×C4—21no—
1130C22×C4—21no—
1131C22×C4—21no—
1132C22×C4—21no—
1133C22×C4—21no—
1134C22×C4—21no—
1135C22×C4—21no—
1136C22×C4—21no—
1137C22×C4—21no—
1138C22×C4—21no—
1139C22×C4—21no—
1140C22×C4—44no—
1141C22×C4—44no—
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×C4C2×D4×C12712yes—
1153C22×C4C2×D4×C12712yes—
1154C22×C4C2×D4×C12712yes—
1155C22×C4C2×D4×C12712yes—
1156C22×C4C2×D4×C12712yes—
1157C22×C4C2×D4×C12712yes—
1158C22×C4C2×D4×C12712yes—
1159C22×C4C2×D4×C12712yes—
1160C22×C4C2×D4×C12712yes—
1161C22×C4C2×D4×C12712yes—
1162C22×C4C2×D4×C12712yes—
1163C22×C4#41×C12712yes—
1164C22×C4#41×C12712yes—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—44no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
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—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
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—41no—
1295C23—41no—
1296C23—41no—
1297C23—41no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23—41no—
1303C23—41no—
1304C23—41no—
1305C23—41no—
1306C23—41no—
1307C23—41no—
1308C23—41no—
1309C23—41no—
1310C23—41no—
1311C23—41no—
1312C23—41no—
1313C23—41no—
1314C23—41no—
1315C23—41no—
1316C23—41no—
1317C23—41no—
1318C23—41no—
1319C23—41no—
1320C23#120×C12714yes—
1321C23#121×C12714yescomplemented
1322C23C22×D4×C12711yescharacteristic
1323C23C22×D4×C12711yescharacteristic
1324C23C22×D4×C12711yescharacteristic
1325C23C22×D4×C12711yescharacteristic
1326C23C22×D4×C12711yescharacteristic
1327C23C22×D4×C12711yescharacteristic
1328C23C2×#41×C12711yescharacteristic
1329C23C2×#41×C12711yescharacteristic
1330C23C2×#41×C12711yescharacteristic
1331C23H(5,𝔽2)×C12711yescharacteristic
1332C23H(5,𝔽2)×C12711yescharacteristic
1333C23H(5,𝔽2)×C12711yescharacteristic
1334C23H(5,𝔽2)×C12711yescharacteristic
1335C23H(5,𝔽2)×C12711yescharacteristic
1336C232−1+4×C12711yescharacteristic
1337D4—416no—
1338D4—416no—
1339D4—416no—
1340D4—416no—
1341D4—416no—
1342D4—416no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—416no—
1377C2×C4—416no—
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—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4—41no—
1404C2×C4—41no—
1405C2×C4—41no—
1406C2×C4—41no—
1407C2×C4—41no—
1408C2×C4—41no—
1409C2×C4—41no—
1410C2×C4—41no—
1411C2×C4—41no—
1412C2×C4—41no—
1413C2×C4—41no—
1414C2×C4—41no—
1415C2×C4—41no—
1416C2×C4—41no—
1417C2×C4—41no—
1418C2×C4—41no—
1419C2×C4—41no—
1420C2×C4#120×C12714yes—
1421C2×C4#121×C12714yescomplemented
1422C22—24no—
1423C22—24no—
1424C22—24no—
1425C22—24no—
1426C22—24no—
1427C22—24no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22—81no—
1471C22—81no—
1472C22—81no—
1473C22—81no—
1474C22—81no—
1475C22—81no—
1476C22—81no—
1477C22—81no—
1478C22—81no—
1479C22—81no—
1480C22—81no—
1481C22—81no—
1482C22C2×#120×C12711yescharacteristic
1483C22C2×#120×C12711yescharacteristic
1484C22C2×#121×C12711yescharacteristic
1485C22C2×#121×C12711yescharacteristic
1486C22#525×C12711yescharacteristic
1487C22#532×C12711yescharacteristic
1488C22#534×C12711yescharacteristic
1489C22#534×C12711yescharacteristic
1490C22#535×C12711yescharacteristic
1491C22#537×C12711yescharacteristic
1492C22#537×C12711yescharacteristic
1493C22#537×C12711yescharacteristic
1494C22#538×C12711yescharacteristic
1495C22#540×C12711yescharacteristic
1496C22#540×C12711yescharacteristic
1497C22D42×C12711yescharacteristic
1498C22D42×C12711yescharacteristic
1499C22D42×C12711yescharacteristic
1500C22D42×C12711yescharacteristic
1501C22D42×C12711yescharacteristic
1502C22D42×C12711yescharacteristic
1503C22D42×C12711yescharacteristic
1504C22#546×C12711yescharacteristic
1505C22#546×C12711yescharacteristic
1506C22#546×C12711yescharacteristic
1507C22#546×C12711yescharacteristic
1508C22#546×C12711yescharacteristic
1509C22#546×C12711yescharacteristic
1510C22#547×C12711yescharacteristic
1511C22#547×C12711yescharacteristic
1512C22#548×C12711yescharacteristic
1513C22#550×C12711yescharacteristic
1514C22#553×C12711yescharacteristic
1515C22#560×C12711yescharacteristic
1516C22#562×C12711yescharacteristic
1517C4—24no—
1518C4—24no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—81no—
1527C4—81no—
1528C2—44no—
1529C2—44no—
1530C2—82no—
1531C2—82no—
1532C2C127×#240311yescharacteristic
1533C2C127×#240711yescharacteristic
1534C2C127×#240811yescharacteristic
1535C2C127×#241011yescharacteristic
1536C2C127×#241611yescharacteristic
1537C2C127×#242411yescharacteristic
1538C2C127×#242811yescharacteristic
1539C2C127×#243011yescharacteristic
1540C2C127×#246411yescharacteristic
1541C2C127×#267111yescharacteristic
1542C2C127×#267111yescharacteristic
1543C2C127×#267311yescharacteristic
1544C2C127×#267511yescharacteristic
1545C2C127×#267611yescharacteristic
1546C2C127×#268811yescharacteristic
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. C22×#121×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#392×C127C2semidirect
6. C2×#386×C127C2semidirect
7. C2×#386×C127C2semidirect
8. C2×#385×C127C2semidirect
9. C127×#1441C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×#1438C2semidirect
15. C127×C22⋊#95C2semidirect
107. C22×D4×C127D4semidirect
108. C22×D4×C127D4semidirect
144. C2×C4⋊C4×C127D4semidirect
184. C2×C22⋊C4×C127D4semidirect
185. C2×C22⋊C4×C127D4semidirect
186. C2×C22⋊C4×C127D4semidirect
547. C23×C127#121semidirect
647. C2×C4×C127#121semidirect
754. #15263C127direct (N × H)
774. C22×#121C2×C127semidirect
775. C22×#121C2×C127semidirect
776. C2×#394C2×C127semidirect
777. C2×#392C2×C127semidirect
778. C2×#392C2×C127semidirect
779. C2×#386C2×C127semidirect
780. C2×#386C2×C127semidirect
781. C2×#385C2×C127semidirect
782. #1441C2×C127semidirect
783. #1439C2×C127semidirect
784. #1439C2×C127semidirect
785. #1438C2×C127semidirect
786. #1438C2×C127semidirect
787. #1438C2×C127semidirect
788. C22⋊#95C2×C127semidirect
789. C127#15263direct (N × H)
881. C22×D4D4×C127semidirect
882. C22×D4D4×C127semidirect
918. C2×C4⋊C4D4×C127semidirect
958. C2×C22⋊C4D4×C127semidirect
959. C2×C22⋊C4D4×C127semidirect
960. C2×C22⋊C4D4×C127semidirect
1321. C23#121×C127semidirect
1421. C2×C4#121×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×#386×C1272
C2×#385×C1272
C127×#14412
C127×#14392
C127×#14382
C127×C22⋊#952
#15263127