Finite Group Databasebeta

← C127×#15315 #44578988

Subgroups — C127×#15315 #44578988

Order 32512.

2922 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic, complemented
2C2×#396×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C211yesmaximal, characteristic, complemented
5C2×#392×C127C211yesmaximal, characteristic, complemented
6C2×#392×C127C211yesmaximal, characteristic, complemented
7C2×#390×C127C211yesmaximal, characteristic, complemented
8C2×#390×C127C211yesmaximal, characteristic, complemented
9C2×#386×C127C211yesmaximal, characteristic, complemented
10C2×#385×C127C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1438C211yesmaximal, characteristic, complemented
15C127×#1436C211yesmaximal, 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×C4⋊C4×C127C2211yescharacteristic
29C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
44C22×C22⋊C4×C127C2211yescharacteristic
45C22×C42×C127C2211yescharacteristic
46#396×C127—24no—
47#394×C127—24no—
48#392×C127—24no—
49#392×C127—24no—
50#392×C127—24no—
51#390×C127—24no—
52#390×C127—24no—
53#386×C127—24no—
54#385×C127—24no—
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—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×C127—41no—
107C22×D4×C127—41no—
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—41no—
115C23×C4×C127—41no—
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
125C23×C4×C127C2311yescharacteristic
126C23×C4×C127C2311yescharacteristic
127#121×C127—232no—
128C2×C4⋊C4×C127—22no—
129C2×C4⋊C4×C127—22no—
130C2×C4⋊C4×C127—22no—
131C2×C4⋊C4×C127—22no—
132C2×C4⋊C4×C127—22no—
133C2×C4⋊C4×C127—22no—
134C2×C4⋊C4×C127—22no—
135C2×C4⋊C4×C127—22no—
136C2×C4⋊C4×C127—22no—
137C2×C4⋊C4×C127—41no—
138C2×C4⋊C4×C127—41no—
139C2×C4⋊C4×C127D414yescomplemented
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—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—22no—
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×C127D414yescomplemented
184C2×C22⋊C4×C127D414yescomplemented
185C2×C42×C127—22no—
186C2×C42×C127—22no—
187C2×C42×C127—41no—
188#95×C127—22no—
189#95×C127—22no—
190#95×C127—22no—
191#95×C127—22no—
192#95×C127—22no—
193#95×C127—41no—
194#95×C127D414yescomplemented
195#95×C127D414yescomplemented
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×C127—21no—
245C24×C127—21no—
246C24×C127—21no—
247C24×C127—21no—
248C24×C127—21no—
249C24×C127—21no—
250C24×C127C2×D412yes—
251C24×C127C2×D412yes—
252C24×C127C2×D412yes—
253C24×C127C2×D412yes—
254C24×C127#4112yes—
255C24×C127#4112yes—
256C24×C127C2411yescharacteristic
257C2×D4×C127—28no—
258C2×D4×C127—28no—
259C2×D4×C127—28no—
260C2×D4×C127—28no—
261C2×D4×C127—28no—
262C2×D4×C127—28no—
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—
293C2×D4×C127—44no—
294C2×D4×C127—44no—
295C2×D4×C127—44no—
296C2×D4×C127—44no—
297C2×D4×C127—44no—
298C2×D4×C127—44no—
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—21no—
310C22×C4×C127—21no—
311C22×C4×C127—28no—
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—44no—
363C22×C4×C127—44no—
364C22×C4×C127—44no—
365C22×C4×C127—44no—
366C22×C4×C127—44no—
367C22×C4×C127—44no—
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×C127C2×D412yes—
375C22×C4×C127C2×D412yes—
376C22×C4×C127C2×D412yes—
377C22×C4×C127C2×D412yes—
378C22×C4×C127C2×D412yes—
379C22×C4×C127C2×D412yes—
380C22×C4×C127C2×D412yes—
381C22×C4×C127C2×D412yes—
382C22×C4×C127#4112yes—
383C4⋊C4×C127—28no—
384C4⋊C4×C127—44no—
385C4⋊C4×C127—44no—
386C4⋊C4×C127—44no—
387C22⋊C4×C127—28no—
388C22⋊C4×C127—28no—
389C22⋊C4×C127—28no—
390C22⋊C4×C127—44no—
391C22⋊C4×C127—44no—
392C22⋊C4×C127—44no—
393C22⋊C4×C127—44no—
394C22⋊C4×C127—44no—
395C22⋊C4×C127—44no—
396C22⋊C4×C127—44no—
397C22⋊C4×C127—44no—
398C22⋊C4×C127—44no—
399C22⋊C4×C127—44no—
400C22⋊C4×C127—44no—
401C22⋊C4×C127—44no—
402C42×C127—44no—
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—22no—
435C23×C127—22no—
436C23×C127—22no—
437C23×C127—22no—
438C23×C127—22no—
439C23×C127—22no—
440C23×C127—22no—
441C23×C127—22no—
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—41no—
535C23×C127—41no—
536C23×C127—41no—
537C23×C127—41no—
538C23×C127—41no—
539C23×C127—41no—
540C23×C127—41no—
541C23×C127—41no—
542C23×C127#12114yes—
543C23×C127C22×D411yescharacteristic
544C23×C127C22×D411yescharacteristic
545C23×C127C22×D411yescharacteristic
546C23×C127C22×D411yescharacteristic
547C23×C127C22×D411yescharacteristic
548C23×C127C22×D411yescharacteristic
549C23×C127C2×#4111yescharacteristic
550C23×C127C2×#4111yescharacteristic
551C23×C127C2×#4111yescharacteristic
552C23×C127H(5,𝔽2)11yescharacteristic
553C23×C127H(5,𝔽2)11yescharacteristic
554C23×C127H(5,𝔽2)11yescharacteristic
555C23×C127H(5,𝔽2)11yescharacteristic
556C23×C127H(5,𝔽2)11yescharacteristic
557C23×C1272−1+411yescharacteristic
558D4×C127—416no—
559D4×C127—416no—
560D4×C127—416no—
561D4×C127—416no—
562D4×C127—416no—
563D4×C127—416no—
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—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—416no—
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—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#12014yes—
640C2×C4×C127#12114yescomplemented
641C2×C4×C127#12714yes—
642C22×C127—24no—
643C22×C127—24no—
644C22×C127—24no—
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—42no—
671C22×C127—42no—
672C22×C127—42no—
673C22×C127—42no—
674C22×C127—42no—
675C22×C127—42no—
676C22×C127—42no—
677C22×C127—42no—
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×C127—81no—
695C22×C127—81no—
696C22×C127—81no—
697C22×C127—81no—
698C22×C127—81no—
699C22×C127—81no—
700C22×C127—81no—
701C22×C127—81no—
702C22×C127C2×#12011yescharacteristic
703C22×C127C2×#12111yescharacteristic
704C22×C127C2×#12111yescharacteristic
705C22×C127#52511yescharacteristic
706C22×C127#52511yescharacteristic
707C22×C127C2×#12711yescharacteristic
708C22×C127#53411yescharacteristic
709C22×C127#53511yescharacteristic
710C22×C127#53511yescharacteristic
711C22×C127#53711yescharacteristic
712C22×C127#53711yescharacteristic
713C22×C127#53711yescharacteristic
714C22×C127#53811yescharacteristic
715C22×C127#53811yescharacteristic
716C22×C127#53811yescharacteristic
717C22×C127D4211yescharacteristic
718C22×C127D4211yescharacteristic
719C22×C127D4211yescharacteristic
720C22×C127D4211yescharacteristic
721C22×C127D4211yescharacteristic
722C22×C127D4211yescharacteristic
723C22×C127D4211yescharacteristic
724C22×C127#54611yescharacteristic
725C22×C127#54611yescharacteristic
726C22×C127#54611yescharacteristic
727C22×C127#54611yescharacteristic
728C22×C127#54611yescharacteristic
729C22×C127#54711yescharacteristic
730C22×C127#54811yescharacteristic
731C22×C127#54811yescharacteristic
732C22×C127#55011yescharacteristic
733C22×C127#55011yescharacteristic
734C22×C127#55311yescharacteristic
735C22×C127#56011yescharacteristic
736C22×C127#56211yescharacteristic
737C4×C127—24no—
738C4×C127—24no—
739C4×C127—24no—
740C4×C127—42no—
741C4×C127—42no—
742C4×C127—42no—
743C4×C127—42no—
744C4×C127—42no—
745C4×C127—42no—
746C4×C127—81no—
747C4×C127—81no—
748#15315C12711yesmaximal, characteristic, direct product factor, Sylow
749C2×C127—44no—
750C2×C127—82no—
751C2×C127—82no—
752C2×C127—82no—
753C2×C127#240711yescharacteristic
754C2×C127#241011yescharacteristic
755C2×C127#241611yescharacteristic
756C2×C127#242411yescharacteristic
757C2×C127#242411yescharacteristic
758C2×C127#243311yescharacteristic
759C2×C127#245611yescharacteristic
760C2×C127#254011yescharacteristic
761C2×C127#254111yescharacteristic
762C2×C127#267511yescharacteristic
763C2×C127#267611yescharacteristic
764C2×C127#267611yescharacteristic
765C2×C127#267811yescharacteristic
766C2×C127#268211yescharacteristic
767C2×C127#271411yescharacteristic
768C22×#121C2×C12711yescharacteristic, complemented
769C2×#396C2×C12711yescharacteristic, complemented
770C2×#394C2×C12711yescharacteristic, complemented
771C2×#392C2×C12711yescharacteristic, complemented
772C2×#392C2×C12711yescharacteristic, complemented
773C2×#392C2×C12711yescharacteristic, complemented
774C2×#390C2×C12711yescharacteristic, complemented
775C2×#390C2×C12711yescharacteristic, complemented
776C2×#386C2×C12711yescharacteristic, complemented
777C2×#385C2×C12711yescharacteristic, complemented
778#1439C2×C12711yescharacteristic, complemented
779#1439C2×C12711yescharacteristic, complemented
780#1438C2×C12711yescharacteristic, complemented
781#1438C2×C12711yescharacteristic, complemented
782#1436C2×C12711yescharacteristic, complemented
783C127#1531511yescharacteristic, direct product factor, Sylow
784C23×D4C22×C12711yescharacteristic
785C23×D4C22×C12711yescharacteristic
786C23×D4C22×C12711yescharacteristic
787C23×D4C22×C12711yescharacteristic
788C23×D4C22×C12711yescharacteristic
789C23×D4C22×C12711yescharacteristic
790C24×C4C22×C12711yescharacteristic
791C2×#121—24no—
792C2×#121—24no—
793C2×#121—24no—
794C22×C4⋊C4C22×C12711yescharacteristic
795C22×C4⋊C4C22×C12711yescharacteristic
796C22×C4⋊C4C22×C12711yescharacteristic
797C22×C4⋊C4C22×C12711yescharacteristic
798C22×C22⋊C4C22×C12711yescharacteristic
799C22×C22⋊C4C22×C12711yescharacteristic
800C22×C22⋊C4C22×C12711yescharacteristic
801C22×C22⋊C4C22×C12711yescharacteristic
802C22×C22⋊C4C22×C12711yescharacteristic
803C22×C22⋊C4C22×C12711yescharacteristic
804C22×C22⋊C4C22×C12711yescharacteristic
805C22×C22⋊C4C22×C12711yescharacteristic
806C22×C22⋊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×C42C22×C12711yescharacteristic
814#396—24no—
815#394—24no—
816#392—24no—
817#392—24no—
818#392—24no—
819#390—24no—
820#390—24no—
821#386—24no—
822#385—24no—
823C2×#95C22×C12711yescharacteristic
824C2×#95C22×C12711yescharacteristic
825C2×#95C22×C12711yescharacteristic
826C2×#95C22×C12711yescharacteristic
827C2×#95C22×C12711yescharacteristic
828C2×#95C22×C12711yescharacteristic
829C2×#95C22×C12711yescharacteristic
830C2×#95C22×C12711yescharacteristic
831C25C23×C12711yescharacteristic
832C25C23×C12711yescharacteristic
833C25C23×C12711yescharacteristic
834C25C23×C12711yescharacteristic
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—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—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4—41no—
866C22×D4—41no—
867C22×D4—41no—
868C22×D4—41no—
869C22×D4—41no—
870C22×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4—41no—
876C22×D4D4×C12714yescomplemented
877C23×C4—22no—
878C23×C4—22no—
879C23×C4—22no—
880C23×C4—22no—
881C23×C4—22no—
882C23×C4—41no—
883C23×C4—41no—
884C23×C4C23×C12711yescharacteristic
885C23×C4C23×C12711yescharacteristic
886C23×C4C23×C12711yescharacteristic
887C23×C4C23×C12711yescharacteristic
888C23×C4C23×C12711yescharacteristic
889C23×C4C23×C12711yescharacteristic
890C23×C4C23×C12711yescharacteristic
891C23×C4C23×C12711yescharacteristic
892C23×C4C23×C12711yescharacteristic
893C23×C4C23×C12711yescharacteristic
894C23×C4C23×C12711yescharacteristic
895#121—232no—
896C2×C4⋊C4—22no—
897C2×C4⋊C4—22no—
898C2×C4⋊C4—22no—
899C2×C4⋊C4—22no—
900C2×C4⋊C4—22no—
901C2×C4⋊C4—22no—
902C2×C4⋊C4—22no—
903C2×C4⋊C4—22no—
904C2×C4⋊C4—22no—
905C2×C4⋊C4—41no—
906C2×C4⋊C4—41no—
907C2×C4⋊C4D4×C12714yescomplemented
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—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—41no—
942C2×C22⋊C4—41no—
943C2×C22⋊C4—41no—
944C2×C22⋊C4—41no—
945C2×C22⋊C4—41no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4—41no—
951C2×C22⋊C4D4×C12714yescomplemented
952C2×C22⋊C4D4×C12714yescomplemented
953C2×C42—22no—
954C2×C42—22no—
955C2×C42—41no—
956#95—22no—
957#95—22no—
958#95—22no—
959#95—22no—
960#95—22no—
961#95—41no—
962#95D4×C12714yescomplemented
963#95D4×C12714yescomplemented
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—
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—
1018C24C2×D4×C12712yes—
1019C24C2×D4×C12712yes—
1020C24C2×D4×C12712yes—
1021C24C2×D4×C12712yes—
1022C24#41×C12712yes—
1023C24#41×C12712yes—
1024C24C24×C12711yescharacteristic
1025C2×D4—28no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—28no—
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—
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—
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—28no—
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—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—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4C2×D4×C12712yes—
1137C22×C4C2×D4×C12712yes—
1138C22×C4C2×D4×C12712yes—
1139C22×C4C2×D4×C12712yes—
1140C22×C4C2×D4×C12712yes—
1141C22×C4C2×D4×C12712yes—
1142C22×C4C2×D4×C12712yes—
1143C22×C4C2×D4×C12712yes—
1144C22×C4C2×D4×C12712yes—
1145C22×C4C2×D4×C12712yes—
1146C22×C4C2×D4×C12712yes—
1147C22×C4C2×D4×C12712yes—
1148C22×C4C2×D4×C12712yes—
1149C22×C4C2×D4×C12712yes—
1150C22×C4#41×C12712yes—
1151C4⋊C4—28no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C42—44no—
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—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—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—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#121×C12714yes—
1311C23C22×D4×C12711yescharacteristic
1312C23C22×D4×C12711yescharacteristic
1313C23C22×D4×C12711yescharacteristic
1314C23C22×D4×C12711yescharacteristic
1315C23C22×D4×C12711yescharacteristic
1316C23C22×D4×C12711yescharacteristic
1317C23C2×#41×C12711yescharacteristic
1318C23C2×#41×C12711yescharacteristic
1319C23C2×#41×C12711yescharacteristic
1320C23H(5,𝔽2)×C12711yescharacteristic
1321C23H(5,𝔽2)×C12711yescharacteristic
1322C23H(5,𝔽2)×C12711yescharacteristic
1323C23H(5,𝔽2)×C12711yescharacteristic
1324C23H(5,𝔽2)×C12711yescharacteristic
1325C232−1+4×C12711yescharacteristic
1326D4—416no—
1327D4—416no—
1328D4—416no—
1329D4—416no—
1330D4—416no—
1331D4—416no—
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—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—416no—
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—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#120×C12714yes—
1408C2×C4#121×C12714yescomplemented
1409C2×C4#127×C12714yes—
1410C22—24no—
1411C22—24no—
1412C22—24no—
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—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—81no—
1447C22—81no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22—81no—
1461C22—81no—
1462C22—81no—
1463C22—81no—
1464C22—81no—
1465C22—81no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22C2×#120×C12711yescharacteristic
1471C22C2×#121×C12711yescharacteristic
1472C22C2×#121×C12711yescharacteristic
1473C22#525×C12711yescharacteristic
1474C22#525×C12711yescharacteristic
1475C22C2×#127×C12711yescharacteristic
1476C22#534×C12711yescharacteristic
1477C22#535×C12711yescharacteristic
1478C22#535×C12711yescharacteristic
1479C22#537×C12711yescharacteristic
1480C22#537×C12711yescharacteristic
1481C22#537×C12711yescharacteristic
1482C22#538×C12711yescharacteristic
1483C22#538×C12711yescharacteristic
1484C22#538×C12711yescharacteristic
1485C22D42×C12711yescharacteristic
1486C22D42×C12711yescharacteristic
1487C22D42×C12711yescharacteristic
1488C22D42×C12711yescharacteristic
1489C22D42×C12711yescharacteristic
1490C22D42×C12711yescharacteristic
1491C22D42×C12711yescharacteristic
1492C22#546×C12711yescharacteristic
1493C22#546×C12711yescharacteristic
1494C22#546×C12711yescharacteristic
1495C22#546×C12711yescharacteristic
1496C22#546×C12711yescharacteristic
1497C22#547×C12711yescharacteristic
1498C22#548×C12711yescharacteristic
1499C22#548×C12711yescharacteristic
1500C22#550×C12711yescharacteristic
1501C22#550×C12711yescharacteristic
1502C22#553×C12711yescharacteristic
1503C22#560×C12711yescharacteristic
1504C22#562×C12711yescharacteristic
1505C4—24no—
1506C4—24no—
1507C4—24no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—42no—
1512C4—42no—
1513C4—42no—
1514C4—81no—
1515C4—81no—
1516C2—44no—
1517C2—82no—
1518C2—82no—
1519C2—82no—
1520C2C127×#240711yescharacteristic
1521C2C127×#241011yescharacteristic
1522C2C127×#241611yescharacteristic
1523C2C127×#242411yescharacteristic
1524C2C127×#242411yescharacteristic
1525C2C127×#243311yescharacteristic
1526C2C127×#245611yescharacteristic
1527C2C127×#254011yescharacteristic
1528C2C127×#254111yescharacteristic
1529C2C127×#267511yescharacteristic
1530C2C127×#267611yescharacteristic
1531C2C127×#267611yescharacteristic
1532C2C127×#267811yescharacteristic
1533C2C127×#268211yescharacteristic
1534C2C127×#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×#396×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#392×C127C2semidirect
6. C2×#392×C127C2semidirect
7. C2×#390×C127C2semidirect
8. C2×#390×C127C2semidirect
9. C2×#386×C127C2semidirect
10. C2×#385×C127C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
13. C127×#1438C2semidirect
14. C127×#1438C2semidirect
15. C127×#1436C2semidirect
108. C22×D4×C127D4semidirect
139. C2×C4⋊C4×C127D4semidirect
183. C2×C22⋊C4×C127D4semidirect
184. C2×C22⋊C4×C127D4semidirect
194. #95×C127D4semidirect
195. #95×C127D4semidirect
640. C2×C4×C127#121semidirect
748. #15315C127direct (N × H)
768. C22×#121C2×C127semidirect
769. C2×#396C2×C127semidirect
770. C2×#394C2×C127semidirect
771. C2×#392C2×C127semidirect
772. C2×#392C2×C127semidirect
773. C2×#392C2×C127semidirect
774. C2×#390C2×C127semidirect
775. C2×#390C2×C127semidirect
776. C2×#386C2×C127semidirect
777. C2×#385C2×C127semidirect
778. #1439C2×C127semidirect
779. #1439C2×C127semidirect
780. #1438C2×C127semidirect
781. #1438C2×C127semidirect
782. #1436C2×C127semidirect
783. C127#15315direct (N × H)
876. C22×D4D4×C127semidirect
907. C2×C4⋊C4D4×C127semidirect
951. C2×C22⋊C4D4×C127semidirect
952. C2×C22⋊C4D4×C127semidirect
962. #95D4×C127semidirect
963. #95D4×C127semidirect
1408. 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×#396×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14392
C127×#14382
C127×#14362
#15315127