Finite Group Databasebeta

← C127×#14068 #44577741

Subgroups — C127×#14068 #44577741

Order 32512.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C127C211yesmaximal, characteristic, complemented
2C2×#386×C127C211yesmaximal, characteristic
3C2×#386×C127C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1443C211yesmaximal, characteristic, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1438C211yesmaximal, characteristic
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C127×#1434C211yesmaximal, characteristic, complemented
13C127×#1434C211yesmaximal, characteristic, complemented
14C127×C22⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33#388×C127—24no—
34#386×C127—24no—
35#386×C127C418yescomplemented
36C4×C22⋊C4×C127—24no—
37C4×C22⋊C4×C127—24no—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C25×C127C2311yescharacteristic
57C25×C127C2311yescharacteristic
58C22×D4×C127—22no—
59C22×D4×C127—22no—
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—41no—
63C22×D4×C127—41no—
64C22×D4×C127C2×C414yes—
65C23×C4×C127—22no—
66C23×C4×C127—22no—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—41no—
73C23×C4×C127—41no—
74C23×C4×C127—41no—
75C23×C4×C127—41no—
76C23×C4×C127—41no—
77C23×C4×C127—41no—
78C23×C4×C127C2×C414yescomplemented
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2311yescharacteristic
88C23×C4×C127C2311yescharacteristic
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—41no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—22no—
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—41no—
116C2×C22⋊C4×C127—41no—
117C2×C22⋊C4×C127—41no—
118C2×C22⋊C4×C127—41no—
119C2×C22⋊C4×C127—41no—
120C2×C22⋊C4×C127—41no—
121C2×C22⋊C4×C127C2×C414yes—
122C2×C22⋊C4×C127C2×C414yes—
123C2×C22⋊C4×C127C2×C414yescomplemented
124C2×C22⋊C4×C127D414yes—
125C2×C42×C127—22no—
126C2×C42×C127—22no—
127C2×C42×C127—22no—
128C2×C42×C127—22no—
129C2×C42×C127—41no—
130C2×C42×C127—41no—
131C2×C42×C127—41no—
132C2×C42×C127—41no—
133C2×C42×C127D414yescomplemented
134#95×C127—22no—
135#95×C127—22no—
136#95×C127—22no—
137#95×C127—22no—
138#95×C127—22no—
139#95×C127—22no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—41no—
146#95×C127—41no—
147#95×C127—41no—
148#95×C127—41no—
149#95×C127—41no—
150#95×C127C2×C414yescomplemented
151#95×C127C2×C414yescomplemented
152C24×C127—21no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127—21no—
157C24×C127—21no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127C22×C412yes—
177C24×C127C22×C412yes—
178C24×C127C2×D412yes—
179C24×C127#4112yes—
180C24×C127#4112yes—
181C24×C127#4112yes—
182C24×C127C2411yescharacteristic
183C2×D4×C127—28no—
184C2×D4×C127—28no—
185C2×D4×C127—44no—
186C2×D4×C127—44no—
187C2×D4×C127—44no—
188C2×D4×C127—44no—
189C2×D4×C127—44no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—28no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—28no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—44no—
269C22×C4×C127—44no—
270C22×C4×C127—44no—
271C22×C4×C127—44no—
272C22×C4×C127—44no—
273C22×C4×C127—44no—
274C22×C4×C127—44no—
275C22×C4×C127—44no—
276C22×C4×C127—44no—
277C22×C4×C127—44no—
278C22×C4×C127—44no—
279C22×C4×C127—44no—
280C22×C4×C127C22×C412yes—
281C22×C4×C127C22×C412yes—
282C22×C4×C127C22×C412yes—
283C22×C4×C127C22×C412yes—
284C22×C4×C127C22×C412yes—
285C22×C4×C127C2×D412yes—
286C22×C4×C127C2×D412yes—
287C22×C4×C127C2×D412yes—
288C22×C4×C127C2×D412yes—
289C22×C4×C127C2×D412yes—
290C22×C4×C127#4112yes—
291C22×C4×C127#4112yes—
292C22×C4×C127#4112yes—
293C22×C4×C127#4112yes—
294C22×C4×C127#4112yes—
295C4⋊C4×C127—44no—
296C22⋊C4×C127—28no—
297C22⋊C4×C127—28no—
298C22⋊C4×C127—28no—
299C22⋊C4×C127—28no—
300C22⋊C4×C127—28no—
301C22⋊C4×C127—44no—
302C22⋊C4×C127—44no—
303C22⋊C4×C127—44no—
304C22⋊C4×C127—44no—
305C22⋊C4×C127—44no—
306C42×C127—44no—
307C42×C127—44no—
308C42×C127—44no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—22no—
317C23×C127—22no—
318C23×C127—22no—
319C23×C127—22no—
320C23×C127—22no—
321C23×C127—22no—
322C23×C127—22no—
323C23×C127—22no—
324C23×C127—22no—
325C23×C127—22no—
326C23×C127—22no—
327C23×C127—22no—
328C23×C127—22no—
329C23×C127—22no—
330C23×C127—22no—
331C23×C127—22no—
332C23×C127—22no—
333C23×C127—22no—
334C23×C127—22no—
335C23×C127—22no—
336C23×C127—22no—
337C23×C127—22no—
338C23×C127—22no—
339C23×C127—22no—
340C23×C127—22no—
341C23×C127—22no—
342C23×C127—22no—
343C23×C127—22no—
344C23×C127—22no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—41no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×C127—41no—
374C23×C127—41no—
375C23×C127—41no—
376C23×C127—41no—
377C23×C127#11714yes—
378C23×C127C4×D414yes—
379C23×C127C23×C411yescharacteristic
380C23×C127C22×D411yescharacteristic
381C23×C127C22×D411yescharacteristic
382C23×C127C2×#4111yescharacteristic
383C23×C127C2×#4111yescharacteristic
384C23×C127C2×#4111yescharacteristic
385C23×C127C2×#4111yescharacteristic
386C23×C127C2×#4111yescharacteristic
387C23×C127C2×#4111yescharacteristic
388C23×C127C2×#4111yescharacteristic
389C23×C127C2×#4111yescharacteristic
390C23×C127H(5,𝔽2)11yescharacteristic
391C23×C127H(5,𝔽2)11yescharacteristic
392C23×C127H(5,𝔽2)11yescharacteristic
393C23×C127H(5,𝔽2)11yescharacteristic
394D4×C127—416no—
395C2×C4×C127—22no—
396C2×C4×C127—22no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—22no—
402C2×C4×C127—22no—
403C2×C4×C127—22no—
404C2×C4×C127—22no—
405C2×C4×C127—22no—
406C2×C4×C127—22no—
407C2×C4×C127—22no—
408C2×C4×C127—22no—
409C2×C4×C127—22no—
410C2×C4×C127—22no—
411C2×C4×C127—22no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—22no—
416C2×C4×C127—22no—
417C2×C4×C127—22no—
418C2×C4×C127—22no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—22no—
422C2×C4×C127—22no—
423C2×C4×C127—22no—
424C2×C4×C127—22no—
425C2×C4×C127—22no—
426C2×C4×C127—22no—
427C2×C4×C127—22no—
428C2×C4×C127—22no—
429C2×C4×C127—22no—
430C2×C4×C127—22no—
431C2×C4×C127—22no—
432C2×C4×C127—22no—
433C2×C4×C127—22no—
434C2×C4×C127—416no—
435C2×C4×C127—416no—
436C2×C4×C127—41no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—41no—
453C2×C4×C127—41no—
454C2×C4×C127—41no—
455C2×C4×C127—41no—
456C2×C4×C127—41no—
457C2×C4×C127—41no—
458C2×C4×C127—41no—
459C2×C4×C127—41no—
460C2×C4×C127—41no—
461C2×C4×C127—41no—
462C2×C4×C127—41no—
463C2×C4×C127—41no—
464C2×C4×C127—41no—
465C2×C4×C127—41no—
466C2×C4×C127—41no—
467C2×C4×C127—41no—
468C2×C4×C127—41no—
469C2×C4×C127—41no—
470C2×C4×C127—41no—
471C2×C4×C127—41no—
472C2×C4×C127—41no—
473C2×C4×C127—41no—
474C2×C4×C127—41no—
475C2×C4×C127—41no—
476C2×C4×C127—41no—
477C2×C4×C127—41no—
478C2×C4×C127—41no—
479C2×C4×C127—41no—
480C2×C4×C127—41no—
481C2×C4×C127—41no—
482C2×C4×C127—41no—
483C2×C4×C127—41no—
484C2×C4×C127—41no—
485C2×C4×C127—41no—
486C2×C4×C127C4×D414yes—
487C2×C4×C127#12114yes—
488C22×C127—24no—
489C22×C127—24no—
490C22×C127—24no—
491C22×C127—24no—
492C22×C127—24no—
493C22×C127—24no—
494C22×C127—42no—
495C22×C127—42no—
496C22×C127—42no—
497C22×C127—42no—
498C22×C127—42no—
499C22×C127—42no—
500C22×C127—42no—
501C22×C127—42no—
502C22×C127—42no—
503C22×C127—42no—
504C22×C127—42no—
505C22×C127—42no—
506C22×C127—42no—
507C22×C127—42no—
508C22×C127—42no—
509C22×C127—42no—
510C22×C127—42no—
511C22×C127—42no—
512C22×C127—42no—
513C22×C127—42no—
514C22×C127—42no—
515C22×C127—42no—
516C22×C127—42no—
517C22×C127—42no—
518C22×C127C2×#11711yescharacteristic
519C22×C127C2×C4×D411yescharacteristic
520C22×C127C2×C4×D411yescharacteristic
521C22×C127C4×#4111yescharacteristic
522C22×C127C4×#4111yescharacteristic
523C22×C127#51811yescharacteristic
524C22×C127#51811yescharacteristic
525C22×C127C2×#12111yescharacteristic
526C22×C127#52511yescharacteristic
527C22×C127#52511yescharacteristic
528C22×C127#52511yescharacteristic
529C22×C127#52911yescharacteristic
530C22×C127#52911yescharacteristic
531C22×C127#52911yescharacteristic
532C22×C127#53211yescharacteristic
533C22×C127#53411yescharacteristic
534C22×C127#53511yescharacteristic
535C22×C127#53811yescharacteristic
536C22×C127#53811yescharacteristic
537C22×C127#54611yescharacteristic
538C22×C127#54611yescharacteristic
539C22×C127#54611yescharacteristic
540C22×C127#54611yescharacteristic
541C22×C127#55111yescharacteristic
542C22×C127#55111yescharacteristic
543C22×C127#55111yescharacteristic
544C22×C127#55111yescharacteristic
545C22×C127#55111yescharacteristic
546C22×C127#55311yescharacteristic
547C22×C127#55311yescharacteristic
548C22×C127#55311yescharacteristic
549C22×C127#55311yescharacteristic
550C22×C127#55311yescharacteristic
551C22×C127#55311yescharacteristic
552C22×C127#55911yescharacteristic
553C4×C127—24no—
554C4×C127—24no—
555C4×C127—42no—
556C4×C127—42no—
557C4×C127—42no—
558C4×C127—42no—
559C4×C127—42no—
560C4×C127—42no—
561C4×C127—42no—
562C4×C127—42no—
563C4×C127—42no—
564C4×C127—81no—
565C4×C127—81no—
566#14068C12711yesmaximal, characteristic, direct product factor, Sylow
567C2×C127—44no—
568C2×C127—44no—
569C2×C127#229011yescharacteristic
570C2×C127C4×#12111yescharacteristic
571C2×C127#232111yescharacteristic
572C2×C127#234211yescharacteristic
573C2×C127#235311yescharacteristic
574C2×C127#236411yescharacteristic
575C2×C127#237411yescharacteristic
576C2×C127#253411yescharacteristic
577C2×C127#253511yescharacteristic
578C2×C127#255711yescharacteristic
579C2×C127#255911yescharacteristic
580C2×C127#257611yescharacteristic
581C2×C127#257811yescharacteristic
582C2×C127#259811yescharacteristic
583C2×C127#260011yescharacteristic
584C2×#388C2×C12711yescharacteristic, complemented
585C2×#386C2×C12711yescharacteristic
586C2×#386C2×C12711yescharacteristic
587C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
588C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
589#1443C2×C12711yescharacteristic, complemented
590#1440C2×C12711yescharacteristic, complemented
591#1439C2×C12711yescharacteristic, complemented
592#1438C2×C12711yescharacteristic
593#1437C2×C12711yescharacteristic, complemented
594#1436C2×C12711yescharacteristic, complemented
595#1434C2×C12711yescharacteristic, complemented
596#1434C2×C12711yescharacteristic, complemented
597C22⋊#95C2×C12711yescharacteristic, complemented
598C22⋊#95C2×C12711yescharacteristic, complemented
599C127#1406811yescharacteristic, direct product factor, Sylow
600C23×D4C22×C12711yescharacteristic
601C24×C4C22×C12711yescharacteristic
602C24×C4C22×C12711yescharacteristic
603C22×C4⋊C4C22×C12711yescharacteristic
604C22×C22⋊C4C22×C12711yescharacteristic
605C22×C22⋊C4C22×C12711yescharacteristic
606C22×C22⋊C4C22×C12711yescharacteristic
607C22×C22⋊C4C22×C12711yescharacteristic
608C22×C22⋊C4C22×C12711yescharacteristic
609C22×C22⋊C4C22×C12711yescharacteristic
610C22×C22⋊C4C22×C12711yescharacteristic
611C22×C22⋊C4C22×C12711yescharacteristic
612C22×C22⋊C4C22×C12711yescharacteristic
613C22×C22⋊C4C22×C12711yescharacteristic
614C22×C42C22×C12711yescharacteristic
615C22×C42C22×C12711yescharacteristic
616C22×C42C22×C12711yescharacteristic
617#388—24no—
618#386—24no—
619#386C4×C12718yescomplemented
620C4×C22⋊C4—24no—
621C4×C22⋊C4—24no—
622C2×#95C22×C12711yescharacteristic
623C2×#95C22×C12711yescharacteristic
624C2×#95C22×C12711yescharacteristic
625C2×#95C22×C12711yescharacteristic
626C2×#95C22×C12711yescharacteristic
627C2×#95C22×C12711yescharacteristic
628C2×#95C22×C12711yescharacteristic
629C2×#95C22×C12711yescharacteristic
630C2×#95C22×C12711yescharacteristic
631C2×#95C22×C12711yescharacteristic
632C2×#95C22×C12711yescharacteristic
633C2×#95C22×C12711yescharacteristic
634C2×#95C22×C12711yescharacteristic
635C2×#95C22×C12711yescharacteristic
636C2×#95C22×C12711yescharacteristic
637C2×#95C22×C12711yescharacteristic
638C2×#95C22×C12711yescharacteristic
639C2×#95C22×C12711yescharacteristic
640C25C23×C12711yescharacteristic
641C25C23×C12711yescharacteristic
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—41no—
647C22×D4—41no—
648C22×D4C2×C4×C12714yes—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4C2×C4×C12714yescomplemented
663C23×C4C23×C12711yescharacteristic
664C23×C4C23×C12711yescharacteristic
665C23×C4C23×C12711yescharacteristic
666C23×C4C23×C12711yescharacteristic
667C23×C4C23×C12711yescharacteristic
668C23×C4C23×C12711yescharacteristic
669C23×C4C23×C12711yescharacteristic
670C23×C4C23×C12711yescharacteristic
671C23×C4C23×C12711yescharacteristic
672C23×C4C23×C12711yescharacteristic
673C23×C4C23×C12711yescharacteristic
674C23×C4C23×C12711yescharacteristic
675C23×C4C23×C12711yescharacteristic
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—41no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4C2×C4×C12714yes—
706C2×C22⋊C4C2×C4×C12714yes—
707C2×C22⋊C4C2×C4×C12714yescomplemented
708C2×C22⋊C4D4×C12714yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42D4×C12714yescomplemented
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—41no—
730#95—41no—
731#95—41no—
732#95—41no—
733#95—41no—
734#95C2×C4×C12714yescomplemented
735#95C2×C4×C12714yescomplemented
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C22×C4×C12712yes—
761C24C22×C4×C12712yes—
762C24C2×D4×C12712yes—
763C24#41×C12712yes—
764C24#41×C12712yes—
765C24#41×C12712yes—
766C24C24×C12711yescharacteristic
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—28no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—28no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C12712yes—
865C22×C4C22×C4×C12712yes—
866C22×C4C22×C4×C12712yes—
867C22×C4C22×C4×C12712yes—
868C22×C4C22×C4×C12712yes—
869C22×C4C2×D4×C12712yes—
870C22×C4C2×D4×C12712yes—
871C22×C4C2×D4×C12712yes—
872C22×C4C2×D4×C12712yes—
873C22×C4C2×D4×C12712yes—
874C22×C4#41×C12712yes—
875C22×C4#41×C12712yes—
876C22×C4#41×C12712yes—
877C22×C4#41×C12712yes—
878C22×C4#41×C12712yes—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C42—44no—
891C42—44no—
892C42—44no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23#117×C12714yes—
962C23C4×D4×C12714yes—
963C23C23×C4×C12711yescharacteristic
964C23C22×D4×C12711yescharacteristic
965C23C22×D4×C12711yescharacteristic
966C23C2×#41×C12711yescharacteristic
967C23C2×#41×C12711yescharacteristic
968C23C2×#41×C12711yescharacteristic
969C23C2×#41×C12711yescharacteristic
970C23C2×#41×C12711yescharacteristic
971C23C2×#41×C12711yescharacteristic
972C23C2×#41×C12711yescharacteristic
973C23C2×#41×C12711yescharacteristic
974C23H(5,𝔽2)×C12711yescharacteristic
975C23H(5,𝔽2)×C12711yescharacteristic
976C23H(5,𝔽2)×C12711yescharacteristic
977C23H(5,𝔽2)×C12711yescharacteristic
978D4—416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—416no—
1019C2×C4—416no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4C4×D4×C12714yes—
1071C2×C4#121×C12714yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22C2×#117×C12711yescharacteristic
1103C22C2×C4×D4×C12711yescharacteristic
1104C22C2×C4×D4×C12711yescharacteristic
1105C22C4×#41×C12711yescharacteristic
1106C22C4×#41×C12711yescharacteristic
1107C22#518×C12711yescharacteristic
1108C22#518×C12711yescharacteristic
1109C22C2×#121×C12711yescharacteristic
1110C22#525×C12711yescharacteristic
1111C22#525×C12711yescharacteristic
1112C22#525×C12711yescharacteristic
1113C22#529×C12711yescharacteristic
1114C22#529×C12711yescharacteristic
1115C22#529×C12711yescharacteristic
1116C22#532×C12711yescharacteristic
1117C22#534×C12711yescharacteristic
1118C22#535×C12711yescharacteristic
1119C22#538×C12711yescharacteristic
1120C22#538×C12711yescharacteristic
1121C22#546×C12711yescharacteristic
1122C22#546×C12711yescharacteristic
1123C22#546×C12711yescharacteristic
1124C22#546×C12711yescharacteristic
1125C22#551×C12711yescharacteristic
1126C22#551×C12711yescharacteristic
1127C22#551×C12711yescharacteristic
1128C22#551×C12711yescharacteristic
1129C22#551×C12711yescharacteristic
1130C22#553×C12711yescharacteristic
1131C22#553×C12711yescharacteristic
1132C22#553×C12711yescharacteristic
1133C22#553×C12711yescharacteristic
1134C22#553×C12711yescharacteristic
1135C22#553×C12711yescharacteristic
1136C22#559×C12711yescharacteristic
1137C4—24no—
1138C4—24no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C2—44no—
1151C2—44no—
1152C2C127×#229011yescharacteristic
1153C2C4×#121×C12711yescharacteristic
1154C2C127×#232111yescharacteristic
1155C2C127×#234211yescharacteristic
1156C2C127×#235311yescharacteristic
1157C2C127×#236411yescharacteristic
1158C2C127×#237411yescharacteristic
1159C2C127×#253411yescharacteristic
1160C2C127×#253511yescharacteristic
1161C2C127×#255711yescharacteristic
1162C2C127×#255911yescharacteristic
1163C2C127×#257611yescharacteristic
1164C2C127×#257811yescharacteristic
1165C2C127×#259811yescharacteristic
1166C2C127×#260011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#388×C127C2semidirect
4. C2×C4×C22⋊C4×C127C2semidirect
5. C2×C4×C22⋊C4×C127C2semidirect
6. C127×#1443C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
12. C127×#1434C2semidirect
13. C127×#1434C2semidirect
14. C127×C22⋊#95C2semidirect
15. C127×C22⋊#95C2semidirect
35. #386×C127C4semidirect
78. C23×C4×C127C2×C4semidirect
123. C2×C22⋊C4×C127C2×C4semidirect
133. C2×C42×C127D4semidirect
150. #95×C127C2×C4semidirect
151. #95×C127C2×C4semidirect
566. #14068C127direct (N × H)
584. C2×#388C2×C127semidirect
587. C2×C4×C22⋊C4C2×C127semidirect
588. C2×C4×C22⋊C4C2×C127semidirect
589. #1443C2×C127semidirect
590. #1440C2×C127semidirect
591. #1439C2×C127semidirect
593. #1437C2×C127semidirect
594. #1436C2×C127semidirect
595. #1434C2×C127semidirect
596. #1434C2×C127semidirect
597. C22⋊#95C2×C127semidirect
598. C22⋊#95C2×C127semidirect
599. C127#14068direct (N × H)
619. #386C4×C127semidirect
662. C23×C4C2×C4×C127semidirect
707. C2×C22⋊C4C2×C4×C127semidirect
717. C2×C42D4×C127semidirect
734. #95C2×C4×C127semidirect
735. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14432
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
#14068127