Finite Group Databasebeta

← C127×#15323 #44578996

Subgroups — C127×#15323 #44578996

Order 32512.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C2×#393×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C211yesmaximal, characteristic
4C2×#386×C127C211yesmaximal, characteristic
5C2×#385×C127C211yesmaximal, characteristic, complemented
6C2×#380×C127C211yesmaximal, characteristic, complemented
7C127×#1446C211yesmaximal, characteristic, complemented
8C127×#1445C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1441C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1439C211yesmaximal, characteristic, complemented
14C127×#1438C211yesmaximal, characteristic
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C2×C22⋊Q8×C127—24no—
21C2×C22⋊Q8×C127—24no—
22C2×C22⋊Q8×C127—24no—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C4⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38#393×C127—24no—
39#386×C127—24no—
40#386×C127—24no—
41#385×C127—24no—
42#380×C127—24no—
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C25×C127C2311yescharacteristic
60C25×C127C2311yescharacteristic
61C22×Q8×C127—22no—
62C22×Q8×C127—22no—
63C22×Q8×C127—22no—
64C22×Q8×C127—22no—
65C22×Q8×C127—22no—
66C22×Q8×C127—41no—
67C22×Q8×C127—41no—
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—22no—
72C22×D4×C127—41no—
73C22×D4×C127—41no—
74C22×D4×C127Q814yescomplemented
75C23×C4×C127—22no—
76C23×C4×C127—22no—
77C23×C4×C127—22no—
78C23×C4×C127—22no—
79C23×C4×C127—22no—
80C23×C4×C127—22no—
81C23×C4×C127—22no—
82C23×C4×C127—22no—
83C23×C4×C127—22no—
84C23×C4×C127—22no—
85C23×C4×C127—41no—
86C23×C4×C127—41no—
87C23×C4×C127—41no—
88C23×C4×C127—41no—
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2311yescharacteristic
102C22⋊Q8×C127—232no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127—22no—
108C2×C4⋊C4×C127—22no—
109C2×C4⋊C4×C127—22no—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—22no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—41no—
114C2×C4⋊C4×C127—41no—
115C2×C4⋊C4×C127—41no—
116C2×C4⋊C4×C127D414yescomplemented
117C2×C4⋊C4×C127D414yescomplemented
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127—22no—
126C2×C22⋊C4×C127—22no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127—22no—
130C2×C22⋊C4×C127—22no—
131C2×C22⋊C4×C127—22no—
132C2×C22⋊C4×C127—22no—
133C2×C22⋊C4×C127—22no—
134C2×C22⋊C4×C127—22no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—22no—
137C2×C22⋊C4×C127—22no—
138C2×C22⋊C4×C127—41no—
139C2×C22⋊C4×C127—41no—
140C2×C22⋊C4×C127—41no—
141C2×C22⋊C4×C127—41no—
142C2×C22⋊C4×C127—41no—
143C2×C22⋊C4×C127—41no—
144C2×C22⋊C4×C127—41no—
145C2×C22⋊C4×C127—41no—
146C2×C22⋊C4×C127D414yes—
147C2×C22⋊C4×C127D414yes—
148#95×C127—22no—
149#95×C127—22no—
150#95×C127—22no—
151#95×C127—22no—
152#95×C127—22no—
153#95×C127—22no—
154#95×C127—22no—
155#95×C127—22no—
156#95×C127—22no—
157#95×C127—22no—
158#95×C127—22no—
159#95×C127—41no—
160#95×C127—41no—
161#95×C127—41no—
162#95×C127—41no—
163#95×C127—41no—
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×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127—21no—
183C24×C127—21no—
184C24×C127—21no—
185C24×C127—21no—
186C24×C127—21no—
187C24×C127—21no—
188C24×C127C2×D412yes—
189C24×C127C2×D412yes—
190C24×C127C2×Q812yes—
191C24×C127C2×Q812yes—
192C24×C127#4112yes—
193C24×C127#4112yes—
194C24×C127C2411yescharacteristic
195C2×Q8×C127—28no—
196C2×Q8×C127—44no—
197C2×Q8×C127—44no—
198C2×Q8×C127—44no—
199C2×Q8×C127—44no—
200C2×Q8×C127—44no—
201C2×Q8×C127—44no—
202C2×D4×C127—28no—
203C2×D4×C127—28no—
204C2×D4×C127—44no—
205C2×D4×C127—44no—
206C2×D4×C127—44no—
207C2×D4×C127—44no—
208C2×D4×C127—44no—
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—28no—
218C22×C4×C127—28no—
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—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—21no—
269C22×C4×C127—21no—
270C22×C4×C127—21no—
271C22×C4×C127—21no—
272C22×C4×C127—21no—
273C22×C4×C127—21no—
274C22×C4×C127—21no—
275C22×C4×C127—21no—
276C22×C4×C127—21no—
277C22×C4×C127—21no—
278C22×C4×C127—21no—
279C22×C4×C127—21no—
280C22×C4×C127—21no—
281C22×C4×C127—21no—
282C22×C4×C127—21no—
283C22×C4×C127—21no—
284C22×C4×C127—21no—
285C22×C4×C127—21no—
286C22×C4×C127—21no—
287C22×C4×C127—21no—
288C22×C4×C127—21no—
289C22×C4×C127—44no—
290C22×C4×C127—44no—
291C22×C4×C127—44no—
292C22×C4×C127—44no—
293C22×C4×C127—44no—
294C22×C4×C127—44no—
295C22×C4×C127—44no—
296C22×C4×C127—44no—
297C22×C4×C127—44no—
298C22×C4×C127—44no—
299C22×C4×C127—44no—
300C22×C4×C127—44no—
301C22×C4×C127C2×D412yes—
302C22×C4×C127C2×D412yes—
303C22×C4×C127C2×D412yes—
304C22×C4×C127C2×D412yes—
305C22×C4×C127C2×D412yes—
306C22×C4×C127C2×D412yes—
307C22×C4×C127C2×D412yes—
308C22×C4×C127C2×D412yes—
309C22×C4×C127C2×D412yes—
310C22×C4×C127C2×D412yes—
311C22×C4×C127C2×Q812yes—
312C22×C4×C127#4112yes—
313C22×C4×C127#4112yes—
314C4⋊C4×C127—28no—
315C4⋊C4×C127—28no—
316C4⋊C4×C127—28no—
317C4⋊C4×C127—44no—
318C4⋊C4×C127—44no—
319C22⋊C4×C127—28no—
320C22⋊C4×C127—28no—
321C22⋊C4×C127—28no—
322C22⋊C4×C127—44no—
323C22⋊C4×C127—44no—
324C22⋊C4×C127—44no—
325C22⋊C4×C127—44no—
326C22⋊C4×C127—44no—
327C22⋊C4×C127—44no—
328C22⋊C4×C127—44no—
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—22no—
346C23×C127—22no—
347C23×C127—22no—
348C23×C127—22no—
349C23×C127—22no—
350C23×C127—22no—
351C23×C127—22no—
352C23×C127—22no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—22no—
357C23×C127—22no—
358C23×C127—22no—
359C23×C127—22no—
360C23×C127—22no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—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—41no—
378C23×C127—41no—
379C23×C127—41no—
380C23×C127—41no—
381C23×C127—41no—
382C23×C127—41no—
383C23×C127—41no—
384C23×C127—41no—
385C23×C127—41no—
386C23×C127—41no—
387C23×C127—41no—
388C23×C127—41no—
389C23×C127—41no—
390C23×C127—41no—
391C23×C127—41no—
392C23×C127—41no—
393C23×C127—41no—
394C23×C127—41no—
395C23×C127—41no—
396C23×C127—41no—
397C23×C127C22⋊Q814yes—
398C23×C127C22⋊Q814yescomplemented
399C23×C127C22×D411yescharacteristic
400C23×C127C22×D411yescharacteristic
401C23×C127C22×D411yescharacteristic
402C23×C127C22×D411yescharacteristic
403C23×C127C22×Q811yescharacteristic
404C23×C127C2×#4111yescharacteristic
405C23×C127C2×#4111yescharacteristic
406C23×C127C2×#4111yescharacteristic
407C23×C127C2×#4111yescharacteristic
408C23×C127H(5,𝔽2)11yescharacteristic
409C23×C127H(5,𝔽2)11yescharacteristic
410C23×C127H(5,𝔽2)11yescharacteristic
411C23×C127H(5,𝔽2)11yescharacteristic
412C23×C1272−1+411yescharacteristic
413C23×C1272−1+411yescharacteristic
414Q8×C127—416no—
415D4×C127—416no—
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—22no—
435C2×C4×C127—22no—
436C2×C4×C127—22no—
437C2×C4×C127—22no—
438C2×C4×C127—22no—
439C2×C4×C127—22no—
440C2×C4×C127—22no—
441C2×C4×C127—22no—
442C2×C4×C127—22no—
443C2×C4×C127—22no—
444C2×C4×C127—22no—
445C2×C4×C127—22no—
446C2×C4×C127—22no—
447C2×C4×C127—22no—
448C2×C4×C127—22no—
449C2×C4×C127—416no—
450C2×C4×C127—416no—
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×C127—41no—
487C2×C4×C127—41no—
488C2×C4×C127—41no—
489C2×C4×C127—41no—
490C2×C4×C127—41no—
491C2×C4×C127—41no—
492C2×C4×C127—41no—
493C2×C4×C127—41no—
494C2×C4×C127—41no—
495C2×C4×C127—41no—
496C2×C4×C127—41no—
497C2×C4×C127—41no—
498C2×C4×C127—41no—
499C2×C4×C127—41no—
500C2×C4×C127—41no—
501C2×C4×C127—41no—
502C2×C4×C127—41no—
503C2×C4×C127—41no—
504C2×C4×C127—41no—
505C2×C4×C127—41no—
506C2×C4×C127—41no—
507C2×C4×C127#12014yes—
508C2×C4×C127#12114yes—
509C22×C127—24no—
510C22×C127—24no—
511C22×C127—24no—
512C22×C127—24no—
513C22×C127—24no—
514C22×C127—24no—
515C22×C127—42no—
516C22×C127—42no—
517C22×C127—42no—
518C22×C127—42no—
519C22×C127—42no—
520C22×C127—42no—
521C22×C127—42no—
522C22×C127—42no—
523C22×C127—42no—
524C22×C127—42no—
525C22×C127—42no—
526C22×C127—42no—
527C22×C127—42no—
528C22×C127—42no—
529C22×C127—42no—
530C22×C127—42no—
531C22×C127—42no—
532C22×C127—42no—
533C22×C127—42no—
534C22×C127—42no—
535C22×C127—42no—
536C22×C127—42no—
537C22×C127—42no—
538C22×C127—42no—
539C22×C127C2×#12011yescharacteristic
540C22×C127C2×#12111yescharacteristic
541C22×C127C2×C22⋊Q811yescharacteristic
542C22×C127C2×C22⋊Q811yescharacteristic
543C22×C127#52511yescharacteristic
544C22×C127#52911yescharacteristic
545C22×C127#53511yescharacteristic
546C22×C127#53511yescharacteristic
547C22×C127#53611yescharacteristic
548C22×C127#53711yescharacteristic
549C22×C127#53811yescharacteristic
550C22×C127#53911yescharacteristic
551C22×C127#54211yescharacteristic
552C22×C127#54211yescharacteristic
553C22×C127#54311yescharacteristic
554C22×C127D4211yescharacteristic
555C22×C127D4211yescharacteristic
556C22×C127#54611yescharacteristic
557C22×C127#54611yescharacteristic
558C22×C127#54611yescharacteristic
559C22×C127#54611yescharacteristic
560C22×C127#54611yescharacteristic
561C22×C127#54611yescharacteristic
562C22×C127#54611yescharacteristic
563C22×C127#54711yescharacteristic
564C22×C127#54811yescharacteristic
565C22×C127#54811yescharacteristic
566C22×C127D4×Q811yescharacteristic
567C22×C127D4×Q811yescharacteristic
568C22×C127#55111yescharacteristic
569C22×C127#55211yescharacteristic
570C22×C127#55411yescharacteristic
571C22×C127#55411yescharacteristic
572C22×C127#56211yescharacteristic
573C22×C127#56211yescharacteristic
574C4×C127—24no—
575C4×C127—24no—
576C4×C127—42no—
577C4×C127—42no—
578C4×C127—42no—
579C4×C127—42no—
580C4×C127—42no—
581C4×C127—42no—
582C4×C127—42no—
583C4×C127—81no—
584C4×C127—81no—
585C4×C127—81no—
586C4×C127—81no—
587#15323C12711yesmaximal, characteristic, direct product factor, Sylow
588C2×C127—44no—
589C2×C127—44no—
590C2×C127#240411yescharacteristic
591C2×C127#240811yescharacteristic
592C2×C127#240911yescharacteristic
593C2×C127#241711yescharacteristic
594C2×C127#242711yescharacteristic
595C2×C127#243711yescharacteristic
596C2×C127#244911yescharacteristic
597C2×C127#245011yescharacteristic
598C2×C127#247711yescharacteristic
599C2×C127#267211yescharacteristic
600C2×C127#267611yescharacteristic
601C2×C127#268711yescharacteristic
602C2×C127#269211yescharacteristic
603C2×C127#269211yescharacteristic
604C2×C127#269611yescharacteristic
605C22×C22⋊Q8C2×C12711yescharacteristic, complemented
606C2×#393C2×C12711yescharacteristic, complemented
607C2×#386C2×C12711yescharacteristic
608C2×#386C2×C12711yescharacteristic
609C2×#385C2×C12711yescharacteristic, complemented
610C2×#380C2×C12711yescharacteristic, complemented
611#1446C2×C12711yescharacteristic, complemented
612#1445C2×C12711yescharacteristic, complemented
613#1441C2×C12711yescharacteristic, complemented
614#1441C2×C12711yescharacteristic, complemented
615#1439C2×C12711yescharacteristic, complemented
616#1439C2×C12711yescharacteristic, complemented
617#1439C2×C12711yescharacteristic, complemented
618#1438C2×C12711yescharacteristic
619C22⋊#95C2×C12711yescharacteristic, complemented
620C127#1532311yescharacteristic, direct product factor, Sylow
621C23×Q8C22×C12711yescharacteristic
622C23×D4C22×C12711yescharacteristic
623C24×C4C22×C12711yescharacteristic
624C24×C4C22×C12711yescharacteristic
625C2×C22⋊Q8—24no—
626C2×C22⋊Q8—24no—
627C2×C22⋊Q8—24no—
628C22×C4⋊C4C22×C12711yescharacteristic
629C22×C4⋊C4C22×C12711yescharacteristic
630C22×C4⋊C4C22×C12711yescharacteristic
631C22×C4⋊C4C22×C12711yescharacteristic
632C22×C4⋊C4C22×C12711yescharacteristic
633C22×C22⋊C4C22×C12711yescharacteristic
634C22×C22⋊C4C22×C12711yescharacteristic
635C22×C22⋊C4C22×C12711yescharacteristic
636C22×C22⋊C4C22×C12711yescharacteristic
637C22×C22⋊C4C22×C12711yescharacteristic
638C22×C22⋊C4C22×C12711yescharacteristic
639C22×C22⋊C4C22×C12711yescharacteristic
640C22×C22⋊C4C22×C12711yescharacteristic
641C22×C22⋊C4C22×C12711yescharacteristic
642C22×C22⋊C4C22×C12711yescharacteristic
643#393—24no—
644#386—24no—
645#386—24no—
646#385—24no—
647#380—24no—
648C2×#95C22×C12711yescharacteristic
649C2×#95C22×C12711yescharacteristic
650C2×#95C22×C12711yescharacteristic
651C2×#95C22×C12711yescharacteristic
652C2×#95C22×C12711yescharacteristic
653C2×#95C22×C12711yescharacteristic
654C2×#95C22×C12711yescharacteristic
655C2×#95C22×C12711yescharacteristic
656C2×#95C22×C12711yescharacteristic
657C2×#95C22×C12711yescharacteristic
658C2×#95C22×C12711yescharacteristic
659C2×#95C22×C12711yescharacteristic
660C2×#95C22×C12711yescharacteristic
661C2×#95C22×C12711yescharacteristic
662C2×#95C22×C12711yescharacteristic
663C2×#95C22×C12711yescharacteristic
664C25C23×C12711yescharacteristic
665C25C23×C12711yescharacteristic
666C22×Q8—22no—
667C22×Q8—22no—
668C22×Q8—22no—
669C22×Q8—22no—
670C22×Q8—22no—
671C22×Q8—41no—
672C22×Q8—41no—
673C22×D4—22no—
674C22×D4—22no—
675C22×D4—22no—
676C22×D4—22no—
677C22×D4—41no—
678C22×D4—41no—
679C22×D4Q8×C12714yescomplemented
680C23×C4—22no—
681C23×C4—22no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4—41no—
694C23×C4C23×C12711yescharacteristic
695C23×C4C23×C12711yescharacteristic
696C23×C4C23×C12711yescharacteristic
697C23×C4C23×C12711yescharacteristic
698C23×C4C23×C12711yescharacteristic
699C23×C4C23×C12711yescharacteristic
700C23×C4C23×C12711yescharacteristic
701C23×C4C23×C12711yescharacteristic
702C23×C4C23×C12711yescharacteristic
703C23×C4C23×C12711yescharacteristic
704C23×C4C23×C12711yescharacteristic
705C23×C4C23×C12711yescharacteristic
706C23×C4C23×C12711yescharacteristic
707C22⋊Q8—232no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—41no—
720C2×C4⋊C4—41no—
721C2×C4⋊C4D4×C12714yescomplemented
722C2×C4⋊C4D4×C12714yescomplemented
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—41no—
751C2×C22⋊C4D4×C12714yes—
752C2×C22⋊C4D4×C12714yes—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—22no—
764#95—41no—
765#95—41no—
766#95—41no—
767#95—41no—
768#95—41no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24C2×D4×C12712yes—
794C24C2×D4×C12712yes—
795C24C2×Q8×C12712yes—
796C24C2×Q8×C12712yes—
797C24#41×C12712yes—
798C24#41×C12712yes—
799C24C24×C12711yescharacteristic
800C2×Q8—28no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
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—28no—
823C22×C4—28no—
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—21no—
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—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4C2×D4×C12712yes—
907C22×C4C2×D4×C12712yes—
908C22×C4C2×D4×C12712yes—
909C22×C4C2×D4×C12712yes—
910C22×C4C2×D4×C12712yes—
911C22×C4C2×D4×C12712yes—
912C22×C4C2×D4×C12712yes—
913C22×C4C2×D4×C12712yes—
914C22×C4C2×D4×C12712yes—
915C22×C4C2×D4×C12712yes—
916C22×C4C2×Q8×C12712yes—
917C22×C4#41×C12712yes—
918C22×C4#41×C12712yes—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23C22⋊Q8×C12714yes—
1003C23C22⋊Q8×C12714yescomplemented
1004C23C22×D4×C12711yescharacteristic
1005C23C22×D4×C12711yescharacteristic
1006C23C22×D4×C12711yescharacteristic
1007C23C22×D4×C12711yescharacteristic
1008C23C22×Q8×C12711yescharacteristic
1009C23C2×#41×C12711yescharacteristic
1010C23C2×#41×C12711yescharacteristic
1011C23C2×#41×C12711yescharacteristic
1012C23C2×#41×C12711yescharacteristic
1013C23H(5,𝔽2)×C12711yescharacteristic
1014C23H(5,𝔽2)×C12711yescharacteristic
1015C23H(5,𝔽2)×C12711yescharacteristic
1016C23H(5,𝔽2)×C12711yescharacteristic
1017C232−1+4×C12711yescharacteristic
1018C232−1+4×C12711yescharacteristic
1019Q8—416no—
1020D4—416no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—416no—
1055C2×C4—416no—
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×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4#120×C12714yes—
1113C2×C4#121×C12714yes—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22C2×#120×C12711yescharacteristic
1145C22C2×#121×C12711yescharacteristic
1146C22C2×C22⋊Q8×C12711yescharacteristic
1147C22C2×C22⋊Q8×C12711yescharacteristic
1148C22#525×C12711yescharacteristic
1149C22#529×C12711yescharacteristic
1150C22#535×C12711yescharacteristic
1151C22#535×C12711yescharacteristic
1152C22#536×C12711yescharacteristic
1153C22#537×C12711yescharacteristic
1154C22#538×C12711yescharacteristic
1155C22#539×C12711yescharacteristic
1156C22#542×C12711yescharacteristic
1157C22#542×C12711yescharacteristic
1158C22#543×C12711yescharacteristic
1159C22D42×C12711yescharacteristic
1160C22D42×C12711yescharacteristic
1161C22#546×C12711yescharacteristic
1162C22#546×C12711yescharacteristic
1163C22#546×C12711yescharacteristic
1164C22#546×C12711yescharacteristic
1165C22#546×C12711yescharacteristic
1166C22#546×C12711yescharacteristic
1167C22#546×C12711yescharacteristic
1168C22#547×C12711yescharacteristic
1169C22#548×C12711yescharacteristic
1170C22#548×C12711yescharacteristic
1171C22D4×Q8×C12711yescharacteristic
1172C22D4×Q8×C12711yescharacteristic
1173C22#551×C12711yescharacteristic
1174C22#552×C12711yescharacteristic
1175C22#554×C12711yescharacteristic
1176C22#554×C12711yescharacteristic
1177C22#562×C12711yescharacteristic
1178C22#562×C12711yescharacteristic
1179C4—24no—
1180C4—24no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C2—44no—
1193C2—44no—
1194C2C127×#240411yescharacteristic
1195C2C127×#240811yescharacteristic
1196C2C127×#240911yescharacteristic
1197C2C127×#241711yescharacteristic
1198C2C127×#242711yescharacteristic
1199C2C127×#243711yescharacteristic
1200C2C127×#244911yescharacteristic
1201C2C127×#245011yescharacteristic
1202C2C127×#247711yescharacteristic
1203C2C127×#267211yescharacteristic
1204C2C127×#267611yescharacteristic
1205C2C127×#268711yescharacteristic
1206C2C127×#269211yescharacteristic
1207C2C127×#269211yescharacteristic
1208C2C127×#269611yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C127C2semidirect
2. C2×#393×C127C2semidirect
5. C2×#385×C127C2semidirect
6. C2×#380×C127C2semidirect
7. C127×#1446C2semidirect
8. C127×#1445C2semidirect
9. C127×#1441C2semidirect
10. C127×#1441C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
13. C127×#1439C2semidirect
15. C127×C22⋊#95C2semidirect
74. C22×D4×C127Q8semidirect
116. C2×C4⋊C4×C127D4semidirect
117. C2×C4⋊C4×C127D4semidirect
398. C23×C127C22⋊Q8semidirect
587. #15323C127direct (N × H)
605. C22×C22⋊Q8C2×C127semidirect
606. C2×#393C2×C127semidirect
609. C2×#385C2×C127semidirect
610. C2×#380C2×C127semidirect
611. #1446C2×C127semidirect
612. #1445C2×C127semidirect
613. #1441C2×C127semidirect
614. #1441C2×C127semidirect
615. #1439C2×C127semidirect
616. #1439C2×C127semidirect
617. #1439C2×C127semidirect
619. C22⋊#95C2×C127semidirect
620. C127#15323direct (N × H)
679. C22×D4Q8×C127semidirect
721. C2×C4⋊C4D4×C127semidirect
722. C2×C4⋊C4D4×C127semidirect
1003. C23C22⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#393×C1272
C2×#386×C1272
C2×#385×C1272
C2×#380×C1272
C127×#14462
C127×#14452
C127×#14412
C127×#14392
C127×#14382
C127×C22⋊#952
#15323127