Finite Group Databasebeta

← C127×#15505 #44579178

Subgroups — C127×#15505 #44579178

Order 32512.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C127C211yesmaximal, characteristic, complemented
2C2×#399×C127C211yesmaximal, characteristic, complemented
3C2×#398×C127C211yesmaximal, characteristic, complemented
4C2×#396×C127C211yesmaximal, characteristic, complemented
5C2×#390×C127C211yesmaximal, characteristic
6C2×#386×C127C211yesmaximal, characteristic
7C2×#385×C127C211yesmaximal, characteristic, complemented
8C2×#380×C127C211yesmaximal, characteristic, complemented
9C127×#1444C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38C22×C42×C127C2211yescharacteristic
39#399×C127—24no—
40#399×C127—24no—
41#398×C127—24no—
42#396×C127—24no—
43#390×C127—24no—
44#386×C127—24no—
45#385×C127—24no—
46#380×C127—24no—
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×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—41no—
66C22×D4×C127—41no—
67C22×D4×C127Q814yes—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—22no—
73C23×C4×C127—41no—
74C23×C4×C127—41no—
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
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
88C2×C4⋊C4×C127—22no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—22no—
98C2×C4⋊C4×C127—22no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—22no—
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—41no—
107C2×C4⋊C4×C127—41no—
108C2×C4⋊C4×C127—41no—
109C2×C4⋊C4×C127—41no—
110C2×C4⋊C4×C127—41no—
111C2×C4⋊C4×C127—41no—
112C2×C4⋊C4×C127—41no—
113C2×C4⋊C4×C127—41no—
114C2×C4⋊C4×C127D414yescomplemented
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
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—41no—
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×C127—41no—
147C2×C22⋊C4×C127D414yes—
148C2×C42×C127—22no—
149C2×C42×C127—22no—
150C2×C42×C127—41no—
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—22no—
160#95×C127—41no—
161#95×C127D414yes—
162#95×C127D414yescomplemented
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×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×C127—21no—
189C24×C127C2×D412yes—
190C24×C127C2×Q812yes—
191C24×C127C2×Q812yes—
192C24×C127#4112yes—
193C24×C127C2411yescharacteristic
194C2×D4×C127—28no—
195C2×D4×C127—28no—
196C2×D4×C127—44no—
197C2×D4×C127—44no—
198C2×D4×C127—44no—
199C2×D4×C127—44no—
200C2×D4×C127—44no—
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—28no—
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—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—44no—
279C22×C4×C127—44no—
280C22×C4×C127—44no—
281C22×C4×C127—44no—
282C22×C4×C127—44no—
283C22×C4×C127—44no—
284C22×C4×C127C2×D412yes—
285C22×C4×C127C2×D412yes—
286C22×C4×C127C2×D412yes—
287C22×C4×C127C2×D412yes—
288C22×C4×C127C2×D412yes—
289C22×C4×C127C2×D412yes—
290C22×C4×C127C2×D412yes—
291C22×C4×C127C2×D412yes—
292C22×C4×C127C2×D412yes—
293C22×C4×C127C2×D412yes—
294C22×C4×C127C2×D412yes—
295C22×C4×C127C2×Q812yes—
296C22×C4×C127#4112yes—
297C22×C4×C127#4112yes—
298C22×C4×C127#4112yes—
299C4⋊C4×C127—44no—
300C4⋊C4×C127—44no—
301C4⋊C4×C127—44no—
302C4⋊C4×C127—44no—
303C4⋊C4×C127—44no—
304C4⋊C4×C127—44no—
305C4⋊C4×C127—44no—
306C4⋊C4×C127—44no—
307C4⋊C4×C127—44no—
308C22⋊C4×C127—28no—
309C22⋊C4×C127—44no—
310C22⋊C4×C127—44no—
311C22⋊C4×C127—44no—
312C22⋊C4×C127—44no—
313C22⋊C4×C127—44no—
314C22⋊C4×C127—44no—
315C22⋊C4×C127—44no—
316C22⋊C4×C127—44no—
317C22⋊C4×C127—44no—
318C22⋊C4×C127—44no—
319C42×C127—44no—
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—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×C127C22⋊Q814yes—
390C23×C127C22×D411yescharacteristic
391C23×C127C22×D411yescharacteristic
392C23×C127C22×D411yescharacteristic
393C23×C127C22×D411yescharacteristic
394C23×C127C22×Q811yescharacteristic
395C23×C127C2×#4111yescharacteristic
396C23×C127C2×#4111yescharacteristic
397C23×C127C2×#4111yescharacteristic
398C23×C127C2×#4111yescharacteristic
399C23×C127H(5,𝔽2)11yescharacteristic
400C23×C127H(5,𝔽2)11yescharacteristic
401C23×C127H(5,𝔽2)11yescharacteristic
402C23×C127H(5,𝔽2)11yescharacteristic
403C23×C1272−1+411yescharacteristic
404C23×C1272−1+411yescharacteristic
405D4×C127—416no—
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—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—416no—
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×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#12114yes—
496C2×C4×C127C22⋊Q814yes—
497C2×C4×C127#12714yes—
498C22×C127—24no—
499C22×C127—24no—
500C22×C127—24no—
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×C127—42no—
519C22×C127—42no—
520C22×C127—81no—
521C22×C127—81no—
522C22×C127—81no—
523C22×C127—81no—
524C22×C127—81no—
525C22×C127—81no—
526C22×C127—81no—
527C22×C127—81no—
528C22×C127C2×#12111yescharacteristic
529C22×C127C2×C22⋊Q811yescharacteristic
530C22×C127C2×C22⋊Q811yescharacteristic
531C22×C127#52511yescharacteristic
532C22×C127#52911yescharacteristic
533C22×C127C2×#12711yescharacteristic
534C22×C127#53411yescharacteristic
535C22×C127#53511yescharacteristic
536C22×C127#53611yescharacteristic
537C22×C127#53711yescharacteristic
538C22×C127#53911yescharacteristic
539C22×C127#53911yescharacteristic
540C22×C127#54011yescharacteristic
541C22×C127#54211yescharacteristic
542C22×C127#54311yescharacteristic
543C22×C127D4211yescharacteristic
544C22×C127D4211yescharacteristic
545C22×C127#54611yescharacteristic
546C22×C127#54611yescharacteristic
547C22×C127#54611yescharacteristic
548C22×C127#54611yescharacteristic
549C22×C127#54611yescharacteristic
550C22×C127#54711yescharacteristic
551C22×C127#54711yescharacteristic
552C22×C127#54711yescharacteristic
553C22×C127D4×Q811yescharacteristic
554C22×C127D4×Q811yescharacteristic
555C22×C127#55011yescharacteristic
556C22×C127#55011yescharacteristic
557C22×C127#55111yescharacteristic
558C22×C127#55211yescharacteristic
559C22×C127#55411yescharacteristic
560C22×C127#55411yescharacteristic
561C22×C127#56211yescharacteristic
562C22×C127#56211yescharacteristic
563C4×C127—24no—
564C4×C127—24no—
565C4×C127—24no—
566C4×C127—42no—
567C4×C127—42no—
568C4×C127—42no—
569C4×C127—42no—
570C4×C127—42no—
571C4×C127—42no—
572C4×C127—81no—
573C4×C127—81no—
574C4×C127—81no—
575C4×C127—81no—
576#15505C12711yesmaximal, characteristic, direct product factor, Sylow
577C2×C127—44no—
578C2×C127—82no—
579C2×C127#241711yescharacteristic
580C2×C127#242511yescharacteristic
581C2×C127#243711yescharacteristic
582C2×C127#244911yescharacteristic
583C2×C127#245411yescharacteristic
584C2×C127#247911yescharacteristic
585C2×C127#253911yescharacteristic
586C2×C127#254111yescharacteristic
587C2×C127#254211yescharacteristic
588C2×C127#267111yescharacteristic
589C2×C127#267211yescharacteristic
590C2×C127#269211yescharacteristic
591C2×C127#269411yescharacteristic
592C2×C127#270611yescharacteristic
593C2×C127#273211yescharacteristic
594C2×#399C2×C12711yescharacteristic, complemented
595C2×#399C2×C12711yescharacteristic, complemented
596C2×#398C2×C12711yescharacteristic, complemented
597C2×#396C2×C12711yescharacteristic, complemented
598C2×#390C2×C12711yescharacteristic
599C2×#386C2×C12711yescharacteristic
600C2×#385C2×C12711yescharacteristic, complemented
601C2×#380C2×C12711yescharacteristic, complemented
602#1444C2×C12711yescharacteristic, complemented
603#1439C2×C12711yescharacteristic, complemented
604#1439C2×C12711yescharacteristic, complemented
605#1439C2×C12711yescharacteristic, complemented
606#1438C2×C12711yescharacteristic
607#1436C2×C12711yescharacteristic, complemented
608C4⋊#95C2×C12711yescharacteristic, complemented
609C127#1550511yescharacteristic, direct product factor, Sylow
610C23×D4C22×C12711yescharacteristic
611C24×C4C22×C12711yescharacteristic
612C22×C4⋊C4C22×C12711yescharacteristic
613C22×C4⋊C4C22×C12711yescharacteristic
614C22×C4⋊C4C22×C12711yescharacteristic
615C22×C4⋊C4C22×C12711yescharacteristic
616C22×C4⋊C4C22×C12711yescharacteristic
617C22×C4⋊C4C22×C12711yescharacteristic
618C22×C4⋊C4C22×C12711yescharacteristic
619C22×C4⋊C4C22×C12711yescharacteristic
620C22×C4⋊C4C22×C12711yescharacteristic
621C22×C22⋊C4C22×C12711yescharacteristic
622C22×C22⋊C4C22×C12711yescharacteristic
623C22×C22⋊C4C22×C12711yescharacteristic
624C22×C22⋊C4C22×C12711yescharacteristic
625C22×C22⋊C4C22×C12711yescharacteristic
626C22×C22⋊C4C22×C12711yescharacteristic
627C22×C22⋊C4C22×C12711yescharacteristic
628C22×C22⋊C4C22×C12711yescharacteristic
629C22×C22⋊C4C22×C12711yescharacteristic
630C22×C22⋊C4C22×C12711yescharacteristic
631C22×C22⋊C4C22×C12711yescharacteristic
632C22×C42C22×C12711yescharacteristic
633#399—24no—
634#399—24no—
635#398—24no—
636#396—24no—
637#390—24no—
638#386—24no—
639#385—24no—
640#380—24no—
641C2×#95C22×C12711yescharacteristic
642C2×#95C22×C12711yescharacteristic
643C2×#95C22×C12711yescharacteristic
644C2×#95C22×C12711yescharacteristic
645C2×#95C22×C12711yescharacteristic
646C2×#95C22×C12711yescharacteristic
647C2×#95C22×C12711yescharacteristic
648C2×#95C22×C12711yescharacteristic
649C2×#95C22×C12711yescharacteristic
650C2×#95C22×C12711yescharacteristic
651C2×#95C22×C12711yescharacteristic
652C2×#95C22×C12711yescharacteristic
653C25C23×C12711yescharacteristic
654C25C23×C12711yescharacteristic
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—41no—
660C22×D4—41no—
661C22×D4Q8×C12714yes—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—41no—
668C23×C4—41no—
669C23×C4C23×C12711yescharacteristic
670C23×C4C23×C12711yescharacteristic
671C23×C4C23×C12711yescharacteristic
672C23×C4C23×C12711yescharacteristic
673C23×C4C23×C12711yescharacteristic
674C23×C4C23×C12711yescharacteristic
675C23×C4C23×C12711yescharacteristic
676C23×C4C23×C12711yescharacteristic
677C23×C4C23×C12711yescharacteristic
678C23×C4C23×C12711yescharacteristic
679C23×C4C23×C12711yescharacteristic
680C23×C4C23×C12711yescharacteristic
681C23×C4C23×C12711yescharacteristic
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—41no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4D4×C12714yescomplemented
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
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—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4D4×C12714yes—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—41no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—22no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—41no—
755#95D4×C12714yes—
756#95D4×C12714yescomplemented
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
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—
783C24C2×D4×C12712yes—
784C24C2×Q8×C12712yes—
785C24C2×Q8×C12712yes—
786C24#41×C12712yes—
787C24C24×C12711yescharacteristic
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
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—28no—
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—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—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4C2×D4×C12712yes—
879C22×C4C2×D4×C12712yes—
880C22×C4C2×D4×C12712yes—
881C22×C4C2×D4×C12712yes—
882C22×C4C2×D4×C12712yes—
883C22×C4C2×D4×C12712yes—
884C22×C4C2×D4×C12712yes—
885C22×C4C2×D4×C12712yes—
886C22×C4C2×D4×C12712yes—
887C22×C4C2×D4×C12712yes—
888C22×C4C2×D4×C12712yes—
889C22×C4C2×Q8×C12712yes—
890C22×C4#41×C12712yes—
891C22×C4#41×C12712yes—
892C22×C4#41×C12712yes—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C42—44no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
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—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
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—
983C23C22⋊Q8×C12714yes—
984C23C22×D4×C12711yescharacteristic
985C23C22×D4×C12711yescharacteristic
986C23C22×D4×C12711yescharacteristic
987C23C22×D4×C12711yescharacteristic
988C23C22×Q8×C12711yescharacteristic
989C23C2×#41×C12711yescharacteristic
990C23C2×#41×C12711yescharacteristic
991C23C2×#41×C12711yescharacteristic
992C23C2×#41×C12711yescharacteristic
993C23H(5,𝔽2)×C12711yescharacteristic
994C23H(5,𝔽2)×C12711yescharacteristic
995C23H(5,𝔽2)×C12711yescharacteristic
996C23H(5,𝔽2)×C12711yescharacteristic
997C232−1+4×C12711yescharacteristic
998C232−1+4×C12711yescharacteristic
999D4—416no—
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—22no—
1019C2×C4—22no—
1020C2×C4—22no—
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—416no—
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×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#121×C12714yes—
1090C2×C4C22⋊Q8×C12714yes—
1091C2×C4#127×C12714yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×#121×C12711yescharacteristic
1123C22C2×C22⋊Q8×C12711yescharacteristic
1124C22C2×C22⋊Q8×C12711yescharacteristic
1125C22#525×C12711yescharacteristic
1126C22#529×C12711yescharacteristic
1127C22C2×#127×C12711yescharacteristic
1128C22#534×C12711yescharacteristic
1129C22#535×C12711yescharacteristic
1130C22#536×C12711yescharacteristic
1131C22#537×C12711yescharacteristic
1132C22#539×C12711yescharacteristic
1133C22#539×C12711yescharacteristic
1134C22#540×C12711yescharacteristic
1135C22#542×C12711yescharacteristic
1136C22#543×C12711yescharacteristic
1137C22D42×C12711yescharacteristic
1138C22D42×C12711yescharacteristic
1139C22#546×C12711yescharacteristic
1140C22#546×C12711yescharacteristic
1141C22#546×C12711yescharacteristic
1142C22#546×C12711yescharacteristic
1143C22#546×C12711yescharacteristic
1144C22#547×C12711yescharacteristic
1145C22#547×C12711yescharacteristic
1146C22#547×C12711yescharacteristic
1147C22D4×Q8×C12711yescharacteristic
1148C22D4×Q8×C12711yescharacteristic
1149C22#550×C12711yescharacteristic
1150C22#550×C12711yescharacteristic
1151C22#551×C12711yescharacteristic
1152C22#552×C12711yescharacteristic
1153C22#554×C12711yescharacteristic
1154C22#554×C12711yescharacteristic
1155C22#562×C12711yescharacteristic
1156C22#562×C12711yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—24no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C127×#241711yescharacteristic
1173C2C127×#242511yescharacteristic
1174C2C127×#243711yescharacteristic
1175C2C127×#244911yescharacteristic
1176C2C127×#245411yescharacteristic
1177C2C127×#247911yescharacteristic
1178C2C127×#253911yescharacteristic
1179C2C127×#254111yescharacteristic
1180C2C127×#254211yescharacteristic
1181C2C127×#267111yescharacteristic
1182C2C127×#267211yescharacteristic
1183C2C127×#269211yescharacteristic
1184C2C127×#269411yescharacteristic
1185C2C127×#270611yescharacteristic
1186C2C127×#273211yescharacteristic
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. C2×#399×C127C2semidirect
2. C2×#399×C127C2semidirect
3. C2×#398×C127C2semidirect
4. C2×#396×C127C2semidirect
7. C2×#385×C127C2semidirect
8. C2×#380×C127C2semidirect
9. C127×#1444C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
14. C127×#1436C2semidirect
15. C127×C4⋊#95C2semidirect
114. C2×C4⋊C4×C127D4semidirect
162. #95×C127D4semidirect
576. #15505C127direct (N × H)
594. C2×#399C2×C127semidirect
595. C2×#399C2×C127semidirect
596. C2×#398C2×C127semidirect
597. C2×#396C2×C127semidirect
600. C2×#385C2×C127semidirect
601. C2×#380C2×C127semidirect
602. #1444C2×C127semidirect
603. #1439C2×C127semidirect
604. #1439C2×C127semidirect
605. #1439C2×C127semidirect
607. #1436C2×C127semidirect
608. C4⋊#95C2×C127semidirect
609. C127#15505direct (N × H)
708. C2×C4⋊C4D4×C127semidirect
756. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#398×C1272
C2×#396×C1272
C2×#390×C1272
C2×#386×C1272
C2×#385×C1272
C2×#380×C1272
C127×#14442
C127×#14392
C127×#14382
C127×#14362
C127×C4⋊#952
#15505127