Finite Group Databasebeta

← C127×#14096 #44577769

Subgroups — C127×#14096 #44577769

Order 32512.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C2×#388×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1445C211yesmaximal, characteristic, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1438C211yesmaximal, characteristic
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C127×#1436C211yesmaximal, characteristic, complemented
13C127×C4⋊#95C211yesmaximal, characteristic, complemented
14C127×C22⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C2×#123×C127—24no—
20C2×#123×C127—24no—
21C2×#123×C127C418yescomplemented
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊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×C42×C127C2211yescharacteristic
36C22×C42×C127C2211yescharacteristic
37C22×C42×C127C2211yescharacteristic
38#388×C127—24no—
39#386×C127—24no—
40C4×C22⋊C4×C127—24no—
41C4×C22⋊C4×C127—24no—
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
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C25×C127C2311yescharacteristic
59C25×C127C2311yescharacteristic
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—41no—
65C22×D4×C127—41no—
66C22×D4×C127C2×C414yes—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—22no—
73C23×C4×C127—22no—
74C23×C4×C127—22no—
75C23×C4×C127—22no—
76C23×C4×C127—41no—
77C23×C4×C127—41no—
78C23×C4×C127—41no—
79C23×C4×C127—41no—
80C23×C4×C127C2×C414yescomplemented
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
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94#123×C127—232no—
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—41no—
102C2×C4⋊C4×C127C2×C414yescomplemented
103C2×C4⋊C4×C127C2×C414yescomplemented
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—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—41no—
125C2×C22⋊C4×C127—41no—
126C2×C22⋊C4×C127—41no—
127C2×C22⋊C4×C127—41no—
128C2×C22⋊C4×C127C2×C414yes—
129C2×C22⋊C4×C127C2×C414yes—
130C2×C22⋊C4×C127C2×C414yescomplemented
131C2×C22⋊C4×C127D414yes—
132C2×C22⋊C4×C127D414yes—
133C2×C22⋊C4×C127D414yes—
134C2×C42×C127—22no—
135C2×C42×C127—22no—
136C2×C42×C127—22no—
137C2×C42×C127—22no—
138C2×C42×C127—22no—
139C2×C42×C127—22no—
140C2×C42×C127—41no—
141C2×C42×C127—41no—
142C2×C42×C127—41no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—22no—
146#95×C127—22no—
147#95×C127—22no—
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—41no—
156#95×C127—41no—
157#95×C127—41no—
158#95×C127—41no—
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×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127—21no—
183C24×C127C22×C412yes—
184C24×C127C22×C412yes—
185C24×C127C2×D412yes—
186C24×C127C2×D412yes—
187C24×C127C2×D412yes—
188C24×C127#4112yes—
189C24×C127C2411yescharacteristic
190C2×D4×C127—28no—
191C2×D4×C127—28no—
192C2×D4×C127—44no—
193C2×D4×C127—44no—
194C2×D4×C127—44no—
195C2×D4×C127—44no—
196C2×D4×C127—44no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
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—28no—
210C22×C4×C127—28no—
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—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—28no—
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—44no—
275C22×C4×C127—44no—
276C22×C4×C127—44no—
277C22×C4×C127—44no—
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×C127—44no—
285C22×C4×C127C22×C412yes—
286C22×C4×C127C22×C412yes—
287C22×C4×C127C22×C412yes—
288C22×C4×C127C22×C412yes—
289C22×C4×C127C22×C412yes—
290C22×C4×C127C2×D412yes—
291C22×C4×C127C2×D412yes—
292C22×C4×C127C2×D412yes—
293C22×C4×C127C2×D412yes—
294C22×C4×C127C2×D412yes—
295C22×C4×C127C2×D412yes—
296C22×C4×C127#4112yes—
297C22×C4×C127#4112yes—
298C22×C4×C127#4112yes—
299C22×C4×C127#4112yes—
300C22×C4×C127#4112yes—
301C22×C4×C127#4112yes—
302C4⋊C4×C127—28no—
303C4⋊C4×C127—28no—
304C4⋊C4×C127—44no—
305C22⋊C4×C127—28no—
306C22⋊C4×C127—28no—
307C22⋊C4×C127—28no—
308C22⋊C4×C127—28no—
309C22⋊C4×C127—28no—
310C22⋊C4×C127—44no—
311C22⋊C4×C127—44no—
312C22⋊C4×C127—44no—
313C22⋊C4×C127—44no—
314C22⋊C4×C127C22⋊C4116yescomplemented
315C42×C127—44no—
316C42×C127—44no—
317C42×C127—44no—
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—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—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×C127C2×C22⋊C414yes—
387C23×C127C4×D414yes—
388C23×C127C23×C411yescharacteristic
389C23×C127C22×D411yescharacteristic
390C23×C127C22×D411yescharacteristic
391C23×C127C22×D411yescharacteristic
392C23×C127C2×#4111yescharacteristic
393C23×C127C2×#4111yescharacteristic
394C23×C127C2×#4111yescharacteristic
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×C1272−1+411yescharacteristic
403D4×C127—416no—
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—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—416no—
447C2×C4×C127—416no—
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×C127C2×C22⋊C414yes—
495C2×C4×C127C2×C22⋊C414yes—
496C2×C4×C127#12314yescomplemented
497C22×C127—24no—
498C22×C127—24no—
499C22×C127—24no—
500C22×C127—24no—
501C22×C127—24no—
502C22×C127—24no—
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—42no—
521C22×C127—42no—
522C22×C127—42no—
523C22×C127—42no—
524C22×C127—42no—
525C22×C127—42no—
526C22×C127—42no—
527C22×C127C22×C22⋊C411yescharacteristic
528C22×C127C2×C4×D411yescharacteristic
529C22×C127C4×#4111yescharacteristic
530C22×C127C4×#4111yescharacteristic
531C22×C127C4×#4111yescharacteristic
532C22×C127#51811yescharacteristic
533C22×C127#52011yescharacteristic
534C22×C127C2×#12311yescharacteristic
535C22×C127#52511yescharacteristic
536C22×C127#52511yescharacteristic
537C22×C127#52511yescharacteristic
538C22×C127#52911yescharacteristic
539C22×C127#52911yescharacteristic
540C22×C127#53211yescharacteristic
541C22×C127#53211yescharacteristic
542C22×C127#53811yescharacteristic
543C22×C127#53911yescharacteristic
544C22×C127#54011yescharacteristic
545C22×C127#54211yescharacteristic
546C22×C127D4211yescharacteristic
547C22×C127D4211yescharacteristic
548C22×C127#54611yescharacteristic
549C22×C127#54611yescharacteristic
550C22×C127#54611yescharacteristic
551C22×C127#54611yescharacteristic
552C22×C127#54611yescharacteristic
553C22×C127#54711yescharacteristic
554C22×C127#54711yescharacteristic
555C22×C127#54711yescharacteristic
556C22×C127#55111yescharacteristic
557C22×C127#55111yescharacteristic
558C22×C127#55211yescharacteristic
559C22×C127#55311yescharacteristic
560C22×C127#55311yescharacteristic
561C22×C127#55911yescharacteristic
562C4×C127—24no—
563C4×C127—24no—
564C4×C127—24no—
565C4×C127—42no—
566C4×C127—42no—
567C4×C127—42no—
568C4×C127—42no—
569C4×C127—42no—
570C4×C127—42no—
571C4×C127—42no—
572C4×C127—42no—
573C4×C127—81no—
574C4×C127—81no—
575#14096C12711yesmaximal, characteristic, direct product factor, Sylow
576C2×C127—44no—
577C2×C127—44no—
578C2×C127#229711yescharacteristic
579C2×C127C4×#12311yescharacteristic
580C2×C127#233511yescharacteristic
581C2×C127D4×C22⋊C411yescharacteristic
582C2×C127#233911yescharacteristic
583C2×C127#235911yescharacteristic
584C2×C127#237411yescharacteristic
585C2×C127#241811yescharacteristic
586C2×C127#242211yescharacteristic
587C2×C127#245511yescharacteristic
588C2×C127#245711yescharacteristic
589C2×C127#246411yescharacteristic
590C2×C127#247011yescharacteristic
591C2×C127#255311yescharacteristic
592C2×C127#255711yescharacteristic
593C22×#123C2×C12711yescharacteristic
594C2×#388C2×C12711yescharacteristic, complemented
595C2×#386C2×C12711yescharacteristic
596C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
597C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
598#1445C2×C12711yescharacteristic, complemented
599#1440C2×C12711yescharacteristic, complemented
600#1439C2×C12711yescharacteristic, complemented
601#1438C2×C12711yescharacteristic
602#1437C2×C12711yescharacteristic, complemented
603#1436C2×C12711yescharacteristic, complemented
604#1436C2×C12711yescharacteristic, complemented
605C4⋊#95C2×C12711yescharacteristic, complemented
606C22⋊#95C2×C12711yescharacteristic, complemented
607C22⋊#95C2×C12711yescharacteristic, complemented
608C127#1409611yescharacteristic, direct product factor, Sylow
609C23×D4C22×C12711yescharacteristic
610C24×C4C22×C12711yescharacteristic
611C24×C4C22×C12711yescharacteristic
612C2×#123—24no—
613C2×#123—24no—
614C2×#123C4×C12718yescomplemented
615C22×C4⋊C4C22×C12711yescharacteristic
616C22×C4⋊C4C22×C12711yescharacteristic
617C22×C4⋊C4C22×C12711yescharacteristic
618C22×C22⋊C4C22×C12711yescharacteristic
619C22×C22⋊C4C22×C12711yescharacteristic
620C22×C22⋊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×C42C22×C12711yescharacteristic
629C22×C42C22×C12711yescharacteristic
630C22×C42C22×C12711yescharacteristic
631#388—24no—
632#386—24no—
633C4×C22⋊C4—24no—
634C4×C22⋊C4—24no—
635C2×#95C22×C12711yescharacteristic
636C2×#95C22×C12711yescharacteristic
637C2×#95C22×C12711yescharacteristic
638C2×#95C22×C12711yescharacteristic
639C2×#95C22×C12711yescharacteristic
640C2×#95C22×C12711yescharacteristic
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
651C25C23×C12711yescharacteristic
652C25C23×C12711yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×C4×C12714yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4C2×C4×C12714yescomplemented
674C23×C4C23×C12711yescharacteristic
675C23×C4C23×C12711yescharacteristic
676C23×C4C23×C12711yescharacteristic
677C23×C4C23×C12711yescharacteristic
678C23×C4C23×C12711yescharacteristic
679C23×C4C23×C12711yescharacteristic
680C23×C4C23×C12711yescharacteristic
681C23×C4C23×C12711yescharacteristic
682C23×C4C23×C12711yescharacteristic
683C23×C4C23×C12711yescharacteristic
684C23×C4C23×C12711yescharacteristic
685C23×C4C23×C12711yescharacteristic
686C23×C4C23×C12711yescharacteristic
687#123—232no—
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—41no—
695C2×C4⋊C4C2×C4×C12714yescomplemented
696C2×C4⋊C4C2×C4×C12714yescomplemented
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
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—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4C2×C4×C12714yes—
722C2×C22⋊C4C2×C4×C12714yes—
723C2×C22⋊C4C2×C4×C12714yescomplemented
724C2×C22⋊C4D4×C12714yes—
725C2×C22⋊C4D4×C12714yes—
726C2×C22⋊C4D4×C12714yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42—41no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
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—
776C24C22×C4×C12712yes—
777C24C22×C4×C12712yes—
778C24C2×D4×C12712yes—
779C24C2×D4×C12712yes—
780C24C2×D4×C12712yes—
781C24#41×C12712yes—
782C24C24×C12711yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
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—28no—
803C22×C4—28no—
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—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—28no—
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—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4C22×C4×C12712yes—
879C22×C4C22×C4×C12712yes—
880C22×C4C22×C4×C12712yes—
881C22×C4C22×C4×C12712yes—
882C22×C4C22×C4×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×C4#41×C12712yes—
890C22×C4#41×C12712yes—
891C22×C4#41×C12712yes—
892C22×C4#41×C12712yes—
893C22×C4#41×C12712yes—
894C22×C4#41×C12712yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C22⋊C4×C127116yescomplemented
908C42—44no—
909C42—44no—
910C42—44no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
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—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—
979C23C2×C22⋊C4×C12714yes—
980C23C4×D4×C12714yes—
981C23C23×C4×C12711yescharacteristic
982C23C22×D4×C12711yescharacteristic
983C23C22×D4×C12711yescharacteristic
984C23C22×D4×C12711yescharacteristic
985C23C2×#41×C12711yescharacteristic
986C23C2×#41×C12711yescharacteristic
987C23C2×#41×C12711yescharacteristic
988C23C2×#41×C12711yescharacteristic
989C23C2×#41×C12711yescharacteristic
990C23C2×#41×C12711yescharacteristic
991C23C2×#41×C12711yescharacteristic
992C23H(5,𝔽2)×C12711yescharacteristic
993C23H(5,𝔽2)×C12711yescharacteristic
994C23H(5,𝔽2)×C12711yescharacteristic
995C232−1+4×C12711yescharacteristic
996D4—416no—
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—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—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—416no—
1040C2×C4—416no—
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×C4C2×C22⋊C4×C12714yes—
1088C2×C4C2×C22⋊C4×C12714yes—
1089C2×C4#123×C12714yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
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—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊C4×C12711yescharacteristic
1121C22C2×C4×D4×C12711yescharacteristic
1122C22C4×#41×C12711yescharacteristic
1123C22C4×#41×C12711yescharacteristic
1124C22C4×#41×C12711yescharacteristic
1125C22#518×C12711yescharacteristic
1126C22#520×C12711yescharacteristic
1127C22C2×#123×C12711yescharacteristic
1128C22#525×C12711yescharacteristic
1129C22#525×C12711yescharacteristic
1130C22#525×C12711yescharacteristic
1131C22#529×C12711yescharacteristic
1132C22#529×C12711yescharacteristic
1133C22#532×C12711yescharacteristic
1134C22#532×C12711yescharacteristic
1135C22#538×C12711yescharacteristic
1136C22#539×C12711yescharacteristic
1137C22#540×C12711yescharacteristic
1138C22#542×C12711yescharacteristic
1139C22D42×C12711yescharacteristic
1140C22D42×C12711yescharacteristic
1141C22#546×C12711yescharacteristic
1142C22#546×C12711yescharacteristic
1143C22#546×C12711yescharacteristic
1144C22#546×C12711yescharacteristic
1145C22#546×C12711yescharacteristic
1146C22#547×C12711yescharacteristic
1147C22#547×C12711yescharacteristic
1148C22#547×C12711yescharacteristic
1149C22#551×C12711yescharacteristic
1150C22#551×C12711yescharacteristic
1151C22#552×C12711yescharacteristic
1152C22#553×C12711yescharacteristic
1153C22#553×C12711yescharacteristic
1154C22#559×C12711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C127×#229711yescharacteristic
1171C2C4×#123×C12711yescharacteristic
1172C2C127×#233511yescharacteristic
1173C2D4×C22⋊C4×C12711yescharacteristic
1174C2C127×#233911yescharacteristic
1175C2C127×#235911yescharacteristic
1176C2C127×#237411yescharacteristic
1177C2C127×#241811yescharacteristic
1178C2C127×#242211yescharacteristic
1179C2C127×#245511yescharacteristic
1180C2C127×#245711yescharacteristic
1181C2C127×#246411yescharacteristic
1182C2C127×#247011yescharacteristic
1183C2C127×#255311yescharacteristic
1184C2C127×#255711yescharacteristic
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
2. C2×#388×C127C2semidirect
4. C2×C4×C22⋊C4×C127C2semidirect
5. C2×C4×C22⋊C4×C127C2semidirect
6. C127×#1445C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
12. C127×#1436C2semidirect
13. C127×C4⋊#95C2semidirect
14. C127×C22⋊#95C2semidirect
15. C127×C22⋊#95C2semidirect
21. C2×#123×C127C4semidirect
80. C23×C4×C127C2×C4semidirect
102. C2×C4⋊C4×C127C2×C4semidirect
103. C2×C4⋊C4×C127C2×C4semidirect
130. C2×C22⋊C4×C127C2×C4semidirect
314. C22⋊C4×C127C22⋊C4semidirect
496. C2×C4×C127#123semidirect
575. #14096C127direct (N × H)
594. C2×#388C2×C127semidirect
596. C2×C4×C22⋊C4C2×C127semidirect
597. C2×C4×C22⋊C4C2×C127semidirect
598. #1445C2×C127semidirect
599. #1440C2×C127semidirect
600. #1439C2×C127semidirect
602. #1437C2×C127semidirect
603. #1436C2×C127semidirect
604. #1436C2×C127semidirect
605. C4⋊#95C2×C127semidirect
606. C22⋊#95C2×C127semidirect
607. C22⋊#95C2×C127semidirect
608. C127#14096direct (N × H)
614. C2×#123C4×C127semidirect
673. C23×C4C2×C4×C127semidirect
695. C2×C4⋊C4C2×C4×C127semidirect
696. C2×C4⋊C4C2×C4×C127semidirect
723. C2×C22⋊C4C2×C4×C127semidirect
907. C22⋊C4C22⋊C4×C127semidirect
1089. C2×C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14452
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×C4⋊#952
C127×C22⋊#952
#14096127