Finite Group Databasebeta

← C127×#14018 #44577691

Subgroups — C127×#14018 #44577691

Order 32512.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic
3C2×#390×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic, complemented
5C2×#385×C127C212yesmaximal, complemented
6C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×C4⋊#95C211yesmaximal, characteristic, complemented
10C127×C4⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2212yes—
14C2×C4×D4×C127—24no—
15C2×C4×D4×C127—24no—
16C2×C4×D4×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C42×C127C2211yescharacteristic
29C22×C42×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31#390×C127—24no—
32#390×C127C418yescomplemented
33#389×C127—24no—
34#385×C127—28no—
35C4×C4⋊C4×C127—24no—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2312yes—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127C2×C414yes—
49C22×D4×C127D414yes—
50C22×D4×C127Q814yes—
51C23×C4×C127—24no—
52C23×C4×C127—24no—
53C23×C4×C127—24no—
54C23×C4×C127—24no—
55C23×C4×C127—24no—
56C23×C4×C127—42no—
57C23×C4×C127—42no—
58C23×C4×C127C2312yes—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2312yes—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C4×D4×C127—232no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—42no—
84C2×C4⋊C4×C127C2×C414yescomplemented
85C2×C4⋊C4×C127D414yes—
86C2×C4⋊C4×C127D414yescomplemented
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—42no—
97C2×C22⋊C4×C127—42no—
98C2×C22⋊C4×C127—42no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127C2×C418yescomplemented
101C2×C22⋊C4×C127C2×C418yescomplemented
102C2×C42×C127—22no—
103C2×C42×C127—22no—
104C2×C42×C127—22no—
105C2×C42×C127—22no—
106C2×C42×C127—22no—
107C2×C42×C127—22no—
108C2×C42×C127—22no—
109C2×C42×C127C2×C414yescomplemented
110C2×C42×C127D414yes—
111#95×C127—22no—
112#95×C127—22no—
113#95×C127—24no—
114#95×C127—24no—
115#95×C127—24no—
116#95×C127—42no—
117#95×C127—42no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127C22×C414yes—
131C24×C127C2×D414yes—
132C24×C127C2×Q814yes—
133C24×C127C2411yescharacteristic
134C2×D4×C127—28no—
135C2×D4×C127—28no—
136C2×D4×C127—28no—
137C2×D4×C127—28no—
138C2×D4×C127—28no—
139C2×D4×C127—28no—
140C2×D4×C127C4⋊C4116yescomplemented
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—216no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—21no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—22no—
181C22×C4×C127—21no—
182C22×C4×C127—22no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—48no—
194C22×C4×C127—48no—
195C22×C4×C127—48no—
196C22×C4×C127—48no—
197C22×C4×C127—48no—
198C22×C4×C127—48no—
199C22×C4×C127C22×C412yes—
200C22×C4×C127C22×C414yes—
201C22×C4×C127C22×C412yes—
202C22×C4×C127C22×C412yes—
203C22×C4×C127C2×D412yes—
204C22×C4×C127C2×D414yes—
205C22×C4×C127C2×D412yes—
206C22×C4×C127C2×D412yes—
207C22×C4×C127C2×D412yes—
208C22×C4×C127C2×D412yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D412yes—
212C22×C4×C127C2×Q812yes—
213C22×C4×C127#4112yes—
214C22×C4×C127#4112yes—
215C22×C4×C127#4112yes—
216C22×C4×C127#4112yes—
217C22×C4×C127#4112yes—
218C4⋊C4×C127—28no—
219C4⋊C4×C127—28no—
220C4⋊C4×C127—28no—
221C4⋊C4×C127—28no—
222C4⋊C4×C127—48no—
223C4⋊C4×C127—44no—
224C22⋊C4×C127—216no—
225C22⋊C4×C127—216no—
226C22⋊C4×C127—48no—
227C22⋊C4×C127—48no—
228C22⋊C4×C127—48no—
229C42×C127—28no—
230C42×C127—28no—
231C42×C127—44no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127C2×C4⋊C418yes—
267C23×C127C23×C411yescharacteristic
268C23×C127C22×D411yescharacteristic
269C23×C127C22×D411yescharacteristic
270C23×C127C22×D411yescharacteristic
271C23×C127C22×D411yescharacteristic
272C23×C127C22×Q811yescharacteristic
273C23×C127C2×#4111yescharacteristic
274C23×C127C2×#4111yescharacteristic
275C23×C127C2×#4111yescharacteristic
276C23×C127C2×#4111yescharacteristic
277C23×C127C2×#4111yescharacteristic
278C23×C127H(5,𝔽2)11yescharacteristic
279C23×C127H(5,𝔽2)11yescharacteristic
280C23×C127H(5,𝔽2)11yescharacteristic
281C23×C1272−1+411yescharacteristic
282D4×C127—232no—
283C2×C4×C127—22no—
284C2×C4×C127—22no—
285C2×C4×C127—22no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—22no—
299C2×C4×C127—24no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—24no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—24no—
310C2×C4×C127—22no—
311C2×C4×C127—24no—
312C2×C4×C127—22no—
313C2×C4×C127—432no—
314C2×C4×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—42no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—42no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—42no—
325C2×C4×C127—42no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—42no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127C2×C4⋊C414yes—
346C2×C4×C127C4×D414yes—
347C2×C4×C127C4×D414yes—
348C2×C4×C127C4×D414yescomplemented
349C2×C4×C127#12014yes—
350C2×C4×C127#12114yes—
351C2×C4×C127C22⋊Q814yes—
352C2×C4×C127C22⋊Q814yes—
353C2×C4×C127#12314yes—
354C22×C127—28no—
355C22×C127—28no—
356C22×C127—28no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—44no—
368C22×C127—44no—
369C22×C127C22×C4⋊C411yescharacteristic
370C22×C127C2×C4×D411yescharacteristic
371C22×C127C2×C4×D411yescharacteristic
372C22×C127C2×C4×D411yescharacteristic
373C22×C127C4×#4111yescharacteristic
374C22×C127#51811yescharacteristic
375C22×C127#52011yescharacteristic
376C22×C127C2×#12011yescharacteristic
377C22×C127C2×#12111yescharacteristic
378C22×C127C2×C22⋊Q811yescharacteristic
379C22×C127C2×C22⋊Q811yescharacteristic
380C22×C127C2×#12311yescharacteristic
381C22×C127#52511yescharacteristic
382C22×C127#52911yescharacteristic
383C22×C127#53211yescharacteristic
384C22×C127#53511yescharacteristic
385C22×C127#53711yescharacteristic
386C22×C127#54011yescharacteristic
387C22×C127#54211yescharacteristic
388C22×C127D4211yescharacteristic
389C22×C127D4211yescharacteristic
390C22×C127#54611yescharacteristic
391C22×C127#54611yescharacteristic
392C22×C127#54611yescharacteristic
393C22×C127#54711yescharacteristic
394C22×C127#54811yescharacteristic
395C22×C127D4×Q811yescharacteristic
396C22×C127#55011yescharacteristic
397C22×C127#55011yescharacteristic
398C22×C127#55411yescharacteristic
399C22×C127#55411yescharacteristic
400C22×C127#55411yescharacteristic
401C22×C127#55611yescharacteristic
402C22×C127#55911yescharacteristic
403C22×C127#55911yescharacteristic
404C4×C127—24no—
405C4×C127—24no—
406C4×C127—42no—
407C4×C127—44no—
408C4×C127—42no—
409C4×C127—42no—
410C4×C127—42no—
411C4×C127—44no—
412C4×C127—82no—
413C4×C127#38518yescomplemented
414#14018C12711yesmaximal, characteristic, direct product factor, Sylow
415C2×C127—48no—
416C2×C127C2×#38511yescharacteristic
417C2×C127C4×#12111yescharacteristic
418C2×C127#232411yescharacteristic
419C2×C127D4×C4⋊C411yescharacteristic
420C2×C127#234911yescharacteristic
421C2×C127#236611yescharacteristic
422C2×C127#236711yescharacteristic
423C2×C127#240711yescharacteristic
424C2×C127#240811yescharacteristic
425C2×C127#244511yescharacteristic
426C2×C127#244711yescharacteristic
427C2×C127#245211yescharacteristic
428C2×C127#245411yescharacteristic
429C2×C127#253811yescharacteristic
430C2×C127#258011yescharacteristic
431C22×C4×D4C2×C12711yescharacteristic
432C2×#390C2×C12711yescharacteristic
433C2×#390C2×C12711yescharacteristic
434C2×#389C2×C12711yescharacteristic, complemented
435C2×#385C2×C12712yescomplemented
436C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
437#1439C2×C12712yescomplemented
438#1439C2×C12712yescomplemented
439C4⋊#95C2×C12711yescharacteristic, complemented
440C4⋊#95C2×C12711yescharacteristic, complemented
441C22⋊#95C2×C12712yescomplemented
442C127#1401811yescharacteristic, direct product factor, Sylow
443C23×D4C22×C12711yescharacteristic
444C24×C4C22×C12712yes—
445C2×C4×D4—24no—
446C2×C4×D4—24no—
447C2×C4×D4—24no—
448C22×C4⋊C4C22×C12711yescharacteristic
449C22×C4⋊C4C22×C12711yescharacteristic
450C22×C4⋊C4C22×C12712yes—
451C22×C4⋊C4C22×C12711yescharacteristic
452C22×C4⋊C4C22×C12711yescharacteristic
453C22×C4⋊C4C22×C12711yescharacteristic
454C22×C22⋊C4C22×C12712yes—
455C22×C22⋊C4C22×C12712yes—
456C22×C22⋊C4C22×C12712yes—
457C22×C22⋊C4C22×C12712yes—
458C22×C22⋊C4C22×C12712yes—
459C22×C42C22×C12711yescharacteristic
460C22×C42C22×C12711yescharacteristic
461C22×C42C22×C12711yescharacteristic
462#390—24no—
463#390C4×C12718yescomplemented
464#389—24no—
465#385—28no—
466C4×C4⋊C4—24no—
467C2×#95C22×C12711yescharacteristic
468C2×#95C22×C12712yes—
469C2×#95C22×C12712yes—
470C2×#95C22×C12712yes—
471C2×#95C22×C12711yescharacteristic
472C2×#95C22×C12712yes—
473C2×#95C22×C12712yes—
474C25C23×C12712yes—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4C2×C4×C12714yes—
480C22×D4D4×C12714yes—
481C22×D4Q8×C12714yes—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—42no—
488C23×C4—42no—
489C23×C4C23×C12712yes—
490C23×C4C23×C12712yes—
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12711yescharacteristic
493C23×C4C23×C12711yescharacteristic
494C23×C4C23×C12712yes—
495C23×C4C23×C12711yescharacteristic
496C23×C4C23×C12711yescharacteristic
497C23×C4C23×C12711yescharacteristic
498C23×C4C23×C12711yescharacteristic
499C4×D4—232no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—42no—
515C2×C4⋊C4C2×C4×C12714yescomplemented
516C2×C4⋊C4D4×C12714yes—
517C2×C4⋊C4D4×C12714yescomplemented
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4C2×C4×C12718yescomplemented
532C2×C22⋊C4C2×C4×C12718yescomplemented
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42C2×C4×C12714yescomplemented
541C2×C42D4×C12714yes—
542#95—22no—
543#95—22no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95—42no—
548#95—42no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24C22×C4×C12714yes—
562C24C2×D4×C12714yes—
563C24C2×Q8×C12714yes—
564C24C24×C12711yescharacteristic
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4C4⋊C4×C127116yescomplemented
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—216no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4C22×C4×C12712yes—
631C22×C4C22×C4×C12714yes—
632C22×C4C22×C4×C12712yes—
633C22×C4C22×C4×C12712yes—
634C22×C4C2×D4×C12712yes—
635C22×C4C2×D4×C12714yes—
636C22×C4C2×D4×C12712yes—
637C22×C4C2×D4×C12712yes—
638C22×C4C2×D4×C12712yes—
639C22×C4C2×D4×C12712yes—
640C22×C4C2×D4×C12712yes—
641C22×C4C2×D4×C12712yes—
642C22×C4C2×D4×C12712yes—
643C22×C4C2×Q8×C12712yes—
644C22×C4#41×C12712yes—
645C22×C4#41×C12712yes—
646C22×C4#41×C12712yes—
647C22×C4#41×C12712yes—
648C22×C4#41×C12712yes—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—48no—
654C4⋊C4—44no—
655C22⋊C4—216no—
656C22⋊C4—216no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C42—28no—
661C42—28no—
662C42—44no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23C2×C4⋊C4×C12718yes—
698C23C23×C4×C12711yescharacteristic
699C23C22×D4×C12711yescharacteristic
700C23C22×D4×C12711yescharacteristic
701C23C22×D4×C12711yescharacteristic
702C23C22×D4×C12711yescharacteristic
703C23C22×Q8×C12711yescharacteristic
704C23C2×#41×C12711yescharacteristic
705C23C2×#41×C12711yescharacteristic
706C23C2×#41×C12711yescharacteristic
707C23C2×#41×C12711yescharacteristic
708C23C2×#41×C12711yescharacteristic
709C23H(5,𝔽2)×C12711yescharacteristic
710C23H(5,𝔽2)×C12711yescharacteristic
711C23H(5,𝔽2)×C12711yescharacteristic
712C232−1+4×C12711yescharacteristic
713D4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—432no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4C2×C4⋊C4×C12714yes—
777C2×C4C4×D4×C12714yes—
778C2×C4C4×D4×C12714yes—
779C2×C4C4×D4×C12714yescomplemented
780C2×C4#120×C12714yes—
781C2×C4#121×C12714yes—
782C2×C4C22⋊Q8×C12714yes—
783C2×C4C22⋊Q8×C12714yes—
784C2×C4#123×C12714yes—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C22×C4⋊C4×C12711yescharacteristic
801C22C2×C4×D4×C12711yescharacteristic
802C22C2×C4×D4×C12711yescharacteristic
803C22C2×C4×D4×C12711yescharacteristic
804C22C4×#41×C12711yescharacteristic
805C22#518×C12711yescharacteristic
806C22#520×C12711yescharacteristic
807C22C2×#120×C12711yescharacteristic
808C22C2×#121×C12711yescharacteristic
809C22C2×C22⋊Q8×C12711yescharacteristic
810C22C2×C22⋊Q8×C12711yescharacteristic
811C22C2×#123×C12711yescharacteristic
812C22#525×C12711yescharacteristic
813C22#529×C12711yescharacteristic
814C22#532×C12711yescharacteristic
815C22#535×C12711yescharacteristic
816C22#537×C12711yescharacteristic
817C22#540×C12711yescharacteristic
818C22#542×C12711yescharacteristic
819C22D42×C12711yescharacteristic
820C22D42×C12711yescharacteristic
821C22#546×C12711yescharacteristic
822C22#546×C12711yescharacteristic
823C22#546×C12711yescharacteristic
824C22#547×C12711yescharacteristic
825C22#548×C12711yescharacteristic
826C22D4×Q8×C12711yescharacteristic
827C22#550×C12711yescharacteristic
828C22#550×C12711yescharacteristic
829C22#554×C12711yescharacteristic
830C22#554×C12711yescharacteristic
831C22#554×C12711yescharacteristic
832C22#556×C12711yescharacteristic
833C22#559×C12711yescharacteristic
834C22#559×C12711yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—44no—
842C4—42no—
843C4—82no—
844C4#385×C12718yescomplemented
845C2—48no—
846C2C2×#385×C12711yescharacteristic
847C2C4×#121×C12711yescharacteristic
848C2C127×#232411yescharacteristic
849C2D4×C4⋊C4×C12711yescharacteristic
850C2C127×#234911yescharacteristic
851C2C127×#236611yescharacteristic
852C2C127×#236711yescharacteristic
853C2C127×#240711yescharacteristic
854C2C127×#240811yescharacteristic
855C2C127×#244511yescharacteristic
856C2C127×#244711yescharacteristic
857C2C127×#245211yescharacteristic
858C2C127×#245411yescharacteristic
859C2C127×#253811yescharacteristic
860C2C127×#258011yescharacteristic
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
4. C2×#389×C127C2semidirect
5. C2×#385×C127C2semidirect
6. C2×C4×C4⋊C4×C127C2semidirect
7. C127×#1439C2semidirect
8. C127×#1439C2semidirect
9. C127×C4⋊#95C2semidirect
10. C127×C4⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
32. #390×C127C4semidirect
84. C2×C4⋊C4×C127C2×C4semidirect
86. C2×C4⋊C4×C127D4semidirect
100. C2×C22⋊C4×C127C2×C4semidirect
101. C2×C22⋊C4×C127C2×C4semidirect
109. C2×C42×C127C2×C4semidirect
140. C2×D4×C127C4⋊C4semidirect
348. C2×C4×C127C4×D4semidirect
413. C4×C127#385semidirect
414. #14018C127direct (N × H)
434. C2×#389C2×C127semidirect
435. C2×#385C2×C127semidirect
436. C2×C4×C4⋊C4C2×C127semidirect
437. #1439C2×C127semidirect
438. #1439C2×C127semidirect
439. C4⋊#95C2×C127semidirect
440. C4⋊#95C2×C127semidirect
441. C22⋊#95C2×C127semidirect
442. C127#14018direct (N × H)
463. #390C4×C127semidirect
515. C2×C4⋊C4C2×C4×C127semidirect
517. C2×C4⋊C4D4×C127semidirect
531. C2×C22⋊C4C2×C4×C127semidirect
532. C2×C22⋊C4C2×C4×C127semidirect
540. C2×C42C2×C4×C127semidirect
571. C2×D4C4⋊C4×C127semidirect
779. C2×C4C4×D4×C127semidirect
844. C4#385×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#390×C1272
C2×#389×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C127×#14392
C127×C4⋊#952
C127×C22⋊#952
#14018127