Finite Group Databasebeta

← C127×#14198 #44577871

Subgroups — C127×#14198 #44577871

Order 32512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C127C211yesmaximal, characteristic
2C2×#387×C127C211yesmaximal, characteristic, complemented
3C2×#385×C127C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
6C127×#1441C211yesmaximal, characteristic, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic
9C127×#1437C211yesmaximal, characteristic
10C127×#1437C211yesmaximal, characteristic
11C127×#1436C211yesmaximal, characteristic, complemented
12C127×#1436C211yesmaximal, characteristic, complemented
13C127×C4⋊#95C211yesmaximal, characteristic, complemented
14C127×#1434C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C42×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33#396×C127C418yescomplemented
34#387×C127—24no—
35#385×C127—24no—
36C4×C4⋊C4×C127—24no—
37C4×C22⋊C4×C127—24no—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C25×C127C2311yescharacteristic
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—41no—
63C23×C4×C127—41no—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—22no—
86C2×C4⋊C4×C127—22no—
87C2×C4⋊C4×C127—22no—
88C2×C4⋊C4×C127—22no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—41no—
91C2×C4⋊C4×C127—41no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127C2×C414yescomplemented
94C2×C4⋊C4×C127C2×C414yescomplemented
95C2×C4⋊C4×C127C2×C414yescomplemented
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—41no—
107C2×C22⋊C4×C127—41no—
108C2×C22⋊C4×C127—41no—
109C2×C22⋊C4×C127—41no—
110C2×C22⋊C4×C127C2×C414yes—
111C2×C22⋊C4×C127C2×C414yes—
112C2×C22⋊C4×C127C2×C414yes—
113C2×C22⋊C4×C127Q814yes—
114C2×C42×C127—22no—
115C2×C42×C127—22no—
116C2×C42×C127—22no—
117C2×C42×C127—22no—
118C2×C42×C127—22no—
119C2×C42×C127—22no—
120C2×C42×C127—22no—
121C2×C42×C127—41no—
122C2×C42×C127—41no—
123C2×C42×C127—41no—
124C2×C42×C127—41no—
125C2×C42×C127D414yes—
126#95×C127—22no—
127#95×C127—22no—
128#95×C127—22no—
129#95×C127—22no—
130#95×C127—22no—
131#95×C127—22no—
132#95×C127—22no—
133#95×C127—22no—
134#95×C127—22no—
135#95×C127—22no—
136#95×C127—22no—
137#95×C127—41no—
138#95×C127—41no—
139#95×C127—41no—
140#95×C127—41no—
141#95×C127—41no—
142#95×C127C2×C414yescomplemented
143#95×C127D414yes—
144C24×C127—21no—
145C24×C127—21no—
146C24×C127—21no—
147C24×C127—21no—
148C24×C127—21no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—21no—
152C24×C127—21no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127C22×C412yes—
157C24×C127C2×Q812yes—
158C24×C127#4112yes—
159C24×C127C2411yescharacteristic
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—28no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—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—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—44no—
240C22×C4×C127—44no—
241C22×C4×C127—44no—
242C22×C4×C127—44no—
243C22×C4×C127—44no—
244C22×C4×C127—44no—
245C22×C4×C127C22×C412yes—
246C22×C4×C127C22×C412yes—
247C22×C4×C127C22×C412yes—
248C22×C4×C127C22×C412yes—
249C22×C4×C127C22×C412yes—
250C22×C4×C127C22×C412yes—
251C22×C4×C127C2×D412yes—
252C22×C4×C127C2×D412yes—
253C22×C4×C127C2×D412yes—
254C22×C4×C127C2×D412yes—
255C22×C4×C127C2×D412yes—
256C22×C4×C127C2×D412yes—
257C22×C4×C127C2×Q812yes—
258C22×C4×C127C2×Q812yes—
259C22×C4×C127#4112yes—
260C22×C4×C127#4112yes—
261C22×C4×C127#4112yes—
262C22×C4×C127#4112yes—
263C22×C4×C127#4112yes—
264C22×C4×C127#4112yes—
265C4⋊C4×C127—28no—
266C4⋊C4×C127—28no—
267C4⋊C4×C127—28no—
268C4⋊C4×C127—44no—
269C4⋊C4×C127—44no—
270C4⋊C4×C127—44no—
271C22⋊C4×C127—28no—
272C22⋊C4×C127—28no—
273C22⋊C4×C127—28no—
274C22⋊C4×C127—44no—
275C22⋊C4×C127—44no—
276C22⋊C4×C127—44no—
277C42×C127—28no—
278C42×C127—44no—
279C42×C127—44no—
280C42×C127—44no—
281C23×C127—22no—
282C23×C127—22no—
283C23×C127—22no—
284C23×C127—22no—
285C23×C127—22no—
286C23×C127—22no—
287C23×C127—22no—
288C23×C127—22no—
289C23×C127—22no—
290C23×C127—22no—
291C23×C127—22no—
292C23×C127—22no—
293C23×C127—22no—
294C23×C127—22no—
295C23×C127—22no—
296C23×C127—22no—
297C23×C127—22no—
298C23×C127—22no—
299C23×C127—41no—
300C23×C127—41no—
301C23×C127—41no—
302C23×C127—41no—
303C23×C127—41no—
304C23×C127—41no—
305C23×C127—41no—
306C23×C127—41no—
307C23×C127—41no—
308C23×C127—41no—
309C23×C127—41no—
310C23×C127—41no—
311C23×C127—41no—
312C23×C127—41no—
313C23×C127—41no—
314C23×C127—41no—
315C23×C127C4×Q814yes—
316C23×C127C23×C411yescharacteristic
317C23×C127C22×D411yescharacteristic
318C23×C127C22×D411yescharacteristic
319C23×C127C22×Q811yescharacteristic
320C23×C127C2×#4111yescharacteristic
321C23×C127C2×#4111yescharacteristic
322C23×C127C2×#4111yescharacteristic
323C23×C127C2×#4111yescharacteristic
324C23×C127C2×#4111yescharacteristic
325C23×C127C2×#4111yescharacteristic
326C23×C127C2×#4111yescharacteristic
327C23×C127H(5,𝔽2)11yescharacteristic
328C23×C127H(5,𝔽2)11yescharacteristic
329C23×C127H(5,𝔽2)11yescharacteristic
330C23×C1272−1+411yescharacteristic
331C2×C4×C127—22no—
332C2×C4×C127—22no—
333C2×C4×C127—22no—
334C2×C4×C127—22no—
335C2×C4×C127—22no—
336C2×C4×C127—22no—
337C2×C4×C127—22no—
338C2×C4×C127—22no—
339C2×C4×C127—22no—
340C2×C4×C127—22no—
341C2×C4×C127—22no—
342C2×C4×C127—22no—
343C2×C4×C127—22no—
344C2×C4×C127—22no—
345C2×C4×C127—22no—
346C2×C4×C127—22no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—22no—
350C2×C4×C127—22no—
351C2×C4×C127—22no—
352C2×C4×C127—22no—
353C2×C4×C127—22no—
354C2×C4×C127—22no—
355C2×C4×C127—22no—
356C2×C4×C127—22no—
357C2×C4×C127—22no—
358C2×C4×C127—22no—
359C2×C4×C127—22no—
360C2×C4×C127—22no—
361C2×C4×C127—22no—
362C2×C4×C127—22no—
363C2×C4×C127—22no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—22no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—22no—
370C2×C4×C127—22no—
371C2×C4×C127—22no—
372C2×C4×C127—22no—
373C2×C4×C127—22no—
374C2×C4×C127—22no—
375C2×C4×C127—22no—
376C2×C4×C127—22no—
377C2×C4×C127—22no—
378C2×C4×C127—22no—
379C2×C4×C127—416no—
380C2×C4×C127—41no—
381C2×C4×C127—41no—
382C2×C4×C127—41no—
383C2×C4×C127—41no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—41no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
404C2×C4×C127—41no—
405C2×C4×C127—41no—
406C2×C4×C127—41no—
407C2×C4×C127—41no—
408C2×C4×C127—41no—
409C2×C4×C127—41no—
410C2×C4×C127—41no—
411C2×C4×C127—41no—
412C2×C4×C127—41no—
413C2×C4×C127—41no—
414C2×C4×C127—41no—
415C2×C4×C127—41no—
416C2×C4×C127—41no—
417C2×C4×C127—41no—
418C2×C4×C127—41no—
419C2×C4×C127—41no—
420C2×C4×C127—41no—
421C2×C4×C127—41no—
422C2×C4×C127—41no—
423C2×C4×C127—41no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127C4×D414yes—
427C2×C4×C127C4×D414yes—
428C2×C4×C127#12114yes—
429C2×C4×C127C22⋊Q814yes—
430C22×C127—24no—
431C22×C127—24no—
432C22×C127—24no—
433C22×C127—42no—
434C22×C127—42no—
435C22×C127—42no—
436C22×C127—42no—
437C22×C127—42no—
438C22×C127—42no—
439C22×C127—42no—
440C22×C127—42no—
441C22×C127—42no—
442C22×C127—42no—
443C22×C127—42no—
444C22×C127—42no—
445C22×C127C2×C4×D411yescharacteristic
446C22×C127C2×C4×D411yescharacteristic
447C22×C127C2×C4×Q811yescharacteristic
448C22×C127C4×#4111yescharacteristic
449C22×C127C4×#4111yescharacteristic
450C22×C127#51811yescharacteristic
451C22×C127#52011yescharacteristic
452C22×C127C2×#12111yescharacteristic
453C22×C127C2×C22⋊Q811yescharacteristic
454C22×C127#52511yescharacteristic
455C22×C127#52511yescharacteristic
456C22×C127#52911yescharacteristic
457C22×C127#52911yescharacteristic
458C22×C127#53211yescharacteristic
459C22×C127#53311yescharacteristic
460C22×C127#53511yescharacteristic
461C22×C127#53711yescharacteristic
462C22×C127#54011yescharacteristic
463C22×C127#54211yescharacteristic
464C22×C127#54611yescharacteristic
465C22×C127#54611yescharacteristic
466C22×C127#54611yescharacteristic
467C22×C127D4×Q811yescharacteristic
468C22×C127#55111yescharacteristic
469C22×C127#55111yescharacteristic
470C22×C127#55111yescharacteristic
471C22×C127#55211yescharacteristic
472C22×C127#55211yescharacteristic
473C22×C127#55311yescharacteristic
474C22×C127#55311yescharacteristic
475C22×C127#55311yescharacteristic
476C22×C127#55411yescharacteristic
477C22×C127#55411yescharacteristic
478C22×C127#55411yescharacteristic
479C22×C127#55611yescharacteristic
480C4×C127—24no—
481C4×C127—24no—
482C4×C127—24no—
483C4×C127—24no—
484C4×C127—42no—
485C4×C127—42no—
486C4×C127—42no—
487C4×C127—42no—
488C4×C127—42no—
489C4×C127—42no—
490C4×C127—42no—
491C4×C127—42no—
492C4×C127—81no—
493C4×C127—81no—
494#14198C12711yesmaximal, characteristic, direct product factor, Sylow
495C2×C127—44no—
496C2×C127C4×#12111yescharacteristic
497C2×C127C4×C22⋊Q811yescharacteristic
498C2×C127#232411yescharacteristic
499C2×C127#236011yescharacteristic
500C2×C127#236411yescharacteristic
501C2×C127#236811yescharacteristic
502C2×C127#237311yescharacteristic
503C2×C127#241111yescharacteristic
504C2×C127#241711yescharacteristic
505C2×C127#245711yescharacteristic
506C2×C127#246511yescharacteristic
507C2×C127#251511yescharacteristic
508C2×C127#252211yescharacteristic
509C2×C127#256611yescharacteristic
510C2×C127#260111yescharacteristic
511C2×#396C2×C12711yescharacteristic
512C2×#387C2×C12711yescharacteristic, complemented
513C2×#385C2×C12711yescharacteristic
514C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
515C2×C4×C22⋊C4C2×C12711yescharacteristic
516#1441C2×C12711yescharacteristic, complemented
517#1441C2×C12711yescharacteristic, complemented
518#1439C2×C12711yescharacteristic
519#1437C2×C12711yescharacteristic
520#1437C2×C12711yescharacteristic
521#1436C2×C12711yescharacteristic, complemented
522#1436C2×C12711yescharacteristic, complemented
523C4⋊#95C2×C12711yescharacteristic, complemented
524#1434C2×C12711yescharacteristic, complemented
525C22⋊#95C2×C12711yescharacteristic
526C127#1419811yescharacteristic, direct product factor, Sylow
527C24×C4C22×C12711yescharacteristic
528C22×C4⋊C4C22×C12711yescharacteristic
529C22×C4⋊C4C22×C12711yescharacteristic
530C22×C4⋊C4C22×C12711yescharacteristic
531C22×C4⋊C4C22×C12711yescharacteristic
532C22×C4⋊C4C22×C12711yescharacteristic
533C22×C4⋊C4C22×C12711yescharacteristic
534C22×C22⋊C4C22×C12711yescharacteristic
535C22×C22⋊C4C22×C12711yescharacteristic
536C22×C22⋊C4C22×C12711yescharacteristic
537C22×C22⋊C4C22×C12711yescharacteristic
538C22×C22⋊C4C22×C12711yescharacteristic
539C22×C22⋊C4C22×C12711yescharacteristic
540C22×C42C22×C12711yescharacteristic
541C22×C42C22×C12711yescharacteristic
542C22×C42C22×C12711yescharacteristic
543C22×C42C22×C12711yescharacteristic
544#396C4×C12718yescomplemented
545#387—24no—
546#385—24no—
547C4×C4⋊C4—24no—
548C4×C22⋊C4—24no—
549C2×#95C22×C12711yescharacteristic
550C2×#95C22×C12711yescharacteristic
551C2×#95C22×C12711yescharacteristic
552C2×#95C22×C12711yescharacteristic
553C2×#95C22×C12711yescharacteristic
554C2×#95C22×C12711yescharacteristic
555C2×#95C22×C12711yescharacteristic
556C2×#95C22×C12711yescharacteristic
557C2×#95C22×C12711yescharacteristic
558C2×#95C22×C12711yescharacteristic
559C2×#95C22×C12711yescharacteristic
560C2×#95C22×C12711yescharacteristic
561C2×#95C22×C12711yescharacteristic
562C2×#95C22×C12711yescharacteristic
563C2×#95C22×C12711yescharacteristic
564C2×#95C22×C12711yescharacteristic
565C2×#95C22×C12711yescharacteristic
566C2×#95C22×C12711yescharacteristic
567C25C23×C12711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C12711yescharacteristic
576C23×C4C23×C12711yescharacteristic
577C23×C4C23×C12711yescharacteristic
578C23×C4C23×C12711yescharacteristic
579C23×C4C23×C12711yescharacteristic
580C23×C4C23×C12711yescharacteristic
581C23×C4C23×C12711yescharacteristic
582C23×C4C23×C12711yescharacteristic
583C23×C4C23×C12711yescharacteristic
584C23×C4C23×C12711yescharacteristic
585C23×C4C23×C12711yescharacteristic
586C23×C4C23×C12711yescharacteristic
587C23×C4C23×C12711yescharacteristic
588C23×C4C23×C12711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4C2×C4×C12714yescomplemented
605C2×C4⋊C4C2×C4×C12714yescomplemented
606C2×C4⋊C4C2×C4×C12714yescomplemented
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4C2×C4×C12714yes—
622C2×C22⋊C4C2×C4×C12714yes—
623C2×C22⋊C4C2×C4×C12714yes—
624C2×C22⋊C4Q8×C12714yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42D4×C12714yes—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C12714yescomplemented
654#95D4×C12714yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C12712yes—
668C24C2×Q8×C12712yes—
669C24#41×C12712yes—
670C24C24×C12711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C12712yes—
757C22×C4C22×C4×C12712yes—
758C22×C4C22×C4×C12712yes—
759C22×C4C22×C4×C12712yes—
760C22×C4C22×C4×C12712yes—
761C22×C4C22×C4×C12712yes—
762C22×C4C2×D4×C12712yes—
763C22×C4C2×D4×C12712yes—
764C22×C4C2×D4×C12712yes—
765C22×C4C2×D4×C12712yes—
766C22×C4C2×D4×C12712yes—
767C22×C4C2×D4×C12712yes—
768C22×C4C2×Q8×C12712yes—
769C22×C4C2×Q8×C12712yes—
770C22×C4#41×C12712yes—
771C22×C4#41×C12712yes—
772C22×C4#41×C12712yes—
773C22×C4#41×C12712yes—
774C22×C4#41×C12712yes—
775C22×C4#41×C12712yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C42—28no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4×Q8×C12714yes—
827C23C23×C4×C12711yescharacteristic
828C23C22×D4×C12711yescharacteristic
829C23C22×D4×C12711yescharacteristic
830C23C22×Q8×C12711yescharacteristic
831C23C2×#41×C12711yescharacteristic
832C23C2×#41×C12711yescharacteristic
833C23C2×#41×C12711yescharacteristic
834C23C2×#41×C12711yescharacteristic
835C23C2×#41×C12711yescharacteristic
836C23C2×#41×C12711yescharacteristic
837C23C2×#41×C12711yescharacteristic
838C23H(5,𝔽2)×C12711yescharacteristic
839C23H(5,𝔽2)×C12711yescharacteristic
840C23H(5,𝔽2)×C12711yescharacteristic
841C232−1+4×C12711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C4×D4×C12714yes—
938C2×C4C4×D4×C12714yes—
939C2×C4#121×C12714yes—
940C2×C4C22⋊Q8×C12714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×D4×C12711yescharacteristic
957C22C2×C4×D4×C12711yescharacteristic
958C22C2×C4×Q8×C12711yescharacteristic
959C22C4×#41×C12711yescharacteristic
960C22C4×#41×C12711yescharacteristic
961C22#518×C12711yescharacteristic
962C22#520×C12711yescharacteristic
963C22C2×#121×C12711yescharacteristic
964C22C2×C22⋊Q8×C12711yescharacteristic
965C22#525×C12711yescharacteristic
966C22#525×C12711yescharacteristic
967C22#529×C12711yescharacteristic
968C22#529×C12711yescharacteristic
969C22#532×C12711yescharacteristic
970C22#533×C12711yescharacteristic
971C22#535×C12711yescharacteristic
972C22#537×C12711yescharacteristic
973C22#540×C12711yescharacteristic
974C22#542×C12711yescharacteristic
975C22#546×C12711yescharacteristic
976C22#546×C12711yescharacteristic
977C22#546×C12711yescharacteristic
978C22D4×Q8×C12711yescharacteristic
979C22#551×C12711yescharacteristic
980C22#551×C12711yescharacteristic
981C22#551×C12711yescharacteristic
982C22#552×C12711yescharacteristic
983C22#552×C12711yescharacteristic
984C22#553×C12711yescharacteristic
985C22#553×C12711yescharacteristic
986C22#553×C12711yescharacteristic
987C22#554×C12711yescharacteristic
988C22#554×C12711yescharacteristic
989C22#554×C12711yescharacteristic
990C22#556×C12711yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C4×#121×C12711yescharacteristic
1007C2C4×C22⋊Q8×C12711yescharacteristic
1008C2C127×#232411yescharacteristic
1009C2C127×#236011yescharacteristic
1010C2C127×#236411yescharacteristic
1011C2C127×#236811yescharacteristic
1012C2C127×#237311yescharacteristic
1013C2C127×#241111yescharacteristic
1014C2C127×#241711yescharacteristic
1015C2C127×#245711yescharacteristic
1016C2C127×#246511yescharacteristic
1017C2C127×#251511yescharacteristic
1018C2C127×#252211yescharacteristic
1019C2C127×#256611yescharacteristic
1020C2C127×#260111yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#387×C127C2semidirect
4. C2×C4×C4⋊C4×C127C2semidirect
6. C127×#1441C2semidirect
7. C127×#1441C2semidirect
11. C127×#1436C2semidirect
12. C127×#1436C2semidirect
13. C127×C4⋊#95C2semidirect
14. C127×#1434C2semidirect
33. #396×C127C4semidirect
93. C2×C4⋊C4×C127C2×C4semidirect
94. C2×C4⋊C4×C127C2×C4semidirect
95. C2×C4⋊C4×C127C2×C4semidirect
142. #95×C127C2×C4semidirect
494. #14198C127direct (N × H)
512. C2×#387C2×C127semidirect
514. C2×C4×C4⋊C4C2×C127semidirect
516. #1441C2×C127semidirect
517. #1441C2×C127semidirect
521. #1436C2×C127semidirect
522. #1436C2×C127semidirect
523. C4⋊#95C2×C127semidirect
524. #1434C2×C127semidirect
526. C127#14198direct (N × H)
544. #396C4×C127semidirect
604. C2×C4⋊C4C2×C4×C127semidirect
605. C2×C4⋊C4C2×C4×C127semidirect
606. C2×C4⋊C4C2×C4×C127semidirect
653. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1272
C2×#387×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14412
C127×#14392
C127×#14372
C127×#14362
C127×C4⋊#952
C127×#14342
C127×C22⋊#952
#14198127