Finite Group Databasebeta

← C127×#15318 #44578991

Subgroups — C127×#15318 #44578991

Order 32512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Q8×C127C211yesmaximal, characteristic
2C2×#398×C127C211yesmaximal, characteristic
3C2×#395×C127C211yesmaximal, characteristic
4C2×#395×C127C211yesmaximal, characteristic
5C2×#391×C127C211yesmaximal, characteristic
6C2×#389×C127C211yesmaximal, characteristic
7C127×#1446C211yesmaximal, characteristic
8C127×#1444C211yesmaximal, characteristic
9C127×#1444C211yesmaximal, characteristic
10C127×#1442C211yesmaximal, characteristic
11C127×#1441C211yesmaximal, characteristic
12C127×#1441C211yesmaximal, characteristic
13C127×#1436C211yesmaximal, characteristic
14C127×#1436C211yesmaximal, characteristic
15C127×#1436C211yesmaximal, characteristic
16C23×Q8×C127C2211yescharacteristic
17C23×Q8×C127C2211yescharacteristic
18C2×C4⋊Q8×C127—24no—
19C2×C4⋊Q8×C127—24no—
20C2×C4⋊Q8×C127—24no—
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×C4⋊C4×C127C2211yescharacteristic
28C22×C4⋊C4×C127C2211yescharacteristic
29C22×C4⋊C4×C127C2211yescharacteristic
30C22×C4⋊C4×C127C2211yescharacteristic
31C22×C4⋊C4×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33C22×C42×C127C2211yescharacteristic
34#398×C127—24no—
35#395×C127—24no—
36#395×C127—24no—
37#391×C127—24no—
38#389×C127—24no—
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
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C22×Q8×C127—22no—
60C22×Q8×C127—22no—
61C22×Q8×C127—22no—
62C22×Q8×C127—22no—
63C22×Q8×C127—22no—
64C22×Q8×C127—22no—
65C22×Q8×C127—22no—
66C22×Q8×C127—22no—
67C22×Q8×C127—22no—
68C22×Q8×C127—41no—
69C22×Q8×C127—41no—
70C22×Q8×C127—41no—
71C22×Q8×C127—41no—
72C22×Q8×C127D414yes—
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
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
88C4⋊Q8×C127—232no—
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—22no—
107C2×C4⋊C4×C127—22no—
108C2×C4⋊C4×C127—22no—
109C2×C4⋊C4×C127—22no—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—22no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127—41no—
115C2×C4⋊C4×C127—41no—
116C2×C4⋊C4×C127—41no—
117C2×C4⋊C4×C127—41no—
118C2×C4⋊C4×C127—41no—
119C2×C4⋊C4×C127D414yes—
120C2×C4⋊C4×C127D414yes—
121C2×C4⋊C4×C127Q814yescomplemented
122C2×C42×C127—22no—
123C2×C42×C127—22no—
124C2×C42×C127—22no—
125C2×C42×C127—22no—
126C2×C42×C127—22no—
127C2×C42×C127—41no—
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—22no—
138#95×C127—22no—
139#95×C127—22no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—41no—
144#95×C127—41no—
145#95×C127D414yes—
146#95×C127Q814yescomplemented
147#95×C127Q814yescomplemented
148C24×C127C2411yescharacteristic
149C2×Q8×C127—28no—
150C2×Q8×C127—28no—
151C2×Q8×C127—28no—
152C2×Q8×C127—44no—
153C2×Q8×C127—44no—
154C2×Q8×C127—44no—
155C2×Q8×C127—44no—
156C2×Q8×C127—44no—
157C2×Q8×C127—44no—
158C2×Q8×C127—44no—
159C2×Q8×C127—44no—
160C2×Q8×C127—44no—
161C2×Q8×C127—44no—
162C2×Q8×C127—44no—
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—21no—
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—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127C2×D412yes—
246C22×C4×C127C2×D412yes—
247C22×C4×C127C2×D412yes—
248C22×C4×C127C2×D412yes—
249C22×C4×C127C2×D412yes—
250C22×C4×C127C2×D412yes—
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×C127C2×Q812yes—
260C22×C4×C127C2×Q812yes—
261C22×C4×C127C2×Q812yes—
262C22×C4×C127C2×Q812yes—
263C22×C4×C127C2×Q812yes—
264C22×C4×C127C2×Q812yes—
265C22×C4×C127C2×Q812yes—
266C22×C4×C127#4112yes—
267C22×C4×C127#4112yes—
268C4⋊C4×C127—28no—
269C4⋊C4×C127—28no—
270C4⋊C4×C127—28no—
271C4⋊C4×C127—28no—
272C4⋊C4×C127—28no—
273C4⋊C4×C127—44no—
274C4⋊C4×C127—44no—
275C4⋊C4×C127—44no—
276C4⋊C4×C127—44no—
277C4⋊C4×C127—44no—
278C4⋊C4×C127—44no—
279C42×C127—28no—
280C42×C127—44no—
281C23×C127C22×D411yescharacteristic
282C23×C127C22×D411yescharacteristic
283C23×C127C22×D411yescharacteristic
284C23×C127C22×D411yescharacteristic
285C23×C127C22×Q811yescharacteristic
286C23×C127C22×Q811yescharacteristic
287C23×C127C22×Q811yescharacteristic
288C23×C127C2×#4111yescharacteristic
289C23×C127C2×#4111yescharacteristic
290C23×C127H(5,𝔽2)11yescharacteristic
291C23×C127H(5,𝔽2)11yescharacteristic
292C23×C1272−1+411yescharacteristic
293C23×C1272−1+411yescharacteristic
294C23×C1272−1+411yescharacteristic
295C23×C1272−1+411yescharacteristic
296Q8×C127—416no—
297Q8×C127—416no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—22no—
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—22no—
310C2×C4×C127—22no—
311C2×C4×C127—22no—
312C2×C4×C127—22no—
313C2×C4×C127—22no—
314C2×C4×C127—22no—
315C2×C4×C127—22no—
316C2×C4×C127—22no—
317C2×C4×C127—22no—
318C2×C4×C127—22no—
319C2×C4×C127—22no—
320C2×C4×C127—22no—
321C2×C4×C127—22no—
322C2×C4×C127—22no—
323C2×C4×C127—22no—
324C2×C4×C127—22no—
325C2×C4×C127—22no—
326C2×C4×C127—22no—
327C2×C4×C127—22no—
328C2×C4×C127—22no—
329C2×C4×C127—22no—
330C2×C4×C127—22no—
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—41no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—41no—
356C2×C4×C127—41no—
357C2×C4×C127—41no—
358C2×C4×C127—41no—
359C2×C4×C127—41no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—41no—
366C2×C4×C127—41no—
367C2×C4×C127—41no—
368C2×C4×C127—41no—
369C2×C4×C127—41no—
370C2×C4×C127—41no—
371C2×C4×C127—41no—
372C2×C4×C127—41no—
373C2×C4×C127—41no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
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#12014yes—
399C2×C4×C127#12114yes—
400C2×C4×C127C22⋊Q814yes—
401C2×C4×C127C4⋊Q814yes—
402C2×C4×C127C4⋊Q814yescomplemented
403C22×C127C2×#12011yescharacteristic
404C22×C127C2×#12111yescharacteristic
405C22×C127C2×C22⋊Q811yescharacteristic
406C22×C127C2×C4⋊Q811yescharacteristic
407C22×C127C2×C4⋊Q811yescharacteristic
408C22×C127#53311yescharacteristic
409C22×C127#53411yescharacteristic
410C22×C127#53611yescharacteristic
411C22×C127#53611yescharacteristic
412C22×C127#53611yescharacteristic
413C22×C127#54111yescharacteristic
414C22×C127#54211yescharacteristic
415C22×C127#54411yescharacteristic
416C22×C127#54411yescharacteristic
417C22×C127#54411yescharacteristic
418C22×C127D4211yescharacteristic
419C22×C127D4211yescharacteristic
420C22×C127#54611yescharacteristic
421C22×C127#54611yescharacteristic
422C22×C127#54711yescharacteristic
423C22×C127#54811yescharacteristic
424C22×C127#54811yescharacteristic
425C22×C127D4×Q811yescharacteristic
426C22×C127D4×Q811yescharacteristic
427C22×C127D4×Q811yescharacteristic
428C22×C127D4×Q811yescharacteristic
429C22×C127D4×Q811yescharacteristic
430C22×C127D4×Q811yescharacteristic
431C22×C127D4×Q811yescharacteristic
432C22×C127#55411yescharacteristic
433C22×C127#55711yescharacteristic
434C22×C127#55711yescharacteristic
435C22×C127Q8211yescharacteristic
436C22×C127#56311yescharacteristic
437C22×C127#56311yescharacteristic
438C4×C127—24no—
439C4×C127—24no—
440C4×C127—24no—
441C4×C127—24no—
442C4×C127—24no—
443C4×C127—42no—
444C4×C127—42no—
445C4×C127—42no—
446C4×C127—42no—
447C4×C127—42no—
448C4×C127—42no—
449C4×C127—42no—
450C4×C127—42no—
451C4×C127—81no—
452C4×C127—81no—
453#15318C12711yesmaximal, characteristic, direct product factor, Sylow
454C2×C127#240911yescharacteristic
455C2×C127#241011yescharacteristic
456C2×C127#242911yescharacteristic
457C2×C127#243411yescharacteristic
458C2×C127#244011yescharacteristic
459C2×C127#245111yescharacteristic
460C2×C127#254611yescharacteristic
461C2×C127#255011yescharacteristic
462C2×C127#255111yescharacteristic
463C2×C127#267411yescharacteristic
464C2×C127#267711yescharacteristic
465C2×C127#271311yescharacteristic
466C2×C127#271311yescharacteristic
467C2×C127#272911yescharacteristic
468C2×C127#273411yescharacteristic
469C22×C4⋊Q8C2×C12711yescharacteristic
470C2×#398C2×C12711yescharacteristic
471C2×#395C2×C12711yescharacteristic
472C2×#395C2×C12711yescharacteristic
473C2×#391C2×C12711yescharacteristic
474C2×#389C2×C12711yescharacteristic
475#1446C2×C12711yescharacteristic
476#1444C2×C12711yescharacteristic
477#1444C2×C12711yescharacteristic
478#1442C2×C12711yescharacteristic
479#1441C2×C12711yescharacteristic
480#1441C2×C12711yescharacteristic
481#1436C2×C12711yescharacteristic
482#1436C2×C12711yescharacteristic
483#1436C2×C12711yescharacteristic
484C127#1531811yescharacteristic, direct product factor, Sylow
485C23×Q8C22×C12711yescharacteristic
486C23×Q8C22×C12711yescharacteristic
487C2×C4⋊Q8—24no—
488C2×C4⋊Q8—24no—
489C2×C4⋊Q8—24no—
490C22×C4⋊C4C22×C12711yescharacteristic
491C22×C4⋊C4C22×C12711yescharacteristic
492C22×C4⋊C4C22×C12711yescharacteristic
493C22×C4⋊C4C22×C12711yescharacteristic
494C22×C4⋊C4C22×C12711yescharacteristic
495C22×C4⋊C4C22×C12711yescharacteristic
496C22×C4⋊C4C22×C12711yescharacteristic
497C22×C4⋊C4C22×C12711yescharacteristic
498C22×C4⋊C4C22×C12711yescharacteristic
499C22×C4⋊C4C22×C12711yescharacteristic
500C22×C4⋊C4C22×C12711yescharacteristic
501C22×C42C22×C12711yescharacteristic
502C22×C42C22×C12711yescharacteristic
503#398—24no—
504#395—24no—
505#395—24no—
506#391—24no—
507#389—24no—
508C2×#95C22×C12711yescharacteristic
509C2×#95C22×C12711yescharacteristic
510C2×#95C22×C12711yescharacteristic
511C2×#95C22×C12711yescharacteristic
512C2×#95C22×C12711yescharacteristic
513C2×#95C22×C12711yescharacteristic
514C2×#95C22×C12711yescharacteristic
515C2×#95C22×C12711yescharacteristic
516C2×#95C22×C12711yescharacteristic
517C2×#95C22×C12711yescharacteristic
518C2×#95C22×C12711yescharacteristic
519C2×#95C22×C12711yescharacteristic
520C2×#95C22×C12711yescharacteristic
521C2×#95C22×C12711yescharacteristic
522C2×#95C22×C12711yescharacteristic
523C2×#95C22×C12711yescharacteristic
524C2×#95C22×C12711yescharacteristic
525C2×#95C22×C12711yescharacteristic
526C2×#95C22×C12711yescharacteristic
527C2×#95C22×C12711yescharacteristic
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—22no—
536C22×Q8—22no—
537C22×Q8—41no—
538C22×Q8—41no—
539C22×Q8—41no—
540C22×Q8—41no—
541C22×Q8D4×C12714yes—
542C23×C4C23×C12711yescharacteristic
543C23×C4C23×C12711yescharacteristic
544C23×C4C23×C12711yescharacteristic
545C23×C4C23×C12711yescharacteristic
546C23×C4C23×C12711yescharacteristic
547C23×C4C23×C12711yescharacteristic
548C23×C4C23×C12711yescharacteristic
549C23×C4C23×C12711yescharacteristic
550C23×C4C23×C12711yescharacteristic
551C23×C4C23×C12711yescharacteristic
552C23×C4C23×C12711yescharacteristic
553C23×C4C23×C12711yescharacteristic
554C23×C4C23×C12711yescharacteristic
555C23×C4C23×C12711yescharacteristic
556C23×C4C23×C12711yescharacteristic
557C4⋊Q8—232no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4D4×C12714yes—
589C2×C4⋊C4D4×C12714yes—
590C2×C4⋊C4Q8×C12714yescomplemented
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—41no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—41no—
614#95D4×C12714yes—
615#95Q8×C12714yescomplemented
616#95Q8×C12714yescomplemented
617C24C24×C12711yescharacteristic
618C2×Q8—28no—
619C2×Q8—28no—
620C2×Q8—28no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—21no—
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×C4C2×D4×C12712yes—
715C22×C4C2×D4×C12712yes—
716C22×C4C2×D4×C12712yes—
717C22×C4C2×D4×C12712yes—
718C22×C4C2×D4×C12712yes—
719C22×C4C2×D4×C12712yes—
720C22×C4C2×D4×C12712yes—
721C22×C4C2×D4×C12712yes—
722C22×C4C2×D4×C12712yes—
723C22×C4C2×D4×C12712yes—
724C22×C4C2×D4×C12712yes—
725C22×C4C2×D4×C12712yes—
726C22×C4C2×Q8×C12712yes—
727C22×C4C2×Q8×C12712yes—
728C22×C4C2×Q8×C12712yes—
729C22×C4C2×Q8×C12712yes—
730C22×C4C2×Q8×C12712yes—
731C22×C4C2×Q8×C12712yes—
732C22×C4C2×Q8×C12712yes—
733C22×C4C2×Q8×C12712yes—
734C22×C4C2×Q8×C12712yes—
735C22×C4#41×C12712yes—
736C22×C4#41×C12712yes—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C42—28no—
749C42—44no—
750C23C22×D4×C12711yescharacteristic
751C23C22×D4×C12711yescharacteristic
752C23C22×D4×C12711yescharacteristic
753C23C22×D4×C12711yescharacteristic
754C23C22×Q8×C12711yescharacteristic
755C23C22×Q8×C12711yescharacteristic
756C23C22×Q8×C12711yescharacteristic
757C23C2×#41×C12711yescharacteristic
758C23C2×#41×C12711yescharacteristic
759C23H(5,𝔽2)×C12711yescharacteristic
760C23H(5,𝔽2)×C12711yescharacteristic
761C232−1+4×C12711yescharacteristic
762C232−1+4×C12711yescharacteristic
763C232−1+4×C12711yescharacteristic
764C232−1+4×C12711yescharacteristic
765Q8—416no—
766Q8—416no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4#120×C12714yes—
868C2×C4#121×C12714yes—
869C2×C4C22⋊Q8×C12714yes—
870C2×C4C4⋊Q8×C12714yes—
871C2×C4C4⋊Q8×C12714yescomplemented
872C22C2×#120×C12711yescharacteristic
873C22C2×#121×C12711yescharacteristic
874C22C2×C22⋊Q8×C12711yescharacteristic
875C22C2×C4⋊Q8×C12711yescharacteristic
876C22C2×C4⋊Q8×C12711yescharacteristic
877C22#533×C12711yescharacteristic
878C22#534×C12711yescharacteristic
879C22#536×C12711yescharacteristic
880C22#536×C12711yescharacteristic
881C22#536×C12711yescharacteristic
882C22#541×C12711yescharacteristic
883C22#542×C12711yescharacteristic
884C22#544×C12711yescharacteristic
885C22#544×C12711yescharacteristic
886C22#544×C12711yescharacteristic
887C22D42×C12711yescharacteristic
888C22D42×C12711yescharacteristic
889C22#546×C12711yescharacteristic
890C22#546×C12711yescharacteristic
891C22#547×C12711yescharacteristic
892C22#548×C12711yescharacteristic
893C22#548×C12711yescharacteristic
894C22D4×Q8×C12711yescharacteristic
895C22D4×Q8×C12711yescharacteristic
896C22D4×Q8×C12711yescharacteristic
897C22D4×Q8×C12711yescharacteristic
898C22D4×Q8×C12711yescharacteristic
899C22D4×Q8×C12711yescharacteristic
900C22D4×Q8×C12711yescharacteristic
901C22#554×C12711yescharacteristic
902C22#557×C12711yescharacteristic
903C22#557×C12711yescharacteristic
904C22Q82×C12711yescharacteristic
905C22#563×C12711yescharacteristic
906C22#563×C12711yescharacteristic
907C4—24no—
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—81no—
921C4—81no—
922C2C127×#240911yescharacteristic
923C2C127×#241011yescharacteristic
924C2C127×#242911yescharacteristic
925C2C127×#243411yescharacteristic
926C2C127×#244011yescharacteristic
927C2C127×#245111yescharacteristic
928C2C127×#254611yescharacteristic
929C2C127×#255011yescharacteristic
930C2C127×#255111yescharacteristic
931C2C127×#267411yescharacteristic
932C2C127×#267711yescharacteristic
933C2C127×#271311yescharacteristic
934C2C127×#271311yescharacteristic
935C2C127×#272911yescharacteristic
936C2C127×#273411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
121. C2×C4⋊C4×C127Q8semidirect
146. #95×C127Q8semidirect
147. #95×C127Q8semidirect
402. C2×C4×C127C4⋊Q8semidirect
453. #15318C127direct (N × H)
484. C127#15318direct (N × H)
590. C2×C4⋊C4Q8×C127semidirect
615. #95Q8×C127semidirect
616. #95Q8×C127semidirect
871. C2×C4C4⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Q8×C1272
C2×#398×C1272
C2×#395×C1272
C2×#391×C1272
C2×#389×C1272
C127×#14462
C127×#14442
C127×#14422
C127×#14412
C127×#14362
#15318127