Finite Group Databasebeta

← C127×#21599 #44585272

Subgroups — C127×#21599 #44585272

Order 32512.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#446×C127C211yesmaximal, characteristic, complemented
2C22×#97×C127C211yesmaximal, characteristic
3C4×C22⋊Q8×C127C211yesmaximal, characteristic
4C127×#1985C211yesmaximal, characteristic, complemented
5C127×#1940C211yesmaximal, characteristic, complemented
6C127×#1917C211yesmaximal, characteristic, complemented
7C127×#1917C211yesmaximal, characteristic, complemented
8C127×#1850C211yesmaximal, characteristic
9C127×#1850C211yesmaximal, characteristic
10C127×#1797C211yesmaximal, characteristic
11C127×#1771C211yesmaximal, characteristic, complemented
12C127×#1771C211yesmaximal, characteristic, complemented
13C127×#1770C211yesmaximal, characteristic, complemented
14C127×#1752C211yesmaximal, characteristic
15C8×C22⋊C4×C127C211yesmaximal, characteristic
16C23×C8×C127C2211yescharacteristic
17C23×C8×C127C2211yescharacteristic
18C2×C22⋊Q8×C127C411yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21#446×C127—24no—
22C2×C4⋊C8×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×C4⋊C8×C127C2211yescharacteristic
26C2×C4⋊C8×C127C2211yescharacteristic
27C2×C4⋊C8×C127C2211yescharacteristic
28C2×C22⋊C8×C127C2211yescharacteristic
29C2×C22⋊C8×C127C2211yescharacteristic
30C2×#97×C127—24no—
31C2×#97×C127C2211yescharacteristic
32C2×#97×C127C2211yescharacteristic
33C2×#97×C127C2211yescharacteristic
34C2×#97×C127C2211yescharacteristic
35C2×#97×C127C2211yescharacteristic
36C2×#97×C127C2211yescharacteristic
37C2×C4×C8×C127C2211yescharacteristic
38C2×C4×C8×C127C2211yescharacteristic
39#391×C127C411yescharacteristic
40#389×C127C411yescharacteristic
41#387×C127C411yescharacteristic
42#387×C127C411yescharacteristic
43#385×C127C411yescharacteristic
44#385×C127C411yescharacteristic
45#380×C127C411yescharacteristic
46C4×C4⋊C4×C127C2211yescharacteristic
47C4×C4⋊C4×C127C2211yescharacteristic
48C4×C4⋊C4×C127C2211yescharacteristic
49C4×C22⋊C4×C127C2211yescharacteristic
50C4×C22⋊C4×C127C2211yescharacteristic
51#336×C127C2211yescharacteristic
52#336×C127C2211yescharacteristic
53#336×C127C2211yescharacteristic
54#336×C127C2211yescharacteristic
55#336×C127C2211yescharacteristic
56#336×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61C22×Q8×C127C2×C411yescharacteristic
62C23×C4×C127C2×C411yescharacteristic
63C23×C4×C127C2×C411yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C22×C8×C127—22no—
66C22×C8×C127—22no—
67C22×C8×C127—22no—
68C22×C8×C127—22no—
69C22×C8×C127—22no—
70C22×C8×C127Q814yescomplemented
71C22×C8×C127C2311yescharacteristic
72C22×C8×C127C2311yescharacteristic
73C22×C8×C127C2311yescharacteristic
74C22×C8×C127C2311yescharacteristic
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79C22⋊Q8×C127—24no—
80C4×Q8×C127—22no—
81C4×Q8×C127—22no—
82C2×C4⋊C4×C127C2×C411yescharacteristic
83C2×C4⋊C4×C127C2×C411yescharacteristic
84C2×C4⋊C4×C127C2×C411yescharacteristic
85C2×C4⋊C4×C127C2×C411yescharacteristic
86C2×C4⋊C4×C127C2×C411yescharacteristic
87C2×C4⋊C4×C127C2×C411yescharacteristic
88C2×C4⋊C4×C127C2×C411yescharacteristic
89C2×C4⋊C4×C127C2×C411yescharacteristic
90C2×C4⋊C4×C127C2×C411yescharacteristic
91C2×C22⋊C4×C127C2×C411yescharacteristic
92C2×C22⋊C4×C127C2×C411yescharacteristic
93C2×C22⋊C4×C127C2×C411yescharacteristic
94C2×C22⋊C4×C127C2×C411yescharacteristic
95C2×C42×C127—22no—
96C2×C42×C127—22no—
97C2×C42×C127C2×C411yescharacteristic
98C2×C42×C127C2×C411yescharacteristic
99C2×C42×C127C2311yescharacteristic
100C2×C42×C127C2311yescharacteristic
101C2×C42×C127C2311yescharacteristic
102C2×C42×C127C2311yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C2×C42×C127C2311yescharacteristic
105C4⋊C8×C127—22no—
106C4⋊C8×C127—22no—
107C4⋊C8×C127—22no—
108C4⋊C8×C127—22no—
109C4⋊C8×C127—22no—
110C4⋊C8×C127—22no—
111C22⋊C8×C127—22no—
112C22⋊C8×C127—22no—
113#97×C127—22no—
114#97×C127—22no—
115#97×C127—22no—
116#97×C127—22no—
117#97×C127—22no—
118#97×C127D414yes—
119C4×C8×C127—22no—
120C4×C8×C127—22no—
121#95×C127C2×C411yescharacteristic
122#95×C127C2×C411yescharacteristic
123#95×C127C2×C411yescharacteristic
124#95×C127C2×C411yescharacteristic
125#95×C127C2×C411yescharacteristic
126#95×C127C2×C411yescharacteristic
127#95×C127C2×C411yescharacteristic
128#95×C127C2×C411yescharacteristic
129#95×C127C2×C411yescharacteristic
130#95×C127C2×C411yescharacteristic
131C24×C127C22×C411yescharacteristic
132C2×Q8×C127—22no—
133C2×Q8×C127—22no—
134C2×Q8×C127—41no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—41no—
144C22×C4×C127—41no—
145C22×C4×C127C22×C411yescharacteristic
146C22×C4×C127C22×C411yescharacteristic
147C22×C4×C127C22×C411yescharacteristic
148C22×C4×C127C22×C411yescharacteristic
149C22×C4×C127C22×C411yescharacteristic
150C22×C4×C127C22×C411yescharacteristic
151C22×C4×C127C22×C411yescharacteristic
152C22×C4×C127C22×C411yescharacteristic
153C22×C4×C127C22×C411yescharacteristic
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C22×C411yescharacteristic
158C22×C4×C127C2×Q812yes—
159C22×C4×C127#4112yes—
160C22×C4×C127C2411yescharacteristic
161C2×C8×C127—28no—
162C2×C8×C127—21no—
163C2×C8×C127—21no—
164C2×C8×C127—21no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—28no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127C2×D412yes—
182C2×C8×C127C2×D412yes—
183C2×C8×C127C2×Q812yes—
184C2×C8×C127C2×Q812yes—
185C2×C8×C127#4112yes—
186C2×C8×C127#4112yes—
187C4⋊C4×C127—22no—
188C4⋊C4×C127—22no—
189C4⋊C4×C127—22no—
190C4⋊C4×C127—22no—
191C4⋊C4×C127—22no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127—41no—
195C4⋊C4×C127—41no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127M1614yes—
200C42×C127—22no—
201C42×C127—22no—
202C42×C127—21no—
203C42×C127—21no—
204C42×C127—21no—
205C42×C127—21no—
206C42×C127—21no—
207C42×C127—21no—
208C42×C127—21no—
209C42×C127—21no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127C2×D412yes—
213C42×C127#4112yes—
214C23×C127—21no—
215C23×C127—21no—
216C23×C127—21no—
217C23×C127—21no—
218C23×C127C4×Q812yes—
219C23×C127C2×M1612yes—
220C23×C127#13112yes—
221C23×C127C23×C411yescharacteristic
222Q8×C127—44no—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—22no—
236C2×C4×C127—22no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—44no—
262C2×C4×C127—44no—
263C2×C4×C127C4×D412yes—
264C2×C4×C127C4×D412yes—
265C2×C4×C127C4×Q812yes—
266C2×C4×C127C2×M1612yes—
267C2×C4×C127C2×M1612yes—
268C2×C4×C127C22×D411yescharacteristic
269C2×C4×C127C22×Q811yescharacteristic
270C2×C4×C127C2×#4111yescharacteristic
271C2×C4×C127C2×#4111yescharacteristic
272C2×C4×C127C2×#4111yescharacteristic
273C2×C4×C127C2×#4111yescharacteristic
274C8×C127—22no—
275C8×C127—22no—
276C8×C127—22no—
277C8×C127—41no—
278C8×C127—41no—
279C8×C127—41no—
280C8×C127—41no—
281C8×C127C22⋊Q814yescomplemented
282C22×C127—22no—
283C22×C127—22no—
284C22×C127—22no—
285C22×C127—22no—
286C22×C127—22no—
287C22×C127—22no—
288C22×C127#44614yescomplemented
289C22×C127C2×C4×D411yescharacteristic
290C22×C127C2×C4×Q811yescharacteristic
291C22×C127C4×#4111yescharacteristic
292C22×C127C22×M1611yescharacteristic
293C22×C127C2×#13111yescharacteristic
294C22×C127#56811yescharacteristic
295C22×C127#56811yescharacteristic
296C4×C127—22no—
297C4×C127—22no—
298C4×C127—22no—
299C4×C127—22no—
300C4×C127—22no—
301C4×C127—41no—
302C4×C127—41no—
303C4×C127—41no—
304C4×C127—41no—
305C4×C127—41no—
306C4×C127—41no—
307C4×C127—41no—
308C4×C127—41no—
309C4×C127C2×C22⋊Q811yescharacteristic
310C4×C127#52511yescharacteristic
311C4×C127#52911yescharacteristic
312C4×C127#53311yescharacteristic
313#21599C12711yesmaximal, characteristic, direct product factor, Sylow
314C2×C127—24no—
315C2×C127C4×C22⋊Q811yescharacteristic
316C2×C127#293311yescharacteristic
317C2×C127D4×M1611yescharacteristic
318C2×C127C2×#44611yescharacteristic
319C2×C127#296111yescharacteristic
320C2×C127#296811yescharacteristic
321C2×C127#297011yescharacteristic
322C2×#446C2×C12711yescharacteristic, complemented
323C22×#97C2×C12711yescharacteristic
324C4×C22⋊Q8C2×C12711yescharacteristic
325#1985C2×C12711yescharacteristic, complemented
326#1940C2×C12711yescharacteristic, complemented
327#1917C2×C12711yescharacteristic, complemented
328#1917C2×C12711yescharacteristic, complemented
329#1850C2×C12711yescharacteristic
330#1850C2×C12711yescharacteristic
331#1797C2×C12711yescharacteristic
332#1771C2×C12711yescharacteristic, complemented
333#1771C2×C12711yescharacteristic, complemented
334#1770C2×C12711yescharacteristic, complemented
335#1752C2×C12711yescharacteristic
336C8×C22⋊C4C2×C12711yescharacteristic
337C127#2159911yescharacteristic, direct product factor, Sylow
338C23×C8C22×C12711yescharacteristic
339C23×C8C22×C12711yescharacteristic
340C2×C22⋊Q8C4×C12711yescharacteristic
341C2×C4×Q8C22×C12711yescharacteristic
342C22×C42C22×C12711yescharacteristic
343#446—24no—
344C2×C4⋊C8C22×C12711yescharacteristic
345C2×C4⋊C8C22×C12711yescharacteristic
346C2×C4⋊C8C22×C12711yescharacteristic
347C2×C4⋊C8C22×C12711yescharacteristic
348C2×C4⋊C8C22×C12711yescharacteristic
349C2×C4⋊C8C22×C12711yescharacteristic
350C2×C22⋊C8C22×C12711yescharacteristic
351C2×C22⋊C8C22×C12711yescharacteristic
352C2×#97—24no—
353C2×#97C22×C12711yescharacteristic
354C2×#97C22×C12711yescharacteristic
355C2×#97C22×C12711yescharacteristic
356C2×#97C22×C12711yescharacteristic
357C2×#97C22×C12711yescharacteristic
358C2×#97C22×C12711yescharacteristic
359C2×C4×C8C22×C12711yescharacteristic
360C2×C4×C8C22×C12711yescharacteristic
361#391C4×C12711yescharacteristic
362#389C4×C12711yescharacteristic
363#387C4×C12711yescharacteristic
364#387C4×C12711yescharacteristic
365#385C4×C12711yescharacteristic
366#385C4×C12711yescharacteristic
367#380C4×C12711yescharacteristic
368C4×C4⋊C4C22×C12711yescharacteristic
369C4×C4⋊C4C22×C12711yescharacteristic
370C4×C4⋊C4C22×C12711yescharacteristic
371C4×C22⋊C4C22×C12711yescharacteristic
372C4×C22⋊C4C22×C12711yescharacteristic
373#336C22×C12711yescharacteristic
374#336C22×C12711yescharacteristic
375#336C22×C12711yescharacteristic
376#336C22×C12711yescharacteristic
377#336C22×C12711yescharacteristic
378#336C22×C12711yescharacteristic
379#336C22×C12711yescharacteristic
380#336C22×C12711yescharacteristic
381#336C22×C12711yescharacteristic
382#336C22×C12711yescharacteristic
383C22×Q8C2×C4×C12711yescharacteristic
384C23×C4C2×C4×C12711yescharacteristic
385C23×C4C2×C4×C12711yescharacteristic
386C23×C4C23×C12711yescharacteristic
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8Q8×C12714yescomplemented
393C22×C8C23×C12711yescharacteristic
394C22×C8C23×C12711yescharacteristic
395C22×C8C23×C12711yescharacteristic
396C22×C8C23×C12711yescharacteristic
397C22×C8C23×C12711yescharacteristic
398C22×C8C23×C12711yescharacteristic
399C22×C8C23×C12711yescharacteristic
400C22×C8C23×C12711yescharacteristic
401C22⋊Q8—24no—
402C4×Q8—22no—
403C4×Q8—22no—
404C2×C4⋊C4C2×C4×C12711yescharacteristic
405C2×C4⋊C4C2×C4×C12711yescharacteristic
406C2×C4⋊C4C2×C4×C12711yescharacteristic
407C2×C4⋊C4C2×C4×C12711yescharacteristic
408C2×C4⋊C4C2×C4×C12711yescharacteristic
409C2×C4⋊C4C2×C4×C12711yescharacteristic
410C2×C4⋊C4C2×C4×C12711yescharacteristic
411C2×C4⋊C4C2×C4×C12711yescharacteristic
412C2×C4⋊C4C2×C4×C12711yescharacteristic
413C2×C22⋊C4C2×C4×C12711yescharacteristic
414C2×C22⋊C4C2×C4×C12711yescharacteristic
415C2×C22⋊C4C2×C4×C12711yescharacteristic
416C2×C22⋊C4C2×C4×C12711yescharacteristic
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×C4×C12711yescharacteristic
420C2×C42C2×C4×C12711yescharacteristic
421C2×C42C23×C12711yescharacteristic
422C2×C42C23×C12711yescharacteristic
423C2×C42C23×C12711yescharacteristic
424C2×C42C23×C12711yescharacteristic
425C2×C42C23×C12711yescharacteristic
426C2×C42C23×C12711yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435#97—22no—
436#97—22no—
437#97—22no—
438#97—22no—
439#97—22no—
440#97D4×C12714yes—
441C4×C8—22no—
442C4×C8—22no—
443#95C2×C4×C12711yescharacteristic
444#95C2×C4×C12711yescharacteristic
445#95C2×C4×C12711yescharacteristic
446#95C2×C4×C12711yescharacteristic
447#95C2×C4×C12711yescharacteristic
448#95C2×C4×C12711yescharacteristic
449#95C2×C4×C12711yescharacteristic
450#95C2×C4×C12711yescharacteristic
451#95C2×C4×C12711yescharacteristic
452#95C2×C4×C12711yescharacteristic
453C24C22×C4×C12711yescharacteristic
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—41no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4C22×C4×C12711yescharacteristic
468C22×C4C22×C4×C12711yescharacteristic
469C22×C4C22×C4×C12711yescharacteristic
470C22×C4C22×C4×C12711yescharacteristic
471C22×C4C22×C4×C12711yescharacteristic
472C22×C4C22×C4×C12711yescharacteristic
473C22×C4C22×C4×C12711yescharacteristic
474C22×C4C22×C4×C12711yescharacteristic
475C22×C4C22×C4×C12711yescharacteristic
476C22×C4C22×C4×C12711yescharacteristic
477C22×C4C22×C4×C12711yescharacteristic
478C22×C4C22×C4×C12711yescharacteristic
479C22×C4C22×C4×C12711yescharacteristic
480C22×C4C2×Q8×C12712yes—
481C22×C4#41×C12712yes—
482C22×C4C24×C12711yescharacteristic
483C2×C8—28no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—28no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×D4×C12712yes—
504C2×C8C2×D4×C12712yes—
505C2×C8C2×Q8×C12712yes—
506C2×C8C2×Q8×C12712yes—
507C2×C8#41×C12712yes—
508C2×C8#41×C12712yes—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4M16×C12714yes—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42C2×D4×C12712yes—
535C42#41×C12712yes—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C4×Q8×C12712yes—
541C23C2×M16×C12712yes—
542C23#131×C12712yes—
543C23C23×C4×C12711yescharacteristic
544Q8—44no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4C4×D4×C12712yes—
586C2×C4C4×D4×C12712yes—
587C2×C4C4×Q8×C12712yes—
588C2×C4C2×M16×C12712yes—
589C2×C4C2×M16×C12712yes—
590C2×C4C22×D4×C12711yescharacteristic
591C2×C4C22×Q8×C12711yescharacteristic
592C2×C4C2×#41×C12711yescharacteristic
593C2×C4C2×#41×C12711yescharacteristic
594C2×C4C2×#41×C12711yescharacteristic
595C2×C4C2×#41×C12711yescharacteristic
596C8—22no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C8C22⋊Q8×C12714yescomplemented
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#446×C12714yescomplemented
611C22C2×C4×D4×C12711yescharacteristic
612C22C2×C4×Q8×C12711yescharacteristic
613C22C4×#41×C12711yescharacteristic
614C22C22×M16×C12711yescharacteristic
615C22C2×#131×C12711yescharacteristic
616C22#568×C12711yescharacteristic
617C22#568×C12711yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4C2×C22⋊Q8×C12711yescharacteristic
632C4#525×C12711yescharacteristic
633C4#529×C12711yescharacteristic
634C4#533×C12711yescharacteristic
635C2—24no—
636C2C4×C22⋊Q8×C12711yescharacteristic
637C2C127×#293311yescharacteristic
638C2D4×M16×C12711yescharacteristic
639C2C2×#446×C12711yescharacteristic
640C2C127×#296111yescharacteristic
641C2C127×#296811yescharacteristic
642C2C127×#297011yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#446×C127C2semidirect
4. C127×#1985C2semidirect
5. C127×#1940C2semidirect
6. C127×#1917C2semidirect
7. C127×#1917C2semidirect
11. C127×#1771C2semidirect
12. C127×#1771C2semidirect
13. C127×#1770C2semidirect
70. C22×C8×C127Q8semidirect
281. C8×C127C22⋊Q8semidirect
288. C22×C127#446semidirect
313. #21599C127direct (N × H)
322. C2×#446C2×C127semidirect
325. #1985C2×C127semidirect
326. #1940C2×C127semidirect
327. #1917C2×C127semidirect
328. #1917C2×C127semidirect
332. #1771C2×C127semidirect
333. #1771C2×C127semidirect
334. #1770C2×C127semidirect
337. C127#21599direct (N × H)
392. C22×C8Q8×C127semidirect
603. C8C22⋊Q8×C127semidirect
610. C22#446×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#446×C1272
C22×#97×C1272
C4×C22⋊Q8×C1272
C127×#19852
C127×#19402
C127×#19172
C127×#18502
C127×#17972
C127×#17712
C127×#17702
C127×#17522
C8×C22⋊C4×C1272
#21599127