Finite Group Databasebeta

← #440×#6157 #28318582

Subgroups — #440×#6157 #28318582

Order 13568.

1206 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811662C211yesmaximal, characteristic
2C2×SD16×#6157C211yesmaximal, characteristic
3C4×Q8×#6157C211yesmaximal, characteristic, complemented
4C4×D4×#6157C211yesmaximal, characteristic
5#20290530C211yesmaximal, characteristic, complemented
6#20290529C211yesmaximal, characteristic, complemented
7#107×#6157C211yesmaximal, characteristic, complemented
8#20290488C211yesmaximal, characteristic, complemented
9#20290487C211yesmaximal, characteristic, complemented
10#20290486C211yesmaximal, characteristic
11#20290485C211yesmaximal, characteristic
12#103×#6157C211yesmaximal, characteristic, complemented
13#102×#6157C211yesmaximal, characteristic
14#97×#6157C211yesmaximal, characteristic, complemented
15#440×D53C211yesmaximal, characteristic
16C2×Q8×#6157C2211yescharacteristic
17C2×Q8×#6157C2211yescharacteristic
18C2×D4×#6157C2211yescharacteristic
19C2×D4×#6157C2211yescharacteristic
20C22×C4×#6157—21no—
21#16811662C418yescomplemented
22SD16×#6157C418yescomplemented
23C2×#13133286C2211yescharacteristic
24C2×#13133285C2211yescharacteristic
25C2×#13133280C2211yescharacteristic
26C2×#13133280C2211yescharacteristic
27C2×#13133279C2211yescharacteristic
28C2×#13133279C2211yescharacteristic
29#16811582C2211yescharacteristic
30C2×#13133271C2211yescharacteristic
31C2×#13133271C2211yescharacteristic
32C2×C8×#6157C2211yescharacteristic
33C2×C8×#6157C2211yescharacteristic
34C4⋊C4×#6157—21no—
35C4⋊C4×#6157—21no—
36C4⋊C4×#6157C2211yescharacteristic
37C4⋊C4×#6157C2211yescharacteristic
38C4⋊C4×#6157C2211yescharacteristic
39C4⋊C4×#6157C2211yescharacteristic
40C4×C4⋊#6157—21no—
41C4×C4⋊#6157C2211yescharacteristic
42C4×C4⋊#6157C2211yescharacteristic
43C22⋊C4×#6157—21no—
44C22⋊C4×#6157—21no—
45C4×C22⋊#6157—21no—
46C42×#6157—21no—
47C42×#6157C2211yescharacteristic
48#16811497C2211yescharacteristic
49#16811497C2211yescharacteristic
50#16811496C2211yescharacteristic
51#16811496C2211yescharacteristic
52#16811496C2211yescharacteristic
53#16811496C2211yescharacteristic
54C2×SD16×D53C2211yescharacteristic
55C4×Q8×D53C2211yescharacteristic
56C4×D4×D53C2211yescharacteristic
57#16810726C411yescharacteristic, complemented
58#16810725C411yescharacteristic, complemented
59#16810724C411yescharacteristic, complemented
60#16810723C411yescharacteristic, complemented
61#16810722C411yescharacteristic, complemented
62#16810721C411yescharacteristic, complemented
63#16810720C411yescharacteristic, complemented
64#107×D53C2211yescharacteristic
65#103×D53C2211yescharacteristic
66#102×D53C2211yescharacteristic
67#97×D53C2211yescharacteristic
68C53×#440C411yescharacteristic, complemented
69C23×#6157—21no—
70C23×#6157—21no—
71C2×D53⋊C8C2311yescharacteristic
72C2×D53⋊C8C2311yescharacteristic
73Q8×#6157—22no—
74Q8×#6157—22no—
75Q8×#6157C2×C414yescomplemented
76Q8×#6157C2×C414yescomplemented
77D4×#6157—22no—
78D4×#6157—22no—
79D4×#6157C2×C414yes—
80D4×#6157C2×C414yes—
81C2×C4⋊#6157—21no—
82C2×C4⋊#6157—21no—
83C2×C4⋊#6157C2311yescharacteristic
84C2×C4⋊#6157C2311yescharacteristic
85C2×C4⋊#6157C2311yescharacteristic
86C2×C4⋊#6157C2311yescharacteristic
87C2×C22⋊#6157—21no—
88C2×C22⋊#6157—21no—
89C2×C4×#6157—21no—
90C2×C4×#6157—21no—
91C2×C4×#6157—21no—
92C2×C4×#6157—21no—
93C2×C4×#6157—21no—
94C2×C4×#6157—21no—
95C2×C4×#6157—21no—
96C2×C4×#6157—21no—
97C2×C4×#6157—44no—
98C2×C4×#6157D411yescharacteristic
99C2×C4×#6157D411yescharacteristic
100C2×C4×#6157D411yescharacteristic
101C2×C4×#6157D411yescharacteristic
102C2×C4×#6157C2311yescharacteristic
103C2×C4×#6157C2311yescharacteristic
104#13133286C2×C414yescomplemented
105#13133285C2×C414yescomplemented
106#13133280C2×C414yescomplemented
107#13133280C2×C414yescomplemented
108#13133279C2×C414yes—
109#13133279C2×C414yes—
110#13133272—21no—
111#13133272—21no—
112#13133271—22no—
113#13133271C2×C414yescomplemented
114C8×#6157—22no—
115C8×#6157C2×C414yescomplemented
116(C2×#6157)⋊C4—21no—
117(C2×#6157)⋊C4—21no—
118(C2×#6157)⋊C4—21no—
119(C2×#6157)⋊C4—21no—
120(C2×#6157)⋊C4—21no—
121(C2×#6157)⋊C4—21no—
122C2×Q8×D53C2311yescharacteristic
123C2×D4×D53C2311yescharacteristic
124C22×C4×D53—21no—
125C2×#11719913C2×C411yescharacteristic
126C2×#11719923C2×C411yescharacteristic
127C2×#11719924C2×C411yescharacteristic
128SD16×D53C2×C414yes—
129SD16×D53C2×C414yes—
130C2×C8×D53C2311yescharacteristic
131C2×C8×D53C2311yescharacteristic
132Q8×Dic53C2×C411yescharacteristic, complemented
133C4×Dic106—21no—
134C4×Dic106C2×C411yescharacteristic, complemented
135#13133182—21no—
136#13133182C2×C411yescharacteristic, complemented
137C4×D212C2×C411yescharacteristic
138D4×Dic53C2×C411yescharacteristic
139#13133179C2×C411yescharacteristic
140C4×C22⋊D53—21no—
141#13133177—21no—
142C4⋊C4×D53—21no—
143C4⋊C4×D53C2311yescharacteristic
144C4⋊C4×D53C2311yescharacteristic
145C22⋊C4×D53—21no—
146C42×D53—21no—
147C42×D53C2311yescharacteristic
148#13133151C2×C411yescharacteristic, complemented
149#13133150C2×C411yescharacteristic, complemented
150#13133150C2×C411yescharacteristic, complemented
151#13133142C2×C411yescharacteristic, complemented
152#13133141C2×C411yescharacteristic, complemented
153#13133140C2×C411yescharacteristic, complemented
154#13133139C2×C411yescharacteristic
155#13133138C2×C411yescharacteristic
156#13133137C2×C411yescharacteristic
157#13133128C2×C411yescharacteristic, complemented
158#13133127C2×C411yescharacteristic, complemented
159#13133127C2×C411yescharacteristic, complemented
160C2×SD16×C53C2×C411yescharacteristic
161C4×Q8×C53C2×C411yescharacteristic, complemented
162C4×D4×C53C2×C411yescharacteristic
163#107×C53C2×C411yescharacteristic, complemented
164#103×C53C2×C411yescharacteristic, complemented
165#102×C53C2×C411yescharacteristic
166#97×C53C2×C411yescharacteristic, complemented
167C23×D53—21no—
168C22×#6157—21no—
169C22×#6157—21no—
170C22×#6157—21no—
171C22×#6157—21no—
172C22×#6157—24no—
173C22×#6157—24no—
174C22×#6157—42no—
175C22×#6157—42no—
176C22×#6157—42no—
177C22×#6157—42no—
178C22×#6157C2×D411yescharacteristic
179C22×#6157C2×D411yescharacteristic
180C22×#6157C2×D411yescharacteristic
181C22×#6157C2×D411yescharacteristic
182C2×Q8×C53C22×C411yescharacteristic
183C2×D4×C53C22×C411yescharacteristic
184C22×C4×C53—21no—
185C2×C22⋊D53—21no—
186C22×Dic53—21no—
187Q8×D53—21no—
188Q8×D53—21no—
189Q8×D53C22×C412yes—
190Q8×D53C22×C412yes—
191D4×D53—21no—
192D4×D53—21no—
193D4×D53C22×C412yes—
194D4×D53C22×C412yes—
195C2×D212C22×C411yescharacteristic
196C2×C4×D53—21no—
197C2×C4×D53—21no—
198C2×C4×D53—21no—
199C2×C4×D53—21no—
200C2×C4×D53—21no—
201C2×C4×D53—42no—
202C2×C4×D53—42no—
203C2×C4×D53C2×D411yescharacteristic
204C2×C4×D53C2×D411yescharacteristic
205C2×C4×D53C2411yescharacteristic
206C2×Dic106—21no—
207C2×Dic106C22×C411yescharacteristic
208C22⋊#6157—24no—
209C22⋊#6157—24no—
210C2×#88324—21no—
211C2×#88324—21no—
212C4⋊#6157—24no—
213C4⋊#6157—24no—
214C4⋊#6157—21no—
215C4⋊#6157—21no—
216C4⋊#6157—21no—
217C4⋊#6157—21no—
218C4⋊#6157C22×C412yes—
219C4⋊#6157C22×C412yes—
220C4⋊#6157C22×C412yes—
221C4⋊#6157C22×C412yes—
222C4×#6157—24no—
223C4×#6157—24no—
224C4×#6157—22no—
225C4×#6157—22no—
226C4×#6157—41no—
227C4×#6157—41no—
228C4×#6157—42no—
229C4×#6157—42no—
230C4×#6157—42no—
231C4×#6157—42no—
232C4×#6157—42no—
233C4×#6157—42no—
234C4×#6157C22×C412yes—
235C4×#6157C22×C412yes—
236C4×#6157#4112yes—
237C4×#6157#4112yes—
238D53⋊C8—21no—
239D53⋊C8—21no—
240D53⋊C8C22×C412yes—
241D53⋊C8C22×C412yes—
242SD16×C53C4214yescomplemented
243C2×C8×C53C22×C411yescharacteristic
244C2×C8×C53C22×C411yescharacteristic
245C4⋊C4×C53—21no—
246C4⋊C4×C53C22×C411yescharacteristic
247C4⋊C4×C53C22×C411yescharacteristic
248C22⋊C4×C53—21no—
249C42×C53—21no—
250C42×C53C22×C411yescharacteristic
251C22⋊Dic53—21no—
252#11719924C4214yescomplemented
253#11719923C4214yescomplemented
254#11719921—21no—
255#11719921—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53C22×C411yescharacteristic
258C4⋊Dic53C22×C411yescharacteristic
259#11719919—21no—
260#11719919—21no—
261#11719919—21no—
262#11719919—21no—
263C4×Dic53—21no—
264C4×Dic53—21no—
265C4×Dic53—21no—
266C4×Dic53C22×C411yescharacteristic
267C4×Dic53#4111yescharacteristic
268C4×Dic53#4111yescharacteristic
269C2×#88322C22×C411yescharacteristic
270C2×#88322C22×C411yescharacteristic
271#11719913C4214yescomplemented
272C8×D53—21no—
273C8×D53—21no—
274C8×D53C22×C412yes—
275C8×D53C22×C412yes—
276C23×C53—21no—
277C22×D53—21no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—41no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53C22×D411yescharacteristic
285C2×#6157—21no—
286C2×#6157—21no—
287C2×#6157—21no—
288C2×#6157—21no—
289C2×#6157—21no—
290C2×#6157—21no—
291C2×#6157—22no—
292C2×#6157—22no—
293C2×#6157—22no—
294C2×#6157—22no—
295C2×#6157—48no—
296C2×#6157—41no—
297C2×#6157—41no—
298C2×#6157—41no—
299C2×#6157—41no—
300C2×#6157—41no—
301C2×#6157—41no—
302C2×#6157—41no—
303C2×#6157—41no—
304C2×#6157—48no—
305C2×#6157C4×D412yes—
306C2×#6157C4×D412yes—
307C2×#6157C4×D412yes—
308C2×#6157C4×D412yes—
309C2×#6157AGL(1,ℤ/8)12yes—
310C2×#6157#13712yes—
311Q8×C53—21no—
312Q8×C53C2×C4212yescomplemented
313D4×C53—21no—
314D4×C53C2×C4212yes—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—42no—
319C2×C4×C53C4×D411yescharacteristic
320C2×C4×C53C4×D411yescharacteristic
321C2×C4×C53C23×C411yescharacteristic
322C22⋊D53—22no—
323C22⋊D53—22no—
324C2×Dic53—21no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—42no—
328C2×Dic53C4×D411yescharacteristic
329C2×Dic53C4×D411yescharacteristic
330C2×Dic53C2×#4111yescharacteristic
331D212—21no—
332D212C2×C4212yes—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—21no—
336C4×D53—21no—
337C4×D53—21no—
338C4×D53—21no—
339C4×D53—42no—
340C4×D53—42no—
341C4×D53—41no—
342C4×D53—41no—
343C4×D53—41no—
344C4×D53—41no—
345C4×D53C23×C411yescharacteristic
346C4×D53C23×C411yescharacteristic
347C4×D53C2×#4111yescharacteristic
348C4×D53C2×#4111yescharacteristic
349Dic106—21no—
350Dic106—22no—
351Dic106—22no—
352Dic106C2×C4212yescomplemented
353#88324—22no—
354#88324—22no—
355C8×C53—21no—
356C8×C53C2×C4212yescomplemented
357#88322—21no—
358#88322C2×C4212yescomplemented
359C4×#440—531nomaximal, Sylow
360C22×C53—22no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53C2×C4×D411yescharacteristic
364C2×D53—22no—
365C2×D53—41no—
366C2×D53—41no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53C2×C4×D411yescharacteristic
372C2×D53C2×C4×D411yescharacteristic
373C2×D53C2×AGL(1,ℤ/8)11yescharacteristic
374C2×D53C2×#13711yescharacteristic
375C2×D53#57511yescharacteristic
376C2×D53#57511yescharacteristic
377#6157—22no—
378#6157—22no—
379#6157—22no—
380#6157—42no—
381#6157—42no—
382#6157—42no—
383#6157—42no—
384#6157#44014yesdirect product factor
385C4×C53—21no—
386C4×C53—21no—
387C4×C53—22no—
388C4×C53—41no—
389C4×C53—41no—
390C4×C53C22×C4211yescharacteristic
391C4×C53C4×#4111yescharacteristic
392Dic53—21no—
393Dic53—21no—
394Dic53—22no—
395Dic53—41no—
396Dic53—41no—
397Dic53C4×#4111yescharacteristic
398Dic53C4×#4111yescharacteristic
399C2×#440—531no—
400C2×#440—531no—
401C2×C4×SD16—531no—
402C42×Q8—531no—
403C42×D4—531no—
404#1776—531no—
405#1776—531no—
406C4×#107—531no—
407#1763—531no—
408#1763—531no—
409#1762—531no—
410#1762—531no—
411C4×#103—531no—
412C4×#102—531no—
413C4×#97—531no—
414C2×C53—42no—
415C2×C53C42×D411yescharacteristic
416C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
417C2×C53C4×#13711yescharacteristic
418D53—42no—
419D53C2×#44011yescharacteristic
420D53#294311yescharacteristic
421D53C4×AGL(1,ℤ/8)11yescharacteristic
422D53C4×#13711yescharacteristic
423C22×SD16—531no—
424C2×C4×Q8—531no—
425C2×C4×Q8—531no—
426C2×C4×Q8—531no—
427C2×C4×D4—531no—
428C2×C4×D4—531no—
429C2×C4×D4—531no—
430C22×C42—1061no—
431#440—538no—
432#440—531no—
433#440—531no—
434#440—531no—
435#440—531no—
436#440—531no—
437#440—531no—
438#440—531no—
439#440#615711yescharacteristic, direct product factor
440C4×SD16—538no—
441C2×#107—531no—
442C2×#107—531no—
443C2×#106—531no—
444C2×#103—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#97—531no—
451C2×#97—531no—
452C2×#97—531no—
453C2×#97—531no—
454C2×C4×C8—531no—
455C2×C4×C8—531no—
456C4×C4⋊C4—531no—
457C4×C4⋊C4—531no—
458C4×C4⋊C4—531no—
459C4×C4⋊C4—531no—
460C4×C4⋊C4—531no—
461C4×C4⋊C4—531no—
462C4×C4⋊C4—1061no—
463C4×C4⋊C4—1061no—
464C4×C4⋊C4—1061no—
465C4×C22⋊C4—1061no—
466C4×C22⋊C4—1061no—
467C4×C22⋊C4—1061no—
468C43—531no—
469C43—1061no—
470#340—531no—
471#340—531no—
472#340—531no—
473#340—531no—
474#340—531no—
475#340—531no—
476C53C4×#44011yescharacteristic, complemented, Sylow
477C22×Q8—531no—
478C22×D4—531no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4—1061no—
482C2×SD16—531no—
483C2×SD16—531no—
484C2×SD16—534no—
485C2×SD16—534no—
486C2×SD16—531no—
487C2×SD16C2×#615711yescharacteristic
488C22×C8—531no—
489C22×C8—531no—
490C22×C8—531no—
491C22×C8—531no—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—531no—
495C4×Q8—531no—
496C4×Q8—531no—
497C4×Q8—1061no—
498C4×Q8—1061no—
499C4×Q8—1062no—
500C4×Q8—1062no—
501C4×Q8C2×#615711yescharacteristic, complemented
502C4×D4—534no—
503C4×D4—534no—
504C4×D4—531no—
505C4×D4—531no—
506C4×D4—531no—
507C4×D4—1061no—
508C4×D4—1061no—
509C4×D4—1062no—
510C4×D4—1062no—
511C4×D4C2×#615711yescharacteristic
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C42—531no—
525C2×C42—531no—
526C2×C42—531no—
527C2×C42—531no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—2124no—
541#107—534no—
542#107—531no—
543#107—531no—
544#107—531no—
545#107C2×#615711yescharacteristic, complemented
546#106—534no—
547#103—534no—
548#103—534no—
549#103—531no—
550#103—531no—
551#103—531no—
552#103C2×#615711yescharacteristic, complemented
553#102—534no—
554#102—534no—
555#102—531no—
556#102—531no—
557#102—531no—
558#102C2×#615711yescharacteristic
559#97—534no—
560#97—531no—
561#97—531no—
562#97—531no—
563#97—1062no—
564#97—1061no—
565#97—1061no—
566#97C2×#615711yescharacteristic, complemented
567C4×C8—534no—
568C4×C8—1062no—
569#95—1061no—
570#95—1061no—
571#95—1061no—
572#95—1061no—
573#95—1061no—
574#95—1061no—
575C24—1061no—
576C2×Q8—532no—
577C2×Q8—532no—
578C2×Q8—531no—
579C2×Q8—1061no—
580C2×Q8—1061no—
581C2×Q8—1061no—
582C2×Q8C22×#615711yescharacteristic
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—531no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—1061no—
589C2×D4C22×#615711yescharacteristic
590C22×C4—21no—
591C22×C4—531no—
592C22×C4—531no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—2122no—
611C22×C4—2122no—
612C22×C4—2122no—
613C22×C4—2122no—
614C22×C4—2122no—
615C22×C4—2122no—
616SD16—534no—
617SD16—534no—
618SD16—534no—
619SD16C4×#615714yescomplemented
620C2×C8—531no—
621C2×C8—532no—
622C2×C8—532no—
623C2×C8—532no—
624C2×C8—532no—
625C2×C8—531no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C2×C8—1061no—
630C2×C8—1061no—
631C2×C8—1061no—
632C2×C8C22×#615711yescharacteristic
633C2×C8C22×#615711yescharacteristic
634C4⋊C4—21no—
635C4⋊C4—532no—
636C4⋊C4—532no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—531no—
640C4⋊C4—531no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1061no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1061no—
648C4⋊C4—1061no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1061no—
652C4⋊C4C22×#615711yescharacteristic
653C4⋊C4C22×#615711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1061no—
656C22⋊C4—1061no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C22⋊C4—1061no—
660C42—21no—
661C42—532no—
662C42—532no—
663C42—532no—
664C42—532no—
665C42—531no—
666C42—531no—
667C42—531no—
668C42—1061no—
669C42—1061no—
670C42—1062no—
671C42—1062no—
672C42—1064no—
673C42—1064no—
674C42—1061no—
675C42—2122no—
676C42—2122no—
677C42—2121no—
678C42—2121no—
679C42—2122no—
680C42—2122no—
681C42—2122no—
682C42—2122no—
683C42C22×#615711yescharacteristic
684C23—21no—
685C23—531no—
686C23—1062no—
687C23—1062no—
688C23—1061no—
689C23—2121no—
690C23—2121no—
691C23—2121no—
692C23—2121no—
693Q8—21no—
694Q8—532no—
695Q8—1062no—
696Q8—1062no—
697Q8—1061no—
698Q8C2×C4×#615712yescomplemented
699D4—21no—
700D4—532no—
701D4—1062no—
702D4—1062no—
703D4—1061no—
704D4C2×C4×#615712yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—532no—
710C2×C4—532no—
711C2×C4—532no—
712C2×C4—531no—
713C2×C4—531no—
714C2×C4—531no—
715C2×C4—531no—
716C2×C4—531no—
717C2×C4—532no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—531no—
721C2×C4—531no—
722C2×C4—1061no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1061no—
726C2×C4—1061no—
727C2×C4—1061no—
728C2×C4—1061no—
729C2×C4—1061no—
730C2×C4—1061no—
731C2×C4—1061no—
732C2×C4—1061no—
733C2×C4—1061no—
734C2×C4—1061no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1061no—
740C2×C4—1061no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2121no—
747C2×C4—2128no—
748C2×C4—2122no—
749C2×C4—2128no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2121no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4D4×#615711yescharacteristic
759C2×C4D4×#615711yescharacteristic
760C2×C4C23×#615711yescharacteristic
761C8—21no—
762C8—532no—
763C8—1062no—
764C8—1062no—
765C8—1061no—
766C8C2×C4×#615712yescomplemented
767C22—22no—
768C22—41no—
769C22—41no—
770C22—531no—
771C22—531no—
772C22—531no—
773C22—531no—
774C22—531no—
775C22—531no—
776C22—1062no—
777C22—2122no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22—2121no—
782C22—2121no—
783C22C2×D4×#615711yescharacteristic
784C4—22no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—41no—
789C4—534no—
790C4—531no—
791C4—531no—
792C4—1062no—
793C4—1062no—
794C4—1062no—
795C4—1062no—
796C4—1061no—
797C4—1061no—
798C4—2122no—
799C4—2122no—
800C4—2122no—
801C4—2122no—
802C4—2121no—
803C4—2121no—
804C4C22×C4×#615711yescharacteristic
805C4#41×#615711yescharacteristic
806C2—42no—
807C2—531no—
808C2—531no—
809C2—531no—
810C2—531no—
811C2—2122no—
812C2C4×D4×#615711yescharacteristic
813C2AGL(1,ℤ/8)×#615711yescharacteristic
814C2#137×#615711yescharacteristic
subgroupG/H
centerC22C2×D4×#6157
commutatorC4×C53C22×C42
FrattiniC2×C4C23×#6157
FittingC53×#440C4
socleC22×C53C2×C4×D4
prime radicalC2×D4×D53C23
cosocleC2×C4×D53C24
hypercenter#440#6157
hypocenterC53C4×#440
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. C4×Q8×#6157C2semidirect
5. #20290530C2semidirect
6. #20290529C2semidirect
7. #107×#6157C2semidirect
8. #20290488C2semidirect
9. #20290487C2semidirect
12. #103×#6157C2semidirect
14. #97×#6157C2semidirect
21. #16811662C4semidirect
22. SD16×#6157C4semidirect
57. #16810726C4semidirect
58. #16810725C4semidirect
59. #16810724C4semidirect
60. #16810723C4semidirect
61. #16810722C4semidirect
62. #16810721C4semidirect
63. #16810720C4semidirect
68. C53×#440C4semidirect
75. Q8×#6157C2×C4semidirect
76. Q8×#6157C2×C4semidirect
104. #13133286C2×C4semidirect
105. #13133285C2×C4semidirect
106. #13133280C2×C4semidirect
107. #13133280C2×C4semidirect
113. #13133271C2×C4semidirect
115. C8×#6157C2×C4semidirect
132. Q8×Dic53C2×C4semidirect
134. C4×Dic106C2×C4semidirect
136. #13133182C2×C4semidirect
148. #13133151C2×C4semidirect
149. #13133150C2×C4semidirect
150. #13133150C2×C4semidirect
151. #13133142C2×C4semidirect
152. #13133141C2×C4semidirect
153. #13133140C2×C4semidirect
157. #13133128C2×C4semidirect
158. #13133127C2×C4semidirect
159. #13133127C2×C4semidirect
161. C4×Q8×C53C2×C4semidirect
163. #107×C53C2×C4semidirect
164. #103×C53C2×C4semidirect
166. #97×C53C2×C4semidirect
242. SD16×C53C42semidirect
252. #11719924C42semidirect
253. #11719923C42semidirect
271. #11719913C42semidirect
312. Q8×C53C2×C42semidirect
352. Dic106C2×C42semidirect
356. C8×C53C2×C42semidirect
358. #88322C2×C42semidirect
384. #6157#440direct (N × H)
439. #440#6157direct (N × H)
476. C53C4×#440semidirect
501. C4×Q8C2×#6157semidirect
545. #107C2×#6157semidirect
552. #103C2×#6157semidirect
566. #97C2×#6157semidirect
619. SD16C4×#6157semidirect
698. Q8C2×C4×#6157semidirect
766. C8C2×C4×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#168116622
C2×SD16×#61572
C4×Q8×#61572
C4×D4×#61572
#202905302
#202905292
#107×#61572
#202904882
#202904872
#202904862
#202904852
#103×#61572
#102×#61572
#97×#61572
#440×D532
C4×#44053