Finite Group Databasebeta

← #27399857

Subgroups — #27399857

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810735C211yesmaximal, characteristic, complemented
2C2×D8×Dic53C211yesmaximal, characteristic, complemented
3#20277545C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20275598C211yesmaximal, characteristic, complemented
6#20275571C211yesmaximal, characteristic, complemented
7#20275065C211yesmaximal, characteristic, complemented
8#20275065C211yesmaximal, characteristic, complemented
9#20275051C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20274748C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14#20274496C211yesmaximal, characteristic, complemented
15C22×AGL(1,ℤ/8)×C53C211yesmaximal, characteristic
16C2×D4×Dic53C2211yescharacteristic
17C2×D4×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic, complemented
19C2×D4×Dic53C2211yescharacteristic, complemented
20C22×C22⋊Dic53—21no—
21#16810735—24no—
22D8×Dic53—24no—
23C2×#13133151C2211yescharacteristic, complemented
24C2×#13133149C2211yescharacteristic, complemented
25C2×#13133141C2211yescharacteristic, complemented
26C2×#13133141C2211yescharacteristic, complemented
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic, complemented
32C2×#13133138C2211yescharacteristic, complemented
33C2×C22⋊#88322C2211yescharacteristic
34C2×#13133127C2211yescharacteristic, complemented
35C2×C8×Dic53C2211yescharacteristic, complemented
36#16810530C2211yescharacteristic, complemented
37#16810530C2211yescharacteristic, complemented
38#16810526C2211yescharacteristic
39#16810526C2211yescharacteristic
40#16810503—21no—
41#16810503—21no—
42#16810503—21no—
43#16810503—21no—
44#16810486—21no—
45#16810483C2211yescharacteristic
46#16810483C2211yescharacteristic
47#16810479—21no—
48C4×C22⋊Dic53C2211yescharacteristic
49C2×#13133124—21no—
50#16810386C2211yescharacteristic, complemented
51#16810386C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C22×#41×C53C2211yescharacteristic
55C23×D4×C53C2211yescharacteristic
56C2×AGL(1,ℤ/8)×C53—24no—
57C2×AGL(1,ℤ/8)×C53—24no—
58C2×AGL(1,ℤ/8)×C53C418yescomplemented
59C22×SD16×C53C2211yescharacteristic
60C22×SD16×C53C2211yescharacteristic
61C22×D8×C53C2211yescharacteristic
62C22×D8×C53C2211yescharacteristic
63C22×M16×C53C2211yescharacteristic
64C23×Dic53—21no—
65C23×Dic53—21no—
66C23×Dic53—21no—
67C23×Dic53—21no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70D4×Dic53—22no—
71D4×Dic53—22no—
72D4×Dic53—22no—
73D4×Dic53—22no—
74D4×Dic53—41no—
75D4×Dic53—41no—
76D4×Dic53—41no—
77D4×Dic53—41no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—44no—
93C2×C22⋊Dic53D411yescharacteristic
94C2×C22⋊Dic53D411yescharacteristic
95C2×C4×Dic53C2311yescharacteristic
96C2×C4×Dic53C2311yescharacteristic
97#13133151—22no—
98#13133149—22no—
99#13133141—41no—
100#13133141—41no—
101#13133138—22no—
102#13133138—22no—
103#13133138—22no—
104#13133138—22no—
105#13133138—41no—
106#13133138—41no—
107C22⋊#88322—22no—
108#13133127—22no—
109C8×Dic53—22no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124D411yescharacteristic
117#13133124D411yescharacteristic
118C25×C53—21no—
119C2×#41×C53—22no—
120C2×#41×C53—22no—
121C2×#41×C53—22no—
122C2×#41×C53—41no—
123C2×#41×C53—41no—
124C2×#41×C53C2×C414yescomplemented
125C22×Q8×C53C2311yescharacteristic
126C22×D4×C53—22no—
127C22×D4×C53—22no—
128C22×D4×C53—21no—
129C22×D4×C53—21no—
130C22×D4×C53—22no—
131C22×D4×C53—41no—
132C22×D4×C53—41no—
133C22×D4×C53C2×C414yescomplemented
134C22×D4×C53C2311yescharacteristic
135C22×D4×C53C2311yescharacteristic
136C22×D4×C53C2311yescharacteristic
137C23×C4×C53—21no—
138C23×C4×C53C2311yescharacteristic
139AGL(1,ℤ/8)×C53—232no—
140C2×SD16×C53—22no—
141C2×SD16×C53—22no—
142C2×SD16×C53—22no—
143C2×SD16×C53—22no—
144C2×SD16×C53C2×C414yescomplemented
145C2×SD16×C53C2×C414yescomplemented
146C2×D8×C53—22no—
147C2×D8×C53—22no—
148C2×D8×C53C2×C414yes—
149C2×D8×C53C2×C414yescomplemented
150C2×D8×C53D414yes—
151C2×D8×C53D414yes—
152C2×M16×C53—22no—
153C2×M16×C53—22no—
154C2×M16×C53C2×C414yescomplemented
155C22×C8×C53C2311yescharacteristic
156C22×C8×C53C2311yescharacteristic
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—24no—
161C24×C53—42no—
162C24×C53—42no—
163C24×C53—42no—
164C24×C53—42no—
165C24×C53—81no—
166C24×C53—81no—
167C24×C53C2×D411yescharacteristic
168#41×C53—28no—
169#41×C53—44no—
170#41×C53—44no—
171#41×C53—44no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53—21no—
175C2×Q8×C53—21no—
176C2×Q8×C53—21no—
177C2×Q8×C53C22×C412yes—
178C2×D4×C53—28no—
179C2×D4×C53—24no—
180C2×D4×C53—24no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—42no—
196C2×D4×C53—42no—
197C2×D4×C53—42no—
198C2×D4×C53—42no—
199C2×D4×C53C22×C412yes—
200C2×D4×C53C22×C412yes—
201C2×D4×C53C22×C412yes—
202C2×D4×C53C2×D412yes—
203C2×D4×C53C2×D412yes—
204C2×D4×C53C2×D412yes—
205C2×D4×C53C2×D412yes—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—24no—
212C22×C4×C53—42no—
213C22×C4×C53—42no—
214C22×C4×C53C22×C412yes—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53#4112yes—
217C22×C4×C53C2411yescharacteristic
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—42no—
223C22×Dic53—42no—
224C22×Dic53—42no—
225C22×Dic53—42no—
226C22×Dic53—42no—
227C22×Dic53—42no—
228C22×Dic53—42no—
229C22×Dic53—42no—
230C22×Dic53—81no—
231C22×Dic53—81no—
232C22×Dic53—81no—
233C22×Dic53—81no—
234C22×Dic53C2×D411yescharacteristic
235C22×Dic53C2×D411yescharacteristic
236C22×Dic53C2×D411yescharacteristic
237C22×Dic53C2×D411yescharacteristic
238SD16×C53—28no—
239SD16×C53—28no—
240D8×C53—28no—
241D8×C53C22⋊C4116yescomplemented
242M16×C53—28no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53C22×C412yes—
246C2×C8×C53C22×C412yes—
247C2×C8×C53C2×D412yes—
248C2×C8×C53C2×D412yes—
249C22⋊Dic53—22no—
250C22⋊Dic53—41no—
251C22⋊Dic53—42no—
252C22⋊Dic53—42no—
253C22⋊Dic53—42no—
254C22⋊Dic53—42no—
255C22⋊Dic53—42no—
256C22⋊Dic53—42no—
257C22⋊Dic53—42no—
258C22⋊Dic53—81no—
259C22⋊Dic53—81no—
260C22⋊Dic53—81no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4×Dic53—21no—
270C4×Dic53—21no—
271C4×Dic53—21no—
272C4×Dic53—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—22no—
292C23×C53—48no—
293C23×C53—48no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—84no—
309C23×C53—84no—
310C23×C53—84no—
311C23×C53—84no—
312C23×C53—84no—
313C23×C53C4×D412yes—
314C23×C53C22×D411yescharacteristic
315Q8×C53—22no—
316Q8×C53—22no—
317Q8×C53—41no—
318Q8×C53—41no—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—22no—
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—22no—
327D4×C53—48no—
328D4×C53—48no—
329D4×C53—41no—
330D4×C53—41no—
331D4×C53C2×C22⋊C414yes—
332D4×C53C2×C22⋊C414yescomplemented
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—48no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53C4×D412yes—
344C2×C4×C53C23×C411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C2×#4111yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C2×C4×C53H(5,𝔽2)11yescharacteristic
350C2×Dic53—21no—
351C2×Dic53—21no—
352C2×Dic53—21no—
353C2×Dic53—21no—
354C2×Dic53—21no—
355C2×Dic53—21no—
356C2×Dic53—21no—
357C2×Dic53—21no—
358C2×Dic53—21no—
359C2×Dic53—21no—
360C2×Dic53—21no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—84no—
374C2×Dic53—84no—
375C2×Dic53—84no—
376C2×Dic53—84no—
377C2×Dic53AGL(1,ℤ/8)12yescomplemented
378C8×C53—22no—
379C8×C53C2×C22⋊C414yescomplemented
380#88322—41no—
381#88322—41no—
382#22442—531nomaximal, Sylow
383C22×C53—22no—
384C22×C53—24no—
385C22×C53—24no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—41no—
400C22×C53—42no—
401C22×C53—42no—
402C22×C53—41no—
403C22×C53—42no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—42no—
407C22×C53—816no—
408C22×C53—81no—
409C22×C53—81no—
410C22×C53—81no—
411C22×C53—81no—
412C22×C53C2×C4×D411yescharacteristic
413C22×C53D4211yescharacteristic
414C22×C53D4211yescharacteristic
415C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C53#57511yescharacteristic
417C22×C53#57611yescharacteristic
418C22×C53#57711yescharacteristic
419C4×C53—22no—
420C4×C53—42no—
421C4×C53C22×C22⋊C411yescharacteristic
422C4×C53#51811yescharacteristic
423C4×C53#54611yescharacteristic
424C4×C53#54611yescharacteristic
425Dic53—22no—
426Dic53—41no—
427Dic53—41no—
428Dic53—41no—
429Dic53—81no—
430Dic53—81no—
431Dic53—81no—
432Dic53—81no—
433C22×AGL(1,ℤ/8)D5311yescharacteristic
434C2×#442—531no—
435C2×C4×D8—531no—
436#2339—531no—
437D4×C22⋊C4—531no—
438#1973—531no—
439#1968—531no—
440#1879—531no—
441#1879—531no—
442#1877—531no—
443#1877—531no—
444#1809—531no—
445#1788—531no—
446#1786—531no—
447#1753—531no—
448C2×C53—42no—
449C2×C53—44no—
450C2×C53—44no—
451C2×C53—82no—
452C2×C53D4×C22⋊C411yescharacteristic
453C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
454C2×C53#294611yescharacteristic
455C2×C53#326411yescharacteristic
456C2×C53#326711yescharacteristic
457C2×C53#327211yescharacteristic
458C2×C53#327311yescharacteristic
459C22×#41C2×D5311yescharacteristic
460C23×D4C2×D5311yescharacteristic
461C2×AGL(1,ℤ/8)—24no—
462C2×AGL(1,ℤ/8)—24no—
463C2×AGL(1,ℤ/8)Dic5318yescomplemented
464C22×SD16C2×D5311yescharacteristic
465C22×SD16C2×D5311yescharacteristic
466C22×D8C2×D5311yescharacteristic
467C22×D8C2×D5311yescharacteristic
468C22×M16C2×D5311yescharacteristic
469C2×C4×D4—531no—
470C2×C4×D4—531no—
471C2×C4×D4—531no—
472C2×C4×D4—531no—
473C22×C22⋊C4—1061no—
474#442—1064no—
475C4×D8—1064no—
476C2×#107—531no—
477C2×#106—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×#102—531no—
486C2×C22⋊C8—531no—
487C2×#97—531no—
488C2×C4×C8—531no—
489#391—531no—
490#391—531no—
491#390—531no—
492#390—531no—
493#386—1061no—
494#386—1061no—
495#386—1061no—
496#386—1061no—
497#381—1061no—
498#380—531no—
499#380—531no—
500#379—1061no—
501C4×C22⋊C4—531no—
502C2×#95—1061no—
503#340—531no—
504#340—531no—
505#336—531no—
506#336—531no—
507C53#2244211yescharacteristic, complemented, Sylow
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×Dic5314yescomplemented
515C22×Q8C22×D5311yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×Dic5314yescomplemented
524C22×D4C22×D5311yescharacteristic
525C22×D4C22×D5311yescharacteristic
526C22×D4C22×D5311yescharacteristic
527C23×C4—21no—
528C23×C4—1061no—
529C23×C4—1061no—
530C23×C4—1061no—
531C23×C4—1061no—
532C23×C4C22×D5311yescharacteristic
533AGL(1,ℤ/8)—232no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16C2×Dic5314yescomplemented
539C2×SD16C2×Dic5314yescomplemented
540C2×D8—22no—
541C2×D8—22no—
542C2×D8C2×Dic5314yes—
543C2×D8C2×Dic5314yescomplemented
544C2×D8C22⋊D5314yes—
545C2×D8C22⋊D5314yes—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16C2×Dic5314yescomplemented
549C22×C8—531no—
550C22×C8—531no—
551C22×C8C22×D5311yescharacteristic
552C22×C8C22×D5311yescharacteristic
553C4×D4—1062no—
554C4×D4—1062no—
555C4×D4—1062no—
556C4×D4—1062no—
557C4×D4—2121no—
558C4×D4—2121no—
559C4×D4—2121no—
560C4×D4—2121no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—531no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—2124no—
578C2×C42—531no—
579C2×C42—531no—
580#107—1062no—
581#106—1062no—
582#103—2121no—
583#103—2121no—
584#102—1062no—
585#102—1062no—
586#102—1062no—
587#102—1062no—
588#102—2121no—
589#102—2121no—
590C22⋊C8—1062no—
591#97—1062no—
592C4×C8—1062no—
593#95—531no—
594#95—531no—
595#95—1061no—
596#95—1061no—
597#95—1061no—
598#95—1061no—
599#95—1061no—
600#95—1061no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—24no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—81no—
610C24—81no—
611C24D4×D5311yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C22×Dic5312yes—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×Dic5312yes—
644C2×D4C22×Dic5312yes—
645C2×D4C22×Dic5312yes—
646C2×D4C2×C22⋊D5312yes—
647C2×D4C2×C22⋊D5312yes—
648C2×D4C2×C22⋊D5312yes—
649C2×D4C2×C22⋊D5312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—531no—
661C22×C4—531no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—4241no—
667C22×C4—4241no—
668C22×C4—4241no—
669C22×C4—4241no—
670C22×C4—2122no—
671C22×C4—2122no—
672C22×C4—2122no—
673C22×C4—2122no—
674C22×C4—2122no—
675C22×C4—2122no—
676C22×C4—2122no—
677C22×C4—2122no—
678C22×C4D4×D5311yescharacteristic
679C22×C4#1171994712yes—
680C22×C4C22×Dic5312yes—
681C22×C4C23×D5311yescharacteristic
682SD16—28no—
683SD16—28no—
684D8—28no—
685D8C22⋊Dic53116yescomplemented
686M16—28no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8C22×Dic5312yes—
696C2×C8C22×Dic5312yes—
697C2×C8C2×C22⋊D5312yes—
698C2×C8C2×C22⋊D5312yes—
699C4⋊C4—1061no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C22⋊C4—1062no—
708C22⋊C4—4241no—
709C22⋊C4—4241no—
710C22⋊C4—4241no—
711C22⋊C4—2122no—
712C22⋊C4—2121no—
713C22⋊C4—2122no—
714C22⋊C4—2122no—
715C22⋊C4—2122no—
716C22⋊C4—2122no—
717C22⋊C4—2122no—
718C22⋊C4—2122no—
719C42—1061no—
720C42—1061no—
721C42—1061no—
722C42—1061no—
723C23—22no—
724C23—22no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23D4×Dic5312yes—
758C23C2×D4×D5311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊Dic5314yes—
776D4C2×C22⋊Dic5314yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—532no—
788C2×C4—1061no—
789C2×C4—1061no—
790C2×C4—1061no—
791C2×C4—1061no—
792C2×C4—1061no—
793C2×C4—1061no—
794C2×C4—1061no—
795C2×C4—1061no—
796C2×C4—1061no—
797C2×C4—1061no—
798C2×C4—1061no—
799C2×C4—4244no—
800C2×C4—4244no—
801C2×C4—4244no—
802C2×C4—4244no—
803C2×C4—2121no—
804C2×C4—2121no—
805C2×C4—2121no—
806C2×C4—2121no—
807C2×C4—2121no—
808C2×C4—2121no—
809C2×C4—2121no—
810C2×C4—2121no—
811C2×C4—2121no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4—2121no—
815C2×C4D4×Dic5312yes—
816C2×C4C23×Dic5311yescharacteristic
817C2×C4C22×C22⋊D5311yescharacteristic
818C2×C4C22×C22⋊D5311yescharacteristic
819C2×C4C2×#1171994711yescharacteristic
820C2×C4#1313326211yescharacteristic
821C2×C4#1313326211yescharacteristic
822C8—22no—
823C8—2121no—
824C8—2121no—
825C8C2×C22⋊Dic5314yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×D4×Dic5311yescharacteristic
856C22D4×C22⋊D5311yescharacteristic
857C22D4×C22⋊D5311yescharacteristic
858C22AGL(1,ℤ/8)×D5311yescharacteristic
859C22#1681141911yescharacteristic
860C22#1681142711yescharacteristic
861C22#1681143311yescharacteristic
862C4—22no—
863C4—42no—
864C4—1062no—
865C4—4241no—
866C4—4241no—
867C4—4241no—
868C4—4241no—
869C4—2121no—
870C4—2121no—
871C4—2121no—
872C4C22×C22⋊Dic5311yescharacteristic
873C4#1681109811yescharacteristic
874C4#1681126711yescharacteristic
875C4#1681126711yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊Dic5311yescharacteristic
881C2AGL(1,ℤ/8)×Dic5311yescharacteristic
882C2#2028354811yescharacteristic
883C2#2028618911yescharacteristic
884C2#2028623411yescharacteristic
885C2#2028630911yescharacteristic
886C2#2028632011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC22×AGL(1,ℤ/8)×C53C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC22×AGL(1,ℤ/8)D53
hypocenterC53#22442
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#16810735C2semidirect
2. C2×D8×Dic53C2semidirect
3. #20277545C2semidirect
4. D4×C22⋊Dic53C2semidirect
5. #20275598C2semidirect
6. #20275571C2semidirect
7. #20275065C2semidirect
8. #20275065C2semidirect
9. #20275051C2semidirect
10. #20275051C2semidirect
11. #20274748C2semidirect
12. #20274655C2semidirect
13. #20274646C2semidirect
14. #20274496C2semidirect
18. C2×D4×Dic53C22semidirect
19. C2×D4×Dic53C22semidirect
23. C2×#13133151C22semidirect
24. C2×#13133149C22semidirect
25. C2×#13133141C22semidirect
26. C2×#13133141C22semidirect
31. C2×#13133138C22semidirect
32. C2×#13133138C22semidirect
34. C2×#13133127C22semidirect
35. C2×C8×Dic53C22semidirect
36. #16810530C22semidirect
37. #16810530C22semidirect
50. #16810386C22semidirect
51. #16810386C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
58. C2×AGL(1,ℤ/8)×C53C4semidirect
124. C2×#41×C53C2×C4semidirect
133. C22×D4×C53C2×C4semidirect
144. C2×SD16×C53C2×C4semidirect
145. C2×SD16×C53C2×C4semidirect
149. C2×D8×C53C2×C4semidirect
154. C2×M16×C53C2×C4semidirect
241. D8×C53C22⋊C4semidirect
332. D4×C53C2×C22⋊C4semidirect
377. C2×Dic53AGL(1,ℤ/8)semidirect
379. C8×C53C2×C22⋊C4semidirect
463. C2×AGL(1,ℤ/8)Dic53semidirect
507. C53#22442semidirect
514. C2×#41C2×Dic53semidirect
523. C22×D4C2×Dic53semidirect
538. C2×SD16C2×Dic53semidirect
539. C2×SD16C2×Dic53semidirect
543. C2×D8C2×Dic53semidirect
548. C2×M16C2×Dic53semidirect
685. D8C22⋊Dic53semidirect
776. D4C2×C22⋊Dic53semidirect
825. C8C2×C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107352
C2×D8×Dic532
#202775452
D4×C22⋊Dic532
#202755982
#202755712
#202750652
#202750512
#202747482
#202746552
#202746462
#202744962
C22×AGL(1,ℤ/8)×C532
#2244253