Finite Group Databasebeta

← C2×#20287035 #28261018

Subgroups — C2×#20287035 #28261018

Order 13568.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811292C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic, complemented
3#20287035C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810940C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810874C211yesmaximal, characteristic, complemented
9C2×#16810873C211yesmaximal, characteristic, complemented
10C2×#16810816C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic, complemented
12C2×SD16×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C2×#16810623C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719947—21no—
19C22×#11719922C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22#16811292—24no—
23#16811292C2218yescomplemented
24#16811273—24no—
25#16811273C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133213—21no—
28C2×#13133213C2211yescharacteristic
29C2×#13133199—21no—
30C2×#13133198—21no—
31C2×#13133194—21no—
32C2×#13133191—21no—
33C2×#13133191C2211yescharacteristic
34C2×#13133188—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810968C2218yescomplemented
44#16810942C2218yescomplemented
45#16810940C2218yescomplemented
46#16810906C2218yescomplemented
47#16810874C2218yescomplemented
48#16810873C2218yescomplemented
49#16810816C2218yescomplemented
50#16810767C2218yescomplemented
51SD16×Dic53C2218yescomplemented
52#16810698C2218yescomplemented
53C2×#13133149C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810624C2218yescomplemented
58#16810623C2218yescomplemented
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#449C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719947—28no—
82C2×#11719947—48no—
83C22×Dic106—21no—
84C22×D212—21no—
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53D411yescharacteristic
92C23×Dic53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C2×#11719917—42no—
100C2×#11719917C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133213—22no—
108#13133213—28no—
109#13133213C2314yes—
110#13133199—28no—
111#13133198—28no—
112#13133194—28no—
113#13133191—28no—
114#13133191—22no—
115#13133191C2314yes—
116#13133188—28no—
117#13133188—22no—
118#13133188—22no—
119#13133188C2314yes—
120#13133188C2314yes—
121Q8×Dic53—22no—
122Q8×Dic53C2314yes—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125C4×C22⋊D53—28no—
126C4×C22⋊D53D414yes—
127C4×C22⋊D53C2314yes—
128C2×C4⋊Dic53—22no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2314yes—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919D411yescharacteristic
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148#13133149C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133137C2314yes—
160#13133129C2314yes—
161C8×Dic53C2314yes—
162C2×#41×C53—22no—
163C2×#41×C53—24no—
164C2×#41×C53—42no—
165C2×#41×C53C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C22×D4×C53C2311yescharacteristic
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C2×SD16×C53—24no—
174C2×SD16×C53C2314yes—
175C2×D8×C53—42no—
176C2×D8×C53C2314yes—
177C22×C8×C53C2311yescharacteristic
178C22×C8×C53C2311yescharacteristic
179#121×C53—22no—
180#121×C53C2314yes—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C22⋊C4×C53—21no—
183#103×C53C2314yes—
184#102×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190C23×D53C2×D411yescharacteristic
191#41×C53—28no—
192#41×C53—44no—
193#41×C53—48no—
194C2×Q8×C53—21no—
195C2×Q8×C53—22no—
196C2×Q8×C53#4114yescomplemented
197C2×Q8×C53C2412yes—
198C2×D4×C53—24no—
199C2×D4×C53—24no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—44no—
207C2×D4×C53—44no—
208C2×D4×C53C2412yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—21no—
211C22×C4×C53—22no—
212C22×C4×C53—22no—
213C22×C4×C53—21no—
214C22×C4×C53—24no—
215C22×C4×C53—44no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2411yescharacteristic
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—44no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—82no—
229C2×C22⋊D53—82no—
230C2×C22⋊D53—82no—
231C2×C22⋊D53C2×D414yes—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—24no—
236C22×Dic53—24no—
237C22×Dic53—44no—
238C22×Dic53—44no—
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241C22×Dic53C2×D411yescharacteristic
242#11719949—28no—
243#11719949—44no—
244#11719949—48no—
245#11719947—432no—
246C2×D212—22no—
247C2×D212—22no—
248C2×D212—24no—
249C2×D212—21no—
250C2×D212—44no—
251C2×D212C2412yes—
252C2×C4×D53—22no—
253C2×C4×D53—22no—
254C2×C4×D53—24no—
255C2×C4×D53—24no—
256C2×C4×D53—44no—
257C2×C4×D53—44no—
258C2×C4×D53C2×D412yes—
259C2×C4×D53C2412yes—
260C2×Dic106—24no—
261C2×Dic106—44no—
262SD16×C53—28no—
263D8×C53—44no—
264C2×C8×C53—22no—
265C2×C8×C53—22no—
266C2×C8×C53C2412yes—
267C2×C8×C53C2412yes—
268C4⋊C4×C53—21no—
269C4⋊C4×C53C2412yes—
270C22⋊C4×C53—24no—
271C22⋊Dic53—24no—
272C22⋊Dic53—24no—
273C22⋊Dic53—24no—
274C22⋊Dic53C2×D414yes—
275#11719922—44no—
276#11719921—24no—
277#11719921C2×D414yes—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53—24no—
281C4⋊Dic53—21no—
282C4⋊Dic53—24no—
283C4⋊Dic53C2412yes—
284C4⋊Dic53C2412yes—
285C4⋊Dic53C2412yes—
286#11719919—24no—
287#11719919—24no—
288#11719919C2×D414yes—
289C4×Dic53—24no—
290C4×Dic53C2×D412yes—
291C4×Dic53C2412yes—
292#11719917—44no—
293C2×#88322—22no—
294C2×#88322—22no—
295C2×#88322C2412yes—
296C2×#88322C2412yes—
297#11719912—44no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53C22×D412yes—
310C23×C53C22×D411yescharacteristic
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53C22×D412yes—
319Q8×C53—24no—
320Q8×C53—22no—
321Q8×C53C2×#4114yescomplemented
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—48no—
327D4×C53—48no—
328D4×C53—42no—
329D4×C53—42no—
330C2×C4×C53—24no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—24no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—48no—
338C2×C4×C53—42no—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53C2×#4112yes—
342C2×C4×C53H(5,𝔽2)12yes—
343C2×C4×C53C2511yescharacteristic
344C22⋊D53—28no—
345C22⋊D53—48no—
346C22⋊D53—48no—
347C22⋊D53—84no—
348C22⋊D53—84no—
349C22⋊D53—84no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—48no—
356C2×Dic53—42no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53—48no—
360C2×Dic53AGL(1,ℤ/8)14yes—
361C2×Dic53C22×D412yes—
362C2×Dic53C22×D412yes—
363C2×Dic53C22×D412yes—
364D212—22no—
365D212—22no—
366D212—48no—
367D212—42no—
368C4×D53—24no—
369C4×D53—22no—
370C4×D53—22no—
371C4×D53—48no—
372C4×D53—48no—
373Dic106—48no—
374C8×C53—22no—
375C8×C53—22no—
376#88322—22no—
377#88322—22no—
378C2×#3332—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—44no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—84no—
390C22×C53—84no—
391C22×C53#54612yes—
392C22×C53C2×AGL(1,ℤ/8)12yes—
393C22×C53#57712yes—
394C22×C53C23×D411yescharacteristic
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—22no—
398C2×D53—44no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—84no—
403C4×C53—24no—
404C4×C53—22no—
405C4×C53—42no—
406C4×C53#54612yes—
407C4×C53C22×#4111yescharacteristic
408C4×C53C2×H(5,𝔽2)11yescharacteristic
409Dic53—22no—
410Dic53—22no—
411Dic53—42no—
412Dic53—42no—
413Dic53—42no—
414Dic53C2×AGL(1,ℤ/8)14yes—
415C2×#550—531no—
416C2×#547—531no—
417#3332—5316no—
418C2×#486—531no—
419C2×#481—531no—
420C2×#481—531no—
421C2×#475—531no—
422C2×#469—531no—
423C2×#469—531no—
424C2×#459—531no—
425C2×#449—531no—
426C2×#449D5311yescharacteristic, complemented
427C2×C4×SD16—531no—
428C2×#436—531no—
429C2×#417—531no—
430C2×#417—531no—
431C2×C53—42no—
432C2×C53—82no—
433C2×C53—82no—
434C2×C53#333214yescomplemented
435C2×C53C2×#54611yescharacteristic
436C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C53C2×#57711yescharacteristic
438D53—42no—
439D53—82no—
440C22×#41—531no—
441C22×#41—1061no—
442C22×#41C2×D5311yescharacteristic
443C22×SD16C2×D5311yescharacteristic
444C22×D8—531no—
445C22×D8C2×D5311yescharacteristic
446C22×M16—531no—
447C22×M16—531no—
448#550—538no—
449#550—1064no—
450#547—538no—
451#547—1064no—
452C2×C4⋊Q8—531no—
453C2×#127—531no—
454C2×#127—1061no—
455C2×#123—1061no—
456C2×#123—1061no—
457C2×C22⋊Q8—1061no—
458C2×#121—531no—
459C2×#121—531no—
460C2×#121—531no—
461C2×#121—1061no—
462C2×#121—1061no—
463C2×#121C2×D5311yescharacteristic
464C2×C4×Q8—531no—
465C2×C4×D4—531no—
466C2×C4×D4—531no—
467C2×C4×D4—1061no—
468C22×C4⋊C4—531no—
469C22×C4⋊C4—531no—
470#486—538no—
471#481—538no—
472#481—538no—
473#475—538no—
474#469—538no—
475#469—538no—
476#459—538no—
477#449—538no—
478#449C2×D5318yescomplemented
479C4×SD16—538no—
480#436—538no—
481C2×#106—531no—
482C2×#106—531no—
483C2×#106—531no—
484C2×C4⋊C8—531no—
485#417—538no—
486#417—538no—
487C2×#103—531no—
488C2×#103—531no—
489C2×#103C2×D5311yescharacteristic
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×#102—531no—
495C2×#102—531no—
496C2×#102C2×D5311yescharacteristic
497C2×C22⋊C8—531no—
498C2×C22⋊C8C2×D5311yescharacteristic
499C2×C4×C8—531no—
500C53C2×#333211yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—24no—
503C2×#41—42no—
504C2×#41—534no—
505C2×#41—1062no—
506C2×#41—1068no—
507C2×#41—1064no—
508C2×#41—2122no—
509C2×#41—2128no—
510C2×#41C22×D5314yes—
511C22×Q8—1061no—
512C22×Q8C22×D5311yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—531no—
516C22×D4—531no—
517C22×D4—1061no—
518C22×D4—1061no—
519C22×D4—1061no—
520C22×D4—1061no—
521C22×D4—1061no—
522C22×D4—1061no—
523C22×D4C22×D5311yescharacteristic
524C22×D4C22×D5311yescharacteristic
525C23×C4—21no—
526C23×C4—531no—
527C23×C4—1061no—
528C23×C4—1061no—
529C23×C4—1061no—
530C23×C4—1061no—
531C23×C4C22×D5311yescharacteristic
532C2×SD16—24no—
533C2×SD16C22×D5314yes—
534C2×D8—42no—
535C2×D8—534no—
536C2×D8—2122no—
537C2×D8C22×D5314yes—
538C2×M16—534no—
539C2×M16—534no—
540C2×M16—2122no—
541C2×M16—2122no—
542C22×C8—531no—
543C22×C8—531no—
544C22×C8C22×D5311yescharacteristic
545C22×C8C22×D5311yescharacteristic
546C4⋊Q8—534no—
547C4⋊Q8—1062no—
548#127—534no—
549#127—1062no—
550#127—1068no—
551#123—1068no—
552#123—1068no—
553C22⋊Q8—1068no—
554#121—22no—
555#121—534no—
556#121—534no—
557#121—534no—
558#121—1068no—
559#121—1068no—
560#121—1062no—
561#121—1062no—
562#121—1062no—
563#121C22×D5314yes—
564C4×Q8—534no—
565C4×Q8—1062no—
566C4×D4—534no—
567C4×D4—534no—
568C4×D4—534no—
569C4×D4—1062no—
570C4×D4—1068no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—531no—
573C2×C4⋊C4—531no—
574C2×C4⋊C4—534no—
575C2×C4⋊C4—531no—
576C2×C4⋊C4—534no—
577C2×C4⋊C4—1062no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4—1061no—
581C2×C4⋊C4—1061no—
582C2×C4⋊C4—1062no—
583C2×C4⋊C4C22×D5311yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—531no—
586C2×C22⋊C4—531no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C42—531no—
592C2×C42—1061no—
593#106—534no—
594#106—534no—
595#106—534no—
596C4⋊C8—534no—
597#103—534no—
598#103—534no—
599#103C22×D5314yes—
600#102—534no—
601#102—534no—
602#102—534no—
603#102—534no—
604#102—534no—
605#102—534no—
606#102C22×D5314yes—
607C22⋊C8—534no—
608C22⋊C8C22×D5314yes—
609C4×C8—534no—
610C24—21no—
611C24—21no—
612C24—531no—
613C24—1061no—
614C24D4×D5311yescharacteristic
615#41—28no—
616#41—44no—
617#41—48no—
618#41—1068no—
619#41—2124no—
620#41—2128no—
621#41—21232no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—1064no—
625C2×Q8—2124no—
626C2×Q8#1171994714yescomplemented
627C2×Q8C23×D5312yes—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—534no—
639C2×D4—532no—
640C2×D4—1064no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1064no—
645C2×D4—1064no—
646C2×D4—1064no—
647C2×D4—1061no—
648C2×D4—1062no—
649C2×D4—1062no—
650C2×D4—4242no—
651C2×D4—4242no—
652C2×D4—4242no—
653C2×D4—2124no—
654C2×D4—2124no—
655C2×D4—2124no—
656C2×D4C23×D5312yes—
657C2×D4C23×D5312yes—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—44no—
664C22×C4—531no—
665C22×C4—531no—
666C22×C4—531no—
667C22×C4—532no—
668C22×C4—532no—
669C22×C4—1064no—
670C22×C4—1064no—
671C22×C4—1064no—
672C22×C4—1062no—
673C22×C4—1062no—
674C22×C4—1064no—
675C22×C4—1061no—
676C22×C4—1061no—
677C22×C4—1061no—
678C22×C4—2124no—
679C22×C4—2124no—
680C22×C4—2124no—
681C22×C4—2124no—
682C22×C4D4×D5312yes—
683C22×C4D4×D5311yescharacteristic
684C22×C4C23×D5312yes—
685C22×C4C23×D5311yescharacteristic
686SD16—28no—
687D8—44no—
688D8—2124no—
689M16—2124no—
690M16—2124no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—532no—
694C2×C8—532no—
695C2×C8—1062no—
696C2×C8—1062no—
697C2×C8C23×D5312yes—
698C2×C8C23×D5312yes—
699C4⋊C4—21no—
700C4⋊C4—534no—
701C4⋊C4—532no—
702C4⋊C4—532no—
703C4⋊C4—532no—
704C4⋊C4—1064no—
705C4⋊C4—1064no—
706C4⋊C4—1064no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1064no—
710C4⋊C4—1061no—
711C4⋊C4C23×D5312yes—
712C22⋊C4—24no—
713C22⋊C4—534no—
714C22⋊C4—534no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C42—532no—
720C42—532no—
721C42—1064no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—532no—
734C23—1062no—
735C23—1062no—
736C23—1062no—
737C23—1062no—
738C23—2122no—
739C23—2122no—
740C23—2122no—
741C23C2×D4×D5312yes—
742C23C2×D4×D5311yescharacteristic
743Q8—22no—
744Q8—24no—
745Q8—2128no—
746Q8C2×#1171994714yescomplemented
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—48no—
753D4—42no—
754D4—42no—
755D4—1068no—
756D4—1062no—
757D4—1062no—
758D4—4244no—
759D4—4244no—
760D4—4244no—
761D4—2128no—
762D4—2128no—
763D4—2128no—
764D4—2122no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—534no—
775C2×C4—532no—
776C2×C4—532no—
777C2×C4—532no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—1064no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—2128no—
787C2×C4—2128no—
788C2×C4—2128no—
789C2×C4—2128no—
790C2×C4—2122no—
791C2×C4—2122no—
792C2×C4—2122no—
793C2×C4C2×D4×D5312yes—
794C2×C4C2×D4×D5311yescharacteristic
795C2×C4C2×#1171994712yes—
796C2×C4#1313326212yes—
797C2×C4C24×D5311yescharacteristic
798C8—22no—
799C8—22no—
800C8—1062no—
801C8—1062no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—84no—
813C22—84no—
814C22—1062no—
815C22—1062no—
816C22—1062no—
817C22—4244no—
818C22—2122no—
819C22—2122no—
820C22—2122no—
821C22—2124no—
822C22#1681126012yes—
823C22AGL(1,ℤ/8)×D5312yes—
824C22#1681143012yes—
825C22C22×D4×D5311yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—534no—
830C4—1062no—
831C4—1062no—
832C4—2122no—
833C4—2122no—
834C4—2122no—
835C4#1681126012yes—
836C4C22×#1171994711yescharacteristic
837C4C2×#1313326211yescharacteristic
838C2—42no—
839C2—82no—
840C2—82no—
841C2—4242no—
842C2—2122no—
843C2#2028703514yesdirect product factor
844C2C2×#1681126011yescharacteristic
845C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
846C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3332
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16811292C2semidirect
2. C2×#16811273C2semidirect
3. #20287035C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810940C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810874C2semidirect
9. C2×#16810873C2semidirect
10. C2×#16810816C2semidirect
11. C2×#16810767C2semidirect
12. C2×SD16×Dic53C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810624C2semidirect
15. C2×#16810623C2semidirect
16. C2×C53×#449C2semidirect
23. #16811292C22semidirect
25. #16811273C22semidirect
43. #16810968C22semidirect
44. #16810942C22semidirect
45. #16810940C22semidirect
46. #16810906C22semidirect
47. #16810874C22semidirect
48. #16810873C22semidirect
49. #16810816C22semidirect
50. #16810767C22semidirect
51. SD16×Dic53C22semidirect
52. #16810698C22semidirect
57. #16810624C22semidirect
58. #16810623C22semidirect
73. C53×#449C22semidirect
196. C2×Q8×C53#41semidirect
321. Q8×C53C2×#41semidirect
426. C2×#449D53semidirect
434. C2×C53#3332semidirect
478. #449C2×D53semidirect
500. C53C2×#3332semidirect
626. C2×Q8#11719947semidirect
746. Q8C2×#11719947semidirect
843. C2#20287035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112922
C2×#168112732
#202870352
C2×#168109682
C2×#168109422
C2×#168109402
C2×#168109062
C2×#168108742
C2×#168108732
C2×#168108162
C2×#168107672
C2×SD16×Dic532
C2×#168106982
C2×#168106242
C2×#168106232
C2×C53×#4492
C2×#333253